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redsovet _knigi@electronics.ru

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Phased Array
Antennas
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J1..0-?... Wt\ '£" A "". t.t JJ\;e: it.'lit.
@ 2012, 3AO «PHI{ «TexHoccpepa», nepeBo,n Ha pyc-
CKHR B3bIK, opHrHHarr-MaKeT, ocpopMJIeHHe
ISBN 978-5-94836-323-3
ISBN 978-0-470-40102-6 (aurJl.)

llOC6RUI,aemCR meM, Kmo CaeflllJl 603MOJICHbiM HanucaHue KHU2U
«CKaHuPYIOUI,Ue aHmeHHble cucmeMbl CBl{»
(<<Microwave Scanning Antennas»):
Nicolas A. Begovich
Robert W. Bickmore
Jesse L. Butler
Lome K. De Size
Robert S. Elliott
Richard C. Johnson
H.C. Ko
Wolfgang H. Kummer
Robert G. Malech
Donald L. Margerum
Arthur A. OHner
Jack F. Ramsay
Joseph A. Vitale

COAEP>KAHME
llpe,lU1CJIOBl1e K PYCCKOMY 113,l(aHI1IO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12
llpe.nI1CJIOBl1e K nepBOMY 113,l(aHI1IO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 14
llpe,l(I1CJIOBl1e KO BTOPOMY 113,l(aHI1IO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16
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17
17
20
22
22
23
23
23
26
27
28
31
33
33
34
37
40
42
42
42
44
46
51
53
55
55
58
59
61
65
67
67
67
69
70
71
71
78
79
79
84
85
1.1. AHTeHHble pemeTKH - I1CTOpl1R Bonpoca. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. CI1CTeMHble <paKTOpbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3. AHHornpoBaHHbIH Cnl1COK nHTepaTYpbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1. JIHTepaTYPa no a,aanTHBHbIM aHTeHHaM. . . . . . . . . . . . . . . . . . . . . . . . . . . .
JII1TepaTYPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . · . . . . . . . . . . . . . . .
- 
f JIaBa 2. OCHoBHble xapaKTepHCTHKH aHTeHHLIX pemeTOK. . . . . . . . . . . . . . . . . . . . . . . .
2.1. JII1HeHHble pemeTKI1 C paBHOMepHbIM B036eHHeM . . . . . . . . . . . . . . . . . . . . . .
2.1.1. ,n;HarpaMMbI HanpaBJIeHHOCTI1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2. IIIHpHHa nyqa . . . . . . . . . . .:". .'. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3. DOKoBble JIeneCTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.4. )];11<ppaKIJ;110HHble neneCTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.5. TIOJIOca nponYCKaHHH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. llJIOCKHe aHTeHHbIe pemeTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1. CHcTeMa KOop,l(HHaT aHTeHHblX pemeTOK. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2. 1lII1pl1Ha JIyqa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3. ,n;H<ppaKIJ;HOHHbIe JIeneCTKH: npHMoyrOJIbHaH ceTKa . . . . . . . . . . . . . . . . . . .
2.2.4. ,AHcl>paKIJ:HOHHbIe JIeneCTKH: reKCarOHaJIbHaH ceTKa . . . . . . . . . . . . . . . . . . .
2.3. YnpaBJIeHHe JIyqOM H JIeneCTKH KBaHTOBaHHR. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1. )];HcKpeTHocTb ynpaBJIeHHR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2. YnpaBJIeHHe nOJIOCOH nponYCKaHHH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3. Pa3MemeHHe JIHHHH 3a,aep)l(l(H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4. JIenecTKH KBaHTOBaHHR $a30BpamaTeJIeH . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5. JIenecTKH KBaHTOBaHHR rro,npemeTOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.6. Pac<pa3HpoBaHHe JIeneCTKOB KBaHTOBaHHH: nepeKpbIBalOmHeCH no.npellIeTKH .
2.4. HanpaBJI e HH OCTh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1. HanpaBJIeHHOCTb JII1HeHHOH aHTeHHOH pellIeTKH . . . . . . . . . . . . . . . . . . . . .
2.4.2. KH,l:{ aHTeHHOH pellIeTKH" CocToRIUeH H3 KOpOTKHX ,L(HnOJIeH . . . . . . . . . . . .
2.4.3. KH,n; aHTeHHOH pellIeTKH, CocToR:w;eH H3 pe30HaHCHbIX 3JIeMeHTOB . . . . . . . .
2.4.4. KH,lJ; nrrOCKOH aHTeHHOH pemeTKH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
JIHTepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
fJlaBa 3. CHUTe3 )UlarpaMM HanpaBJIeHHOCTH JlHHeHHOH aHTeHHOH pemeTKH. . . . . . . . . . . .
3.1. BBe.neHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1. Bblpa)KeHHR .lUIR ,l(HarpaMMbI HanpaBneHHOCTH. . . . . . . . . . . . . . . . . . . . . . .
3.1.2. Cl>H3HKa H MaTeMaTHKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3. llpHHUl1nbI paCqeTa Y3KHX JIyqeH, rrpeMO>KeHHbIe TeibIopoM . . . . . . . . . . . .
3.2. AHTeHHble pemeTKH ,AoJIb<pa-Qe6bImeBa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1. PellIeTKH C nOJIyBOJIHOBbIM llIarOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2. PemeTKH C nepHO,ZUNHOCTblO, MeHbmeH nOJIyBOJIHOBOH . . . . . . . . . . . . . . . .
3.3. O,nHonapaMe1pWleCKOe pacnpe.neJIeHHe TeibIopa . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1. PaCqeT o,nHonapaMeTpI1QeCKOrO pacnpe,neJIeHHH. . . . . . . . . . . . . . . . . . . . . .
3.3.2. ,n;ByxnapaMe1'pHQeCKOe pacnpe,neJIeHHe DHKMOpa-CneJIMaHpa . . . . . . . . . . .
3.4. N-napaMeTpHQeCKOe aMnJIHTY,nHoe pacnpe,neJIeHHe TeHJIOpa . . . . . . . . . . . . . . . . .

CoiJepJICaHUe 
3.5. Pacrrpe,n:eJIeHI-UI C HI13Kl1M ypOBHeM 60KOBbIX JIerreCTKOB . . . . . . . . . . . . . . . . . . .. 91
3.5.1. CpaBHeHHe pacrrpe,n:eJIeHI1M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91
3.5.2. Cpe,n:HI1M ypOBeHb 60KOBbIX JIerreCTKOB . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94
3.6. N-rrapaMeTjJHqeCKOe aMIIJIHTY,n:Hoe pacrrpe,n:eJIeHl1e BI1JIbHeBa . . . . . . . . . . . . . . .. 95
3.7. Pa3HOCTHbIe ,n:HarpaMMbI HarrpaBJIeHHOCTI1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 98
3.7.1. KTIacCHqeCKl1e ,n:HarpaMMbI HarrpaBJIeHHOCTI1 . . . . . . . . . . . . . . . . . . . . . . .. 98
3.7.2. )];l1arpaMMbI HarrpaBJIeHHOCTH fieHJIHCCa . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.7.3. OrrTI1MH3aUJUI cYMMapHoH 11 pa3HocTHOH ,nHarpaMM HarrpaBJIeHHOCTH . . . . . . 104
3.7.4. )];l1cKpeTHbIe pacrrpe,n:eJIeHI1SI 30JIOTapeBa . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.8. <1>opMa orH6alOIUeH 60KOBbIX JIerreCTKOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.9. CHHTe3 DJfarpaMMbI HarrpaBJIeHHOCTI1 CrreII;l1aJIbHOH <pOpMbI. . . . . . . . . . . . . . . . . . 112
3.9.1. CI1HTe3 By,n:Bop,na-JIoycoHa (Woodward-Lawson) . . . . . . . . . . . . . . . . . . . 112
3.9.2. C I1HTe3 :3 JIJII1 OTTa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.10. He3KBI1D:I1CTaHTHbIe aHTeHHble perneTKI1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.10.1. CTaTI1CTWIeCKI1M MeTO,n: paCqeTa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118
3.10.2. CrreII;l1aJIbHOe He3KBM,n:I1CTaHTHoe pacrrOJIO)l(eHl1e 3JIeMeHTOB. . . . . . . . . . . 123
3.10.3. AHTeHHbIe perneTKM C MI1HMMaJIbHOH H36bITOqHOCTblO . . . . . . . . . . . . . . . 124
JII1TepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
fJlaBa 4. CHHTe3 ,lI.HarpaMM HanpaBJIeHHOCTH ,lI.BYMepHblX H KpyrJlblx aHTeHHbIX pemeTOK. . . 128
4.1. )];BYMepHbIe KpyrJIbIe aHTeHHbIe perneTKM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.1.1. nJIOCKHe IUeJIeBbIe aHTeHHble perneTKM. . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.1.2. O,n:HonapaMeTjJMqeCKaSI ,n:MarpaMMa HarrpaBJIeHHOCTM XaHceHa . . . . . . . . . . . 129
4.1.3. )];MarpaMMa HarrpaBJIeHHOCTI1 rrpl1 n -napaMeTpl1QeCKOM pacnpe,n:eJIeHMH
TeMJIOpa ,lLJHI KpyrJIbIX anepTYp. . . . . . . . . . . . . '_ . . . . . . . . . . . . . . . . . . . . 133
4.1.4. Pa3HOCTHaSI ,nMarpaMMa HanpaBJIeHHOCTH npM pacnpe,n:eJIeHMI1
neHJII1CCa )1)ISI KpyrJIbIX anepTYp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.1.5. OnTHMH3allIDI pa3HocTHOM ,n:HarpaMMbI HanpaBJIeHHOCTI1 . . . . . . . . . . . . . . . 142
4.2. ,lJ.BYMepHbIe anepTYPbI, OTJII1QHble OT KpyrJIbIX . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.2.1. OrrTHMH3alll1SI .nHarpaMMbI HanpaBJIeHHOCTI1 ,n:BYMepHbIX perneTOK. . . . . . . . . 144
4.2.2. CI1HTe3 ,nl1arpaMM HanpaBJIeHHOCTI1 C KOJIbIleBbIMH 60KOBbIMM JIeneCTKaMH . . 145
JIHTepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
fJlaBa 5. 3J1eMeHTbI aHTeHHOH pemeTKH. . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.1. )];Mrr OJIH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.1.1. T OHKHe .nMrrOJII1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.1.2. )];l1nOJIM THna «Bow-Tie» If «Open-Sleeve». . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.2. I.IJ:eJIM B BOJIHOBo.ne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.2.1. npO.nOJIbHble m:eJIM B rnHpoKoM CTeHKe BOJIHOBo.na. . . . . . . . . . . . . . . . . . . . 161
5.2.2. I.IJ:eJIH B 60KOBOM CTeHKe BOJIHOBo,na. . . . . . . . . . . . . .  . . . . . . . . . . . . . . . 166
5.2.3. I.IJ:eJIH B nOJIOCKOBOM JIMHMH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.2.4. BOJIHOBO.nbI C OTKpbITbIM KOHII;OM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
5.2.5. BOJIHOBO.n, BCTpoeHHbIM B rrO)1)lO)l(KY (SIW). . . . . . . . . . . . . . . . . . . . . . . . . 168
5.3. PynopHbIe TEM 113JIyqaTeJII1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.3.1. :3BOJIlOllHSI pynopHbIX TEM H3JIyqaTeJIeM . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.3.2. PaCQeT H KOHCTpYl1pOBaHHe pynopHbIX H3JIyqaTeJIeH. . . . . . . . . . . . . . . . . . . 172
5.3.3. AHTeHHbIe perneTKH Ha OCHOBe TEM pynopOB. . . . . . . . . . . . . . . . . . . . . . . 173
5.3.4. AHTeHHbI MMJlJIHMeTpOBoro ,nHarra30Ha . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
5.4. MHKpOnOJIOCKOBbIe neQaTHbIe aHTeHHbI M ,n:HnOJIH . . . . . . . . . . . . . . . . . . . . . . . . 175
5.4.1. MOn;eJIb B Bl1D:e JIMHMH nepe,n:aQH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.4.2. MO.lleJIb pe30HaTopa H .npyrMe Mo,n:eJIH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
5.4.3. MHKpOrrOJIOCKOBble aHTeHHbI C naCClfBHbIMM 3JIeMeHTaMM . . . . . . . . . . . . . . 181
5.4.4. neQaTHbIe aHTeHHbI C CMMMeTI>l1QHbIM nHTaHMeM. . . . . . . . . . . . . . . . . . . . . 184
JIMTepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185


CoiJepJICaHUe
rJIaBa 6. CHCTeMbi DHTaHHJI aHTeHHhIX peweTOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
6.1. nOCJIe.noBaTeJIbHbIe JIHHHH nHTaHH$I . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 191
6.1.1. Pe30HaHcHbIe aHTeHHbIe pemeTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
6.1.1.1. I1Mne,naHc H nOJIoca nponYCKaHHSI . . . . . . . . . . . . . . . . . . . . . . . . . 192
6.1.1.2. PaCqeT aHTeHHOH pemeTKH Ha OCHOBe pe30HaHCHbIX rueJIeH. . . . . . . . 196
6.1.2. AHTeHHbIe pemeTKH 6erymeH BOJIHbI .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.1.2.1. qacToTHoe CMemeHHe MaKCHMYMa ,l(HarpaMMhI HanpaBJIeHHOCTH
H YCJIOBHe e,l(HHCTBeHHOCTH JIyqa . . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.1.2.2. BbIqHCJIeHHe aKTHBHOH npOBO,l(HMOCTH 3JIeMeHTa . . . . . . . . . . . . . . . 202
6.1.2.3. PaCqeT meJIeBOH aHTeHHOH pemeTKH 6erymeH BOJIHbI . . . . . . . . . . . . 206
6.1.3. qacToTHoe CKaHHpOBaHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
6.1.4. CKaHHpoBaHHe C nOMOmblO <pa30BpamaTeJIeH . . . . . . . . . . . . . . . . . . . . . . . 214
6.2. napaJIJIeJIbHbIe JIHHHH nHTaHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
6.2.1. 06'be,l(HHeHHbIeJIHHHHnHTaHHSI................................ .216
6.2.2. Pacnpe,neJIeHHbIe aHTeHHbIe perneTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.3. )J;BYMepHbIe cxeMbI nHTaHHR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
6.3.1. AHTeHHbIe pemeTKH C <pHKcHpoBaHHbIM nOJIOXeHHeM JIyqa. . . . . . . . . . .  . . 219
6.3.2. AHTeHHbIe pemeTKH C nOCJIe,l(OBaTeJIbHbIM B036yx,aeHHeM. . . . . . . . . . . . . . . 221
6.3.3. 3JIeKTPoHHOe CKaHHpOBaHHe B O.nHOH llJIOCKOCTH . . . . . . . . . . . . . . . . . . . . 221
6.3.4. 3JIeKTpOHHOe CKaHHpOBaHHe B ,l(BYX llJIOCKOCTSlX . . . . . . . . . . . . . . . . . . . . . 223
6.4. OnTHQeCKHe (<pOToHHbIe) CHCTeMbI nHTaHHSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
6.4.1. BOJIOKOHHO-OIITHqeCKHe JIHHHH 3a,nepXKH . . . . . . . . . . . . . . . . . . . . . . . . . 230
6.4.1.1. )];BOHqHbIe JIHHHH 3a.nepXKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
6.4.1.2. AKycTo-OnTHqeCKHe nepeKJIlOqaeMbIe JIHHHH 3a.nepXKH. . . . . . . . . . . 232
6.4.1.3. MO.nYJISlTOpbI H <poTO,l(eTeKTOpbI . . . . . . . . . . . . . . . . . . . .  . . . . . . 233
6.4.2. OnTOBOJIOKOHHbIe JIHHHH 3a.nepXKH C pa3.neJIeHHeM no .lVIHHaM BOJIH. . . . . . . 234
6.4.2.1. JIHHHH 3a.nepXKH Ha OCHOBe .nHCIIeprHpYlOm HX
OIITHqeCKHX BOJIOKOH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
6.4.2.2. OnTOBOJIOKOHHbIe JIHHHH 3a.nepXKH C perneTKoH Ep3rra . . . . . . . . . . 235
6.4.2.3. OnTOBOJIOKOHHbIe JIHHHH 3a.nepXKH 6erymeH BOJIHbI. . . . . . . . . . . . . 236
6.4.3. YCTPOHCTBa OIITHqeCKOH 3a.nepXKH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .236
6.4.4. OnTHQeCKOe npeo6pa30BaHHe <I>YPbe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
6.5. CHCTeMaTHqeCKHe norpernHOCTH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
6.5.1. napaJIJIeJIbHbIe <pa30BpamaTeJIH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
6.5.2. nOCJIe.noBaTeJIbHbIe <pa30BpamaTeJIH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
6.5.3. KOMneHCaIJ.IDI CHCTeMaTHqeCKHX norpernHocTeH . . . . . . . . . . . . . . . . . . . . . 240
JIHTepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
fJIaBa 7. B3aHMHaJi CBJl3b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
7.1. BBe.neHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
7.2. OCHoBHbIe npHHIJ.HnbI CKaHHpYlOmHX aHTeHHbIX perneTOK. . . . . . . . . . . . . . . . . . . 244
7.2.1. Mo.neJIb JIHCTa TOKa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
7.2.2. CBo6o.nHoe H BbIHyx,aeHHoe B036yx,aeHHe. . . . . . . . . . . . . . . . . . . . . . . . . . 246
7.2.3. I1Mne.naHc CKaHHpOBaHHSI H .nHarpaMMa CKaHHpOBaHHSI 3JIeMeHTa . . . . . . . . . 248
7.2.3.1. CpaBHeHHe .nHarpaMMbI CKaHHpOBaHHSI 3JIeMeHTa
Ha npHeM H nepe.naqy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
7.2.3.2. 113MepeHHe HMne.naHca CKaHHpOBaHHSI . . . . . . . . . . . . . . . . . . . . . . 257
7.2.4. AHTeHHbI C MHHHMaTIbHbIM pacceSlHHeM . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
7.3. npOcTPaHCTBeHHbIe no.nxo.nbI K 3<p<peKTaM B3aHMHOH CBSl3H. . . . . . . . . . . . . . . . . . 259
7.3.1. KrracCHqeCKHe BH,l(bI CBSl3H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
7.3.1.1. B3aHMHbIH HMne.naHC .nHnOJIeH H m;eJIeH . . . . . . . . . . . . . . . . . . . . . 259
7.3.1.2. B3aHMHbIH HMne.naHC MHKpOnOJIOCKOBbIX H3JIyqaTeJIeH . . . . . . . . . . . 263
7.3.1.3. B3aHMHbIH HMne.naHC pynOpHbIX H3JIyqaTeJIeH . . . . . . . . . . . . . . . . . 264
7.3.2. PaCqeT Ha OCHOBe MaTPHUbI HMne.naHCOB. . . . . . . . . . . . . . . . . . . . . . . . . . . 266
7.3.3. )J;H<ppaKI.{HOHHble JIeneCTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
I

CoiJepJlCaHUe 
7.4. IIO,axO,abI B CneK1]>aJIbHOH 06JIaCTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
7.4.1. ,lI.HnOJIH H menH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
7.4.2. MHKpOnOJIOCKOBbIe aHTeHHbIe perneTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
7.4.3. neqaTHbIe ,aHnOJIH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
7.4.4. lleqaTHbIe pynopHbIe TEM -H3JIyqaTeJIH . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
7.4.5.I1MHTaTopbIe.n;HHHqHbIXHqeeK................................. .289
7 .5. KOMneHcaHH 3<p<peKTOB CKaHHpOBaHHH H YC'rpaHeHHe yrJIOB OCJIenJIeHHH . . . . . . . 289
7.5.1. YrJIbI OCJIellJIeHHH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
7 .5.2. KOMneHcaHH CKaHHpOBaHHH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
7.5.2.1. YMeHbrneHHe BeJIHqHHbI CBH3H . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
7 .5.2.2. KOMneHcaHH no enHM IIHTaHIDI. . . . . . . . . . . . . . . . . . . . . . . . . . 294
7.5.2.3. MHoroMo,aoBbIe 3JIeMeHTbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
7.5.2.4. BHellIHHH BOJIHOBOH <PlUIbTp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
JIHTepa'fYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
fJIaoa 8. KOHe1JHhle aHTeHHble pemeTKH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
8.1. MeTO,lJ;bI aHaJIH3a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
8.1.1. 0630p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .307
8.1.2. KOHeqHO-6eCKOHeQHbIe pellIeTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
8.2. XapaKTepHcTHKH CKaHHpOBaHHH MaJIbIX pellieTOK . . . . . . . . . . . . . . . . . . . . . . . . . 315
8.3. MO,lJ;eJIb fH66ca KOHeQHO-6eCKOHeqHOH perneTKH . . . . . . . . . . . . . . . . . . . . . . . . . 320
8.3.1. Oco6eHHocTH nOBe,lJ;eHHH HMne,lJ;aHCa npH CKaHHpOBaHHH. . . . . . . . . . . . . . . 320
8.3.2. Mo.aeJIH fH66ca KOHeQHbIX perneTOK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
JIHTepa1Ypa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
fJIaoa 9. CoepxnanpaBJIeHHhle aHTeHHhle peweTKH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
9.1. M CTOpHQeCKaH cnpaBKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
9.2. MaKCHMaJIbHaH HanpaBJIeHHOCTb aHTeHHOH perneTKH . . . . . . . . . . . . . . . . . . . . . . 338
9.2.1. HanpaBJIeHHOCTb aHTeHHOH perneTKH C <pHKcHpoBaHHbIM rnarOM
B HanpaBJIeHHH HOpMaJIH K paCKpbIBY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
9.2.2. HanpaBJIeHHOCTb AP npH C1]>eMJIeHHH Me:>K3JIeMeHTHoro paCCTOHHHH K HYJIIO 340
9.2.3. HanpaBJIeHHOCTb aHTeHHbIX perneTOK IIpO,aOJIbHOrO (oceBoro) H3JIyqeHHH. . . . 341
9.2.4. llIHpHHa nOJIOCbI, 3<p<peKTHBHOCTb H ,lJ;OnYCKH. . . . . . . . . . . . . . . . . . . . . . . 343
9.3. OnTHMH3aUHH C orpaHHQeHHHMH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
9.3.1. CBepxHanpaBJIeHHOCTb ,lI.oJIb<pa-Qe6bIrneBa . . . . . . . . . . . . . . . . . . . . . . . . 350
9.3.2. OrpaHHQeHHe Q IUIH .aOnyCKOB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
9.4. COfJIaCOBaHHe CBepXHanpaBJIeHHbIX perneTOK. . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
9.4.1. YBeJIHQeHHe nOTepb pacnpe.aeJIHTeJIbHOH CHCTeMbI. . . . . . . . . . . . . . . . . . . . 359
9.4.2. PerneTKH C HCnOJIb30BaHHeM BbICOKOTeMnepa1)'pHbIX CBepXnpOBO,lJ;HHKOB
(High-Temperature Superconductors - HTS) . . . . . . . . . . . . . . . . . . . . . . . 361
JIHTepa'fYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
fJIaBa 10. MHoroJIY1leBhle aHTeHRhI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
10.1. BBe.aeHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
10.2. YCTPOHCTBa <pOpMHpoBaHHH JIyqeH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
10.2.1. CxeMbI .n;HarpaMMoo6pa3YlOmHx YC1]>OHCTB. . . . . . . . . . . . . . . . . . . . . . . . 364
10.2.1.1. ,lI.OY Ha OCHOBe .n;eJIHTeJIeH . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
1 0.2.1.2. MaTPHa EaTJIepa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
1 0.2.1.3. Ma'rpHbI EJIacca H HOJIeHa. . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
10.2.1.4. ,lI.BYMepHbIe ,lJ;HarpaMMoo6pa3yK>mHe YC'rpoHcTBa . . . . . . . . . . . . . 371
10.2.1.5. ,lI.BYMepHaH MaTpHua MaK<1>apJIeH.aa . . . . . . . . . . . . . . . . . . . . . .371
10.2.2. JIHH3bI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
10.2.2.1. ,LJ;HarpaMMoo6pa3YlOmee YCTpOHCTBO - JIHH3a POTMaHa . . . . . . . . 374
10.2.2.2. ,LJ;BYMepHbIe <pH.LJ:epHbIe JIHH3bI . . . . . . . . . . . . . . . . . . . . . . . . . . 388
10.2.2.3. KynOJIbHbIe JIHH3bI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
10.2.2.4. )];pyrHe JIHH3bI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395


cOaepJICaHUe
10.2.3. I..J;McJ;>poBoe cJ;>OpMMpOBaHl1e JIyqeH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
10.3. HI13KI1e 60KOBbIe JIeneCTKI1 H HHTepnOJI5IQI151 JIyqeH . . . . . . . . . . . . . . . . . . . . . . 398
10.3.1. MeTo,abI CHM)I(eHH5I 60KOBbIX JIeneCTKOB . . . . . . . . . . . . . . . . . . . . . . . . . 398
10.3.1.1. Qepe.n:ylOllU1eC5IJIyql1................................ .398
10.3.1.2. Pe311CTI1BHOe cna.n:aHHe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
10.3.1.3. <l>opMHpoBaHHe HI13KI1X 60KOBbIX JIeneCTKOB cxeMaMH C nOTep5lMH 399
10.3.1.4. Cynepn03HQM5I JIyqeH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
10.3.2. CxeMbI I1HTepnOJI5IQHH JIyqa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
10.4. OpTOrOHaJIbHOCTb JIyqeH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
10.4.1. OpTOrOHaJIbHbIe Jlyql1 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
10.4.1.1. TIoH5ITl1e opTOrOHaJIbHOCTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
10.4.1.2. OpTOrOHaJIbHOCTb pacnpe.n:eJleHMH . . . . . . . . . . . . . . . . . . . . . . . 406
10.4.1.3. OpTOrOHaJIbHOCTbpemeToK........................... .409
10.4.2. 3cJ;>cJ;>eKTbI HeopTOrOHaJIbHOCTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
10.4.2.1. TIoTepM 3<p<peKTMBHOCTI1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
10.4.2.2. 113MeHeHI151 60KOBbIX JIeneCTKOB. . . . . . . . . . . . . . . . . . . . . . . . . 411
nMTepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
r JIaBa 11. KOHopMHbIe aHTeHHble pemeTKH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
11.1. BBe.n:eHl1e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .418
11.2. KOJIbueBbIe pemeTIGI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
11.2.1. HenpepbIBHa51 KOJIbQeBa51 aHTeHHa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
11.2.2. LJ:I1CKpeTHa51 KOJlbQeBa51 pemeTKa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
11.2.3. CI1H<pa3Hoe B036yx,neHHe JIyqa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
11.3. AHTeHHbIe pemeTKI1 Ha QMJIMH.n:pI1QecKoH nOBepXHOCTI1 . . . . . . . . . . . . . . . . . . . . 430
11.3.1. ,LJ;MarpaMMbI ll.{eJleBbIX 3J1eMeHTOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
11.3.2. ,LJ;l1arpaMMa HanpaBJIeHHOCTI1 aHTeHHoH pemeTKI1 . . . . . . . . . . . . . . . . . . . 432
11.3.2.1. )];M$paKQI10HHble JleneCTKI1 . . . . . . . . . . . . . . . . . . . . . . . . . . . .434
11.3.2.2. OCHoBHble JIeneCTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
11.3.2.3. lJ,I1JII1H.n:pMQeCKa51 .n:enOJl5lpI13aQI151 . . . . . . . . . . . . . . . . . . . . . . . 442
11.3.3. B3aMMHa51 npOBo.n:MMOCTb meJIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .442
11.3.3.1. MO.n:aJIbHble p5l.n:bI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
11.3.3.2. LJ:aHHble 0 nOJlHOH npoBo.n:I1MOCTM . . . . . . . . . . . . . . . . . . . . . . . 448
11.3.4. L(HarpaMMa CKaHMpOBaHIDI 3JIeMeHTa. . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
11.4. CeKTopHble pemeTKI1 Ha UIUIMHJJ:paX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
11.4.1. LJ:MarpaMMbI M HanpaBJIeHHocTb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
11.4.2. CpaBHeHMe nJIaHapHbIX (ITJIOCKI1x) H ceKTopHbIX pemeTOK. . . . . . . . . . . . . 454
11.4.3. AnnapaTYPHa51 peaJIH3aUlf51 KOJlbueBOH If UIUIMHJJ:pWIeCKOH pemeTOK . . . . . 457
11.5. PerneTKI1 Ha KOHycax 11 c$epax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
11.5.1. KOHlfQeCKlfe pemeTKIf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461
11.5.1.1. CeTKI1 Ha KOHyce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464
11.5.1.2. KOHlfQeCKa51 ,n:enOJI5IpH3aUH5I M Koop,aHHaTHble CHCTeMbI. . . . . . . . 466
11.5.1.3. I1pOeKl.{HOHHbIH CHHTe3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
11.5.1.4. ,lJ,HarpaMMbI HanpaBJIeHHOCTH H B3aHMHa51 CB5I3b . . . . . . . . . . . . . 473
11.5.1.5. 3KcnepMMeHTbI C KOHI1QeCKI1MH pemeTKaMH . . . . . . . . . . . . . . . . 474
11.5.2. CcJ;>epI1QeCKHe pemeTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .474
nHTepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .476
fJIaBa 12. CBJl3aHHbIe pemeTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
12.1. I1CTOpl151 CB5I3aHHbIX pemeToK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
12.2. npl1HUHnbI pa60TbI CB5I3aHHOH pemeTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
12.3. TOKH B CB5I3aHHblX .n:HnOJI5IX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .483
12.3.1. Pe3YJIbTaTbI Mo.n:eJlHpOBaHI151: cJ;>a3bI TOKa . . . . . . . . . . . . . . . . . . . . . . . . . 484
12.3.2. Pe3YJIbTaTbI Mo.n:eJlHpOBaHH5I: aMnJlHTY,n;bI TOKa. . . . . . . . . . . . . . . . . . . . . 485
12.3.3. Pe3YJIbTaTbI Mo.n:eJlHpOBaHH5I: K03$cJ;>HUHeHT YCMJleHH5I 3J1eMeHTa (SEP) . . . 491

CoiJep:J/CaHue 
12.4. Coe.nHHeHHe 3JIeMeHTOB nocpe,nCTBOM peaKTHBHOrO conpOTHBJIeHHB. . . . . . . 491
12.5. Pa3BHTHe npHHQHna CBB3aHHbIX perneTOK. . . . . . . . . . . . . . . . . . . . . . . . . . 493
JIHTepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
fJl8B8 13. OT))81K8TeJlbHbIe H nepeH3JI)"I8lOIIUle 8HTeHHbIe pemeTKH. . . . . . . . . . . . . . . . . 495
13.1. OTpIDKaTeJIbHbleaHTeHHbleperneTKH................................ .495
13.1.1. I1cTopHB OTpIDKaTeJIbHbIX aHTeHHbIX perneTOK . . . . . . . . . . . . . . . . . . . . . 495
13.1.2. feoMeTpHqeCKHe COOTHorneHHB .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496
13.1.3. 3JIeMeHTbI OTpa)l(aTeJIbHbIX peIlIeTOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
13.1.4. <l>a3HpoBaHHe 3JIeMeHTOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
13.1.5. llIHpHHa nOJIOCbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
13.1.6. Pa3BHTHe OTpa)l(alOllUIX peIIIeTOK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
13.2. llepeH3JIyqalOll.(He aHTeHHbIe peIIIeTKH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
13.2.1. I1cTopHB nepeH3JI)"IalOll.(HX aHTeHHbIX peIIIeTOK . . . . . . . . . . . . . . . . . . . . 502
13.2.2. TIoCJIe,nHHe ,nOCTIDKeHIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
13.2.3. COBpeMeHHbIe BH,LI;bI npHMeHeHIDI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506
JIHTepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507
fJl8Ba 14. 3epKaJIbHbIe 8HTeHHbie pemeTKH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
14.1. PeIIIeTKH, pa3Mell.(eHHbIe B <l>OKaJIbHOH llJIOCKOCTH . . . . . . . . . . . . . . . . . . . . . . . 511
14.1.1. TIOJID B <l>OKaJIbHOH llJIOCKOCTH H KOMa . . . . . . . . . . . . . . . . . . . . . . . . . . 511
14.1.2. BocCTaHOBJIeHHe nOTepb CKaHHpOBaHHD, BbI3BaHHbIX KOMOH . . . . . . . . . . . 516
14.1.3. OrpaHHqeHHB no KOppeKQHH KOMbI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
14.2. 3JIeKTpOMarHHTHaB onTHKa 6JIIDKHerO nOJIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
14.2.1. AHTeHHa KaccerpeHa 6JIIDKHerO nOJID . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
14.2.1.1. CHcTeMHble Tpe60BaHHB H orpaHHqeHHB. . . . . . . . . . . . . . . . . . . 522
14.2.2. AHTeHHa fperopH 6JIIDKHerO nOJIB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522
JIHTepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
f JlaBa 15. H3MepeHHJI H ,nonYCKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
15.1. 113MepeHHe ,l(HarpaMM HanpaBJIeHHOCTH aHTeHH C HH3KHM ypOBHeM
60KOBbIX JIeneCTKOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
15.2. ,IJ;HarHocTHKa aHTeHHOH peIIIeTKH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
15.3. BOJIHOBo,nHbIe HMHTaTopbI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
15.4. ,IJ;onycKH B aHTeHHbIX perneTKax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
15.4.1. CHH)I(eHHe HanpaBJIeHHOCTH H yaeJIHqeHHe Cpe,l(HerO ypOBHB
60KOBbIX JIeneCTKOB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539
15.4.2. OIlIH6Ka YCTaHOBKH Jlyqa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
15.4.3. TIHKoBbIe 3HaqeHHB 60KOBbIX JIeneCTKOB . . . . . . . . . . . . . . . . . . . . . . . . . 541
JIHTepaTYpa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
CnHCOK nOHDTHH H COKpall.(eHHI1 ....................................... 546
II pe,l(MeTHbIH yJ(a3aTeJIb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548
WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING. . . . . . . . . . . . .554
MOHorpa<pHH OTeqeCTBeHHbIX aBTopOB, nOCBBll.(eHHbIe B cYll.(eCTBeHHoH CTeneHH
aHTeHHbIM peIIIeTKaM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559

nPEAMcnOBME K PYCCKOMY M3AAHMIO
HaCTORm:aR KHMfa HarrHCaHa P06epTOM C. XaHCeHOM (R. C. Hansen) - 113Bec-
THbIM yqeHbIM B 06JIaCTH aHTeHHOM HaYKH 11 TeXHHKH, aBTopOM H pelIaKTopOM
MHOrl1X MOHOfpa<pMM, B qaCTHOCTI1, TpeXTOMHI1Ka «Microwave Scanning Antennas»,
BbIrrym:eHHOfO H3,[(aTeJIbCTBOM Academic Press B 1964-1966 ro,[(ax. nepeBe,[(eHHaR
Ha PYCCKHM R3bIK no,[( Ha3BaHHeM «CKaHI1PYJOm:He aHTeHHbIe CHCTeMbI CBq» MO-
Horpa<pI1R CTaJIa HaCTOJIbHOM KHHfOM ,[(JIR CrreI.J;l1aJIHCTOB.
UeJIb ,[(aHHoM KHHrH - rrpe,[(CTaBI1Tb rrOJIHOe 11 06mHpHoe paCCMOTpeHHe c):>a311-
pOBaHHbIX aHTeHHbIX pemeTOK rr}'TeM ,[(orrOJIHeHI1R 11 06HOBJIeHHR COOTBeTCTBYIO-
m:HX pa31IeJIOB rrpelIbIlIym:efO H31IaHI1R. CJIelIyeT OTMeTI1Tb, qTO aBTOp rrpH,aep)J(HBa-
eTCR xapaKTepa H3JIO)l(eHHR MaTepHaJIa, opHeHTHpOBaHHOfO B rrepBYIO Oqepe,[(b Ha
CneUHaJIl1CTOB B 06JIaCTI1 TeOpHI1 H TeXHHKH <l>AP.
C<pepoM OXBaTa KHHfH RBJIRIOTCSI Bce THnbI aHTeHHbIX perneTOK (AP), KpOMe
a,uanTI1BHbIX. TIoCJIelIOBaTeJIbHO 06C)')K.1leHbI OCHOBHbIe xapaKTepHCTHKI1 JIHHeM-
HbIX H nJIOCKI1X aHTeHHbIX pemeTOK (fJIaBa 2), paCCMOTpeHbI MeTO,[(I1KI1 paCqeTa H
v
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perneTOK (rJIaBbI 3, 4). 3JIeMeHTbI C HI13KHM K03<P<PHI.J;HeHTOM YCI1JIeHHR, HCnOJIb-
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AP - B fJIaBe 6. B fJIaBaX 7, 8 HCCJIe,[(OBaHbI <pYHJJ:aMeHTaJIbHbIe OCHOBbI B3aHM-
HOM CBR3H Me)l():(y 3JIeMeHTaMH, OCHOBHbIe MeTO,[(bI aHaJIH3a xapaKTepHCTHK AP B
npocTpaHcTBeHHoH (n03JIeMeHTHbIH no,[(xo,[() H B CrreKTpaJIbHOH 06JIaCTRX (rrepHo-
,[(HqeCKHe RqeHKH), a TaIOKe KpaeBble 3<p<peKTbI KOHeqHOH AP. CBepxHarrpaBJIeH-
HOCTb AP - HanpaBJIeHHOCTb 60JIee BbICOKaR, qeM HarrpaBJIeHHOCTb, nOJIyqaeMaR
MR perneTKH TOH )l(e ,[(JIHHbI H C paBHOMepHbIM B036)')K.1leHHeM H3JIyqaTeJIeH, pac-
CMOTpeHa B fJIaBe 9.
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nJIOCKHe TOpI.J;bI coe,[(HHeHbI BMeCTe rrpOBO,[(HHKaMH HJIH HMne,[(aHcaMH; TaKHe AP
rr03BOJIRIOT paCIIIHpl1Tb pa60qylO rrOJIOcy nporrYCKaHHR. B fJIaBe 13 paCCMOTpeHbI
OTpa)J(aTeJIbHbIe aHTeHHble peIIIeTKH, KOTopbIe HHor,[(a RBJISIIOTCH 3aMeHoH <pa3HpO-
BaHHbIX pemeTOK 11 MaJIbIX 3epKaJIbHbIX aHTeHH, 06eCneqHBaR 60JIee KOMnaKTHbIe
ra6apHTbI 11 60JIee npocT)'1O cxeMY B036)')K.1leHHR.
B npOI.J;eCce nepeBo,aa coxpaHeH CTI1JIb, TepMHHOJIOfHR 11 0603HaqeHHR aBTopa.
B qaCTHOCTH, HapRAY C KJIaCCHqeCKHM TepMHHOM «ypOBeHb 60KOBMX JIeneCTKOB
(YEJI»> (B aHfJIOR3bIqHOH TpaHCKpHrrI.J;HH Sidelobe Level - SLL) IIIHpOKO HCnOJIb-
3yeTcR 06paTHaR YEJI BeJIHQI1Ha, onpe,[(eJIReMaH KaK OTHOIIIeHl1e ypOBHR JIyqa K
ypOBHIO 60KOBOfO JIeneCTKa (B aHrJIOR3bIQHOH TpaHCKpHnI.J;I1H Sidelobe Ratio -
SLR). ABTOpOM BBe,aeH TepMHH «lIHarpaMMa CKaHHpOBaHHR 3JIeMeHTa» (Scan Ele-
ment Pattern - SEP), paHee, no MHeHHIO aBTopa, Hey,[(aqHO Ha3bIBaeMaR «,[(Ha-
v
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CCbIJIKH Ha JII1TepaTypy 11 rrpe,aCTaBJIeHHbIe PHCYHKH CKoppeKTHpOBaHbI B COOT-
BeTCTBHH C npaBI1JIaMI1, rrpHHHTbIMH B OTeQeCTBeHHOM JIHTepaT)'pe. 06Hap)')KeHbI H
YCTpaHeHbI HeKOTopbIe OIIIH6KH B <popMYJIaX, a TaIOKe Ha pHCYHKax. nOCKOJIbKy
nepe,a CrreI.J;HaJII1CTaMI1 Bcer,aa CTOHT Borrpoc «Ky,[(a I1,aTH?» (a B KHl1re OTBeT Ha 3TOT
Borrpoc OTC}'TCTByeT), OTMeTI1M Tpl1 npeBOCXO,[(HbIe KHHrH, B KOTOpbIX (rrycTb II B

.
IIpeiJuCflo6ue K PYCCKOMY U3iJaHU1o 
-
.
MaJIOH CTeneHH) HaMqHbI rOpH30HTbI pa3BHTHH aHTeHHoi1 HaYKH H TeXHMKH,
BKJIIOqaH aHTeHHbIe perneTKH:
- Frontiers in antennas: next generation design & engineering. Ed. Frank B.
Gross. - McGrow- Hill, 2011, pp.526.
- Modern antenna handbook. Ed. C. A. Balanis. - John Wiley & Sons, 2008,
pp.1680.
- Phased array antennas: floquet analysis, synthesis, BFNs, and active array sys-
tems. A. Bhattacharyya, Hoboken, NJ: Wiley-Interscience, 2006, pp.516.
B ,aaHHoH KHHre B OCHOBHOM HCnOJIb30BaHbI pa60TbI 3apy6e)I(Hblx aBTopOB, o,n-
HaKO 6y,aeT HeJIHllIHe OTMeTHTb, qTO BKJIan; OTeqeCTBeHHblX aBTopOB B TeopHIO H
TeXHHKY aHTeHHblX pellieTOK HeCOMHeHeH. TIo3TOMY ,aonOJIHHTeJIbHO B KHHre npH-
Be,neH cnHCOK OCHOBHbIX MOHOrpacPHM OTeqeCTBeHHblX aBTopOB, nOCBHI..IJ:eHHbIX B
CYJ-l(eCTBeHHoH CTeneHH aHTeHHbIM pemeTKaM. TaK, HanpHMep, nepBoH pa6oToH no
nOJlyqeHHIO YCTOHqHBbIX, npaKTHqeCKH peaJIH3yeMblx aMTIJIH1)',nHo-ij)a30Bblx pac-
npe,n;eJleHHH npH pellIeHHH CMemaHHblX 3an;aq CHHTe3a 6bma MOHorpaij)HH [2], a Te-
OpeTHQeCKHe H KOHCTPYKTOpCKO-TeXHOJIOrHqeCKHe np06J1eMbI C03,naHHH O,L{HOH H3
nepBbIX 60pTOBbIX aHTeHHblX CHCTeM C 3JIeKTpOHHbIM ynpaBJleHHeM JIyqOM npe,a-
CTaBJleHbI B [18].
I1epeBo,n KHHrM Ha PYCCKMH H3bIK HHMIJ.MMpOBaH DAD «HI1I1 I1pH6opocTpoe-
HMH MM. B.B. TMxoMHpoBa». I1MeHHo B 3TOM MHCTHTYTe BnepBble B MMpOBOi1 npaK-
TMKe 6bIJla pa3pa6oTaHa 6opToBaH <DAP ,lUIH CYB «3aCJIOH» MCTpe6MTeJIH Ml1f -31.
Ha COBpeMeHHOM 3Tane pa3BMTMH TeopM H TeXHMKH aHTeHHbIX CMCTeM C 3JIeKT-
pOHHbIM ynpaBJIeHl1eM JIyqOM M pan;apOB Ha I1X OCHOBe B HI1I1TI C03,naHbI 06pa3IJ.bI
Cl>AP 11 ACI>AP, COOTBeTCTBYIOI..IJ:Me nepe,nOBOMY Ml1pOBOMY YPOBHIO. 3TO ,nOCTl1fHY-
TO 6J1aro,napH 3ij)ij)eKTI1BHOH pa60Te 60JIbllIOH rpynnbI CneIJ.MaJIMCTOB B 06J1aCTI1
CBq-YCTPOHCTB, aHTeHH M pan;apoB M BblcoKoTeXHOJlOrMqHOH HayqHoH, npoM3Bo,n-
cTBeHHoH H McnbITaTeJlbHOH 6a3bI.
B nepeBo,n KHMrH 3Haql1TeJlbHbIM TPY,n BJlO)l(RJIH COTpy,nHI1KH DAD «HI1I1
I1pI160pOCTpOeHI1H MM. B.B. TMXOMl1pOBa»: TI.A. AreeB, M.A. DaJII1Ha, C.E. faBpl1-
JlOBa, A.H. fpH6aHoB, B.I1. fpH,LI;HeB, B.H. EnHmKHHa, B.A. MHTHH, B.A. HHKH-
TOQKHHa, P.,l(. I103,nIDIKoBa, M.r. CTPYHCKHH, D.TI. J[cTpe6oB, nepeBo,aQHK
E.B. TIJIHllIeqHHK H oco6eHHo, npoij)eccop MAI1 ,n.T.H. A.IO. [pHHeB co CBOMMH
COTpy,nHHKaMM.
KHHra npe,nHa3HaqeHa HayqHbIM pa60THHKaM M MIDKeHepaM, 3aHHMalOI..IJ:MMHCH
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paHTaM, CneIJ.MaJIM3MpyIOIIJ:HMCH B 06J1aCTM aHTeHH H YCTPOHCTB CBq. KHMra TaK-
)l(e npe,aCTaBJlHeT MHTepec ,lUIH llMpOKoro Kpyra CneIJ.HaJIMCTOB, npe)l(,[(e Bcero TeM,
QTO B HeH npe,aCTaBJleHa o6llHpHaH HH<popMaIJ.HH 0 pa3J1HqHbIX THnax aHTeHHblX
pellieTOK M HX xapaKTepMCTHKax.
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nPEAMcnOBME K nEPBOMY M3AAHMIO
XOTSI MCTOpMSI aHTeHHbIX perneTOK HaCql1TbIBaeT yxe MHoro neT, nOCneJIHMe JIBa
....
,neCSITHneTIDI CTaJIM BpeMeHeM nonHoro pa3BMTMSI B03MO)l(HOCTeM KaK I1X paCqeTa,
TaK H Hcnonb30BaHHSI 60nbrnHX cnOXHbIX aHTeHHbIX perneTOK. pa,napbl, B KOTOpblX
HCnOJIb3yroTCSI aHTeHHble perneTKH C 3neKTpOHHblM nepeMeI.UeHHeM JIyqa, nOJIyqH-
JIH rnHpOKoe npHMeHeHHe, HaqHHaSi OT ,nHcneTqepCKHX cnyx6 a3ponopTOB JIO CHC-
TeM 06HapyxeHHSI H COnpOBO)K,[(eHHSI paKeT; xoporno H3BeCTHbI Ha3BaHI-UI aMepH-
KaHCKHX BoeHHbIX CHCTeM, TaKHX KaK Aegis, Patriot Ii Pave Paws. B 3TOH KHHre
.aaeTCSI BceCTopOHHee paCCMOTpeHHe Bcex aCneKTOB <pa3HpoBaHHblx aHTeHHbIX pe-
.... ....
rneTOK, CIDIbHO li3MeHHBIIIHXCSI co BpeMeH H3,naHHSI npe.n;b:r,nyrn:eH, e,L(HHCTBeHHOH B
,naHHoH 06JIaCTH pa60Tbl «CKaHuPYIOUI,Ue aHmeHHble cucmeMbl CRg», KOTopaSI BbInma
B CBeT B 1966 ro,ny. HaH60nee npHMeqaTenbHbIM CTaJIO napaJIJIeJIbHOe pa3BHTHe He-
,L(OpOrHX BblqHCnHTeJIbHbIX CpeJICTB H TeOpeTHqeCKHX pa3pa60ToK npHMeHHTenbHO
nOqTH KO BceM acneKTaM npOeKTHpOBaHHSI <pa3HpoBaHHbIx aHTeHHbIX pellieTOK.
Oc060e 3HaqeHHe nplf.aaeTCSI aJIrOpHTMaM paCqeTa, npHrO,L(HbIM ,l(JISI KOMnblOTep-
HbIX CHCTeM, npH 3TOM Bce rJIaBbI CO,L(ep)l(aT 60JIbrnOe qHCnO peKOMeH,L(aUHH H KO-
pOTKHX aJIrOpHTMOB. B pa60Te peaJIH30BaH ,L(BOHHOH nOJIXo.n K npeJIMeTY - C TOqKH
3peHHSI npOeKTHpOBI.UHKa H HCCJIe,L(OBaTenSi aHTeHHblX pellieTOK.
B rJIaBe 2 npo.nOJDKeHO paCCMOTpeHHe OCHOBHblX xapaKTepHCTHK aHTeHHbIX pe-
IIIeTOK, BKJIIOqaSI 60KoBbIe JIeneCTKH, JIeneCTKH KBaHTOBaHHSI, .nHana30H qaCTOT M
K03<P<PHUHeHT HanpaBneHHoro .n;eHcTBHSI, HaqaTOe BO BBO,nHOH rJIaBe. BbICOK03<p-
<peKTHBHble MeTo.nbI CHHTe3a JIHHeHHOH anepTYPbI H aHTeHHblX perneTOK, BKJIlOqaSl
.... ....
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rnaBe 3. B rJIaBe 4 paCCMOT})eH CHHTe3 nrrOCKHX aHTeHHbIX pellieTOK. B rnaBe 5 pac-
....
CMaTPHBalOTCSI 3JIeMeHTbl aHTeHHOM perneTKH, BKJIlOqalOI.UMe He TOJIbKO KJIaCCMqeC-
KHe ,nHnonH H I.UenH, HO TalOKe TEM pynOpbl H MHKpOnOJIOCKOBbIe H3JIyqaTenM.
B rJIaBe 6 Hccne.l{ylOTCSI CHCTeMbl B036y)K,[(eHHSI nHHeHHbIX H nnOCKHX aHTeHHbIX
pellieTOK, KaK C HenOJIBIDKHblM nyqoM, TaK H CKaHHpyroI.UHX, BKJIlOqaSl OnTHqeCKHe
JIMHMH 3a,nep)f{K.H H CHCTeMbI B036y)K,[(eHHSI. Ha pa60qHe xapaKTepHCTHKH aHTeH-
HOH peIIIeTKH OKa3bIBaeT CHJIbHOe BJIIDIHHe B3aHMHbIH HMne.naHC. B rJIaBe 7 Hccne-
.nyroTCSI cnoc06bl ero paCqeTa .LUISI pa3nMqHbIX 3neMeHTOB aHTeHHbIX pellieTOK M
no.np06HO paCCMaTpMBaroTcSI cnoco6M BbPlliCneHHSI pa60qHX xapaKTepHCTHK aH-
TeHHbIX pellieTOK C yqeToM B3aHMo.neHcTBIDI. B MX qMCJIe MeTOJIbI eJIHHMqHOH SlqeH-
....
KH, CneKTpaJIbHOrO MOMeHTa, MaTpHUbI HMne.naHCOB KOHeqHOH peIIIeTKH H MeTO-
,nbl, yqHTbIBaroI.UHe pacceSIHHe. KOHeqHbIe aHTeHHble perneTKH paCCMaTpHBaroTcSI B
rJIaBe 8 C yqeToM He.naBHO pa3pa60TaHHbIx MOJIeneH fH66ca. Cne,nyroI.UaSI, 9-SI rJIa-
Ba npe.nCTaBJISIeT C060H 06IIIMpHbIH 0630p no CBepXHanpaBJIeHHbIM aHTeHHbIM pe-
IIIeTKaM, BIDKHOH oc06eHHOCTblO KOToporo SlBlliIlOTCSI BbIBO.nbI, KaCalOIII.HeCSI HC-
nOJIb30BaHHSI B aHTeHHax BblCOKOTeMnepaTypHbIX CBepxnpOBo.nHHKOB. B rnaBe 10
npOBo.nHTCSI cpaBHeHHe MHOrOJIyqeBblx aHTeHHblX perneTOK Ii 06JIyqaTeJIei1 3ep-
.... ........
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3JIeCb paCCMaT})HBaIOTCSI TalOKe O,nHO- M .nB}'MepHbIe JIMH3bI 6aTJIepa H POTMaHa
H npaKTHqeCKOe npHMeHeHHe opTOrOHaJIbHOCTH nyqeH. 3aTeM paCCMaTpHBalOTCSI
KOH<popMHble aHTeHHble peIIIeTKH, OT KOJIbueBbIX .no KOHMqeCKHX; B 3TY rnaBY

llpeaUCJI08Ue K nep80MY U3aaHUIO 
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CSI BonHOBo,n;HbIe Mo,n;eJ111 11 ,n;orrYCKI1 Ha napaMeTpbI aHTeHHbIX pellleTOK. B Ka)K)J,OM
rnaBe npI1BO,lJ;SlTCSI MHOrOQI1CJ1eHHbIe CCbIJ1KI1 Ha apXI1BHYIO nI1TepaTYPY, co.aep)J(a-
YIO ,lJ;OnOnHI1TenbHbIe ,naHHbIe.
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Co BpeMeHH BbIXO,[(a nepBOrO H3,[(aHHH KHHrH BHHMaHHe Cne[{HaJIJfCTOB npH-
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TOK. AHTeHHble perneTKH Ha OCHOBe CBR3aHHbIX ,[(HnOJIeM 06eCne1.JHBa1OT 60JIee rnl1-
pOKyIO nOJIOcy nponYCKaHIfH no cpaBHeHlf10 C 06bI1.JHbIMll aHTeHHbIMH pemeTKaMIf;
OHH no,[(p06HO 06Cy)I():(alOTCH B rJIaBe 12 (rJIaBa 12 npe)l(HerO H3,[(aHIfR Tenepb ny6-
JIHKyeTCH KaK rJIaBa 15). OTpIDKaTeJIbHble perneTKH xapaKTepH3YIOTCH MeHbllIeH
CTOHMOCTblO H3rOTOBJIeHHH no cpaBHeHHIO C <}>a3HpoBaHHoM aHTeHHOH pemeTKoH.
A peTpaHCJIH[{HOHHble aHTeHHble pemeTKH npe,[(OCTaBJIHIOT HHTepeCHble B03MO)l(HO-
CTH ,lLJIH KaHaJIOB CBH3H. 06e 3TH TeXHOJIOrHH paCCMOTpeHbI B rJIaBe 13. KOM6HHa-
[{HH pe<}>JIeKTOpOB H aHTeHHblX pemeTOK paCCMaTpHBaeTCH B rJIaBe 14 KaK .LLJIH aH-
TeHHblX perneTOK C pacnOJIO)l(eHHeM B <}>OKaJIbHOH ITJIOCKOCTI1 C yqeToM KOppeK[{HH
KOMbI, TaK H ,lLJIH 6JIIDKHerO nOJIH aHTeHH KaccerpeHa H fperopH.
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<PYH,[(aMeHTaJIbHble OrpaHH1.JeHHH Ha MCKyCCTBeHHble MarHI1TOnpOBO,[(bI; 3aMeHa
npHMoyrOJIbHOrO BOJIHOBo,[(a BOJIHOBO,[(OM, HHTerpHpOBaHHbIM B nO,lLJIO)l(Ky; aHTeH-
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pa601.JMM xapaKTepHCTHKaM H orpaHH1.JeHHHM, BKJII01.JaR OrpaHH1.JeHHH no KpllTepl110
fio,[(e; 06pa60TKa BbI1.JHCJIeHHH H H3MepeHHM HMne,[(aHca CKaHHpOBaHHH 11 ,[(MarpaM-
MbI HanpaBJIeHHOCTH 3JIeMeHTa npH CKaHHpOBaHIfI1; 11 HaKOHeu, KOMMeHTapI1H, Ka-
CalOIl(erOCH nOJIHOCTblO nepeKpbIBalOl.I.(HXCH no,[(perneTOK.

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r
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cJIe.aoBaHHH aHTeHHhlX pellieTOK (AP); I1HTepec K AP B0306HOBHJICH B HaqaJIe
1960-x.
3aMeTHhIM C06hITHeM CTaJI BhIIIYCK H3,n;aTeJIhCTBOM Academic Press TpeXTOMHI1-
Ka «CKaHuPYIOU{ue aHmeHHble cucmeMbl CBg» (Microwave Scanning Antennas -
MSA), I-H TOM KOToporo BhIIIleJI B I964-M, a 2-H 11 3-H TOMa - B 1966 ro,n;y.
3Ta pa60Ta 6hIJIa IIepBhIM 0611IHpHhIM 0630pOM no <l>a3HpoBaHHbIM AP (<DAP),
C aKu;eHTOM Ha TeopHIO B3aHMHoH CBH3H, KOTopaH JIe)l(l1T B OCHOBe paCQeTa Bcex
xapaKTepl1CTHK AP.
l(eJlb iJaHHou KHU2U - IIpe,n;CTaBHTh nOJIHOe M 06111l1pHOe paCCMOTpeHHe <DAP
nyreM ,n;OIIOJIHeHI1H 11 06HOBJIeHHH COOTBeTCTBYIOWHX pa3,n;eJIOB MSA. C<pepoH ox-
BaTa KHl1rl1 HBJIHIOTCH Bce THilhI AP, KpOMe au.anTI1BHbIX, KOTOpbIM nOCBHrn;eHO He-
CKOJIhKO npeBocxo,n;HhIX KHHf (CM. CChlJIKH B KOHl.{e fJIaBhI). IIoCKOJIbKY 60JIbllIlfH-
CTBO AP pa60TaeT Ha qaCTOTax, n03BOJIHIOll.{HX CQI1TaTb paCCTOHHHe Me)l(,L(Y
aHTeHHoH If 3eMJIeti ,n;OCTaTOQHO 60JIbllll1M D)IH YCTpaHeHI1H BJIHHHHH 3eMJIH Ha
BHyrpeHHHe napaMeTpbI AP, Bce peIIleTKH npe,n;nOJIaralOTCH Haxo,n;Hrn;HMHCH B CBO-
60,n;HOM npOCTpaHCTBe. AIcrHBHble AP, TO eCTb peIIleTKH, co,n;ep)l(aWHe aKTHBHble
3JIeMeHTbI, He paCCMaTpHBaIOTCH, paBHO KaK If CBH3aHHble C <DAP CBq KOMnOHeH-
TbI cxeM, 3a HCKJIlOqeHHeM <l>a30Bpall.{aTeJIei1, KOTopble 06Cy)I(,L(alOTCH BKpaTu;e.
IIpe,n;noJIaraeTcH TaIOKe, QTO Bce 3JIeMeHTbI AP H,LJ;eHTI1QHbI, XOTH COrJIaCOBaHHe
HMne,n;aHCOB MO)l(eT H3MeIDIThCH B 3aBHCHMOCTH OT nOJIO)l(eHIDI 3JIeMeHTa.
CyrI(ecTByeT CMbICJIOBa51 Tpy,n;HOCTb npH HCnOJIh30BaHHH <ppa3bI «<pa3HpoBaH-
HaH aHTeHHaH pellIeTKa». ,[LITH HeKOTopbIX JIIO,n;eH 3TO CJIOBOCOQeTaHl1e npe,n;nOJIara-
eT ynpaBJIeHHe nOJIO)l(eHl1eM JIyqa IUIH CKaHHpOBaHl1e. O,n;HaKO ,LLJI5I ,n;pyrHx Bce AP
HBJIHIOTCH <pa3HpOBaHHbIMH; CHH<pa3Hble AP C Heno,n;BH)l(JIhIM JIyqOM TO)l(e <pa3HpO-
BaHHbIe. I1MelOTCH 11 60JIee Ba)l(HbIe TepMHHOJIOrHqeCKl1e BonpOCbI; OHH paCCMaT-
pHBalOTCH ,n;aJIee.
l'
\
1.2. CMCTeMHble <l>aKTOpbl
...
,
Ba)I(HbIMI1 napaMeTpaMI1 AP .lI.lliI pa3pa60TQHKa CI1CTeMbI HBJI.HIOTCH ,n;HarpaMMa Ha-
npaBJIeHHOCTH aHTeHHbI, 3aBHCI1MOCTb K03<P<PHl.{HeHTa YCI1JIeHI1H OT yrJIa CKaHHpo-
BaHH5I, BXOLIHOH HMneLIaHC 3JIeMeHTa 11 Kn,lJ.. ,LJ;JIH Bcex 3KBH,IU1CTaHTHblX AP LIl1a-
rpaMMa HanpaBJIeHHOCTH 3au.aeTCH npOH3Be,n;eHl1eM .IJ.HarpaMMbI HanpaBJIeHHOCTH
3JIeMeHTa If MHO)I(HTeIDI H30TponHoH AP, B KOTopoH H3JIyqaTeJIH HBlliIIOTC.H Bce-


Fflaea 1. Beeaenue
HanpaBJIeHHbIMH. O,n:HaKO B036}')K,lI.eHHe 3JIeMeHTOB ,n:OJI)I(HO 6bITb TaKHM xe, KaK H
,LlJUI peaJIbHOll AP. KaK nOKa3aHO HH)I(e, OHO OnpeLleJI5IeTC5I nyreM perneHI151 ypaB-
HeHHM, yqHTbIBalOII.J:HX c06CTBeHHbIll H B3aHMHbIMI1Mne,n:aHCbI 3JIeMeHTOB perneTKI1
I1JII1 MaTpHUY ee KOMTIJIeKCHOll npOBo,n:HMOCTI1. Bo06I..l.(e rOBopR, Bce 3JIeMeHTbI AP
HMelOT pa3HbIe Bxo,n:HbIe HMne,n:aHCbI. ,[(JI5I AP C Heno,n:BH)I(HbIM JIyqOM OHI1 Ha3bIBa-
IOTC5I «BCTpoeHHbIMH HMne,n:aHcaMH»; HCnOJIb30BaHI1e YCTapeBrnero 11 BBO,Ll,51merO B
3a6JI}')K,lI.eHHe TepMI1Ha «aKTI1BHbIll HMne,n:aHC» He peKOMeH,n:yeTC5I. Y 3JIeMeHTOB
CKaHI1PYIOll.{ell AP He TOJIbKO pa3JIHqHbIe HMne,Ll,aHCbI, HO Ka)l(J{bIll 1'13 HI1X 113MeH5I-
eTC5I B 3aBHCHMOCTH OT yrJIa CKaHHpOBaHH5I. 3TH BXO,Ll,HbIe HMrren:aHcbI 3JIeMeHTOB
Ha3bIBalOTC5I uMneiJancaMu cKanupo6anuR (scan impedance).
3aBHcHMoCTb K03<P4>HUHeHTa YCHJIeHH5I 3JIeMeHTa aHTeHHOll perneTKI1 OT
yrJIOB CKaHHpOBaHH5I Ha3bIBaeTC5I iJua2paMMou CKanup06anUR 31leMenma (Scan
Element Pattern - SEP), paHee Hey,n:aqHO Ha3bIBaeMbIll ,n;HarpaMMoll HanpaBneH-
HOCTH aKTHBHoro 3JIeMeHTa. ,l(ua2paMMa CKanup06anUR 31leMe1lma TIpe,n;CTaBJI5IeT
C060ll qpe3BblqaHHO rrone3HbIll KOHCTPYKTHBHbIH napaMeTp. ,[(HarpaMMa HanpaB-
JIeHHOCTH 3JIeMeHTa 1'1 3<p<peKTbI B3aHMOCB5I3H BKJIIOQeHbI B orrpe,n;eJIeHHe SEP;
nOJIHa5I ,n:HarpaMMa HarrpaBneHHOCTH H3JIyqeHH5I 51BJI5IeTC5I npOH3Be,n;eHHeM iJua2-
paMMbl CKa1lUp06anUR 31leMenma H ,n:HarpaMMbI HanpaBJIeHHOCTH perneTKI1 H30-
TponHbIX 3JIeMeHTOB npH CKaHHpOBaHHH no,n: COOTBeTCTBYIOII.J:HM yrnOM. MHOXH-
TeJIb H30TporrHoll AP BKJIIOQaeT 3<p<peKTbI BJIH5IHH5I pa3Mepa 1'1 ceTKH AP, Tor,n:a
KaK iJua2paMMa CKanup06anUR 3JleMenma, KaK OTMe'-laJIOCb, BKJIIOQaeT n:l1arpaMMY
HanpaBJIeHHOCTH H3JIyqaTeJI5I, BJIH5IHHe 3MHero 3KpaHa, eCJII1 OH HCnOJIb3yeTC5I, 11
3<t><peKT B3aHMHoro BJIH5IHH5I 3JIeMeHTOB. IIoCKOJIbKY iJua2paMMa CKanup06anUR
31leMenma rrpe,n:CTaBJI5IeT C060M orH6alOII.J:Yro 3aBHCHMOCTH K03<P<PHUHeHTa YCHJIe-
HH5I AP OT yrJIOB CKaHHpOBaHH5I, OHa TOQHO YKa3bIBaeT npoeKTHpOBIUI1KY KOMMY-
HI1KaUHOHHOll CHCTeMbI HJIH PMapa, KaK <PYHKUHoHHpyeT aHTeHHa51 perneTKa rrpH
CKaHl1pOBaHHH, HMeIOTC5I JIH yrJIbI OCJIerrJIeHH5I H 3<p<peKTHBHO JII1 KOHKpeTHoe
3HaQeHHe yrna CKaHHpOBaHH5I. ,l(ua2paMMa CKanup06anUR 3JleMenma HCnOJIb3yeTc5I
.IUI5I rronyqeHH5I K03<P<PHUHeHTa YCHneHH5I aHTeHHbI B CTaH,LI,apTHbIX 3HepreTI1QeC-
KHX ypaBHeHH5IX pa,n:HOJIOKaUHH. Y 6eCKOHeQHOll aHTeHHOH perneTKI1 SEP ,n:JI5I
Bcex 3neMeHTOB O,L(Ha H Ta )l(e, Tor,n:a KaK B KOHeQHOH perneTKe y Ka)l(J{OrO 3JIe-
MeHTa HMeeTC5I pa3nHQHOe OKpyxeHHe, TaK QTO SEP 51BJI5IeTC5I rrapaMeTpOM Bcell
AP. HCrrOJIb30BaHHe iJua2paMM CKanup06anUR 3JleMenm06 6eCKOHeQHOll AP rr03BO-
JI5IeT BbIQneHHTb BKJIa,L( 3TH X ,n:HarpaMM H KpaeBbIX 3<P4>eKToB B pa60QHe xapaKTe-
pHCTHKH AP. <l>opMynbI ,n:n51 iJua2paMM cKanupo6anuR 31leMenm06 KaK KOHeQHOM,
TaK 1'1 6eCKOHeQHOH AP BbIBO,n:51TC5I ,n:aJIee; KpaeBbIe 3<p<peKTbI TaIOKe 06C}')K,lI.aIOTC5I
HH)I(e.
lIpH 06paTHOM paCCe5lHHH OT AP aHaJIOrHQHbIM napaMeTpoM 51BJI5IeTC5I iJua-
2paMMa cKanupo6anuR 31leMenma npu pacceRnuu (Scattering Scan Element Pattern -
SSEP). 3TOT rrapaMeTp xapaKTepH3yeT HHTeHCHBHOCTb nOJI5I, pacceHBaeMoro 3JIe-
MeHTOM AP, rrpH B036}')K,lI.eHHH AP nMalOrn;eH nJIOCKOll BOJIHOM. OH OTJII1QaeTC5I OT
SEP, CB5I3bIBalOrn;eM HHTeHCHBHOCTb IIOJI5I H3JIyqeHH5I C nOJIHOH MOllJ,HOCTblO H3JIY-
QeHH5I. CooTHorneHHe Me)l(,[(y HHTeHCHBHOCTblO rrepeH3JIYQeHHOrO rr01l51 H HHTeH-
CHBHOCTblO rrMalOrn;ero IIOJI5I orrpe,n:eJI5IeTC5I 3<p<peKTHBHoM oTpaxalOIUeM nOBepx-
HOCTblO (RCS) C yqeToM K03<P<PHUHeHTa 4nR2. SSEP rrpen:CTaBJI5IeT C060M
OTHorneHHe HHTeHCHBHOCTeH nepeH3nyqeHHoro 1'1 na.n:alOIUero H3JIyqeHI151; rrpH
3TOM y,n:06HO HCrrOJIb30BaTb HOpMHpOBKY K 3HaQeHHIO B HarrpaBJIeHHI1, neprreH,LI,H-

1.2. CUCmeMHble rjJaKmOpbl 
KYJI5IpHOM paCKpbIBY aHTeHHbI. KaK H .lLJI5I H3JIyqalOI..Uei1 AP, BJIM5IHMe KOHeQHOrO
pa3Mepa paCCeMBalOI..UeH AP H KpaeBbIX 3<p<peKTOB pa3,neJI5IeTC5I, n03TOMY SSEP
YCTaHaBJIMBaeT CB5I3b Me)l{)];Y 3<p<peKTaMH BJIH5IHH5I KOHCTPYKIJ;l1H 3JIeMeHTOB H CeT-
KOH AP. BnOCJIe,nCTBMM 3TO MOXeT 6bITb MCnOJIb30BaHO npM paC'leTe TMna 3JIeMeH-
TOB M CeTKH; yqeT OC06eHHocTei1, 06YCJIOBJIeHHbIX pa3MepOM AP, npOM3BOJJ;I1TC5I
npOCTO nyreM YMHOXeHH5I Ha K03<P<PMUMeHT ,lLTI5I M30TpOnHOH aHTeHHOM perneTKH.
KOHeQHO, SSEP CB5I3aHa C ,nHarpaMMOH HanpaBJIeHHOCTH RCS. Ee MOXHO pac-
CMaTpl1BaTb KaK JJ;HarpaMMY HanpaBJIeHHOCTH RCS OJJ;HOM 3JIeMeHTapHoi1 51QeMKH
AP. CHCTeMHbIe <paKTOpbI TaIOKe np05lBJI5IIOTC5I npH HCnOJIb30BaHHM AP B llIMpOKO-
nOJIOCHbIX npHJIOXeHH5IX (6e3 HeCym:ei1).
OCHOBHOe 3HepreTH'leCKOe ypaBHeHHe .IIJUI O.IJ:HOHanpaBJIeHHOrO paCnpOCTpaHe-
HI151 (CHCTeMbI CB5I3H), HanHCaHHOe 6e3 51BHOH 3aBHCHMOCTH OT )J,JIHHbI BOJIHbI,
I1MeeT BI1.l1
Pr
PrGAe
4nR2 '
(1.1)
rJJ;e, KaK 06bI'lHO, Pr H Pt - npHHHMaeMa51 H H3JIyqaeMa51 MOIl.(HOCTb, R - paaHYC
JJ;eHCTBM5I, a G H Ae - K03<P<PHUHeHT YClUleHH5I OJJ;HOi1 aHTeHHbI H 3<p<peKTHBHa51
nOBepXHOCTb .n;pyrOH. KaK K03<P<PH:QHeHT YClUleHH5I, TaK M 3ct><peKTHBHa51 nOBepx-
HOCTb BKJIIOqalOT K03<P<PM:QHeHT paCCOrJIaCOBaHM HMneJJ;aHca - (I-IfF). npeJJ;no-
JIaraeTC5I, qTO PI cpHKcHpoBaHo 11 He 3aBMCMT OT 'laCTOTbI. ECJIM np0l13Be,aeHHe GAe
B I1HTepeCYlOmeM qaCTOTHOM ,aHarra30He OTHOCHTeJIbHO nOCT05lHHO, TO nocTynalO-
v v
[1(1111 CMrHaJI He MMeeT CYI..UeCTBeHHOM JJ;HcrrepCHH, rrpH YCJIOBHH qTO aHTeHHa 11 CO-
OTBeTCTBYlOml1M cpa30BbIH 3JIeMeHT TaIOKe MMelOT cTa6MJIbHbIe napaMeTpbI [2].
B npOTMBHOM CJIyqae MoxeT B03HHKaTb 3Ha'lHTeJIbHa51 ,nMcrrepCH5I.
TIpH nOBepXHOCTHOM B3rJIMe Ha AP MOXHO rrpe,nnOJIOXHTb, qTO nJIOCKa pe-
llIeTKa npelICTaBJI5IeT c060i1 aHTeHHY C nOCTOHHbIM 3HaqeHHeM 3<1><l>eKTHBHoi1 no-
BepXHOCTM. O,aHaKo K03<t>CPH:QHeHT YCMJIeHH5I 3KBH,aHcTaHTHoH AP H3 3JIeMeHTOB C
MaJIbIM YClUleHHeM npH YBeJIH'leHHH qaCTOTbI B03paCTaeT, Ha'lHHa51 co 3Ha'leHH5I,
v v
COOTBeTCTBYIOru:ero HOMHHaJIbHOH nOJIYBOJIHOBOH nepHOJJ;H'lHOCTH, ,ao Tex nop,
nOKa He rr05lBHTCH nepBbIH ,aH<ppaK:QHOHHbIH JIeneCTOK, nOCJIe 'lero K03<P<PHUHeHT
YClUleHH5I B03Bparu:aeTC5I K nepBOHaqanbHOMY ypOBHIO. ,LJ;anbHeHIIIee YBeJIH'leHHe
qaCTOTbI BbI3bIBaeT ,nonOJIHHTeJIbHbIH pOCT K03cpcpH:QHeHTa YCHJIeHH5I, COnpOBO)l()]:a-
IOI..UHHC5I ero naaeHH5IMH no Mepe n05lBJIeHH5I ,nH<ppaK:QHOHHbIX MaKCHMYMOB pe-
IIIeTKH. B KOHeqHOM HTore K03<P<PH:QHeHT YClUleHH5I AP B llIHpOKOH nOJIOce npo-
nYCKaHIDI B JIyqIlIeMcnyqae npl1MepHO nOCT05lHeH M paBeH 3Ha'leHMIO,
COOTBeTCTByromeMY nOJIyBOJIHOBOH nepHo,aH'lHOCTH [1]. 3,aeCb He yqHTbIBaeTC5I 3<p-
<t>eKT paccornaCOBaHH5I HMne,aaHCOB BCTpOeHH'bIX 3JIeMeHTOB npH H3MeHeHHH 'lac-
TOTbI - BneHHe, ,aonOJIHHTeJIbHO CHJIbHO YMeHbllIalOI..Uee' K03<l>CPHUl1eHT YCMJIe-
HI151. TaKHM 06pa30M, 3KBH,[(HCTaHTHa51 AP He cnoco6Ha KOMneHCMpoBaTb
,aHcnepCMIO. PellIeTKa C rrceB,nOCJIyqaHHoi1 rrepMo,aM'lHOCTblO rrpM YBeJII1QeHHM qac-
TOTbI He 06Hap}')KHBaeT peryJI5IpHbIX ,aH<l>paKI(HOHHbIX JIeneCTKOB. B rrpaBMJIbHO
crrpoeKTMpOBaHHOH He3KBH,nMCTaHTHOH AP ,nOJI5I MOI..UHOCTH, co,aepxama5lc5I B 60-
KOBbIX JIerreCTKax, npHMepHO rrOCT05lHHa, TaKHM o6pa30M, K03<PCPH:QMeHT YCHJIeHH5I
rrpH H3MeHeHHH 'laCTOTbI npHMepHO rrOCT05lHeH. DOJIee CYIl.(eCTBeHeH, o,aHaKO, TOT
ct>aKT, qTO .IIJI5I 1I0CTIDKeHH5I .n;axe YMepeHHO HH3KHX YPOBHei1 60KOBbIX JIerreCTKOB
He06xoJJ;HMO OqeHb 60JIbiliOe KOJlH'leCTBO 3JIeMeHTOB. TaKHM 'o6pa30M, 3TH TMnbI


Filaea 1. BeeiJeHue
AP TaIOKe He npl1To,nHbI ,lLJI}I KOMneHcaUHH ,nHcnepCHH. AHTeHHbIe perneTKH, CO-
CTORIllJle H3 3neMeHTOB C 60nee BhICOKHM K03<P<PHUHeHTOM YCHneHHR, KpOMe Toro,
06na.n:a1OT LIHcnepCHeH, o6ycnoBneHHOH caMHMH 3neMeHTaMH, If ell.{e MeHee nplf-
v
ro,nHbI ,lLJIR ,naHHbIX uenel1.
1.3. AHHOTMpOBaHHblM cnMCOK nMTepaTypbl
AHTeHHble perneTKI1 Onl1CbIBalOTCR BO MHOrl1X yqe6HHKax, HO B ,AaHHbIM nepeqeHb
BKJIlOqeHbI KHl1rH 11 0630pbI, B KOTOpbIX <pa3l1poBaHHble AP paCCMaTpHBalOTCR Bce-
CTopOHHe.
Microwave Scanning Antennas, R. C. Hansen, Ed., 3 vols., Academic Press, 1964,
1966 [Peninsula Publishing, 1985, 442 pp., 400 pp., 422 pp.].
3TO nepBaR nO,Ap06HaR pa60Ta no <l>AP Bce elI.(e OCTaeTCR BeCbMa rrone3HOM.
B TOMe 1 I1MeeTCR rnaBa, B KOTOpOM paCCMaTpl1BaeTCR pacnpe,AeneHlfe nonR B pac-
KpbIBe. TOM 2 CO,Aep)l(HT TeopHIO AP H aHaJIH3 6eCKOHeqHOM If KOHeqHbIM perneTOK;
BepORTHO, nepBYIO pa3pa6oTKY MeTo.na aHaJII13a CneKTpaJIhHOrO npe.nCTaBneHlfR LIJIR
AP. B 3-M TOMe paCCMaTpHBalOTCR <pHJJ:epHbIe CHCTeMbI nHTaHHR, qaCTOTHoe CKa-
HlfpOBaHlfe If MHoroneneCTKOBble ,AHarpaMMhI, C03,AaBaeMbIe MHoronyqeBbIMIf MaT-
pHuaMH EaTnepa.
Proceedings of the 1964 RADC Symposium on Electronically Scanned Array Techni-
ques and Applications, report RADC-TDR-64-225, AD-448 481.
CIO,Aa BOlliJIH paHHl1e pa6oTbI, nOCBHlI.(eHHble norpeIIIHOCTHM KBaHTOBaHHR
<pa3bI, Q:>epplfToBbIM H nonynpOBO,AHHKOBbIM <l>a30BpalI.(aTenHM Ii MaTplfuaM <l>op-
MlfpOBaHlfR JIyqa.
The Theory and Design of Circular Antenna Arrays, James D. Tillman, University
of Tennessee Engineering Experiment Station, 1966, 235 pp.
B 3TOM MOHorpaQ:>HH no KonbueBbIM AP aHaJIH3 HMne,[{aHca 11 ,[{lfarpaMMbJ Ha-
v
npaBneHHOCTI1 npOBO,[{I1TCH C nOMOlI.(hlO nOCne,lJ.OBaTenhHOIf Teoplfli a3lfMyraJIbHbIX
MO,A. 06Cy)I()]:alOTCH TaIOKe BonpOCbI CKaHHpOBaHlUI AP.
Proceedings of the 1970 NELC Conformal Array Conference, TD-95, Naval Elect-
ronics Lab. Center, AD-875 378.
B CTaTbHX KOHcI>epeHUHI1 paCCMaTpHBalOTCH KaK KonbueBbIe, TaK If UHnHHLIpH-
qeCKl1e AP C TOqKH 3peHlfH HX TeopHH H npHMeHeHHH.
Phased Array Antennas, A. A. OHner and G. H. Knittel, Artech, 1972, 381 pp.
C60PHHK Tpy.nOB ClfMn03HYMa no <l>AP. BKJIlOqeHO MHoro pa6oT, KaCalOll.{lfXCH
BbIQI1CJIeHHH I1Mne,AaHCa, yrnoB ocnenneHHH 11 T.,A., a TaIOKe npaKTlfqeCKI1X acneK-
TOB, TaKI1X KaK KOMneHcaUHH npH CKaHHpOBaHHIf, cl>11,AepHOe B036Y)K)].eHlfe 11 <l>a-
3MpOBaHHe.
Theory and Analysis of Phased Array Antennas, N. Amitay, V. Galindo, and C. P. Wu,
Wlley-Interscience, 1972, 443 pp.
PaccMaTplfBalOTcH perneTKH BOnHOBO,lJ.HhIX 113nyqaTeneH. llIl1pOKO HCnOJIb3yeT-
CH MeTO,[{ CrreKTpaJIbHOrO npe,lJ.CTaBneHI1}1. TIpHBO,AHTCH perneHI1R ypaBHeHI1H ,lLJIH
MaJIhIX KOHeqHbIX AP B TepMlfHax MO,lJ. H 3neMeHTOB. 3Ta pa60Ta - O,lJ.HO 113 nep-
v
BbIX I1CrrOJIb30BaHI111 MHOrOMO)lOBOrO CrreKTpaJIbHOrO aHaJIl13a.

1.3. AHHomupo6aHHblu cnucOiC Ilumepamypbl 
Proceedings of the 1972 NELC Array Antenna Conference, TD-155, 2 Parts, Naval
Electronics Lab. Center, AD-744 629, AD-744 630.
Co,aep)f(HTCH MHOfO pa60T, KaCalOl.I.(HXCH BonpOCOB TeXHOJIOfHH aHTeHHbIX pe-
rneTOK 11 KOMnOHeHTOB, auanTI1BHbIX 11 KOH<pOpMHbIX aHTeHHbIX perneTOK.
Theory and Application of Antenna Arrays, M. T. Ma, Wiley-Interscience, 1974,
413 pp.
PaccMaTpHBaeTcH CIfHTe3 aHTeHHbIX perneTOK C HenO,l(BI1)1(HbIM JIyqOM 11 MHO-
rOql1CJIeHHbIMH npHMepaMlf aHTeHHbIX perneTOK. CYl.I.(eCTBeHHYIO qaCTb KHl1rH 3a-
HI1MaeT OnIfCaHl1e 3<p<peKTa BJII1HHHH 3eMJII1 Ha xapaKTepl1CTHKI1 aHTeHHbIX pe-
rneTOK.
Conformal Antenna Array Design Handbook, R. C. Hansen, Ed., Naval Air Sys-
tems Command, 1982, AD-A110 091.
B OTqeTe no,aBo,aHTCSI HTorH ,aecSlTI1JIeTHeM pa60TbI no UI1JIHH,l(pl1qeCKHM If KO-
HHQeCKI1M l.I.(eJIeBbIM AP, BbInOJIHeHHOM npl1 nOMep}l(Ke NAVAIR (Naval Air Sys-
tems Command - KOMaH,l(OBaHHe aBHaUHOHHbIX CHCTeM BMC CiliA) H BKJIIOQalO-
'-'
l.I.(e" IfCnOJIb30BaHHe aJIrOpHTMOB B3aHMHoro MMne,aaHca.
Antenna Theory and Design, R. S. Elliott, Prentice-Hall, 1981, 594 pp.
TIpeBocxo,aHbIM HCTOQHI1K I1H<popMaUMM no aHaJIM3Y M CMHTe3Y BOJIHOBO,a-
HO- Il(eJIeBbIX aHTeHHbIX perneTOK. nO,ap06HO paCCMaTpMBaeTCSI cPopMa orM6alOI.I.(eM
60KOBbIX JIeneCTKOB.
The Handbook of Antenna Design, A. W. Rudge, K. Milne, A. D. Olver, and P.
Knight, Eds., IEE/Peregrinus, 1983, vol. 2, 945 pp.
B CnpaBOQHMK BKJIlOqeHbI rJIaBbI no JIHHeMHbIM, nJIOCKMM, KOH<pOPMHbIM 11
KOJIbueBbIM AP M 06pa60TKe CMrHaJIOB Ha BbIxo,ae AP. Co,aep)l(MT HCQepnbIBalOI.I.(Me
)laHHbIe, KacalOlliMecSI aHaJIM3a 11 CMHTe3a AP C yqeToM 3<p<peKToB B3aMMHoro BJIH-
SlHI1S1.
Proceedings of the 1985 RADC Phased Array Symposium, H. Steyskal, Ed., report
RADC-TR-85-171, AD-AI69 316.
)].aHHbIM C60PHMK co,aep)l(I1T, B QaCTHOCTM, pa60TbI no MHKpOnOJIOCKOHbIM Ii
a,n:anTHBHbIM aHTeHHbIM perneTKaM M MMne,aaHCY CKaHHpOBaHMH. BTOPOH TOM HMe-
eT OrpaHHQeHHOe pacnpOCTpaHeHHe.
Antenna Handbook, Y. T. Lo and S. W. Lee, Van Nostrand Reinhold, 1988.
B CnpaBOQHHK BXO,l(SlT rJIaBbI no TeopHH AP, l.I.(eJIeBbIM perneTKaM, 3KBH.aMCTaH-
THbIM H He3KBM,aHCTaHTHbIM AP, npaKTMqeCKMM acneKTaM AP M MHOrOJIyqeBbIM
pellleTKaM.
Antenna Engineering Handbook, R. C. Johnson and H. Jasik, McGraw-Hill,
1993.
06HOBJIeHHbIM BbInYCK CTaporo KJ1aCCI1QeCKOrO CnpaBOQHI1Ka COlIep)l(J1T rJIaBbI
no TeopHM AP, Il(eJIeBbIM perneTKaM, QaCTOTHOMY CKaHHpOBaHHIO, <t>a3HpoBaHHbIM
H KOH<POpMHbIM AP.
Phased Array Antenna Handbook, R. J. Mailloux, Artech, 1994, 534 pp.
B ,l(aHHOM CneUHaJIH3HpOBaHHOM PYKOBO,l(CTBe OCBern;aeTCSI 60JIbrnHHCTBO TeM,
KacalOrn;MXCSI AP, C aKl.(eHTOM Ha HX aHaJIH3e H CHHTe3e. B O,l(HOH M3 rJIaB onHCbI-
BalOTCH HeKOTopbIe BH,l(bI CKaHHpyroml1X perneTOK H AP C JIHHHHMI1 3a,n:ep)l(KH.


rJlaBa 1. BBeaeltue
Phased Array-Based Systems and Applications, N. Fourikis, Wiley:-Interscience,
1997.
B KHHre BbmeJIeH CMCTeMHbIH acrreKT HCrrOJIb30BaHH5.l AP.
1.3. 1. nMTepaTypa no aAanTMBHblM aHTeHHaM
Compton, R. T., Jr., Adaptive Antennas, Prentice-Hall, 1988.
Hudson, J. E., Adaptive Array Principles, IEEjPeregrinus, 1981.
Monzingo, R. A. and Miller, T. W., Introduction to Adaptive Arrays, Wiley, 1980.
Widrow, B. and Stearns, S. D., Adaptive Signal Processing, Prentice-Hall, 1985.
JIHTepaTYpa
1. Hansen, R. C., «Comparison of Square Array Directivity Formulas», Trans. IEEE, Vol.
AP-20, Jan. 1972, pp. 100-102.
2. Hansen, R. C. and Libelo, L. F., «Wideband Dispersion in Baseband Systems», Trans.
IEEE, Vol. AES-31, July 1995, pp. 881-890.

r l1ABA 2
OCHOBHblE XAPAKTEPPACTPAKPA
AHTEHHblX PEWETOK
B rJIaBe paCCMaTpI1BaIOTC5I OCHOBHbIe xapaKTepllCTI1KH JII1HeHHbIX 11 rrJIOCKllX aH-
TeHHbIX perneTOK, llMelOIIJ.llX, rJIaBHbIM 06pa30M, paBHOMepHoe B036)')K.II:eHl1e. Teo-
pll51 11 MeTO,lU1KH paCqeTa KOHCTPYKUHH aHTeHHbIX perneTOK, 06JIa,n:alOIIJ.HX OCTpO-
HarrpaBJIeHHbIM nYQOM, ,n:l1arpaMMon HarrpaBJIeHHOCTH C HH3KHM ypOBHeM 60KOBbIX
JIerreCTKOB llJIH nyqoM CrreQHaJIbHOH <t>OpMbI, rro,n:p06HO orrMCbIBalOTCH B rJIaBe 3.
HMrre,n:aHcHbIe 3<p<peKTbI, 06ycnoBneHHbIe B3aHMHbIM BnllHHHeM 3JIeMeHTOB perneT-
KM, paCCMaTpMBalOTCH B rnaBe 7. B rJIaBe paCCMOTpeHbI TaKlle xapaKTepHCTllKH, KaK
,n:l1arpaMMa HarrpaBJIeHHOCTM, rnMpl1Ha nyqa, rronoca rrporrYCKaHI151, CTpYKTypa 60-
KOBbIX, ,n:11<ppaKQI10HHbIX JIerreCTKOB M neneCTKOB KBaHTOBaHI1S1, a TaIOKe HanpaB-
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C paBHOMepHblM B036Y>KAeHMeM
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B036)')K.II:eHMe aHTeHHOH perneTKll 06bIQHO Orrl1CbIBaeTCH pacrrpe.neJIeHHeM aMrrJII1-
TY,n: H <t>a3 B Ka)l(,l].OM 3neMeHTe. 3TO ,n:HCKpeTHoe pacnpe,l:(eJIeHHe qaCTO Ha3bIBaeTC5I
arrepTYpHbIM pacrrpe,l:(eneHHeM, r,n:e arrepTYPY 06pa3yeT ,n:HCKpeTHaH aHTeHHaH pe-
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lOT Mo,n:eJIb «BbIH)')K.II:eHHoro B036)')K.II:eHHH» 3neMeHTOB AP, rrpM KOTOpOM <pI1KCMpO-
BaHO l'pe6yeMoe anepTypHoe pacnpe,n:eneHMe.
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pbI ynpaBJIeHM5I 3JIeMeHTaMM <pMKCMpOBaHbI, a B036)')K.II:eHMe 3JIeMeHTOB orrpe,n:en5l-
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aMnnMTy.ne, HO MO)l(eT MMeTb ynpaBJI5IeMYIO cJ:>a3Y.
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yrJIOBaH nepeMeHHaH. OHa onpe,n:eJIHeTCH Bblpa)l(eHHeM U = (sinS - sinSo) r,n:e So -
yrOJI CKaHMpOBaHHH. B 3TOM rJIaBe paCCMOTpeHbI 3KBH,l:(HCTaHTHble perneTKM (c paB-

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HMHqHeM qeTHOrO IillH HeqeTHOrO qMCna 3neMeHTOB. PaCCMOTpHM 60nee 06lUMH
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cnyqaH, npH KOTOpOM HaqMO CMCTeMbI Koop,n;MHaT Haxo,n;MTCR Ha O,n;HOM M3 KOH-
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neM HanpaBneHHOCTM AP, lfMeeT BM,n;
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r,n;e An - KOMrrneKCHbIM K03<P<PMUHeHT B036y)K,L(eHlfR, KOTOpbIM B 60nbrneM qaCTI1
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AP MO)l(}fO npe,n;CTaBHTb B Bl1,[(e npOH3Be,n;eHHH ,n;eMCTBHTenbHOM qaCTH ,n;HarpaMMbI
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xapaKTepHCTHK)' JIMHeMHOM AP
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2
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3neMeHTHbIX paCCTOHHHHX Me)l(J(Y HHMlf no roplf30HTMH H HaQMbHbIX <pa30BbIx
c,n;BHrax [18].
qalUe Bcero nHHeHHbIe aHTeHHbIe perneTKM npoeKTHpyJOTCH B paCqeTe Ha <pop-
MHpOBaHHe Y3Koro nyqa. Ha pHC. 2.3 nOKa3aHO, KaK H3MeHHeTCH nyq npH CKaHH-
pOBaHHH. B OTCyrCTBHH CKaHlfpOBaHlfH Y3KMM nyq HBnHeTCH BceHanpaBneHHbIM B
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Ba 3JIeMeHTOB AP
BaeMble ,LIJI<l>paKIJJloHHbIMH JIeneCTKaMH (,l].JI); 3TO npOHCXO,l(HT nOToMY, qTO 60JIb-
mOM nepl10Ll: pemeTKH Ll:onYCKaeT cHH<l>a3Hoe CJIO)l(eHHe BOJIH OT Ka)J()IOrO
3JIeMeHTa nOL( yrJIOM ,l(H<l>paKI(HOHHOro JIeneCTKa, paBHo KaK H no,l( yrJIOM OCHOB-
Horo JIeneCTKa.
JIerKo nOJIyqHTb ypaBHeHHe ,l(JI ,l(H<ppaKUHoHHbIX JIeneCTKOB:
d n
-
A sin eo - sin e ,[(J1
(2.7)
IIpH nOJIy:BOJIHOBOM mare pemeTKH ,l(JI JIyqa, OTKJIOHeHHOro no,l( yrJIOM +90 0 ,
,Z:J;l1cppaKUHoHHbIM JIeneCTOK B03HHKaeT no,l( yrJIOM -90 0 . II1ar, paBHbIH O,l(HOi1. ,l(JIH-
He BOJIHbI, nOpO)l(,[(aeT ,l(H<ppaKI(HOHHbIH JIeneCTOK npl1 + 90 0 , eCJIH OCHOBHOH JIyq
nepneHLl:HK)'JIHpeH paCKpbIBY AP. Ha pl1C. 2.8 nOKa3aH ,l(11<l>paKUHoHHbIH JIeneCTOK,
pacnOJIO)l(eHHbIH nOLI: yrJIOM -45 0 , npl1 CKaHHpOBaHl111 JIyqa Ha +45 0 H mare 0,707'A.
Ha pHC. 2.9 H306pa)l(eHa 3aBHCHMOCTb yrJIa nOHBJIeHH ,l(H<l>paKUHoHHbIX JIeneCT-
KOB OT yrJIa CKaHl1pOBaHI1H 11 mara AP. 06I.Uee npaBRJIO, COCTOI.Uee B TOM, qTO
nOJIYBOJIHOBbIH mar pemeTKH YCTpaHHeT ,l(11<l>paKUI10HHble JIeneCTKI1, BJIeTC He
BnOJIHe CTporHM, nOCKOJIbK)' B 06JIaCTH npelI.eJIbHbIX yrJIOB CKaHl1pOBaHI1 MO)l(eT
Ha6JIIO,l(aTbC qaCTb ,l(H<l>paKI(HOHHOro JIeneCTKa.
IIpH JII060M yrJIe CKaHl1pOBaHH )l(eJIaTeJIbHO y,l(aJIHTb Bce ,l(11<l>paKUHoHHble JIe-
neCTKH 113 06JIaCTH BI1lI.I1MOCTH. B npl1HUl1ne MO)I(HO nO,l(06paTb mar TaKHM o6pa-
30M, t.ITo6bI ypOBeHb Ll:H<l>paKUHoHHoro JIeneCTKa Ha KpalO BI1,l(HMOH 30HbI 6bIJI TOqHO
paBeH ypOBHIO 60KOBoro JIeneCTKa. O.n:HaKO, H3-3a 6oJIbmoH KpyrH3Hbl <ppOHTOB
,l(H<l>paKlU10HHoro JIeneCTKa, nO'Tpe60BaJIl1Cb 6bl )l(eCTKHe ,l(OnYCKH. IJ;eJIeC006pa3-
Hee B 06JIaCTH ,l(H<l>paKl.(HOHHOro JIeneCTKa npl1 -90 0 peaJIH30BaTb iIyJIb ,l(HarpaMMbI


FJlaoa 2. OCHooHble xapaKmepucmUKU aHmeHHblX pewemOK
1
0.8
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0.4
0.2
o
-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90
fpMYCbI
PHC. 2.8. ,[(HarpaMMa HarrpaBJIeHHOCTH aHTeHHOH pemeTKH rrpH yrJIe CKaHHpOBaHH5I
45°, d/A = 0,7071, N = 10
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20
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YroJI cKaHHpoBaHlul (rpM.)
70
80
90
PHC. 2.9. YrOJI rr05lBJIeHH5I .D;H<l>paKUHoHHbIX JIerreCTKOB rrpH pa3JIHQHOM mare pa3-
MeI.IJ;eHHR 3JIeMeHTOB H yrJIe CKaHHpOBaHH5I

2. 1. JIuHeUHlJle pewemlCu C pa8HOMepHblM 8036YJICiJeHUeM 
HarrpaBJIeHHOCTH aHTeHHbI, 3THM HCKJIIOqaeTCH BeCb ,L(HQ:>paHOHHbIH JIeneCTOK.
Ha pHC. 2.10 M:306pa)l(eHa qaCTb .aHarpaMMbI HanpaBJIeHHOCTH, rL(e HanpaBJleHHe
OCHOBHoro Jlyqa 3a;::(aHO yrJIOM 8 0 , a nHK ,L(HQ:>paHoHHoro JIeneCTKa - yrJIOM 8,l])]'
1
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PHC. 2.10. ,l:(MarpaMMa HarrpaBJIeHHOCTH aHTeHHOH pemeTKM C ,ZIM<ppaKuMoHHhIM
JIeneCTKOM
YMeHblIleHHbIH mar aHTeHHoM pemeTKH onpe.aeJIHeTC5I ypaBHeHHeM
d
A
N - l + B2
N(l + sin8 0 )
.
(2.8)
3Ta 06lI.(aH Q:>oPMYJIa OTHOCHTCH TaIOKe K c.rryqalO, KOr,L(a aMTIJIHTY,L(HOe pacnpe,L(e-
JIeHHe cna,n:aeT K KpaHM pemeTKM. IIapaMeTp B - ypOBeHb nOJIR Ha KpalO pacKpbIBa,
nO,L(p06HO 06Cy)I(,I{aeTCR B rJIaBe 3. YMeHbmeHHe mara pemeTKH, onpe,L(eIDIeMOe YCTa-
HOBKOH HYJIR ,[(11<l>pal1oHHoro JIeneCTKa, npeL(CTaBJIeHO Ha pHC. 2.11, r,L(e BeJIHqHHa
SLR RBJIReTCR napaMe1pOM. Heo6xo,L(HMO nOMHHTb, QTO 3KBI1,lJ:HCTaHTHoH pemeTKH
C paBHOMepHbIM B036y)1(,I{eHHeM COOTBeTcTByeT KpHBaH SLR = 13,26 .aE.
2.1.5. nonoca nponYCKaHMSI
Ha mHpHHY nOJIOCbI nponYCKaHHR aHTeHHOH perneTKH BJIHReT MHoro Q:>aKTopoB,
HanpHMep, 3aBHCHMOCTb BXO,L(HbIX HMne,L(aHCOB 3JIeMeHTOB OT qaCTOTbI, H3MeHeHHe
rnara aHTeHHOM perneTKH, npHBo.aHlI.(ee K nOHBJIeHHIO .aH<ppaKUHoHHbIX JIeneCTKOB,
H3MeHeHHe nOJIOCbI nponYCKaHHH 3JIeMeHTOB H TaK L(aJIee. TIpH CKaHHpOBaHHH
C <pHKcHpoBaHHbIMI1 3HaqeHHHMH <pa30Boro CJ(BHra, 06eCneQHBaeMOro <pa30-


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22
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,LU1<ppaKI.{110HHOro JIeneCTKa no,a yrJIOM 90°
Bpall.(aTeJIHMM, TaIOKe MMeeTCH OrpaHMQeHMe nOJIOCbI nponYCKaHMH, nOCKOJIbKY
nOJIOXeHMe OCHOBHoro JIeneCTKa M3MeHHeTC C qaCToToH. ECJIM cKaHMpoBaHMe
npoM3BOn;MTCH C nOMOll.(blO JIMHMH 3a,aep)l(KH, nOJIOXeHMe JIyqa B nepBoM npH6JIH-
xeHMM He 3aBMCMT OT qaCTOTbI.
YrJIOBOe nOJIOXeHMe JIyqa S CBH3aHO C yrJIOM CKaHMpOBaHM So npOCTbIM COOT-
HOllIeHMeM
sinS = (fo / f) sinSo.
3Ta 3aBHCMMOCTb M306paJKeHa Ha pHC. 2.12. ,[LITH HaXO)l(J(eHH nonOCbI nponyc-
KaHH AP npH CKaHMpOBaHMM rrpe.lIrrOnO)KJfM, qTO rnaBHbIH JIyq nepeMell.(aeTC OT
yrJIa CKaHHpOBaHIDI So K yrnaM, Ha KOTOpbIX nyq HMeeT ypOBeHb -3 .lID IIpM qaCTO-
Tax BbIllie If HM)I(e HOMMHaJIbHOH. nYCTb lflI,L\eKCbI 1 If 2 0603HaqalOT HH)l(HIOIO If
BepXH1010 qaCTOTbI COOTBeTCTBeHHO. Tor,Ua OTHOCHTeJIbHa nonoca nponYCKaHHH
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10
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llIupMHa nOJIOCbI nponYCKaHMR (BW) ,UIISI 3KBU,UHCTaHTHbIX perneTOK C paBHO-
aMnnMT)',n;HbIM B036y)1(,[{eHHeM onpe.lIeJIHeTC <J;>opMynoH
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(2.10)

2.2. IlAocKue OHmeHHble peUJemKU 
75
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nOJIO)l(eHMe JIyqa Ha l{eHTpaJIbHOH qaCTOTe (rpa,n,.)
75
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11 ,LJ)IR perneToK C aMnJII1Ty,n;HbIM pacnpe,n;eJIeHMeM, cnaaalOIUMM K KpaRM pacKpbIBa,
BW - 'A
L sin e 0
TIpM yrJIe OTKJIOHeHMR JIyqa 30° 06bPIHO MCnOJIb3yeMaR <popMYJIa JL]IR OTHOCM-
....
TeJIbHOM llIMpl1HbI nOJIOCbI MMeeT BM,n;:
(2.12)
BW ,... 2'A .
L
(2.13)
B pe3YJIbTaTe Ha KpaRX rrOJIOCbI JL]IMHHbIe aHTeHHbIe perneTKH MMelOT MeHbJ.IIylO
llIMPMHY nOJIOCbI rrponycKaHMR B e,n;MHMl(aX CMeIUeHMR .rryqa. CM01'pMTe TalOKe pa3-
,n;eJI 2.3.2.
2.2. nnOCKMe 8HTeHHbie peweTKM
2.2.1. CMCTeMa KOOPAMHaT aHTeHHblX peweTOK
B 3TOM pa3,n;eJIe xapaKTepMCTMKM JIMHeHHbIX aHTeHHbIX perneTOK o606IUalOTcR Ha
CJIyqaH llJIOCKMX aHTeHHbIX perneTOK. I1pM 3TOM y,n06HO MCnOJIb30BaTb c<l>epMqe-
.... ....
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u
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rJloeo 2. OCHoeHble xopOKmepucmUKU OHmeHHblX peUlemOK
z
8
I
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I
0 0 0 0 0
0 0 0 0 0
y
0 0 , 0 0
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0 0 0 o '

X
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HMH 3JIeMeHTOB
llIeTKa C oCTpoHanpaBneHHbIM nyqoM HMeeT cHMMeTpHQHOe B036}')K.[(eHHe, n03ToMY
,LI,HarpaMMa HanpaBneHHocTH onpe,Ll,enSleTCSI CYMMl1poBaHl1eM TOJIbKO no nOnOBI1He
.... ....
3neMeHTOB B,[(OJIb Ka)l(llOI1 113 oceM:
F(u, v) =  Anm cos[( n -  }dxU }os[( m -  }dyV 1
(2.14 )
YrJIOBbIMH nepeMeHHbIMH SlBJISlIOTCSI HanpaBJISlIOrn;He KOCMHYCbI
u = sin 8 cos <I> - sin 8 0 cos <1>0'
. v = sin 8 sin <I> - sin 8 0 sin <Po
. ,
r,[(e 8 0 , <1>0 - yrJIbI, 3arralOrn;He HanpaBJIeHHe nyqa. Me)J{3JIeMeHTHbIe paccToSlHMSI
0603HaQalOTCSI d x Ii dye Me)J{3JIeMeHTHbIe <pa30BbIe ClIBHfH, Heo6xo,lU1Mble ,lLJISI CKa-
HMpOBaHliSl JIyqa:
(2.15)
<I> u = k dxuo = k d x sin 8 0 cos <1>0'
<I>v = k dyvo = k d y sin 8 0 sin <1>0.
qacTo Mcnonb3yeTcSI TpeyrOJIbHaSl ceTKa, H306pa)J{eHHaSl Ha pHC. 2.14, nOCKOJIb-
ICY OHa ,LI,OnYCKaeT MCnOJIb30BaHHe HeCKonbKO 60JIbIllefO Me)J{3JIeMeHTHoro paCCTOSl-
HliSl 6e3 B03HMKHOBeHHSI ,LI,M<ppaKUHOHHbIX JIeneCTKOB.
(2.16)
2.2.2. WMpMHa nya
npH CKaHMpOBaHHH B fJIaBHOH nnOCKOCTI1 llIHpHHa JIyqa onpe,Ll,eJISleTCSI npHBe,[(eH-
HbIM paHee ypaBHeHHeM (2.3). B KOCbIX CeqeHMSlX BbIpa)l(eHMe ,lUISI llIHpliHbI JIyqa
60JIee CJIO)J{Hoe, TaK KaK Ha Hee OKa3bIBalOT BnHSlHMe KaK ,lUIMHa L aHTeHHoH pe-
IlleTKH B fJIaBHOH nJIOCKOCTH, TaK H IlIHpHHa WaHTeHHoH pemeTKH. B CJIyqae CKa-
I

2.2. IlAocKue aHmeHHllle peUJemKU 
v
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HHpOBaHH5I B rJIaBHOH nJIOCKOCTH C cJ>0 = 0 H 9 = 9 0 o606ll.{eHHbIe yrJIOBbIe nepe-
MeHHbIe HMelOT BH,LJ;
'II x = L sineo(l-coscjl); 'II y = W sine o sincjl. (2.17)
A A
llIHpHHa JIyqa no ypOBHIO nOJIOBHHHOH MOll.{HOCTH onpe.neJUIeTCR KOpH5IMH
ypaBHeHH5I
. . 1t2'V 3x'V 3y
SInc mv 3x SInc mv 3y = .J2
B KOCbIX nJIOCKOCT5IX llIHpHHa .rryqa onpe.neIDIeTC5I H3 BbIpIDKeHH5I
<l>3 y 2 arcsin(sin eo sin <1>3), (2.19)
r.n;e K03<P<PHI.J;HeHT sin 9 0 yqHTbIBaeT rrpoeKl{HIO paCKpbIBa. 51 60JIbllIHX aHTeHHblX
perneTOK OTJIHqHbIM npH6JIIDKeHHeM 6y.n;eT
<l>3y -- 2 sin eo sin <1>3. (2.20)
nOCKOJIbKy perneHHe cJ>3y MoxeT 6bITb BbIpaxeHO KaK <pyHKUH5I (W fA) sin 9 0 ,
y.n;06HbIM napaMeTpOM 51BJIReTC5I COOTHorneHHe pa3MepOB aHTeHHOH perneTKH W/L.
IIIHpHHa JIyqa B CJIyqae KOCOH nJIOCKOCTH MoxeT 6bITb TaIOKe BbIpaxeHa Qepe3 v3:
W
-<I>3Y ::: 2'V3y. (2.21)
A
(2.18)
Ha pHC. 2.15 nOKa3aHa 3aBHCHMOCTb rnHpHHbI .rryqa B WIOCKOCTH CKaHHpOBa-
HHR OT .ZJ:]IHHbI aHTeHHOH pemeTKH H yrJIa CKaHHpOBaHH5I; Ha pHC. 2.16 mHpHHa
JIyqa B HaKJIOHHOH WIOCKOCTH npe.nCTaBJIeHa KaK <pyHKl{IDI COOTHOmeHH5I pa3Me-
pOB aHTeHHOH pemeTKH H HOpMHpOBaHHoro napaMeTpa CKaHHpOBaHH5I. MO:>KHO
BH,l1eTb, QTO npH HOpMHpOBaHHOM napaMe1pe CKaHHpOBaHHH, paBHOM 1 HJIH 6oJIee,
IIIHpHHa JIyqa B HaKJIOHHOH nJIOCKOCTH 6JIH3Ka K HOMHHaJIbHOMY 3HaQeHHIO.


rfla8a 2. OCHo8Hble xapaKmepucmUKU aHmeHHbIX peUJemOK
80
70
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60
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.
 50


---


r=; 40

::c LI)' = 5
:s:

:s: 30
E3 10
20
10
o
o
10
30 40 50 60
YrOJI cKaHHpOBaHlul (rpa,a.)
70
20
80
90
PHC. 2.15. UUHpHHa nyqa B rrnOCKOCTH CKaHHpOBaHHR 3KBHHcTaHTHoH aHTeHHOH
perneTKH C KBa.n;paTHbIM paCKpbIBOM
70
60
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.
 50
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r=;

::c
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x
;<
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 20
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10
0 0
0.5
1.5 2 2.5
(W fA) x sin eo
1
3
3.5
4
PHC. 2.16. UUHpHHa nyqa B HaKJIOHHOH IIJIOCKOCTH 3KBH,lU1CTaHTHoH aHTeHHOH
perneTKH C rrpRMoyrOJIbHbIM paCKpbIBOM

2.2., llllocKue aHmeHHble pewemKU 
<l>opMa JIyqa npM cKaHMpoBaHMM MeHHeTCH BCJIe,aCTBMe M3MeHeHMH npOeKl(MM
pacKpbIBa aHTeHHoH pellIeTKM. JJ:JIH npHMoyrOJIbHbIX aHTeHHbIX pellIeToK M30JIMHMH
JIyqa no YPOBHIO -3 .nE HBJIHeTCH 6JIM3KOH K 3JIJIMnTl1qeCKOH. O,aHaKo npM CKaHI1-
pOBaHl111 He B rJIaBHbIX llJIOCKOCTHX KOM6MHaUl1H BJII1HHI1H llIl1pl1HbI M ,[{JII1HbI npo-
eUl1pyeMoro paCKpbIBa 11 yrJIOB CKaHl1pOBaHMH npl1Bo,aI1T K 3JIJII1nTI1QeCKOH <popMe
JIyqa, 60JIbllII1H .nl1aMeTp KOToporo 06bIQHO Opl1eHTl1pOBaH He B nJIOCKOCTI1 CKaHI1-
pOBaHI1H M He B rJIaBHbIX nJIOCKOCTHX. TaK KaK nJIOII.J;a,Qb 3JIJII1nCa nponOpUl10HaJIb-
Ha npOM3Be,aeHMIO 60JIbllIOrO 11 MaJIOrO ,al1aMeTpOB, llJIOII.J;a,Qb CeQeHMH JIyqa no
ypOBHIO -3 .n;E onpe.n;eJIHeT nJIOII.J;a,Qb JIyqa, nponOpUl10HaJIbHYlO npOM3Be.n;eHI1IO
3HaQeHI1H llIHpHHbI .rryqa B,aOJIb 60JIbllIOH H MaJIOH oceH 3JIJIHnca. TIJIOII.J;a.L(b JIyqa B
nepBOM npH6JIIDKeHI111 He 3aBMCHT OT a3HMyrarrbHoro yrJIa , XOTH <t>opMa JIyqa H
opHeHTaUI1R 60JIbllIOH OCH 3JIJIHnCa MOryr 3aBHceTb OT e. Ha pHC. 2.17 nOKa3aHO
M3MeHeHHe <pOpMbI HeCKOJIbKl1X JIyqeH npl1 CKaHHpOBaHHH.
z
.
PUC. 2.17. 3aBHCHMOCTb <pOpMbI OCTpOHanpaBJIeHHOrO JIyqa OT yrJIa CKaHHpOBaHHSI
2.2.3. AMc!>paKu.MOHHble neneCTKM: npRMoyronbHaR ceTKa
ITpH CKaHHpOBaHHH B JII060H H3 rJIaBHbIX nJIOCKOCTeH aHTeHHaR pellIeTKa C npHMO-
yrOJIbHOH ceTKOH pacnOJIOXeHHH 113JIyqaTeJIeH Be,aeT ce6H TOqHO TaK xe, KaK JIH-
HeHHaH aHTeHHaH perneTKa, onMcaHHaH B pa3,aeJIe 2.2. TIpM ,apyrMx yrJIax CKaHMpo-
BaHI1H cHTyal(HH CJIOXHee. ,[(JIR nOHI1MaHHH nOBe,aeHHH ,a11<ppaKl(HOHHbIX
.....
JIeneCTKOB Qpe3BbIQaHHO nOJIe3HO I1CnOJIb30BaHI1e U, V-llJIOCKOCTH, MHor,aa Ha3bIBa-
eMOH nJIOCKOCTblO HanpaBJIHIOII.J;I1X KOCI1HYCOB [19]. TIOJIOXeHI1H ,aH<ppaKUHOHHbIX
JIeneCTKOB MO)I(HO oT06pa311Tb Ha U, V-nJIOCKOCTH; OHI1 pacnOJIaralOTCH B Y3JIaX ceT-
KI1 C rnaraMH 'A/d x H 'A/d y (CM. pHC. 2.18). Bce .n;eHcTBHTeJIbHbIe yrJIbI, npe,aCTaBJIH-


rJla8a 2. OCHo8Hble xapaKmepucmUKU aHmeHHblX peUiemOK
/
/
v
/

/iy

fnaBHaH nnOCKOCTb
/
/
/

/
/
PHC. 2.18. nJlOCKOCTb HanpaBJlRIOll.{HX KOCHHYCOB
/
/
u
/
/
IOmHe 06JIaCTb BIf.nHMOCTH, HaXOJUlTCR BHyrpH HJIH Ha e.f(HHHqHOH OKpyxHOCTH.
nOCJIe.f(HRR cooTBeTcTByeT HanpaBJIeHHRM 8 = 90°. YrJIbI BHe e.f(HHHqHOH OKp)')KHO-
CTH HBJIRIOTCR «MHHMhIMH», OHH pacnOJIOXeHbI BHe 06JIaCTH BIf.nHMOCTH.
npH CKaHHpOBaHHH rJIaBHOrO JIyqa ueHTP U, v .f(HarpaMMbI C.f(BHraeTCR K HOBOMY
3HaqeHHIO, H COOTBeTCTBeHHO CMemalOTCR Bce .f(H<ppaKUHoHHhIe JIeneCTKH (,l{JI).
O.f(HaKO e.f(HHHqHaR OKPyxHOCTb' OCTaeTCR <pHKcHpoBaHHoit TaKHM 06pa30M, npH
CKaHHpOBaHHH B U-ITJIOCKOCTH (cp = 0) H 8 0 > 0 TOqKa OCHOBHoro JIeneCTKa nepeMe-
maeTCR K TOqKe + 1, H Bce ueHTphI WI nepeMeIUalOTCR Ha TO xe paCCTORHHe. ECJIH
nepeMemeHHe WI, HaXOJUlmerOCR He.f(aJIeKO 3a npe.f(eJIaMH e.f(HHHqHOrO Kpyra, .f(0-
CTaTOqHO .LLJUI nepeCeqeHHR e.f(HHHqHOH OKpy)ICHOCTH, ,[(JI CTaHOBHTCH BIUU1MbIM.
CJIe.nOBaTeJIbHO,
A
uJ1)I < --l
d x
HJIH
d x > 1
A 1 + sin8
(2.22)
BbI60p 3HaKa > B 3TOM HepaBeHcTBe' 06YCJIaBJIHBaeT nORBJIeHHe .f(H<ppaKUHoH-
Horo JIeneCTKa. CKaHHpoBaHHe B.f(OJIb V-OCH (cp = 90°) npHBO,lIHT K aHaJIOrHqHOMY
pe3YJIbTaTY:
d y 1
- >
A 1+sin8
llpH 60JIbIIIeM IIIare aHTeHHoR peIIIeTKH CKaHHpOBaHHe no JII060R nape yrJIOB
MoxeT nOpO.f(HTb O.f(HH HJIH 60JIee .f(H<ppaKUHoHHbIX JIeneCTKa. I1HTepecHbI .f(Ba
npe.f(eJIbHbIX c.rryqaR: .nHarOHaJIbHbIH H KaCaTeJIhHhIH. CKaHHpoBaHHe B .f(HarOHaJIb-
HOR llJIOCKOCTH, nOKa3aHHoe Ha pHC. 2.19, BbI3bIBaeT nORBJIeHHe ,[(JI JIeneCTKa,
(2.23)

2.2. IlJ/ocKue altmeltltble peUJemKU -d
v
o
o
KaCaTeJIbHhI:H
,I:(JI
u
,aHarOHaJIbHbIH
M
o
PUC. 2.19. n pe,n:eJIbHbIe CJIyqaH B03HHKHOBeHHH ,n:H<ppaKl.{HOHHOro JIeneCTKa
eCJlH ,aHarOHaJIbHaR TOqKa rrepeceKaeT e,aHHHqHyro OKpyxHOCTb nepneH,aHKYJlRpHO.
3TO rrpOHcxo,aHT rrpH CJIe,ayroIUHX 3HaqeHHRX U, v :
SQ-I
U - .
M - SQd x I'A'
sinS lV1 = SQ -I;
SQ-I
v - .
M - SQd y I 'A '
d x
tan<p M =-,
d y
(2.24 )
f}le SQ =  d; I 'A 2 + dl I 'A 2 .
3TOT ,aHarOHaJIbHbIH JlerreCTOK B03HHKaeT TOJIbKO rrpH SQ > 2. 06bIqHO ,aH<p-
paKUHoHHbIH JIerreCTOK B03HI1KaeT, eCJIH IIOCTORHHaR pacnpOC1]>aHeHHR BOJIHbI RB-
  
JIReTCR ,aeHCTBHTeJIbHOH BeJIHqHHOH; B TOqKe ero B03HHKHOBeHHR OHa paBHa HYJIIO:
J!. =  1- (u - n'A. / d x )2 - (v -m'A. / d y )2.
k
(2.25)
CKaHHpOBaHl11O B rJIaBHbIX llJIOCKOCTIDC COOTBeTCTByroT 3HaqeHHR n = 0 HJII1
m = o. B c.rryqae ,aHarOHaJIbHOH ITJIOCKOCTH n = I, m = I. ,l].ocTaTOqHO 60JIbllIOH llIar
pellIeTKH ,aorrYCKaeT B03HI1KHOBeHI1e HeCKOJIbKHx,lJ.JI, B pe3YJIbTaTe qero nOCTORHHaR
pacnpoc1]>aHeHHR BOJIHbI ,aeHcTBHTeJIbHa,lUUI 60JIbllIerO n H/HJIH 60JIbllIerO m. Kaca-
TeJlbHbIH npe.neJIbHbIH c.rryqaH HMeeT MeCTO, Kor.na MaKcHM}'M ,lJ.JI pacrrOJIO)l(eH Ha
U-OCI1, HeMHoro CJIeBa OT e.nI1HI1QHOH OKpyxHOCTH. ,lJ.l1arOHaJIbHOe cKaHHpOBaHlie
MO)l(eT rrepeMecTHTb TOqKY ,lJ.JI Ha OKpyxHOCTb no KaCaTeJIbHOH K HeH (CM. pMC.
2.19). 3.necb <pMrypMpyeT TOJIbKO BeJIMqMHa d x , H rrpe.neJIbHbIe 3HaqeHMR COCTaBJIRIOT
U _ 1 - d; I 'A 2 .
VITrr = ' l-d x 2 I 'A2;
M - d x I'A' I V
. S I - d; I 'A 2 . d x
sin M = ; Sln<p M =.
d x I 'A 
(2.26)


Tllaea 2. OCHo6Hble xapaKmepucmUKU aHmeHHblX pewemOK
MI1HI1MaJIbHOe 3HaqeHI1e dxf'A COCTaBJIReT 1 I .fi. KaK 11 O)l(H,[{aJIOCb, B CJIyqae
KaCaTeJIbHOrO v pe3YJIbTaT aHaJIOfl1qeH npl1 3aMeHe MeCTaMH U H v, a TalOKe d x Ii d y .
npl1 npOli3BOJIbHbIX yrJIax CKaHHpOBaHliR M B rJIaBHOH llJIOCKOCTH nORBJIReTCR
nepBbIM, qTO onpe,l1eJIReTCR MeHbllIHM H3 3HaqeHHH A/d x If Ald y . MCnOJIb30BaHI1e
U,V-nJIOCKOCTIi He TOJIbKO .aaeT npeBocxo.aHyro cl>H3I1QeCKYIO KapTHHY B03HHKHOBe-
HliR ,[(11, HO TalOKe n03BOJIReT JIerKO BbIBeCTH COOTBeTCTByrom:He cl>OPMYJIbI. MTaK,
npl1 dxl'A < 11(1 + sin e) " dyl'A < 11(1 + sin e) Y pemeTKIi C npRMoyrOJIbHOH ceT-
KOH M OTC}'TCTByroT.
2.2.4. AMcI>paKMoHHble neneCTKM: reKcarOHanbHaR ceTK8
I1Hor.aa npl1MeHRIOTCR ceTKIf Ha OCHOBe paBHo6e.apeHHbIX lpeyrOJIbHI1KOB, Hanpl1-
Mep, BOJIHOBo.aHaR aHTeHHaR pemeTKa, onHcaHHaR B rJIaBe 7. PacnpocTpaHeHHbIM
qaCTHbIM CJIyqaeM RBJIReTCR paBHOCTOpOHHIDI lpeyrOJIbHaR ceTKa, RJII1 npaBRJIbHaR
reKCarOHaJIbHaR ceTKa. llYCTb Bce 3JIeMeHTbI perneTKIf HaXO.lUlTCR Ha paBHbIX pac-
CTORHI1RX 2d ,l1pyr OT ,l1pyra, 11 X-OCb npOXO,l1I1T Qepe3 pR,[( 3JIeMeHTOB, pacnOJIOXeH-
HbIX C ,l1aHHbIM I1HTepBaJIOM. Tor.aa d x = d Ii d y =.J3 d I 2, r.ae d x 11 d y - nOJIOBliHa
paCCTORHI1R ,l10 CJIe.ayrom:ero 3JIeMeHTa no x- RJIIi Y-OCI1. AHaJIH3 reKCarOHaJIbHOH
pemeTKIf npOBo.nliTCR n}'TeM ee pa36HeHIDI Ha .aBe BJIOXeHHbIe .apyr B .apyra pellIeT-
KH C npRMoyrOJIbHOH ceTKOH. ,[(HarpaMMa HanpaBJIeHHOCTH B 3TOM CJIyqae RBJIReT-
CH CYMMOH .al1arpaMM HanpaBJIeHHOCTI1 3TliX .aBYX pemeTOK. llOJIOXeHI1R .alicl>paK-
U:110HHbIX JIeneCTKOB B OTC}'TCTBHe CKaHl1pOBaHI1R nyqa onpe.aeJISIIOTCR CJIe.aYlOmI1M
o6pa30M:
n'A
U = +-.
M -2d'
_ + m1t _ + m'A
v)J.JI - - .J3d - - 2d y ·
(2.27)
CeTKa B U,V-IDIOCKOCTH nOKa3aHa Ha pHC. 2.20; TOQKH M pacnOJIOXeHbI 3KBH-
.aliCTaHTHO C llIarOM "Ald. CKaHHpoBaHHe B U-llJIOCKOCTH .aaeT Te xe pe3YJIbTaTbI,
OJ
qTO Ii ,lLJISi npRMoyrOJIbHOI1 ceTKH.
CKaHl1pOBaHl1e B .nl1arOHaJIbHOH llJIOCKOCTI1, .nOCTHralOm:ee e,l1HHHQHOH OKpYX-
HOCTI1 no HOpMaJIH, nopO)K)];aeT ,l111cl>paKl.{110HHbIH JIeneCTOK npH
I-dl"A .J3Q-d/
U - . v - ·
M - 2dl'A' lIJI - 2dl'A '
· e I-dl'A 1t
SIn lIJI = ; <p lIJI = -.
dl'A 3
(2.28)
MHHHMaJIbHOe 3HaQeHHe djA, Heo6xo.nI1MOe ,lLJISi B03HHKHOBeHI1R .aaHHoro JIe-
neCTKa, COCTaBJISIeT 1 / .fi. MMeeTcSI .aBa KaCaTeJIbHbIX CJIyqaSl, B nepBOM - TOQKa
M, HCXO,l1HO pacnOJIOXeHHaSi Ha U-OCI1, CTaHOBHTCSI TOQKOH KacaHHSI C e,l1I1HHQHOH
OKpyxHOCTblO, BO BTOpOM - HCXO.nHbIH ,l1HarOHaJIbHbIH M KacaeTCSI e,l1HHHQHOH
OKpyxHOCTH. llepBbIH H3 3TI1X .aBYX CJIyqaeB HMee T MeCTO np l1
U - 1 - d 2 I 'A 2 . V"n = ' I _ d 2 I 'A2 , .
lIJI - d I 'A ' I-IfJl V
.  1 - d 2 I 'A 2 . d
sIne lIJI = ; Sln<p lIJI =-.
dl'A 'A
(2.29)

r
l'"
2.2. IInocKue anmeHHble pewemKU 
.f ( ..Ji:
. . .
v
o
o
o
o
o
.A
o cr;
- ---0
o
o
u
),./ d x
o
o
o
o
o
PHC. 2.20. nJIOCKOCTb HanpaBJI})]OI..UHX KOCHHYCOB
MlfHHMaJIbHOe 3HaqeHlfe dl')..., Heo6xo,nHMoe ,nJUI B03HHKHOBeHHH ,naHHoro M,
COCTaBJIHeT 1 I Ji.
PaCqeT )])IH ,nlfarOHaJIbHOH TOqIGI HeCKOJIbKO CJIO)f(}fee, B 3TOM CJIyq:ae JIeneCTOK
B03HHKaeT npH
U ,lIJI = .Jl -d 2 /"-2 .Jl- d 2 / ,,-2 + J3 ) V = .Jl-d 2 / ,,-2 ( .J 3 (l- d2 / "-2) -1 ) .
2 dl A A1I 2 dl A '
1 - d 2 I ')...2 1t . d
sinS A1I = ; <p A1I = - - arCSIn-.
dl A 3 A
(2.30)
CpaBHeHHe KBa,npaTHoH Ii reKCarOHaJIbHOH ceTo nOKa3bIBaeT, qTO B o6olfx
CJIyqaHx nOHBJIeHlie M npOHcxo,nHT npH sin S = Aid -. 1. nJIOma,ab 3JIeMeHTapHoH
.HqeHKH KBa,apaTHoH ceTKH paBHa tfl, Tor,na KaK ,lLJIH reKCarOHaJIbHOM OHa COCTaBJI.H-
eT 2d"2 I J3.
TaKlfM o6pa30M, ,l(.1UI o6eCneqeHHH O,nHOH If TOM )Ke 06JIaCTH cKaHHpoBaHlfH,
CBo6o,nHOH OT M, perneTKa C reKCarOHaJIbHOH ceTKoH Tpe6yeT TOJIbKO 0,866 OT KO-
JIHqeCTBa 3JIeMeHTOB perneTIGI C KBa,apaTHoH ceTKOH. 3TO n03BOJIHeT COKpaTlfTb
qHCJIO 3JIeMeHTOB Ha 15% [19, 12].


rJla6a 2. OCHo6Hble xapaKmepucmUKU aHmeHHblX peUlemOK
2.3. YnpaBneHMe nY'IOM M neneCTKM KBaHTOBaHMR
)];JIH ynpaBJIeHHH JlyqOM He06xo,lJ;JIMO C03.aaHHe c.aBHra <l>a3 Me)l(,[{y 3JIeMeHTaMH pe-
llIeTKH, a YCTpOMCTBa, ocyrn;ecTBJIHIOrn:He 3TOT c.aBHr <t>a3, Ha3bIBalOTCH rjJa308paa-
meJlRMU. CaMbIM npOCTbIM cnoc060M, .aa)l(e )J)IH KOJIbu;eBblX aHTeHHbIX pellIeTOK,
HBJIHeTCH <l>a3HpoBaHHe no CTpOKaM H cToJI6u;aM. TIpH 3TOM Ka)l(,II;bIM <l>a30Bparn:a-
TeJIb ynpaBJIHeTCH KOMaH.ZJ:HbIM CI1THarrOM, onpe.aeJIHeMbIM <t>a3aMH no X-H Y-OCHM.
,LJ;HcKpeTHocTb ynpaBJIHIOrn:ero CHrHaJIa BJIHHeT Ha TOqHOCTb ynpaBJIeHHH JlyqOM,
IIOJIOCY IIponYCKaHHH H IIOpO)l(,[{aeT B .aHarpaMMe HanpaBJIeHHOCTH JIeneCTKH, 06-
YCJIOBJIeHHble KBaHTOBaHHeM <l>a3bI. Bce 3TH <l>aKTopbI 06Cy)I()I;alOTCH .aarree.
2.3.1. AMcKpeTHocTb ynp8BneHMR
HaHMeHbllIHM ,LI;HCKpeT nepeMern:eHHH COOTBeTcTByeT HaHMeHbllIeMY .aBOlfqHOMY
pa3PMY <l>a3bI
8 err
8 3
1
2 MI,029'
(2.31 )
K03<P<PHQHeHT 1.029 OIIpe,aeJIHeT HOpMHpOBaHHYIO llIHPHHY JIyqa npH TlfnOBOM
aMIIJlHTy.aHOM paCIIpe,aeJleHHH, npe,aCTaBJIeHHyIO B Ta6JI. 4.1, a M - qHCJIO pa3pH-
,n;OB. B Ta6JI. 2.1 npHBe,n;eHbI 3HaqeHHH ,aHCKpeTOB nepeMern:eHHH, .aeJIeHHble Ha
llIHPHHY 8 3 JIyqa no ypOBHIO IIOJIOBHHHOM MOIUHOCTH. OTMeTHM, qTO HaH60JIbllIlfM
pa3PM COCTaBJIHeT 1t. TaKHM 06pa30M, 4 pa3pH.aa ,aalOT HaHMeHbllIee nepeMem;e-
HHe, COOTBeTCTByIOrn:ee 0.061, llJIH npHMepHO 1/16 IIlHpHHbI JIyqa.
Ta6JIHua 2.1. TOqHOCTb nepeMem;eHHH JIyqa IIPH ,aHCKpeTH3aQHH <pa3bI
P83PSl,lJ,HOCTb cl»830BPaIIUlTeJIJI 8err/ 8 3
3 0.121 - 1/8
4 0.0607 - 1/16
5 0.0304 - 1/32
,LJ;06aBJIeHHe pa3pH.aa YMeHbIIlaeT ,n;HcKpeT ynpaBJIeHHH B 2 pa3a. Ha,LLJIe)l(am;aH
TOqHOCTb ynpaBJIeHHH qaCTO 06eCneqHBaeTCH 4-pa3PMHbIMH <pa30Bparn:aTeJIHMH.
TaKoM <pa30Bparn:aTeJlb YCTaHaBJIlfBaeTCH Ha KIDK.IJ:OM 3JIeMeHTe; <pa3bI npHHHMalOT
3HaqeHHH 180, 90, 45 H 22.5°.
2.3.2. YnpaBneHMe nonOCOM nponYCK8HMR
IlIHpHHa IIOJIOCbI qaCTOT aHTeHHOM perneTKIf C 3JIeKTpOHHbIM CKaHHpOBaHHeM
06blqHO OIIpe.aeJIHeTCH H3 npe,n;nOCbIJIKH, qTO Ha KpaHX nOJIOCbI OCHOBHOU JIeneCTOK
C,ilBHraeTCH Ha nOJIOBHHY IlIlfpHHbI JIyqa, TO eCTb K03<l><PHU;HeHT YCHJIeHHH na,aaeT

1
2.3. Ynpa6AeHUe AJl'IOM U AenecmICU IC6aHm06aHUR 
Ha 3 ,n:b. ,LJ;JIR aHTeHHOH pe.IQ:eTIrn TOJIhKO C <l>a30BhIM ynpaBJIeHHeM IIIHpHHa nOJIO-
-fit J. '
CbI rrpOnYCKaHHR (BW) COCTaBJIReT npH6JIH3HTeJIhHO BW = 8 3 /sin 8 0 . MCnOJIh3YR
npH6JIIDKeHHOe 3HaqeHHe 8 3 - A/ L JUIR yrJIa CKaHHpOBaHHR 30°, no.rryqaeM IIIHPHHY
nOJIOCbI nponYCKaHHR BW - 2A/ L. 3TO qaCTO HCnOJIh3yeMaR ou;eHKa, o,nHaKO ,nalO-
u
lI.(aSl HeTOqHhIH pe3YJIhTaT.
I1cnoJIh30BaHHe B HeKOTopbIX pa3pR.aaX cpa30BpalI.(aTeJIR BpeMeHHoH 3an;epXKH
,
YBeJIHqHBaeT IIIHPHHY nOJIOChI qaCTOT; onpe,neJIHM 3TO }'BeJIHqeHHe. nYCTh to -
l.(eHTpaJIbHaR qaCTOTa, a 12 H II - BepXHHH H HHXHHH KpaR qaCTOTHoro ,nHana30Ha.
AHaJIOrHqHhIM 06pa30M, nYCTh So - CHHYC yrJIa OTKJIOHeHIDI OCHOBHoro JIeneCTKa
Ha rpaHHu;e ceKTopa CKaHHpOBaHIDI JUIR :QeHTPaJIhHOH qaCTOThI, a S2 H SI - Te )f{e
3HaqeHHR Ha KpaRX nOJIOChI. ,LJ;arree, nyCTb N - qHCJIO pa3PMOB JIHHHH 3a.z:J;epXKH.
qacToTHbIe OTKJIOHeHIDIMH, onpe,neJIRIOlI.(He IIIHPHHY nOJIOChI, onpe,neJUIIOTCR COOT-
HOllIeHHRMH
(2 N - 1) JiSo + foSo = 2 N fiSI,
(2 N - 1) hSo + foSo = 2 N hS2.
(2.32)
llpH He60JIbllIOH llIHpHHe nOJIOCbI rpaHHqHbIe qaCTOThI MO)I(HO npH6JIIDKeHHO
BbIpa3HTb B BH,n:e 12 = to + !!,,2 H II = to - !!" I. HOpMHpoBaHHaR IIIHpHHa nOJIOChI qac-
TOT Tor,na COCTaBJIReT (!!"I + !!,,2). llpH 60JIbllIHX yrJIax CKaHHpOBaHHR BbIpIDKeHHR
MR S2 H SI MOXHO ynpOCTHTb. O,nHaKO npH paCCMaTpHBaeMOM 3,neCh MarrOM yrJIe
CKaHHpOBaHHR H paBHOMepHOM aMITJIHTY.D:HOM pacnpe,neJIeHHH 3TH ynpOlI.(eHHMe
3HaqeHHR CTaHOBHTCSI HeTOqHbIMH. ll03TOMY JUIR ypaBHeHHH 6bIJIH nOJIyqeHbI TOq-
HbIe pellIeHHR.
Y,n06HO HOpMHpOBaTb llIHPHHY nOJIOCbI qaCTOT C HCnOJIh30BaHHeM K03cp<l>HUH-
eHTa sin 8 0 /8 3 . ECJIH HCnOJIh3yIDTCR Bce pa3pR.abI cpa3bI, TO HOpMHpOBaHHaR nOJIOca
qaCTOT paBHa 1. 3aMeHa 3HaqeHHR cpa3hI 3HaqeHHeM 3an;epXKH JUIR KIDK,lJ.OrO 6HTa
YBeJIHqHBaeT K03cpcpH:QHeHT paCllIHpeHHR nOJIOCbI H IIIHPHHY nOJIOChI qaCTOT npH-
MepHO B,UBoe. OTMeTHM, qTO IIIHpHHa nOJIOChI B03pacTaeT 6hIcTpee, qeM 2 M , KaK H
,l(OJI)l(HO 6bITb, nOCKOJIbK)', eCJIH Bce pa3pR.abI RBillIlOTCR JIHHHRMH 3an;epXKH,
ynpaBJIReMaR nOJIOca HMeeT 6eCKOHeQHyID IIIHPHHY (CM. Ta6JI. 2.2). O,nHaKo AJUI
60JIbllIHX aHTeHHbIX pellieTOK 3TO YBeJIHqeHHe MeHhllIe.
Ta6J1Hu;a 2.2. Pa3p».D:HOCTb 38,lJ,ep:>KKII II IIIlIpHHa nOJIOCbI qaCTOT,
eo = 30 0 , e 3 = 1 0
HOpMHpoB8HHhle 3H8qeHHJI
qHCJlO p83pJI,IJ.OB JlHHHH 3Mep1KKH I 1111 II  pacnotpeHHJIlIWIOChl1J3C1Ur
0 1
1 2.002
2 4.016
3 8.124
4 17.016


rfla6a 2. OCHo6Hbie xapaKmepucmUKU aHmeHHbLX peUlemOK
2.3.3. P83MeeHMe nMHMM 38Aep>KKM
Bo MHorHX <t>a3HpoBaHHbIx aHTeHHbIX pellIeTKax HCnOJIb3yeTcH 06I.I.(ee <t>H,IJ;epHOe
B036)')K.l1:eHHe, H B c.rryqae llIHpOKOnOJIOCHbIX aHTeHHbIX perneTOK B03HHKaeT Bonpoc
o HaIDIyqrneM MeCTe pa3MemeHMH JIMHMH 3a,n:epXKH. CHaqaJIa paCCM01'pHM 06I.I.(ee
<t>H)J;epHOe B036)')K.l1:eHHe aHTeHHOH pellIeTKH, He MMelOI.I.(ei1 no,aperneTOK. B H)J;eaJIb-
HOM BapHaHTe KIDK,l(bI:U 3JIeMeHT cHa6xeH MHoropa3PMHbIM <pa30BpaI.I.(aTeJIeM 1'1
JIHHHeH 3a,n:ep)l(l(H, npHqeM JIHHHH 3a,n:ep)KI(H 06pa3yIOT JIeCTHHqHyIO CTPYKTYPY, CO-
OTBeTCTByIOI.I.(yIO yrJIaM CKaHHpOBaHIDI (CM. pHC. 2.21). 3TOT no,axo,n, XOTH H 06ecne-
qHBaeT llIHpOKOnOJIOCHOe CKaHHpOBaHHe, HCnOJIb3yeTcH pe,nKO, nOCKOJIbKY 1'pe6yeT
HaJIHqIDI Y KIDK,l(OrO 3JIeMeHTa KOMMyrHpyeMoH OT 21t ,no 21t(L / 'A) JIHHMH 3an;ep)l(l(H.
CooTHollIeHHe Me)J()Jy MHHOH JIHHHH 3a;::(ep)l(l(H H BpeMeHeM 3aaep)l(l(H 1'pHBHaJIbHO:
L/A. = tHaHoceK hHrarepIJ.. (2.33)
3JIeMe HTbI
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
<1>a30BpaI.IJ;aTeJIH
.
JIHHHH 3a.aep)l(KH
PUC. 2.21. 16-3J1eMeHTHaH pemeTKa c <pH,I{epHbIM B036)')K.l(eHHeM
Pa3MeI.I.(eHHe YCTPOHCTB MJIa;:I:rnero pa3PMa 3a;:I:epXKH (0 HJIH 'A) HHor,aa npe,n:y-
CMaTpHBaeTCR Ha KIDK,l(OM 1'13 CYMMaTOpOB nepBOrO YPOBHH, Cpa3Y nOCJIe 3JIeMeHTOB
pellIeTKH. JIHHHH 3an;ep)lQ(Jf CJIe,nyIOI.I.(erO pa3PMa (0 HJIH 2'A) pa3MeI.I.(a1OTCH Ha
Ka)l(.[lOM H3 CYMMaTOpOB BTOpOrO YPOBHH, H T.,a. O,aHaKO TOqHbIH aHaJIH3 ,n:aHHOH
TOnOJIOrHH nOKa3bIBaeT, qTO 3HaqeHHH 6HTa 3an:ep)l(J(H 0 HJIH n'A He 06eCneqHBalOT
qaCTOTHO-He3aBHCHMoro yrrpaBJIeHIDI JIyqOM [9].
B O,aHOM H3 BapHaHTOB BTOpO:U TOnOJIOrHH npOH3BO,l(HTCH ycpe,n:HeHHe 3an;ep-
)l(eK Ha Ka)l(J(OM H3 CYMMaTopOB no ,n:wana30HY CKaHHpOBaHHSI; 3aTeM pa3PMbI <t>a-
30BpaI.I.(aTeJISI onTMMM3HPYlOTCSI )J)ISI ,aaHHoro ,n:Hana30Ha CKaHHpOBaHHR. 3TO no-
3BOJISIeT npeBOCXO,l(HO ynpaBJISlTb JIyqOM, HO npH 3TOM B03HMKalOT JIeneCTKH
BbICOKoro ypOBHSI (-6 ,a6), 06YCJIOBJIeHHbIe KBaHTOBaHHeM <t>a3bI.
EI.I.(e B O,aHOM BapHaHTe, 06eCneqMBalOll.{eM llIHpOKOnOJIOCHOe CKaHHpOBaHHe,
3JIeMeHTbI C HeqeTHbIM HOMepOM MMelOT HYJIeByIO 3an;epXKY, a qeTHbIe 3JIeMeHTbI -
06eCneqHBaeMbIH <t>a30BpaI.I.(aTeJIeM 3JIeMeHTa <t>a30BbIH c,n:BHr kd sin e, r,ae d - Mex-
3JIeMeHTHoe paCCTOHHHe. Ha ypOBHe nepBbIX C}'MMaTopOB qeTHbIe nrreqH HMelOT HY-


--
2.3. Ynpa8llenue JlYlfOM U J/enecmKU K6anm06anUJI 
JIeBYID 3an;epXKY, a HeqeTHbIe - 3a,aepXKY, BKJIlOqalOmYK> npe,nbmyIUHe 6HTbI 4>a-
30BpamaTeJI5I H Bce MJIan;llIHe 6HTbI 3an;ep)K](H. Ha pHC. 2.22 npHBe,neH npHMep
16-3JIeMeHTHoH aHTeHHOH pellIeTKH C CeKTOpOM CKaHHpOBaHIDI 45°. B ,naHHoH Tono-
v
JIOrHH HCnOJIb3yeTcR B,nBoe MeHbllIe JIHHHH 33,L1ep)f{KH, qeM B H.LJ:eaJIbHOM BapHaHTe;
npH 3TOM KOJIWIeCTBO 4>a30Bpall{aTeJIeH OCTaeTC5I TeM xe.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
3J1eMeHTbI
<I>a30Bpam:aTeJIH
127
<I>a30Bpam:aTeJlH +
+ JIHHHH 3a,n:ep)I(KH
Pac. 2.22. Cl>a30BpamaTeJIH H JIHHHH 3a,aepXKH ,lI,JUI ceKTopa CKaHHpOBaHHH 45°
nepeeM Tenepb K CXeMaTHqeCKH H306paxeHHoH Ha pHC. 2.23 aHTeHHOH pe-
llIeTKe, COCTORll{eH H3 no,npellieTOK, Ka)l(,lJ;bIH 3JIeMeHT KOTOpOH cHa6xeH <l>a30Bpa-
ll{aTeJIeM, a JIHHHH 3an;epXKH pacnOJIaralOTCR Ha 06ll{eM <l>H.LJ:epe. JIHHHH 3an;ep)K](1i
v
pacnpe,neJIeHbI no JIeCTHHqHOH cxeMe, Ii TeOpeTHqeCKH ,l(OCTIDKHMaR llIHpHHa nOJIO-
CbI paBHa llIHpHHe nOJIOCbI, 06YCJIOBJIeHHOH <}>a30BpamaTeJIRMH, YMHOXeHHOH Ha
KOJII1QeCTBO no,npellieTOK. HanpHMep, llIHpHHa nOJIOCbI qaCTOT, 06YCJIOBJIeHHaR <l>a-
3HpOBaHHeM, COCTaBJIReT npH6JIH3HTeJIbHO e 3 /sin eo. IIIHpHHa nOJIOCbI aHTeHHOH
pemeTKH C 16 nOLJ:pemeTKaMI1 B 16 pa3 60JIbme. IIp06JIeMa JIl1mb B TOM, qTO Y 00-
,npemeTOK, COCTORll{HX 60nee QeM H3 Tpex 3neMeHTOB, MOryr B03HHKaTb JIeneCTKH,
06ycnoBneHHbIe KBaHTOBaHHeM <}>a3bI, KOTopbIe He y,naeTCR nonHOCTblO YCTpaHHTb
nceB,nopaH,lJ;OMH3aU;HeH [10].
1 2 3 4 5 6 7 8 9 10 11 12
3JIeMeHTbI
<I>a30Bpam:aTeJIH
JIHHHH 3a,a;ep:>KKH
PHC. 2.23. Y cpe,nHeHHbIe 3a,aepXKH Ha ypOBHe TpeTbero CYMMaTopa MH ceKTopa
CKaHHpOBaHH.SI 45°


rAa8a 2. OCHo8Hble xapaKmepucmUKU aHmeHHbIX pewemOK
2.3.4. nenecTKM KBaHTOBaHMR cl>a30BpaaqaTeneM
DOJIbIIIHHCTBO <l>a30Bpam:aTeJIeH HMelOT I.J;H<ppoBoe ynpaBJIeHHe He3aBHCHMO OT
TOfO, KaK B HHX ocym:eCTBJlHeTCH <l>a30BbIH C,ZJ;BHf - aHaJIOfOBbIM HJIH I.J;H<I>POBbIM
o6pa30M. Y TaKHX <pa30Bpam:aTeJIeH HMeeTCH HaHMeHbIIIHH <l>a30BbIH C,ZJ;BHf, COOT-
BeTCTByIOW:HH O,ZJ;HOMY pa3pMY. M-pa3pH.nHbIH <pa30Bpaw:aTeJIb 06eCne1JHBaeT <}>a-
30BbIe C,ZJ;BHfH, paBHbIe 21t/2M, 2'1t/2M-I,.., 'It. TIpH 3JIeKTpOHHOM CKaHHpOBaHHH
J.f,L(eaJIbHaR JIHHeHHaH <1>a30BaH xapaKTepHCTHKa annpOKcHMHpyeTcR cTyneH1JaTOH
<l>a30BoH KpHBOH, 1JTO nOpOJK.naeT nRTI006pa3HyIO KPHByIO OIIIH60K (CM. pHC. 2.24).
OllIH6Ka <}>a3bI
Heo6xoAHMoe 3HaqeHHe <}>a3b1
<l>aKTHQeCKOe 3HaQeHHe £,ba3b1
Pac. 2.24. OWH6KH .nHCKpeTH3al(HH <l>a3bI
TIOCKOJIbKY aHTeHHWI peIIIeTKa ,ZJ;HcKpeTHa caMa no ce6e, B3JKHyIO pOJIb HrpaeT
nOJIOXeHHe 3JIeMeHTOB Ha nRTI006pa3HoH KpHBOit MMeeTcR ,ZJ;Ba 1JeTKO BbIpIDKeHHbIx
CJIyqWI. B nepBoM KOJIH1JeCTBO 3JIeMeHTOB MeHbIIIe, 1JeM 1JHCJIO c'fYIIeHeK KpHBOH.
B 3TOM cJIyqae norpelliHocTb <l>a3bI HMeeT CJIyqaHHbIH xapaKTep. OHa OI.J;eHHBaeTCH
nyreM annpOKCHMaI.J;HH ,ZJ;HcnepCHH <l>a3bI 3Ha1JeHHeM 1/3 nHKOBO:H norpeIIIHOCTH
IIHJIoo6pa3HoH KpHBOH, COCTaBlliIIOw:eH 'It/2M. AHcnepCIDI paBHa
1t 2
0'2 -
3.4 M
.
(2.34)
-

r
-
f
.  '
2.3. YnpoBllenue IlJ"lOM U lleneCmKU KBonmOBOnUJl 
Cpe.n;HeKBpaTHqHbIit ypoBeHb (RMS) 6oKoBoro JIeneCTKa (KoMMyraUMoHHoro
JIenecTKa) COCTaBJIReT (j2/G. npH paBHoMepHoM B036y)1()];eHHH aHTeHHoM perneTKH
cpe.n;HeKBpaTMqHbIM YPoBeHb 6oKoBoro neneCTKa paBeH (j2/N. Ha pHC.. 2.25 npH-
Be.n;eHO c'pe.n;HeKBpaTHqHOe 3HaqeHMe YPOBHR 6oKoBoro JIeneCTKa, 06YCJIOBJIeH-
Hoe CJIyqaMHoM norpelIIHOCTblO KBaHTOBaHHR <pa3bI npH nOnepeqHOM H3JIyqeHHM.
npM yrJIe CKaHHpOBaHMR eo OCHOBHOM JIeneCTOK YMeHbllIaeTCR npMMepHO B Cos 2 e o
pa3, n03TOMY cpe.n:HeKBa,apaTMqHbIM ypOBeHb 60KOBoro JIeneCTKa OTHOCMTeJIbHO
OCHOBHoro YMeHbllIaeTCR. YBeJIMQeHHe 60KOBbIX JIeneCTKOB COnpOBO)l():(aeTCR He-
60JIbllIMM YMeHbllIeHMeM K03<P<PMUMeHTa YCMJIeHMH:
-20
-30

 -40
t:)
-so
-60
10
100
KOJUIQeCTBO 3JIeMeHTOB B AP
1000
PHC. 2.25. 3aBI1CI1MOCTb cpe.n:HeKBa.n:paTHqHOrO ypOBHH 60KOBoro JIerreCTKa OT
JJ:HCKpeTHOCTH a30BparqaTeJIH
G
- "' I-a 2 .
Go
(2.35)
YMeHbllIeHMe K03<P<PMUMeHTa YCHJIeHMH .LUIH CJIyqaMHo BbI6paHHbIx BapHaHToB
npMBe.n:eHo B Ta6JI. 2.3.
Ta6J1Hu;a 2.3. YMeHbIIIeHl1e K03<tJ"U:l1eHTa YCHJIeHMH
,lUIH He60JIbIIIHX aHTeHHbIX pemeTOK
M YMeHbweHHe K034»4»HlUIeHT3 YCHJleHHH (.liB)
2 1,000
3 0,229
4 0,056
5 0,014


rAa8a 2. OCHo8Hble xapaKmepucmuKu aHmeHHblX pewemOK
Bo BTOpOM cJIyqae Ha <pa30Byro clyneHbKy rrpl1XO,LJJITCR ,n:Ba I1JIH 60nee 3JIeMeH-
TOB, H ,n:HcKpeTHa5I aHTeHHaR pellIeTKa arrrrpOKCI1Ml1pyeTcR HerrpepblBHoH. 3TO
KBaHTOBaHHe rrOpO)l(,[(aeT PM JIerreCTKoB, Ha3bIBaeMbIX JIerreCTKaMI1 KBaHTOBaHI1JI
(QL), HMelOll{HX rrpe,nCKa3yeMbIe aM I1JIHTY,l1bI H yrnoBbIe rronoxeHHR. H3MeHeHHe
<pa3bI Me)l(,L(Y KOHaMH N-3JIeMeHTHOH aHTeHHOH pellIeTKH paBHO (N - 1) kd sin eo.
KOJIHqeCTBO 3JIeMeHTOB J, rrpHxo,nRIl.(eeCR Ha <pa30Byro cTyrreHbKy rrpH M-pa3pR,n:-
HOM H3MeHeHHH <pa3bI, COCTaBJIReT:
J=
(N -1)2 M (d / A) sin eo
!{
(2.36)
3TO rr03BOn5IeT orrpe,l1enHTb HaH60nbllIHH yron CKaHHpOBaHI15I, WIR KOToporo
J > 2. ,IJ;JIR 60nbllIHx aHTeHHbIX pellIeTOK H3 (2.36) cne.uyeT sin eo '" 1/[(d/A)2 M + 1 ].
MaKcHManbHbIe 3HaqeHHH yrna npH rron)'BonHOBOM MeX3neMeHTHOM mare rrpHBe-
,l1eHbI B Ta6n. 2.4. DonbllIHe yrnbI npHBO,lUIT K 60nee cnOXHblM I1CKIDKeHHRM ,l1Ha-
rpaMMbI HanpaBJIeHHOCTH. ,[(nR J, 3aKJIIOqeHHOrO B ,l1Hana30He Me)l(,L(Y 1 If 2, cYIl.(e-
cTByeT nepeXO,l1HaR 06naCTb Me)l(,[(y onHcaHHOH cnyqaHHoH CTPYKTYPOH 60KOBMX
nerreCTKOB (J < I) H ClpyKTYPOH neneCTKOB, o6ycnoBneHHbIx KBaHTOBaHHeM. YroJI
pacnOJIOXeHH5I JIerreCTKOB KBaHTOBaHHR e q orrpe.n:eJI5IeTCR IlIHpHHOH cTyneHbKH W
(He rrYTaTb C W B <popMYJIe (2.27»:
W
A
1
2 M sineo
(2.37)
Ta6J1Hna 2.4. MaKCHMaJIbHbIM yrOJI CKaHHpOBaHHH,
npH KOTOpOM nOHBJIHeTCH OTQeTJIHBO
BbIpalKeHHbIM JIeneCTOK KBaHTOBaHHH
(d/A = 1/2)
M6HT emax (rpa.a)
1 30
2 14.48
3 7.18
4 3.58
5 1.79
KaK OTMeQanOCb BbIllIe, 3TO rrpHBO,l1HT K rrHKoBoMY 3HaQeHHIO OllIH6KH p = n/2M
,LJ)UI rrIDIoo6pa3HoH KpHBOH. AMI1JIHTY.n:bI JIerreCTKOB KBaHTOBaHHR orrpe,n:eJIRIOTCR
BbIpIDKeHHeM sinc (13 + in), r,n:e i = 0 cooTBeTcTByeT OCHOBHOMY nyqy. AMIIJII11)',n:bI
rrepBblx ,l1BYX JIeneCTKOB KBaHTOBaHHH H OCHOBHoro JIyqa npHBO,lUlTC5I B pa60Te [14]:
....
OCHOBHOH JIyq
sincJ3;
sin p .
,
n + p
sinp
2n + J3
(2.38)
....
rrepBbIH JIerreCTOK KBaHTOBaHHR
....
BTOpOH JIeneCTOK KBaHTOBaHI1H


2.3. YnpaSJleHUe JlY'tOM U JlenecmlCu ICsaHmOOaHUJI 
npH f3 = nl2 aMnJIHTy,nbI OCHOBHoro JIyqa H nepBoro JIeneCTKa KBaHTOBaHHR
paBHbI, qTO, HecoMHeHHo, RBJIReTCSI nJIOXHM BapHaHToM. Ho 3TO npoHcxo,n:HT TOJIb-
KO B npe,n:eJIbHOM cJIyqae, Kor,na HCnOJIb3}'IOTCR 0,n:H06HToBbIe <})a30Bpam:aTeJIH.
B Ta6JI. 2.5 npHBe,neHbI 3HaqeHHR YPoBHeH JIeneCTKOB B 3aBHCI1MOCTH OT pa3pR,n:HO-
CTH <t>a30BpalUaTeJIeH.
Ta6JIHu.a 2.5. AMnJIHT)'.nbI JIeneCTKOB KBaHTOBaHI1H cl>a30BpamaTeJ1ei1:
,
M OCHOBHOH JIY1I ()J;B) QL. ()J;B) Q Lz ()J;B)
1 -3.92 -3.92 -13.46
2 -0.912 -10.45 -14.89
3 -0.224 -17.13 -19.31
4 -0.056 -23.58 -24.67
5 -0.014 -29.84 -30.38
6 0 - 35.99 - 36.26
YMeHbmeHHe K03<P<PH[(HeHTa YCHJIeHHSI BbIpa)l(aeTCSI qepe3 npH6JIIDKeHHOe
YMeHbmeHHe aMnJIHTy,nbI OCHOBHoro JIyqa [1]:
.£ -- sinc 2 f3, (2.39)
Go
r,ne sinc(x) = sin x I x.
3TH ,n:aHHbIe n03BOJIRIOT pa3pa60TqHKY aHTeHHOH pemeTKH pa[(110HaJIbHO BbI-
6paTb pa3pSI,aHOCTb <pa30Bpam:aTeJIR.
B CJIyqae npRMoyrOJIbHbIX ceTOK YCJIOBHSI nORBJIeHHR ,n11<ppaK[(110HHOrO JIeneCT-
Ka (J].J1), BbIBe,neHHbIe .l(JIR JIHHeHHbIX aHTeHHbIX pellIeToK, OCTalOTCSI CnpaBe.l(JIHBbI-
MI1 ,LLJISI nOJIOC, napaJIJIeJIbHbIX U- H V-OCRM. OHH nepeCeKalOTCR, 06pa3YR 30HbI, r,ne
MOryT nOSIBJIRTbCR J].JI, KaK nOKa3aHO Ha pl1C. 2.26. ,lJ;HcKpeTHocTb pacnOJIO)l(eHI1SI
,lJ;JI, KOHeQHO, 3aBHCI1T OT yrJIOB CKaHHpOBaHIDI. Ha6JIIO,n:aeMbIe JIeneCTKH KBaHTO-
BaHI1R npe,n:CTaBJIRIOT C060H J].JI, pacnOJIO)l(eHHbIe Ha nOJIocax B npe,n:eJIax e,n:HHHQ-
HOH OKp}')KHOCTI1 B ITJIOCKOCTI1 yrJIOBbIX nepeMeHHbIX u-v.
TIPI1 I1CnOJIb30BaHI111 reKCarOHaJIbHOH ceTKH H3JIyqaTeJIeH C reKCarOHaJIbHbIM
peXI1MOM ynpaBJIeHHSI <pa30Bpam:aTeJIRMI1 nOJIOCbI JIeneCTKOB KBaHTOBaHI1SI pacno-
JIO)l(eHbI no rJIaBHbIM ,nHarOHaJUIM. B 60JIbllIHHCTBe CJIyqaeB e,nHHHQHYIO OKp)')K-
HOCTb nepeceKalOT TOJIbKO ,nBe nOJIOCbI. O,nHaKo TaKHe reKCarOHaJIbHbIe CTpyKTypbI
CJIO)l(HbI H n03TOMY npHMeHSIIOTCR pe,lIKO. qawe HCnOJIb3YIOTCR cxeMbI co CTPOQHO-
CTOJI6[(OBbIM pacnOJIO)l(eHHeM <pa30Bpam:aTeJIeH, npH 3TOM nOJIOCbI JIeneCTKOB
KBaHTOBaHHSI napaJI.JIeJIbHbI u- H V-OCRM [15]. Ha pHC. 2.27 H306pa)l(eHa reKcaro-
HaJIbHaR ceTKa co CTPOQHO-CTOJI6[(OBbIM pacnOJIO)l(eHHeM <pa30BpalI(aTeJIeH. B 3TOM
CJIyqae MOryr B03HHKaTb ,lIOnOJIHHTeJIbHbIe nOJIOCbI JIeneCTKOB KBaHTOBaHHR. B ue-
JIOM, Y reKCarOHaJIbHOH ceTKH eCTb npeHMymecTBa B OTHomeHHH ,n11<ppaK[(HOHHbIX
JleneCTKOB, HO npH CTPOQHO-CTOJI6U:OBOM pacnOJIO)l(eHI1H <pa30BpalI(aTeJIeH OHa He
HMeeT npeHMymecTB B OTHOllIeHl111 JIeneCTKOB KBaHTOBaHHSI.


FJla6a 2. OCllo611ble xapaKmepucmUKU allmellllblX peUlemOK
........ .. -.
.'. . .. .... : . : . : . . . : . . . . : . : . : . : .
.:.:.:.:.:
:.:.:.:.:. :::::=::::
.......... . . . . .
..... .....
..... .....
..... .....
.:.; .;.;. ;..;. . . '......".-.. -. ......... ............. -. -. -... .-. -..... .:..:.:.:. ;.;..
..-. ........... ...... -. -. ............. ......... ..................... . ......... -.-
............... ............... ......... .... -. ........:.. .:.:.:.: .  ...... w. _. e._
. ... ......... .................................... .-. ... ... .. .. .. .. .
.:.:.:............ ........................................=... .- . .. .
:::::=:::: .::..- .
:::::::::: .... .. .:::::
.......... ..........
..... .....
.......... ..........
:::::::::: ::::::::::
.......... ..........
:.:.:.:.:. .:.:.:.:.:
.......... ..........
.......... ..........
.:.:.:.:.: :.:.:.:.:.
.......... ..........
.......... :..........
..... .....
. , . . : :  . : :  . : : . . : . . . : . . = : ::: ::::::::
. . ... :::::::::::
............. ...............-..---.. --- ........
. . . . ... ..  . . . . . . . . .. .. . - . . . .. . . .. ....",.r ,I.r . ..........
:::::::::::::: ::::::::::::::::::;:::::::::::::::::::::. .::: /, ,. ::::.:.:.:.:.
.:.:.:.:.:.:.: .:.:.:.:.:.:.:.:.:.:.:-:.:.:.:.:.:.:.:.:.: ..    :-:.:.:.:.:-:
. . . . . .. :.:.:.:.:.......... - . . . . . . . . . . .- ..:.::...............
..... . ...
 .  . ; .  .  .  .  .  .  .  .  . ::::: .::::
:::::::::::
: . :' . .:: . :: . :: . :: . :::::::::::
...........
\@ 11\1
:::.:::.:.: . .. .. . .
 .  .  .  .  .  .  . ; .  . : . . ;i
:.:.:.:.:.
........... ..........
.:.:.:.:.:.:.:. -,.; ......-.-.-.-.-...-...-.-.-.-.-...-.......-.... ... ...". -.;.;.;.;.;.;
.:.:.:.:.:.:.:  .. ::::::::::::::::::::::::::::::::::::::::::::::: '.  :.:.:.:.:.:.
:::::::::::::: ::, ....:... =:::::::::::::::::::::::::::::::::::::::::::::: :- - -":: ::::::::::::
.:.:.:.:.:. ........... . . . . . -
::=:::::=:: ::=:=:::::
........... .'.:.'.:.:.
. .......... .:....:.....
.:........_ ..............
v
r,
. .... . . .
.:.:.:.:.:.:
...........
::::::::::::
......
......
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.:.:.:.:.::::::::::::=:::::::::: "\ .
. ........... \
. . . . . . . . ........,
. ... . . .
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.:.:.:.:.:.:
............
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.......
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...
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....
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....
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. . . . . . . . . . . . . .. . '..."'..'.. "." -.-.-.-
............................... J. ....- -.. - .. .
..... ...... -. ................ ........ .......
............. .......
... . . . . . . . - ..... FJ . . -.-........
. . . . .... . .. . . . . ... 11'1..... . . .. _ .
......................... ... ::::;:::: . ... . . . .. .
:::::::::::
::::;::
...........
:.:.:.:.:.:
........-..
.. .. .. . .
..-........
.....-.....
......
.:.:.:.:.:.
!!!ij
::::::::::: ::::: ::::::::::::::: . :::::::::::::::
.... ......... ..-..-:.-.:.:.:.:. .:.:.:.:.: -:.:..
................... ... . . .. . . . . . . . . . . . . . . . .
_._..._.N........o.o.o._...o ::=:::::::: 0 . ... . . ...
............
::::::::::=
:..:.:..:
PHC. 2.26. llonOCbI pacrronoxeHMH neneCTKOB KBaHTOBaHMH ,L(JUI
pacrronoxeHMH 3neMeHTOB
.:.:.:.:.:. .:.:.:.:.: -:.:.:.:.;.
:.:.:.:.:.: :::::::::: :.:.:::.:::
.. . ::::::.:.:.:.:.:.:.:.:.:.:.:.:.:. . :.:.:.:$:.:.:.:.:.:.:.:.:.:.:::::.::. . ::::.:::-:::::::::;:;:;
'.  . . . . . . . . . . . . . . .................... .. ... . .. . . . . . .
:. .:.:.:.:.:.:.:.:.:.:.:.:.:.:. .............:.:.:.:.:.:.:.:. ..:.:.:.:.:.:.
.: :.:.:.:.:.:.:.:.:.:.:.:.:.:.: :.:.:.:.:.:................ 'II.. .--:.....:.:
:.:.:.:.:. ::.::::::: :::::::::::
:::::::::: :::::::::: :..:-:.:.:.:
.......... . . . . . ...........
:::::::::: :::::::::: ::::::.' .,
:.:.:.:.:.: :::::::::: .. . ..:
.:.:.:.:.:. .:.:.:.:.: ..:.:.:.
. . . . . . . . . . . ..........
.:.:.:.:.:. 'II:.:.:.:.: ..........
:.:.:.:.:.: :.:.:.:.:- ::::::::::
::::::::::: -.:.:.:.:.: .:.:.:.:.:
.:.:.:.:.:. ::::::::::: ::::::::::
.:.:.:.:.: .:.:.:.:.:. ..........
.:.:.:.:.:. :.:.:.:-:.: :.:.:.:.:.
:.:.:.:.:.: .:.:.:.:.: ::::::::::
:.:.:-:.:.: ...-...... .:.:.:.:.:
::::::::::: :.:.:.:.:. ::::::::::
':':.:.:.:11 :::::=:=:: :.:.:.:.:.
::::::::::: .:.:.:.:-: ::.:.:.:.:
. . ............................. . P!...............-.. .... ....;,..   ... .;.;.........
: .:.:.:.:.:.:.:.:.:::.:.:.: ::::::::::::::::.. ::.:..- - -'"- -:.:.:.:.:.:.
. .................... ....... . . . . . . _'II_ ......... .r .............
.1t :.:.:.:.:.:.:.:.:.:.:.:.:.:.* .:.:.:.:.:.:...:........ - ".........-
.......... ....a:a:.: ........:
.:.:.:.:.:. :::::.:.:. .. -.:.
:::::::::: .:.:.:.::: :::::....
.:::::::::: ::::::::.: ::::::::::
:.:.:.:::: :::::::::: ::::::::::
:::=:::.:. :.:.:-:.:. .:.:.:.:.:
:::::::::: :::::::::: ::::::::::
:::::=:::: :::::::::. ::::::::::
.:.::::::: :::::::::: ::::::::::
:.:....... .:.:.:.:.: ..........
.......... a. . e.. .........,
...:.:.:.: .:.:.:...: :.:.:.:.:.
.:........ ..:.'.:.:. ..........
.......... .. ... . . ..........
:::::::::=: :::::::::: ::::::::::
:.:.:.:.:. :.:::::::: .:.:.:.:.:
:.:.:.:.:.: .:..:.:.:. :.:.:.:.:6
.:.:.:.:.:. :.:......6 .:.:.:.:.:
. . . -.... .........: ...........
t; . .:::.::::::::;:::::;::::::::: . :;:;:;:::;:;:;::.:.::.:. . ,. .:.:.:.:.:.:.
  .............. ... .
, :.:.:.:.:.:.:.:.:.:.:.:.:.:.: ................:.:.:.:.:.:.: :.:.:.:.:.:.:
.'....... .................... ..............!.......... ...... _............
.:.:.:.:.: ::.:.:.:.: .:.:.:.:.
.:.:.:.:.:t :......... ..........
. . . . . . ......... .........
...:...:.:. .......... ..........
... .._... -.........
v
.;........ ..........
::::::::::. .::::::::::
- . . . . . :.:.:.:::. . . . .::::::::::
:::::::::::: .:: --.. -': :::::::::::::::::::::::::::: . .:
:::::::::::: :. -': :::::::::::::::::::::::::::: .=
............ . - - .........-.-............-.-.. .
.:.:.::::: :::::::::::
...... . . . . . . . .
:::::::::: :::::::::::
.. ..:::: ::-;::::::
.... . ...........
........ ..........,
.......... ...........
:.:.:.:.:. .:..:.:.:-:.
.:.:.:.::= ::::::::::
::::::::.: :.:.:.:.:.:
:.:.:.:.:. .:..:.:.:.:.
:::::::::: :::::::::::
.:.:.:.:.: :.:.::::::
:.:.:.:.:. :::::.:.:.
...-. .....
.:.::::::: :.:.:.:.:.
:.:-.:.:.: ::::::::::
.:.:...... ..........
:.:.:.:.:. .:.:.:.:.:
:.:.:.:.:.:.: ... :::.:.. :::::::::::::;:;::: . :;
:::::::::.: /"  :--: :..: :.:.:.:.:.:.:.:.:II:. ::
............. " ..,.....,.. ...................... "..
- .. . . . . .. . . .". . . . . . . . . . . . . ..........
.:::.:.- .:.:.:.:.:
... ..:.:: :::::::::
.:.:.::::: :::::::::
::::::..:.: .:.:.:.:.:.
:::::::::: :::::::::::
-:.:.:..:.:. :.:.:.:.:.:
:.:.:.:.:.: :::::::::::
::::::::::: :::::::::::
.:.:.:.:.:. .:.:.;.:.:.
::::::::::: :::::::::::
::::::::::: :::::::::::
::::::::::: :::::::::::
:.:.:.::::: :.:.:.:.:.:
:::::::.:.: ::::::::::
::::::::::: .:.:.:.:.:.
,.......... ...........
..:.:.:.:.:. . :.:.:.:.:.:.:.:.:.:.:.:.:.:. ' f
:........... ........................:.:.:. . '::
:::::::::::: :::::::::::::::::::::: . :' . :' . :. . ' ;;:; ..
......- ..........
:.:.:.:.:. :.:.:.:.:.:
:::::::::: :::::::::::
:::::::::: .:.:-:.:.:.
PHC. 2.27. llonOCbI
ceTKM
pacnonoxeHMH
neneCTKOB
KBaHTOBaHMH
u
v
KBa,lJ,paTHOM ceTKH
u
.LLITH
reKcarOHMbHOH


I
2.3. Ynpa6AeHue Il}"tOM U lleneCmKU KsaHmosaHUJ/ 
2.3.5. nenecTKM KB8HTOB8HMR nOApeweTOK
I(
AHTeHHaH pellIeTKa, COCTOHwaH H3 CMe:>KHbIX no,npellIeTOK, npH CKaHHpOBaHHH
HMeeT cTyneHqaTOe <pa30Boe pacnpe,neJIeHHe, npH 3TOM Ha Ka)f()I.yIO no,npellIeTKY
npHxo,nHTCH O,nHO 3HaqeHHe <!>a3bI. KaK H B CJIyqae UH<PPOBbIX <pa30BpamaTeJIeH,
3TO npHBo,nHT K B03HHKHOBeHHIO JIeneCTKOB KBaHTOBaHHH, o,nHaKO no,npellIeTKa
HMeeT, no KpaHHeH Mepe, ,nBa 3JIeMeHTa. TI03TOMY JIeneCTKH KBaHTOBaHHH 3.aeCb
Bcer,na ,neTepMHHHpOBaHbI. 0603HaqHM, KaK H npe)K,L(e, llIHPHHY CTyneHbKH (llIH-
pHHa no,npellIeTKH) Qepe3 W, a nHKOBoe 3HaQeHHe OllIH6KH ,l])IH nRJI006pa3HOH
KpHBOH - . ,LLrrSi 60JIbllIHX aHTeHHbIX pellIeTOK ,nHCKpeTHbIe no,npellIeTKH MO:>KHO
3aMeHHTb CllJIOllIHbIM paCKpbIBOM C nRJI006pa3HOH <pa30H. PaCCMOTpHM N o,nHHa-
KOBbIX no,npellIeTOK C O,nHOpO,lJ;HbIM B036}')K,lJ;eHHeM. ,LJ;HarpaMMa HanpaBJIeHHOCTH
aHTeHHbI HMeeT BH,lJ;
F(u) =   exp{j[ G kdu - Nf3 ) + f3 (2n -1 - N)]},
(2.40 )
r,ne nepe,lJ; CYMMHpoBaHHeM 3KcnOHeHT npOH3Bo,nHTCH HHTerpHpOBaHHe no BceM
no,nperneTKaM C yqeToM OllIH60K KBaHTOBaHHH, H
2n-N
u = (sin eo - sin e); Nt = N ; N 2 -
2n - 2 - N
N
Y,l(06HO nepeHTH K nepeMeHHbIM
w = W (sine o - sine);  = 1tV;
A
W' e W' e
v = -SIn; Vo = -sm o.
A A
(2.41 )
Pe3YJIbTaT HHTerpHpoBaHIDI H CYMMHpoBaHHSI MoxeT 6bITb npe.acTaBJIeH B aHa-
JIHTH1.JeCKOM BH,lJ;e
sin N1tW .
F(u) = . SIDC 1tV.
N SIn 1tW
(2.42)
B 3TOM BbIpIDKeHHH JIerKO Y3HaTb ,lJ;HarpaMMY HanpaBJIeHHOCTH 3KBH,lJ;HCTaHT-
HOH aHTeHHOH perneTKH H3 N H301ponHbIX 3JIeMeHTOB, pacnOJIO)l(eHHbIX Ha paCCTO-
HHHH W, C HanpaBJIeHHeM OCHOBHoro .rryqa e = v = O. TIpH 3HaQeHHHX W, 60JIbllIHX
O,l(HOH ,LLJIHHbI BOJIHbI, nepBbIH 1.JJIeH npHBo,nHT K B03HHKHOBeHHIO )];JI. aHHbIe )];11
HMelOT e,nHHHQHyIO aMllJIHTY,lJ;Y H pacnOJIaralOTCSI B TOQKaX w = 0, 1, 2, ... nepBbIH
H3 HHX HBJIHeTCH OCHOBHbIM. Ha 3TH JIeneCTKH HaKJIaabIBaeTCH sinC-MHOXHTeJIb
<pOpMbI JIyqa.
npH paCCTOHHHH Me)K,L(y ,I:W, paBHOM e,nHHHue (B 3HaQeHHHX w), H JIHHeHHOH
llIHpHHe JIyqa, paBHoH 2 (B 3HaQeHHSIX v), nepBbIH J1 BCer,lJ;a HaXO,l(HTCH Ha KpalO
RJIH BHYTPH sinc-06pa3Horo JIeneCTKa. HanpHMep, B OTcyrcTBHe CKaHHpOBaHHH
nepBbIH )];11 Ha6JIIO,naeTcSI npH nepBOM HYJIe sinc-MHOXHTeJISI. npH CKaHHpOBaHHH
MaKCHMYM JIyqa OTO,lJ;BHraeTCH OT nHKa sinc-<PYHKl(HH H, n03TOMY, YMeHbllIaeTCH.
npH 3TOM ,I:W C,lJ;BHraeTCSI OT HYJUI sinc-<PYHKUHH K nHKOBOMY 3HaQeHHIO. TaKHM
06pa30M, ypOBeHb nepBoro JIeneCTKa KBaHTOBaHIDI 6JIH30K K 3Ha1.JeHHIO sinc-MHo-

b
rJla6a 2. OCHo6Hble xapaKmepucmUKU aHmeHHbLX peUlemOK
)l(HTen$I B nonoxeHMM nepBoro ;J:JI: v = Vo - 1. Cne,L:(YIOIIJ;MH JIeneCTOK KBaHTOBaHMH
Ha6nlO.LJ:aeTCH npM BTOpOM JI: v = Vo - 2, npM 3TOM sinc-06pa3Ha51 ,AMarpaMMa Ha-
npaBneHHOCTM 60KOBMX neneCTKOB 3aeT YPOBeHb neneCTKa KBaHTOBaHMH. AnH
TOqHOrO onpe,u;eJleHMR nMKOB neneCTKOB KBaHTOBaHlliI nOTpe6oBaJIOCb 6bI ,L:(M<;l><;l>e-
peHl.(MpOBaHMe ypaBHeHMR (2.42) C nOCne,L:(YIOIIJ;MM npMpaBHMBaHMeM pe3ynbTaTa K
HYJlIO. llpM 60nbIIIMX 3HaqeHMHX N IIIMpMHa JIyqa JI 6Y.LJ:eT He6oJIbillOH no cpaBHe-
HMIO C llIMpMHOH sinc-06pa3Horo JIyqa, M npMBO,L:(MMbIe 3,L:(eCb pe3YJIbTaTbI 6y,L:(yr
TOqHbI. ECJIM OCHOBHOH JIyq N-3JIeMeHTHoH aHTeHHOH perneTKM OKa3bIBaeTCH B
HYJIe sinc-06pa3HoH ,L:(MarpaMMbI HanpaBJIeHHOCTM nO,L:(perneTKM, JIeneCTOK KBaHTO-
BaHMH pa3,L:(BaMBaeTCR, o6pa3YH He60JIbllIMe JIeneCTKM C KIDK,l(OM CTOpOHbI HYJIH [13].
llOCJIe,u;HMe MaJIOMHTepeCHbI H3-3a MX MaJIOM aMIIJIMTY,L:(bI. AMnJIMTY,LI,bI JIeneCTKOB
KBaHTOBaHMH M OCHOBHoro JIeneCTKa HaXO.lUlTCH M3 ypaBHeHMH (2.38), pa3)'MeeTCH,
C MCnOJlb30BaHMeM 3HaqeHMH J3 )J)UI nO.LJ:perneTKM. JIeneCTKM KBaHTOBaHMH Ha6JIIO-
,LI,aIOTCH npM6J1M3MTeJIbHO fIO,L:( yrnaMM pacnOJIOXeHMH )];JI:
. e . e m'A 1 2 3
sin JUI = sm 0 + - m = , , ,...
W
(2.43)
llpM6JIM3MTeJIbHbIe ypOBHR JIeneCTKOB KBaHTOBaHMH onMCbIBaIOTCH BbIpa)J(eHMeM
sinc 1tV q ; 3aBHCI1MOCTb I1X 3HaqeHI1H OT Vo = (W/A) sin eo ,lLJIH pa3JIHqHbIX ypoBHeH
(QL) npMBe,L:(eHa B Ta6J1. 2.6. Ta6JIHl.(a n03BOJUIeT MCnOJIb30BaTb pa3JIMQHbIe KOM6M-
Hal.(I1M pa3Mepa nO,L:(pellIeTKM 11 yrJIa CKaHMpOBaHMR. HanpHMep, JIeneCTOK KBaHTOBa-
HMH C ypOBHeM He BbIllie ypOBHH 60KOBoro JIeneCTKa O,L:(HOpO.LJ:HOM peIlleTKH nOJIyqa-
eTCH ,[(JIH WI'A = 2 npH CKaHHpOBaHHI1 Ha yrOJI 5.37°, MJII1 ,[(JIH WIA = 1 npH
CKaHHpOBaHMH Ha yrOJI 10.79°. 3TH ypOBHM npMBO,L:(HTCH OTHOCMTeJIbHO OCHOBHoro
JIyqa B HanpaBJIeHHI1, nepneH,L(HK)'JIHpHOM paCKpbIBY aHTeHHbI. Ha pMC. 2.28 nOKa3a-
HbI JIeneCTKH KBaHTOBaHI1H ,lI)IH 75-3JIeMeHTHoH aHTeHHOH pelIIeTKM C nOJIYBOJ1-
HOBbIM rnarOM pacnOJIOXeHIDI 113JIyqaTeJIeH. KIDK,l(aH nO,L:(perneTKa CO,Aep)J(HT n5lTb
3JIeMeHTOB; yrOJI CKaHHpOBaHMH COCTaBJUIeT 3°, npl1 3TOM P/1t = 0.1308. DJIIDKaMlIIHe
JleneCTKH KBaHTOBaHHH HMeIOT ypOBeHb -16.69 ,L:(D npH -20.34° 11 -18.98 ,L:(D npM
26.89°. ,[(JIH 60Jlee TOQHOrO onHcaHHR nOBe,L:(eHM5I JIeneCTKOB KBaHTOBaHHH paCCMaT-
pMBaeTCH MO,L:(eJlb ,L:(HCKpeTHbIX, a He HenpepbIBHbIX nO.LJ:perneTOK. O,LI,HaKO, TOQHOCTb
MCnOJIb30BaHHOH 3,L:(eCb MO,L:(eJIH ,L:(OCTaTOQHa, H OHa 60JIee npOCTa.
Ta6JIHQa 2.6. JlerreCTIGI KBaHTOBaHIUI rro,nperneTOK
Pin OcHOBHOii JIenecroK (,zd) Q Ll ()J;6) Q Lz ()J;6)
0.025 -0.01 -31.83 -32.26
0.05 -0.04 -25.61 -26.48
0.1 -0.14 -19.23 -20.97
0.15 -0.32 -15.39 -18.02
0.2 -0.58 -12.62 -16.14
0.3 -1.33 -8.69 -14.06
0.4 -2.42 -5.94 -13.30
0.5 - 3.92 -3.92 -13.46

I
2.3. Ynpa8JleHUe Jly'tOM U JleneCmKU K8aHm08aHUR 
o
-10
,-....,


'-"

t:::1
-20
::so:
r=::
t::

I .1
,
I'
-30  a I
I :  A
I ,
I
, i
1IIIIII I ' 11111 " j
I
-40 , , I ' I I
-90 -60 -30 0 30 60 90
e (rpa.a)
PUC. 2.28. 15 no,n;perneTOK, B Ka)l(.nOH 113 KOTOpbIX 5 3JIeMeHTOB, pacnOJIO)l(eHHbIX
c rnarOM Aj2, yrOJI CKaHl1pOBaHI1 3°
,l],aHHbIe pe3YJIbTaTbI 061>HCHHIOT rrpHqHHbI Toro, rrOqeMY 3TH JIerreCTKH Ha3Ba-
HbI JIerreCTKaMH KBaHTOBaHHH, a He ,l],JI. XOTR OHI1 Ha6JIIO,aaIOTCR rro,a yrJIaMI1 pac-
rrOJIOXeHHR ,l],JI, I1X BI1,a 11 aMrrJIHT)',aa RBJISIIOTCR <pyHKl(HRMH yrJIa CKaHl1pOBaHHR.
B TO BpeMR KaK ,l],JI B03HI1KalOT ,aaxe B OTcyrcTBHe CKaHHpOBaHI1S1, JIerreCTKI1 KBaH-
TOBaHHH <pa3bI 11 JIeneCTKI1 KBaHTOBaHI1R rro,apellIeTOK 6e3 CKaHHpOBaHI1R He rrORB-
IDIIOTCSI. I1x ypOBeHb B03paCTaeT C yBeJIHqeHl1eM yrJIa CKaHl1pOBaHI1S1.
,l],JIR y.narreHHbIX ,a11<ppaKl(110HHbIX JIerreCTKOB xapaKTepeH BbICOKHH ypOBeHb,
 
KOTOpbII1 MeHbllIe YPOBIDI OCHOBHoro .rryqa TOJIbKO 113-3a Me,lLJIeHHO MeIDIlOmeHCR
,al1arpaMMbI HanpaBJIeHHOCTI1 3JIeMeHTa. C ,apyroH CTOpOHbI, JIeneCTKH KBaHTOBa-
HI1R 06blqHO HaMHoro cJIa6ee, qeM OCHOBHOH JIyq, a KIDK,lI:bIH ,aonOJIHHTeJIbHbIH JIe-
rreCTOK KBaHTOBaHHR 3HaQHTeJIbHO MeHbllIe npe.n:bJ.nYll]:ero.
2.3.6. PaccI>a3MpoBaHMe neneCTKOB KBaHTOBaHMR:
nepeKpblBalOUJ.MeCR nOApeweTKM
Cym;ecTByeT HeCKOJIbKO cnoc060B pac<pa3HpoBaHHR (HapymeHHe cHH<pa3HocTH) JIe-
neCTKOB KBaHTOBaHHR <t>a30BpamaTeJIeH, JIyqllIHM H3 KOTOpbIX SlBJIReTCR MeTO,n ,no-
6aBJIeHHOH <t>a3bI [17, 10]. B 3TOM MeTo.ae <pa3bI 3JIeMeHTOB paCCQHTbIBalOTCR ,lLJIH
TaKOH pa3PMHOCTH <pa30BpamaTeJIH, KOTopaSi 06eCrreQHBarra 6bI ,nOCTaTOQHO Ma-
JIbIH ypOBeHb JIeneCTKOB KBaHTOBaHHH. 0603HaQHM 3TO QHCJIO pa3PMOB N. <l>a30B-
pamaTeJIH ynpaBJISIIOTCR Cl1rHaJIOM C MeHbllIHM QHCJIOM 6HT M. OCYJ..U;ecTBJIHIOTCH
reHepal(HSI H coxpaHeHHe pH,L(a CJIyqaHHbIx QHCeJI C pa3PMHOCTblO N 611T no O,l(HO-

b
rAa8a 2. OCHo8Hbie xapaKmepucmUKU aHmeHHblX peUlemOK
MY ,lLJ]:$1 Ka)I(JI:OfO <pa30BpaIl(aTeJISI. 3aTeM CJIyqaHHbIe qMCJIa Ta6JIMQbI YKOpaqMBaIOT-
CSI ,[(0 M 6MT M COXpaHSlIOTCSI OT,L(eJIbHO. llocJIe BbIqMCJIeHMSI 3HaqeHMH ynpaBJISlIO-
Il(MX pa3pSl,L(OB <pa30BpaIl(aTeJIeH ,L(JISI ,L(aHHOrO HanpaBJIeHMSI CKaHMpOBaHMSI K HMM
npM6aBJISlIOTCSI CJIyqaHHbIe N-pa3pSI.aHbIe qMCJIa, no O,L(HOMY K Ka)l(,[(OH ynpaBJISlIO-
Il(eH KO,L(OBOH rpyrrne <pa30BpaIl(aTeJISI. 3aTeM KO,L(OBbIe rpynnbI <pa30BpaIl(aTeJIeH
YKopaqMBalOTCSI ,L(O M 6MT, M M3 HMX BbIqMTalOTCSI CJIyqaHHbIe M-pa3pSl,L(HbIe qMCJIa
no O,L(HOMY ,L(JISI Ka)I(JI:OH KO,L(OBOH rpynnbI <pa30BpaIl(aTeJISI. llocJIe qero nOJIyqeH-
HbIe KO,L(OBbIe CMrHaJIbI MCnOJIb3yIOTCSI ,L(JISI ynpaBJIeHMSI <pa30BpaIl(aTeJISlMM. Pe3YJIb-
TaTOM TaKoro nO,L(XO,L(a SlBJISleTC}I pac<pa3MpOBaHMe JIeneCTKOB KBaHTOBaHM}I M He60-
JIbIIIOH pOCT Cpe,L(HerO 3HaqeHM}I orM6alOIl(eH 60KOBbIX JIeneCTKOB. Ba)I(Ho, qTO 3TOT
MeTO,L(, B OTJIMqMe OT HeKOTopbIX ,L(pyrMX, 06eCneqMBaeT HYJIeBOe Cpe,L(Hee 3HaqeHMe.
Cpe,L(HeKBan;paTMQHbIH YPOBeHb 60KOBOfO JIeneCTKa 3an;aeTC}I BbIpaxeHMeM
2
SLL - a
RMS - (1 _ 2 )N '
a elem
(2.44 )
f,L(e napaMeTp a = 1t / (.J32 M), aHTeHHa}l perneTKa MMeeT N elem 3JIeMeHTOB. Pa3pSl,L(-
HOCTb cPa30BpaIl(aTeJUI paBHa M, f,L(e, KaK M paHee, HaM60JIbrnMH pa3pSI.a COOTBeTCT-
ByeT 1t (CM. Ta6JI. 2.7).
Ta6JIHna 2.7. Pac<I>a3HpoBaHHe JIerreCTKOB KBaHTOBaHHH
Pa3pH,LUIOCTb a Cpe.nueKBMpaTJI1IIIWH ypOBeHb
.a30BpamaTeJIJI 6oKoaoro JIeneCTK8 (,lJ,6)
3 0.2267 -44.1
4 0.1134 - 50.1
5 0.0567 -56.1
He06xo,l(HMO MCCJIe,L(OBaTb, KaK pa60TaeT MeTO,l( pac<pa3MpOBaHM}I npH 60JIbIIIMX
3JIeMeHTax HJIH nO,l(perneTKax, O,L(HaKO CHIDKeHMe K03<P<PMQHeHTa YCHJIeHHSI He MO-
)l(eT 6bITb KOMneHCHpOBaHO. B e,L(MHCTBeHHOH cxeMe, 3HaQMTeJIbHO YMeHbmalOIl(eH
3TOT 3<p<peKT M YCTpaHSlIOIUeH rrOTeplO K03<P<PMQHeHTa YCHJIeHH}I, MCnOJIb3yIOTCSI
qaCTHqHO rrepeKpbIBalOIl(MeCSI nO,l(perneTKH (Mailloux, 1994). KaK rrOKa3aHO Ha
pMC. 2.29, BbIXO,l(HOH CMfHaJI Ka)I(,[(OrO 3JIeMeHTa pa3,l(eJISleTC}I Ha ,L(Ba HJIH 60JIee
CMrHaJIa. 3TO n03BOJISleT CBSl3aTb C O,l(HHM Ii TeM )l(e 3JIeMeHTOM ,l(Be HJIM 60JIee
KOH<pHrypaQMH nO,L(perneTOK. 3aTeM 3TM BbIXO,l(HbIe CHfHaJIbI rrO,l(perneTOK MOryr
6bITb CKOM6HHHpoBaHbI TaKHM 06pa30M, qT06bI 06eCneQHTb 3Q>Q>eKTHBHoe cnan;a-
HHe aMrrJIHTY,l(bI K KpaSlM paCKpbIBa. B pe3YJIbTaTe ypOBeHb JIerreCTKOB KBaHTOBaHH}I
CHM)I(aeTCSI M BOCCTaHaBJIHBaeTCSI K03<P<PMQMeHT YCHJIeHM}I. K CO)l(aJIeHMIO, cxeMa
B036y)1(,L(eHM}I B 3TOM CJIyqae }lBJISleTCSI OQeHb CJIO)I(HOH ,l(IDKe ,L(JISI JIHHeHHOH aHTeH-
HOR perneTKH. <l>opMa ,L(HarpaMMbI HarrpaBJIeHHOCTH 3JIeMeHTa 3HaQHTeJIbHO YMeHb-
rnaeT BJIHSlHHe JIerreCTKOB KBaHTOBaHIDJ:, nOCKOJIbKy K03<PcPHQHeHT YCHJIeHHSI HMe-
eT MHHHMaJIbHOe 3HaQeHHe rrpM rrpe,l(eJIbHOM yrJIe CKaHHpOBaHHSI, ,L(JISI KOTOpOfO
ypOBeHb JIerreCTKa KBaHTOBaHMSI HaH60JIbrnHH.
-

2.4. Hanpa8JleHHOCmb 
I
.
I
,
I
I
I
I
.
I
I
I
I
.
,
fH6pH.aHaH
cxeMa
CHCTeMa ct>OpMHpoBaHHR Ll.H
Pac. 2.29. nepeKpbIBalOll{HeCH IIo.n;perneTKH
2.4. HanpaBneHHocTb
2.4. 1. HanpaBneHHocTb nMHeMHoM aHTeHHoM peweTKM
K03<P<PI1T(HeHT HarrpaBJIeHHOrO ,l:(eHCTBHR (KH,1J) JIHHeHHOH aHTeHHOH pemeTKH,
KaK 06bIqHO, rrpe,l{CTaBJIReT C060H rrJIOTHOCTb rrOTOKa 3HeprHH B HarrpaBJIeHHH HH-
TepeCYI()J,l(ero yrJIa, ,l:(eJIeHHYIO Ha ycpe,l:(HeHHyIO rrpOHHTerpHpOBaHHYIO no c<l>epe
,l:(HarpaMMY HarrpaBJIeHHOCTH no MOII.J:HOCTH. npH yrJIe 8, OTC1JHTbIBaeMOM OT HOp-
MaJIH K pemeTKe, KH HMeeT BH,l:(
G=
21t 1t1 2
J J I F(8,<p)12 cos8d8d<p
o -1t I 2
4nl FI2
,
(2.45)
r,l:(e G HCrrOJIb3yeTcR ,l])UI 0603HaqeHHH KH, XOTH HM QaCTO 0603HaQaeTCH TaIOKe KO-
3<P<PHnHeHT YCHJIeHHH (KY). nOCKOJIbKy pe3HCTHBHbIe nOTepH TaIGIX aHTeHHbIX pe-
meTOK, KaK npaBHJIO, HaMHoro MeHbllIe, QeM nOTepH Ha corrpOTHBJIeHHe H3JIyqeHHIO,
K03<P<PHUHeHT YCHJIeHHH H KH no cym:eCTBY paBHbI, eCJIH He yqHTbIBaeTCH BJIHH-
HHe 3<p<peKTOB paCCOrJIaCOBaHHH HMne,l:(aHCOB. )J)rn H30TporrHbIX 3JIeMeHTOB MHO)I(H-
....
TeJIb aHTeHHOH pemeTKH oceCHMMeTpHQeH, QTO cpa3Y)l(e npHBO,l:(HT K ynpOII.J:eHHIO:
G = 21 Ell (2.46)
1t/2
JIF(8)12 cos8d8
-1t/2
I1crroJIb3YH 3,l:(eCb aHaJIHTHQeCKOe BbIpaxeHHe .LLJIH ,l:(HarpaMMbI HarrpaBJIeHHOCTH
.... ....
3KBH,L(HCTaHTHOH aHTeHHOH perneTKlf rrpH HOpMaJIbHOM H3JIyqeHHH, nOJIyqaeM
N2
G = (2.47)
1t/2 sin2 1 Nkdu
J 2 cos8d8
sin 2 1 kdu
o 2


rlla8a 2. OCHo8Hble xapaKmepucmUKU aHmeHHblX pewemOK
3aMeHa Bcex yrJlOBbIX nepeMeHHbIx Ha u ,QaeT
G = N 2 d / A
d/Asin 21 Nkdu
J 2 au
sin 2 1 kdu
o 2
(2.48)
3TO BbIpa)l(eHHe ,QonycKaeT HHTerpHpoBaHHe C nOMOIIJ;blO pa3JIO)l(eHH B pmx:
N 2 d / A
G
d/A [ N-I ] d 2d N-I
- J N+2L(N-n)cosnkdu au=N-+- L(N-n)sincnkd. (2.49)
o n= I A A n= I
Pe3YJIbTHPYIOIIJ;HH KH,LJ; HMeeT CJIe.n;yIOIIJ;HH BlI,[(, r.n;e sinc x 0603HaqaeT sin(x)/x
N2
G = N-I (2.50)
N + 2 L(N - n)sincnkd
n=l
Ha pHC. 2.30 H306pa)l(eHa 3aBMCHMOCTb K03<P<PHUHeHTa HanpaBJIeHHOCTM aH-
u u
TeHHOH perneTKH OT rnara pacnOJlO)l(eHH H3J1yqaTeJIeH LUI pa3JIHQHbIX perneTOK,
co.n;epXaIIJ;HX OT 2 .n;o 24 3JIeMeHTOB. OTMeTHM, QTO rrpH rrOBJleHHH rrepBoro .n;H<p-
paKIJ;HOHHOro J1eneCTKa HanpaBJIeHHOCTb pe3KO YMeHbllIaeTC .n;o 3HaQeHH, npH-
6JIH3HTeJIbHO paBHoro 3HaQeHHIO npH nOJIYBOJIHOBOM llIare.
18
4
--
-- ,
/  1
.J'
/ v
-
----- \
/ / ,
./ N=24
/ / / v- \ \.--..

 V v ,
J / .- ..... \ 16.....
V / / / - \ \'-- ....-

23---
I / / / iI""""  \\ '--

/ II , V v \ \
/ 8
-
1/ V / / - \
/ ""'" 6
 \.
II I / /  '\ '- -----
J r-"
 ...........
, 'I J 1/ , V V """"- "
/ "- 4
I '/ / / V , '" "--
....3
II / / / .,- ,
IJ ""-..
, r/ J 1/ V -.......... -...2
-
j j
r'// / V

 /'
16
14
12
 10

--

:I::
 8
6
2
o
o
0.2
0.4
0.6
df).,
0.8
1
1.2
PHC. 2.30. AHTeHHaH pemeTKa, COCTOHll.{aH 113 1130TPOllHbIX 3JIeMeHTOB

2.4. Hanpa6JleHHOCmb 
Ha 3THX rpa<pHKax He nOKa3aHO, qTO npH ,n;aJIbHeHmeM YBeJIHqeHHH mara
KH,[( B03paCTaeT .[(0 Tex nop, nOKa He nORBJIReTCR BTOpOH ,a1f<ppaKUIfOHHbIH JIe-
neCTOK, B TOqKe B03HllKHOBeHMR KOTOpOfO Ha6JIIo,aaeTCR BTOpOH cnan; KHLJ; ,ao
3HaqeHHR, npllMepHO paBHoro Ha6JIIO,aaeMOMY npM nOJIYBOJIHOBOM HHTepBaJIe [5].
no cymeCTBY, KH.n. paBeH N BCRKMH pa3, Kor,aa mar RBJIReTCR KpaTHbIM 0.5A.
He3HaqllTeJIbHbIe KOJIe6aHllR HIDKe nllKOBOfO 3HaqeHllR KH,[( onpe,n;eJIRIOTCJI TeM,
COBnan;aeT JII1 rpaHl1qHOe 3HaqeHMe peaJIbHOrO Me)l(3JIeMeHTHoro paCCTOJIHHJI C
nHKOM 60KOBoro JIeneCTKa MJIM C ero HYJIeM. TaKoe nOBe,aeHHe MO)l(eT TaIOKe
06'bJICHJITbCJI 3<p<peKToM H3MeHeHMR B3aHMHOH CBJI3M Me)l(,L{Y 3JIeMeHTaMH npl1 113-
MeHeHllll mara. Pe3YJIbTaT CYMMHpOBaHll.H B (2.50) npe,n;CTaBJIJIeT C060H B3BemeH-
Hyro CYMMY B3aHMHbIX conpOTllBJIeHllH, nOCKOJIbK)' 3<p<peKTllBHoe B3aHMHoe co-
npOTllBJIeHHe Me)l(,L{y ,aBYMR M30TponHbIMIf 1f3JIyqaTeJlJIMH, pacnOJlO)KeHHbIMIf C
HHTepBaJIOM s, paBHO rrpOCTO 120 sinc ks. ,[(JIJI yrJIOB CKaHHpOBaHHR, y,aaJIeHHbIX
OT HanpaBJIeHHJI, neprreH,lU1K)'JI.HpHOrO paCKpbIBY aHTeHHbI, K03<P<PI1UHeHT Ha-
npaBJIeHHOCTH HMeeT BIf,a
G = N-I
N + 2 L (N - n) sinc nkd cos(nkd sin e 0)
n=l
N2
(2.51 )
3TO BbIpa)KeHl1e onlfCbIBaeT H3MeHeHll.H KH,[( B6JII1311 TOqKH nOJIBJIeHIfJI ,alf<p-
paKl(IfOHHOro JIeneCTKa, aHaJIOrHqHbIe H306pIDKeHHbIM Ha pllC. 2.30. qacTHbIM CJIY-
qaeM JIBJIReTC.H HanpaBJIeHlfe B,n;OJIb OCM aHTeHHbI, M.H KOToporo KH,[( paBeH
N2
G = N-I
N + 2 L (N - n) sinc 2nkd
n=l
(2.52)
3TOT pe3YJIbTaT COBrran;aeT C pemeHHeM ,aJUI aHTeHHOH pemeTKH 60KOBoro 113-
JIyqeHIfJI C nOJIOBMHHbIM marOM. AHaJIOflfqHO, npH mare, KpaTHOM qeTBepTIf Mll-
HbI BOJIHbI, KH,[( paBeH N.
TIpll nOJIYBOJIHOBOM mare apryMeHT sinc <PYHKl(1l1l B ypaBHeHllll (2.50) paBeH
nn, qTO .n:eJIaeT KH,[( He 3aBlfCJIII(lfM OT yrJIa CKaHHpOBaHIf.H If paBHbIM N. B TO )Ke
BpeM.H Y paBHOMepHO B036y)1()];aeMOro HerrpepbIBHoro JIHHeHHOro HCTOqHHKa KH,[(
B oceBO HanpaBJIeHIfH paBeH 4L/A, a B HanpaBJIeHHH, nepneH,aHK)'JI.HpHOM pac-
KPbIBY aHTeHHbI, - 2L/A.
TIpH 60JIbmlfX N MaKCllMaJIbHOe 3HaqeHlfe KH,[( 60JIblliHX aHTeHHbIX pemeTOK
Ha6JIIO,aaeTCJI npM mare HeCKOJIbKO MeHbIIIe A B HanpaBJIeHIfIf, nepneH,aHK)'-
JIJIpHOM paCKpbIBY aHTeHHbI, H HeCKOJIbKO MeHbme A/2 B oceBOM HanpaBJIeHHH;
KH,LJ: npH 3TOM npll6JIH)I(aeTCR K 2N. TIpH BbIpa)KeHI1If KH,[( qepe3 ,lI)IHHY pac-
KpbIBa L = (N - 1 )d, OqeBI1,aHO, ({TO ero MaKCMMaJIbHOe 3HaqeHlfe npH6JIIf)KaeTC.H
....
K COOTBeTCTBYIOIl(eMY 3HaqeHHIO ,aJIR HenpepbIBHoro JII1Hel1HOrO I1CTOqHHKa, a
HMeHHO: 2L/A B HanpaBJIeHHI1, nepneHJJ:HK)'JI.HpHOM paCKpbIBY aHTeHHbI, H 4L/A B
oceBOM HanpaBJIeHHIf.
Y aHTeHHOH peIIIeTKll H30TponHbIX 3JIeMeHTOB CO cnan:alOlI(HM aMnJlIfTYlIHbIM
pacnpe.n:eJIeHHeM no paCKpbIBY MHO)l(MTeJlb HanpaBJIeHHOCTH HMeeT BI1,lJ, (CM. (2.1»
F(u) = L An expUkd(n - l)u].
(2.53)


rlla6a 2. OC1l061lble xapaKmepucmUKU allmellllbLX pelUemOK
IIpH nO,l(CTaHOBKe 3Toro BbIpIDKeHHR B ypaBHeHHe (2.46) H HHTerpHpOBaHHIf
nOJIyqaeM ,aJUI KHL(
G= N N
LLAnA;' sinc(n - m)kd
n=l m=l
N
LAn
n=l
2
(2.54)
,LJ;IDKe IIPH KOMTIJleKCHbIX K03<P<PHl(HeHTaX B036y)K,[{eHHR qHCJIHTeJIb H 3HaMeHa-
TeJIb ,l(eticTBHTeJIbHbI. ,LJ;JIR aHTeHHoti perneTKH C paBHOMepHbIM B036y)K,[{eHHeM Bce
An = 1, qTO Be,aeT K ypaBHeHHIO (2.50). ,lLrrR CHMMeTpHqHbIX aHTeHHbIX pemeTOK
C}'MMHpOBaHHe B BbIpIDKeHHH ,lUIR KHL( MO)l(eT IIpOBO.lUiTbCR no nOJIOBHHe aHTeH-
HOM perneTKH. HanpHMep, IIPH qeTHbIX N KHL( npH06peTaeT BH,lJ;
): 2
2 An
n=l
G= WW ·
L L An A;' [sinc(n + m -l)kd + sinc(n - m)kd]
n= 1 m= 1
(2.55)
2.4.2. KHA 8HTeHHOM peweTKM,
- -
COCTOReM M3 KOpOTKMX AMnoneM
AHTeHHbIe perneTKH, COCTORIUHe H3 KOpOTKHX ,l(HnOJIeti, HHTepeCHbI, rJIaBHbIM 06-
pa30M, IIOTOMY, qTO BbIpa)l(eHHR ,l(lliI KH,lJ; 1I0nYCKalOT HHTerpHpOBaHHe B aHaJIHTH-
qeCKOM BH,l(e. HanpaBJIeHHOCTb H3JIyqeHI1R napaJIJIeJIbHbIX KOpOTKHX ,l(HnOJIeM 3a-
BHCHT OT yrJIa <1>; B ypaBHeHl111 ,lUIR KHL( I1CnOJIb3yeTcR COOTBeTCTByJOlI(aR
,l(HarpaMMa HanpaBJIeHHOCTH 3JIeMeHTa
1(8, <1» = .J I - cos 2 8 sin 2 <1>.
(2:56)
JIexaIUHe Ha O,aHOM JIHHHH KopOTKHe ,aHnOJIH 06eCneqHBalOT HanpaBJIeHHOCTb
B I1JIOCKOCTH aHTeHHOM perneTKH; COOTBeTCTByJOIUaR ,l(HarpaMMa HanpaBJIeHHOCTH
3J1eMeHTa HMeeT BH,lJ; cos 8. Pe3YJIbTHPYIDIUHti KHL( JIHHetiHoH cHHij>a3HoH aHTeH-
HOH perneTKH C paBHOMepHbIM B036y)K,[{eHHeM, COCTORIUeH H3 lIapaJIJleJIbHbIX KO-
....
pOTKHX ,l(HIIOJleH, B HanpaBJIeHI1H, neplIeH,aHKYJIRpHOM paCKpbIBY, paBeH
G = 3N2 / 2 .
N + 3I(N _ n) [ sinnkd + cosnkd _ s innkd ]
n=l nkd (nkd) 2 (nkd) 3
(2.57)
B qaCTHOM CJIyqae nOJIYBOJIHOBOrO Me)l(3JIeMeHTHOrO paCCTORHHR 3TO BbIpIDKe-
HHe npH06peTaeT BH,LJ:
G = 3N2 / 2 .
l(-l)n(N - n)
N+3LJ
n=l ']t2 n 2
(2.58)

r
I
2.4. Hanpa6lleHHOCmb 
KopOTKHe .aHnOJIH, RJIH IUeJIH, JIeXaIUHe Ha O,l(HOH npRMoH, o6eCneQHBalOT
aHaJIOrHqHYID HanpaBJIeHHocTb:
G = 3N2 / 2 .
N _61(N -n) [ COSnkd _ S innkd ]
n=l (nkd) 2 (nkd) 3
(2.59)
11 B 3TOM qaCTHOM c.rryqae IIO.rryBOJIHOBOrO MeX3JIeMeHTHOrO paCCTORHHR, HMeeM
G = 3N2 / 2
N 1 .
 (N - n)(-I)n
N -6 L.J
n=l 1t 2 n 2
(2.60 )
,aJIR 06eHX opHeHTaI.J;HH ,l(HIIOJIeH B3aHMHoe conpOTHBJIeHHe onHCbIBaeTC.H TPH-
rOHOMeTpHqeCKHMH qJIeHaMH B cKo6Kax, YMHoxeHHbIMH Ha KOHCTaHTY. HecMoTpR
Ha npOCTOTY 3THX BbIpaJKeHHH MR KH,lJ., KopOTKHe 3JIeMeHTbI pe,nKO HCnOJIb3YIDT-
CR B aHTeHHbIX perneTKax H3-3a HX BbICOKOH peaKTHBHOCTH (peaKTHBHOH npOBO,l(H-
MOCTH), HH3Koro COnpOTHBJIeHIDI H3JIyqeHHR H Y3KOH nOJIOCbI nponYCKaHIDI. TIOq-
TH Bcer.aa HCnOJlb3YIDTCR IIO.rryBOJIHOBbIe HJIH pe30HaHCHbIe 3JIeMeHTbI. MOXHO
npe,l(nOJIOXHTb, qTO KH,lJ. 06bIqHOH ,nHnOJIbHOH, IUeJIeBOH HJIH MHKpOnOJIOCKOBOH
u
aHTeHHOH perneTKH MO)I(HO BblqHClliITb MeTO,l(OM, HCnOJIb3YlOIUHM B3aHMHbIe co-
npOTHBJIeHHR, BnepBbIe npe,l(JlOXeHHbIM B pa60Te [2]. 3TO 3aKJIIOQeHHe OKa3bIBaeT-
CR BepHbIM H 6y.aeT 06C)')KlI:aTbCR HlUKe.
2.4.3. KHA aHTeHHoM peweTKM,
-
COCTORU4eM M3 pe30HaHcHbix 3neMeHTOB
KH)J. 6Y,l(eT BbIBe,l(eH ,lUUI JIHHeHHOH cHH<pa3HoH aHTeHHOH perneTKH C paBHOMep-
HbIM B036)')Kl1:eHHeM, COCTORII.J;eH H3 nO.rryBOJIHOBbIX ,l(HnOJIeH npOH3BOJIbHOH OPH-
eHTaI.J;HH, B HanpaBJIeHHH, nepneH,nHKYlliIpHOM paCKpbIBY aHTeHHbI. KaK H paHee,
KH)); B HanpaBJIeHHH MaKCHMaJIbHOfO H3.rryqeHHR npe,l(CTaBlliIeT C060H OTHorneHHe
u u
MaKCHMaJIbHOH nJIOTHOCTH MOIUHOCTH K BXO,nHOH MOIUHOCTH:
G = 41tr 2 EoHo .
P
(2.61 )
J],JIR JIHHeHHOH perneTKH nOJIyaOJIHOBbIX ,l(HnOJIeH MaKCHMaJIbHOe 3HaqeHHe
nOJIR Eo
60
Eo =- LIn;
r
H = Eo
o 1201t'
(2.62)
3.aeCb In - TOKH .aHnOJIeH. TIpH paBHOMepHOM B036)')Kl1:eHHH Bce In = 1 0 , H qHCJIH-
TeJIb paBeH
120[LI n]2 = 1201 6 N2 .
(2.63)
BXO,l(HaR MOIUHOCTb
P = LRe(InV n *) = LIn LI;"Rm = 16 LLRnm,
f,l(e Rnm B3aHMHoe MeX3JIeMeHTHoe COIIpOTHBJIeHHe.
(2.64 )


rJlaea 2. OCHoeHble xapaKmepucmUKU aHmeHHbLX peUlemOK
B pe3YJIbTaTe HMeeM ,l(JIR KH)J;
G = 120N2
N N
L L Rnm
n=l m=l
120N2
(2.65)
N-I
RoN + 2 L(N - n)Rn
n=l
3J:(eCb Ro - co6cTBeHHoe conpOTHBJIeHHe, a Rn - B3aHMHoe conpOTHBJIeHHe Me)l(-
J:(Y J:(HTIOJI5IMH, HaXOJ:(5IIUHMHC5I Ha paCCTORHHH nd ,n:pyr OT J:(pyra. KH)J; JIHHeHHbIx
....
aHTeHHbIX perneTOK, COCTORII(HX KaK H3 napaJIJIeJIbHbIX nOJIYBOJIHOBbIX J:(HnoneH,
.... ........
TaK H ,n:HnOJIeH, JIe)l(alI(MX Ha OJ:(HOH npSlMOH, BbIQI1CJIeH C nOMOlUblO KOMrraKTHbIX
H 3<P<l>eKTHBHbIX KOMrrbIOTepHbIX aJIfOpHTMOB paCQeTa nOJIHbIX B3al1MHbIX HMne-
,n:aHCOB [6, 8]. Ha pHC. 2.31 rrpe,n:CTaBJIeHbI pe3ynbTaTbI ,l(JI5I perneTOK C rrapaJIJIeJIb-
HbIMI1 ,n:HnOJUlMI1, a ,l(JISI aHTeHHblX perneTOK C KOJIJIHHeapHbIMH J:(HrrOJISlMI1 3HaQe-
HI1R KH)J; OTpa)l(eHbI Ha pHC. 2.32.
20
8
--
___ '1
/'"
V ,
/ /
 
V / /
I // V
I V / / \ V
/ IV /V /-\ \ \ ;Y
I J' / /" V' \ \'-' 
 /I V / ____/" \'-"
1:/ / /!/ V - \ ''-V
// Jf / / // '\ \ '-..V
I' /I V V \.  4
/ / / / /-, " '"3""-
, / I I / ", "
4 rJV/ /
u v .../
,
18
16
14
.J"',
N=2
 12
t::t
---
t::t
:t
 10
6
-
2
o
0.2
0.4
0.6
dlA.
0.8
1
1.2
PHC. 2.31. AHTeHHaH perneTKa, COCToHIUaH 113 rrapaJIJIeJIbHbIX nOJIYBOJIHOBbIX .D:l1nOJIeH
OTMeTHM, qTO ,l(JISI aHTeHHOH perneTKI1, COCTORlI(eH H3 napaJIJIeJIbHbIX J:(I1TIOJIeH,
xapaKTepHO na,n:eHl1e KH,l:(, 06YCJIOBneHHoe J:(11<ppaKl{110HHbIMH JIeneCTKaMH, aHa-
JIOfl1QHOe Ha6JIIOJ:(aeMOMY ,l(JIR 1130TponHbIX 3neMeHTOB. B o6ol1x CJIyqa5IX I1MeeT
MeCTO CHJIbHaH B3al1MHaH CBR3b. O,n:HaKO JUIH KOnJIMHeapHbIX perneTOK B3aHMHaR
CBR3b MeHbrne, H n03TOMY Y HI1X MeHee 3aMeTeH 3<p<peKT BnHHHHR J:(H<ppaKl{HOH-
HbIX JIeneCTKOB. B TO )l(e BpeMR, perneTKa 113 napaJIJIenbHbIX 3JIeMeHTOB HMeeT

or
2.4. Hanpa8JleHHOCmb 
18
8
v - N = 24
./ -......-..
'/ 
.
.
./
/ , / V--  
/ r - 
/   .............
/ / '/ 
./
, V ,,- r--!.
/ / ,,/ ..........- ...........
V / V / /' 
../  ............
/ / / / / 
./

Ii VI / / I"'" 
 -
 .JI
I I. V / V V ,
3
J  .-..-
I II / / / / / /
/J '/ / V /' 2
J
./ ---- 
IJ II , ,  V ,,-
/ / /
'I '//  , '/ "
./
  ,......-
-r
16
14
12
-


--
 10
::x=

6
4
0.6
dll
PHC. 2.32. AHTeHHaH pemeTKa, COCTOHmWI 113 KOJIJIIIHeapHbIX nOJIYBOJIHOBbIX .lU1nOJIeti
2
o
0.2
0.4
0.8
1
1.2
nHKOBoe 3HaqeHHe KH,LJ: npHMepHO Ha 3 )(1) 60JIbme BCJIe)(CTBHe cyxeHHH JIyqa
v
B nOnepeqHOH nJIOCKOCTH.
TIpH rrOCTORHHOM mare H KOJIHqeCTBe 3JIeMeHTOB MaKCHMYM KH)]. Ha6JIIO)(aeT-
CH He B HanpaBJIeHHH, nepneH,LJ;HKYIDIpHOM paCKpbIBY aHTeHHbI, HJIH no OCM aHTeH-
HbI. 3TO 06Cy)I()];aeTC.H B rJIaBe 9, nOCB.H:rn;eHHoH CBepXHanpaBJIeHHbIM aHTeHHbIM
pemeTKaM.
2.4.4. KHA nnocKoM aHTeHHoM peweTKM
Bblpa)l(eHHe MH KH)]. rrJIOCKOM aHTeHHOH pemeTKH MMeeT BH,lJ;
41[/:2
o
(2.66)
G=
21t 1t
f f F2 (e) sine ded<p
o 0
)].JIH perneTKM, CocToHll.{eM H3 H30TponHbIX 3JIeMeHTOB, pacnOJIO)l(eHHbIX no
rrpHMoyroJIbHoM ceTKe, H C JIyqOM, HanpaBJIeHHbIM nepneH,LJ;HKYJI.HpHO paCKpbIBY
aHTeHHbI, qHCJIHTeJIb BbIpa)l(eHHH MH KH)); paBeH
[ w 2 ] 2
47t !:t!::.. Anm ·
(2.67)

 DlO8a 2. OcH08Hble xapalCmepucmU1CU aHmeHHblX pewemolC
B 3HaMeHaTeJIe F npe,n:cTaBJUleT C060H qeTbIpeXIq)aTHyro C}'MMY:
p2 = L L L L AnmApq cos(2n -1)a cos(2m -1)13 cos(2p -1)a cos(2q -1)13,
n m p q
(2.68)
r.n:e a = (1td x /'A)u If  = (1td y /'A)v. MHoroKpaTHoe IfCnOJIb30BaHHe 1'pHrOHOMeTpHQe-
CKHX TO)l():leCTB n03BOJI5IeT npeo6pa30BaTb npOH3Be,n:eHHe qeTbIpex KOCHHYCOB B
C}'MMY BOCbMH qJIeHOB, r.ae BO BceB03MOXHbIX KOM6HHaUHRx npHcyrcTBYIOT ueJIO-
qHCJIeHHbIe MHOXHTeJIH A H B. I1pH 3TOM o6m;HH qJIeH HMeeT BH,n:
1
- cos(Aa + B),
8
(2.69)
a 3HaqeHHR A H B paBHbI
A= { n+ p -\
n-p
B = { m + q -1.
m-q
(2.70)
3TO BbIpIDKeHHe MO}KHO npeo6pa30BaT b CJIe,n: yrom;HM o6pa30M
COS (a coscjl + b sincjl) = cos[ .Ja 2 + b 2 sin ( cjI + arctan  ) 1
(2.71 )
HHTerpHPYR ,n:aHHoe ypaBHeHHe no «1>, nOJIyqaeM:
r cos[ .J a 2 + b 2 sin( cjI + arctan  )] dcjl = 27t.l o (.Ja 2 + b 2 ).
(2.72)
nO.rryqeHHbIH pe3YJIbTaT ,aonYCKaeT HHTerpHpOBaHHe no «I>
7t
2 J Jo (a 2 + b 2 ) sine de = 41t sincC.
o
(2.73)
r,ae  A 2 + B 2 = C sin e. HaKoHeu, KH,a MoxeT 6bITb BbIpIDKeH Qepe3 QeTbIpex-
KpaTHyro CYMMY:
4( Anm r
D= WW'V..2 ·
L L L LA nm A pq [SI + S2 + S3 + S4]
n=1 m=1 p=1 q=1
(2.74)
r,n:e
SI = sinc 21t (n + p -1)2 d; / 'A 2 + (m + q -1)2 d; / 'A 2 .
S2 = sinc 21t (n + p -1)2d; / 'A 2 + (m -q)2d; / 'A 2 .
S3 = sinc 21t (n - p)2 d; / 'A 2 + (m + q -1)2 d; / 'A 2 .
S4 = sinc 21t  (n - p)2 d; / 'A 2 + (m - q)2 d; / 'A 2 .
(2.75)

2.4. Hanpa8/leHHOCmb 
K coxarreHlllO, ,Z:(aHHbIH pe3YJIbTaT 3aMeTHO He ynpOll.{aeTCR B CJIyqae paBHO-
MepHoro B036eHllH llJIll npu IIOJIyaOJIHOBOM rnare. qJIeHbI Si paBHbI HYJIIO TOJIb-
KO ,l(JIH Crrel(llaJIbHbIX MHoxeCTB l(eJIbIX qUceJI, rrOCKOJIbKY qJIeHbI, onllCbIBalOll.{Ue
v
B3allMHbIll llMrrel1aHC, KaK npaBUJIO, He HYJIeBble.
XOTR nOJIyqeHHoe ypaBHeHue ,LIJIR KHLI. npUMeHI1MO B CJIyqae npRMoyrOJIbHOH
AP C rrpHMoyrOJIbHOH ceTKOH, OHO JIerKO MOl1l1cPUl(llpyeTcR ,l(JIR ,Z:(pyrllx KOH<Pllry-
paUllH. K npllMepy, ,lJJIH TIJIOCKOH ,aB)'MepHOH AP, B KOTOpOH BOJIHOBo,aHbIe 3JIe-
MeHTbI 06'be,allHRIOTCH B anepType Ha pa3JIllQHbIX paCCTOHHllHX, OHO pernaeTCR ny-
TeM KoppeKl(llll npe,aeJIOB CYMMl1pOBaHllR. OHO rrpllMeHI1MO TaIOKe K perneTKaM C
l1pyrllMH Bll,[(aMll ceTOK, HarrpllMep, reKCarOHaJIbHbIMll.
B 60JIbllIllHCTBe CJIyqaeB, )])IH KH.il. I1JIOCKOH aHTeHHOM perneTKll rrpHXOl1llTCR
llCrrOJIb30BaTb arrnpOKCllMaUHI1. HarrpHMep, K03<P<PHUlleHT HarrpaBJIeHHOrO l1CHCT-
BllH npH6JII1)I(eHHO paBCH
G -- 2G x G y ,
(2.76)
r,ne G x II G y - KH,L( JIHHeMHbIX perneTOK B,aOJIb x II Y oceM. K03<P<PllUlleHT 2 06ec-
v
rreqllBaCT xopOllIee COBIIa.n;eHI1C C pe3YJIbTaTOM TOqHOrO paCqeTa KBan;paTHOll aH-
TeHHOM pcrneTKll [5]; OH TaIOKe yqllTbIBaeT, QTO Y3KHH JIyq ll3JIyqaeTcH TOJIbKO B
Ol1HY CTOPOHY.
TIpel1bIJJ:Yll.{llR paCqeT rrpOll3Bo,allJICH ,lUIH KH,L( nJIOCKOR AP, COCTOHll.{eH 113
ll30TporrHbIX 3JIeMeHTOB. KH,lJ. AP, COCTORll.{eM ll3 pearrbHbIX ll3JIyqaTeJIeH, MoxeT
6bITb BblqllCJIeH, eCJIll BbIqllCJIReTCH B3allMHbIH I1Mrre,aaHC Me)f(,Il;y JII06bIMll ,aBYMH
3JIeMeHTaMll. CJIel1YH MeTOl1Y, onllcaHHOMY B pa3l1eJIe 2.4.3, nOJIyqaeM 06ll.{)'IO <pop-
MYJIY)])lH KH,L(
D = I2{ Anm r
LLLLAnmApqRnmpq'
n m p q
(2.77)
3l1eCb C)'MMl1pOBaHHe rrp0I13B0l1HTC5I rro BceM 3JIeMeHTaM nm, a R nmpq rrpe,nCTaB-
JIHeT C060R B3allMHoe corrpOTllBJIeHHe Me)l()];y nm II pq 3JIeMeHTaMll.
npll6JII1)I(eHHOe rrOHHMaHlle 3<P<l>eKTllBHoCTH paCKpbIBa IIJIOCKOM AP MoxeT
6bITb YCTaHOBJIeHO rrpH paccMoTpeHHH KH,L( paBHoMepHo B036aeMoM I1JIOCKOH
pellIeTKll. TIYCTb paCKpbIB Haxo,aI1TC5I B y, z-rrJIOCKOCTll c<l>epHqeCKOH CllCTeMbI KO-
op.nllHaT, B KOTOpOM B03MO)I(Ha 3aMeHa sin e Ha cos e. HanpaBJIeHl1e HOpMaJIll K
paCKpbIBY aHTeHHbI 3a.n;aeTCH yrJIaMll eo = n12, <1>0 = O. llpocTpaHcTBeHHbIH MHO)l(ll-
TeJIb F = sinc 1tU sinc nv, r.ne
L
u = -(cosS -cosSo);
A
w . S . th
V = - SIn SIn 'f.
A
(2.78)
npel1rrOJIaraeTCH, qTO CKaHMpOBaHlle npOllCXOl1I1T B nJIOCKOCTll <1>0 = 0, qTO ,[(JIH
KH,L( ,Z:(aCT
G=
21t 1t/2
J J F2 sinSdSd<p
o -1t / 2
4n
(2.79)


rJla6a 2. OCHo6Hble xapaKmepucmUKU aHmeHflblX pewemOK
I1HTerpaJI no <I> ynpomaeTcSl nyreM 3aMeHbI nepeMeHHoH Ha v. BBO,l(HTCR He06-
u
XO,UHMbIH KOCHHYC, nOCKOJIbKY OH, no cyu.I;ecTBY, paBeH e,l(HHHue no OCHOBHOMY
JIenecTKY )J,JIH 60JIblllHX pacKpbIBOB. ,lLrrR yrJIOB, f,[(e HHTeHCHBHOCTb 60KOBOfO JIe-
neCTKa HH3Ka, norpelliHocTb 60JIbllIe. 3TO ,[(aeT npH6JIH:>ICeHHOe 3HaqeHHe HHTerpa-
JIa no <I>
nl2 A
J F 2 d<p ::: ·
-n12 W sin 8
(2.80)
Tenepb KH,[( npM6JIM)I(eHHO paBeH
41t ,...,  I n sin 2 1tU d8.
G W 1t 2 U 2
o
(2.81 )
AHaJIOfMqHaR 3aMeHa nepeMeHHOH U npHBO,[(HT K pe3YJIbTaTY [11], npHMeHHMO-
MY npH YCJIOBHH MaJIOH llIHpHHbI JIyqa B 06eHX ITJIOCKOCTHX:
G ,..., 41tL W sin 8 0 .
A2
(2.82)
B03BpamaRCb K OTCqeTY YfJIa e OTHOCHTeJIbHO HOpMaJIH K llJlOCKOCTH aHTeHHOH
pellIeTKM, OTMeqaeM, qTO 3<p<peKTMBHaR nOBepXHOCTb aHTeHHbI (3<}><}>eKTMBHaR nJIO-
II.J:Mb paCKpbIBa, effective aperture ) M3MeIDIeTCR KaK cos 8 0 . O.l1HaKO, M3-3a paCIlIM-
peHHH JIyqa npM CKaHHpOBaHHM, npH6JIH:>ICeHHe CTaHOBMTCH HeCnpaBe,ll)lHBbIM. IIpH
yrJIax B6JIH3H oceBoro HanpaBJIeHHH HCnOJIb3yeTcR Ta :>ICe annpOKCHMaQH.H no no <1>,
HO ,LlJIR HHTerpaJIa no 8 annpOKCMMaUMR OTJIMqaeTCH. TIYCTb
L
u =-(8+8 0 )(8-8 0 ),
2A
(2.83)
QTO ,[(aeT B6JIM3H oceBoro HanpaBJIeHHH
41t _ '),,.2 1 sin 2 1tU duo
G LW 0 1t2U2  (2AU/ L)2 -8
(2.84)
B oceBOM HanpaBJIeHHM pe3YJIbTaT MMeeT BH)].
G - 3-J21t WL .
A Iv
(2.85)
Ha pHC. 2.33 M306pa)l(eHa 3aBHCHMOCTb 3<}><}>eKTMBHOH nOBepXHOCTH aHTeHHbI
OT yrJIa CKaHHpOBaHMR B rJIaBHOH nJIOCKOCTM, OTKY,[(a MO)l(eT 6bITb onpe.neJIeH ,l(Ha-
na30H npHMeHMMOCTH <PYHKI..{HH cos 8 0 )J,JIR 3<}><}>eKTHBHoCTM paCKpbIBa. 3HaqeHMe
cos 8 0 CHH)KaeTCH .no 3HaqeHMR, Ha6JIIO,[(aeMoro B HanpaBJIeHHH OCM AJIH
3
cos 8 0 = .
2  2L / A
(2.86)
,[(aHHaR 3aBMCHMOCTb .nOJDKHa MCnOJIb30BaTbCH TOJIbKO ,LlJIH YfJIOB CKaHHpOBa-
HMH, MHoro 66JIbIIIHX 3TOH KpMTMqeCKOH BeJIMQHHbI. OTMeTHM, QTO 3aBMCMMOCTM
I'
---

JIumepamypa 
o
LIA = 5
---
---
---
-------........
-.

I::[
--- -2
:a
::r:
::r:


::r:
cd
..Q -4

u
o
::r:
><
0.

j:Q
o
t::: -6

cd
::r:
j:Q
:=


-9 -8
-9
(T)

'......_ 10
---
....----..-
---
cos8
-10
o
10
20
30 40 50 60
YrOJI CKaHlfpOBaHlfH (rpa,L:(.)
70
80
90
PHC. 2.33. 3aBI1CHMOCTb 3<p<peKTI1BHoi1: IIOBepXHOCTH aHTeHHbI OT yrna CKaHl1pOBaHHjI
Tlfna cos e .lUUI 3<p<peKTIfBHoH nOBepXHOCTIf He yqlfTbIBalOT 3<p<peKTbI BJIIf.HHIf.H 1f3-
MeHeHIf.H IfMne,l(aHCa 3JIeMeHTOB nplf CKaHlfpOBaHIfH (UMneoaHca cKaHup06aHUJl -
scan impedance effects) - CM. rJIaBY 7.
JIHTepaTYPa
1. Allen J. L. H ,n:p., Phased Array Radar Studies, Lincoln Lab., TR-228, Aug. 1960.
2. Bloch, A., Medhurst, R. G., and Pool, S. D., «A New Approach to the Design of Su-
per-Directive Aerial Arrays», Proc. lEE, Vol. 100, Part III, 1953, pp. 303-314.
3. Elliott, R. S., «The Theory of Antenna Arrays», in Microwave Scanning Antennas, Vol. II,
R. C. Hansen, Ed., Academic Press, 1966 [Peninsula Publishing, 1985], Chapter 1.
4. Hansen, R. C., Microwave Scanning Antennas, Vol. 1, Academic Press, 1964 [Peninsula
Publishing, 1985], Chapter 1.
5. Hansen, R. C., «Comparison of Square Array Directivity Formulas», Trans. IEEE, Vol.
AP-20, Jan. 1972a, pp. 100-102.
6. Hansen, R. C., «Formulation of Echelon Dipole Mutual Impedance for Computer»,
Trans. IEEE, Vol. AP-20, Nov. 1972b, pp. 780-781.
7. Hansen, R. C., «Linear Arrays», in Handbook of Antenna Design, A. W. Rudge 11 .np., Eds.,
IEEjPeregrinus, 1983, Chapter 9.
8. Hansen, R. C. and Brunner, G., «Dipole Mutual Impedance for Design of Slot Arrays»,
Microwave J., Vol. 22, Dec. 1979, pp. 54-56.
9. Hansen, R. C., «Phase and Delay in Corporate-Fed Arrays», IEEE AP Magazine. Vol. 44,
Apr. 2002, pp. 24-29.
10. Hansen, R. C. and Charlton, G. G., «Subarray Quantization Lobe Decollimation», Trans.
IEEE, Vol. AP-47, Aug. 1999, pp. 1237-1239.


FJla8a 2. OCl1081lbie xapaKmepucmUKU allmellllblX peUlemOK
11. King, M. J. and Thomas, R. K., «Gain of Large Scanned Arrays», Trans. IRE, Vol. AP-8,
Nov. 1960, pp. 635-636.
12. Lo, Y. T. and Lee, S. W., «Affine Transformation and Its Application to Antenna Arrays»,
Trans. IEEE, Vol. AP-13, Nov. 1965, pp. 890-896.
13. Mailloux, R. J., Phased Array Antenna Handbook, Artech House, 1994.
14. Miller, C. J., «Minimizing the Effects of Phase Quantization Errors in an Electronically
Scanned Array», RADC Symposium Electronically Scanned Array Techniques and Applicati-
ons, April 1964, RADC- TDR-64-225, AD-448 481.
15. Nelson, E. A., «Quantization Sidelobes of a Phased Array with a Triangular Element Ar-
rangement», Trans. IEEE, Vol. AP-17, May 1969, pp. 363-365.
16. Sharp, E. D., «A Triangular Arrangement of Planar-Array Elements That Reduces the
Number Needed», Trans. IRE, Vol. AP-9, Mar. 1961, pp. 126-129.
17. Smith, M. S. and Guo, Y. C., «A Comparison of Methods for Randomizing Phase Quan-
tization Errors in Phased Arrays», Trans. IEEE, Vol. AP-3l, Nov. 1983, pp. 821-827.
18. Southworth, G. C., «Certain Factors Affecting the Gain of Directive Antenna Arrays»,
Proc. IRE, Vol. , Sept. 1930, pp. 1502-1536.
19. Von Aulock, W. H., «Properties of Phased Arrays», Proc. IRE, Vol. 48, Oct. 1960, pp.
1715-1727.
20. Whittaker, E. T. and Watson, G. N., Modern Analysis, 4th ed., Cambridge University
Press, 1952.
I
I'
--

rl1ABA 3
.
CHTE3 AArPAMM
HAnPABI1EHHOCT
I1HEHHOH
AHTEHHOH PEWETK
3.1. BBeAeHMe
JIHHeHHbIe aHTeHHbIe perneTKH H3 H3J1yqa1OIUHx 3JIeMeHTOB pa3pa6aTbIBalOTcH B Te-
qeHHe MHorHX ,n;eCHTHJleTHH. B ,n;aHHOH rJlaBe H3JIaralOTCH Ba)I(HbIe pe3YJIbTaTbI, Ka-
calOIUHeCH ,n;eTaJIeH MeTo,n;HK paCqeTa H CHHTe3a aHTeHHbIX perneTOK. PaCCMaTpHBa-
eTCH paCqeT OCTpOHanpaBJleHHbIX aHTeHHbIX perneTOK C HH3KHM ypOBHeM 60KOBbIX
JIeneCTKOB, perneTOK C pacrnHpeHHbIM JlyqOM, YCJlOBHO onTHMH3HpOBaHHbIX perne-
TOK H anepHo,n;HqeCKHX aHTeHHbIX perneTOK. MHorHe no.rryqeHHbIe paHee .aaHHbIe
rrepeCqHTaHbI nOBTopHO C HCnOJlb30BaHHeM CTaBrnHX ,ZJ;OCTYTIHbIMH MOIUHbIX BbI-
qHCJlHTeJlbHbIX cpe,ZJ;CTB, a TaIOKe ,ZJ;onOJIHHTeJIbHbIX HOBbIX pe3YJIbTaTOB.
3.1.1. Bblpa>KeHMSI AnSI AMarpaMMbl HanpaBneHHOCTM
3JIeKTpOMarHHTHoe nOJIe, H3.rryqaeMoe JIHHeHHOH AP, npe,ZJ;CTaBJIHeT C060H cyrrep-
rr03HUHIO nOJIeH, H3.rryqaeMbIX Ka)l(,lJ:bIM H3 3JIeMeHTOB B rrpHcyrcTBHH ,ZJ;pyrHX 3JIe-
MeHTOB. Y Ka)l(J(oro 3JIeMeHTa HMeeTCH napaMe1'p B036yx.n:eHH.SI, .1LJI.SI ,ZJ;HnOJIH -
TOK, .1LJI.SI IUeJIH - HanpIDKeHHe, B CJIyqae MHorOMO,ZJ;OBoro 3JIeMeHTa - MO,ZJ;OBoe
HanpIDKeHHe. B ,ZJ;aHHOH rJIaBe onHCbIBaeTC.SI, npe)l(J(e Bcero, CJIyqaH «BbIJIy)K,lJ;eHHO-
ro B036yx.n:eHH.SI», Kor,ZJ;a B036yx.n:eHHe KIDK,L(oro H3 3JIeMeHTOB B OT,ZJ;eJIbHOCTH no.a-
,n;epXHBaeT Tpe6yeMyro BeJIHqHHY. IIpH TaKOM B036yx.n:eHHH KOMneHcHpyeTcH B3a-
HMHaH CBH3b <pH.II:epOB nHTaHH.SI, H3MeH.SIIOIUaH BXO,ZJ;HOH HMne,ZJ;aHC (a,n;MHTaHc)
3JIeMeHTOB. BOJIee qaCTO BCTpeqaeTC.SI c.rryqaii «cB060,n;Horo B036yx.n:eHHH», npH KO-
TOpOM CHCTeMa B036yx.n:eHH.SI C03,ZJ;aeTCH B paCqeTe Ha 1'pe6yeMoe B036yx.n:eHHe, HO
H3MeHeHHe «HMne.aaHca CKaHHpOBaHHH» 3JIeMeHTa npH H3MeHeHHH yrJIa CKaHHpo-
BaHHH HJlH qaCTOTbI npHBO,ZJ;HT K H3MeHeHHIO 3Toro B036yx.n:eHH.SI. 3TH BonpOCbI
60JIee nO,ZJ;p06HO 06cyx.n:aIOTCH B rJIaBe 7.
B036yx.n:eHHe Ka)l(,lJ:OrO 3JIeMeHTa HMeeT KOMlIJIeKCHOe 3HaqeHHe, xapaKTepH3Y-
IOll(eeC.SI aMIIJIHTY,n;oH H <pa30H. 3TO ,ZJ;HCKpeTHoe pacnpe,ZJ;eJIeHHe qaCTO Ha3bIBaeTCH
pacnpe,n;eJIeHHeM nOJIH B paCKpbIBe, KOTOpbIH 06pa3yeT aHTeHHaH perneTKa. )];Ha-
rpaMMa HanpaBJIeHHOCTH H3JIyqeHHH B ,ZJ;aJIbHeH 30He npe,ZJ;CTaBlliIeT c060ii ,n;HCKpeT-
Hoe npe06pa30BaHHe <l>YPbe OT B036yx.n:eHHH AP. ,lJ;HarpaMMa HanpaBJleHHOCTH
HHor,ZJ;a Ha3bIBaeTC.SI rrpOCTpaHCTBeHHbIM MHO)l(JfTeJIeM (B ,n;aHHOH rJIaBe paCCMaTpH-
BalOTCH perneTKH, COCTOHIUHe H3 H30TponHbIX H3.rryqaTeJIeii). B rJlaBe HCnOJIb3yeTcH
06bIqHaH ,lLIDI aHTeHHbIX perneTOK CHCTeMa 0603HaqeHHH: e - yrOJI, OTCqHTbIBae-


rJla6a 3. CUHme3 iJuazpaMM Hanpa6JleHHOCmu JlUHeUHOu aHmeHHOU pewemKU
MbIM OT HarrpaBJIeHI1JI, rreprreH,LJ:HK)'JIRpHOrO pacKpbIBY aHTeHHbI, d - MeX3JIeMeHT-
Hoe paCCTORHHe H U - o606meHHaR yrnoBaR rrepeMeHHaH CKaHHpyrolUeM pemeTKM
u = d (sine - sin eo).
A
(3.1)
XOTR ,nHarpaMMa HarrpaBneHHOCTH B ,naJIbHeM 30He MoxeT 6bITb 3arrHcaHa rrpo-
CTO B BH,[(e CYMMbI qneHOB, co,nepxalUHX aMIIJII1T)',nHYK> 11 3KcrrOHeHUl1aJIbHyro
qaCTb, 3aBI1CRlUYK> OT 3neKTpHqeCKOM ,lUII1HbI nyrH, ,lI)IR 06eCrreqeHIDI lIeMCTBI1Tenb-
HOM ,nHarpaMMbI HarrpaBneHHOCTM y.n:06HO rrpe,nCTaBI1Tb BbIpIDKeHHe B BMe, rrpl1-
ro.n:HOM KaK .lUUI qeTHOrO, TaK 11 .lUUI HeqeTHOrO ql1cna 3neMeHTOB pemeTKI1. Ilpl1
TaKOM orrpe.n:eneHI1I1 <pa3a OTCqHTbIBaeTCR OT ueHTpa aHTeHHOM pemeTKH, qTO npl1-
BO,nHT K cne,nyromeMY BH,[(Y .n:l1arpaMMbI HarrpaBneHHOCTH
N
F(u) = LAn exp[j21t(n -l)u]. (3.2)
n=l
r,ne An - K03<P<P H Ul1eHTbI B036y)1()]:eHI1R, N - qHCnO 3neMeHTOB perneTKH, 8 0 -
HarrpaBneHl1e OCHOBHoro JIyqa. AHTeHHaR pemeTKa 11306paxeHa Ha pHC. 3.1.
B
n = 1
2
3
4
N
PUC. 3.1. KOH<pHrypal.{IUI JIHHeHHOH aHTeHHOH pemeTKH
)];n.SI rrOHHMaHHR 3<p<peKTa BKJIaI(a KIDK.LI:OrO 3JIeMeHTa B (3.2), cornaCHO MeTO.n:y
e.n:HHHqHOM OKpyxHOCTI1 [58], BBO,nI1TCR HOBa.SI nepeMeHHa.SI:
w = exp (j2'Jtu).
(3.3)
3TO rr03BOn.SIeT BbIpa3HTb .l(l1arpaMMY HarrpaBneHHOCTI1 B BH,[(e rronHHOMa no w:
N
F(u) = LAnwn-l. (3.4)
n=l
<I>113HqeCKOe rrpOCTpaHCTBO, 06bIqHO Ha3bIBaeMoe peaJIbHbIM rrpOCTpaHCTBOM,
COOTBeTcTByeT qaCTH e.l(HHHqHOH OKpyxHOCTI1 Ha KOMnneKcHoM nnOCKOCTI1 w. TIo-
nSlpHbIM yron paCCqHTbIBaeTCSI KaK $ = 2'Jtu; OXBaTbIBaeMaSl qaCTb e.n:I1HHqHOH
OKpyxHOCTH orrpe.n:enSleTCSI KaK
-kd( 1 + sin 8 0 ) < 11' < kd( 1 - sin 8 0 ).
(3.5)

3.1. B8eoeHue -.d
I1pH nonYBonHoBoM rnare W 06XO,n:HT e,n:HHHqHYID OKpyxHOCTb O,n:HH pa3. I1pH
rnare perneTKII, paBHoM.:WIHHe BonHbI - .n;Ba)l(,I{bI H T..n;. Y nonHHOMa no CTenelUlM
W HMeeTC N - 1 KopHeH, nexaIUHX HJIH He nexaIUHX Ha e.n;HHHqHOH OKp)')KHOCTH.
)];HarpaMMa HanpaBJIeHHOCTH onpe.n;eneTC npOH3Be.n;eHHeM paCCTOHHH OT
TOqKH Ha6nlO.n;eHH W (Haxo.n;:rn:eHC Ha OKpyxHOCTH) .n;o KaJK,[(OrO H3 HyneH (KOp-
HeH) (CM. pHC. 3.2). I1pH nepeMe:rn:eHHH w no OKpyxHOCTH B03HHKalOT H HCqe3alOT
JIeneCTKH .n;HarpaMMbI. I1pH pacnOJIOXeHHH KopHeii Ha e.n;HHHqHOH OKpyxHOCTH
06pa3YIDTC HYJIH .n;HarpaMMbI HanpaBJIeHHOCTH; KOpHH, pacnOJIOXeHHbIe BHe e.n;H-
HHqHOH OKp)')KHOCTH, .n;alOT MHHHMYMbI .n;HarpaMMbI. B npOCTOM cnyqae 3KBI1,L1H-
CTaHTHOH aHTeHHOH perneTKH C paBHOMepHbIM B036)')K.1IeHHeM:
F(u) = sin!"'nu exp[j1t(N -l)u] = w N -1 .
N sIn 1tU W - 1
(3.6)
"-
"
'"
"
" \
------ " \ I
---- "
--
---
30Ha
OCHOBHoro
JIyqa


30Ha 60KOBoro JIerreCTKa
PUC. 3.2. E.rUfHI1QHaH OKpy)KHOCTb ,lUIH CeMI13JIeMeHTHOH aHTeHHOM pellIeTKH
KOpHH pacnOJIOXeHbI Ha OKpyxHOCTH paBHOMepHO C rnarOM 21f./ N, a 3Kcno-
HeHI.(HaJIbHbIH MHO)I(HTeJIb <popMHpyeT 3HaqeHHe <pa3bI B I.(eHTpe aHTeHHoH perneT-
KII. YnpaBJIeHHe .n;HarpaMMoH HanpaBJIeHHOCTH nyreM nepeMeIUeHH KopHeH B
W-llJIOCKOCTH 6y.n;eT Hcnonb30BaTbC n03.n;Hee .IUI CHHTe3a pacrnHpeHHbIx JIyqeH.
B MeTo.n:e e.n:HHHQHOH OKp)')KHOCTH, npe.IUIOXeHHOM IJJ:enKYHOBbIM, MO)I(HO Y3HaTb
Z-npeo6pa30BaHHe, Hcnonb30BaHHoe B TeopHH I(eneif MHoro JIeT cnycT.
3. 1.2. CbM3MKa M M8TeM8TMKa
PaCCqHTaTb pa60QHe xapaKTepHCTHKH aHTeHHOH perneTKH npH paBHOMepHOM
B036)')K.1IeHI1H cpaBHHTenbHo HeTpy.n:HO; 3a.n:aQa OCJIOXHeTC npH HCnOJIb30BaHHH
aMnnHT)',lI;HOrO pacnpe,neJIeHH, cna.n:alOIUero K KpaM paCKpbIBa, KOTopoe Hcnonb-
3yeTc ,nJI YMeHbrneHH5I 60KOBbIX JIeneCTKOB. Ha paHHHX 3Tanax aMnJIHTy.n;HbIe
pacnpe,neJIeHH BbI6HpaJIHCb, HCXO.n: H3 YCJIOBI1H HX JIerKOH HHTerpHpyeMocTH H
B03MO)I(HOCTH npe.n:CTaBI1Tb pe3ynbTaT B aHaJIl1THQeCKOM Bl1,L1e. HanpHMep, pac-
npe.n:eJIeHH BH,na KOCHHYC B CTeneHH n Ha' nbe.n.eCTaJIe nerKO paCCQHTbIBaIOTC H


FJlaea 3. CUHme3 iJua2paMM HanpaeJleHHOCmu JlUHeUHOU aHmeHHOU petuemKU
,lIOrrYCKaIOT KoppeKUHIO YPOBHR 60KOBbIX JIerreCTKOB. O,lIHaKO 3THM pacrrpe.aeJIe-
HIIRM CBoHcTBeHHbI ):(Ba He):(OCTaTKa. B rrpHBe.aeHHoM rrpIIMepe HMeeTC5I .aBa .na-
paMeTp: nOKa3aTeJIb CTeneHH II BbICOTa nbe,lIeCTaJIa. npH 3a,n:aHHbIX 3HaqeHH5IX
3TIIX napaMeTpoB MO)I{HO BbIqIICJIHTb Bce Ba)KHbIe xapaKTepHcTIIKH (1IIIIPIIHY
JIyqa, K03<1><PHUIIeHT HCnOJIb30BaHIIH nOBepxHocTH, ypoBeHb 60KoBoro JIeneCTKa,
KnJ]; no MOll(HOCTH JIyqa H T..u:.). Ho He cyrn:eCTByeT npOCToro cnoc06a BbI60pa
3THX ,aBYX napaMeTpOB, n03BOJIRlOmerO, K npIIMepy, onTHMH3HpOBaTb K03<P<PHl(H-
eHT HCnOJIb30BaHHR nOBepXHOCTH ,lIJI5I ,lIaHHOrO ypOBHR 60KOBoro JIeneCTKa. DO-
u
Ree cyrn:eCTBeHeH BTOpOH He,aOCTaTOK: ,lIaHHble pacnpe,lIeJIeHHR, 3aBHCRll(IIe OT
3HaqeHHH rrapaMeTpOB, BbI6paHHbIX B KaqeCTBe rrepeMeHHbIX, MOryr 6bITb KpaHHe
He3<p<peKTHBHbI npH BbIpaJKeHHII Qepe3 IIIIIPHHY JIyqa, K03<P<PHUHeHT HCnOJIb30-
BaHHH nOBepXHOCTH H TaK ):(aJIee. J];pyrHM npHMepOM RBJIReTCR H3BeCTHoe pacnpe-
,n:eJIeHHe faycca Ha nbe,lIeCTaJIe. 3TO pacnpe,lIeJIeHHe RBRReTCR MHoronapaMeTpH-
qeCKIIM H, qTO eIUe xyxe, HMeeT CJIO)l(HOe <l>YPbe-npe06pa30BaHHe. n03TOMY B
COBpeMeHHbIX pa60Tax no aHTeHHaM JIerKOCTb MaTeMaTHKII YCTyrrHJIa MeCTO XOpO-
lIIeH <pH3HKe: aMIIJIH1)'):(HbIe pacnpe,l(eJIeHHR paCCqHTbIBalOTcR nyreM Ha,n:JIe)Kame-
ro pa3MeIUeHH$I HYJIeH ):(HarpaMMbI HanpaBJIeHHOCTH, npe,l(nOqTHTeJIbHO C Hcrro-
JIb30BaHHeM O,l(HOrO rrapaMeTpa. 3TO 06eCrreQHBaeT xopOIliHe <pH3HQeCKHe
xapaKTepHCTHKH aHTeHH, npe,l(rrOJIaralOmHe BbICOK03<p<peKTHBHYIO anepTYPY C
HH3KHM 3HaQeHHeM ):(06pOTHOCTH Q. nepBbIM, KTO npHMeHHJJ TaKOH no,l(xo):( K
HaXO)l(,[(eHHIO pacnpe,aeJIeHHH, <pOPMHPYIDIUHX ,lIHarpaMMY HanpaBJIeHHOCTH C Y3-
KHM JIyqOM H HH3KHM ypOBHeM 60KOBbIX JIeneCTKOB, 6bIJI TeHJIOp; npe,l(JIOXeH-
HbIe HM npHHUHrrbI paCQeTa 06cyx.aaIOTCR ,lIaJIee.
3. 1.3. npMHL\Mnbl paClLleTa Y3KMX nYlLlei1,
npeAJ10>KeHHble Tei1nopoM
 ,
06bIQHbIMH Tpe60BaHHRMH, npe,lI1>$IBJIReMbIMH K ,l(HarpaMMe HanpaBJIeHHOCTH
aHTeHHbI, $IBJI$lIOTCR BbICOKHH KHJ]; II HH3KHH ypOBeHb 60KOBbIX JIerreCTKOB, QTO
rrOJIe3HO ,lLJIR npHJIO)KeHHH pa,n:HOJIOKaUHH, TeJIeKOMMYHHKaUHH, KapTorpa<pHH H
T.,l(. Yp08eHb 60K08020 JleneCmKa (YEJI) (B aHrJIOR3blqHOH T}JaHCKpHnUHH Sidelobe
level - SLL» rrpe):(CTaBJUleT C060H HOpMHpOBaHHyID K aMIIJIHTYJIe OCHOBHoro JIyqa
aMnJIHTY,l(Y HaH60JIblIIerO 60KOBoro JIeneCTKa, 06bIQHO 6JIlUKaHlIIero K OCHOBHOMY.
Y,lI06HO HCnOJIb30BaTb TaIOKe 3HaqeHHe, npeJICTaBJIRIOmee C060H BeJIHQHHY, 06paT-
HYID YEJI, TepMHHOJIOrlf1leCKH 0603HaQaeMyID KaK omHOCUmeJlbHblU yp08eHb 60K080-
20 JleneCmKa (B aHrJIOR3bNHOH TpaHCKpHnUHH Sidelobe ratio - SLR). OCHOBHOH
JIeneCTOK MO)KeT 6bITb HanpaBJIeH nepneH,lIHKYJIRpHO pacKpbIBY aHTeHHbI IUIH rro,l(
HeKoTopbIM yrJIOM, MO)KeT npOH3BO,lIHTbCR TaIOKe 3JIeKTpOHHOe cKaHHpoBaHHe Ha
JII060H )KeJIaeMbIH yrOJI. TepMHHbI «aHTeHHaR pelIIeTKa C 3JIeKTpOHHbIM CKaHH-
pOBaHHeM» H «<pa3HpoBaHHaH aHTeHHa$l pelIIeTKa» RBJUlIOTCH CHHOHHMaMH. J];JIR
rrOJIyqeHHR MaKCHMaJIbHOrO K03<P<PHUHeHTa HanpaBJIeHHOCTH B pelIIeTKax, He 06-
JIa,r(aIOIUHX CBepXHanpaBJIeHHOCTbIO, MCnOJIb3yeTcR paBHOMepHoe B036yx.aeHHe.
ECJIH He06xo,lIHM ypOBeHb 60KOBbIX JIeneCTKOB MeHbIIIHH, qeM npH paBHOMepHOM
B036yx.aeHHH, TO aMIIJIH1)'JIa YMeHblIIaeTCH K KpaRM paCKpbIBa (anO,lIH3aUHR).
B pa60Te [61] C<POPMYJIHpOBaH PM BaJKHbIX 06IUHX rrpaBHJI ,lLJIR ,l(HarpaMM Ha-
npaBJIeHHOCTH C HH3KHM YPOBHeM 60KOBbIX JIeneCTKOB.
, .

3.2. AHmeHHble peUlemKU ,4oflb£jJa- Tfe6blUleea 
1. CHMMeTpWIHOe aMI1JllITYlIHoe pacnpe.ueJIeHHe CHIDKaeT ypOBeHb 60KOBbIX JIe-
rreCTKOB.
2. <l>YHKllJI5I F(u) J];OJDKHa 6bITb u;eJIOH <PYHKll;lleH u.
3. Pacnpe.ueJIeHHe C nbe,n:eCTaJIOM ,n:aeT orH6alOII{yIO ,n:aJIbHHX 60KOBbIX JIeneCT-
KOB BH,n:a Iju.
4. Pacnpe,n:eJIeHHe, JIHHeHHO CTpeM5IIUeeCH K HYJIIO Ha Kpa5IX paCKpbIBa, .uaeT
orH6alOIUyIO .uaJIbHHX 60KOBbIX JIeneCTKOB BH.ua I/u 2 .
5.' Pacnpe.ueJIeHHe C aMrrJIHTY,n:oH Ha Kpa5IX paCKpbIBa, OTJIHqHOH OT HYJI5I (c
nbe.ueCTaJIOM), 5IBJI5IeTC5I 60JIee 3<p<peKTHBHbIM.
6. HYJIH ,n:HarpaMMbI .uOJDKHbI 6bITb ,n:eHcTBHTeJIbHbIMH (pacnOJIaraTbC5I Ha en:H-
HHqHOH OKp)')KHOCTH w).
7. MHTepBaJI (no u) Me)l(,I(y,n:aJIbHHMH HYJI5IMI1 ,n:OJDKeH 6bITb paBeH e.uHHHl(e.
B nOCJIe.uYIOIUHX pa3,n:eJIaX 3TI1 npaBI1JIa 6y,n:YT rrpHMeH5ITbC5I .uJI5I nOJIyqeHI15I
BbICoK03<p<peKTI1BHOrO 11 YCTOHqHBOrO (c HH3KHM Q) B036y)1(,I(eHI15I 11 COOTBeTCTBY-
IOIUI1X ,n:HarpaMM HanpaBJIeHHOCTH.
Cym:ecTByeT HeMHoro cIIoc060B paCqeTa 3<p<peKTHBHbIX pacnpe.ueJIeHI1H, 06ec-
rreql1BalOIUHX 3a,n:aHHYIO ,n:HarpaMMY HanpaBJIeHHOCTH; B 60JIbllII1HCTBe aJIrOpHTMOB
CHHTe3a paCCMaTpHBaeTC5I HenpepbIBHa5I anepTYpa, npH KOTOpOH arrepTYpHoe pac-
rrpe,n:eJIeHl1e ,n:HCKpeTH3HpyeTC5I M5I CJIyqaH B036y)1(,I(eHH5I aHTeHHOH pellIeTKH. 3TOT
MeTO,n: Ha,n:eXHO pa60TaeT ,n:o Tex nop, nOKa llIar aHTeHHOH pellIeTKH 6JIH30K K rro-
JIYBOJIHOBOMY H qHCJIO 3JIeMeHTOB BeJII1KO. ECJIH KOJIHqeCTBO 3JIeMeHTOB CJIHIlIKOM
Marro, MoxeT 6bITb HCrrOJIb30BaH ,n:HCKpeTHbIH n CHHTe3, onHcaHHbIH B pa3,n:eJIe 3.6.
He,n:ocTaToK .uaHHoro MeTo,n:a B TOM, qTO M5I H3MeHeHHoro ql1CJIa 3JIeMeHTOB He06-
XOJ];HMO rrpOBo,n:HTb HOBbIH CHHTe3. B 60JIee CJIO)I(HOH MeTo,n:HKe npOH3Bo,n:HTC5I
conOCTaBJIeHHe HYJIeH Tpe6yeMoH ,n:HarpaMMbI HartpaBJIeHHOCTI1 HerrpepbIBHOH
pellIeTKH C HYJI5IMH .uHarpaMMbI HanpaBJIeHHOCTI1 .uHCKpeTHOH pellIeTKH (CM. pa3-
J];eJI 3.9.2). KOHeqHO, paccMoTpeHHbIH B pa3,n:eJIe 3.2 CHHTe3 ,LJ;oJIbcPa-Qe6bIIIIeBa
,n:HCKpeTeH C caMoro HaqaJIa, HO 3TH paCqeTbI HCnOJIb3yIOTCH pe,n:KO H3-3a BbICOKoro
ypOBH5I y,n:aJIeHHbIX 60KOBbIX JIeneCTKOB.
3.2. AHTeHHble peweTKM .Qonb«!>a-'-Ie6blweBa
3.2.1. PeweTKM c nonYBonHOBblM warOM
PerneTKH C nOJIYBOJIHOBbIM rnarOM 06JIa,n:a1OT MaKCHMaJIbHOH HarrpaBJIeHHOCTblO
rrpl1 3a,n:aHHOM SLR (6y,n:eM I1CnOJIb30BaTb aHrJIOH3bIqHOe cOKpaIUeHHe) B TOM CJIY-
qae, Kor.ua Bce 60KOBbIe JIeneCTKH I1MelOT o.uI1HaKOBbIH ypOBeHb. L{OJIb<p [15] 06Ha-
PYXHJI, qTO 3TOMY c.rryqalO l1):(eaJIbHO COOTBeTCTByIOT rrOJIHHOMbI Qe6bIrneBa. B .uHa-
rra30He + 1 ,n:aHHbIH rrOJIHHOM OCll;lUlJIl1pyeT C aMIIJII1Ty.uOH, paBHoH e,n:HHHl(e, a BHe
3Toro .ul1ana30Ha MOHOTOHHO B03paCTaeT. IIpl1Mep rpa<pI1Ka nOJIHHOMa Qe6bIIIIeBa
.ueB5ITOrO nOp5I,n:Ka rrpHBe,n:eH Ha pl1C. 3.3. ,LJ;aHHbIH nOJII1HOM ,n:orrYCKaeT rrpOCToe
BbIpa)l(eHl1e qepe3 TpHrOHOMeTpl1qeCKHe <PYHKJJ:I1I1:
(-I)n cosh(n arccoSlI xl)
Tn (x) = cos(n arccos x)
cosh(n arccoSl x)
x< -1
Ixl < 1
x > 1.
(3.7)


rflaea 3. CUHme3 iJuazpaMM HanpaefleHHocmu flUHeUHOU aHmeHHOU pewemlCu
3
. '.
2
1
-
o

-1
-2
-3
-1.020 -0.816 -0.612 -0.408 -0.204
o
x
0.204 0.408 0.612 0.816 1.020
PHC. 3.3. nORHHOM qe6bIIIIeBa
KpOMe Toro, OH JIerKO BblqHCJIReTCR no peK}'ppeHTHoH <popMyne. IlpRMoe co-
OTBeTCTBHe Me)l(,ay rrOJIHHOMOM aHTeHHoH pelIIeTIGI II nOJIHHOMOM qe6bIlIIeBa He
ocyrueCTBHMO, TaK KaK OCHOBHOH JIyq aHTeHHOH pemeTKH .nOJIXeH 6bITb CHMMeTpH-
qeH If IIMeTb HyneByIO KpyrH3HY B u;eHTpe. TIOCKOJIbK}' N-3JIeMeHTHaR aHTeHHaR
pemeTKa HMeeT N - 1 HYJIb, eH COOTBeTcTByeT nOJIHHOM Qe6blweBa CTeneHII
(N - 1) C aHaJIOrHqHbIM qHCJIOM HYJIeH. OCURJlJIHpyIOlUaR qaCTb nOJIHHOMa qe6bI-
meBa COOTBeTcTByeT 60KOBbIM JIeneCTKaM, Haxo.nRlUHMCR no o.nHY CTOPOHY .rryqa;
JIyq BIIJIOTb ,lI.O BeplIIHHbI COOTBeTcTByeT 06JIaCTH x > 1 nOJIHHOMa Qe6bIlIIeBa. 3TO
ocymecTBJIReTCR C nOMOlUblO rrpeo6pa30BaHIDI x = Xo cos(uj2). OHO rrpe06pa3yeT
rrOJIHHOM qe6bIllieBa T N _ 1 (x) B ,lI.HarpaMM)' HanpaBJleHHOCTH F(u).
TIepeMeHHaR .nHarpaMMbI HanpaBJIeHHOCTH 3a,n:aeTCR BbIpIDKeHHeM u = kdsin e.
TaKHM 06pa30M, ,lI.HarpaMMa HMeeT npOCTOH BH,I:{
F(u) = TN-{ Xo COS  )
(3.8)
IlpH H3MeHeHHH e OT -'Jtj2 ,lI.0 'Jtj2, x H3MeIDIeTCR OT (Xo cos 'Jtdj'A.) .no 3HaqeHHR
Xo npH e = 0, a 3aTeM 06paTHO K 3HaqeHHIO (Xo COS 'Jtdj'A.). IlpH nOJlYBOJlHOBOM
mare MHHHMaJIbHOe 3HaqeHHe x paBHO HYJIIO. MaKCHMaJIbHO B03MO)K}fbIH mar
onpen:eJIReTCR He06xo,lI.lfMOCTblO npe.nOTBpaTHTb YMeHblIIeHHe x HIDKe -1. 3TO .naeT
BbIpaxeHHe ,lI.JIR MaKCHMaJIbHOrO HHTepBaJIa pa3MelUeHHR 3JIeMeHTOB cHH<pa3HoH
....
aHTeHHOH pemeTKH
d = 1- arccos ( _1- ) ,
A. 1t Xo
(3.9)

3.2. AHmeHHble peUlemKU )I,OJlbfjJa- Cfe6blUle6a 
QTO ,lUIR 60JIbllIHX aHTeHHbIX pellieTOK npH6JIIDKaeTCR K nepHO,[(HqHOCTM pacnoJIo-
xeHHR H3JIyqaTeJIeH, paBHoH AJlHHe BOJIHbI. 3HaqeHHe SLR no HanpIDKeHHIO co-
CTaBJIReT
SLR = T N - 1 (XO); SLR> 1. (3.10)
IIpH 3a,aaHHOM SLR K03<P<PHUHe HT rrpeo6 pa30BaHHR Xo ,[(a eTCR Bblp a)KeHHeM
Xo =cosh arccoSl. SLR =![SLR+ .J SLR2 -1]l/N +![SLR- .J SLR2 -1]l/N. (3.11)
N -1 2 2
BTopaR <popMYJIa npHBo,[(HTCR B CBR3H C TeM, qTO HeKOTopble KOMnblOTepbI He
HMelOT rro,nrrporpaMM BblqHCJIeHHR 06paTHQH rHrrep6oJIHqeCKOH <pyHKIJ;HH. IIo,nxo,[(
JJ:OJIb<pa CnpaBeAJIHB TOJIbKO rrpH rrepHo,nHqHOCTH aHTeHHOH pellieTIGI paBHOM O.5A
H 6oJIee. THrrHqHaR .l(HarpaMMa HarrpaBJIeHHOCTH aHTeHHOM pellieTIGI H306paxeHa
Ha pHC. 3.4. I1cnoJIb3YR ueHTP aHTeHHOM perneTKH KaK TOqKY OTCqeTa <l>a3bI, MO)K-
HO 3arrHcaTb .l(HarpaMMY HanpaBJIeHHOCTH B BH.IJ:e pR.D:a:
F(u) = An exp{j[ (2n - N -1) ; ]} (3.12)
06paI.IJ;eHHe 3Toro KOHeqHOrO pR,L(a .l(aeT BblpIDKeHHe MR K03<l><I>HUHeHTOB:
An =  LF e: }xp{-j[(2n-N -I) ; ]}. (3.13)
I10,[(CTaBJIRR clO,na nOJIHHOM Qe6bIllieBa, BblpaxaeM K03<P<PHUHeHTbI qepe3 CYM-
MY nOJIHHOMOB Qe6bIllieBa:
An ' TN-I (xo coo ; }xp{-j[ (2n - N -1) ; ]} (3.14)
o
'\
f\ f\""" f1 f\ f1 1\ (\ f\ " f\
\
-' I
-10
,-..,.

t::t
--
C\3
-20
:s:
t=:
t:

-30
-40
-90
o
e (rpa,n;.)
PHC. 3.4. ,nHarpaMMa HanpaBJIeHHOCTH 20-3JIeMeHTHoH aHTeHHOH perneTKH ,L:LOJIb<l>a-
Qe6bIrneBa, d = 0,5)"
-60
-30
30
60
90

.,

Fflaea 3. Cunme3 aUa2paMM nanpaeflennocmu fluneunou anmennou peUlemKU
B CHJIY cl1MMeTpHqHOCTI1 ,L(l1arpaMMbI MOryT 6bITb C,L(eJIaHbI ,L(OnOJIHI1TeJIbHbIe
yrrpomeHII5I. .lI:JI5I BbIQIICJIeHIDI K03<P<PI1II;l1eHToB B036y)l()J;eHM5I yn:06HbIe <POPMYJIbI
nOJIyqeHbI B pa60Te [59], pa3JIHQHbIe ,lLJI.H QeTHbIX M HeQeTHbIX N ( 3JIeMeHTbI HYMe-
pyK>TCH OT u;eHTpa aHTeHHoH pellIeTKM). JLrr51 qeTHbIX N = 2M:
An =  [SLR+2 :TN-l (XO cos ; }OS( (2n -1) ; )] 1 < n < M. (3.15)
,L(JI5I HeqeTHbIX N = 2M + 1:
2 [  ( m1t ) ( 2nmn )]
An = N SLR+2TN_l XOCOS N cos N .
(3.16)
3TM pe3YJIbTaTbI CnpaBe,lLJIMBbI ,lLJIH Me)l(3JIeMeHTHoro paCCT05lHM.H > A/2.
ITOCKOJIbKY ,lLJI5I 60JIbllIMX aHTeHHbIX pellIeTOK 3TM <POPMYJIbI rpOM03,II;KI1, B pa-
60Tax [62, 8] 6bIJIM rrpe,lLJIO)l(eHbI MX ynpomeHHbIe rrpM6JII1)1(eHHbIe BepCMM. O,II;HaKO
npM COBpeMeHHbIX B03MO)I(HOCTHX KOMrrblOTepOB no,ao6HbIe arrnpOKCMMaII;I1H He
Tpe6YIOTC.H. cD0PMYJIbI [59] MOryT HCnOJIb30BaTbC5I HenOCpe,lICTBeHHO. B pa60Te [14]
npM 3an:aHHOM qMCJIe 3JIeMeHTOB N = 3(1)40 (MMHMMYM-rnar-MaKcHMYM) JI OTHO-
rneHH5IX 60KOBbIX JIeneCTKOB SLR = 1 O( 1 )40 ,aD ,lLJI5I d = A/2 npI1Bo,aMTC5I rro,apo6-
Ha51 Ta6JIMua K03<P<PHUMeHToB, HarrpaBJIeHHOCTI1 11 llIMpMHbI JIyqa. O,aHaKo B6JIM311
BepXHI1X 3HaqeHMH N II SLR IIMelOTCH cym:eCTBeHHbIe norpellIHOCTH, rrO-BH,aHMO-
MY, 06YCJIOBJIeHHbIe OllIH6KOH oKpyrJIeHIUI.
lloJIb30BaTeJI5IM Heo6xOLU1MO BbIqMCJI5ITb 3HaqeHM5I ,lLJI5I CBoero CJIyqa51 C nOMO-
IIJ:blO CPOPMYJI, npl1Ben:eHHbIX BbIllIe MJIH HIDKe.
Ha pMC. 3.5 nOKa3aHbI aMnJIII1Y,L(bI B036y)l()J;eHH5I TMnMqHOH 30-3JIeMeHTHoH
aHTeHHoH perneTKM. MO)I(HO OTMeTHTb, qTO HM O,n:HO 113 Tpex aMIIJIMTy,n:HbIX pac-
npe,aeJIeHMM He 51BJIHeTC.H MOHOTOHHbIM, H 3HaQeHIUI K03cp<pI1UHeHTOB ,lLJI5I pacnpe-
,n:eJIeHH5I, 06eCrreQI1BalOm:ero YPOBeHb SLR = 20 ,n:D, 60JIbllIe Ha KOHuax pellIeTKH,
qeM B II;eHTpe. B u;eJIOM, KpaeBbIe 3HaqeHHH B03paCTalOT C YBeJIMQeHMeM pa3Mepa
aHTeHHoH pellIeTKH M CHIDKeHl1eM ypOBH.H SLR. ,IIaHHa51 KpHBa5I ,n:eMOHcTpMpyeT
OCHOBH)'IO Tpy,n:HOCTb, CBH3aHHyro C MCnOJIb30BaHMeM perneTOK .lI:oJIbcpa-Qe6bIllIe-
Ba, a HMeHHO: CJIO)I(HOCTb peaJII13aUI1M HeMOHOTOHHoro pacrrpe,aeJIeHHH Ii KpaeBbIX
MaKCMMYMOB. .lI:onOJIHI1TeJIbHbIM He,n:OCTaTKOM 51BJI.HeTC5I TO, QTO YJIaJIeHHbIe 60KO-
BbIe JIeneCTIill paBHoro ypOBIDI rrpI1Bo,L(51T B PaJI.MOJIOKaUMOHHbIX 3aJI.aqaX K rrOBbI-
IIIeHl110 He)l(eJIaTeJIbHOH MHTep<pepeHUI1I1 0TPIDKeHHbIx CMrHaJIOB 11 naCCI1BHbIX rro-
Mex. no 3TMM rrpMQMHaM aHTeHHbIe perneTKI1 ,L(OJIb<pa-Qe6bIllieBa I1CrrOJIb3yroTC5I
pe,aKo. Ha pl1C. 3.6 npl1BOMTCH MaKCHMaJIbHbIe 3HaQeHI151 N npI1 3aLJ:aHHOM 3Haqe-
HI1I1 SLR, o6eCneQl1BalOml1e MOHOTOHHoe paCIIpe,n;eJIeHl1e, a TaIOKe nOKa3aHa 3aBI1-
CI1MOCTb MaKCI1MaJIbHOrO N OT SLR, IIPM KOTOpbIM aMrrJII1T)',L(a Ha KpalO He npeBbI-
maeT 3HaQeHM5I aMIIJIMTy,n:bI B ueHTpe.
111l1pl1Ha JIyqa onpe,n:eJIHeTC.H 113 BbIpIDKeHIUI (3.12) ,lLJIH paCqeTa ,II;MarpaMMbI Ha-
rrpaBJIeHHOCTH; O,II;HaKO ,lLJIH HaXOJK.ll:eHMH 3HaQeHM.H llII1pHHbI JIyqa Tpe6yeTc5I HaMTM
KopeHb ypaBHeHI1.H
.,fiT N - 1 (XO Cos u ; ) = TN-l(XO).
(3.17)

3.2. AHmeHHble pelUemKU ,lJollbfjJa-Cfe6bllUeBa ..d
1.50
1.25
(Ij
E-<
::r::
Q)

Cl)
 1
CI')

:s::
::r::
Cl)
 0.75
\.0
M
0
CQ
(Ij
 0.50
E-<
:s::

I=:

0.25
--  -.-
--
--
......-..
-. '-.:..: - .. - -
""""'"
..... ...............--------
 .........
..... .._-------
, ----)---

40 ,zd>
.....

,
,
,
I
,
,
,
,
.. -'
.....

.....
....
-
o
16
18
20
22 24
HOMep 3JIeMeHTa
26
28
30
PUC. 3.5. AMTIJIIfT)'.D:bI B036}')K.lJ;eHIfR 30-3neMeHTHOH aHTeHHOH perneTKH ,LJ;onb<t>a-
qe6blrneBa
30
N
..
MOHOTOHHoe
pacnpe.neJIeHHe
10
B036yx.n:eHHe
B I.I.eHTpe =
= B036yx,aeHHIO Ha KpaIO,
N CJIe.nyeT YMHO)KaTb Ha 10
2
20
30
SLR (.n6)
40
PUC. 3.6. MaKCIfMaJIbHOe 3HaqeHlfe N nplf 3a;:J;aHHOM 3HaqeHIflf SLR


rJla6a 3. CUHme3 iJuazpaMM Hanpa6JleHHOCmu JlUHeUHOU aHmeHHOU peUlemlCU
Ha pllC. 3.7 npllBe,aeHa 3aBI1CI1MOCTh HOpMlIpoBaHHoMllilIpllHbI nyqa B rpa,n;y-
cax OT SLR )])IR aHTeHHOM pellieTKIf C nOJIyBOnHOBOM nepllo,aI1QHOCThlO M KOnMQe-
CTBOM 3neMeHTOB OT 10 ,ao 100. KaK II O)l(J1,aanOCb, IlIl1pl1Ha nyqa npH YBenl1qeHHI1
ypOBHR 60KOBhIX neneCTKOB paCTeT IIpll6nl13lfTenhHo nlfHeMHo.
1.3
1.2
-..
.



--
..<
........... 1.1

x



 1
:I:
:s::

:s::
:3
0.9
QJ1CJIO 3JIeMeHTOB N = 100 ""r _____
_,-' 20 -
.-.---_.-. ' 
.,,'  -
,,'
"r-"" ....
-,.",,/ -
.,.-.;/ -
r-'/ -
,,,.' 
....
-----
0.8 20
25
30
SLR (.nn)
35
40
PHC. 3.7. IlIHpHHa JIyqa rrpH pacnpe,neJIeHHH ,[I;OJIb<pa-Qe6blIIIeBa
KH,L( aHTeHHOM pellIeTKH ,L(onbQ:>a-Qe6bIllieBa BhIQlfCnReTCR C IIOMOm:blO COOT-
BeTCTByIOm:HX Q:>opMyn rnaBhI 2, nplf IICnOnh30BaHlIlI BhIllienplfBe,aeHHhIX K03Q:>Q:>I1-
l(HeHTOB B036y)1()J;eHIDI.
Eonee none3HOM xapaKTeplfCTI1KOM RBnReTCR He HanpaBneHHOCTh aHTeHHOM
pellIeTKH (KH,L(), a K03Q:>Q:>I1l(lIeHT I1cnonh30BaHlfR nOBepXHOCTII (KI1TI) aHTeH-
u u u
HOlf pellieTKIf, npe,n:CTaBnRIOm:lIlf OTHOllIeHlfe HanpaBneHHOCTlf aHTeHHOlf pellIeT-
KI1. K HaIIpaBneHHOCTII OL(HOpOL(HO B036y)1()J;aeMOM aHTeHHOM pellieTKIf C TeM )Ke
llIarOM 11 QI1CnOM 3nMeHrOB. Ha pl1C. 3.8 nOKa3aH KI1TI aHTeHHOM pellieTKI1 C
nonYBonHoBoH nepI10,n:lfqHOCThlO. HyxHo OTMeTI1Tb, QTO npl1 KOHKpeTHOM 3HaQe-
HI1H SLR KnTI ,aOCTl1raeT MaKCI1MyMa nplf orrpe,n:eneHHOM KOnllQeCTBe 3neMeH-
TOB aHTeHHOM pellIeTKII. TIpllQI1Ha ,n:aHHoro RBneHI1R COCTOIlT B TOM, QTO 3Heprl1R
60KOBoro neneCTKa RBnReTCR Q:>YHKII.lIeH, rnaBHbIM 06pa30M, ero OTHOClfTenbHoro
ypOBHR (SLR), Tor,n:a KaK 3HeprllR OCHOBHoro nyqa 3aBIICIIT, npe)l()];e Bcero, OT
KOnlfQeCTBa 3neMeHTOB. TI03TOMY, Kor,n:a 3Heprl1R 60KOBoro neneCTKa HaQI1HaeT
COCTaBnRTh 60nhllIyIO QaCTb OT nonHOH 3Heprlllf, 3<l>Q:>eKTlfBHOCTb YMeHbllIaeTCR.
Ha pl1C. 3.9 npe,n:CTaBneHbI 3HaQeHI1R KOnllQeCTBa 3neMeHTOB H SLR, 06eCneQI1Ba-
IOIUlfe MaKClfManbHbIM KlfIT. 3Ta KplfBaR nplf6nIDKeHHo annpOKcl1MHpyeTcR 3a-
BlfClfMOCThlO log N  0.08547 SLR dB - 0.4188.

1
:s:
E--
o
o
:I: 0.95
><
Q.;
(1)
/XI
o

0:: 0.90
:s:
:I:
ro
/XI
o

 0.85
o

o
:s:
E--
 0.80
:s:

:s:
-e
-e
8 0.75

0.70
20
/
22
3.2. AHmeHHble peUJemlCU )JOJlbfjJa-lfe6blUJe8a 
"'.... qHCJIO 3JIeMeHTOB N = 20
.....
.'
.,/ 100
24
..
.....,
-
......

.., .....
'.'h.'""'
.............,..... - 
'" ......
.... '..........-......
...............,... 
... '.
... -."
...'.... -.  ,...
....., .....
, '.
.. "
.." '.'-.
............. "'  ,......,.,..
.... -..-
.. '.
.. '.
... ...... -.-...
..'
.'
.'
.'
26
28 30
SLR (.n;E)
32
34
36
38
40
PHC. 3.8. K03<P<PHIJ;ileHT HCnOJIb30BaHIDI nOBepXHOCTH aHTeHHOH perneTKH ,LI;OJIb<pa-
Qe6bIrneBa, d = 0, SA
100
N
10
15
20 25
SLR (.n;E)
30
PHC. 3.9. AHTeHHaH perneTKa ,LI;oJIb<pa-Qe6bIrneBa C MaKCHMaJIbHbIM KMIT


rJla6a 3. CUHme3 iJuazpaMM Hanpa6JleHHOCmu JlUHeUHOU aHmeHHOU pelUemKU
3.2.2. PeweTKM C nepMOAM'iHOCTblO,
- -
MeHbweM nonYBonHoBoM
TIOJIyqeHHbIe B pa3.[(eJIe 3.2.1 pe3YJIbTaTbI orpaHI1QI1BalOTCR c.rryqaeM, Kor.[(a mar pe-
meTIGI COCTaBJUleT nOJIOBI1HY lIJIl1HbI BOJIHbI 11 6oJIee, nOCKOJIbKy npl1 MeHbmeM ne-
pIfO,l(I1QHOCTll IfCnOJIb3yeTcR TOJIbKO MarraR qaCTb 06JIaCTll OCIJ;I1JlJIRUllM nonHHOMa.
B pa60Te [54] nOKa3aHO, qTO npH HeqeTHbIX N 3TO OrpaHl1qeHl1e MO)l(eT 6bITb CHR-
TO; MHO)KIfTeJIb HanpaBJIeHHOCTI1 <popMl1pyeTcR, Haql1HaR C rpaHI1UbI + 1 06JIaCTH
Qe6blmeBa, npoxo,nR qepe3 o6nacTb OCUI1IDIRUHM K ,l(pyrOH rpaHIfl(e, B03Bparn:aRCb
3aTeM K HCXO,l(HOM)' KOHUY 11 MOHOTOHHOH qaCTI1, o6pa3YR npIf 3TOM nOJIOBHHY
OCHOBHoro JIeneCTKa. TOqHaR HCXO.[(HaR TOqKa 3aBHCHT OT 3HaqeHIfR Nkd. TIo-
CKonbKy nOJII1HOM Qe6bImeBa nopMKa M If MeeT M - 1 OCl(I1JlJIRl(IfIO, npOXO,l(HMYIO
,l(Ba)l()J;bI, If npoxo,n: OT 0 K 1 H o6paTHo <popMHpyeT 6oKoBbIe nerreCTKH, MHO)l(HTeJIb
HarrpaBJIeHHOCTH Bcer.[(a If MeeT HeqeTHOe KOnIfqeCTBO 60KOBbIX neneCTKOB C Ka)K-
,l(OH CTOpOHbI, Ii, CJIe.[(OBaTenbHO, qeTHOe ql1CJIO HyneH. B pe3ynbTaTe qe6bIIIIeBCKaR
AP C rrepIfO.[(HqHOCTblO MeHee rrOJIyBOJIHOBOH MO)KeT 6bITb C<pOpMHpOBaHa MeTO,l(OM
[54] TonbKO H3 HeqeTHOrO qHCna 3JIeMeHTOB. ,[(IfarpaMMa HanpaBJIeHHOCTH ,l(aeTCR
BbIpa)KeHlieM
F(u) = T M (a cos(u) + b);
a = Zo + 1 ; b = Zo cos(kd) + 1 .
1 - cos(kd) cos(kd) - 1
KaK If paHbme, u = kd sin e 11 M = (N - 1)/2. 3HaqeHHe Zo paBHO
h arccoS1(SLR)
Zo = cos M .
CooTBeTcTByJOrn:He <POp MYJIbI 6blJII1 no.rryqeHbI BO MHorHX pa6oTax, BKJIIOqaR
pa60TbI [19, 13, 14, 16, 17, 56]. 3,n:ecb HCrrOJIb3yJOTCR <POPMYJIbI [16, 17], nOCKOnbKy
OHI1 rrpIfrO.[(HbI ,l(JIR KOMnblOTepHoro paCqeTa CBepXHanpaBneHHbIX aHTeHHblX peIIIe-
TOK (CM. rJIaBY 9). HYMepal(IfR 3neMeHTOB peIIIeTKH TaIOKe npOBO,l(I1TCR, HaqIfHaR C
HYJIeBOrO 3neMeHTa B u;eHTpe; K03<P<PIfUIfeHTbI B036y)1(.[(eHHR HMelOT BH,[(
(3.18)
(3.19)
An = En ""EmEM Tn(xn)TM(ax n +b)+(-I)nT M (b-ax n ),
4M L..J 2-m
r,l(e £j = 1 ,l(JIR i = 0, If £j = 2 .[(lliI i > o. IIepeMeHHaR X n = cos n'Jt/ M. l(eJIbIe QI1CJIa
M 1 11 M 2 COCTaBnRIOT ueJIYlO qaCTb M/2 11 (M + 1)/2 COOTBeTCTBeHHO. MarrbIH mar
MO)KeT nOTpe6oBaTb BblnonHeHIfR apIf<l>MeTl1qeCIGIX onepaUI1H C Y,l(BOeHHOH TOQHO-
CTblO 113-3a BbIqHTaHHR QJIeHOB. TIpl1 no.rryBOJIHOBOM mare BbImerrpl1Be,n:eHHbIe ne-
peMeHHbIe a 11 b CBO,l(5lTCR K
(3.20)
1
a = - (zo + 1);
2
1
b = - (zo -1).
2
(3.21)
TIpH rrOJIYBOJIHOBOH nepHo.[(I1QHOCTI1 peIIIeTIGI o6a rrO,l(xo.[(a ,nalOT IUJ:eHTIfqHble
pe3YJIbTaTbI. B 3TOM CJIyqae ,n:HarpaMMa HanpaBJIeHHOCTIf, onIfCbIBaeMaR ypaBHeHH-
eM (3.8), COBnan;aeT C ,l(HarpaMMoH, nOJIyqeHHoH H3 ypaBHeHHR (3.18):
( N-l U ) _ ( Z(COS(U)+I)+COS(U)-I )
TN-I Xo cos- = T M .
2 2
(3.22)

3.3. OOHOnapGMempu'teC1we pacnpeoeneHue Teii.nopa JIJ
B [18] pacnpOCTpaHeH MeTO,n: paCqeTa perneTOK ,JJ,OJIb<pa-Qe6bIrneBa Ha aHTeH-
HbIe peIIleTKM oceBoro 113.rryqeHMH, HO TOJIbKO ,lLJIH CJIyqaH IIlara, MeHbIIlero, qeM
nOJIynOJIHOBoit 3TO OrpaHMqeHl1e He cymecTBeHHO, nOCKOJIbKY perneTKM oceBoro
M3JIyqeHMH 06blqHO MMelOT qeTBepTbBOJIHOBbIH rnar BO 1136e)KaHMe 60JIbrnOrO ypOB-
HH 3aL(HerO JIeneCTKa. TIpM JII060M yrJIe CKaHMpOBaHMH JIyqa U onpe,UeJIHeTCH COOT-
HOIIleHMeM, rrpMHHTbIM ,lLJIH CKaHMpyroll.(I1X aHTeHHbIX perneTOK:
u == ka(sin 8 - sin 8 0 ),
(3.23)
r,n:e 8 0 - yrOJI CKaHMpOBaHI1f1 OCHOBHoro JIyqa. Me)l(3J1eMeHTHbIH <pa30BbIH C,UBMr
COCTaBJIfleT kd sin 8 0 , a K03<P<PI111MeHTbI a M b MM elOT BI1,n:
3 + Zo + 2 .J 2(zo + 1) coskd
a==
2 sin 2 kd '
(3.24 )
( .Jzo + 1 +.J2 coskd f
b== .
2 sin 2 kd
(3.25)
B pa60Te [18] nOKa3aHO, qTO npl1 rnare B I1HTepBaJIe OT nOJIOBHHbI ,n:o nOJIHOH
,lUIHHbI BOJIHbI, npH KOTOpOM He B03HHKaeT ,U11<ppaKUI10HHbIX nerreCTKOB, HarrpaB-
JIeHHOCTb 60JIbIIlOH aHTeHHOM perneTKI1 ,L(onb<pa-Qe6bIIIleBa He 3aBI1CMT OT yrJIa
CKaHHpOBaHHH. B pa60Te [47] nOKa3aHO, qTO ,n:JIH CMHTe3a Qe6bIrneBcKoH ,n:HarpaM-
u u
MbI HarrpaBJIeHHOCTM aHTeHHOM perneTKM, COCTOHll.(el1 113 qeTHOrO ql1cna 3JIeMeHTOB
C rnarOM MeHbIIle nOJI)'BOJIHOBOrO, MOryr MCnOJIb30BaTbCH rrOJIMHOMbI 30JIOTapeBa
(CM. TaIOKe pa3,n:en 3.7.4).
3.3. OAHonapaMeTpM"IeCKOe pacnpeAeneHMe TeMnopa
3.3.1. PaC'IeT OAHonapaMeTpM'IeCKOrO pacnpeAeneHMSI
B pa60Te [62] [pe3YJIbTaTbI KOTOpOH 3,n:eCb KpaTKO 113JIO)l(eHbI] yrBep)l(,L(aeTCH, qTO
,lLIDI CJIyqaH JIMHeMHOH perneTKM rrpM rrOMCKe aMIIJIHTy,n:Horo pacrrpe,n:eJIeHI1H, <pop-
MMpyromero ,JJ,H C Orl16alOmeH 60KOBbIX JIerreCTKOB, cna)J:alOll.(eH KaK Iju, MO)I(HO
Hcnonb30BaTb B KaqeCTBe oTrrpaBHoH TOqKM ,Ul1arpaMMY HarrpaBJIeHHOCTI1 BRII:a
sin(x)jx, KOTOPYIO I1MeeT perneTKa C paBHOMepHbIM pacnpe,n:eJIeHl1eM.
TeitTIop 06HapyxMJI, QTO HHTeHCI1BHOCTb JII060ro 60KOBoro JIerreCTKa 3aBHCI1T
u
OT HHTepBaJIa Me)l(,L(y HYJIHMI1 MHO)KJ1TenH HanpaBJIeHHOCTI1 C Ka)J()J.OI1 113 CTOpOH
3Toro JIerreCTKa. ITOCKOJIbKY sinc-06pa3HaH ,Ul1arpaMMa I1MeeT ofl16alOmyro 60KO-
BbIX JIeneCTKOB BI1,n:a 1 j u, ,lLIDI )'MeHbrneHIDI 6JII1)1(HI1X 60KOBbIX JIeneCTKOB He06xo-
,n:I1MO CKOppeKTl1pOBaTb TOJIbKO nOJIO)KeHHe 6JIIDKHI1X HYJIeH. ,L(aJIbHHe HYJIH 6bIJIH
OCTaBJIeHbI l(eJIOQMCJIeHHbIMI1. C,UBl1f ocymecTBJIIDICH rryreM YCTaHOBKI1 HYJIeH ,n:Ha-
rpaMMbI B HanpaBJIeHHflX
u==  n2 +B2,
(3.26)
r,n:e B - rrOJIO)l(l1TeJIbHbIM ,n:eHcTBHTeJIbHbIH napaMe1]J. LJ;l1arpaMMa HanpaBJIeHHO-
CTM rrOJIyqaeTcfI C nOMOIIJ;blO BbIpa)l(eHMfI sinc-<PYHKl(1111 B BMLI,e OTHorneHHfI ,n:BYX


FJlaea 3. CUHme3 iJua2paMM HanpaeJleHHOCmu JlUHeUHOU aHmeHHOU peLUemKU
6eCKOHeqHbIX rrpoH3BeJ(eHHH. 3aTeM HynH J(HarpaMMbI CMern:aIOTCH,
BbIllie. B 3TOH cl>opMe J(HarpaMMa HarrpaBneHHocTH HMeeT BHL(
CfI [ l- u2 -B2 ]
F(u) = n=! n 2
00 [ B2 ] ,
!] 1 + n 2
rJ(e C - KOHCTaHTa. 3TO BbIpa)l(eHHe M O)I(HO yn pOCTMTb
sinh n .J B2 - u 2
F(u) = u < B,
n .J B2 - u 2
sin n .J u 2 - B2
F(u) = u > B.
7t .J u 2 - B2
I1YCTb Tenepb KOHCTaHTa C = sinh(nB)/nB. 3Ta .nnarpaMMa HanpaBJleHHOCTn HBITH-
eTCH MOL(H<pn:QHpOBaHHOH sinc-L(MarpaMMoH C eL(MHCTBeHHbIM napaMe1'pOM B, onpeL(e-
IDIIOrn:nM Bce xapaKTepHCTIlKH aHTeHHoH pellIeTKM: ypoBeHb 6oKoBoro neneCTKa, IllM-
pHH)' .rryqa, KH)]., 3<p<peKTHBHOCTb rnaBHoro .rryqa M TaK L(aJIee. I1epexo,a OT
sinc-<PYHKQMM K rnnep6onWIecKoH cl>YHKQHH npoMcxoJ(HT CO CTOpOHbI OCHOBHoro
nyqa npM U = B. IIpM MeHbIlleM U u;eH1paJIbHaH qaCTb OCHOBHoro nyqa OITHCbIBaeTCH
rnnep6onWIecKoH cl>YHKIJ;HeH C nHKOBbIM 3HaqeHMeM sinh(nB)/nB. HIDKHIDI qaCTb
OCHOBHoro nyqa n 6oKoBble neneCTKH OilllCbIBalOTCH TpHrOHOMe1'pWIeCKOif <PYHKIJ.Hei1.
3HaqeHHe SLR npeL(CTaBJUIeT C060R Henocpe,aCTBeHHO cooTBeTcTB)'IOrn:ee 3HaqeHMe
,lJ)UI sinc-<PYHKQMH, YMHO)l(eHHOe Ha MaKCHM}'M nyqa. 3TO COCTaBJUIeT B .neUM6enax
sinh 7tB
SLR = 20log + 13,2614 .an. (3.29)
7tB
KaK YKa3aHO
(3.27)
(3.28)
Ha pHC. 3.10 H306pa)l(eHa THnMqHaH o,aHonapaMeTpMQeCKa51 ,aMarpaMMa Ha-
npaBneHHOCTH Teifnopa B 3aBHCHMOCTH OT u.
IIlHpHHa nyqa onpeL(enHeTCH nyreM HaXO)l([{eHM5I KOpHH ypaBHeHH5I
.J2F(U3) = sinh 7tB . (3.30)
7tB
B Ta6n. 3.1 npHBe,aeHbI napaMeTpbI pacnpe.aeneHH5I LUI5I SLR ,ao 50 ,an. IIlMpH-
Ha nyqa u3 rrpeo6pa3yeTcH B cl>H3HqeCKHR yron 8 3 npH COOTHOIIIeHMH
8 3 2L . U 3
= -arCSin (3.31)
AIL ALIA
LJ:n51 ,lLJIMHHbIX nMHeHHblx anepTYP HOpMMpOBaHHa5I IIIHpHHa nyqa He 3aBHCHT
OT LIA M COCTaBnHeT
8 3 
= 2U3.
AIL
Ha pMC. 3.11 npe.aCTaBneH rpa<pMK HOpMHpoBaHHoM IIIMpHHbI Jlyqa ,lLJIH anepTYP
,lLJIHHOM B 5, 10 H 50 ,lLJIHH BonH. MO:>KHO Blf.Ll:eTb, qTO anepTypbI .LLJIMHOM B 5 H 10
.LLJIHH BonH no YPOBHIO 6oKoBoro neneCTKa He3HaQHTenbHO OTnHQalOTCH OT Gonee
npOTIDKeHHbIX anepTYp. IIo3ToM)' B 60nbllIHHcTBe cnyqaeB rrpHeMJleMa rrpH6nIDKeH-
HaH <popMyna.
(3.32)

3.3. OiJnonapflMempU'leCKOe pacnpeaeJlenue TeUizopa 
o
-10
-..

I::[
'-"

 -20
E-<
:s:

I::

<:
-30
-40
-6
-5
-4
-3
-2
-1 0 1
U = kd sin e
2
3
4
5
6
PUC. 3.10. O,LlHOnapaMeTPHQeCKIDI .n:RarpaMMa HanpaBJIeHHOCTR TeHJIopa, SLR = 25 .n:E
Ta6JIuna 3.1. XapaKTepRCTHKH O,LlHOnapaMeTpRQeCKOH ,LllfarpaMMbI HanpaBneHHOCTIf
Teitrropa
SLR (,n6) B "3 (pa,n) 11, 11,u3 YpOBeHb nOJUI Ha
KpalO paCKpbma (,n6)
13.26 0 0.4429 1 0.443 0
15 0.3558 0.4615 0.993 0.457 2.5
20 0.7386 0.5119 0.933 0.478 9.2
25 1.0229 0.5580 0.863 0.481 15.3
30 1.2762 0.6002 0.801 0.481 21.1
35 1.5136 0.6391 0.751 0.480 26.8
40 1.7415 0.6752 0.709 0.479 32.4
45 1.9628 0.7091 0.674 0.478 37.9
50 2.1793 0.7411 0.645 0.478 43.3
)J;JIH HeKOTopbIX KapTorpaQ:>HqeCKHX H pa,n:HOMeTpHqeCKMX npHJIO)l(eHHM Ba)l(Ha
,lI;OJIH 3HeprHH, H3JIyqaeMaH B TeJIeCHOM yrJIe, 3aKJIIOqeHHOM Me)l{)J;Y HYJIHMH rJIaB-
Horo JIyqa, KOTopaH Ha3bIBaeTCH 3Q:>Q:>eKTHBHOCTblO fJIaBHOrO JIyqa llb- 3<t><peKTHB-
HOCTb rJIaBHOrO nyqa BbIqHCnHeTCH nyreM HHTerpHpOBaHI1JI KBa,n:paTa ,lIHarpaMMbI
HanpaBJIeHHOCTH no OCHOBHOMY nyqy C nOCJIe,n:YIOllI.HM ,n:eJIeHHeM pe3ynbTaTa Ha
HHTerpaJI KBa,n:paTa ,n:HarpaMMbI HanpaBJIeHHOCTH no BceMY npocTpaHcTBY. 06bIQHO
3TO Tpe6yeT QHCJIeHHOrO HHTerpHpoBaHHH no BceM 60KOBbIM JIeneCTKaM ,lI;HarpaM-


FJlaea 3. CUHme3 aUa2paMM HanpaeJleHHOCmu JlUHeUHOU aHmeHHou peUlemKU
1.5
1
U)' = 50
----- 10
-----. - -... 5
,.-.
1.4
,,/
....:
--
.


c:l.
 1.3
---
.<
............

x
 1.2

I=:

::r::
:s::
c:l. 1. 1
:s::
S
0.9
15
20
25
30 35
SLR (JIE)
40
45
50
PHC. 3.11. HOpMMpoBaHHaH IlIMpMHa JIyqa rrpM O,L(HOrrapaMeTpMQeCKOM pacrrpe,L(eJIe-
HMH TeMJIOpa
MbI, qTO 5IBJI5IeTC5I 3a1'paTHOM M cpaBHMTeJIbHO HeTOqHOM onepalU1eM. OL(HaKO, KaK
6y,aeT nOKa3aHO ,aaJIee, BbIqMCJIeHMe KI1II pacKpbIBa 111 TaIOKe BKJUOqaeT TaKoe MH-
TerpMpoBaHMe no BceM 60KOBbIM JIeneCTKaM ,aMarpaMMbI. 3TO n03BOJI5IeT BbIpa3MTb
3<p<peKTHBHoCTb fJIaBHOrO JIyqa Qepe3 KMII anepTypbI aHTeHHbI M HHTerpaJI TOJIbKO
no OCHOBHOMY JIyqy, qTO BbIqMCJI5IeTCH OTHOCMTeJIbHO npocTo H 6bICTpO. B pe3YJIb-
TaTe HMeeM
2L 8)
11b = 2 111 J I FI2 cos8d 8.
FoA 0
Ha pMC. 3.12 npMBeL(eHa 3aBMCMMOCTb 3<p<peKTMBHoCTM rJIaBHOrO JIyqa OT 3Ha-
qeHM5I SLR. )].JIH MaJIbIX 3HaQeHMM L/A -- 5 KpMBaH He 3aBMCMT OT L/A.
AMnJIMTy,aHoe pacnpeL(eJIeHMe ,n:aeTCR 06 pameH MeM ypaBHeHMH (3.28):
g(P) == 10 (1tB .J l - p2 ), (3.34)
(3.33)
r,n:e p - paCCTOHHMe OT u:eHTpa ,ao KpaR paCKpbIBa, npMqeM 3HaqeHMe p == 1 COOT-
BeTcTByeT KpalO. fIepeMeHHaH /0 npe,n:CTaBJIHeT C060M MO,n:M<pMU:MpoBaHHyIO <PYHK-
II;MIO EeCCeJIH HYJIeBOrO nopMKa. BbIcoTa nbe,n:eCTaJIa COCTaBJI5IeT 1/ /o('JtB). AMnJIM-
ry,n:Hble pacnpe.n:eJIeHMH no aneprype OT II;eHTpa K KpalO paCKpbIBa nOKa3aHbI Ha
pMC. 3.13 ,l(JIH HeCKOJIbKJ1X 3HaqeHMM SLR. KMII anepTypbI aHTeHHbI onpe.n:eJI5IeTC5I
BbIpa)l(eHMeM
111 ==
1 F(0)12
L/2A
J 1 F(u)12 d u
- L/2 A
(3.35)

0.98
C'j


..Q 0.96

u
o
:I:

::so:

e 0.94
-&
(T)
0.92
0.90
15
3.3. OOnonapllMempU'leClCOe pacnpeoeJlenue TewlOpa 
1
20
25
SLR (,n;E)
30
35
Pac. 3.12. 3<p<peKTHBHOCTb .rryqa rrpH o,n;HorrapaMe1pWIeCKOM pacrrpe,n;eJIeHHH T eitJIopa
0.8


:a


u
C'j

o 0.6
t::::
0::

o
t::::
C'j
 0.4
::so:
2

0.2
1
'........ .... ..
........ ........
'. ..
.....<::,  :.....................
....- ....,
'. ..
""'-".:.  .......,......
'. ..
.c,._ ..
-, -.
"'," ....
"".  .......
". ..
'. ...
'. 
''" ".., 25
'-I '- '
........  30........
. ...
......-.40 .........
-'.' ....
SLR = 50 ,n;E........... '" ................
. ..
. ,
-.'.... " '" .. ......
'-::],.11, ....,
"'. ....
 '
...-...-...... . ",- ..................
.  '.
............ .... '" "'...........
-'.- .
_, 'IIr..
'. ...
..-....... .... ............ ............
........""....,,-.. 
I. "'''_',. ....
°0
0.9
02 0.3 0.4 0.5 0.6 0.7 0.8
PaccToHHHe OT ueHTpa ,n;0 KpaH anepTYPbI
1
0.1
PUC. 3.13. O,n;HorrapaMe1pHQeCKOe aMIIJIHTY,n;Hoe pacrrpe,n;eJIeHHe Te:HJIopa

 Dlaea 3. Cunme3 iJua2pl1MM nanpa8Jlennocmu Iluneunou anmennou pewemKU
B clUIY 6bIcTporo YMeHbilleHIUI 60KOBbIX JIeneCTKOB C pOCTOM U rrpe,n:eJIbI MH-
TerpMpoBaHlfH MOryT 6bITb nplfHHTbI 6eCKOHeQHbIMlf ,n:a)f(e ,l(JIH He60JIbillMX arrep-
TYp. TorlIa lfHTerpaJI MoxeT 6bITb CBe.aeH K Ta6JII1QHoMY [55]:
2 sinh 2 1tB ( 3.36 )
11t = 1t BIo (21tH)'
r,n:e 10 - MHTerpaJI looT HYJIH ,n:0 3HaqeHI1H apryMeHTa. 3HaQeHI15I KI1IT npe,n:CTaB-
JIeHbI B Ta6JI. 3.2.
Ta6JIHa 3.2. lloKa3aTeJIH 3<l><l>eKTHBHOCTH npH O.D:HOrrapaMeTpI1QeCKOM pacrrpe.n:eJIe-
HHH TeHJIopa
SLR (,aB) B 1), 1)b
13.26 0 1 0.9028
15 0.3558 0.9931 0.9364
20 0.7386 0.9329 0.9820
25 1.0229 0.8626 0.9950
30 1.2762 0.8014 0.9986
35 1.5136 0.7509 0.9996
40 1.7415 0.7090 0.9999
45 1.9628 0.6740 , 1.0000
50 2.1793 0.6451 1.0020
3.3.2. AByxnapaMeTpM'IeCKOe pacnpeAeneHMe
6MKMopa-CnenMa£1pa
MHor,n:a He06xo,n:I1MO 06eCneQlfTb crraaaHlfe Orl16alOrn:ell 60KOBbIX J1eneCTKOB 6bICT-
pee, QeM l/u. Peilll1Tb TaKYIO 3aaaQY n03BOlliIeT ,n:ByxnapaMeTplfQeCKOe ceMeMCTBO
pacnpe,n:eJIeHMM, npe.lUIOXeHHOe B [11]. ,[(ByxnapaMeTpWIeCKa5I ,n:MarpaMMa HanpaB-
JIeHHOCTI1. MMeeT BM,LJ;
J 1t  u2 -C 2
F(u) = v .
(1t  u2 -C2)v
3HaQeHlfe v = 1/2 ,n:aeT O,lI;HonapaMeTpI1QecKYIO ,n:lfarpaMMY HarrpaBJIeHHOCTlf, a
rrpl1 v > 1/2 orn6alOrn:aH cna,aaeT K KpaHM paCKpbIBa 6bIcTpee l/u. TIpH v = -1/2 HMeeT
MeCTO «H)leaJIbHaH» .aMarpaMMa, onHCbIBaeMa5I ypaBHeHMeM (3.28). TIapaMeTp C
orrpe,n:eJIHeT HaQaJIbHbIll ypOBeHb 60KOBoro JIerreCTKa. OTMeTlfM, qTO ,n:aHHhIe ,n:Ba rra-
paMeT}Ja He3aBMClfMbI, B OTJIWIHe OT MaJIoynoT}Je6lfTeJIbHbIX MHororrapaMeTplfqeCKMX
pacnpe,lI;eJIeHl1ll, onMcaHHbIX paHee. AMITJIMT)',lI;HO e pacrr pe,n:eJIeHMe MMeeT B:H,[(
J v -1 / 2 U1t C 1 - p2 )
g(P) = . (3.38)
U1tC  1 - p2 ) v -1 / 2
TIpM V < 1/2 B03HMKalOT CMHrylliIpHOCTH no Kpa5IM paCKpbIBa. 3HaqeHMe v = 3/2,
K nplfMepy, ,n:aeT crran; orM6alOIIJ:eM 60KOBbIX JIerreCTKOB Bl1,n:a 1/ u 2 . 3TH 6bICTpocrra-
,n:alOIIJ:lfe pacnpe,n:eJIeHIDI HCrrOJIb3yroTCH pe,nKO H3-3a CBOllCTBeHHoro lfM MaJIOrO KO-
3<t><PMIJ:MeHTa I1CnOJIb30BaHHH nOBepXHOCTM.
(3.37)

3.4. N-napaMempu'leclCoe aMllJIumyonoe pacnpeoeJlenue TewlOpa 
3.4. N-napaMeTpM'IeCKOe aMnnMTYAHoe
pacnpeAeneHMe Te£1nopa
PacrrpeeneHMe Tennopa C xapaKTepHCTMqeCKMM napaMeTpOM n pa3pa60TaHo KaK
KOMrrpOMMCCHoe Me)l()]:Y pacrrpeeneHHeM ,lJ.onb<pa-Qe6bIllieBa, MnM «M,neaJIbHOH»
arrepTYPoH C 60KOBbIMM nerreCTKaMH nOCTOHHHoro ypOBHH, M pacnpe,neneHMeM C
OfM6alOmen 60KOBbIX neneCTKOB, cna.n:alOmeM KaK Iju, xapaKTepHbIM L(nH ,nMarpaM-
MbI HarrpaBneHHOCTM BMlIa sin (x)jx. 3TO n paCrrpelIeJIeHMe I1crronb3yeTcH JIH rrOJIY-
qeHI1R 60nbllIeM 3<p<peKTI1BHOCTI1 rrpM coxpaHeHMM 60nblIII1HCTBa rrpel1MymecTB
pacrrpe,neneHMn co cnaalOmeH K KpaHM aMnnMTYoM. OTnpaBHoH TOqKOH ,lLJUI
TeMJIOpa CTaJI no,n;xo,n, OTJIl1qHbIn OT Hcnonb3YIOmerOCH B cnyqae OHorrapaMeTpM-
qeCKOrO pacnpeeJIeHH5I. OH HaqaJI C pellieTKI1 C <<If.[{eaJIbHoH>) nMHeHHOM anepTY-
pOM, MMelOmetl L(l1arpaMMY HarrpaBneHHOCTI1 C 60KOBbIMI1 JIeneCTKaMI1 paBHoro
ypOBHH, KaK npl1 pacnpeL(eneHI1M JJ;onb<pa-Qe6bIIIIeBa. TeM caMbIM JUI5I nlO60H nM-
HenHoH anepTypbI C nOCT05lHHOM <pa30H 06eCrreQMBaeTCH HaM60nbllIaH HanpaBneH-
HOCTb npM 3a,LlaHHOM SLR. PaBHbIH ypOBeHb 60KOBbIX neneCTKOB 06eCneQl1BaeTCH
<PYHKr(HeiI KOCI1Hyca, a OCHoBHon neneCTOK - <PYHKQl1en rl1nep60JII1QeCKOrO KO-
CI1Hyca:
F(u) = cosh 1t .J A2 - u 2 U < A,
F(u) = COS1t .J u 2 - A2 U > A
(3.39)
Pacnpe,LleneHl1e H xapaKTepMCTI1KH ,n;MarpaMMbI HanpaBneHHOCTM onMCbIBalOTCH
e,n;HHCTBeHHbIM napaMeTpOM A. HynH ,n;HarpaMMbI HanpaBneHHOCTH ,n;aIOTC5I BbIpa-
)l(eHHeM Zn = +  A 2 + (n - Ij2) 2 , SLR Onpe,lIelliIeTC5I 3HaQeHI1eM npH U = 0:
SLR = cosh A,
a BbIpa)](eHHbIH Qepe3 SLR rrapaMeTp HMeeT BM,n
A =  In(SLR+ .J SLR2 -I).
(3.40 )
(3.41)
IIIHpHHa nyqa Ha ypOBHe 3-dB ,lIaeTC5I BbIpa)](eHHeM
U3 =  [ln 2 (SLR+ .JSLR2 -1 ) -ln 2 (SLRj.J2 + .JSLR2 j 2 -1 )T 2 . (3.42)
IIpl1 U = A lUI51 rnaBHoro nerreCTKa rrpOHCXOHT rrepexo OT 1pHfoHoMeTpMqe-
CKOM K fHnep60nHQeCKOH <popMe. ,lJ.aHHoe KaHOHMQeCKOe pacrrpe,neJIeHMe HMKor,na
He MCrrOJIb3yeTC5I, rrOCKOJIbKY y Hero He TOJIbKO BbICOKMH ypOBeHb ,naJIbHHX 60KO-
BbIX JIerreCTKoB, HO M rrHK C 6eCKOHeQHOM aMnnMTY,n;oH Ha KOHQax pacKpbIBa. 3TO,
KOHeQHO, rrpe,LlenbHbIH cnyqati pacrrpe.n:eJIeHMH ,lJ.OJIb<pa-1Je6bIllieBa rrpl1 yneJIMQe-
HI1M KOJIHQeCTBa 3JIeMeHTOB. OHaKo OT «I1,neaJIbHOfO» pacrrpe,neJIeHMH MO)](HO ne-
petiTH K llIMpOKO HCnOJIb3yeMoMY n pacrrpe,LleneHHIO TeitJIopa [61].
OT «H,n;eaJIbHoro» pacrrpe,neJIeHM5I TeitJIop B3IDI HeCKOJIbKO nepBbIX 60KOBbIX JIe-
neCTKOB paBHoti aMTIJIHTY,n;bI, 06eCneQHBalOlI(HX nOBbIllIeHHYIO 3<p<peKTI1BHOCTb, H
C,lJ;BHHyn HYJIH ,naJIbHMX 60KOBbIX JIeneCTKOB, lUI51 no.rryqeHHH orM6alOmeM Bl1)];a Iju, B
u:eIDIx YMeHbIIIeHM5I BnIDIHIDI rrOMex H C03,LlaHIUl pacrrpe.n:eneHIDI C HH3KOH ,n06POT-
HOCTblO Q. )J;JIH 3Toro MaCllITa6 no U HeMHoro paCTHfHBaeTC5I C K03<P<PHQHeHTOM 0,


rJla6a 3. CUHme3 auazpllMM Hanpa6JleHHOCmu JlUHeUHOu aHmeHHOU pelUemKU
r,lJ.e a HeMHoro 60JIbllIe e,lJ.HHHl(bI. TaKHM 06pa30M, 6JIH3Ka5I K lIYJIIO 06JIaCTb 3aMeT-
HO He MeH5IeTC5I. B HeKOTopbIH MOMeHT HYJIb npHXO,lJ.HTC5I Ha l(eJIoe 3HaqeHl1e; Haql1-
HaR C 3TOH rrepeXO,lJ.HOM TOqKJ1 lIYJIH npHXOJUlTC5I Ha + n. B pe3YJIbTaTe ,lJ.HarpaMMa
HarrpaBJIeHHOCTH HMeeT n npH6JIH3HTeJIbHO paBHbIX 60KOBbIX JIeneCTKOB, a BHe 06JIa-
CTH U = n orH6aIOll(aR 60KOBbIX JIerreCTKOB BeI(eT ce6R KaK l/u. BbICOTa nepBbIX n JIe-
neCTKOB HeCKOJIbKO pa3JIHqaeTC5I, rrOCKOJIbKY B6JIH3J1 nepexo,n;HOM TOqKH rrpol1cxo-
,lJ.HT HeKOTopoe )'MeHbllIeHHe 60KOBbIX JIeneCTKOB. 3a rrepeXO,lJ.HOM TOqKOM
Orl16aIOrn:aH HeCKOJIbKO OTJII1QaeTC R OT l/u. HYJI H 3a;:I.aIOTC5I BbIpIDKeHl1eM
Zn= + cr  A2+(n-  J l < n <n
(3.43)
Zn = + n n < n.
fiapaMeTJ) YMHHeHI1R cr HMeeT BH,n;
n
cr =  A2 + ( n -  J ·
(3.44 )
,[(HarpaMMa HanpaBJIeHHOCTH C 3THMI1 HYIDIMH rrepBOHaQaJIbHO 6bIJIa 3anl1CaHa
I1CXOJUI H3 YMHHeHHH «H,[(eaJIbHOH» arrepTYPbI B BH,[(e 6eCKOHeQHOrO npOH3Be,lJ.eHH5I C
COOTBeTCTByIDrn:HMH KOpIDIMH. KaK no KOHl(errTYaJIbHbIM, TaK H rro BbIqMCJIMTeJIb-
HbIM rrpHqHHaM nOJIe3HO BBeCTH peryIDIpHo pacnOJIOXeHHbIe KOpHM B TpMrOHOMeT-
pHQecK)'IO <pyHKIJ;MIO, HMelOI.I.JyIO n - 1 BH.aOH3MeHeHHbIX KopHeH B 5IBHOM BH,JJ;e B KO-
HeQHOM npOH3Be,lJ.eHHH:
F(u) = sin1tu n l-u 2 / d .
1CU n= 1 1 - U 2 / n 2
3Ta ,lJ.MarpaMMa HanpaBJIeHHOCTH MO)l(eT 6bITb TaIOKe npe,Z:(CTaBJIeHa B BM,Z:(e CY-
nepn03Hl(HH sinc-06pa3HbIX JIeneCTKOB C KOH H3 CTOpOH u;eHTparrbHoro JIyqa,
pacnOJIO)l(eHHbIX C e,Z:(HHHQHbIM HHTepBaJIOM no u:
(3.45)
n-I
F(u) = L F(n, A, if) sinc [1t(u + n)].
n=-(n-I)
(3.46 )
Ha pHC. 3.14 nOKa3aHa THnHQHa5I 3aBHCHMOCTb ,Z:(HarpaMMbI HanpaBJIeHHOCTM
OT u npH pacnpe,n;eJIeHHH TeitJIopa C napaMeTpoM n . MO)l(HO BH,JJ;eTb, qTO <t>op-
Ma orH6alOll(ei1: rrepBbIX qeTbIpex 60KOBbIX JIeneCTKOB 6JIIDKe K KOHCTaHTe, qeM K
<pyHKIJ;HH l/u, a onepaUH5I n -conpIDKeHHR npHBO,lJ.HT K nocTeneHHoMY H3MeHeHMIO
BbICOTbI 60KOBbIX JIeneCTKOB. ,lLrr5I 60JIbllIHX n nOCTORHCTBO ypoBHen 60KOBbIX JIe-
neCTKOB BbIpa)l(eHO 60JIee 5IBHO.
llIHpHHa .rryqa TOqHO onHCbIBaeTC5I BbIpIDKeHHeM cru, r,Z:(e u - «H,JJ;eaJIbHaR»
llIHpHHa JIyqa, onpe,Z:(eJIReMaR ypaBHeHHeM 3.42. B Ta6JI. 3.3 rrpe,Z:(CTaBJIeHa 3aBHCH-
MOCTb rrapaMeTpa A OT 3HaqeHH5I SLR, a TaIOKe llIHpHHa .rryqa H napaMeTJ) YMHHe-
HH5I. HOpMHpoBaHHaR llIHpHHa .rryqa BW x L/'A nOKa3aHa Ha pHC. 3.15. HenpepbIB-
HaR KpHBaR 3,lJ.eCb He npOBe,Z:(eHa, nOCKOJIbICy ,lUllI Koro SLR 3HaqeHIIe n
pa3JII1QHO. 11306pIDKeHa TaIOKe KplIBaH MH mHpHHbI .rryqa O,Z:(HonapaMeTJ)WIeCKoro
pacnpe.ueJIeHIDI Teitrropa. KaK II CJIe,[(OBaJIO O)l(J1)1aTb, xapaKTepHCTHKH n pacrrpe.ne-
JIeHIDI 3HaQlITeJIbHO JIyqme, oc06eHHO npH 60JIbllIHX 3HaQeHH5IX SLR.

3.4. N-naptlMempu'teclCoe tlMT/JlUmyoHoe pacnpeOeJleHUe Teiinopa 
o
-10
-.

t:::[
--

 -20

::s::
r:::
t:::

-30
-410
-8
-6
-4
-2 0 2
U = kd sin e
4
6
B
10
PHC. 3.14. ,L(MarpaMMa HanpaBJIeHHOCTM n -napaMeTpMQeCKOrO pacnpe.n:eJIeHH5I Teil-
JIopa, SLR == 25 .n:E, n == 5
Ta6J1Hna 3.3. XapaKTepMcTMKM n pacnpe.n:eJIeHM5I TeHJIOpa
(J
SLR (,aB) A u3
n =2 n =4 n =6 n =8 n = 10
20 0.9528 0.4465 1.1255 1.1027 1.0749 1.0582 1. 0474
25 1.1366 0.4890 1.0870 1.0683 1.0546 1. 0452
30 1.3200 0.5284 1.0693 1.0608 1.0505 1.0426
35 1. 5032 0.5653 1.0523 1. 0459 1.0397
40 1.6865 0.6000 1.0430 1. 0407 1.0364
45 1.8697 0.6328 1.0350 1.0328
50 2.0530 0.6639 1.0289
AMTIJIHTy,n:Hoe pacnpe,n:eJIeHHe JIyqrne Bcero BbIpaxaeTCSl B BH)].e KOHeqHOrO
pSl,n:a <l>YPbe:
n-I
g(P) = 1 + 2 L F(n, A, n) cos n 1t p.
n=1
(3.47)
3HaqeHHe anepTYPHoM nepeMeHHoM p TaIOKe npHHIIMaeTCSI paBHbIM HYJIIO B
n:eHTpe II e,n:HHHl(e Ha KpaSlX paCKpbIBa. AMnJII1TY,n:Hoe pacnpe,n:eJIeHl1e, I1CnOJIb3ye-
Moe B 3TOH 11 rrpe,n:bI,n:yrn;eM <popMYJIaX, onpe.n:eJISleTCSI BbIpIDKeHl1eM
[ ( - 1) , ] 2 n -I [ 2 ]
F(n, A, n) = n - . 1 -  ,
(n - 1 + n)! (n -1 - n)! g d,
(3.48)


rJla6a 3. CUHme3 iJua2paMM Hanpa6JleHHOCmu JlUHeUHOU aHmeHHOU peUlemKU
r,Z:(e F(O, A, n) = 1. AMIIJIH1)',Z:(Hoe n pacrrpe,Z:(eJIeHHe ,WIH rrOJIOBHHbI paCKpbIBa H30-
6paxeHo Ha pHC. 3.16. no cpaBHeHHIO co c.rryqaeM oOHonapaMempUttecKo2o
pacnpeoefleHuR, H306pa)KeHHOrO Ha pHC. 3.13, «XBOCTbI» n pacrrpe,neJIeHMH HaMHoro
BbIIIIe. To eCTb rrbe,Z:(eCTaJI pacrrpe,Z:(eJIeHIDI 60JIee BbICOK, qTO rrpHBO,Z:(HT K JIytIIIIeti
1.5
1.4
°10
-..
.


-=- 1.3
«<
..........
.....J
x
 1.2



::r::
:s:
 1.1
a
OHonapaMeTpMqeCKOe
pacnpeeJIeHMe
°9
°8
0- 7
n=
06
05
1
0.9
20
25
30
35
SLR (E)
40
45
50
PHC. 3.15. IlIHpHHa JIyqa lIPH aMlIJIlrry.aHbIX paClIpe.aeJIeHHHX TellJIOpa
1
. -.6 6'.. ...
.......  .........
'. ...
'. ,
-.. .....
....... '...."....
....  ..."
.... ......
'. ...
-.. "
" ...
'. ...
. ,
......"  .......
. ..
'. ..
.. ..
-w. ...,
., ..
. ,
....." ' ...
-....".. ......,....
-.-.. '" "
'. ..
-".."..."  ............,..
-0. '...
-.0 '..,
....".,,'  .... .....o
". .....
SLR = 50.l!D "., ..,'.. 
.....
0.8


:a


u 0.6


o
t::


:s: 0.4

t::

'-
-..._-
'.
0.2

.....
'..
"----
...
".
.......
.....
......... .
°0
0.4 0.6
PaccToRHHe OT l(eHTpa .ao KpaR anepTYpbI
PHC. 3.16. AMlIJIHT)'.aHoe n rrapaMeTpHqeCKOe paClIpe.aeJIeHHe TellJIOpa
0.2
0.8
1

3.4. N-napllMempU'leClwe llMrLIlumyiJnoe pacnpeiJenenue TewlOpa -d
3<p<peKTMBHOCTM B COOTBeTCTBMH C npaBMJIaMH TeitJIopa. B pa60Te [29] ,l(aHbI
Ta6JIHUbI ,l(JIH aMTIJIM1)'.aHoro pacnpe.aeJIeHMH M K03<P<PMUMeHToB npll SLR = 20 (5)
40 .aD II n = 3 (1) 10. DOJIee nOJIHbIe Ta6JIMUbI MMelOTCH B pa60Te [14].
KH)J. If Kl1n JIerKO BbIqMCJIHIOTCH. AMTIJIH1)',l(HOe pacnpe.aeneHHe IIHTerpHpo-
BaTb JIerqe, qeM ,l(HarpaMMY HanpaBJIeHHOCTH, nOCKOJIbKY OHO BbIpIDKaeTCH B BH,lJ,e
pH.aa cDYPbe H3 OpTOrOHaJIbHbIX qJIeHOB; 3TO BbIpa)J(eHHe HBJIHeTCH TOqHbIM ,lI)IH
TIpOTIDKeHHbIX B e,n;HHHuaX .LUIHH BOJIH anepTYP [27]
2
11=
I
f g(p)d p
o
I
f g2 (P)d p
o
(3.49)
I1cnoJIb3YH ypaBHeHHe (3.47) )lJIH <PYHKl.{HH pacnpe,n;eJIeHIDI, nOJIyqaeM B qHCJIH-
TeJIe BbIpa)J(eHH5I .LUI5I KI1TI e.rUfHHUY, TaK KaK q)JeHbI, co.aep)KaIUHe KOCHHyC, npH
HHTerpHpOBaHMH 06HYJIHIOTCH. B 3HaMeHaTeJIe npOH3Be.aeHHe g2 .n.aeT e.n.IIHHU:Y TIJIIOC
,l(Ba O.n.HHOqHbIX pMa M .n.BOMHOM pM. KIDK.ZJ:bIM H3 q)JeHOB O,l(IIHOqHOrO pMa npH HH-
TerpHpOBaHHH 06HYJIHeTCH. I1HTerpaJI OT .n.BOMHOrO pMa paBeH HynlO npll n *- m H
paBeH 1/2 npH n = m. TaKlIM o6pa30M, ,l(JIH KI1TI nOJIyqaeM
1 n-I
- = 1 + 2 L F2 (n, A, ii). (3.50)
11 n=I
BbIqHCJIeHHe 3Toro 3HaqeHHH HeCJIO)I(HO .n.IDKe .l(JUI 60JIblliHX n . llpH JII060M
3HaqeHHIf SLR cymecTByeT n , o6eCneqHBalOwee MaKCHMaJIbHyro 3<l><peKTIIBHoCTb,
TIOTOMY qTO 3HeprHH OCHOBHoro nyqa C pOCTOM n YMeHblliaeTCH 6bIcTpee, qeM pac-
TeT 3HeprHH 60KOBbIX JIeneCTKOB. O.n.HaKo npH 66JIblliliX n 3HeprHH OCHOBHoro
JIyqa H3MeHHeTCH Me,lIJIeHHee. THnHqHbIe 3HaqeHHH Kl1n npH n pacnpe.n.eneHIIH
npe.aCTaBJIeHbI Ha pHC. 3.17. nOCKOJIbKY JL]IH Ka)l([(OrO H3 3HaqeHHM SLR BeJIllqllHa
n pa3JIHqHa, HenpepbIBHaH KpMBaH He npOBe,l(eHa. )J..rr51 cpaBHeHHH nOKa3aHa TaIOKe
3<P<l>eKTHBHOCTb OOllonapaMempU"leCK020 pacnpeoefleHUR. B Ta6JI. 3.4 npHBe.n.eHbI
3HaqeHHH n , o6eCneQHBalOIUHe HaH60JIblliee 3HaqeHHe KilTI.
Ta6JIHUa 3.4. 3HaQeHIUI n , o6eCrreQl1BalOllUIe MaKCHMaJIbHbIH KMn 11 MOHOTOHHoe
aMITJIHT)'.aHoe pacrrpe.aeJIeHHe
aKC. 3HaeHHB, OHOTOHHoe pacnpe,neJIeHHe
SLR
n 11, n 11,
20 6 0.9667 3 0.9535
25 12 0.9252 5 0.9105
30 23 0.8787 7 0.8619
35 44 0.8326 9 0.8151
40 81 0.7899 11 0.7729
45
50


rllaea 3. CU1lme3 iJuazpaMM llanpaelle1l1l0Cmu IlU1leU1l0U a1lme1l1l0U peUlemKU
1
0.9
°5
°6
t::
g 0.8
°n=7
°8
OHorrapaMeTpHqeCKOe
pacnpe.aeJIeHMe
°9
0.7
0.6
20 25 30 35
SLR (.aD)
PHC. 3.17. KMIT pacrrpe.aeJIeHHH TeHJIOpa
40
45
50
TIpHBO,1J;5ITC5I TalOKe HaH60JIbIIlHe 3HaqeHH5I n , IIPH KOTOpbIX peaJIH3yeTC5I MOHO-
TOHHoe pacnpe.n:eJIeHHe, a TalOKe cooTBeTcTByJOIl{He 3HaqeHH5I KMTI. MO)I(Ho BH-
,n:eTb, qTO IIPH BbI60pe n , o6eCneQHBalOII(eM MOHOTOHHOCTb, CHIDKeHHe KHTI He-
3HaQHTeJIbHO.
3<t><t>eKTHBHoCTb fJIaBHOrO nyqa onpe,n:eJI5IeTC5I H3 ypaBHeHH5I (3.33) C yqeToM
nonyqeHHoro BbIIIle BbIpaJKeHH5I LLIDI KHTI. B Ta6n. 3.5 IIpHBe,neHbI 3HaQeHH5I SLR
B ,n:Hana30He OT 20 ,n:o 35 ,nI> H THnHqHbIe 3HaQeHH5I n ,lUI5I Ka)l(,[(OrO cnyqa5I. 3TH
pe3YJIbTaTbI MO)I(HO cpaBHHTb c ,n:aHHbIMH, npHBe,n:eHHbIMH Ha pHC. 3.12 ,l(JI5I OOHO-
napaMempUlfeCK020 pacnpeOeAeHUJl.
Ta6JIHua 3.5. 3<l><l>eKTHBHoCTb JIyqa ,lLJISI n - napaMeT-
pHQeCKOrO pacrrpe.aeJIeHIUI TeHJIOpa
SLR (JJ:B) n t)b
20 4 0,9658
25 5 0,9861
30 6 0,9947
35 7 0,9980
Ba)l{}{o npaBHnbHo BbI6HpaTb ,nHana30H 3HaQeHHH n . KaK 6bIJIO nOKa3aHo,
CJIHIIlKOM 60JIbllIOe n ,l(JI5I KOHKpeTHoro 3HaQeHM5I SLR IIpHBO,n:HT K HeMOHOTOHHO-
MY aMIIJIHTY,1J;HOMY pacnpe,neJIeHHIO; MO)l(eT ,n:a)l(e B03HHKaTb 60nbllIOH nHK Ha Kpa-
5IX paCKpbIBa. CJIHIIlKOM 60JIbllIOe 3HaqeHHe n yxy,n:rnaeT TalOKe rrOBe,neHHe HYJIeH B
rrepexo,n:HOH 30He. Ha pHC. 3.18 IIOKa3aHa 3aBHCHMOCTb paCCT05IHH5I Me)l(,[(Y HynRMH
L

3.5. PacnpeiJeAeHUJl C HU3lCUM ypoBHeM 6olC08blX lleneCmlCOB 
1.1

n=4 , /
,
",/,
,
, ./
:7
"=9
.,- -......,
.. - - - "
-- .-. -
MaKC. KH,l:{
1
n=23
-
--
"'
:s::

 0.9

::r=


 0.8
o
:s::
::r=

o
t 0.7
u
cIj

MOHoToHHoe pacnpe.neJIeHHe n = 8
I
0.6
0.5
1
j
6
11 16
HOMep 3JIeMeHTa
21
26
Poc. 3.18. PaccToHHHe Me:>KJJ:Y HYJIHMH .lL7IH n napaMeTpHqeCKOrO pacnpe,n:eJIeHHH
TetiJIopa, SLR = 30 ,n:fi
OT n ,lLJIH SLR, paBHoro 30 ,nB. HaH60JIbillHH BbI6poc napaMeTpa HMeeT MeCTO ,lLJIH
n = 9, OH HeCKOJIbKO BbIille MaKCHMaJIbHOrO 3HaqeHHH ,lUIH n = 8 npH MOHOTOHHOM
pacrrpe,neJIeHHH. BbI6poCbI rrpOHcxo,nHT rrpH 3HaqeHHH MaKCHMaJIbHOH 3<p<peKTHB-
HOCTH n = 23 (HJIH BbIille). O,nHaKo rrpH n = 4 BbI6poCOB HeT; n = 5 H 6 ,nalOT He60-
nbllIHe BbI6pOCbI. 3TH oc06eHHOCTH rrpoHBmilOTCH TaIOKe rrpH ,npyrHX 3HaqeHHHX
SLR, HO ,lUIH HHbIX 3HaqeHHH n .
OTMeTHM, qTO n -rrapaMeTpHqeCKOe pacnpeiJeAeHue TeitJIopa HCrrOJIb3yeTcH .[(0-
BOJIbHO illHpOKO, TaK KaK OHO 06eCrreQHBaeT HeCKOJIbKO JIyqillHe KMTI H illHPHHY
nyqa, QeM oiJHonapaMempulleCKoe pacnpeiJeAeHue TeitJIopa rrpH TOM )l(e ypOBHe 60KO-
BbIX JIerreCTKOB.
3.5. PacnpeAeneHMR c HM3KMM YPOBHeM
60KOBbiX neneCTKOB
3.5. 1. CpaBHeHMe pacnpeAeneHMM
Pacrrpe,neJIeHHH, cpOpMHPYIOIUHe ,LJ;H C HH3KHM, OT -30 ,no -60 ,nB, ypOBHeM 60KO-
BbIX JIerreCTKOB, rrpe,nCTaBlliIlOT HHTepec 110 P5I.aY rrpHQHH, HarrpHMep: YMeHbllIeHHe
B03MO)I(HOCTH rrepeXBaTa pa,nHOJIOKaUHOHHbIX H TeJIeKOMMyJIHKaUHOHHbIX CHrHa-
nOB, CHIDKeHHe pa.n;HOJIOKaUHOHHbIX rrOMex, H YH3BHMOCTH co CTOpOHbI cpe,nCTB
rrpOTHBo,neHCTBHH H B03paCTaHHH rreperpeHHOCTH .crreKTpa rrpH rrepe,naQax rro
crryrHHKoBOH CBH3H.


FJlaea 3. CUHme3 aUa2paMM HanpaeJleHHOCmu JlUHeUHOU aHmeHHOU pew.emKU
113 rrpe,nbI,nYIlIJIX pa3,neJIOB CJIe,nyeT, qTO TaKMe paCrrpe,L(eJIeHMSJ ,L(OIDKHbI MMeTb
CMJIbHOe yMeHbIIIeHMe aMrrJIMTY,L(bI K Kpa5lM paCKpbIBa H, rro rrpaBHJIaM Te:itJIopa,
YMepeHH)'IO BbICOT)' rrbe,L(eCTaJIa. XapaKTepHCTHKa HarrpaBJIeHHOCTH, 06eCrreQHBae-
Ma51 n rrapaMeTpMqeCKHM pacrrpe,neJIeHMeM, rro- BII,II;HMOMY, II,II;eaJIbHO rrO,L(Xo,nMT ,[(JI5I
no.n;06Horo MCnOJIb30BaHHH.
ITpM CHHTe3e BbICOK03<p<peKTHBHOM .n;HarpaMMbI HanpaBJIeHHOCTH C MaJIbIM
ypOBHeM 60KOBbIX JIeneCTKOB TalOKe oc060e 3HaqeHHe npII,II;aeTC5I HYJI5IM .n;HarpaM-
MbI. nOJIO)l(eHHe 6JIIDKHMX HYJIeM BbI6HpaeTC5I TaKHM 06pa30M, qT06bI rrOJIyqMTb
HeCKonbKO nOqTM paBHbIX 60KOBbIX nerreCTKOB paCqeTHOrO ypOBH5I, a y.n.aJIeHHbIe
HynH pa3MeIUalOTCH TaK, qT06bI 06eCneQHTb orH6alOIU)'IO BM.n;a Iju. 3Ta TeOpeTMqe-
CKM pa3pa60TaHHaH ,lIMarpaMMa M cooTBeTcTB)'IOIUee eM pacrrpe.aeneHMe Kap.n.HHaJIb-
HO OTnMQalOTCH OT KJIaCCMQeCKHX pacnpe.n.eneHMM, BbI6HpaBIIIHxcH MCXO.n.H M3 ycno-
BMM nerKoM MHTerpMpyeMocTM. TIpMMepoM MO)l(eT cn)')KMTb pacnpe.n;eneHHe
XeMMHHra, npe,ncTaBJIHIOIUee C060M KOCHHYC y.aBoeHHoro apryMeHTa Ha nbe.n.eCTa-
ne [12]. 3TO pacrrpe.aeneHMe MMeeT BM.a
g(P) = 0,54 + 0,46 cos np = a + b cos np, (3.51)
QTO .n.aeT e,nMHMUY B ueHTpe paCKpbIBa M 0,08 Ha KpalO paCKpbIBa. KI1TI COCTaBnHeT
a 2
111 = = 0,7338,
a 2 + 2b 2
a IIIMpl1Ha JIyqa Ha ypOBHe nonOBHHbI MOIII.HOCTI1 u3 = 0,6515. HynM ,nl1arpaMMbI
HanpaBneHHOCTI1 pacrrOnO)l(eHbI B TOqKaX u = 2, 3, 4, ..., 11 eIII.e O.n;I1H HOJIb npl1 u =
= aj(a - b) = 2,5981. D:MarpaMMa HarrpaBneHHOCTH MMeeT Bll)].
F(u) = [(a - b)u 2 - a] sin 1tu . (3.53)
1tau(u 2 -1)
(3.52)
MaJIoe paCCTOHHMe Me)K)]:y rrepBbIMM JIBYMH HYJIHMH rrpMBo.aHT K 113pe3aHHOCTH
orM6alOIUeM 60KOBbIX JIeneCTKOB; caMbIM BbICOKHM HBJIHeTCH QeTBepTbIM JIeneCTOK C
ypOBHeM -42.7 ,nE. ITepBbIM H BTOpOM nerreCTKJi MMelOT YPOBHI1 -44.0 M -56.0 ,nE.
TIoKa3aTenbHo cpaBHeHMe o,nHonapaMe1]JHQeCKOrO pacnpe,neneHIUI TeMJIOpa,
n rrapaMeTpMQeCKOrO pacrrpe,lIeneHH5I TeRJIOpa 11 pacnpe.n;eJIeHMH XeMMMHra. 110-
CKOJIbKY Y pacrrpe,neneHI1H XeMMMHra SLR = 42.7 .n.E, OHO TaIOKe Mcrronb3yeTc5I rrpl1-
MeHHTenbHO K .apyrl1M BapHaHTaM pacrrpe.aeJIeHIDI B paMKax cpaBHeHMH. B Ta6n. 3.6
rrpMBe.aeHbI nepBbIe 10 RYneR .aHarpaMMbI HanpaBneHHocTM .lI)I5I 3THX pacnpe.n;eneHHM
co 3HaqeHMHMH n = 6 M 10. )])rn Bcex pacnpeJIeJIeHMM Te:itJIopa xapaKTepHa OTHOCH-
TeJIbHO rnan;Ka51 nocne.aOBaTenbHOCTb RyJIeM, a y pacrrpe.n.eJIeHHH XeMMHHra BO BTO-
pOM Ryne I1MeeTCH CI1Hryn5lpHbIR pa3pbIB. B Ta6JI. 3.7 rrpMBen:eHbI 3HaqeHIDI paCCTOH-
HMM Me)l(Qy HynHMM, COOTBeTCTBYIOIUHX .uaHHbIM Ta6JI. 3.6. OTcIOn:a CHOBa OQeBM,I:{Ha
rJIan;KOCTb Bcex pacnpe.n.eJIeHMR Teitrropa, XOTH MMeeTC5I He3HaQMTenbHa5I OCl(l1n-
nHUM5I IIPM rrepexon:HOM n .LLIDI n = 10. OTMeTMM, QTO y pacnpe.n;eJIeHMH XeMMMHra
paCCT05lHMe Me)l(Qy JIylliIMM M3MeHHeTC5I rrpMMepHO OT 0,6-0,4 .n.o 1, QTO CBM,I:{eTenb-
cTByeT 0 He3<p<peKTMBHOCTM ,naHHoro crroc06a CMHTe3a aMllJIMTY,nHoro pacnpe-
,L(eneHM5I. HaKoHeu, B Ta6JI. 3.8 npMBe.n.eHbI 3HaqeHI1H IIIMpMHbI nyqa B e.n;MHMuax u
II 3HaqeHMH KI1IT. no 060MM nOKa3aTelliIM pacnpe,neJIeHMe XeMMMHra YCTY-
naeT npMMepHO Ha 3%. Pacrrpe,neneHM5IM Teitrropa CBOMCTBeHHO 60nee HM3Koe 3Ha-
qeHMe Q, XOTH COOTBeTCTB)'IOIII.He ,lIaHHble He rrpMBo.a5lTCH. TaKMM 06pa30M,

3.5. PacnpeiJe.neHUR c HU3ICUM yp06HeM 6oICo6bIX J/enecmIC06 
Ta6JIHQa 3.6. PaCIIOJIO)l(eHHe HYJIeH IIPH SLR = 42,7 .nE
O.lUlOnapaMeTpll'leCKOe n napaMeTpJl1lecKoe pacnpe,neJIeHHe TeiiJIopa Pacnpe,neJleHHe
n pacnpe,neJleHHe XeMMHHra
TeuJlopa n =6 n = 10
1 2.112 1.894 1.897 2
2 2.732 2.398 2.396 2.598
3 3.550 3.173 3.166 3
4 4.412 4.069 4.056 4
5 5.335 5.020 5.002 5
6 6.282 6 5.978 6
7 7.243 7 6.970 7
8 8.214 8 7.974 8
9 9. 190 9 8.984 9
10 10.172 10 10 10
Ta6JIHua 3.7. PaccToHHHe Me)l(l{Y HYJIHMH IIPH SLR = 42,7 .nE
O.lUl On apaMeTpJl1leCKOe n napaMeTpJl1lecKoe pacnpe,neJIeHHe TeiIJIopa Pacnpe,neJleHHe
n pacnpe,neJleHHe XeMMHHfa
TeiIJIopa n =6 n = 10
1 0.619 0.503 0.499 0.598
2 0.799 0.776 0.770 0.402
3 0.881 0.895 0.890 1
4 0.923 0.951 0.946 1
5 0.947 0.980 0.976 1
6 0.961 1.0 0.993 1
7 0.970 1.0 1.003 1
8 0.977 1.0 1.011 1
9 0.981 1.0 1.016 1
10 0.985 1.0 1.0 1
Ta6JIHua 3.8. CpaBHeHHe pacIIpe.neJIeHHH .lL7IH SLR = 42,7 .nE
O.lUlOnapaMeTpll'leCKOe n napaMeTpJl1lecKoe pacnpe,neJleHHe TeiIJIopa Pacnpe,neJleHHe
n pacnpe,neJleHHe XeMMHHra
TeiIJIopa n =6 n = 10
u3 0.694 0.637 0.635 0.651
llt 0.690 0.754 0.755 0.734
u 311t 0.478 0.480 0.480 0.478


rJlaBa 3. CUHme3 iJuazpaMM HanpaBJleHHOCmu JlUHeUHOU aHmeHHOU peUlemKU
BJIlfJlHlfe norpellIHocTeM anepTYPHoro B036}')K,l(eHIDI 60Jlbrne B cJlyqae pacnpe,n:eJIe-
HlfJl XeMMI1Hra B cIDIY 60JlbllIerO 3HaqeHI1J1 Q.
nOCKOJlbKy Ha ,n:l1arpaMMbI HanpaBJleHHOCTI1 C HI13KHM ypoBHeM 60KOBbIX JIe-
rreCTKOB CHJIbHO BJIIDIIOT <pa30BbIe ollIl16KH, MO)I(HO rrpe,n:nOJlOXlfTb, qTO 113MeHe-
Hl1e paCCTOJlHI1J1, Ha KOTOpOM rrp0I13Bo,n:51TCJI H3MepeHIDI, nOBJIeqeT 3a C060M H3Me-
HeHHe ,n:HarpaMMbI.
,L:(Jl5I aHTeHH C HH3KHM ypoBHeM 60KOBbIX JIerreCTKOB o6menpHHHToe paccToH-
HHe, Ha KOTOpOM npH H3MepeHH5IX H 3KCTIJIyaTaU;HH BbInOJIHHIOTCH YCJIOBHJI ,n:anb-
HeM 30HbI, paBHoe 2L 2 /'A, r,n:e L - .lUIHHa aHTeHHOH pellIeTKH, MoxeT OKa3aTb-
CJI He.n:ocTaTOqHbIM. lIo Mepe npH6J1IDKeHIDI Ha6J1IO,n:aTeJIJI H3 6eCKOHeqHOCTI1
K aHTeHHOH perneTKe nepBbIe 60KOBbIe JIeneCTKI1 H HYJlH HaqHHalOT 3arrOJlH5ITbCH.
,L:(anee 60KOBOH JIeneCTOK CTaHOBHTCH BbICTYTIOM Ha <pOHe 60JIee llIl1pOKOrO Te-
nepb rJIaBHOrO JIyqa, If n05lBJI5IeTCH BTOpOM HYJIb. no Mepe yMeHbllIeHHH paCCToH-
HH5I 3TOT npou;ecc rrpo.n:OJDKaeTC5I. Pe3YJlbTaTbI 3aBHC5IT, rJIaBHbIM 06pa30M, TOJIb-
KO OT paCqeTHOrO ypOBHJI 60KOBoro JleneCTKa. IIo,n:po6HOCTI1 rrpHBo.n:HTC5I B
rJIaBe IS.
3.5.2. CpeAHMM YPOBeHb 60KOBbiX neneCTKOB
I1Hor.n:a Heo6xo.n:I1Ma o:u:eHKa cpe.n:Hero ypOBIDI 60KOBbIX JIeneCTKOB aHTeHHbI. 3TO
B03MOXHO c.n:eJIaTb, nOCKOJIbKy cpe,n:HHM ypOBeHb H orH6alOmaH .n:HarpaMMbI Ha-
npaBJleHHOCTH CB5I3aHbI npH6JIIDKeHHbIMH COOTHOrneHH5IMH C KH,L:( aHTeHHbI.
B KaqeCTBe npHMepa paCCMOTpHM o,n:HorrapaMeTpHqeCKOe pacnpe,n:eJIeHHe Tei1JIopa.
IIoCKOJlbKy orH6alOIUa51 60KOBbIX JIeneCTKOB .n:HarpaMMbI HanpaBJIeHHOCTH 60JIb-
llIHHCTBa aHTeHH aCHMnTOTHqeCKH cnan:aeT KaK Ilu, .n:aHHbIM npHMep HMeeT llIHpO-
Koe npHMeHeHHe. Cpe.n:HHM ypOBeHb 60KOBbIX JleneCTKOB onpe.n:eJI5IeTCJI KaK HHTer-
pan OT nepBoro HYlliI .n:o n12:
LIA
SLL = A J du
ave 1t 2 F.2 L u 2 - B2
o Uo
A In (L I A - B)(uo + B) .
21t 2 FJ LB (L I A + B)(uo - B)
(3.54 )
IIepBbIM HYJIb pacnOJIOXeH npH Uo = .J I + B2 . LlrrH 60JIbllIHX anepTYP LI'A » B,
qTO .n:aeT
 A Uo + B
SLL ave = 2 In .
1t2FO LB uo-B
(3.55)
PeanbHbIH ypOBeHb 60KOBbIX JleneCTKOB MeHbllIe, nOCKOJIbKy JIerreCTKH I1MelOT
orrpe.n:eJIeHHyIO <POPMY. THnHqHa51 <popMa, He 3aBHC5IIUa51 OT Orl16alOmeM, COOTBeT-
cTByeT sin 2 nu, qTO .n:aeT HHTerpan, paBHbIH 1/2. TaKHM o6pa30M, ypOBeHb 60KOBbIX
JIerreCTKOB Ha 3 .aD MeHbllIe TOM, qTO paCCQI1TaHa no orH6alOrueM.
KH,L:( COCTaBJIJleT G = 2111LIA, r,n:e 111 - K03<P<PHU;HeHT HCnOJIb30BaHI151 nOBepx-
HOCTH, H cpe.n:HI1M ypOBeHb 60KOBbIX JIeneCTKOB MoxeT 6bITb BbIpaxeH Qepe3 KH,lJ;:
 111 ( u o + B J
SLL ave = 2 In .
21t 2 Fo GB Uo - B
(3.56)

3.6. N -napOMempU'leClCOe OMl!JlumyiJHoe pacnpeiJeJleHUe BUJlbHe6a -:)
o
..Q
r:::
Q)
E-- -1

0
::z::

):s::

u
Q)
::r -2
:s::
:;
-&
:s:
P..


0
r:::
x
0 -3
-
-4
10
15
20
25
30
SLR CuE)
35
40
45
50
PHC. 3.19. Cpe,L(HMM ypOBHeHb 60KOBbIX JIeneCTKOB
IIpll 3a,aaHHOM SLR 3HaqeHlle B orrpe,n:eneHo, II MO)l(eT 6bITb BbIqllCneH rrpa-
BbIM COMHO)l(J{Tenb; ero rrOBe,n:eHlle rrOKa3aHO Ha pllC. 3.19, .lUI5I 60nbllIllX 3HaqeHllM
SLR OH ,n:aeT KOppeKl{lllO < 3 ,n:o. BbIpa)l(eHHbIM B ,n:eUll6enax cpe,n:HllM ypOBeHb 60-
KOBbIX nerreCTKOB paBeH
[ l1t uo+B ]
SLR ave '" G llE + (SLR -13,26 Ll,o) -10 log -In + 9,95 ,n:B.
2B Uo - B
(3.57)
KaK II O)l(lfJ(MOCb, 66nbllIlle 3HaqeHll5I KaK KH,lJ" TaK II SLR rrpllBOMT K MeHb-
llIeMY cpe,n:HeMY YPOBHIO 60KOBbIX nerreCTKOB.
3.6. N-napaMeTpM"IeCKOe aMnnMTYAHOe
pacnpeAeneHMe BMnbHeBa
B 60nbllIllHCTBe pa3pa60TOK nllHeHHbIX aHTeHHbIX pellieTOK KOnllqeCTBO 3neMeHTOB
6bIBaeT ,n:OCTaTOqHO 60nbllIllM, rr03TOMY MOryT 6bITb llcrronb30BaHbI orrllcaHHbIe pa-
Hee HerrpepbIBHbIe pacrrpe,n:eneHllH Teiillopa. B pa60Te [66] pa3pa60TaH ll35III(HbIH
MeTO,n: paCqeTa n -rrapaMeTpMqeCKMX -TeiillopoBcKllX aHTeHHbIX perneTOK C He60nb-
llIHM qHCnOM 3neMeHTOB. 3TO 6billO ,n:OCTHrH)'TO rr)'TeM KoppeKUHll n - 1 6nH)I(HHX
HyneH rronHHOMa perneTKll )J,onb<pa-Qe6bIrneBa (BMecTo 6JIIDKHllX HyneH Herrpe-
pbIBHOH arrepTYPHoH <PYHKUllll). IIonHHoM Qe6bIllieBa 3arrllCbIBaeTC5I B Bll,n;e rrpo-
H3Be,n:eHll5I TaK, qTO MO)f(HO c,n:BllraTb 6nIDKaHllIlle HynH. Hcrronb3yeTC5I TalOKe TeM-


rfla6a 3. CUHme3 auazpaMM Hanpa6fleHHocmu flUHeUHOU aHmeHHOU pememKU
JIOpOBCKMH K03<P<PI1I.UfeHT Y.lUII1HeHI1H o. B pe3YJIbTaTe rrOJIyqaeTcH ,Ul1arpaMMa
HarrpaBJIeHHOCTI1 cJIe,UyroI.IJ:ero Blf.[(a:
. 2N + 1
sm 'V
SIn - 'V n -l
2 IT sin
m=1
IT sin ( 'V - 'V ' m ) sin ( 'V + 'V ' m )
m=1 2 2
m2n m2n
'V - 2N + 1 . 'V + 2N + 1
sm
2 2
, (3.58)
r,Ue 1IJ = kd sin 8, U = Uo cos 1IJ/2 a lIJ' = mtJ.
3Ta ,Ul1arpaMMa HarrpaBJIeHHOCTI1 1II1CKpeTHoM aHTeHHOH perneTKM 3KBI1BaJIeHT-
Ha .II:l1arpaMMe HerrpepbIBHoH arrepTypbI TeHJIOpa C rrapaMeTpOM n . K03<P<PI1IJ:l1eHT
Y.lUlI1HeHI1H I1MeeT BI1.II:
2n n
a=
(2N + 1)'11 n
AMIIJII11)',nHbIe K03<P<PI1IJ:l1eHTbI B036}')K)J:eHI1H orrpe,neJIHIOTCH c nOMOI.IJ:blO rrpl1-
MeHeHI1H K ,Ul1arpaMMe HarrpaBJIeHHOCTI1 rrpeo6pa30BaHIDI C KOHeQHbIMI1 npe,neJIaMI1.
,[J;JIH QeTHOrO 11 HeqeTHOrO QI1CJIa 3JIeMeHTOB K03<P<PI1IJ:l1eHTbI HeMHoro pa3JII1QaIOTcH.
npl1 QeTHOM QI1CJIe 3JIeMeHTOB N = 2M CrrpaB elIJIl1BbI CJIe.n:yroI.IJ:l1e COOTHorneHHH:
Uo = cosh [ 1 In(ll + .J 1l 2 -1) ] ,
2N -1
'V p = 2 arccos [ COS(2P -1) n ] p = 1,...,2N -1, (3.60)
Uo 2(2N -1)
n 2n n n
a= -
2N'II Ii 2N arccos [  cos ( 2 n -1) n )] .
Uo 2(2N -1)
(3.59)
K03<P<PI1IJ:l1eHTbI 3,neCb HMelOT BIf.[(
a p =  E ( m2n ) eX P {-J1(P-l/2)m2nl(2N)]} =
2N m=-(Ii-l) 2N
=  { E(O) + 2 E ( m2n ) cos [ (p -1/2) mn ]} -(N -1) < p < N,
2N m=l 2N N
(3.61 )
r.n:e
-I ( ' ) ( ' )
n - . mn 'V q . mn 'V q
2N(-I)mITsIn --- SIn -+-
E m2n = q=l 2N 2 2N 2
SIn - SIn SIn sm
2N 2N q=l 2N 2N
q*m
(3.62)
n-I ( 'V' )
2NIT sin 2 
E(O) = _ q=l 2 .
n-l ( )
IT sin 2 qn
q=l 2N

3.6. N-napOMempU'lecKoe OMf/JlUmyoHoe pacnpeoe.neHue BUJlbHe6a 
llPH HeqeTHOM qHCJIe 3JIeMeHTOB N = 2M + 1 CnpaBe,lLJIHBbI CJIe,n:yroIUHe BbIpa-
)l(eHH5I
-
nn
0'=
(2N + I) arccos [ u1o cas (2n -I) 4 )J
Uo = cosh [ 2 In(T] + .J rr -I)}
'V p = 2 arccos [ COS(2P -I)  ] p = 1,...,2N.
Uo 4N
(3.63)
K03<l><l>Hl.{HeHTbI HMelOT BH,lJ;
a p = I  E ( m2n ) eXP{- J1p m2n/(2N + I)]} =
2N + 1 m=-(n-l) 2N + 1
= 1 [ E(0)+2E ( m2n ) cos ( pm2n )] -N < p < N,
2N + 1 m=1 2N + 1 2N + 1
(3.64 )
r,n:e
(2N+I)(-I) mIT sin ( mn - 'V J Sin ( mn + 'V J
E m2n = q=1 2N + 1 2 2N + 1 2
SIn sm SIn SIn
2N + 1 2N + 1 q=1 2N + 1 2N + 1
, q*m (3.65)
n-l ( 'VI J
(2N + l)IT sin 2 
E(O) = _ q= 1 2
n-l ( )
IT sin 2 qn
q=1 2N + 1
3TH <l>OPMYJIbI Ka)I()'TC5I rpOM03,n:KHMH, HO OHH JIerKO nporpaMMHpYJOTCSI ,lLJIR
BbIqHCJI e HI1M.
K03<l><l>I1Ql1eHT I1CnOJIb30BaHIDI nOBepXHOCTH aHTeHHbIX pellIeTOK BHJIbHeBa BbI-
QI1CJUIJICSI II)'TeM CYMMHpOBaHIDI ,n:eMCTBHTeJIbHbIX B3aHMHbIX conpOTHBJIeHI1M [29]
c nOMOIUblO BbIpa)l(eHI1SI
llt = N N
L LAnAm sinc[(n -m)kd]
n= 1 m= 1
(An J
(3.66)
B Ta6JI. 3.9 npHBe.n.eHbJ 3HaQeHI1SI KMll aHTeHHbIX pellIeTOK BI1JIbHeBa C HeqeT-
HbIM qHCJIOM 3JIeMeHTOB B ,n:Hana30He OT 5 .n:o 41 11 3HaQeHHeM SLR 25-40 .n:E.
B Ka)l()];OM CJIyqae BbI6HpaeTC5I HaH60JIbllIee n , 06eCneQHBarorn;ee MOHOTOHHoe pac-
npe.n.eJIeHHe. 3TH 3HaqeHH5I MO}I(HO CpaBHHTb C COOTBeTCTByroIUHMH K03<l><PHl.{HeH-
TaMH ,lLJI5I n -napaMeTpHQeCKOrO TeMJIOpOBCKOrO pacnpe,n:eJIeHHH, npHBe.n.eHHbIMH B
Ta6JI. 3.10. Pe3YJIbTaTbI 06Hap)l)KHBa1OT JIHllIb He6oJIbllIOe pa3JIHQl1e ,l(lliI AP C Ma-


filaea 3. CUHme3 aua2paMM Hanpa6ileHHocmu ilUHeUHOU aHmeHflOU peLUemKU
JIbIM « 10) KOJII1QeCTBOM 3JIeMeHTOB. TIplfBelleHHble Ta6JIlfUbI rr03BOJISIIOT KOHCT-
PYKTOpy orrpe,L(eJII1Tb, rrpl1 KaKOM pa3Mepe AP Heo6xo.rrI1MO I1CnOJIb30BaTb pacrrpe-
,l(eJIeHlfe BI1JIbHeBa.
Ta6J1HQa 3.9. KI1 n n - rrapaMeTpIft-leCKOH perneTKI1 BI1JIbHeBa
SLR (.a6)
N 25 30 35 40
- -
n 1]1 n 1]1 n 1], n 1]1
41 5 0.9026 7 0.8551 9 0.8098 12 0.7701
31 5 0.9000 7 0.8528 9 0.8078 12 0.7693
21 5 0.8947 7 0.8479 11 0.8060 11 0.7630
15 6 0.8917 7 0.8409 8 0.7949 8 0.7540
11 6 0.8807 6 0.8276 6 0.7825 6 0.7447
9 5 0.8674 5 0.8158 5 0.7732 5 0.7384
7 4 0.8468 4 0.7987 4 0.7608 4 0.7310
5 3 0.8182 3 0.7725 3 0.7448
Ta6J1HQa 3.10. Kl1n n -rrapaMeTpl11JeC-
KOH perneTKM TeHJIOpa
SLR (.aE) n 1]1
25 5 0.9105
30 7 0.8619
35 9 0.8151
40 11 0.7729
3.7. Pa3HocTHbie AMarpaMMbl HanpaBneHHOCTM
3.7.1. KnaccMecKMe AMarpaMMbl HanpaBneHHocTM
Pa3HOCTHble ,l(l1arpaMMbI HanpaBJIeHHOCTI1 06bIQHO I1MelOT HYJIb B HarrpaBJIeHI1I1,
rreprreHlU1KYJI5IpHOM paCKpbIBY aHTeHHbI; 3TI1 ,l(l1arpaMMbI I1CrrOJIb3yIOTC5I l(JI5I TOt}-
HOrO OrrpeL{eJIeHI1SI yrJIa rrplfXO,l(a Cl1rHaJIa. Pa3HOCTHaSI ,l(l1arpaMMa HarrpaBJIeHHO-
CTI1 I1CrrOJIb3yeTcSI B IlIl1pOKO paCrrpOCTpaHeHHbIX aHTeHHaX MOHOlfMrrYJIbCHbIX
P 11 C. PaCCMaTpl1BaeMble 3n:eCb arrepTYpHble pacnpe.rreJIeHI1SI 51BJI5IIOTC5I ,l(Byx<pa3HbI-
MI1, KOr,L(a O,l(Ha rrOJIOBI1Ha paCKpbIBa pa60TaeT B ClfH<pa3HOM pe}KlfMe, a ,l(PyraR rro-
JIOBI1Ha - C <pa30BbIM CL{BlfrOM Ha 180°. IIpocToM JII1HeMHOM AP C pa3HocTHOM
JI:lfarpaMMoM HarrpaBJIeHHOCTlf 5IBJI5IeTCR paBHOMepHO B036)')Kl1:aeMa5I 'JII1HellHaR AP
C cPlf,l(epHbIM nl1TaHlfeM ,L(BYX rrOJIOBlfH peIlIeTKI1 Qepe3 rl16pl1llHyIO 180° cxeMY.
-

3. 7. Pt13HOCmHl>le iJuaZpllMMbl HanpaBAeHHOCmU 
fH6pl:f,lI;HaH cxeMa o6eCneQHBaeT nonyqeHHe CYMMapHOH .aHarpaMMbI HanpaBneHHo-
. U
CTH, T.e. SInc nu, H pa3HOCTHOH .aHarpaMMbI BH.aa
F(u) = .,fi (1 - COS nu) . (3.67)
1tU
Pa3HocTHoe pacnpe.aeneHHe HopMHpyeTC.H TaKHM o6pa30M, qTo6bI HHTerpaJI OT
KBa.n;paTa aMITJIHTy.aHoro pacnpe.aeneHIDI 6bIJI paBeH e.aHHHl{e. llHKoBoe 3HaqeHHe
3TOH npocToH pa3HocTHOH .aHarpaMMbI HanpaBneHHOCTH COCTaBn.HeT 1,0248, a KPy-
TH3Ha B l{eHTpe 0,7071. llepBbIH 60KOBOH JIeneCTOK Ha 10,57 .aB HIDKe nHKOBoro
3HaqeHIDI. 113-3a BbICOKoro YPOBIDI 60KOBbIX neneCTKOB TaKaH .aHarpaMMa HBJIHeTCH
U
BeCbMa HenpHBJIeKaTeJIbHOH.
3<t><t>eKTHBHoCTb B036y)K):(eHIDI 111onpe.aenHeTCH no MO.aH<t>Hl{HpOBaHHOH <l>opMY-
ne wrn paCqeTa KMll CHH<t>a3HbIx anepTYP nonyqeHHoH B [27], BKJIIOQalOrn;eH MeCTO-
IIOJIO:>KeHHe nHKa .aHarpaMMbI HarrpaBJIeHHOCTH Uo (TOQHO H3BeCTHoe .lUUI 60JIbIIIHX
anepTYP):
(J g(p)exp(jrrpuo)dp r
111 = 21 g2 (P)dp .
,[(JI5I pa3HOCTHOH arrepTypbI C paBHOMepHbIM pacnpe.aeneHHeM pe3YJIbTaT CO-
CTaBJI5IeT 111 = 0,7420.
BOKoBbIe neneCTKH pa3HocTHOH .aHarpaMMbJ HarrpaBJIeHHOCTH C MaKCHMaJIbHOH
KpyrH3HOH [51, 39] HMelOT ern;e 60nbIIIHH ypOBeHb. TaK)'IO ));H <l>opMHpyeT pacnpe-
,neJIeHHe TpeyronbHoH <l>OpMbI C HyneM B ueHTpe H MaKCHMYMaMH Ha KpaRX. llpH
TOH :>Ke HOpMHpOBKe nHKOBoe (KpaeBoe) 3HaQeHHe paBHO 1,2247. KpyrH3Ha B l{eH-
Tpe COCTaBJIReT 0,8165, a nepBbIH 60KOBOH neneCTOK Ha -8,28 .aD MeHbllIe rnaBHO-
ro .rryqa. ,[(HarpaMMa HanpaBneHHOCTH HMeeT BR,[{
F(u) = .J6(sinc 1tU - COS 1tu) . (3.69)
1tU
(3.68)
3<l><t>eKTHBHOCTb B036y)K):(eHHR paBHa 111 = 0,5708.
TpeTbe pacnpe.aeneHHe o6eCneQHBaeT MaKCHMaJIbHyK> HanpaBneHHOCTb. .D:Ha-
rpaMMa HarrpaBneHHOCTH C MaKCHMaJIbHbIM KH)); HMeeT BHL(
F(u) = sinc [n(u - urn)] - sinc [n(u + urn)], (3.70)
r,ne nOCTORHHaH urn = 0,715148. CooTBeTCTByK>rn;ee aMIIJIHTy.aHoe pacnpe.aeneHHe
orrHCbIBaeTCR BbIpIDKeHHeM g = sin U rn 1ty. llepBbIH 60KOBOH JIeneCTOK Ha 12.59 .uB
HIDKe nHKOBoro. K03<l><l>HUHeHT Hcnonb30BaHHR rrOBepXHOCTH COCTaBJIReT 0,6086.
Ha pHC. 3.20 H306pIDKeHbI .aHarpaMMbI HanpaBJIeHHOCTH .lUUI paBHOMepHoro pacnpe-
,neJIeHHH H MR pacnpe.aeneHHH, o6eCneQHBalOrn;ero MaKCHMaJIbHbIH KH));. KaK H
O)l(H,L(aJIOCb, rJIaBHbIe nytIH nocne.aHero HeCKOJIbKO Yxe, a ypOBeHb 60KOBbIX JIeneCT-
KOB MeHbllIe. IIJIaToH 3a 3TO, KOHeQHO, HBJUleTCH CnO)I(HOCTb aMIIJIHTy.aHoro pacnpe-
,neJIeHIDI, H306pIDKeHHoro Ha pHC. 3.21. Ka)K,Lurn H3 rronOBHHOK pacnpe.aeneHIDI
rrpe,nCTaBJIHeT C060H QaCTb CHHYCOl:f,lI;aJIbHOH <PYHKUHH. Arm y.ao6cTBa npe.aCTaBJIe-
HHH nHKOBoe 3HaQeHHe aMIIJIHTyD:HOrO pacnpe.aeneHIDI HOpMHpOBaHO K e.aHHHl{e.
Y.aaQHbIH MeTO.a C03.aaHHH pa3HocTHOH .aHarpaMMbI HanpaBneHHOCTH nJIOCKOH
MOHoHMnynbcHoH aHTeHHOH peIIIeTKH H3 rn;eneH Ha KOHl{aX BonHOBo.aOB 6bIJI npo-
,neMOHC'TpHpOBaH B pa60Te [38].

b
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2
4
-8
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-4
PHC. 3.20. Pa3HOCTHbIe .lUiarpaMMbI HarrpaBJIeHHOCTH rrpH paBHoMepHoM B036y;K,L(e-
HHH H rrpH B036y;K,L(eHHH, o6eCrreQHBalOI.UeM MaKCHMaJIbHbIH KH,LJ;
1
o
-1
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KOOp,aHHaTbI B anepType
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PHC. 3.21. AMrrJIHTY,aHoe pacrrpe,aeJIeHHe, <pOpMHPYIDI.Uee pa3HocTHYIO .ilHarpaMMY
HarrpaBJIeHHOCTH C MaKCHMaJIbHbIM KH)J.

3. 7. P03HocmHble iJuaZpaMMbl Hanpa6JleHHOCmu 
3.7.2. AMarpaMMbl HanpaBneHHocTM &eMnMcca
BbICOKM:H ypOBeHb 60KOBbIX JIeneCTKOB )].H OT npe,l:J:bI.n:YlllJIX pacnpe.n:eJIeHH:H MO)l(-
OJ
HO YMeHbllIHTb, npHMeHHH K pa3HOCTHOH ,l:J:HarpaMMe HanpaBJIeHHOCTH npaBHJIa
Te:HJIopa. 3TO 6bIJIO C,l:J:eJIaHO B pa60Te neH1IHCCa [9], r,l:J:e nOCTpoeHa pa3HOCTHaH
,lJ,HarpaMMa, aHaJIOrHqHaH n -napaMeTpHqeCKOH ,l:J:HarpaMMe TeitJIopa. neHJIMCC Ha-
qaJI C «H,l:J:eaJIbHoH» ,l:J:HarpaMMbI TeHJIOpa (CM. pa3,l:J:eJI 3.4), a 3aTeM MO,n:H<pHUMPO-
BaJI ee TaKHM 06pa30M, QT06bI nOJIyqHTb pa3HOCTH)'IO ,lJ,MarpaMM-y. TIpM 3TOM, B03-
MO)l(HO, CTaJIO HeO)l(H)];aHHOCTblO, qTO II01lyqMBllIMec5I 60KOBble JIeneCTKH I1MelOT
HeperyJIHpHbIH ypOBeHb C HeMOHOTOHHOH orH6alOme:H. )].11$1 KOppeKl.(MM HX HYJ1e:H M
npMBe,neHHH JIeneCTKOB K paBHOMY ypOBHIO HCnOJIb30BaJIaCb MTepaUMOHHaH npoue-
,lJ,ypa. B KOppeKTHpOBKe H)T)K.[(aIOTCH TOJIbKO qeTblpe HYJI5I, HO OHM 3aBHCHT OT 3Ha-
qeHHH SLR.
neHJIHCC Bblpa311JI 3TH qeTbIpe HYJIH, IIapaMeTp TeHJIOpa A H nOJIO)l(eHMe Uo
IIMKa pa3HocTHOH ,lJ,HarpaMMbI Qepe3 nOJIHHOMbI qeTBepToro nOp5I,l(Ka no SLR (,l:J:n).
IIapaMeTpbI EeHJIHCCa, CKoppeKTHpOBaHHble C MCnOJIb30BaHMeM nOJIMHOMHaJIbHbIX
K03<P<PHUHeHToB H3 Ta6JI. 3.12, npHBe,n:eHbI B Ta6JI. 3.11. TIOJIOXeHMe OCTaJIbHbIX
OJ OJ -
HYJIeM TaKoe xe, KaK M B CJIyqae JIHHeHHOro n-napaMeTpMQeCKOrO pacnpe,lJ,eJIeHH5I
TeMJIOpa:
Zn = +.J A2 +n 2
n > 4.
(3.71)
Ta6JIHua 3.11. HYJIM ,l(MarpaMMbI HarrpaBJIeHHOCTM M rrapaMeTpbI pacrrpe.neJIeHIHI
EeHJIMCCa
SLR (.n;6)
15 20 25 30 35 40
A 1.00790 1.22472 1.43546 1.64126 1.84308 2.04154
ZI 1.51240 1.69626 1.88266 2.07086 2.26025 2.45039
Z2 2.25610 2.36980 2.49432 2.62754 2.76748 2.91234
Z3 3.16932 3.24729 3.33506 3.43144 3.53521 3.64518
Z4 4.12639 4.18544 4.25273 4.32738 4.40934 4.49734
Uo 0.66291 0.71194 0.75693 0.79884 0.83847 0.87649
Ta6J1Hu;a 3.12. nOJIMHOMMaJIbHbIe K03<l><t>MUMeHTbI EeHJIMCCa
C 1 10C 2 I03C 3 10 5 C 4 10'C s
A 0.30387530 -0.5042922 -0.27989 -0.343 -0.2
Ul 0.98583020 -0.3338850 0.14064 0.190 0.1
U2 2.00337487 -0.1141548 0.41590 0.373 0.1
u3 3.00636321 -0.0683394 0.29281 0.161 0.0
u4 4.00518423 -0.0501795 0.21735 0.088 0.0
Uo 0.47972120 -0.1456692 -0.18739 -0.218 -0.1

 Dla8a 3. CUHme3 iJua2paMM Hanpa8JleHHOCmU AUHeuHou aHmeHHOU peUJemlCu
K03<P<PHlIJleHT YMHHeHJiUI 3a,aaeTCR BbIpa)l(eHHeM
n + 1
cr = 2
Zn
(3.72)
,L(HarpaMMa HanpaBJIeHHOCTH CTpOHTCR nyreM 3aMeHbI nepBbIX n HYJIeH <PYHK-
I(MM COS jtU MO,n:H<pHI(HpOBaHHbIM Ha6opOM HYJIeit Pe3YJIbTaT BbIpa)l(aeTCR B BH.LJ;e
OTHOmeHHR KOHeqHbIX npOM3Be,neHMH ,l(HarpaMM HanpaBJIeHHOCTH:
n-I ( 2 J
n 1- U
2 2
n-I a Z n
F(u) = UCOS1tU - .
(3.73)
n-I
n
n=o
U 2
I -
(n +  J
,L(MarpaMMa HanpaBJIeHHOCTH MO)l(eT 6bITb TaIOKe 3anHcaHa B BH.LJ;e KOHeqHOH
C)'MMbI no n HYlliIM:
n -I ( l ) n B
F(u) = UCOS1tU L - 2 n
n=O ( 1 )
n + 2 - u 2
(3.74)
Ha pHC 3.22 nOKa3aHa THnMqHaH ,nMarpaMMa BeibIHCCa,lI)Ul SLR = 25,aB M n = 5.
KaK H B cJIytlae n -napaMel'pHqeCKOH ,aHarpaMMbI TeibIopa, HMeeTCR rJIa,aKHH nepe-
xo,a Me)l(,L{Y 60KOBbIMH JIeneCTKaMH nOqTI1 paBHoro YPOBHR 11 JIeneCTKaMI1 C orl16alO-
meH BH.LJ;a Iju. AMllJIHTY,aHoe pacnpe,n:eJIeHl1e TaIOKe ,aaeTCR KOHeqHOH CYMMOH n
qrreHOB:
n-I
g(P) = L Bn sin
n=O
1tp
1 '
n+-
2
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r,ne K03<P<PI1I(MeHTbI HMelOT BH.LJ;
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n
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a2z
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n-I
n
n=O
n:#m
(m+  f
1-
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(3.76)
Ha pHC. 3.23 nOKa3aHO aMTIJIHTY,nHoe pacnpe,neJIeHHe, COOTBeTCTBYIOmee ,al1a-
rpaMMe HanpaBJIeHHOCTI1, H306pIDKeHHoH Ha pl1C. 3.22. KaK 11 O)KH,l(anOCb, C yqe-

-
---


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 0.4

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3. 7. Pa3HocmHble iJuaZpaMMbl Hanpa6JleHHOCmu 
o
-10
-30
-40
-10
-8
-6
-4
-2 0
u = LIA sin 8
2
4
6
8
10
PHC. 3.22. Pa3HOCTHa51 ,lJ}IarpaMMa HanpaBJIeHHOCTIi EeMJIIiCCa, n = 5
1
o
-1
0.8
1
-0.6
-0.4
- 0.2 0 0.2 0.4
KOOp.lU1HaTbI B anepType
0.6
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PHC. 3.23. AMnJIl1ry.n:Hoe pacnpe.n:eJIeHHe ,WUI pa3HOCTHOM ,lll1arpaMMbI EeMJIIiCCa

 Dla6a 3. CUHme3 iJuazpllMM Hanpa6lleHHOCmU J/UHeUHOU aHmeHHou pewemKU
TOM rrpaBHJI TeibIopa, pacrrpe,n:eJIeHHe HMeeT 3aMeTHhIH rrhe,n:eCTaJI Ha KpaHX pac-
KphIBa. 3<p<peKTHBHOCTh B036)')K.lIeHHH lLJUI arrepTYphI EeitrrHcca COCTaBJIHeT
 . (_1)n Bn 2
n=O [U6 -( n+t f]
n-I
LB
n=O
'I1t = 2U5 COS2 1tUO
(3.77)
KpYTH3Ha B IJ;eHTpe TaIOKe BhIpIDKaeTCH qepe3 K03<P<PHIJ;HeHThI:
2 n-I (-I)n Bn
S=-L 2 '
, 1t n=O ( I )
n+-
2
(3.78)
K03<P<PHIJ;lfeHT IfCrrOJIh30BaHHH nOBepXHOCTH If KpYTlf3Ha ,n:lfarpaMMhI rrpH aMn-
JIHTy,n:HOM pacrrpe,n:eJIeHHIf EeibIHcca rrpHBe,n:eHhI B Ta6JI. 3.13.
Ta6JIHna 3.13. KI1IT 11 Kpyrl13Ha ,[(l1arpaMMbI HalIpaBJIeHHOCTI1 IIpl1 aMIIJII1TY,[(HOM
paClIpe,[(eJIeHI1I1 EeHJII1CCa
SLR ()J;B) n Kiln HOpMHpOBaHHaH KpYTH3Ha
,lUfarpaMMhI HanpaBJIeHHOCTH
15 4 0.5959 0.9567
20 4 0.5846 0.8974
25 5 0.5633 0.8427
30 6 0.5393 0.7912
35 7 0.5162 0.7448
40 8 0.4951 0.7037
)].JIH pa3HOCTHhIX ,n:HarpaMM HanpaBJIeHHOCTH EeibIlfcca xapaKTepHO TaKoe )l(e
.... ....
YBeJIHQeHHe paCCTOHHIDI ,n:o ,n:aJIhHeH BOJIHOBOH 30HhI, KaK H B CJIyqae ,n:lfarpaMM C
HH3KHM ypoBHeM 60KOBhIX JIeneCTKOB, paCCMOTpeHHhIX B pa3,n:eJIe 3.5. YpoBeHh
rrepBOfO 60KOBOfO JIerreCTKa H fJIy6lfHa HYJIH TaIOKe YMeHhllIalOTCH npH YMeHhllIe-
HHIf paCCTOHHIfH ,[(0 3HaQeHHH, MeHhllIHX 2L2 fA. I1pH YMeHhllIeHHIf R npOHcxo,n:IfT
MOHOTOHHhIH pOCT H B3aHMHoe HaJIO)l(eHHe 60KOBhIX JIeneCTKOB. DOJIee no,n:p06HO
3TOT Borrpoc paccMoTpeH B fJIaBe 15.
3.7.3. OnTMMM3au,MR cYMMapHoM M pa3HocTHOM
AMarpaMM HanpaBneHHOCTM
M3 rrpe,n:hI'[(YIUHX pa3,[(eJIOB HCHO, QTO aMTIJIHTy,n:HhIe pacnpe,n:eJIeHIfH, 06eCneQH-
BalOIUHe rrpHeMJIeMhIH BIf,n: 60KOBhIX JIeneCTKOB CyMMapHOH ,n:HarpaMMhI HanpaB-
JIeHHOCTIf, OTJIIfQalOTCH OT pacnpe,n:eJIeHIfH, 06eCneQHBalOIUHX COOTBeTCTByIOIUHe

3. Z Pa3HOCmHble iJuaZpaMMbl Hllnpa6lleHHOCmU d
IIapaMeTpbI pa3HocTHOH ,n;HarpaMMbI. HanpHMep, cyrn;ecTBeHHo pa3JIHqalOTCH
n -IIapaMeTpHqeCKOe pacnpe,n;eJIeHHe TeHJIOpa H n -napaMeTpHqeCKOe pacnpe,n;e-
JleHHe EeHJIHCca. EbIJIH pa3pa60TaHbI cnoc06bI, n03BOJIHIOlUHe OLJ:HOBpeMeHHo
 v 
peaJIH30BaTb nOJIO)lillTeJIbHbIe CBOHCTBa KaK cYMMapHoH, TaK H pa3HocTHOH ,n;Ha-
rpaMM HanpaBJIeHHocTH. ,lJ.Ba HaH60JIee Ba)l(HbIX TaKHX cnoc06a - 3TO IIOCJIeLJ:O-
BaTeJIbHOe nHTaHHe H HCnOJIb30BaHHe nOLJ:pemeToK.
IIocJIe,n;oBaTeJIbHoe nHTaHHe 6blJI0 npe.LLJIO)l(eHO B [36]; 06bIqHO OHO npeLJ:-
CTaBJIHeT C060H JIeCTHHqHYID cxeMY C HanpaBJIeHHbIMH OTBeTBHTeJIHMH B KOHIJ;e
Ka)l():(OH CTYTIeHH. BHyrpeHHHe nJIeqH OTBeTBHTeJIeH nOLJ:KJIlOqeHbI K cTyneHHM,
a BHemHHe llJIeqH - no O,n;HOMY HanpaBJIeHHIO K 3JIeMeHTaM AP, a no LJ:PyrOMY
HanpaBJIeHHIO - K COrJIaCOBaHHOH HarpY3Ke. B ueHTpe KIDK.IJ:OH CTYTIeHH JIeCT-
HWqHOH cxeMbI HaXOLJ:HTCH rH6pH,n;HaH cxeMa, ,BbIXOLJ:HbIe CHrHaJIbI KOTOpOH <pop-
MWPYIOT CYMMapHYIO H pa3HOCTHYID ,n;HarpaMMbI HanpaBJIeHHOCTH. CTyneHH
oTBeTBHTeJIeH, Henocpe,n;CTBeHHO npHJIeralOlUHX K aHTeHHOH pemeTKe, 06eCneqH-
BalOT C03LJ:aHHe cYMMapHoH LJ:HarpaMMbI, TOrLJ:a KaK 06e cTyneHH oTBeTBHTeJIetl,
pa60TalOlUHe COBMeCTHO, C03LJ:a1OT pa3HOCTHYIO LJ:HarpaMMY. CxeMa ,n;aHHoH KOH-
<pwrypaUHH npHBe,n;eHa Ha pHC. 3.24. TaKoe YCTPOHCTBO 06eCneQHBaeT xopomee
ynpaBJIeHHe CYMMapHOH H pa3HocTHOH ,n;HarpaMMaMH HanpaBJIeHHOCTH [43, 33],
XOTH H HBJIHeTCH CJIO)l(}{bIM.
JII1HeHHaH perneTKa
fl16PMHaH
cxeMa

I
PUC. 3.24. OIITHMH3alU1R CYMMapHOH H pa3HOCTHOH HarpaMM HanpaBJIeHHOCTH
c nOMOIUbIO JIeCTHHqHOH cxeMbI
B BapHaHTe C HCnOJIb30BaHHeM no,n;pemeTOK AP pa3,n;eJIeHa Ha nOLJ:pemeTKH,
He06H3aTeJIbHO paBHOH .LLJIHHbI, XOTR B ueJIOM aHTeHHaH pemeTKa CHMMeTpMqHa OT-
HOCHTeJIbHO ueH1]Ja.
CHMMeTpMqHbIe napbI no,n;pemeTOK no,n;KJIlOqalOTCR K rM6plf,lJ:HOH cxeMe; CM.
pwc. 3.25. ,lJ.JIH nOJIyqeHIDI CYMMapHOH ,n;MarpaMMbI CYMMHPYIDlUHe llJIeqH rH6pl1.a-
HbIX cxeM no,n;KJIlOqalOTCR K CYMMaTOpy (,n;eJIHTeJIIO) MOII(HOCTH, aHaJIOrHqHbIM 06-
v
pa30M ,n;JUI no.rryqeHHH pa3HOCTHOH ,n;HarpaMMbI K CYMMaTOpy no,n;KJIlOqalOTCH pa3-
HOCTHbIe llJIeqH rH6plf,lJ:HbIX cxeM. TaKHM 06pa30M, MH nOJIyqeHMH CYMMapHOH
,n;warpaMMbI HanpaBJIeHHOCTH MCnOJIb3yeTcH CTYTIeHqaTaR annpOKCMMaIJ;HH He06xo-
v
,n;HMoro CYMMapHoro pacnpe,L:{eJIeHHH, a .LLJIH nOJIyqeHHH pa3HOCTHOH ,L:{HarpaMMbI -

b
rflaBa 3. CUHme3 aua2pOMM HanpaBfleHHocmu flUHeUHOU aHmeHHOU pememKU
JIMHeHHaH perneTKa
fH6pH.D:Ha51
cxeMa
HepaBHOMepHbIH
CYMMaTOp
HepaBHOMepHbIH
C)'MMaTOp
6
r
PHC. 3.25. OnTMMIf3aU;IfH cyMMapHOH If pa3HocTHOM ,lIMarpaMM HanpaBJIeHHOCTM
c nOMOIl{blO nO,lIperneTOK
cTyrreHqaTaH arrrrpoKcHMaUHH He06xo,aHMoro pa3HocTHoro pacrrpe,aeJIeHMH [37].
llpl1 HCrrOJIb30BaHHH 60nbIIIero qHCna no,apellieTOK C MeHbIIIMMM pa3MepaMM CTY-
rreHqaTble arrrrpOKCHMaUHH YJIyqIIIaIOTcH, M rrOJIyqalOmHecH ,lIHarpaMMbI npn6nIDKa-
IOTCH K HCKOMbIM. ITpHMeHeHne 3Toro MeTo,aa K nnOCKMM perneTKaM 06Cy)K,[(aeTCH
B rJIaBe 4.
Ha pMC. 3.26 rrOKa3aHa cxeMa rrMTaHMH [43]; B HIDKHeH QaCTI1 BI1,aHbI ,aBe B01l-
HOBo,aHble nHHHM [52]. CTYIIeHM He rro,aKJIlOqeHbI K COrJIaCOBaHHbIM HarpY3KaM,
QTO YBenHqHBaeT KITL( YCTpOHCTBa.
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PHC. 3.26. MOHoMMnYJIbCHOe YCTPOHCTBO OpMMpoBaHMH JIyqa [52] no MeTOJJ:Y [43]

3. 7. P03HOCmH/>le iJua2pllMMbl Hanpa8JleHHOCmU ' 
3.7.4. AMcKpeTHbie pacnpeAeneHMSI 30noTapeBa
YqeHHKOM Qe6bIllieBa, 30JIOTapeBbIM, paCCMO'TpeH KJIacc HeqeTHbIX rrOJIHHOMOB,
,nalOI.UHX paBHOMepHYID arrrrpOKCHMaUHIO B 38,[(aHHOM HHTepBaJIe, rrO,n06HyIO TOM,
KOTOpyro ,nalOT qeTHbIe rrOJIHHOMbI qe6bIllieBa. llOJIHHOMbI 30JIOTapeBa rrpHMeHeHbI
K pacqeTY MHKpOBOJIHOBOrO cpIDIbTpa B pa60TaX JIeBH [40, 41], r,ne rrpHBe,neHbI TaK-
:>Ke HCTOpHqeCKHe rrO,L(p06HOCTH H ,neTaJIH paCqeTa. B pa60Tax [44, 45], 06HapY:>Ke-
v
HO, qTO 3TH nOJIHHOMbI MOryr HCrrOJIb30BaTbCH TalOKe ,L(JIH CHHTe3a pa3HOCTHOH
,nHarpaMMbI C paBHbIM ypOBHeM 60KOBbIX JIeneCTKOB. aHHbIM nOJIHHOM orrpe,neJIH-
eTCH KaK rHrrep60JIHqeCKHH KOCHHYC apryMeHTa, HBIDllOlUerOCH rrpOH3Be,L(eHHeM
<PYHKU;HH Ha K03cp<pHU;HeHT N, qTO ,L(aeT rrOJIHHOM 2N + 1 rrOPMKa. K COXaJIeHHIO,
Haxo,nHI.UaHCH B apryMeHTe <PYHKUHH co,nep)I(HT 3IDIHrrTHQeCKHe HHTerpaJIbI, a TaK-
:>Ke 11 H  <PYHKUHH 5IKo6H. llpoue.n:ypa CHHTe3a 3.n:eCb onlicaHa KpaTKO; no.npo6HO-
CTH CM. B pa60Te [45]. llpH 38,[(aHHOM 3HaQeHHH SLR H AP H3 2N 3JIeMeHTOB,
YCTaHaBJIHBaeM nHKOBoe 3HaqeHHe SLR nOJIHHOMa (2N - 1) rrOPMKa. PerneHHe
3Toro ypaBHeHHH .n:aeT K03<P<PHUHeHTbI 5IKo6H, H nOJIHHOM onpe.n:eJIHeTCH nOJIHO-
CTblO. llpH nOJIYBOJIHOBOM nepHo.n:WIHOCTH ,naHHbIM nOJIHHOM paCKJI8,[(bIBaeTCH B
TPMHU;HOHHbIM nOJIHHOM, H3 K03<P<PHUHeHToB KOToporo MOryT 6bITb HaeHbI KO-
3<P<PHU;HeHTbI B036y)1(,L(eHHH AP. KOHKpeTHbIe .n:eTaJIH BbIQHCJIeHHH CneUHaJIbHbIX
<PYHKUHM npHBe.neHbI B UHTHpyeMoH BbIrne pa6oTe. Ha pHC. 3.27 H306pa:>KeH rpa-
<p HK nOJIHHOMa 30JIOTapeBa ,neBHToro nOPMKa, r,ne Xl H X3 - TOQKH B03HHKHOBe-
HHH pe)I(HMOB C paBHbIM ypOBHeM 60KOBbIX JIeneCTKOB. Ha pliC. 3.28 H306pIDKeHa
THnHqHa» pa3HOCTHaH ,nHarpaMMa MH 20-3JIeMeHTHoH AP C SLR = 30 .nD; Ha
pHC. 3.29 nOKa3aHbI aMIIJIHTY,nbI B036y)1(,L(eHIUI ,lUUI nOJIOBHHbI perneTKH.
B pa60Te [46] nOJIyqeHa TaIOKe pa3HOCTHaH ,nHarpaMMa HanpaBJIeHHOCTH MH
- v
n -rrapaMeTpHQeCKOrO ,nHCKpeTHoro pacnpe.n:eJIeHIDl, aHaJIOrHqHaH CYMMapHOH ,L(Ha-
rpaMMe ,L(JIH n - napaMeTpHqeCKOrO .n:HCKpeTHoro pacnpe.n:eJIeHHH BIDIbHeBa. llo aHa-
Z9(.)
Ao
)( = -)
)(:0
)( = 1
PUC. 3.27. IlOJIHHOM 30JIOTapeBa ,LJ;eBRTOro IIOpR,LJ;K8 Zg [45]

 f/la6a 3. CUHme3 iJuazpflMM Hanpa6JleHHOCmu /lUHeUHOu aHmeHHOU pememKU
o
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-20
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PUC. 3.28. ,[(HarpaMMa HarrpaBJIeHHOCTH 20-3JIeMeHTHOH perneTKH 30JIOTapeBa [45]
a
1.0
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PUC. 3.29. B036}')K,lJ;eHHe aHTeHHOH perneTKH [45]
u u u
JIOrHH MO)l(}lO O)l(H)];aTb, qTO OTlipaBHOH TOqKOH CJIyxHT paBHOMepHbIH IIOJIH-
HOM 30JIOTapeBa. ITepBbIe n RYneR Y.LJ;ep)KHBaIOTCR, a y,narreHHbIe HynH 3aMeIDIIOTCH
HYJIHMH 6a30BoH .LJ;HarpaMMbI, BbI6paHHoR TaK, QTo6bI o6eCneQHTb HarLJIeXall(ee co-
OTBeTCTBHe .LJ;BYX ,l(HarpaMM. B KaQeCTBe 6a30BoH ,nHarpaMMbI Hcnonb3yeTcH pa3HO-
CTHaH .LJ;HarpaMMa C MaKCHMaJIbHOH KpyrH3HOH. ,lJ:nH onHcaHHR nepeXO.LJ;HOR o6nac-

3.8. (/)opMa o2u6alOU4eu 60lC06bIX lleneCmlC06 
TH Me)I()I:Y n Hyn5IMH ,lJ;HarpaMMbI 30JIOTapeBa H Hyn5IMH 6a30BoM ,lJ;HarpaMMbI, KaK H
paHee, BBO,lJ;HTC5I K03<P<PHUHeHT Y.llJIHHeHH5I. )];aHHbIM paCqeT HeCKOJIbKO TPY'uO-
eMoK, O,lJ;HaKO nOJIyqaeMbIe pe3ynbTaTbI npeBOCXO,lJ;HbI. Ha pHC 3.30 H306paxeHa
,lI;llarpaMMa HanpaBJIeHHOCTH 20-3JIeMeHTHoH aHTeHHOM pemeTKH C HOMHHaJIbHbIM
3HaqeHHeM SLR = 25 ,lJ;E H n = 4. K03<P<PHIJ;HeHT Y.llJIHHeHHH a = 1,01051. 3Haqe-
HID! no OCH a6cUHCC npHBe,lJ;eHbI B e,lJ;HHHuaX (2djA) sin 8.
o
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PHC. 3.30. JlwarpaMMa HarrpaBJIeHHOCTI1 .lUUI n - rrapaMeTpl1QeCKOrO pacrrpe.n:eJIeHI1H
30JIOTapeBa [46]
3.8. CbopMa orM6alOw,eM 60KOBbiX neneCTKOB
OrM6alOmyIO 60KOBbIX JIeneCTKOB ,n:H aHTeHHOH pemeTKH C OCTpOHanpaBJIeHHbIM
JIytIOM MOXHO H3MeH5ITb, peryJIHPY5I ypOBeHb OT.QeJIbHbIX 60KOBbIX JIeneCTKOB C no-
MOIIJ:blO MeTO,lJ;OB, pa3pa6oTaHHbIX B [20]. OCHoBHa» If,l(e5I OCHOBaHa Ha TOM <paKTe,
QTO paCCT05IHHe Me)I()I:Y Ryn5IMH ,lJ;HarpaMMbI HanpaBJIeHHOCTH BJIH5IeT Ha ypOBeHb
60KOBbIX JIeneCTKOB. IIpH CMern:eHHH CMe)I{HbIX RyJIeH ,n;pyr K ,n;pyry 60KOBOH JIene-
CTOK YMeHbmaeTC5I. O,lJ;HaKO, nOCKOJIbK)' qHCnO HYJIeH Y Ka)l(,L(OH AP <pHKCHpOBaHO,
c6nIDKeHMe O,n;HHX HYJIeH rrpe,lJ;rrOJIaraeT OT,l(aJIeHHOCTb ,lJ;pyrHX. IIpH .QaHHOM MeTO-
,n:e BbI6HpaeTC5I KJIaCCHqeCKa5I ,l(HarpaMMa, Y KOTOpOH mHpHHa .rryqa H Cpe,L(HHM
ypOBeHb 60KOBbIX JIeneCTKOB rrpHMepHO Te xe, qTO Y HCKOMOH .QHarpaMMbI. 3Ta
v
KJIaCCMqeCKa5I ,l(HarpaMMa ,l(OJDKHa HMeTb TO )l(e qHCJIO RyneM, qTO H HCKOMaH ,L(Ha-
rpaMMa; TOr,l(a ,lJ;HarpaMMa HarrpaBJIeHHOCTH 3arrHCbIBaeTCH B Blf,l(e npOH3Be.QeHHH
COOTBeTCTByJOrn:HX KopHeBbIX COMHO)f(HTeJIeH. B KaqeCTBe HCXO,L(HOM MO)l(eT Hcno-
JIb30BaTbC5I, HanpHMep, O,L(HOnapaMeTpHqeCKa5I RITH n -napaMeTpMqeCKa5I .lI:HarpaM-
MbI TeHJIOpa.
AnropHTM <pOpMHpOBaHIUI OfH6alOrn:eii HaQHHaeTC5I C Toro, qTO nOJIO)l(eHH5I
v v v
Bcex HYJIeH HCKOMOM .QHarpaMMbI 3arrHCbIBalOTC5I B BH.Qe nOJIO)l(eHH5I HYJIeH KJIaCCH-
qeCKOH ,n;HarpaMMbI IIJIIOC He6oJIbllIOe CMern:eHHe. IIpH npeHe6pe)l(eHHH 3<p<peKTa-
MH 60JIee BbICOKoro nOPMKa HCKOMa5I ,n;HarpaMMa BbIpa)l(aeTC5I B BM,1J.e rrpOH3Be,n;e-

 rlla6a 3. Cunme3 iJua2paMM nanpa6llennocmu Iluneunou anmennou pelUemlCU
HHH KJIaCCHqeCKOH ,nHarpaMMbI H K03<P<PHUHeHTa, paBHoro 1 TIJIIOC CYMMa HYJIeH
,LJ;HarpaMMbI. 3Ta CyMMa BKJIlOqaeT HYJIH KJIaCCHqeCKOH ,nHarpaMMbI H HeH3BeCTHbIe
CMeIneHIUI HYJIeH. MaKCHMyMbI Y3KHX 60KOBbIX JIerreCTKOB HaXO)UlTCH rrpHMepHO
rrocepe,aHHe Me)K)J;Y CMe)I{JIbIMH HYIDIMH. IIo,n;cTaBJIIDI nOJIO)l(eHHH 60KOBbIX JIerreCT-
KOB B ypaBHeHHe, no.rryqaeM 3HaqeHHH YPoBHeH Bcex 60KOBbIX JIeneCTKOB KaK npo-
u u
Me)I()'TOqHbIe Mex.ay HCKOMOH H KJIaCCHqeCKOH ,n;HarpaMMaMH, a TaIOKe rrOJIO)l(eHHH
pa3JIHQHbIX HYJIeH. TaKHM o6pa30M nOJIyqaeM rrOCJIe,n;OBaTeJIbHOCTb CHCTeM ypaBHe-
u u
HHH C HeH3BeCTHbIMH CMeIneHHHMH RYJIeH, B KOTOpbIX onpe,n;eJIeHbI pa3JIHqHH
YPoBHeH 60KOBbIX JIeneCTKOB. 3TH ypaBHeHHH pellialOTCH HTepaUHoHHbIM MeTo,n;OM
C I1CnOJIb30BaHHeM rrOJIyqeHHbIx ,n;HarpaMM B KaQeCTBe KJIaCCHqeCKHX ,LI,JUI cJIe,n;ylO-
III:ero mara. 06bIQHO TPe6yeTcH MeHee 10 HTepa:QI1H. EbIC'TpO HaRTH c,n;Bl1rH HYJIeH
n03BOJIHeT MeTO,n; rpan;HeHTa, HanpHMep, H3 pa60TbI Stark, P. A., Introduction to
Numerical Methods, MacMillan, 1970.
I1ToroBaH ,n;HarpaMMa HMeeT BH.a JIerKO BbIqHCJIHeMOrO npOH3Be,aeHHH QJIeHOB,
3aBHCHIII:HX OT nOJIOXeHHH HYJIeH. HaXO)K)J;eHHe K03<P<PHUMeHToB B036}')K,L(eHIUI aH-
TeHHOH perneTKH 60JIee CJIO)I{JIoe. IIpoH3Be,n;eHHe B BbIpaJKeHI1M MH ,n;MarpaMMbI
HanpaBJIeHHOCTM paCKpbIBaeTCH, H o6pa3yeTcH rrOJIHHOM. Ero K03<P<PMUMeHTbI 3a-
,n;alOT 3HaqeHMH B036}')K,L(eHMH AP. PacCMOTPMM, K rrpl1Mepy, ,n;HarpaMMY HanpaB-
JIeHHOCTH MH pacnpe,n;eJIeHH5I Teitrropa C napaMe'TpOM n = 8 M SLR = 20 ,n;I>, 3a
HCKJIIOQeHMeM Tpex 6JIIDKaHlIIMX 60KOBbIX JIeneCTKOB C O,n;HOH 113 CTOpOH OCHOBHO-
ro nyqa, ypOBeHb KOTOpbIX ,n;OJDKeH COCTaBJUlTb -30 ,n;E. Ha pHC. 3.31 nOKa3aHa
MTorOBaH ,n;MarpaMMa, rrOJIyqeHHaH rr}'TeM TPex MTepa:QHH [21], a Ha pHC. 3.32 11306-
pa)l(eHbI aMIIJIHTY,n;bI M <pa3bI nOJIyqeHHoro anepTYpHoro pacnpe,n;eneHHH.
o
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PRC. 3.31. JJ;HarpaMMa HarrpaBJIeHHOCTH C 3a.n:aHHoH <pOpMOH ofH6alOrn;eH 60KOBbIX
JIerreCTKOB [20]

3.8. C/JopMa oi!u6aloUl,eu 60K06blX JleneCmK06 
1.0


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PHC. 3.32. ArrepTYPHoe paCrrpelleJIeHl1e, COOTBeTCTBYIOIlI.ee )J)larpaMMe HarrpaBJIeH-
HOCTI1 C 3aaHHoti cpOpMOM Orl16aIOIlI.eti 60KOBbIX JIeneCTKOB [20]
I1oCJIe,n;Hee, KOHeqHO, CJIO)l(HO, nOCKOJIbKY ,n;MarpaMMa HanpaBJIeHHOCTM 60JIee
He CMMMeTpMqHa. ,LJ;aHHbIM MeTO,n; cPOpMMpOBaHM5.I 3a,n;aHHOM ,LJ;H n)'TeM KOppeK1..(MM
HYJIeM ,l(OKa3aJI CBOIO 3<PcPeKTMBHOCTb 11 nOJIe3HOCTb.
,LJ;pyrOM cnoc06 peaJIM3aUJ1M 3TOM rrpouellypbI COCTOHT B TOM, qT06bI 3anHcaTb
,[(MarpaMMY HanpaBJIeHHOCTM AP B cPopMe Z-npe06pa30BaHM5I, r,n;e HYJIH ,n;MarpaMMbI
pacnOJIO)l(eHbI Ha e,n;HHMQHOM OKp)')KHOCTH (CM. rJIaBY 2). CMemeHMe HYJIeM ,n;pyr K
,[(pyry CHIDKaeT ypOBeHb 60KOBoro JIeneCTKa, Ha KOTOpbIM OHM BJIM5.lIOT, HO YBeJII1QM-
BaeT coce,n;HI1M 60KOBO:H JIeneCTOK. I10JIyqeHMe TOM )l(e IIIMpl1HbI JIyqa npM 60JIee
HM3KOM 06meM ypoBHe 60KOBbIX JIeneCTKOB Tpe6yeT 60JIbllIerO KOJIHQeCTBa RyJIeR B
,[(HarpaMMe M, CJIe,n;oBaTeJIbHO, LUIMHHOM AP. HYJIM 60KOBbIX JIeneCTKOB MOryr 6bITb
qaCTWIHO HJIH nOJIHOCTblO 3anOJIHeHbI nyreM rrepeMern:eHM5I COOTBeTCTByIOrn:MX KOp-
u u
HeM C e,n;MHMqHOH OKp)')KHOCTM BO BH)'TpeHHIOIO MJlM BHelliHlO1O qaCTb e,n;HHWlHoro
Kpyra. 06bIQHO OllHH M TOT )l(e ypOBeHb 60KOBbIX JIerreCTKOB MO)I(HO 06eCrreQHTb rrpH
MHorMX BapMaHTax pa3Mern:eHH5I KopHeM (M TMnax B036y)1()].eHM5.I aHTeHHOM peIlleT-
KIf). O,n;HaKO HeKOTopbIe BM,n;bI B036y)1()].eHIDI MOryr 6bITb 60JIee Ha,I(e)I(HbI B 3Kcrmya-
TaIUfM, QeM ,n;pyrMe, n03TOMY He06xOllMM paCQeT M cpaBHeHl1e ,lI)UI Bcex CJIyqaeB.
ECJIM ,n;JI5.I AP Tpe6yeTC5I ,n;eMCTBMTeJIbHOe pacnpe,n;eJIeHMe, KaK, HanpHMep, ,lUI5.I
pe30HaHCHbIX AP I1JIM HeKOTopbIX MI1KpOnOJIOCKOBbIX pellieTOK, TO MO)l(eT I1CnOJIb-
30BaTbC5.I Ta )l(e 06ma5I MeTOllMKa CMHTe3a C TeM OTJIMqHeM, QTO BBO,n;RTC5.I ,n;orrOJIHM-
TeJIbHbIe KOMnneKCHbIe KOpHH [4].

 Dla6a 3. CUHme3 iJuai!paMM Hanpa6JleHHOCmu JlUHeUHOU aHmeHHou peUJemKU
3.9. CMHTe3 AMarpaMMbl HanpaBneHHOCTM
cneu.ManbHoM 4>OpMbl
3.9.1. CMHTe3 BYABoPAa-nOycoHa
B HaqaJIbHbIX pa3,n:eJIaX 3TOH rJIaBbI paCCMaTpMBaJICH CMHTe3 llMarpaMMbI HanpaB-
JIeHHOCTI1 C OCTpOHanpaBJIeHHbIM JIyqOM (BbICOKllM KH,LI). qacTo 6bIBaeT He06xo-
,n:llMO nOJIyqeHMe llIMpOKllX JIyqeR Cnel.{IHUIbHOH <pOpMbI. HanpMMep, KoceKaHC-
Horo JIyqa pallapa MJIll JIyqa C nJIOCKOH BepllIMHoM, MCnOJIb3yeMoro llJIH pa60TbI
no rrOBepXHOCTM. npOToTMn MeTo.ua CMHTe3a JIyqa OC060M <pOpMbI pa3pa60TaH
BYllBOPllOM M JIOYCOHOM (Woodward and Lawson) [68,69]; B HeM MCnOJIb3yeTcH
.
MHO)l(eCTBO BMPTYaJIbHbIX aHTeHHbIX pemeTOK, C03n:aIOIUMX opTOrOHaJIbHbIe Slnc-
06pa3HbIe JIyqM. Ka)l()1bIR sinc-06pa3HbIH JIyq MMeeT CBOIO aM rrJIMTYllY , orrpe-
lleJIeHHYIO TaKMM 06pa30M, QTO nMKOBoe 3HaqeHMe JIyqa COOTBeTcTByeT TOqKe Ha
'-'
3a,n:aHHOM ,n:MarpaMMe HanpaBJIeHHOCTM, rrpMqeM TOqKM annpOKCMMal.{MM pacrro-
JIO)l(eHbI paBHOMepHO. Ka)l()1bIR COCTaBJIHIOllJ,MR JJ:MarpaMMY JIyq 06pa30BaH BMPTY-
aJIbHOR JIHHeRHOM AP C nOCTOHHHOH aMnJIHTYJJ:OM H JIMHeRHO pacnpeJJ:eJIeH-
HOM <))a30H. ECJIM AP HMeeT N 3JIeMeHTOB C Me)l(3JIeMeHTHbIM paCCTOHHHeM d,
u == kd(sin e - sin en), TO n-M JIyq 3a,r(aeTCH <pyHKl.{MeR sin(N'Jtu)/(N sin 'Jtu). JIyqM
pa3HeceHbI (no 3HaqeHMIO sin e) Ha BeJIMqMHY nn/ Nd, TaKJ1M 06pa30M, B MaKCM-
MYMe n-ro JIyqa aMnJIMTYlla Bcex OCTaJIbHbIX JIyqei1 paBHa HYJIIO. 3aTeM MCKOMaH
,n:HarpaMMa HarrpaBJIeHHOCTH JJ:MCKpeTH3MpyeTcH rrpM6JIH3MTeJIbHO no NA/2d TOq-
KaM, B KOTOpbIX B036y)1()].eHMe 3JIeMeHTOB AP COOTBeTcTByeT aMnJIMTyn:aM BbI60p-
KM. I1ToroBoe pacnpe,n:eJIeHMe no AP rrpe.n;CTaBJIHeT C060M npOCTO CYMMY B036yx-
lleHMM COCTaBJIHIOllJ,MX BMPTYaJIbHbIX perneTOK. DpM 3an:aHHOM n:MarpaMMe F(u)
CMHTe3MpyeMaH llMarpaMMa MMeeT BHll
WL(u) = fF(un) sin1[U .
n=l N SIn 1tU
(3.79)
HepaBHOMepHOCTb ,n:MarpaMMhI onpe.n;eJIHeTCH BeJIHqHHOM Me)l(3JIeMeHTHoro
paCCTOHHMR. Ha pMC. 3.33 npHBe,n;eH npMMep KoceKaHCHOM JJ:HarpaMMhI, CMHTe3M-
pOBaHHoH M3 21 JIyqa ,lUIH 21-3JIeMeHTHo:H aHTeHHoH pellIeTKJ1 C nOJIYBOJIHOBhIM
marOM. O,n:MH HYJIb pacrrOJIO)l(eH npH e == O. KaK BMHO Ha pMC. 3.34, MeHbllIaH aM-
rrJIMTYJJ:a OCl.{IDIJIHl.{M:H ,n:OCTMraeTCH rryreM CMeIUeHMH HYJIeH. ITplf rrepMo,n:MqHO-
CTM 60JIhIlleti, qeM nOJI)'BOJIHOBaH, B03HMKalOT ,n;M<ppaKIJ;IfOHHbIe JIeneCTKH, a npM
MeHbmeR nepMo,n:lfqHOCTM nORBIDIeTCH TeH.IJ:eHl.{HH K CBepXHarrpaBJIeHHOCTM. TaKMM
06pa30M, )l(eJIaTeJIhHO MCnOJIb30BaTb rrOJIYBOJIHOBbIH mar.
B CMHTe3e By,n:Bop,n:a-JIoycoHa MCnOJIb3yIOTCH COCTaBJI5IIOIUHe JIyqM, nOJIyqeH-
HhIe B pe3YJIbTaTe paBHOMepHoro pacnpe,n:eJIeHMH, qTO ,n:aeT ypOBeHb 60KOBbIX JIe-
neCTKOB -13.3 ,n]) ,lUIH npOTIDKeHHbIX AP. MO)I(Ho HaqaTb C HYJIeR ,[{MarpaMMbI Ha-
npaBJIeHHOCTM, MMelOIUeR HM3KMH ypOBeHb 60KOBbIX JIeneCTKOB, a 3aTeM, qT06bI
C<pOpMMpoBaTh Tpe6yeMYIO <POPMY JIyqa, CMeCTMTb KOpHM C eJJ:MHlfqHO:H OKPYX-
HOCTM (BHyrpb MJIIf Hap)')KY). O,n;HaKo npM 3TOM IfHTepBaJI Me)l().1Y opTOrOHaJIbHbI-
MM JIyqaMM nOJIyqaeTcR 60JIbllIe; nrraTOH 3a ,n;OCTJiOKeHlfe MeHbmero YPOBHH 60KO-
BbIX JIeneCTKOB (If 60JIee BbICOKOH HanpaBJIeHHocTM) KoceKaHCHOH JJ:MarpaMMbI

3.9. CUHme3 iJua2paMMbl Hanpa61/eHHOCmu Cnel(uOJ/bHoU rjJopMbl 
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$IBJIHeTC$I, K npMMepy, 66JIhIIIaH HepaBHOMepHOCTh ,UMarpaMMhI MJIM 60JIhllIa.H
anepTypa.
CMHTe3 BY,lJ;BOpTa-JIOYCOHa MMeeT Ba)KHOe 3HaqeHMe, nOCKOJIhKY OH npMMeHMM
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HYIO TOqKY ,lJ;JI.H MTepaU;HOHHOH npOu;e,lJ;yphI KOppeKIJ;MM, CXO,lJ;HYIO TOH, KOTopaH 06-
C)')K.LI:arraCh B pa3,lJ;eJIe 3.8. KOppeKTMpOBKoti napaMeTpOB B036)')K.L1:eHM.H AP MO)I(HO
MMHHMM3MpOBaTh HepaBHOMepHOCTh ,lJ;MarpaMMhI M KOHTpOJIMpOBaTh <POPMY orM6a-
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I1HT)'HTMBHO MO)KHO O)KM,lJ;aTh, qTO onTMMarrhHaH KoceKaHCHa$l ,UHarpaMMa 6YJIeT
MMeTh HYJIM B cBoeti HM)I(HeH qaCTH, COOTBeTCTByIOlUMe 3aHHOMY YPOBHIO 60KO-
BbIX JIeneCTKOB. ECJIH MO)KeT 6bITh TOqHO 3a,UaHa nOJIHaH ,lJ;MarpaMMa, HanpMMep, B
CJIyqae nepen;aIOlUMX aHTeHH, TO Cpe,lJ;HeKBa,UpaTHqHhIH MHTerparr 01lIM60K MMHMMH-
3MpyeTcH O,lJ;HMM 113 qMCJIeHHbIX MeTOI(OB, HanpMMep, MeTOJIOM rpa,IIMeHTHOrO cnyc-
Ka [50]. 113 rpMeHTHbIX arrrOpHTMOB llIMpOKO MCnOJIb3YIOTCH arrrOpMTMbI <I>JIeTqe-
pa-IIaY3J1JIa [24-26, 28].


Fflaea 3. CUH.me3 aua2paMM H.anpaefleH.H.OCmu flUH.eUH.OU aH.meH.H.OU pelUemKU
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Poc. 3.34. Y JIyqrneHHa5I )J}larpaMMa HanpaBJIeHHOCTJ1 KoceKaHCHOM <pOpMbI [69]
CHHTe3 MeTo,n;OM HaHMeHbllIllX KBa,n;paTOB qaCTO npllBo,n;HT K HepaBHOMepHbIM
OTKJIOHeHIl5IM; rrpll6nIDKeHlle K IIpaBHnbHOMY MHHHMaKCHOMY CHHTe3Y o6eCneqH-
BaeTC5I B pe3ynbTaTe CllHTe3a MeTo,n;OM MllHHMH3aU;Hll p-ro nOp5I,n;Ka [63, 7]. 3Tll
MeTo,n;bI He ,n;alOT IIone3HbIX pe3ynbTaToB npH paCCMOTpeHHH 06naCTH 60KOBbIX ne-
neCTKOB, nOCKonbK)' KOnllqeCTBO H nOnO)KeHH5I 60KOBbIX neneCTKOB 06bIqHO He
Ba)KHbI, BIDKHa TonbKO HX orH6alOrn:a5I. TaKHM 06pa30M, OT,n:enbHbIe 60KOBbIe ne-
neCTKll He MOryr 6bITb 3<p<peKTHBHO onpe,n;eneHbI.
OCHOBHOM He,I:(OCTaTOK MeTO,I:(a CHHTe3a BYLJ;BOp,I:(a-JIOYCOHa COCTOHT B TOM, qTO
 
IIPH Hcnonb30BaHHll e,I:(IlHllqHOH OKp)')KHOCTH H ,I:(HarpaMMbI, 3aIIHcaHHOH B Bl1,I:(e
IIpOH3Be,n;eHH5I KopHeM, B 06naCTH paCIlIHpeHHoro nyqa KOpHH YX0,I:(5IT C OKp)')KHO-
CTH nonapHO. TaKHM 06pa30M, qHCnO ,I:(OCTynHbIX CTeneHeM CBo60,I:(bI COKparn:aeTC5I
B,I:(BOe, a OHll BnH5IIOT Ha KOnHqeCTBO OCIl11JIJI5IU;HM B 06naCTH paCIlIHpeHHoro nyqa
11, Cne,I:(OBaTenbHO, Ha TOqHOCTb COOTBeTCTBH5I ,I:(HarpaMMbI )KenaeMOMY BH,I:(Y. HIDKe
06Cy)I(,[(aeTC5I MeTO,I:(, B KOTOpOM HCIIonb3YIOTC5I Bce ,I:(OCTYITHbIe CTeneHH CBo60,I:(bI.
L.

3.9. CUHme3 iJuaZpaMMbl Hanpa8JleHHOCmU Cnel(UaJlbHOU rPoPMbl 
3.9.2. CMHTe3 3nnMoTTa
3<t><t>eKTMBHbIe MeTO,lI;:bI CMHTe3a ,lI;MarpaMM Cnel.(MaJIbHOH cpOpMbI pa3pa6oTaHbI B
pa60Te 3IDIMoTTa [22], r,lI;e ,lLJUI onTMMM3aUMH ,lI;HarpaMMbI KoppeKTHpYIOTCH Bce
KOpHH nonMHOMa AP (B TepMHHOJIOrHH e,lI;I1Hl1qHOH OKp)')KHOCTI1). TIocKOnbK)' pa3-
JIO)l(eHHe KOMnneKCHbIX nOJII1HOMOB Ha MHO)l(JfTeJII1 - 3a.naQa TPYL{HaH, IfTepaUI1-
v v v
OHHbII1 npOl.(eCC CI1HTe3a nyqIIle HaQI1HaTb C COOTBeTCTByIOll.(el1 KJIaCCI1QeCKOIf ,lJ;l1a-
rpaMMbI, BbIpa)l(eHHOH B <popMe npOH3Be,lI;eHIDI. XOpOIIlHM BapHaHTOM HBlliIeTCH
'-II U V U u
,[(l1arpaMMa 3KBIUJ:I1CTaHTH0I1 nHHel1HOM aHTeHHOI1 peIIleTKlf, KOpHH KOTOpOIf paB-
HOMepHO pacnOnO)l(eHbI Ha eL(HHI1QHOH OKpyxHOCTI1 (npM non)'BonHOBOM mare).
TIepBbIH 3Tarr np0l.(e,aypbI CI1HTe3a npe,lI;CTaBnHeT C060H I1TepaUI10HHYIO KoppeK-
UlflO pacnonoxeHIDI KopHeH Ha e,lI;MHHQHOH OKpyxHOCTI1 TaKlfM o6pa30M, QTo6bI
60KOBbIe neneCTKlf COOTBeTCTBOBaJIl1 I1CKOMOH Orl16alOll.(eH B 06naCTIf 60KOBbIX JIe-
neCTKOB 11 B 06naCTI1 paCIIlMpeHI1H nyqa.
IlpM 3TOM I1Tepal.(110HHOM rrpOl.(eCce npe,arrOJIaraeTCH, qTO nl1K Ka)l([(OrO JIene-
CTKa Haxo,aI1TCH nocepe.n:MHe Me)K):(Y CMe)I(HbIMH HYJIHMI1. Ka)l(,[(OMY HYJIIO 3a,IJ;aeTCH
npMparn;eHMe Ha BenMQI1HY ,IJ;enbTa, H nonyqaeMaH ,aHarpaMMa paCCQI1TbIBaeTCH B
TOQKaX MaKCI1MYMOB JIeneCTKOB. Pa3HocTM Me)l(,[{Y nl1KOBbIMI1 aMTInMTY.n:aMIf nene-
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HeHHH, CBH3bIBalOll.(yIO npMparn;eHIDI (,lI;eJIbTbI) H npOH3BO,lI;HbIe. 3TH ypaBHeHI1H
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v v v
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cosec 2 e cos e B ceKTope 40° H 06JIaCTb 60KOBbIX JIerreCTKOB, COCTO}lll.(yIO 113 qeTbI-
pex 6nl13KHX 60KOBbIX JIerreCTKOB C ypOBHeM -30 .n:E, H OCTaJIbHbIX nerreCTKOB C
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BbIMH JIerreCTKaMH [23]

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Ha BTOpOM mare KOpHIf, cooTBeTcTByJOIIJJ'le 06JIaCTH npo<plfJIHpOBaHHoro nyqa If
...,
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JIe6aHlliI. KOHeQHbIH pe3YJIbTaT rrpe,n:CTanneH Ha pHC. 3.37, r,n:e nOKa3aHbI QeTbIpe
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PHC. 3.36. ,[(HarpaMMa HarrpaBJleHHOCTH CrreU;HaJIbHOH <pOpMbJ C 3anOJIHeHHbIMH HY-
lliIMH [23]
Ta6JIHua 3.14. PacnOJIOXeHHe KopHeH OTHOCHTeJlbHO e,aHHHQHOH OKp)')KHOCTH
PaCCTOBHHe YrJlOBOe paCCTOJlHHe PaCCTOJIHHe YrJIOBOe paCCTOBHHe
no P3.lUlYCY (rpa,n;. ) no P3.lUlYCY (rpa,a.)
1.0000 -8.76 1.0000 148.74
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HbIMM 60KOBbIMH JIeneCTKaMM [23]
B036y)K)!eHIDI AP orrpeJIenRIOTCR rryreM rrepeMHO)ICeHIDI KopHeBbIX COMHO)l(JfTe-
JIeH, qTO ,n:aeT rronHHOM pellIeTKH; rrpH 3TOM K03cp<PHllJleHTbI orrpe,n:emnoT 3HaqeHHR
aMrrJIHTY,n: H <pa3 B036y)K)!eHIDI. OHH .1I.JUI rrpHMepa rrpHBe.1IeHbI B Ta6n. 3.15. I1HTe-
peCHaH oco6eHHOCTb .1IaHHOrO CHHTe3a COCTOHT B TOM, qTO KIDK.1IbIH KopeHb H3 o6na-
CTH paCllIHpeHHoro nyqa MO)ICeT 6bITb rrepeMern:eH BHyrpb HJIH 3a rrpe.1IenbI e.1IHHWI-
HOH OKp)')KHOCTH. llpll KOnllqeCTBe TaKllX KopHeH, paBHOM M, cym:ecTByeT 2 M
pellIeHHH, .1IaIOIUHX TY )ICe .1IHarpaMMY HanpaBneHHocTH. AMllnHTY.1Ia 11 <pa3a B036yx-
,LI;eHHH 3neMeHTOB 6y.1IYT pa3nllqHbIMH, 11 HeKoTopbIe HX 3HaqeHHH C TPY.1IOM MO)I(HO
BorrnOTllTb Ha npaKTllKe. HarrpllMep, ,[(JIH rn:enen B BOnHOBOJIaX cym:ecTByJOT rrpaKTll-
qeCKlle orpaHllQeHHR Ha 3HaqeHIDI rronHon rrpoBo,n:llMOCTll. ,[(mI o6eCneQeHHR YCTOi1-
qHBbIX K ollIH6KaM pellIeHHH OTHOllIeHHe HaH6onbllIero 3HaQeHIDI K03<P<PHl(HeHTOB
B3aHMHon CBR3H rn:enei1 K HaHMeHbllIeM)' He .1IOIDKHO 6bITb cnHllIKOM 60nbIIlHM. B3a-
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3J1eMeHT AMnJIHTYJJ;a <l>a3a (rp3)J;.) 3J1eMeHT AMrunrryJJ;a <l>a3a (rp3)J;.)
1 0.300 231. 71 9 1.000 -29.68
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3 0.307 198.35 11 0.431 -123.71
4 0.378 161.79 12 0.337 -132.12
5 0.337 132.12 13 0.378 -161.79
6 0.431 123.71 14 0.307 -198.35
7 0.753 85.44 15 0.242 -211.46
8 1.000 29.68 16 0.300 -231.71

 flla6a 3. CUHme3 iJua2paMM Hanpa6JleHHOCmu IlUHeUHOU aHmeHHOU peUlemlCU
,lJ;JI Toro qTo6bI c,n:eJIaTb HaRJIyqllIHH BbI60p C Toinrn: 3peHH BHyrpeHHero HM-
rre,n:aHca 3JIeMeHTOB, )l(eJIaTeJIbHO paCCqHTaTb 60JIbllIHHCTBO HJIli Bce 2M CJIyqaeB.
ECJIH He Ba)l(Ha <pa30Ba xapaKTepHCTHKa ,lJ;H, TO MO)l(eT 6bITb CHHTe311pOBaHa
,l(l1arpaMMa HarrpaBJIeHHOCTI1 rro MOIUHOCTH; 3TO ,l(aeT ,n:orrOJIHHTeJIbHbIe CTerreHI1
CBo60,l(bl. B 3TOM CJIyqae I1TepaU:I1OHHa rrpou:e,n:ypa rrpI1MeHeTC K KBa;J:paTY aMrr-
JIMTY,l(bI rrp0I13Be,l(eHH KopHeH Ha e,n:MHHqHOH OKp)')KHOCTI1 [9]. ,lJ;pyrOH ,l(OrrOJIHM-
TeJIbHOM B03MO)I(HOCTblO rrOJIyqeHH ,n:eHcTBHTeJIbHOrO pacrrpe,n:eJIeHI1 ,lLJI AP HB-
JIeTC rrorrapHa rpyrrrrl1pOBKa KopHeH [4, 5].
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HlI, Harrpl1Mep, rrOJIO)l(eHH HYJIeH, ypaBHeHHH AP CTaHOBTCH rrepeorrpe,n:eJIeHHbI-
MH. OHH MOryr 6bITb pellIeHbI B qaCTM MHHHMM3ar(HM cpe,n:HeKBa,n:paTHqHOrO 3Ha-
qeHH 3a CqeT crrer(HaJIbHOrO MeTo,n:a ,n:eKOMrr03Hr(HH [6].
3.10. He3KBMAMCT8HTHbie 8HTeHHbie peweTKM
3. 10. 1. CTaTMCTMLleCKMM MeTOA paCLIeTa
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Moryr 6bITb HerrpMeMJIeMbIMM, qTO CBH3aHO co CTOHMOCTblO, BeCOM 11 T.,n:. KpoMe
Toro, B3aMMHoe BJIMHHMe 3JIeMeHTOB MO)l(eT cepbe3HO yxy,n:IlIHTb xapaKTepMCTI1KM
CKaHl1pOBaHMH. IIoCKOJIbKY IlIHpHHa JIyqa rro ypOBHIO rrOJIOBMHHOH MOIUHOCTH
rrpl16JIM311TeJIbHO rrporropr(HOHaJIbHa AIL, ,l(JIHHY aHTeHHOH pellIeTKH L HeJIb3H co-
KpaTMTb, He YBeJIMQI1BaH llII1pMHbI JIyqa. B HeKOTopbIX CJIyqaHx BbI60p pa3Mepa
AP 06YCJIOBJIeH IlIMpMHOH JIyqa, HO He Tpe6yeTc HarrpaBJIeHHOCTb, xapaKTepHaH
,lLJIH 3arrOJIHeHHOH AP. TaKl1M 06pa30M, He3KBH,n:HCTaHTHaH AP MO)l(eT o6ecrre-
qMTb <paKTI1QeCKH TY )l(e llIl1PHHY JIyqa rrpH MeHbllIeM KHL( 11 C MeHbllIMM qHCJIOM
3JIeMeHTOB. KH,lJ; rrpH6JII1311TeJIbHO paBeH KOJIMqeCTBY 3JIeMeHTOB N. 3 <p<peKTbI
B3al1MHOrO BJIMHI1H TaKJKe CYIUeCTBeHHO YMeHbllIalOTCH [2]. Cpe,n:Jiee 3HaQeHHe
SLR (rro MOIIJ;HOCTH) ,lLJIH JII1HeMHOH AP rrporropr(HOHaJIbHO II N (3aBI1CI1T OT aMrr-
JIHTy,n:Horo pacrrpe,n:eJIeHH). IIepHo,n:HQecKoe rrpOpe}KHBaHHe rrOpO)l():(aeT ,n:11<ppaK-
UMOHHbIe JIerreCTKH, HO OHM MOI)'T 6bITb qaCTHQHO rro,n:aBJIeHbI ,l{JIH He3KBI1,n:I1-
CTaHTHoro Me)l(3JIeMeHTHoro llIara. TaK B03HHKaeT rrp06JIeMa BbI60pa MeTo,n:a
orrpe,n:eJIeHM Me)l(3JIeMeHTHoro llIara: paH,n:OMI13HpOBaHHoro (CJIyqaHHoro ) I1JIH
,n:eTepMMHMpOBaHHoro. B 60JIbllIeH QaCTH TeOpeTHQeCKI1X pa60T aBTopbI MCXO,n:I1JII1
H3 HCKOMOH ,n:HarpaMMbI HarrpaBJIeHHOCTH, BbIpa)l(eHHOH B BH,n:e p,l(a <l>YPbe, a
3aTeM pa3pa6aTbIBaJIH pa3JIHQHbIe crroco6bI arrrrpOKCHMar(HH CYMM p.n:OM <l>YPbe.
B pa60Te [57] pa3BHBaeTC rro,l(XO,l( C HCnOJIb30BaHHeM PMa 3KBH,I(HCTaHTHO pac-
rrOJIO)l(eHHbIX AP; B [31] paCCMOTpeHa pellIeTKa C He60JIbllIHMH OTKJIOHeHMHMI1 OT
3KBH,l(HCTaHTHOCTH; B [64] paCKJIa;J:bIBaIOT Bce pellieTOQHbIe qrreHbI B pH,n: rro <PYH-
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paKTepHa o6IIJ;a rrp06JIeMa: ,lLJI pa3JIO)l(eHH )l(eJIaeMOH ,l(HarpaMMbI B pH,l( <l>YPbe
MJIM JII060H ,l(PyroH p,l( Heo6xo,l(HMO nOJIHOe onHcaHHe ,l(HarpaMMbl. ECJIM H3Be-
CTHa TOJIbKO aMrrJII1Ty.n:a, 3a.n:aqa CTaHOBHTC ropa3,n:o Tpy,n:Hee; B H,n:eaJIbHOM CJIY-
qae 3a;J:aHbI H aMrrJIHTy,n:a, M <pa3a. O,l(HaKO <pa3a rrOqTH HHKOr,l(a He 3a.n:aeTCH, a
,l(JIH AP C HI13K11M ypOBHeM 60KOBbIX JIeneCTKOB H Y3K11M JIyqOM He MO)l(eT 6bITb
---

3.10. He3K6UaUCmanmHlJle anmennble peUlemKU 
3a):(aHa ,L{a)l(e aMnnHTY,L{a. 06bIqHO 3aIJ;aeTC5I orw6alOIIlaR 60KOBbIX nenecTKoB, HnH
orH6alOl.I.(aR, HH)I(e KOTOpOH ,L(OJI)l(HbI JIe)l(aTb Bce 6oKoBbIe JIerreCTKH. OrH6alOl.I.(eH
He MO)l(eT 6bITb conOCTaBneH HHKaKOH p5l,L{ <I>YPbe, nOCKonbKY p5l,L{ COOTBeTcTByeT
peaJIbHbIM neneCTKaM. HTaK, MO)I(HO CqHTaTb, qTO aHaJIHTHqeCKaR pa60Ta OKa3a-
naCb MaJIOnOne3HOM.
113BecTeH KOMnblOTepHbIH nO,L(60p Me)l(3neMeHTHoro paCCTORHHR. O,L{HaKO, KaK
nOKa3bIBaeT npOCTOH paCqeT, 3Ta 3a):(aqa qpe3BbIqaHHO TpY,L{Ha. PaCCMOTpl1M AP
npOTR)I(eHHOCTblO B 100 MHH BonH H ,L{OrrYCTHM, qTO paCCTORHHe Me)l(,[(Y 3neMeH-
TaMH MO)l(eT 6bITb KpaTHO OlIHOH BOCbMOH lIJIHHbI BOnHbI. PaCnOJIO)l(HM Ha HeH
40 3JIeMeHTOB, T.e. 3anonHHM Ha 20%. npH rrpRMOM nepe60pe BapHaHTOB HMeeTCR
B 06l.I.(eH CJIO)I(HOCTH
(;000) - 10 70
(3.80)
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nO,L{60pa nbITaJIHCb npHMeHHTb ,L{HHaMHqeCKOe nporpaMMHpOBaHHe, HO OHO OKa3a-
JIOCb HenpHMeHHMO, nOCKonbKY OnTHMaJIbHOe nOJIO)l(eHHe 3neMeHTa 3aBHCHT OT no-
JIO)l(eHHR COCe,L(HHX C HHM 3neMeHTOB. )];pyrHe MeTO,L{bI YCKopeHH5I nO,L{60pa TaIOKe
OKa3aJIHCb HeY,L(OBJIeTBOpHTeJIbHbIMH. AnropHTMbI onTHMH3aQHH, HCnOJIb3yIOl.I.(He
MeTO,L{ conpIDKeHHoro rpa,n:HeHTa, TaKHe KaK <I>JIe]'qepa-TIaY3JIJIa I1JIH ero pa3HO-
BH,lJ;HOCTH (HMelOl.I.(HeCR B 6H6nHoTeKe rrOlI,nporpaMM MR HayqHbIx paCqeTOB B 60JIb-
llIHHCTBe KOMnbIOTepoB), ,L(alOT OnTHMaJIbHO He3KBH,IJ:HCTaHTH)'IO AP C MHHHMaJIbHbIM
ypOBHeM orH6alOl.I.(eH 60KOBbIX JIeneCTKOB npH 3auaHHoH MHHe AP, HO pa60TalOT
qpe3BbIqaHHO Me)])leHHO. EOJIbllIHHCTBO KOMnblOTepHbIX HCCJIelI,OBaHHH He3KBH,IJ:H-
CTaHTHblX pellieTOK npOBO,[(HJIOCb MR He60nbllIHX aHTeHHbIX pellIeTOK [33, 3, 53, 60].
Mcnonb30BaHHe TaKHX perneTOK OrpaHHQHBaeTCR THnOM CTPYKTypbI <pOpMHpyIO-
IUHXCR 60KOBbIX JIeneCTKOB. EOKOBbIe JIeneCTKH BbICOKoro ypOBIDI nORBJIRIOTCR no,[(
u
cnyqaHHbIMli yrJIaMI1, a Me)l(,[(Y HllMH pacnOnO)l(eHbI neneCTKH, BenHqHHa KOTOpbIX
Kone6neTCR B 1lI1ipOKOM ,L(llarra30He. TI03TOMY npll KOMnblOTepHOM npoeKTllpOBaHlili
06bIqHO CTpeM5ITCR 06eCneQHTb BeJIllqHHay Bcex 60KOBbIX JIeneCTKOB HIDKe <pllKCH-
pOBaHHoro 3HaqeHllR. CpaBHeHl1e aJIrOpliTMOB npOBe,UeHO B pa60Te [60].
EOJIbllIOH nporpecc B rrOHHMaHHH rrOBe,L(CHH5I He3KBH,IJ:HCTaHTHblX AP ,UOCTHrHyr
B pa60Te [42]. B HeM npe,UnonaraeTcR, qTO H30TponHblc 3JIeMCHTbI C e,UlfHHqHbIM
B036)')K,[(eHllcM pa3MCl.I.(eHbI CJIyqaHHbIM 06pa30M C 3a,n:aHHoH <PYHlleH nJIOTHOCTli
BepORTHoCTli. OTCIO,Ua rryreM annpOKcllMaQHH aBTOKOppeJUlQllOHHOH <PYHHH npR-
MOyrOJlbHllKOM IIIlIplIHOH 2"-/ L BbIQllCJlIDIaCb BepORTHOCTb no.rryqeHIliI ,L(llarpaMMbI
HanpaBJIeHHOCTH C Y3KHM JIyqOM If ypOBHCM Bcex 60KOBbIX JIeneCTKOB, He npCBbIIIIa-
lOru:eM 3a,n:aHHbIH. O,L(HaKO ,[(JIR Hc60JIbIIIlfX 3HaQeHlfM BCpOHTHOCTH lIJIH ,[(JIR MaJIbIX
AP TOqHOCTb OKa3bIBaCTCR HC,L{OCTaTOqHa. B pa60Te [2], r,L{e lfCCnelI,OBaJIaCb BepORT-
HOCTb nepCCeqeHlIR ,L(HarpaMMoH HanpaBJIeHHOCTli onpe,UeJIeHHOrO ypOBHR 60KOBbIX
JIeneCTKOB, llCnOJIb30BaJICR .n:PyroH MeTO,[(. Oo.rryqaeMoe lfHTerpaJIbHOC ypaBHeHHe
pellIaJIOCb QHCJleHHO n)'TeM pa36HeHH5I llHTCpBaJIa Ha pR,L( KOpOTKlIX cerMeHTOB, rrpH-
qeM BCpORTHOCTb ncpCCeqeHlIR rrpe.n:nOJIaraJIaCb nOCTORHHOH no cerMCHTY. B npe-
.n:eJIe KOHCqHbIH PC3YJIbTaT ,L(aeT npe.n:CTaBllMyIO B aHaJIlITWICCKOM BH,IJ:e BepORT-
HOCTb, KOTopaR ,LLJUI H1I3KllX 1I BbICOKllX 3HaQeHlIH XOpOllIO BbI,Uep)l(lfBaCT cpaBHeHHe
C pe3YJlbTaTaMH MO,L(CJIHpOBaHliR no MCTO,L(Y MOHTe-KapJIo ,[(JIR KOpOTKHX ("'5 ,[(JIHH
BOJIHbI) aHTeHHbIX pcrneTOK. Pe3YJIbTaT, rronyqeHHbIM B [2], Bblpa:>KaeTCR qepe3 ,[(JIH-

 Dlaea 3. CUHme3 auazpllMM Hanpa8JleHHOCmu flUHeUHOU aHmeHHOU pememKU
MY AP L/'A H KOM6HHHpoBaHHbIM napaMeTP a, $IBlliIlOIIJ;HMC$I OTHOIIIeHHeM 'IHCJIa N
3JIeMeHTOB K YPOBHIO MOIIJ;HOCTH 60KOBbIX JIeneCTKOB:
N
a== .
SLR
(3.81)
3,l(eCb SLR 0603HaQaeT OTHOIIIeHHe YPQBH$I MOrn:HOCTH 60KOBbIX JIeneCTKOB. Bblpa-
xeHHe M$I BepO$lTHOCTH ypOBIDI 60KOBbIX JIeneCTKOB HIDKe I/SLR IIMeeT BH,L(
( 2L r;;; J
P = [l-exp(-a)]exp -TV)" exp(-a) .
(3.82)
TaKHM 06pa30M, Tpe60BaHIDI no ypOBHIO 60KOBbIX JIeneCTKOB If KOJIWIeCTBY 3JIe-
MeHTOB 3KBHBaJIeHTHbI. Ha pllC. 3.38 nOKa3aHa 3aBIfCHMOCTb P OT a ,rUUI L/'A == 10,
30, 100, 300, 1000.
1.0
0.9
0.8
0.7
to'I 0.6
E-t
0
0
:I:
E-t 0.5
c::
0

Q,)

0.4
o
o
0.3
0.2
0.1
2
4
6 8
NISLR
10
12
14
PUC. 3.38. BepORTHOCTb ypOBHR SLR, He npeBbIlliaroru:ero 3a,n:aHHoro 3HaqeHlfR no
MOru:HOCTIf
HanpHMep, SLR -- 20 nJ> C 80%-HoM BepO$lTHOCTblO ,l(OCTHraeTC$I npH L == 1000'A
H N == 1028 HJIH npH Cpe,l(HeM MeX3JIeMeHTHOM IIIare, paBHOM O,l(HOll MIIHe BOJIHbI.
,[(lliI 60JIbIIIOrO 3HaQeHIDI N <poPMYJIa MoxeT 6bITb ynporn:eHa [42]:
P == [1 - exp(-a) ]6L/A.
(3.83)

3.10. He3K8UaUCmaHmHble aHmeHHble pelUemKU 
,lJ;JI5I P > 0.5 If L/"A > 100 3TO ,L(aeT L(OCTaTOqHO xopOllIee npH6JIIDKeHHe. Ha
pllC. 3.39 11306pa)l(eHa npM6JII1)1(eHHaSI 3aBlfCI1MOCTb SLR OT L/"A ,lUI5I P = 0.8, 0.09
II 0.99. 3,L(eCb OTJIO)l(eHbI 3HaqeHMSI 10 log N - SLR, H CHOBa 3TH pe3ynbTaTbI
CnpaBe,L(JIMBbI TOJIbKO ,L(JI5I 60JIbllII1X AP. Bce pe3YJIbTaTbI nOJIyqeHbI JUI5I aCHMMeT-
PHqHOH AP. ECJIH pellIeTKa CIfMMeTpMqHa OTHOCI1TeJIbHO ueHTpa, HeKOTopble CTe-
neHH CB060,L(bI TepSIIOTCSI, M 60KOBbIe JIeneCTKH CTaHOB5ITC5I BbIllie.
12
11
9
0.90 _---
--
--
--
--
.---
--
--
-
-
-
--
_-- 0.80
-
--
--
-
10
--
--
--
--
--
p = o. 99 __
--
--
--
--
.n;E
-
,..-
8
-
-
-
--
-
",-
",
7
10
L/A
100
1000
PRC. 3.39. 3HaqeHlfe 10 log N - S LR .1UUI He3KBlf.n:lfCTaHTHbIX AP
ITpl1 I1CnOJIb30BaHI111 KplfBbIX pHC. 3.39 He06xo,L(HMO HMeTb B BHJJY, qTO nony-
qeHHOe N He ,n:OJDKHO npeBbIllIaTb 3HaQeHH5I, COOTBeTCTByJOruero 3anOJIHeHHOH AP
2L/"A; HanpHMep, 3anOJIHeHHa5I perneTKa C L = 100"A HMeeT N = 200 (npH nOJIYBo-
JIHOBOH nepHO,L(lfqHOCTH), qTO ,L(aeT a = 0.44 ,l]JUI SLR = 13.26 ,n:E. 11.3 rpa<t>HKa BH,L(-
HO, qTO Bep05ITHOCTb 6JII13Ka K e,n:HHl1ue, 3TO 03HaqaeT, QTO anepTYpa B 100 "A cno-
c06Ha 06eCneQHTb SLR  13.26 ,L(D 11 BbIllIe. O,L(HaKO JUI5I L = 30 "A, N = 60
3HaqeHI1e a npH ,L(aHHOM SLR COCTaBJI5IeT 2.83, qTO, COrJIaCHO KpI1BOH, ,L(aeT Bepo-
RTHOCTb, 6JIH3KylO K HYJIIO. 3TO 03HaqaeT, QTO npOpe)l(eHHa5I 30 "A anepTYpa, Bepo-
RTHO, 6y,n:eT I1MeTb ypOBeHb 60KOBbIX JIeneCTKOB xyxe, qeM -13 ,n:E. TaKHM 06pa-
30M, npH JII060H BeJII1QI1He anepTypbI cyrueCTByeT TPY,L(HO npeBbIllIaeMbIH ypOBeHb
SLR, Tor,n:a KaK 60JIee JUIHHHble paCKpbIBbI 06eCneQHBalOT JIyqllIHe SLR B03-
MO)KHOCTH.
K npHMepy, ,L(JI5I YPOBH5I Bep05ITHOCTH, paBHoro 80%, 3TH 3HaqeHH5I npHBe,n:e-
HbI B Ta6JI. 3.16. TaKI1M 06pa30M, Ll1I5I ocyrueCTBJIeHH5I 3HaqHTeJIbHOrO pa3pe)l(e-
HH5I npl1 pa3YMHO HH3KOM ypOBHe 60KOBbIX JIeneCTKOB Tpe6YIOTC5I OqeHb 60JIb-
lille aHTeHHbIe pellIeTKM. Ho nOCKOJIbKy ,L(HarpaMMa HanpaBJIeHHOCTH TaKHX
pellieTOK xapaKTepl13yeTC5I 60JIblIIHM QIfCJIOM 60KOBbIX JIeneCTKOB, ,lUI5I CHJIbHOrO
CHIDKeHH5I HanpaBJIeHHOCTIf 11 3<P<t>eKTIfBHoCTH JIyqa no MOruHOCTH JIHllIb He60JIb-
rna5I qaCTb 3THX JIeneCTKOB .n:OJI)I(Ha HaXO,L(HTbC5I Ha YPOBHe orH6alOm;eH. 3Toro
MO)KHO O)l(H,L(aTb, nOCKOJIbKy HanpaBJIeHHOCTb npHMepHO nponOpUHOHaJIbHa KO-
JIHqeCTBY 3JIeMeHTOB.

 FJlaBa 3. CUHme3 iJua2pllMM HanpaBfleHHocmu JlUHeUHOU aHmeHHou peUlemKU
Ta6JIHu,a 3.16. BepxHMM rrpe.aeJI S LR
LjA SLR (.al» LjA SLR (.al»
10 5.7 300 18.2
30 9.6 1000 22.9
100 14.1 3000 27.2
LJ:JI OueHKI1 KOHKpeTHoM CTPYKTypbI pa3pe)l(eHHOM aHTeHHoi1: pellIeTKH ,[(OJI-
)l(HbI 6bITb paCCqHTaHbI ,aHarpaMMbI HanpaBJIeHHOCTI1 no BceM nOJIOce qaCTOT 11
,L(BYMepHoMY .ul1ana30HY CKaHl1pOBaHI1H. HHKpeMeHTbI nOJIO)l(eHI1R JIyqa ,aOJI)l(HbI
6bITb paBHbI npl16JII1311TeJIbHO nOJIOBI1He llIl1pl1HbI JIyqa Ha YPoBHe nOJIOBI1HbI
MOlI(HOCTI1 - KaK no qaCTOTe, TaK 11 no yrJIy. 3TO nOTpe6yeT 06llII1pHbIX Bblql1CJIe-
HI1M, HO rapaHTl1pyeT oTcyrcTBl1e HeO)l(I1.n:aHHO BbICOKHX 60KOBbIX JIeneCTKOB y pe-
rneTKI1.
3<t><t>eKTI1BHOCTb JIyqa no MOIll.HOCTI1 Ba)I(Ha B cl1TyaUI1Hx 113MepeHI1H 11 nepe,aa-
ql1 MOIll.HOCTI1. Cna,aaHl1e Or116aIOIll.eM 60KOBbIX JIeneCTKOB YMeHbrnaeT MOIIJ;HOCTb
60KOBbIX JIeneCTKOB 11 YBeJII1QI1BaeT 3<t><t>eKTI1BHOCTb JIyqa no MOIll.HOCTI1. 3TOT pe-
3YJIbTaT oc06eHHo Ba)l(eH .lIlliI rrJIOCKHX aHTeHHblX pellIeToK, TaK KaK Y HHX MHoro
60KOBbIX JIerreCTKOB pacrrOJIO)l(eHO no,a 60JIbllIHMH yrJIaMH OT HarrpaBJIeHI1R, nep-
neH,aHKYJIHpHOrO pacKpbIBY aHTeHHbI.
Ilpl1Be.ueHHoe BbIllIe paccMoTpeHHe Hero pe3YJIbTaTbI npHMeHHMbI K pa3pe-
)l(eHHbIM AP 1130TponHbIX 3JIeMeHTOB. IlOJIyBOJIHOBble 3JIeMeHTbI I1MeIOT TeH,aeH-
UI1IO K CHIDKeHHIO ypOBHH y,[(aneHHblx 60KOBbIX JIerreCTKOB B OlIHOM nJIOCKOCTH
6JIaro,aapR <t>opMe ,al1arpaMMbI HarrpaBJIeHHOCTM 3JIeMeHTa.
qacTo 6bIBaeT Bblro,aHO I1CnOJIb30BaTb 3JIeMeHTbI C pa3MepaMI1 60JIbllIe rrOJIY-
BOJIHOBOrO; OHI1 ,llOrrOJIHI1TeJIbHO CHIDKalOT ypoBeHb y,llaneHHblx 60KOBbIX JIeneCT-
KOB. B pa60Te [60] nOKa3aHO, QTO BJII1HHl1e HarrpaBJIeHHOCTI1 3JIeMeHTa ,aOJDKHO
YMeHbllIaTb <t>l1rypI1PYIOIl{YIO B ypaBHeHl111 (3.82) 3<t><t>eKTI1BHyro ,lIJII1HY AP. Pe3YJIb-
TaT I1MeeT BI1,[(
L eff L I A
A  W IA'
(3.84 )
OH CnpaBe,llJII1B TOJIbKO L(JIH WI'A < 1/2 113-3a anrrpOKCI1MaUI1M, I1CnOJIb3yeMbIx
npl1 oueHKe I1HTerpana. BJIIDIHl1e HanpaBJIeHHOCTH 3JIeMeHTa paCCMOTpl1M Ha npl1-
Mepe. B03bMeM LI'A = 1000, P = 80% 11 SLR = 15 ,[(E. Tor,aa ,lIJIH He3KBI1,aI1CTaHTHoM
AP 113 1130TponHbIX 3JIeMeHTOB Heo6xo.n:I1MO 325 3JIeMeHTOB. 3a<pI1KCl1pOBaB 3HaQe-
Hl1e SLR 11 KOJII1QeCTBO 3JIeMeHTOB, paCCMOTpl1M 3JIeMeHTbI Tl1na nOJI)'BOJIHOBOrO
,JIl1nOJIH (W/'A = 1/2) 11 2'A rrOlIpellIeTKH. B Ta6JI. 3.17 npl1Be.n:eHbI BepORTHOCTI1 no-
JIyqeHI1R 3HaqeHI1R SLR 15 ,aE 11 BbIllIe. CJIe,aoBaTeJIbHO, KaK M O)I(H,aaJIOCb, Ha-
rrpaBJIeHHbIe 3JIeMeHTbI YMeHbllIaIOT 60KoBble JIeneCTKH.
B MHTepeCHOM MeTo,ae, npeL(JIO)l(eHHOM B pa60Te [34], ,lIJIR paH,llOMI13aUI1M pa3-
MeIll.eHI1H 3JIeMeHTOB B He3KBI11II1CTaHTHblX AP I1CnOJIb3yeTcH <t>paKTanbHaH Teo-
pl1H. TpeX3JIeMeHTHaH no,aperneTKa C peryJIHpHOM nepMo,aI1QHOCTblO 0.8'A RBJIHeTCH
«reHepaTopOM», a <ppaKTaJIbHbIM CJIyqaMHbIH npouecc «<I1HI1Ul1aTop») pa3MeIl{aeT

3.10. He3K8uiJucmaHmHble aHmeHHble peUJemKU 
Ta6JIuaa 3.17. Pa3pe)KeHHaH aHTeHHaH perneTKa C HanpaBJIeHHbIMI1 3JIeMeHTaMH L =
= 1000A-, P = 0.8, SLR = 15 L1:E
W/A P K03«)J«)JUl(HeHT 3anOJIUeHml
M30TponHble 3JIeMeHTbI 0.8 0.163
0.5 0.87 0.163
2 0.97 0.651
rro.n;pellIeTKH Ha nceB,nocnyqaHHbIx rr03HIU ' HIX. B rrpHMepe AP pa3MepoM 360A co
180 3JIeMeHTaMH caMbIH BbICOKHH 60KOBOM JIerreCTOK HMeeT aMrrJIHTY,ny -12.5 ,nE,
HO orH6alOlUaH 60KOBbIX JIerreCTKOB - rrpHMepHO rrOCTOHHHbI:H ypOBeHb B -20 ,nE.
I1 HarrpOTHB, rrpH paBHOMepHOM pacrrOJIO)KeHHH 3JIeMeHTOB LLJIH rrepBoro 60KOBoro
JIeneCTKa 6bIJIO 6bI xapaKTepHO 3HaqeHHe -13.2 ,nE, a ypOBeHb OrJ16alOlUeM rra,naJI
6bI npJ1 YBeJIHqeHHH yrJIa OT HarrpaBJIeHIDI, neprreH,nHKYJIHpHOrO paCKpbIBY aHTeH-
RbI, ,[(0 3HaqeHHH MeHee -60 ,nE rrpH yrJIe 90°, O,[(HaKO llIHpHHa JIyqa 6bIJIa 6bI B qe-
TbIpe pa3a 60JIbllIe 3a CqeT rOpa3,l(0 60JIee KOpOTKOM lUIHHbI AP.
3.10.2. CneManbHoe He3KBMAMCTaHTHoe
pacnOnO>KeHMe 3neMeHTOB
B He3KBH,nHCTaHTHbIX AP J(JIH C03,[(aHH.H 3KBHBaJIeHTHOro OCJIa6JIeHH.H aMIIJIH'fY,[(bI
K KpaHM paCKpbIBa HCrrOJIb3yeTC.H M3MeHeHHe Me)K3JIeMeHTHoro llIara. 3cmaqa 3a-
KJIlOqaeTC.H B nOJIyqeHHM crra,nalOweH orH6alOlUeM 60KOBbIX JIerreCTKOB [67]. KaK
11 y Bcex He3KBH,nMCTaHTHbIX AP, KOJIHqeCTBO 3JIeMeHTOB pellIeTKH ,l(OJDKHO 6J>ITb
60JIbllIMM. 3TO oc06eHHO 3<p<peKTHBHO B CJIyqae aKTHBHbIX AP, r,ne KIDK.LJ:bIM 3JIe-
MeHT MMeeT c06CTBeHHbIW rrpHeMo-nepe,naIOIUHH MO,[(YJIb. He3KBM,[(McTaHTHoe pac-
nOJIO)KeHHe n03BOJIHeT peaJIH30BbIBaTb 60JIee HH3KHW ypOBeHb 60KOBbIX JIerreCTKOB
npll o,nMHaKOBOM B036)')K.lJ:eHHH Bcex 3JIeMeHTOB. O,nHaKo 3KCrrepl1MeHT rrOKa3aJI,
qTO 60KOBble JIerreCTKll He YMeHbllIalOTC.H C TOW CKOpOCTblO, KaKYIO npe,[(CKa3bIBaeT
TeOpll.H. KpOMe Toro, HHor.n:a rrO.HBJIHeTC.H BbICOKllW 60KOBOH JIeneCTOK. MO)KeT rro-
Tpe6oBaTbC.H KoppeKTHpoBKa nepHo,[(HQHOCTI1 HJII1 K03<P<PHUlleHTa 3anOJIHeHHH.
OueHOqHbIe paCQeTbI II03BOlliIIOT onpe,neJII1Tb CTerreHb pa3pe)KeHHH B 3aBHCI1-
MOCTH OT YPOBIUI 60KOBbIX JIeneCTKOB. TIpll 3TOM HCnOJIb3yeTC.H o,nHonapaMeTpllQe-
CKoe pacrrpe,[(eJIeHlle TeRrropa (CM. pa3,neJI 3.3.1).
KOJIHqeCTBO 3JIeMeHTOB no OTHOllIeHHIO K 3arrOJIHeHHOH AP C llIarOM A/2 M
qIICJIOM 3JIeMeHTOB No onpe,neJI.HeTC.H BbIpIDKeHHe!d
N = No 1 Io ( 1t B -JI - p2 ) dp.
I 0 (7tH) 0
(3.85)
HHTerHpOBaillle 3Toro ypaBHeHIDI (c rrOMOIl(blO Q:>oPMYJI 11.4.1011 10.2.13 [1]) ,l(aeT
N = N 0 sinh 1tB .
1tB1o (1tB)
(3.86)

 DW8a 3. CUHme3 aUa2paMM Hanpa8lleHHOCmu llUHeUHOU aHmeHHOU peUJemKU
,lI;aHHble 3HaqeHI1.H npl1BelIeHbl B Ta6JI. 3.18, rlIe YKa3aHa TaIOKe OTHOCI1TeJIbHa.H
1III1pl1Ha JIyqa. ,[J;a)l(e rrpl1 S LR = 40 ,aE CTeneHb pa3pe)l(eHI151 COCTaBJI.HeT MeHbIlle
rrOJIOBI1HbI. TaKHM o6pa30M, XOT.H He3KBI1.lll1CTaHTHOCTb ,aeMCTBI1TeJIbHO rr03BOJI.HeT
'-'
ocym:eCTBI1Tb Mo,aeJIl1pOBaHl1e crra,aalOI.I.J:I1X aMIIJII1TY,aHbIX pacrrpe,aeJIeHI1I1, npou:eHT
C3KOHOMJIeHHbIX 3JIeMeHTOB npl1 3TOM OKa3blBaeTCH He6oJIb1lI11M. B CJIyqae npHMO-
yrOJIbHblX AP KOM611HI1PYlOTCH 3HaqeHIDI .lUIH Ka)l(J]:OM 113 KOOp,aI1HaT.
Ta6JIHua 3.18. JIMHeHHa51 aHTeHHa51 perneTKa co CrreUMaJIbHbIM
He3KBM,lIMCTaHTHbIM pacrrOJIO)l(eHMeM 3JIeMeHTOB
SLR (.a6) NINo 9 3 /0 30
13,26 1 1
15 0.9133 1.042
20 0.7562 1.156
25 0.6647 1.260
30 0.6030 1.355
35 0.5577 1.443
40 0.5223 1.524
3.10.3. AHTeHHble peweTKM
C MMHMManbHOM M36bITO"lHOCTblO
B HeKOTopblX npI1JIO)l(eHMHX, Hanpl1Mep, B anepTYPHOM CI1HTe3e B pa,a110aCTpOHO-
'-'
MMM, MCrrOJIb3yeTcH rrpOCTpaHCTBeHHbl11 cneKTP QaCTOT, 11 Ba)l(HO paCCMOTpeTb npo-
CTeMllIl1e AP, ,IIalOI.I.J:l1e Bce npOCTpaHCTBeHHble qaCTOTbI ,ao BepXHero rrpe,aeJIa. 3TM
pellIeTKH Ha3blBalOTCH pellIeTKaMI1 C MMHI1MaJIbHOM 1136bITOQHOCTblO. M36bITOq-
HOCTb R orrpe,aeJUleTCH [48] KaK
R = N(N -1)
2 L spacings'
(3.87)
r,ae AP I1MeeT N 3JIeMeHTOB M rrpMCYTCTByroT Bce KpaTHble 3HaqeHMH nepMo,al1qHO-
CTI1 < N s . ,[J;JUI OQeHb 60JIbllIMX AP HIDKHMM npe,aeJI M36blTOQHOCTH COCTaBJIHeT 4/3
[10]. Ha pMC. 3.40 CXeMaTMqeCKM 11306pa)l(eH npl1Mep AP, B3HTblM M3 pa60Tbl [48].
Ha pMCYHKe nOKa3aHbl ceMb 3JIeMeHTOB C Me)l(3JIeMeHTHblMM paccToHHMHMH 1, 3,
6, 2, 3, 2. B 3TOM CJIyqae OXBaT npOCTpaHCTBeHHblX qaCTOT ,aOXO,aMT ,ao 17, a 1136bl-
TOqHOCTb COCTaBJUIeT 1.24. HaXO)K,[{eHMe TaKHX pellieTOK .lUIH 60JIbllIMX 3HaQeHMM N
'-' '-'
HBJIHeTCH MHTepeCHOI1 3a,aaqeM TeOpMI1 qMCeJI.
- ..
- -
-
-
..
-
-
-
..
-
..
-
PHC. 3.40. CeMM3JIeMeHTHafI AP c MMHMMaJIbHOH M36bITOQHOCTblO
6J1aro.aapHOCTH
<DoTorpa<pMM JII06e3HO rrpelIOCTaBJIeHbI Ph.D J. B. L. Rao.

JIumepamypa 
JIuTepaTypa
1. Abramowitz, M. and Stegun, L., Handbook of Mathematical Functions, NBS, 1970.
2. Agrawal, V. D. and Lo, Y. T., «Mutual Coupling in Phased Arrays of Randomly Spaced
Antennas», Trans. IEEE, Vol. AP-20, May 1972, pp. 288-295.
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D anepTypbI, LI;eneHHoro Ha ,lLJIHHY BonHbI, rrpH 3TOM MO}KHO Bl1,[{eTb, qTO IIIHpHHa
JIyqa npaKTHQeCKH He 3aBHCHT OT Dj'A, a 3aBHCHT, rnaBHbIM 06pa30M, OT 3HaQeHHSI
SLR. M30nHpOBaHHbIe TOQKH Ha rpa<pHKe 6y.n:yr 06caTbCSI B cne.n:yrolI1eM pa3.n:e-
ne. AMrrnHTYLI;Hoe pacrrpe.n;eneHHe (pacnpe.lIeneHHe Ha nonOBHHe arrepTYPbI) .LLJISI
HeCKOnbKMX 3HaQeHHM SLR rrOKa3aHO Ha pHC 4.4. XapaKTepHbIe 3HaQeHHSI napa-
MeTpOB npHBOLI;SlTCSI B Ta6n. 4.1. 3HaQeHHe KMn anepTypbI llt Haxo.n:HTCSI nyreM
HHTerpHpOBaHHSI pacrrpe,n;eJIeHHSI
1t
2 J g(P)pdp
o
2
llt =
1t
n 2 J g2 (P)pdp
o
4I? (7tH)
n 2 H2 [15 (nH) - If (nH)].
( 4.5)
1.6
OIl = 50
1.5 -
------- 10
-. --- 5
.
 1.4
0.. 10

-- 0
c<
............. 9
 1.3 0
x n=8
ro 0
 1.2 - 7
r=:
ro 0
:z::
::s:: 6
0..
::s:: 1.1 0
a 5
1
0.9 20
25
30 .
35
SRL CaB)
40
45
,50
PHC. 4.3. IIIupMHa JIyqa o.n;HorrapaMeTpMqeCKOrO pacrrpe.n;eJIeHIUI XaHceHa

b DlaBa 4. CUHme3 ouazpflMM Hanpa6JleHHOCmU oBYMepHbIX U ICpY2JlbIX aHmeHHbIX pewemoIC
1
-  ..
..
...........
.... '..
.......
" ....
 .........

" ....
 ........
..
" ....
 "';0'"
" ....
SLR = 40 J(E  .......
"
0.8

co
:s
0-

u
 0.6
o
t::


E--4
:s:
t::: 0.4
t::
::E
..(

..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
....
'" .. ..
..
..
.. ..
.. ..
" ..
0.2 ..
 ... ...
...
... 
.. ..
....

-
°0
0.1
0.9
1
0.2 0.3 0.4 0.5 0.6 0.7 0.8
PaccToHHue no pacKpbIBY: OT ueHTpa K KpalO
Puc. 4.4. OJIHOnapaMeTpHQeCKOe anepTypHoe pacnpe.neJIeHHe XaHceHa
3TO 3HaqeHMe KMn JIerKO CqMTaeTCR H npHBo.nHTCR B Ta6JI. 4.1. B Ta6JIHu:e
npHBe.neHO TaIOKe 3HaqeHHe npOH3Be.neHHR KI111 H HOpMHpoBaHHoH IIlMpHHbI
JIyqa. Pacnpe.neJIeHHe XaHceHa HeCKOJIbKO MeHee 3<p<peKTHBHo no cpaBHeHHIO C
n -napaMeTpHqeCKHM pacnpe.neJIeHHeM TeMJIOpa .LLJIR KpyrJIbIX anepTYP, HO npH
3TOM xapaKTepM3yeTcR 60JIbIIleH paBHOMepHOCTblO H Ha.lleXHOCTblO B pa60Te.
BbIqMCJIeHMe 3<p<peKTHBHoCTH rJIaBHOrO JIyqa 11b, .nOJIH MOIUHOCTH, co.nepxa-
IUeHcR B OCHOBHOM JIyqe, MoxeT nOTpe60BaTb HHTerpHpOBaHHH no 60KOBbIM JIene-
CTKaM, qTO HBJIHeTCH Tpy.noeMKoH 3a,aaqeH. O.nHaKo 3Ta BeJIHqHHa BblpaxaeTCR qe-
pe3 3HaqeHHe KI1TI 11/' JIerKO BblqHCJIHeMOe H3 pacnpe.ueJIeHHH nOJIR no anepTYpe.
BblpaxeHHe ,lJ)IR KI1TI HMeeT BH,l(
1 1t 2 D2 1t / 2 E2 .
- = J 2s1n8d8, (4.6)
111 2').} 0 Eo
Tor.na KaK 3<p<peKTHBHoCTb rJIaBHOrO JIyqa npe.ncTaBHMa B BH,L(e
eN E2
J 2sin8d8
o Eo
11b = 1t/2 . (4.7)
J E2
2 sin8d8
o Eo
3L1eCb eN - yroJI, 3a,aaIOIUMM nOJIOXeHHe HYJIR rJIaBHOrO JIeneCTKa. Tenepb 3<!><!>eK-
TMBHOCTb rJIaBHOrO JIyqa BbIpaxaeTcR qepe3 npOCTOM HHTerpan: no 06JIaCTH rJIaBHO-
ro JIeneCTKa:
2 D 2 eN £ 2
= 1t 111 J - sin8d8.
llb 2').} £2
o 0
( 4.8)

'-, . ": 4.1. j(eYMepHble ICpYi!JIble aHmeHHble pewemlCu 
1
- -
0.98


0

0
:I: 0.96

C\:I
E:
,.Q

u
0 Of). = 50
::c
 0.94
:s::
 ------- 10
(]) --- 5
-&
-e
Ct)
0.92
0.90
20
25
30
SRL (.no)
35
40
PHC. 4.5. 3<t><t>eKTI1BHOCTb rJIaBHOrO JIyqa OD:HOrrapaMeTpI1QeCKOrO pacrrpen:eJIeHI1$1
XaHceHa
Pe3YJIbTaTbI npeCTaBJIeHbI Ha pl1C. 4.5. ,[(JIR l1aMeTpOB anepTypbI B 10 ,lJ)II1H
BOJIH H 60JIee llb npaKTHQeCKH He 3aBHCHT OT D/'A. B CHJIY HH3Koro ypOBHR 60KO-
BbIX JIeneCTKOB npH JII06bIX a311MYTaJIbHbIX yrJIax 3<p<peKTHBHOCTb rJIaBHOrO JIyqa
v
HaMHoro npeBbIlliaeT COOTBeTCTBYIO:w;ee 3HaQeHHe ,lJ)IR JIHHeHHOro pacnpeeJIeHI1R.
4.1.3. AMarpaMMa HanpaBneHHOCTM npM
n -napaMeTpM"IeCKOM pacnpeAeneHMM TeMnopa
AllSi Kpyrnblx anepTYP
,[J;JIR KPyrJIbIX anepTYP n -napaMeTpHqeCKOe pacnpeeJIeHHe TeHJIOpa 06eCneqHBaeT
HeMHoro 60JIbllIee 3HaqeHHe KHIT 6JIarOapR HeCKOJIbKO 60JIee Me,lJ)leHHOMY cna,ay
ypOBHR nepBbIX n 60KOBbIX JIeneCTKOB, QTO B TOqHOCTH aHaJIOrHqHO CJIyqalO JIH-
HeHHoro n -napaMeTpHqeCKOrO pacnpeeJIeHI1R TeHJIOpa. ITpenOJIO)I(HM BHOBb, qTO
pacnpeeJIeHHe nOJIR no anepType CI1MMeTpl1qHO. B KaqeCTBe HCXO,l(HOH 6epeTcR
,l(l1arpaMMa HanpaBJIeHHOCTH 2J 1 ('Jtu)/'Jtu ,lJ)IR paBHOMepHoro pacnpe.n;eJIeHI1R 11 KOp-
peKTHpyeTcR nOJIO)l(eHl1e n HYJIeM C Ka)l(,I(OH CTOpOHbI rJIaBHOrO JIeneCTKa ,lJ)IR o6ec-
rreQeHI1R npMMepHO paBHbIX YPoBHeM 60KOBbIX JIeneCTKOB npl1 3a,aaHHOM ypOBHe
SLR. EOJIee OTaJIeHHble HYJII1 COOTBeTCTBYIOT HarpaMMe HanpaBJleHHOCTI1 paBHO-
MepHoro pacnpe,l(eJIeHJilR. KaK 11 paHee, K03<P<l>MUJileHT Y,l(JIJilHeHJilR a Onl1CbIBaeT
nepeXO,l(HyIO 06JIaCTb Me)l(,I(Y n HYJIRMI1 II rpaHJilqa:W;JilMJiI C HJilMI1 HYJIRMJiI. 3HaQeHMe
SLR CBR3aHO C OCHOBHbIM napaMeTpOM A:
SLR = cosh A.
( 4.9)

'  rAa6a 4. CUHme3 iJuazpt1MM Hanpa6AeHHocmu iJ6)lMepHbIX U KPY2llbIX aHmeHHbIX pewemOK
,il;HarpaMMa HanpaBJIeHHOCTH n -napaMeTpHQeCKOrO pacnpe.aeJIeHHH TeRJIopa
.ruUI KpyrJIbIX anepTYP HMeeT BH,l( (Taylor, 1960)
u 2
- I 1- 2
F(u) = 21 1 (1tu) fi u; .
1tU n=1 1 _ 
Jl
(4.10)
TIOJIO)l(eHHH HOBbIX HYJIeR ,l(aIOTCH BbIpa)l(eHHeM
Un = + a  A2 +(n-  J,
(4.11 )
a K03<P<PHIJ;HeHT Y.lUIHHeHHH paBeH
a = A2 +(: -tJ ·
(4.12)
3HaqeHHH f.1 n npe.aCTaBJIHIOT C060H KOpHH <PYHKI.J;HH J I (3tu). THnHqHaH n -napa-
MeTpHqeCKaH .aHarpaMMa HanpaBJIeHHOCTH nOKa3aHa Ha pHC. 4.6. llIHpHHa JIyqa
paBHa llIHpHHe U3 JIyqa H,l(eaJIbHOrO JIHHeHHOro HCTOqHHKa, YMHO)l(eHHOR Ha K03c1>-
<pHlI.HeHT o. B Ta6JI. 4.2 npHBelleHbI 3HaqeHHH napaMeTpa A, nOJIynIHpHHbI u3 JIyqa
H a MH pa3JIHqHbIX 3HaqeHHR SLR H n . B pa60Te [9] npHBO,l(HTCH Ta6JIHUbI MH
anepTYpHoro pacnpe.aeJIeHHH.
o
-10
--

I::[
---
CI:S
t::!
 -20
::s::
a

-30
-40
-10
-8
-6
-4
-2 0 2
U = kD sin 8
4
6
8
10
PHC. 4.6. )];HarpaMMa HanpaBJIeHHOCTH npH n - napaMeTpHqeCKOM pacnpe.neJIeHHIf
TeHJIOpa .nJUI KpyrJIbIX anepTYP, SLR = 25 .n6, n = 5
II...-

4.1. J{eyMepHble KpY2/1ble aHmeHHble pewemKU 
Ta6JJHua 4.2. XapaKTepHCTHKI1 ,D;HarpaMMbI HarrpaBJIeHHOCTH rrpH n - rrapaMe1'pHIJe-
CKOM pacnpe.neJIeHHH T eHJIOpa ,U)UI KpyrJIbIX anepTYP
SLR cr
A "3
(.z.6)
n =3 n =4 n =5 n =6 n =7 n =8 n =9 n = 10
20 0.9528 0.4465 1.2104 1.1692 1.1398 1.1186 1.1028 1.0906 1.0810 1.0732
25 1.1366 0.4890 1.1792 1.1525 1.1296 1.1118 1.0979 1..0870 1.0782 1.0708
30 1.3200 0.5284 1.1455 1.1338 1.1180 1.1039 1.0923 1.0827 1.0749 1.0683
35 1. 5032 0.5653 1.1134 1.1050 1. 09 51 1.0859 1.0779 1.0711 1.0653
40 1.6865 0.6000 1. 0916 1. 091 0 1.0854 1.0789 1.0726 1.0670 1.0620
45 1.8697 0.6327 1.0759 1.0748 1.0711 1.0667 1.0624 1.0583
50 2.0530 0.6639 1.0636 1.0628 1.0604 1.0573 1.0542
AnepTYPHoe pacnpe,n;eJIeHMe npMHMMaeT BM,n; [22]
g(P) = 2- I F<o(1tpl1n) .
n 2 n=O J 0 (7tJ.l n)
( 4.13)
OTMeTMM, qTO ,lUIH n - napaMeTpMqeCKOrO pacnpe,n;eJIeHMR TeMJIOpa ,l(JIR KpyrJIbIX
anepTYP paaMaJIbHaR nepeMeHHaR p = 23tp/ D. K03<P<PMUMeHTbI Pm MMelOT BM,n;
n-l ( 2 J
I1 1 - J.lm
n=l u
Pm = -JO(nJ.lm) - ( J
n-l 2
I1 1 - 11;
n=l J.l n
n=t;m
m>O
( 4.14)
Fo = 1.
TMnMqHbIe anepTypHbIe pacnpe,n;eJIeHMR (,l(JIR nOJIOBMHbI paCKpbIBa) IIOKa3aHbI
Ha pMC. 4.7 M 4.8. CJIMlliKOM BbICOKoe 3HaqeHHe n npMBo,n;MT K HeycTOMqMBOCTIf
MHTepBaJIOB Me)l(,l(Y HYJIRMH, qTO npORBJIReTCR B HeMOHOTOHHOCTM pacnpe,n;eJIeHMR.
nOCKOJIbKY 60JIee BbICOKMe 3HaqeHMR n ,n;alOT 60JIbllIee 3HaqeHMe KI1TI, TOqHO
onpe,n;eJIeHHOe ,l(JIR 60JIbllIMX anepTYP M IIOCTORHHOH <!>a3bI, ,lUIR Ka)l(,l(OrO 3HaqeHMR
SLR HMeeTCR OIITMMaJIbHOe, HaM60JIee BbIro,n;Hoe 3HaqeHHe n .
KI1TI onpe,n;eJIReTCR BbIpa)l(eHHeM
2
1t
2 f g(P)pdp
o
( 4.15)
111 =
1t
f g2 (P)pdp
o

b
rllaea 4. CUHme3 ouazpOM.M Hanpa61leHHOCmu oeYMepHblx U KPY2JlblX aHmeHHblX pewemOK
1
..
"=6
0.8

CQ
:a
0..

u 0.6

0..
0
t:

 0.4
::s:
t=;
t:

I'
/
/
....
..-
5
----
SLR = 25 .afi
.... '-. ... 
...
4
0.2
o
o
0.2 0.4 0.6 0.8
PaCCTOHl1.e no pacKpbIBY: OT ueHTpa K KpalO
1
PHC. 4.7. n - napaMeTpHqeCKOe pacnpe.neJIeHMe T eMJIOpa ,L(JISI KpyrJIblX anepTYP
(SLR = 25 .nE)
1
0.8

CQ
::is
0..

 0.6
0.
o
t:


f-o
::s: 0.4

t::

:-..
n =B
------- 10
12
- - - --
0.2
SLR = 40 n:E
0 0
0.2 0.4 0.6 0.8
PaccToSlHHe no pacKpbIBY: OT ueHTpa K KpalO
1
Pac. 4.8. n -napaMeTpMqeCKOe pacnpe.neJIeHHe TeMJIOpa lUISI KpyrJIbIX anepTYP
(SLR = 40 .(6)
.......-.

..
4.1. )l,8)'MepHble KpYi!JIble aHmeHHble peUlemKU 
B BbIllIenpHBeeHHoH Q>opMYJIe ,lJ,JISi g(P) qJIeHbI B qHCJIHTeJIe npH m > 0 coep-
)KaT MHO)l(}lTeJIH J O (3tJ..l m ), He paBHble HYJIIO TOJIbKO AJI5I m = O. I1HTerpHpoBaHMe
npOH3Be.aeHMH .n;BYX pSl.n;OB B 3HaMeHaTeJIe aeT HHTerpaJI ,L{BYX opTOrOHaJIbHbIX
<l>YHKUHH fieCCeJIH, n03TOMY OCTaeTCSI TOJIbKO O,L{HH pSl.n;:
1 ii-I £.2
-=I+L n
11t n=l 15 (1tJ..ln)
(4.16)
B Ta6JI. 4.3 npHBe,aeHbI 3HaqeHHSI 3<l><l>eKTHBHoCTH B036y)K)];eHHSI AJISI pSI.D:a 3Ha-
qeHH:H SLR H n , B3S1Tble M3 pa60TbI [21]. 3<l><l>eKTHBHOCTb rJIaBHOrO JIyqa BHOBb Ha-
XO.n;HTCSI II)'TeM HHTerpHpOBaHHSI IIO fJIaBHOMY JIeneCTK)'. 3aBHcHMoCTb 3<l><l>eKTHB-
HOCTH fJIaBHOfO JIyqa OT 3HaQeHHSI SLR rrpe,L{CTaBJIeHa B Ta6JI. 4.4.
Ta6JIHQa 4.3. 3HaqeHI1H Kl1n rrpl1 n -ilapaMeTPI1QeCKOM paCIIpe.neJIeHI1I1 TeiiJIopa
,[(JIH KpyrJIbIX anepTYP [21]
SLR (AI» n =4 n =5 n =6 n =8 n = 10
20 0.9723 0.9356 0.8808 0.7506 0.6238
25 0.9324 0.9404 0.9379 0.9064 0.8526
30 0.8482 0.8623 0.8735 0.8838 0.8804
35 0.7708 0.7779 0.7880 0.8048 0.8153
40 0.7056 0.7063 0.7119 0.7252 0.7365
45 0.6484 0.6494 0.6575 0.6663
50 0.5986 0.6016 0.6076
Ta6J1Hua 4.4. 3<l><l>eKTHBHoCTb rJIaBHOrO
JIyqa IIPH n-rrapaMeTPHQeCKOM pacrrpe-
,n;eJIeHHH TeMJIOpa ,lUIH KpyrJIbIX arrepTYP
SLR (,n;6) n lib
20 4 0.8271
25 5 0.9142
30 6 0.9621
35 7 0.9844
40 8 0.9938
45 9 0.9976
50 . 10 0.9991

 Dla6a 4. CUHme3 ouazpaMM Hanpa6AeHHocmu o6YMepHblX U KPY2JlblX aHmeHHblX pewemOK
4. 1 .4. Pa3HocTHaR AMarpaMMa HanpaBneHHocTM npM
pacnpeAeneHMM &eMnMcca AJ1R Kpyrnblx anepTYP
fiepe,a 06cY2K,LI,eHI1eM pa3HocTHOH ,al1arpaMMbI HanpaBJIeHHOCTIi pacnpe,aeJIeHHSI
EeHJIHCCa C napaMeTpOM n nOJIe3HO paCCMOTpeTb KpyrJIYID anepTYPY pa,aHyca a
C paBHOMepHbIM pacnpe,aeJIeHHeM, B036}')K,IJ:eHHH ,aBYX nOJIOBHH KOTOpOH no «p a3 e
pa3JIHQaIDTCH Ha :Tt. I1HTerpaJI n:HarpaMMbI HanpaBJIeHHOCTH no <t> CBO,aI1TCSI K
cos <t>Ho(kp sin e cos <t», (4.17)
r,ae Ho - «PYHKIJ:J1R CTPYBe HYJIeBOrO IIOPMKa [11]. Pa3HocTHaH ,al1arpaMMa Ha-
rrpaBJleHHOCTH B nJIOCKOCTI1 <t> = 0 onpe,aeJIReTCR BbIpa)l(eHl1eM
a
F(8,<t» = cos<t>J Ho(kpsin8cos<t»pdp.
o
KaK rrOKa3bIBaeT pl1C. 4.9, <PYHKIJ:HR CTPYBe HMeeT 60JIbIIIOe CXO,aCTBO C J}
«PYHKUl1eH EeCCeJIR, XOTR ,nmI 60JIee BbICOKHX nopH,aKOB Cxo,aCTBa He Ha6JIID,aaeTCSI.
Ha pHC. 4.10 H306pa)l(eHa ,aHarpaMMa HanpaBJIeHHOCTH, nOJIyqeHHaR C nOMOIUblO
qHCJIeHHOrO HHTerpHpOBaHHH, npH 3TOM ee aMrrJlI1TY,aa HOpMl1pyeTcR TaK, QT06bI
cooTBeTcTBYIDIUHH nHK cYMMapHoH ,lJ;l1arpaMMbI 6bIJ1 paBeH e,allHl1ue. nHKH pa3HO-
CTHOH ,aHarpaMMbI pacnOJIO)l(eHbI B TOqKaX Uo = + 2.653, H HX ypOBeHb COCTaBJIReT
-3.19,aE. nepBbIe 6oKoBble J1erreCTKM pacrrOJlO)l(eHbI rrpH U = + 9.775 H HMelOT ypo-
BeHb -14.90 ,aE, MJlH Ha 11.72 ,afi MeHbIIIe rrHKOB pa3HocTHOH ,aHarpaMMbI.
Pa3HocTHaH ,aHarpaMMa HarrpaBJ1eHHOCTH EeUJIMCCa )])IH J1HHeHHOro HCTOqHHKa
H3J1yqeHHH o6C}')K,IJ:aJIaCb B pa3,aeJIe 3.7.2. B pa60Te [3] paCCMOTpeHa aHaJIOrHQHaR
pa3HOCTHaR ,n:HarpaMMa HarrpaBJleHHOCTH npH n - rrapaMeTpHqeCKOM pacnpe,n:eJIeHHH
)])IH KpyrJlOH anepTYPbI. I1cxollHaH llHarpaMMa lIBJIReTCH npoH3Bo,n:HOH «PYHKUHeH
( 4.18)
1
0.8 ,'..
..
,
\ Ho(x)
0.6 ,
\
\
,
,
 .
\
I:Q 0.4 ,
:is ,
,
 \
. , ,
 , ..
, , ..
(,) . , ,
0.2 , , ,
 . , ,
 , . \
, . \
. \
0 . , \
, . ,
t:: \ , ,
0 \ . ,
 , . \
, . ...
 , . \
\ ..
, ,
.. .
::s:: -0.2 ..
..
t:::
t::
 -0.4
-0.6
-0.8
-1
0 2 4 6 8 10 12 14 16 18 20
X
PHC. 4.9. <1>YHKUliH J} EeCCeJIH Ii <PYHKUIUI Ho CTPYBe
......-

" ' ," .' 4.1. J(f/YMepHble K.PYVlble aHmeHHble peUJemK.U  '
o

.
:.:;  ;" 
,..
-10
..-.

t:::(
-
-30
C'd
t:::(
 -20
:s:
t:::::
t::

-40
-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90
YroJI (rpau.)
Pac. 4.10. Pa3HocTHaH ,n;HarpaMMa HarrpaBJIeHHOCTH KpyrJIOH arrepTypbI C paBHO-
MepHbIM pacrrpe,n;eJIeHl1eM, D = 20A
OT «H,LJ;eaJIbHOH» CYMMapHOH J(HarpaMMbI TeHJIOpa cos(1t .J u 2 - A2), nOCKOJIbKY ,lUUI
v
paBHoMepHoro pacnpeJ(eJIeHHR nOJIR no KpyrJIOH anepTYpe npHMeHHMoro BapHaHTa
pa3HocTHOH lIHarpaMMbI He CYIl(eCTByeT. npOM3Bo,n:HaR C oT6porneHHbIMM K03<P<PM-
U;MeHTaMH HMeeT BHJ( __
!ideal (U) = U sin(1t .J u 2 - A2 ).
( 4.19)
Pa3HOCTHaR J(HarpaMMa C napaMel'pOM n nonyqaeTcR npH 3aMeHe n HYJIeH HJ(e-
v
aJIbHOH J(HarpaMMbI CMeIl(eHHbIMH HYJIRMH Zn:
n Z - U 2
f(u) = !ideal (U) n 2 2 . (4.20)
n= 1 J.l n - U
HOBbIMH HYJIRMH RBlliIlOTCR Zn; OHH 3aMeIl(alOT HYJIH Jl n :H.IJ:eaJIbHOH ,n:HarpaMMbI.
npOCTpaHCTBeHHbIH MHO)KlfTeJIb (J(HarpaMMa HanpaBJIeHHOCTH) MO)l(eT 6bITb 3anM-
caH B <popMe npOH3BeJ(eHHR KopHeBbIX COMHO)KlfTeJIeH:
n-I ( U 2 ) 00 ( U2 )
f(u)=ucos4>n 1- 2 n 1- 2 ,
n=l 0'2 Zn n=n J.ln
(4.21 )
nOCKOJIbKY KOpHRMH BToporo npOM3Be,n:eHMR RBJIRIOTCR KOpHH <PYHKQMM
J{(1tJln), 3TO npOH3BeJ(eHHe MO)l(eT 6bITb J(onOJIHeHO OTC)'TCTBYIOIl(HMH KopHeBbI-
MM COMHO)l(MTeJIRMH H 3aMeHeHO <PYHKQMeH J{(1tU), M B pe3YJIbTaTe nOJIyqaeM
n-I ( 2 )
n 1- U
, n-I 0'2 Z
f(u) = U cos4> J I (1tU) -=- ( ) .
n-I 2
n 1-;-
n=1 J.l n
nm
( 4.22)

b DW6a 4. CUHme3 auazpllMM Hanpa61leHHOCmu a6YMepHbIX u "PYi!IIbIX aHmeHHbIX peUiemOK
AnbTepHaTI1BHbIM Bapl1aHTOM CYMMl1pOBaHI1R no n J1eHaM SlBlliIeTCR CJ1eL(ylOIIJ:I1H:
n -1 B J ( 1t 11 )
feu) = u cos<t> J 1 (1tu) L n 2 1 r n . (4.23)
n=O fln - u 2
Y nOJ1yqeHHo H pa3HO CTHOH l1arpaMMbI HYJIM npl1 n > n onpe.n:eJIRIOTCR BbIpa-
)l(eHl1eM Zn = +,J A 2 + n 2. n OCKOJ1bKY l1.n:eaJ1bHaH pa3HOCTHaR .n:MarpaMMa I1MeJIa
HeperyJ1HpHbIH ypOBeHb 6J1IDKaHlllI1X 60KOBbIX J1erreCTKOB, B [3] CKoppeKTMpOBaHbI
3TI1 n HYJ1H H nOJ1yqeHa MOHOTOHHaR orM6alOllJ,aR 60KOBbIX J1eneCTKOB. 3TO .n:eJ1a-
....
JIOCb ':Il1CJIeHHbIM nYTeM C annpOKCHMaUMeH COOTBeTCTBYIOll.(I1MH nOJ1HHOMaMI1 ':IeT-
BepToro nopMKa. fIo,n:6I1paJ1HCb TaIOKe napaMeTp A 11 n0J10)l(eHHe fIHKa pa3HO-
CTHOH ,n:HarpaMMbI. 3TH napaMeTpbI Te )l(e, ':ITO 11 )];JIR JIHHeHHOH ,n:HarpaMMbI
HanpaBJ1eHHOCTH OeH.rrHCCa, H npI1BO)];RTCR B Ta6JI. 3.11. fIOJII1HOMI1aJ1bHbIe K03<P-
cPHlll1eHTbI npHBe.n:eHbI B Ta6JI. 3.12. Ha pMC. 4.11 M306pa)l(eHa ,n:HarpaMMa HanpaB-
JIeHHOCTH OeHJIHCa MR KpyrJIbIX anepTYP MR SLR = 25 ,n:o 11 n = 5.
AnepTYPHOe pacnpe,n:eJIeHHe Haxo,n:HTC5I C nOMOlI(blO PMa no <PYHKUJUIM oecceIDI:
n-l
g(P) = cos<t> L BnJo(J.!nP), (4.24)
n=O
r.n:e p = np, a p - paaHYC anepTYpbI, M3MeIDIIOIlJ:IfHCH OT HYIDI ,n:o e)];I1HI1UbI. K03cP-
<pHllHeHTbI Bn HMelOT BM)];
2 i1( 1- 2)
B m ( ) m = 0 , 1 , 2 ' ... ' n = 1
= n=ln_l cr z
Jl(1tm)n 1- ; (4.25)
n=O Jl n
n=l:-m
Bo =0
m > n .
o
-10
.-

1::1
'-"
ro

Eo-< - 20
:s:
J:::::


-30
-40
-10 -8 -6 -4 -2 0 2 4 6 8 10
u == (D/)') sin 6
PHC. 4.11. ,lll1arpaMMa HarrpaBJIeHHOCTM npH pacnpe.aeJIeHI1I1 EeHJIlICCa .aJIR KpyrJIOH
arrepTypbI, SLR = 25 .aE, n = 5
-

4.1. ,l(6YMepHble KpY2/lble aHmeHHble peUlemKU 
K03<l>cl>HUHeHT YMHHeHHR a 3a,rt;aeTCR BbIpa)l(eHHeM
(j = Jln . (4.26)
 A2 + n 2
Ha pHC. 4.12 nOKa3aHO anepTypHoe pacnpe.aeJIeHHe MR CJIyqaR, 11306pa)l(eHHOrO
Ha pl1C. 4.10. KaK H O)f(H)J;aJIOCb, 66JIblUHe 3HaqeHHR n rrpH 3a,rt;aHHOM SLR rrpI1BO,lUIT
K pocTY aMrrJIHTY.abI Ha KpalO pacKpbIBa, KOTopaR MO)l(eT rrpeBbIlUaTb aMnJII1TY.ay B
ueHTpe. Ha pHC. 4.13 H306pIDKeH KBa,rt;paHT .aB}'MepHoro (2D) pacrrpe.aeJIeHI1R.
1
0.8
-
 0.6

--


E-<
:s:
a 0.4

0.2
1
-0.8 -0.6
-0.4 -0.2 0 0.2 0.4
Pa,aMaJIbHall KOOp,lJ;lIHaTa
0.6
0.8
1
PHC. 4.12. Pacrrpe,n:eJIeHHe EeHJIHCCa ,ruUI KpyrJIOH arreprypbI, SLR = 25 ,n:E, n = 5
........
........
........
........
........
X
PHC. 4.13. KpyroBoe pacrrpe,n:eJIeHHe EeRrrHCa, SLR = 35 dB, n = 10

 Dzaea 4. Cunme3 ouazpaMM nanpaeJlennocmu oeYMepnbIX u KPY2JlbIX anmennbIX pewemOK
KI1Il onpe,LJ;eJIReTCR KaK KH,L( B IIHKe pa3HocTHOM ,n;HarpaMMbI, ,LJ;eJIeHHbIH Ha
KH,[( .lUISI CYMMapHOH ,LJ;HarpaMMbI npM paBHoMepHoM anepTypHoM pacnpe,n;eJIeHHH.
B CMJIY opTOrOHaJIbHOCTM qJIeHOB anepTypHoro pSl,lJ,a I1HTerpaJI KHJJ. JIerKO oueHM-
BaeTcH, qTO ,LJ;aeT
1 1t 4 n-I ( 1 J
-=- LI B nl 2 1- 2 2 J(1tfln)'
11t 8 n=O 1t fln
( 4.27)
BTOPOH BIDKHbIH rrapaMeTp - KpyrH3Ha ,LJ;HarpaMMbI - 3,lJ,eCb HOpMMpOBaH K
MaKCHMaJIbHOMY 3HaqeHHIO. 3Ta HCXO,LJ;HaH ,lJ,HarpaMMa HarrpaBJIeHHOCTH orrHCbIBa-
eTCSI <PYHKUHeH J 2 (nu)/nu, H ee KpyrH3Ha COCTaBJISleT (0,5/1t) .JG o , r,lJ,e Go - KH,L{
.lUIH CyMMapHOH ,LJ;HarpaMMbi. ,[(JIR ,LJ;MarpaMMbI EeHJII1CCa HOpMHpOBaHHaH KpyrH3Ha
COCTaBJIReT
S = L  Bn!) (1tfln)
V 11t  2 .
n=O fl n
( 4.28)
3HaqeHHH KI1Il H KpyrH3HbI ,LJ;MarpaMMbI ,lLJISI THnHqHbIX COqeTaHHH SLR M n
rrpMBe,LJ;eHbI B Ta6JI. 4.5.
Ta6J1Hu.a 4.5. Kl1n H KpYTH3Ha lUiarpaMMbI HanpaBneHHOCTH npM KpyroBoM pac-
npeeneHHH EeHnMcca
SLR (AI) n 1]t FlOpMHpOBaHHaB KpYTH3Ha
25 5 0.4931 0.8754
30 6 0.4593 0.8156
35 8 0.4285 0.7638
40 10 0.3988 0.7144
45 12 0.3717 0.6691
,
50 14 0.3475 0.6286
4.1.5. OnTMMM3aMSI pa3HocTHOM
AMarpaMMbl HanpaBneHHocTM
B rJI. 3 06Cyx.L{aJIOCb HCnOJIb30BaHMe nO,LJ;perneTOK, KaaR 113 KOTOpbIX MO)KeT
3anMTbIBaTbCSI C pa3JIHQHoi1: aMnJIMTy.nOM (M <pa3oi1:) ,LJ;JIH nOJIyqeHMSI CYMMapHoi1:
H pa3HOCTHOH ,LJ;HarpaMM HanpaBJIeHHOCTM JIMHeMHbIX AP. B pa60Te [14] TOT )Ke
nO,LJ;XO,LJ; 6bIJI npHMeHeH K KpyrJIbIM nJIOCKMM aHTeHHbIM perneTKaM. AHTeHHaSl pe-
meTKa pa3,aeJIHeTCH Ha no,apemeTKH C 90° cMMMeTpMeH. <l>opMa rro,aperneTOK H KO-
JIMqeCTBO 3JIeMeHTOB B HHX 06bIQHO pa3JIMQaIOTCR;. CM. pMC 4.14. 3aTeM CMMMeT-
pMQHbIe napbI rro,apemeTOK no,aKJIlOqalOTCSI K rM6pl1lIHbIM cxeMaM; 3TH cxeMbI
rrO,LJ;KJIIOQeHbI K u;errHM CYMMaTopOB, p6eCneQMBalOIIJ:HX CYMMapHYIO 11 ,LJ;Be pa3HOC-
THbIX ,LJ;HarpaMMbI HanpaBJIeHHOCTH (CM. pHC. 4.15). KaK H B CJIyqae JIHHeHHOH AP,
ill...-....

4.1. J(8JlMepnble K.pYZIlbie anmennble peUJemK.u 
0 0 0 0
0 0 0 0 0 0 0 0
11
0 0 0 0 0 0 0 0 0 0
8 7
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
2 1
0 0 0 0 0 0 0 0 0 0 0 0
6 5
0 0 0 0 0 0 0 0 0 0 0 0
4 3
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
10 9
0 0 0 0 0 0 0 0 0 0
12
0 0 0 0 0 0 0 0
0 0 0 0
PHC. 4.14. CxeMa no.n;perneTOK nJIOCKOH AP
1 2
3 4
7 8
9 10
5 6
11 12
6 t
HepaBHOMepHbIH
cYMMaTop ·
6
.x
HepaBHOMepHbIH
cYMMaTop
HepaBHOMepHbIH
c}'MMaTOp
6
y
PHC. 4.15. CxeMa nHTaHHH, o6eCneQHBalOlUaH CYMMapHYIO H pa3HOCTHyIO .n;HarpaMMbI
HanpaBJIeHHOCTH
2

 DW6a 4. CUHme3 aUa2paMM Hanpa611eHHocmu a6YMepHblX U KPYi!IlblX aHmeHHblX peUlemOK
DJI5I nOJIyqeHI151 Tpex pacnpe,UeJIeHMi1, cooTBeTcTBYIOI.I.J:MX Tpe6yeMbIM ,Ul1arpaMMaM
HanpaBJIeHHOCTH, I1CnOJIb3yeTcSI cTyneHqaTa51 annpOKCI1Mau.I151. n peBOCxOL(HbIe pe-
3YJIbTaTbI nOJIyqalOTcH Y)I(e C He60JIblIII1M QI1CJIOM nO,LJ,perneTOK Ha KBa,LJ,paHT. 3Ta
KOH<pl1rypaUI1H oc06eHHo nepCneKTI1BHa B cJIae neqaTHbIX aHTeHH, nOCKOJIbKY
TaKoe o<popMJIeHl1e eCTeCTBeHHhIM 06pa30M nOL(XOL(MT ,UJI5I peaJII13aUMM C nOMOI.UhlO
v
nOJIOCKOBbIX JII1HI1I1.
4.2. ABYMepHble anePTYpbl, OTnM"IHble OT Kpyrnblx
4.2.1. OnTM3aL-'S1 AarpaMMbl
HanpaBneHHocT ASYMepHblx peweToK
ECJIM aHTeHHa51 perneTKa HMeeT anepTYPY, OTJIMQHYIO OT KPyrJIOM, MJIM pacnpeL(e-
JIeHI151 no x 1'1 y He pa3,lJ;eJIHIOTC5I, He06xoL(MMO 06paI.I.J:aThC5I K qMCJIeHHbIM MeTO-
L(aM, TaKMM KaK YCJIOBHa51 onTMMM3aIU151. K CO)l(aJIeHMIO, OTHOCMTeJIbHO rrpOCTOH
MeTOL{ (L{MHaMI1QeCKOe rrporpaMMMpOBaHl1e) HenpMMeHI1M, rrOCKOJIbKY OR Tpe6yeT
He3aBMCMMOCTI1 BML(a M3MeH5IeMOM <PYHKllJIM OT npOM3BOL(MMhIX I13MeHeHI1M. Ho
KOppeKUI151 o.aHoro HYJI5I MJIM OL(HOrO K03<P<PllllJleHTa B036)')K.lJ.eHM5I JII060M AP
OKa3bIBaeT BJII151HlIe Ha BCIO L(l1arpaMMY HarrpaBJIeHHOCTM. 3.aeCb npMrO,UHbI TaKMe
nporpaMMbI onTMMM3aUMM, KaK MeTOn; COrrp5l)l(eHHOrO rpaL(MeHTa, npM YCJlOBI1M,
lITO MO)l(eT 6hITb XOpOlliO onpe,lJ;eJIeH KpMTepMH BbI60pa, HO OHI1 pa60TalOT Me,n;-
JleHHO. nOCKOJIbKY nOJIO)l(eHM5I 60KOBhIX JIerreCTKOB He nOMaIOTC5I oueHKe Ha
paHHMX CTa,LJ,I151X, MaKCMMM3aI.{I1R KH npH YCJIOBHH, qTO ypOBeHh Bcex 60KOBbIX
JIeneCTKOB JIe)l(l1T HH)I(e 3a,n,aHHOM Orl16alOmeM, Tpyn;HO ocymecTBI1Ma. 111'160 L(OJI-
)l(Ha HCnOJIb30BaTbCH nporpaMMa HaXO)l()J,eHI1JI rrOJIO)l(eHMH 60KOBbIX JIeneCTKOB,
onpen;eJIRlOma5I Bce ,LJ,O e,lJ;MHOrO nHKM 60KOBbIX JIeneCTKOB JJ:JIH Bcex OI.{eHI1BaeMbIX
<PYHKIJ.I1H (,lJ,MarpaMM HarrpaBJIeHHOCTI1), JIM60 ,n;HCKpeTM3aUHH Bcex L(MarpaMM Ha-
npaBJIeHHOCTI1 ,n;OJI)I(Ha 6hITh n;OCTaTOqHO qaCTOH, QT06bI TOQHO onpeLJ:eJII1Tb nOJ1O-
)l(eHMe Bcex rrHKOB 60KOBbIX JIeneCTKOB. AnrOpl1TMbI nOMCKa 60KOBbIX JIeneCTKOB
XOpOIIJO pa6oTalOT TOJIbKO C KJIaCCMqeCKHMH ,nHarpaMMaMH, MMelOmMMM-HpKO Bbl-
pa)l(eHHble 6oKoBble JIeneCTKH C peryJIHpHblM pacrrOJIO)l(eHHeM. qHCJIeHHO M3Me-
peHHble 11 OnTMMI13HpOBaHHble n;MarpaMMbI 06bIqHO HMelOT HeMOHOTOHHyIO orH-
6alOmyIO 60KOBbIX JIeneCTKOB. KpoMe Toro, cymecTByeT MHoro. «paCmenJIeHHbIX»
60KOBbIX JIeneCTKOB C rOpa3L(0 MeHhllIeM IlIHpHHOM. ,[(a)l(e ,lLJIH OLJ:HOMepHbIX (1 D)
LJ:HarpaMM pa60Ta 60JIbllIHHCTBa aJIrOpHTMOB HapyrnaeTcH M3-3a CJIO)l(HOM CTPYK-
Typbl 60KOBbIX JIerreCTKOB. ,[(JIH HaXO)l()J,eHHH orH6alOmeM MO)l(HO MCnOJIb30BaTb
qaCTYIO n;HCKpeTM3aUHIO C <pHJIbTpaUHeM, HO B CJIae ,UBYMepHbIX (2D) ,Ul1arpaMM
3TOT npouecc MO)l(eT 6bITb Qpe3BbIqaHHO Me,[(JIeHHbIM. llOCKOJIbKY rrpM OnTI1MH3a-
UI1H MO)l(eT rroTpe60BaTbcH oueHKa COTeH L(MarpaMM, BbIqHCJIHTeJIbHble 3aTpaTbI
MorYT 6bITb OqeHb BeJIHKM.
,L{JI5I LJ:MarpaMM HarrpaBJIeHHOCTH AP MaJIblX HJII1 cpe,nHI1X pa3MepOB C npOCTOH
CTPYKTYPOM 60KOBbIX JIerreCTKOB ocymecTBHMa orrTMMM3aUM5I KH,L{, KPYT"3HbI 11
T .LJ:. C OrpaHMQMBalOIIlI1MI1 YCJIOBM5IMM Ha orH6alOI.I.J:yIO 60KOBoro JIeneCTKa, rrOJIO-
cy nponYCKaHH5I, ,UonYCKH 1'1 T.L(. (CM., HarrpMMep, [20]). CymecTByeT HeCKOJIbKO
KJIaCCOB aJIrOpMTMOB orrTHMH3aIJ;HM. Bo-rrepBblx, MeTO,n; rpa,lJ;MeHTa. TIpocTble aJI-
ropHTMbl rpa,UHeHTa 11 COnpH)I(eHHOrO rpa,n,HeHTa 06bIQHO pa6oTalOT 6bICTpO, HO

4.2. j/,8YMepHble anepmypbl, OT1lJ/U'iHble om KPY2llblX 
qaCTO OCTaHaBJIlfBaIOTC5I B JIOKaJIbHOM MaKclfMYMe lfJIM 3aBlfcalOT B ceMoBoM TOq-
Ke. C nOMOllJ;blO 60JIee CJIO)f(HbIX aJIrOpl1TMOB 06e 3TI1 CJIO)f(HOCTI1 MO)f(HO 060MTlf,
11, KaK npaBlfJIO, onpe.n.eJI5IeTC5I a6COJIIOTHbIM MaKCMMYM [5]. HeKoTOpbIMI1 M3 Ta-
KI1X aJIrOplfTMOB 5IBJI5IIOTC5I MeTO)];bI <l>JIeTqepa [6-8]. AJIrOpI1TM, pa3pa60TaHHbIM
B [12], rr03BOJI5IeT YCTaHOBlfTb npe.n.eJIbHbIe 3HaqeHM5I no 06JIaCT5IM, HanpH-
Mep, 06JIaCT5IM 60KOBbIX JIeneCTKOB; qaCTa5I 11I1CKpeTI13aUMH 06eCrre1..JI1BaeT ocyme-
CTBJIeHIIe MlfHMMaKcHoH OnTI1MM3aUIIM no aJIrOpMTMY [18]. 0630p MeTo.nOB OnTI1-
MI13aUlflf 6e3 OrpaHHqeHMM ,[(aeTC5I B pa60Te [19]. llOMcKoBble MeTOLlbl B u:eJIOM
He3<p<peKTHBHbI, 3a lfCKJIlOqeHMeM ClfMTIJIeKC-MeTO,[(OB. B CMMnJIeKC-MeTOLle cpaB-
HlfBalOTCH <PYHKIJ.110HaJIbHbIe 3HaqeHlf5I, II 06pa3yeTC5I nOCJIen.OBaTeJIbHOCTb CMMn-
neKCOB, Ka)l(,[(bIM H3 KOTOpbIX npe.LI.CTaBJIHeT C060M MHO)f(eCTBO TOqeK C BepllIl1-
HOM, B KOTOpOM <PYHKUI10HaJIbHOe 3HaqeHHe MaKClfMaJIbHO. 3Ta BepIllI1Ha
OTpa)l(aeTCH B ueHTpOH,[(e .LI.pyroM BepIIII1HbI, 06pa3YH ROBbIll CI1MITJIeKC. OueHI1Ba-
eTCH 3HaqeHlfe B 3TOll HOBOM BepIII11He, H npouecc nOBTOp5IeTC5I. npH OCTaHOBKe
CrreUMaJIbHble npaBlfJIa rrepe3anYCKalOT npou:ecc. B paMKax Toro He60llbIlloro
orrbITa pa60TbI B .LI.aHHOM ccPepe, KOTOpbIM 06llaLlaeT aBTOp, npeBOCXO,[(HbIM aJIro-
pMTMOM OKa3aJICH aJIrOpMTM C nepeMeHHoM MeTpMKoM [5], peaJIM30BaHHbIM Ha
<l>OPTPAHe.
ITOCKOJIbICy npll H3MeHeHI1H B036)')K.lJ:eHHR ll3MeH51IOTCR rr0J10)l(eHlf}J 60KOBbIX
JIeneCTKOB, 06bIqHO MCnOJIb3yeTC5I lfTepaUMOHHa5I rrpou;e.n.ypa. ,lJ,JISI nepBoM MTepa-
UI1I1 3LleCb I1Cn0J1b3YIOTC5I rrOJIO)f(eHlf5I 60KOBbIX J1eneCTKOB cooTBeTcTBYJOllleH KJIac-
CMQeCKOM ,[(l1arpaMMbI HanpaBJ1eHHOCTH. n pM Ka)l()],OH J1TepaUI1M onpe,[(eJI5IIOTCH
HYJIH J],l1arpaMMbI HanpaBJIeHHOCTI1, npl1 3TOM rrpeLlrrOJIaraeTC51, lITO MaKCMMYMbI
60KOBbIX J1eIIeCTKOB pacn0J10)l(eHbI IIocepeLllfHe Me)l()],Y HYJISIMM.
npM CMHTe3e C OrpaHHqMBalOLUMMH YCJIOBM5IMM no 60KOBbIM JIeneCTKaM JillH
u u
CHHTe3e C MMHHMM3aQI1eM OCIJ;HJIJI5IQMH .LI.HarpaMMbI HanpaBJIeHHOCTH C JIyqOM cne-
UMaJIbHOM cPOpMbI qaCTO MHHHMH3HpyeTcH CYMMa KBa.LI.paTOB OTKJIOHeHI1M. OJ],HaKO
HCnOJIb30BaHlfe MeTOJ],a HalfMeHbllIHX KBa,npaTOB .lUI5I OnTlfMJi3aUHH llMarpaMMbI
,[(aeT XY,[(IIIee COOTBeTCTBHe Ha Kpa5IX HHTepBaJIa. BOJIee y.naqHbIM aJIrOpHTM onTH-
u
MH3aIJ.1111 MCnOJIb3yeT MeTO)]; HaHMeHbIlIlfX p-X CTeneHel1, npM KOTOpOM MHHI1MH311-
pyeTcH KopeHb CTeneHH p H3 C)'MMbI P-M CTeneHH OTKJIOHeHI1M [2, 23]. 3HaQeHI1C
p = 10 06eCneQl1BaeT rrpeBOCXO)];HOe COOTBeTCTBHe, Tor,[(a KaK IIpl1 OQeHb 60JIbllIHX
3HaQeHI1HX p )];OCTHraIOTCH MHHHMaKCHbIe pe3YJIbTaTbI. O)1HaKO nOCJIe)1HI1M CJIyqaM
Tpe6yeT TllJ;aTeJIbHOM 06pa60TKH QlfCeJI C IIJIaBalOm:ei1 3aIUlTOM.
4.2.2. CMHTe3 AMarpaMM HanpaBneHHOCTM
C KonbeBblMM 60KOBblMM neneCTKaMM
DpM rrp5IMoyrOJIbHOH anepType QaCTO Tpe6yeTC5I cna,nalOIlJ,aSl C pOCTOM e ofl16alO-
IlJ,aR 60KOBbIX JIeneCTKOB, aHaJIOrl1QHa5I TOM, KOTOpa51 nOJIyqaeTCSI npM OllHonapa-
MeTpMQeCKOM pacnpe,[(eJIeHlfM XaHceHa HJIM n -napaMeTpMQeCKOM pacnpelleneHMI1
TeMnopa ,lJ.JIH KpyrJIbIX anepTYp. TaKOM CHHTe3 MO)l(eT oCYJ.I.I.eCTBJI5ITbCH MeTon.aMI1
KOMnblOTepHoro nepe60pa, onlfcaHHbIMM B npe,[(bI,[(yIUeM pa3,lleJIe, MJII1 HTepaUI10H-
HbIMlf MeTo,[(aMI1 no,[(roHKH KopHeH (2D) nOJII1HOMa, Onl1CaHHbIMI1 B pa3,[(eJIe 3.9.2.
nOCJIe)];HMH no)];xo,[( ropa3,[(0 JIyqIlIe.

(::;
rflaea 4. CUltme3 auazpaMM ltanpaefleltltOCmu aeYMepllblx u KPY2IlbiX allmeltllbLX peUlemOK
I1pH 60JIee cTporoM aHaJIHTHqeCKOM no.n;xo.n;e HcnoJlb3yeTC}I npeo6pa30BaHlie
EaKJIaHOBa [1], C nOMOIl(blO KOToporo .n;BYMepHa51 (2D) 3a;:I,aQa CBO,n:HTC5I K O.n.HO-
MepHoH (1 D). B pa60Te [24] 3TO npeo6pa30BaHHe npHMeHeHO K KBa;:I,paTHOH AP, 11
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HanpaBJIeHHOCTH KBa,n;paTHoH aHTeHHOH pellIeTKH lOx 10 C ypOBHeM nepBoro 60-
KOBoro JIeneCTKa -30 .nD [16]. <I>opMa KOJIen; 60KOBbIX JIeneCTKOB He KOJIbIJ:eBaR,
HO OHa COOTBeTcTByeT KOH<pHrypan;HH anepTYpbI. TIpH paBHOM ypOBHe 60KO-
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U;HeHT YCHJIeHHH, qeM paCqeT Ha OCHOBe npoH3Be.neHHH ,[(BYX JIHHeHHbIx pacnpe-
v
.n:eJIeHHH.
6JIaro,napHOCTb
<I>oTorpa<pHH JII06e3HO npe,[(OCTaBJIeHbI Ph.D Winifred Kummer.
JIHTepaTY)Ja
I. Baklanov, Y. V., «Chebyshev Distribution of Current for a Planar Array of Radiators», Ra-
dio Eng. Electron. Phys., Vol. 11, 1966, pp. 640-642.
2. Bandler, J. W. and Charalambous, C, «Theory of Generalized Least Pth Approximation»,
Trans. IEEE, Vol. CT-19, May 1972, pp. 287-289.
3. Bayliss, E. T., «Design of Monopulse Antenna Difference Patterns with Low Sidelobes»,
BSTJ, Vol. 47, No.5, May-June 1968, pp. 623-650.
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AD-AI53 257.
5. Fletcher, R., Practical Methods of Optimization, Wiley, 1986.
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Inst. Math. Appl., Vol. 9, 1972, pp. 91-108.
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10. Hansen, R. C., «A One-Parameter Circular Aperture Distribution with Narrow Beam-
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IEEE, Vol. AU-20, June 1972, pp. 171-173.
13. Nonrecursive Digital Filters Subject to Upper and Lower Function Constraints», Trans.
IEEE, Vol. AU-20, June 1972, pp. 171-173.

J DlO6a 4. CUHme3 auazpaMM Hanpa6JleHHOCmu aeyMepHbIX U KPY2/lbIX aHmeHHbIX peUlemOK
14. Josefsson, L., Moeschlin, L., and Sohtell, V., «A Monopulse Flat Plate Antenna for Mis-
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de lobe Leveh), Proc. IEEE, Vol. 56, Vol. 11, Nov. 1968, pp. 1771-1778.
--

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npe,l(JIO:>KeHbI B [8]. B pa60Te [10] HX KOHCTPYKUHH cyrn:eCTBeHHO YJIyqmeHa nYTeM
paCKpbITllH 060JIOQKH, 6JIaro,aapH QeMY ,n:OCTHraIOTCH 60JIbIIIaH KOMnaKTHOCTb H
YHHBepCaJIbHOCTb.
CooTBeTcTBYlOlI(He MaTepllaJIbI no pO,l(CTBeHHoH TeMaTHKe MO}I(HO HaHTll, Ha-
npHMep, B ny6JIHKaIJ;H"Hx [64, 130], r,n:e onTHMH3HpOBaH HMne,l(aHC B ,nHana30He OK-
TaBbI, a B [132] npOll3Be,neH QHCneHHbIH aHaJIH3. «PYKaB» (Sleeve) Ha3bIBaeTCH «OT-
KpbITbIM» (open), nOCKOJIbKy OH He OKpyxaeT ,l(l1nOnb, a COCTOI1T 113 ,[(BYX TPy60K
HJIH nnaCTHH, pacnOJIO:>KeHHbIX C ,[(BYX CTOpOH ,[(l1nOJIH. Ha pl1C. 5.13 npl1Be,[(eHa
cxeMa JIHHeHHO nOJIHpH30BaHHoro ,[(HnOJIH THna «open sleeve». B03MO)I(HO TaIOKe
npHMeHeHHe CKpelI(eHHbIX' ,n:HnOJIeH THna «open sleeve» ,nJIH nOJIyqeHHH KPyroBoH
nOJIHpH3aIJ;HH. CKpelI(eHHble «PYKaBa»,
u
pacnOJIO}l(eHHble no CTopOHaM ,n:HlIOJIeH,
Moryr 6bITb 3aMeHeHbI MeTaJIJIl1qeCKOH
u u u
nJIaCTHHOII KpyrJIOII HJIH KBa,n:paTHOll
<pOpMbl. lloJIoca nponYCKaHHH IIp II
KCBH < 2 MO:>KeT 6bITb OKTaBHOH. Pa3-
u
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3KpaHIIPYIOII(eH nJIOCKOCTblO ,JJ;aJIO npe-
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,nlflIOJIb TMna «open sleeve» lIpe,JJ;CTaBJIH-
eT C060H 3JIeMeHT C HI13KHM K03<t><t>H-
UlfeHTOM YCllJIeHllH II Hall60JIee lliHpO-
KOH Y H3JIYQalOII(HX 3JIeMeHTOB nOJIOCOH Poc. 5.13. )].HnOJIb Tna «open sleeve»
nponycKaHllH. CooTBeTcTBYlOlI(llM cpe,l( - «<OTKPbITbIH PYKaB») [64]
CTBOM paCQeTa BHOBb HBJIHIOTCH MeTo,n:bI
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5.2. UJ.enM B BonHOBOAe
BOJIHOBo,n:Hble lI(eJIll 6bIJIH 11306peTeHbI BaTcoHoM [126, 128] B 1943 r. B YHI1BepCI1-
TeTe MaKrMJIJIa (MOHpeaJIb, KaHa,n:a) QTO COnpOBO}l(l(aJIOCb pa60TaMI1 CTI1BeHCOHa,
KYJIJIeHa H ,n:p. IICCJIe,aOBaTeJIeH B BeJII1K06pHTaHHII. llocJIe BTOpOH Ml1pOBOH BOHHbI
ueHTp IICCJIe,n:OBaHI1H no BOJIHOBO,n:HbIM lI(eJIHM nepeMeCTRJIC5I B JIa60paTopl11O
Hughes Aircraft Microwave Laboratory B KaJIBep-CHTH, KaJIl1<t>OpHIDI, r,n:e 3TH pa-
60TbI BeJIMCb no,n PYKOBO,n:CTBOM 11ec BaH ATI'bI. B rpyrrny I1CCne,l(OBaTeJIeH BXO-
,n11J1ll ,[(. AHOKa, A. Kn3BllH, D. 3JIJIHOIT, <1>. fo66enc, JI. fYCTa<t>COH, K. KeJIJIH,
JI. KypTQ, D. MaKCYM, LJ;. CnpeJI)IH, 11. CTapK, E. CTereH, )):. CbepH, P. TaHr, H. Jlpy.
WeJIM B BonHOBo,n:e 6bIJIH npe,L(JIO:>KeHbI B [127, 128] . BOJIHOBO,l(HOH ll(enblO
Ha3bIBaeTCH Y3KaH lI(eJIb, npope3aHHaH B ml1pOKOH CTeHKe I1JII1 60KOBOH rpaHI1
npHMoyrOJIbHOrO BOJIHOBo,n:a. I.U;eJIH MOryr 6bITb TOQHO ll3rOTOBJIeHbI I1YTeM
<ppe3epoBaHHH, oco6eHHo Ha CTaHKe C nporpaMMHbIM yrrpaBJIeHHeM, a BOJIHOBO,n:
npe,nCTaBJI5IeT C060H <t>H,n:epHyIO JII1HI1IO C HI13KlfMll I10Tep5IMI1.

 FAa8a 5. 3AeMeHmbl aHmeHHou peutemKU
B03MO)l(HOCTb nOJIyqcHMJI TOqHOrO ancpTypHoro pacnpe.n.eJIeHMR B meJICBbIX
aHTeHHbIX perneTKax npMBeJIa K TOMY, qTO OHM 3aMeHMJIM pe<pJIeKTOpHbIe aHTeHHbI
MHorMX 60pTOBbIX P J] C paKeT M JIeTaTeJIhHbIX annapaTOB 11 IllMpOKO MCnOJIh3YIOTCR
BO MHOfl1X .n.pyrl1x npMJIO)l(eHI1RX. Y3Ka.H mCJIh, pacnOJIO)l(eHHaH BJ(OJIh OCM 1lI11pO-
\
KOti CTeHKIi BOJIHOBO,LI.a, He H3JIyqaeT: MR C03,LI.aHHR H3JIyqeHMR meJIb ,LI.OJ1)I(Ha 6hITh
CMem:eHa K KpalO MJIH nOBepHyra no,l( yrJIOM K Cpe,LI.HeH JIHHHM. AHanorHqHbIM 06-
.....
pa30M He 113JIyqaeT rn:eJIb B Y3KOH CTeHe BOJIHOBOJ(a, pacnOJIO)l(eHHaH nepneH,LI.HKY-
JIRpHO pe6py; np" HaKJIOHe m:eJIM npOMCXO,lIMT ee B036y)1([(eHHe BOJIHOBO,l(HOH MO-
,n;oti. nOCKOJIbKY m:CJIh Ha 60KOBOM CTeHKe ,L(JJR nOJIyqeHMR pe30HaHCHOM .lWMHhI
06blqHO 3aXOLU1T Ha llIHPOKYIO CTeHKY, CMelI(eHHe TaKOM m;eJIH K cpe,LI.HeH JIMHMH
HcueJIeco06pa3HO. TpH HaM60JIee Ba)J(HbIX THn'a BOJIHOBO,l(HbIX m:eJIeH nOKa3aHhI Ha
pMC. 5.14. CMcrn:eHHaR m:eJIh B llIMpOKOH CTeHKe qaCTO Ha3bIBaeTCH lIlyHTHPYlOlI(eH,
..... .....
nOCKOJIbKy ce 3KBI1BaJIeHTHOH cxeMOH 51BJIReTCR IlIYHTl1pyromaR npOBO,LI.HMOCTb,
BKJIIOQeHHaR napaJIJICJIhHO JIMHMH rrepe,n;aqH. HaKJIOHHaR m:eJIh B IJ;eHTpe IlIl1pOKOM
.....
CTCHKI1 Ha3bIBaCTCR nOCJIc.n:OBaTeJIbHOM, TaK KaK ec 3KBHBaJIeHTHaR cxeMa npe,l(-
CTaBJIHCT C060H nOCJIe,LI.OBaTeJlhHbIM I1Mne.n:aHC. EOKoBa51 meJIh RBJIReTCR meJIhlO
IlIYHTMpYIOrn:ero THna. qamc Bccro MCrrOJIh3yroTCR 60KoBaR rn:eJIb M CMel.l{eHHaR
lI(CJ1b B IlIUpOKOti CTCHKC, npM 3TOM pcrnalOI..QMM <paKTopoM BhI60pa qaCTO RBJIReTCR
rrOJIHpJ13aUI151 H3J[yqeHH}I. Y 60KOBOH rn:CJIH E nOJIRpH3aIJ;MR HanpaBJICHa B,n;OJIb OCll
BOJIHOBo,n;a, a Y CMCmeHHbIX mCJICH - noncpCK OCM. )J,MarpaMMa HanpaBJICHHOCTH
BOJ1HOBO,lIHbIX meJIci1 6JIM3Ka K .l1.HarpaMMe HanpaBJIeHHOCTH m:eJICM B 6eCKOHeQHOM
3a3eMneHHOM 3KpaHe, 3a I1CKJII01.JeHl1eM 06JIaCTH CKOJIh3Hm:HX yrJIOB, f,l(e MrpalOT
Ba)l(HYIO pOJ1b pc6epHble 3<p<peKTbI.
CMemeHHaH
npo,nOJIbHaH
HaKJIOHHaSl
PHC. 5.14. TMnbJ BOJIHOBO,JJ;HbIX meneH
PC30HaHCHbIC aHTeHHblC pelIleTKM (fJI. 6) Tpe6YlOT MCnOJIh30BaHHR CMH<pa3HbIX
3JIeMeHTOB, pa3MemeHHbIX C rnarOM, paBHbIM nOJIOBHHe ,l(JIMHbI BOJIHbI B BOJ1HOBO-
,lIC. ,L{JIH YCTpaHeHHR 3cP<peKTa H3MeHeHHR <l>a3bI B BOJIHOBO,lJ.e Ka)l()J;aR BTopaR m:eJIh
pacrrOJIaraeTCR C ,lIpyroM CTOpOHbI OT reOMeTpl1qeCKott OCM BOJIHOBo,n:a (B CJIyqae
rrpO,lIOJ1bHbIX meJIei1) I1JII1 nOBepHyra no,lJ. npOTMBOnOJIO)l(HhIM K HeM yrJIOM (B CJIY-
qae 60KOBbIX meJ1eti). TI03TOMY ,n;warpaMMa HanpaBJIeHHOCTH aHTeHHoH pellieTKI1
<l>opMl1pyeTc5I MHO)l(MTeJIeM pellieTKI1 C Y,lJ.BOeHHhIM llIarOM 11 ,n;HarpaMMOH HanpaB-
JICHHOCTM 3JTeMeHTa, COCTORll.{CrO 113 napbI m:eJIeH. B CJIyqae npOll.OJIhHbIX meJIeH
60KOBble JIenCCTKM nO,lJ.pCrneTKM (,l(Byxrn:eJIeBOrO 3JIeMeHTa) MO)l(HO KoppeKTHpo-

5.2. Il(e;zu 660/lH0600e 
BaTb, MeHHH mar pa3Meru:eHHH 3neMeHTOB. O,nHaKO B CJIyqae 60KOBbIX me11eM np"
HeKOTopbIX yrJ1ax Ha6J1IO,n:aIOTCH 60KOBbIe neneCTKH C nOnepeqHOM n011.HpM3aQMeti.
3TH neneCTKH MOryr 6bITb no,n:aBJ1eHbI nyreM 3aMeHbI K3.)I(,[(0H H3 me11eM 611113KO
u u u
pacnOnO)l(eHHOH napo" ru:eJIeH C MeHbIIIHM yrJIOM HaKJIOHa.
5.2.1. npOAonbHble l1.\enM B WMpOKOM CTeHKe BonHOBOAa
BeJIHqMHa nOJIHOH npOBo,n:HMOCTH (HJIH nOJIHOrO conpOTHBJIeHH) BOJ1HOBOJJ:HOM
meJIH onpe,UeJIeTCH BHeIIIHMM BKJHllI;OM, KOTOpbIH MO)l{eT 6bITb BblqHCneH C no-
u
MOmblO 3KBHBaJIeHTHOH ru:eJIM B 3a3eMJIeHHOM 3KpaHe HJIH C nOMoru:blO 3KBI1BaJIeH-
THoro ,L(MnOJI Ea6HHe, H BHYTpeHHHM BKJI3JJ;OM, 06YCJIOBJIeHHbIM 3anaCOM 3HeprMH
B 3aTYXaIorn:HX BOJIHOBO,lJ;HbIX Mo,n:ax B 06JIaCTH ru:eJIH.
llOCKOnbK)' BHyrpeHHHM BKJ1a,zJ. HBJIeTCH peaKTHBHbIM, npOBO,lJ,HMOCTb pe30-
HaHCHOM IUenH G MO)l{eT 6bITb npH6nH3HTeJIbHO onpe,lJ;eJIeHa C MCnOJIb30BaHlleM
,n:HnOJI Ea6HHe C yqeToM CB3M C BOJIHOM TEIO. B pa60Te [120] nOJIyqeHa <popMYJIa
 = 480(a / b) Sin 2 ( 1tX ) COS2 ( 1t P ) , (5.4)
Yo 1tRo (J3 / k) a 2k
r,L(e Ro - conpOTMBJIeHHe ,n:IInOJI, x - CMeru:eHMe ru:enH, a M b - llIHpHHa M BbICO-
Ta BOJIHOBo,n:a 11 (3 - BonHOBoe qHCnO .n;JI BonHbI B BonHOBo,n:e, Yo - xapaKTepl1C-
TlIqeCKaH npOBo,n:HMOCTb nlITalOmero BonHOBo.n;a. 3Ta <popMyna npHrO,lJ;Ha ,lI)IH Ha-
u u
XO)I(,LJ:eHH aKTHBHOH npOBo,n:HMOCTM ru:enH, HO ,lUI ee peaKTIIBHOH npOBO,L(HMOCTI1
npOCTaH <t>opMyna OTCYTCTByeT. Bapl1aI.J;HOHHaR <POPMYJIl1pOBKa 3a.L1,aqH 0 peaKTHB-
HOM npOBO,lJ,HMOCTH npe,ll,JIO)l(eHa B [85, 86]. OJIHHepOM 6bInH nOJIyqeHbI ynpomeH-
HbIe aHaJIHTMQeCKHe BbIpa)l(eHI1, KOTopbIe, XOTH H nOJIe3HbI, He,L(OCTaTOqHO TOqHbI
,UlUI paCqeTa aHTeHHOH peIlleTKH. C nOBJIeHHeM MOru:HbIX KOMnblOTepOB CTaJI B03-
MO)l(eH 60JIee TOqHbIM paCqeT no BapHaI.J;HOHHbIM <popMynaM. TaKOM nO,lJ;XOI( ocy-
rueCTBneH B pa60Te [135], pe3YJIbTaTbI KOTOpOH Hcnonb3YIOTCR HH)I{e.
.n;pyroH cnoco6 peIlleHHH npe,lLJIO)l{eH B pa60Tax [59, 60]), r,n:e npHBo,n:TCH CHC-
u
TeMbI MHTerpaJIbHbIX ypaBHeHMH, onHCbIBalOrn:HX BHeIIIHHe II BHYTpeHHlIe 3JIeKTpM-
qeCKHe nonH. 3aTeM CHCTeMbI HHTerpaJIbHbIX ypaBHeHHH peIllalOTCR MeTOI(OM MO-
MeHTOB C HCnOJIb30BaHHeM HMnyJIbCHbIX <PYHKI.J;HH pa3JIO)l{eHH H TeCTOBbIX
.aeJIbTa-<PYHKIJ;HM. B 060HX CJIyqaHx TOJIIUHHa CTeHKH BOJIHOBo,n:a ytIMTbIBaeTCH Me-
TO.nOM OJIHHepa, npH KOTOpOM BHemHHe If BHyrpeHHHe nonR CB3aHbI BOJIHOBO,a-
u u u
HOH nepe,n:alOrn:eH nHHMeH, npHqeM ru:eJIb RBJIHeTCR nOnepeqHbIM CeqeHHeM BonHO-
Bo.na, a TOJIru:HHa CTeHKH - ,nJIHHOH BOJIHOBo,na. B 060HX nO,lJ;xo,nax ,lJ;OCTHfHyr
y.n;oBJIeTBOpHTeJIbHbIH ypOBeHb COrJ1aCOBaHHOCTH C .n;aHHbIMH M3MepeHHll. LJ:aJIb-
HeHIIIee YJIytIIIleHHe 6bIJ10 c.neJIaHO C HCnOJIb30BaHHeM K)'COqHO-CHHYCOH,[(aJIbHbIX
<PYHKUHH B KaqeCTBe <PYHKI.J;HH pa3JIOXeHHR H TeCTOBbIX <PYHKUHH B CTall.HOHapHoM
<t;>opMynHpoBKe MeTo,na rarrepKHHa [91].
C nOMOIUbIO BapHaUHOHHoro MeTo,na 6bma BblqlfCJIeHa nOJIHaR npOBo.n;HMOCTb
meJIeH B BOJIHOBo,ne WR-90: 3aBlfCHMOCTb pe30HaHcHoH ,lUIHHbI IUeJIH OT ee CMerue-
HHS! If aKTHBHaH npOBo,nHMOCTb Ha pe30HaHce. CMeru:eHlfe x y,n06HO HopMl1pyeTcSl
K IIlHpHHe a BOJIHOBo.n;a, a pe30HaHCHaH ,lLJIHHa Ir - K ,lUIHHe BOJIHbI B BaK)'YMe Ao.
Ha pHC. 5.15 npe,lJ;CTaBJIeHbI KpHBble pe30HaHcHoH ,lLJIHHbI m:eJIIf ,lJ;JI.H 3HaqeHHH a =
= 0.9, TOJIlI(HHbJ CTeHKH = 0.05 If IIIHpHHbI rn;eJIH = 1/16, r,ne Bce pa3MepbI .naHbI B
...........-...

-....
 FAaea 5. 3AeMeHmbl aHmeHHoii peUJemKU
0.516
0.508
9,375 MHz
II ,. 0.9
b = 0.2
0.500
0.492

............
...
- 0.484
9375 MHz
II - 0.9
b ... 0.4
0.476
a - 0.9
0.458
b - O. 4
0.460
o
0,05
0,10
0.15
0,20
0.25
x/a
Pac. 5.15. Pe30HaHCHaH .LLJIHHa npo,nOJIbHOH I.QeJIH
.lUOHMax. IlpHBo,ll,HTCH ,lI,aHHbIe ,lLTIH qaCTOT 9.375 H 10 fr npH b = 0.4 Ii 0.2 ,lI,IOHMa.
CTaH,lIapTHb[U BOJIHOBO,ll, WR-90 HMeeT BbICOTY, paBHyro 0.4 ,lI,IOHMa, HO ,lUIH npHeM-
v
HbIX aHTeHHbIX pelIIeTOK npe,nCTaBJIHeT 3HaqHTeJIbHbIH HHTepec BOJIHOBO.ll. C nOJlo-
BHHHOH BbICOTOH. KpHBaH pe30HaHcHoH npOBo,nHMOCTH MH o,aHoro H3 cJlyqaeB
nOKa3aHa Ha pHC. 5.16; Ha6JIIO,naeTcH xopomee COOTBeTCTBHe $opMYJIe (5.4). TIocJIe
u
3Toro paCqeTHaH nOJIHaH npOBo,nHMOCTb HopMHpyeTcH K pe30HaHCHOH npOBo,aHMO-
CTH G r , a MHHa rn;eJIH - K pe30HaHcHoH ,lJ)IHHe. 3TH YHHBepCaJIbHbIe KpHBbIe no-
JIyqeHbI B pa60Te [55] Ha OCHOBaHHH TOqHbIX H3MepeHHit Ha pHC. 5.17 3TH ,naHHbIe
npHBO,ll,HTCR .lUIH BOJIHOBo,na WR-90 Ha qaCTOTe 9375 Mfl(, onHTb-TaKH ,lLTIH .nBYX
3HaqeHHH CMern;eHHH rn;eJIH. )],aHHbIe KpHBbIe HBJIHIOTCH YHHBepCaJIbHbIMH B cJle.ny-
lOrn;eM CMbICJIe. B nepBOM npH6JIIDKeHHH BapHal(HH Y/G r no nepeMeHHbIM l/lr H x/a
He 3aBHCHT OT f3/k, TO eCTb OT qaCTOTbI. TaKHM 06pa30M, .lLITH BOJlHOBo,na 3an;aHHoro
u
pa3Mepa npHro,nHbI ,[(aHHbIe, H3MepeHHbIe HJIH BbIqHCJIeHHbIe npH O,nHOH qaCTOTe.
npH MaJIbIX CMemeHHRX (0.05 H MeHee) H3MeHeHHe HOpMHpoBaHHoH npOBO,[(HMO-
CTH He 3aBHCHT TaIOKe OT a/b. O,[(HaKo npH 60JIblIIHX CMemeHHHX He06xo,[(HMO yqH-
TbIBaTb TOQHOe 3HaQeHHe a/b. «YHHBepCaJIbHbIe» KpHBbIe MH BOJIHOBOJJ;a WR-90 c
nOJIOBHHHOH BbICOTOH Ha qaCTOTe 9375 Mru; npe,[(CTaBJIeHbI Ha pHC. 5.18; npHBe.ne-
u
HbI ,[(aHHbIe ,lLTIH ,[(BYX 3HaqeHHH CMeru;eHHH ll(eJIH.
BbIqHCJIeHHe nOJIHOH npOBO,[(HMOCTH BapHaU;HOHHbIM cnoco6oM HJlH MeTO-
,[(OM MOMeHTOB npeJJ;CTaBJIHeT C060H ,aOCTaTOQHO Me,lLTIeHHYIO npoue,aypy. DOJIee
npHrOlJ;Ha nOJIHHOMliaJIbHaH arrrrpOKCHMaUHH. OJJ;HaKO YHHBepCaJIbHbIe KpHBbIe
Tpy,nHO arrnpOKCHMHpOBaTb OJJ;HHM BbIpIDKeHHeM. DOJIee TOqHaH annpOKCHMaUHSI

5.2. Il(eJlU 8 80AH0800e 
1
0,1
Stevenson [120]
GrlYo
000
Yee [135]
0,01
o
0,05
0,10
015
x/a
0,20
025
PHC. 5.16. Pe30HaHcHaH npOBO,l(HMOCTb npO,l(OJIbHoi1 rueJIH
Stegen [55] 0 xis = 0.07
0.6 D 0.17
(] x/a = 0.05
0
0.4 0.2
1.0
0.2 .
0.8
....
(!) 0
en
C)
x/a = 0.2 0.6 C5
...
-0.2
B 0.4
-0.4
-0.6
0.90
0.92
0.94
0.96
0.98
1.00
f/l r
1.02
1.04
1.06
1.06
o
1.10
PHC. 5.17;' nOJIHaH npOBO,l(HMOCTb npO,l(OJIbHoi1 rueJIH, 9375 Mfu;, a = 0.9, b = 0.4 [55]

b Dzaea 5. 3JleMeHmbl aHmeHHOU peUlemKU
0.6
1.0
0.2 G
0.8
...
 0
-
C[J G>
0.6 Gs
...
-0.2
-0.4
-0.6
0.90
0.92
0.94
0.96 0.98
1.00
I/l r
1.02
1.04
1.06
1.08
o
1.10
PRC. 5.18. nOJIHaH npOBOL(HMOCTb npo.aOJIbHOH meJIH, 9375 Mfu;, a = 0.9, b = 0.2
,L(OCTHraeTCR rrpH pa36HeHHH KpHBOM Ha yqacTKH, HO rrpM 3TOM Heo6xo,L(HMO 1136e-
raTb pa3pbIBoB KYCOQHO-JIHHeHHOH <PYHKIJ;I1H B TOqKaX corrpIDKeHHR, rrOCKOJIbKY
u
OHM BJIMSIIOT Ha rpaIIHeHTHble MeTO,L(bI, HCrrOJIb3yeMhle LUIR paCqeTa aHTeHHOM pe-
meTKI1. TIpl1 aJIbTepHaTHBHOM rro,n:XO,L(e HCrrOJIb3yeTcR He rronHaR rrpOBO,l(I1MOCTb, a
rrOJIHOe conpOTHBJIeHHe. TIpl1 HOpMl1pOBaHHH HMne,l(aHCa rn;enH K 3HaqeHHIO pe30-
HaHCHoro conpOTHBJIeHHR KpHBbIe HMelOT BH,l(, H306pa)l(eHHbIH Ha pHC. 5.19 M
5.20. rpa<pI1K COnpOTI1BJIeHHR B nepBOM rrpU6JIH)I(eHHI1 npe,l(CTaBnReT C060M rrpR-
MYIO nHHl110 C HaKJIOHOM, He 3aBHCRIl(I1M OT a/h. TIoKa3aHo H3MeHeHHe HaKJIOHa
npH Bapl1aUHU (3/k. KpHBaR peaKTHBHoro corrpOTHBneHHR HMeeT He3HaqHTenbHYID
KPHBH3HY H TO)l(e He 3aBI1CHT OT (3/k, a ,n:nR He6onbIIII1X CMem:eHHM He 3aBHCI1T TaK-
)l(e 11 OT a/b. TIpH 60nbIIII1X CMeIUeHI1RX KpHBbIe peaKTHBHoro corrpOTHBneHHR 3a-
BHCRT KaK OT x/a, TaK H OT a/b. TaKI1M o6pa30M, KpHBbIe HMne,n:aHca RBnRIOTCSI
u
CTonb )l(e «YHHBepCaJIbHbIMI1», KaK M KpHBble nOJIHOH rrpOBO,l(MMOCTM, H rOpa3,l(O
nerqe arrnpOKCI1MHpyIOTC$J nOJIHHOMaMH. TIpH OTCYTCTBHH ,l(aHHbIX LUIR BOJIHOBo,n:a
C KOHKpeTHbIMH pa3MepaMH 11 napaMeTpaMI1 TOJIIUI1HbI CTeHKI1, KOTOpbIH npe,l(no-
JIaraeTCR Hcrronb30BaTb B aHTeHHOM peIIIeTKe, Heo6xo,L(HMO BbIqMCnl1Tb I1JIH 113Me-
pl1Tb 3HaQeHI1R, ,[(OCTaTOQHble ,[(JIR IIOCTpoeHHR YHMBepCaJIbHbIX KpHBbIX. Donee
rrpe,lIIIOQTHTeJIbHbI KpHBble HMne,L(aHCa, nOCKonbKy OHH H3MeHRIOTCR Me,lLJIeHHO.
CHHYCOH,L(aJIbHOe pacrrpe,L(eneHHe nOJISI RBJIReTCR y.n;OBJIeTBOpI1TeJIbHbIM ,l(orry-
meHHeM ,[(JIR 60JIbIIIHHCTBa BOJIHOBO,l(HbIX meJIeM. O,l(HaKO ,[(JIR meJIeH B BOJIHOBO-
,L(ax C ,l(H3JIeKTpI1QeCKHM 3arrOJIHeHHeM 60JIee TOQHOM arrrrpoKcHMaUHeM RBJIReTCSI
IIOJIYKOCHHYCOI1,L(aJIbHOe pacrrpe,L(eneHl1e [26]. 3TO, K CO)l(aJIeHHIO, 03HaQaeT, QTO
paCqeT rronHOH B3al1MHOM rrpOBO,L:(HMOCTH Tpe6yeT QHCneHHoro HHTerpl1pOBaHI1SI no
06eHM meJI5IM, QTO CHJIbHO 3aTpY,L:(H5IeT CHHTe3 ,L:(HarpaMM HarrpaBneHHOCTH rn;ene-
BbIX aHTeHHblX perneTOK.

5.2. lI(enu 6 60JlH0600e 
1.2
0.8
X
0.4 1.08
10 GHz
...
 0 R 1.04
)(
-1.2
:tJ
1.00 
...
-0.4
-0.8
0.96
0.92
0.90
0.92
0.94
0.96
0.98
1.02
1.04
1.06
1.08
1.10
1.00
III,
Puc. 5.19. ITOJIHOe corrpOTHBJIeHHe rrpo.n;OJIbHO:H meJIH, a = 0.9, b = 0.4
1.2
x/a = 0.05
0.8
0.4
1.08
...
 0
)(
-0.4
JJ
1.00 53
...
-0.8
0.96
-1.2
0.92
0.90
0.92
0.94
0.96
0.98
1.02
1.04
1.06
1.08
1.10
1.00
1/1,
Puc. 5.20. 3aBHcHMoCTb corrpOTHBJIeHH5I rrpo.n;OJIbHOH meJIH OT ee ,LLJIHHbI, a = 0.9,
b = 0.2
TIpocToe COOTHOIIIeHHe Me}l(,[(Y .nB)'M.SI 3HaQeHH.SIMH IIOJIHOH B3aHMHoH npOBO-
,aHMOCTH npHBe.neHO B pa60Te [101]. qacTHqHOe .l(H3JIeKTpHQeCKOe 3anOJIHeHHe
BOJIHOBO.l(a no IIIHpHHe cnoco6cTByeT rrO.l(aBJIeHHIO .l(H<l>paKIJ;HOHHbIX JIeneCTKOB;
paCQeT nOrrepeQHOH Il(eJIH MeTO.l(OM MOMeHTOB .naH B pa60Te [54].

 DlO6a 5. 3JleMenmbl anmennou peUlemKU
Ha <ppe3epHbIx CTaHKax y,a06HO 113rOTaBJII1BaTb BOJlHOBo,aHbIe m:eJIIf co cKpyr-
JIeHHbIMI1 KOHQaMH. B nepBoM npl16JII1)1(eHHH TaKa$! m:eJIb 3KBI1BaJIeHTHa np$!MO-
yrOJIbHOH meJIH C TOM )l(e Illl1pl1HOM' Ii nJIOma,L(blO [85, 86]. ,[(JISI nOJIyqeHIiSl 60JIee
TOqHbIX pe3YJIbTaTOB MO)f(HO llCnOJIb30BaTb paCqeT MeTo,aOM MOMeHTOB [106].
CMem:eHHbIe npo,aOJIbHbIe meJII1 Ha IIIHpOKOM CTeHKe BOJIHOBo,aa 06bIQHO HC-
nOJIb3YIOTC5I H3-3a OTHOCI1TeJIbHOH rrpOCTOTbI HX paCqeTa H H3rOTOBJIeHIiSl. DOJIee
06m:HM CJIyqaeM SlBJISleTCSI KOM6MHHpOBaHHa$! meJIb, KOTOpa$! He TOJIbKO CMemeHa,
HO H nOBepHyTa no,a yrJ10M KOCH. KOM6I1HIipOBaHHa$! rn:eJIb 06eCneQHBaeT 60J1ee
mIipOKHH ,aHana30H aMnJIHTYJIHbIX 11 <t>a30BbIX CBSl3eH. PaCQeTHble ,aaHHbIe npMBO-
,aSlTCSI B pa60Te [101].
5.2.2. enM B 60KOBO" CTeHKe BonHOBOAa
PaCqeT 60KOBbIX m:eJ1eH Tpy,aeH, nOCKOJIbKy HX KOHQbI OXBaTbIBalOT BOJIHOBO,n. no
3TOH )l(e npHQMHe TOJ1ll.{HHa CTeHKH CHJIbHO BJ1H$!eT Ha nOJ1HYIO npOBo,nHMOCTb. ,[(J1S1
u u u
BOJIHOBo,aa C YMeHbllleHHOH BbICOTOI1, r,L(e ,naHHbIM OXBaT 3HaQHTeJIeH, Tpy,nHO pac-
CQMTaTb JIa)l(e ,nHarpaMMY HanpaBJIeHHOCTM. B HaCTOSlm:ee BpeMSI OTCyTCTBYIOT Me-
TOJIMKH paCqeTa 60KOBbIX meJIeH, I1CnOJIb3YIOm:He BapHaUHoHHbIH MeTO,n MJIH Me-
TO,a MOMeHTOB. npoeKTHpoBaHlle aHTeHHoH pemeTKIf CTPOHTC$! Ha ,naHHbIX,
nOJIyqeHHbIx nyTeM H3MepeHI1H, 11 ,aa)l(e B 3TOM CJIyqae pa60Ta C 60KOBbIMH m:eJISI-
MI1 I1MeeT CJIO)l(HOCTI1. 113-3a 60JIbIllOM B3al1MHOH CBSl311 Me)l()],y 60KOBbIMH rn:eJISlMM
(no cpaBHeHlf10 co CJIyqaeM CMell.{eHHbIX m:eJIeH, pacnOJIO)l(eHHbIX Ha IlIlfpOKOH
CTeHKe BOJIHOBO,l{a) npOBo,l(HMOCTb 06bIQHO H3Mep$!eTC5I HHKpeMeHTHbIM 06pa30M.
To eCTb H3MepSllOTCSI JIaHHbIe ,nJI5I KaCKa,LI,a pe30HaHCHbIX m:eJIeH; 3aTeM On;Ha H3
u u
rn:eJIeH 3aKpbIBaeTC5I, H CHOBa npOH3BO,l(5ITCSI H3MepeHH5I .LUISI OCTaBllIHXC5I m:eJIeH.
B pe3YJIbTaTe TaKHX HHKpeMeHTHbIX H3MepeHHH [83] onpe,lIeJI5IeTCSI npOBOJIH-
MOCTb pe30HaHcHoH meJ1H npH HaJII1 1 fHH B3aHMHoH CB5I3H. O,l(HaKO ,l(JISI onpen;eJIe-
HH$! pe30HaHcHoM ,l(JIHHbI KaCKan;a m:eJIeH C 3a,LI,aHHbIM yrJIOM HaKJIOHa He06xo,LUfMO
HCnOJIb30BaTb MeTOn; np06 H OIIIH60K. ,l],J1$! yrJIOB HaKJIOHa, MeHbllIHX 15°, paCCQH-
TaHHa5I pe30HaHCHa5I npOBO,l{HMOCTb H3MeH5IeTC5I npOnOPQHOHaJIbHO sin 2 8:
G
Yo
480a / b . 2 e
SIn .
nRo(2a / A) 4(3 / k
(5.5)
3Ta BeJIHqHHa H 3HaQeHH5I, nOJIyqeHHbIe nyreM MHKpeMeHTHbIX 1f3MepeHHH ,LLJISI
BOJIHOBO,lIa WR-90 Ha QaCTOTe 9375 MfQ ,LUISI m:eJIH mHpHHoH 1/16 tUOHMa, npeJI-
CTaBJIeHbI Ha pHC. 5.21. 06e KpHBbIe CJIe,l(yIDT 3aBHCHMOCTH sin 2 8, oc06eHHo JIJUI
MaJIbIX yrJIOB. IIpH 3TOM HHKpeMeHTHoe 3HaqeHHe 60JIbllIe, qeM npOBOn;HMOCTb ,l{JUI
oT,aeJIbHOH m:eJIH. KOHeqHO, pe30HaHCHble ,aJIHHbI ll.{eJIeH B aHTeHHOH pellIeTKe 6y-
,lIyr pa3JIHqaTbCSI; n03TOMY ,LUISI nOJ1yqeHH5I ,aaHHbIX, .l(OCTaTOQHbIX ,l(JI5I paCqeTa, He-
06XO,lIHMbI nO.l(p06HbIe H3MepeHH5I. XOTSI TaKHe H3MepeHH5I npOBO.l(HJIHCb Ha MHO-
rHX npe.l(npHSlTH5IX, .l(OcTynHaSl no 60KOBbIM I.IJ;eJISlM 6a3a ,aaHHbIX CKy.l(Ha. PaCqeT
MeTO.l(OM KOHeqHbIX 3JIeMeHTOB, npH KOTOpOM 06JIaCTb m:eJIH 3anOJIH5IJIaCb QMJIHH-
u u
,apaMH TpeyrOJIbHOrO CeqeHH5I C ,l(JIHHOH, paBHOM TOJIIl{HHe CTeHKH, BbInOJIHeH B
pa60Te If .lIp. [50]. OXBaTa BOJIHOBOn;a KOHuaMH 60KOBbIX m:eJIeH MO)l(HO H36exaTb
npH HCnOJIb30BaHHH m:eJIH H-06pa3HoH Q:>OPMbI [21], y KOTOpOH npope3b, nepneH-
,l{HKyJI5IpHaSl pe6py BOJIHOBOn;a, ,L(OnOJIHeHa Ha KOHQax npOpe35IMH, naparrJIeJIbHbIMH

0.2
0011
..Q
f--
U
o

:s:
I::!
o
r::Q
o
0..
t::
0::
ro
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r::Q 0 .01 '
::s:

0.002
o
5.2. menu 8 80J/H0800e 
:X
10
20
30
YrOJI HaKJIOHa (rpaJ];.)
PRC. 5.21. Pe30HaHCHaR npOBO,Z:(HMOCTb 60KOBOH rn;eJIH, 9375 Mfu, a = 0.0, b = 0.4
pe6paM. TaKHM o6pa30M, meJIb noxoxa Ha 6)'KBY H. ,n;eJIaR HapYXHbIe npope311
HeCI1MMeTpI1QHbIMI1, MO)I(HO Bapbl1pOBaTb CBR3b; npl1 3TOM MoxeT 6bITb nOJIyqeHa
,[(IDKe KpyroBaH nOJIpI13al(HH [43]. PaCQeT H-06pa3Hblx lI(eJIeM MeTO,l(OM MOMeHTOB
np0I13BO,l(I1TCH B pa60Te [135].
-
J];pyrl1e Tl1nbI meJIe:ti, Hanpl1Mep, B036y)1(,[(aeMble IIITbIpeM, ,l(l1a<pparMoH, 11
CKpeweHHbIe weJIH 06Cy)I(,[(alOTCH B pa60Te [87].
5.2.3. enM B nonOCKOBOM nMHMM
meJII1 B nOJIOCKOBOM JII1HHH 06hIQHO npe,l(CTaBJIRIOT C060H Y3K11e npRMoyrOJIbHble
v
pe30HaHCHbIe meJII1, npope3aHHble BO BHelliHeM npOBO,l(HlI(eM 3KpaHe nOJIOCKOBOH
v v
JII1HI1I1, npl1 3TOM l(eHTpanbHMH npOBO,l(HI1K nOJIOCKOBOI1 JII1HI1I1 Opl1eHTl1pOBaH
nepneH,[{I1KYJIRpHO I..QeJIH H CMemeH OTHOCHTeJIhHO ee u;eHTpa, a ,l(JII1Ha lI(eJIH COOT-
BeTcTByeT YCJIOBHRM pe30HaHca. B 3TOM CJIyqae MO)l(eT 6hITh BhIQHCJIeHa npOBO,l(H-
MOCTh [11]. K npHMepy, nOCpe,l(CTBOM TpaBJIeHHH <pOJIhrHpOBaHHoro ,l(H3JIeKTpH-
qeCKOrO JIHCTa C03,l(aIOTCH m:eJIeBbIe H3JIyqaTeJIH, a 3aTeM <pOJIbrHpOBaHHbIM C ,l(BYX
v v
CTOpOH ,l(H3JIeKTpHQeCKHH JIHCT npOTpaBJII1BaeTCH C O,l(HOH H3 CTOpOH ,l(JI C03J(aHHR
JII1HHH nI1TaHHH. 3TI1 ,l(Ba JII1CTa CKpeTIIDlIOTCH BMeCTe, 11 nOJIyqaeTcH lI(eJIeBaR no-
JIOCKOBaR aHTeHHaH perneTKa. XOTH BHellIHHe (H3JIyqaTeJIhHbIe) xapaKTepHCTI1KJi1
meJIH B nOJIOCKOBOll JIHHHH aHanOrHQHhI xapaKTepHCTHKaM weJIH B 6eCKOHeQHOM
3a3eMJIeHHOM 3KpaHe, Ha BHyrpeHHlO1O nOJIH}'IO npOBO,l(HMOCTh lI(eJII1 CIDIbHO BJIH-
HeT 6JIH3KO pacnOJIO)l(eHHbIll no,l( HeM 3a3eMJIeHHbIH 3KpaH. B pe3YJIbTaTe nOJIOca
nponycKaHHH, onpe,l(eJIHeMaH no IIOJIHOMY BXO,l(HOMY conpOTHBJIeHHIO, OKa3bIBaeT-
v
CR CHJIbHO orpaHHQeHHoH.

b DW60 5. 3J1eMeHmbl oHmeHHou peUlemKU
B J1PyroH KOHCTPYKUI1I1 I1CnOJlb3yeTc5I nOJlOCKOBa51 JII1HI15I, norvlemeHHa51 B Me-
TaJIJIMQeCKI1H Kop06 (nOJlOCKOBa51 JII1HM5I C 3aKOpOQeHHblMI1 60KOBblMl1 cTeHKaMI1,
napaJIJIeJlbHbPvfM npoBollHMKY n0J10CKOBOM JIJ1HJ1I1). KIDKD,a51 J1I1HeHKa aHTeHHoH
perneTKI1 noxo)l(a Ha BOJIHOBOL( (CM. pRC. 5.22) C TeM OTJII11.Jl1eM, LITO Bce ll(eJIM
HaXO)JJITC5I Ha ueHTpaJIbHOH JII1HI1I1 [90]. TIOJIOCKOBbIl1: npOBOllHI1K nOlI Ka)K)10H
u u u
llleJIblO CHMMeTpl1QHO nOBepHyr OTHOCMTeJlbHO QeHTpa Ka)l()lOM JII1Hel1HOI1 CeKUMI1,
npl1 3TOM BeJIlf1IMHa CBH3M npOnOpLI.MOHaJIbHa yrJ1Y HaKJIOHa nOJIOCKOBOfO npOBO.LI.-
HI1Ka. l1cnoJlb30BaHI1e 3MeeBHL(HOrO nOJIOCKOBOro npOBOllHI1Ka C weJIHMI1, pacno-
J10)l(eHHbIMM BJIOJlb cpe,UHei1 JII1HI1I1, YCTpaHHeT np06JIeMbl pa36aJIaHCl1pOBKM 11 He-
paBHOMepHOCTM HarpY3KI1, KOrL(a rrOJlOCKOBbl:H npOBOllHI1K 6bIJI np5IMbIM, a JlJ.eJIJ1
HaKJIOHHbIMlf. llieJIlf 3L(eCb pacnOJIO)l(eHbI C rnarOM, paBHbIM .lIJIlfHe BOJIHbI (B no-
JIOCKOBOH JIMHMM), n03TOMY I1HBepCMI1 <pa3bI He Tpe6yeTCH. Ll.JIH yqeTa B3alfMHoi1
CBH311 IICnOJIb3yIDTCH MeTOL(bI, Onl1CaHHbIe B rJI. 7. I1cCJIellOBaJIMCb TalOKe nonepe1.J-
Hble ll.(eJIlf co CMew:eHlleM [107]
;t"- ..:s'
....,.... .... .,.t\o _...,.,., _ 1......
'_......" :' j of -,' i'
". 07' ;
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.
'''':r,;\i; 1. '.'
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-. t ". '". .
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.: '.', .'.:. .:..;' .. .'... . . .':'.:.:.. .' . .-. ...... .. .':.
. \ i \ r \ 1\  1\ \ \ I\" \
PHC. 5.22. AHTeHHa5I peweTKa Ha 6a3e nOJIOCKOBOM JII1HI1I1, nOMellleHHoH B Kopo6
5.2.4. BonHoBoAbl C OTKpblTblM KOHLJ.OM
BOJIHOBOl[Hble 113JIyqaTeJIl1 OTJIMQalOTCH OT ll(eJIeBbIX 11 lllInOJIbHbIX TeM, 1.JTO ,UJI5I
HI1X Ba)l(HOe 3Ha4eHlfe I1MelOT 3aTyxalOll(Me MOL(bI. HeCOMHeHHO, 3TH MOllbl MO)l(HO
KOHTpOJIMpOBaTb, MlfHI1MM3MPYH 3cpcpeKTbI CKaHl1pOBaHMH. ll03TOMY L(aHHble 3JIe-
MeHTbI 06C)')K1J,a1OTC51 B fJI. 7.
5.2.5. BonHoBoA, BCTpoeHHbl B nOAnO>KKY (SIW)
O.uHI1M 113 cnoc060B YMeHbllleHI15I CTOMMOCTM II np0,UOJI)I(I1TeJlbHOCTI1 113rOTOB-
JleHI151 meJIeBblX aHTeHHbIX perueToK 5IBJI5IeTC5I I1CnOJIb30BaHI1C SIW TeXHOJlOfI1H:
BOJIHOBOll 06pa3yeTC5I pH.lIaMM npOBOD:5IlUMX lllTbIpbKOB Me)K)J.y napaJIJIeJ1bHbIMM
nJIaCTJ1HaMI1. 3TOT BOJlHOBOll 6bl1l npl1MeHeH paHee B CI1CTeMe TIMTaHRH TIJIOCKOna-
paJIJIeJ1bHOrO 113JIYQaTeJI5I [44 J. CJ1eD:YIOIllJ1M ruaroM CTaJIO C03,UaHl1e BJ1pTYaJ1bHOrO
np5IMoyrOJIbHOrO BOJIHOBO.lIa B 06JIaCTl1 Me)l()],Y naparrJIeJIbHbIMI1 nJIaCTI1HaMM [24].
Ha plfC. 5.23 nOKa3aHa cxeMa SIW C Y.lIaJIeHHOM BepxHei1: npOBO.lIHIlle:H nJIaCTI1Hoit
06JIaCTb Me)K)1y napaJIJIeJIbHbIMI1 TIJIaCTI1HaMI1 MO)l(eT 3anOJIH5ITbCH JII13JIeKTpJ1KOM


5.3. PynopHlJle TEM U3flyrtameJ/U 
. I
PHC. 5.23. SIS; BepXHHH nJIaTa y.n;arreHa
HJIH B03.n;YXOM. CooTHolIleHHH 3KBHBaJIeHTHOCTH, CBH3bIBalOIl(He SIW co CTaHJ(ap-
THbIM npHMoyrOJIbHbIM BOJIHOBO,n:OM, npHBoMTCH B pa60Te [17]:
, 2a [ nw w ]
a = -arc cot -In- .
1t 4a 4R
(5.6)
B 3TOH $OpMYJIe a' - llIHpHHa SIW; W - Me)l(QeHTpOBoe paCCTOHHHe Me)l()];Y
IllTblpbKaMH; R - pa;:J;HYC I1ITbIpbKa; a - IlIHpHHa 3KBHBaJIeHTHOro npHMoyrOJIbHO-
ro BOJIHOBo,n:a. B ypaBHeHHH (5.6) no,n:pa3yMeBaeTCH, qTO R < wj4, a > a'. ECJIH R >
> wj4, TO a > a'. C 3THMH <poPMYJIaMH MOryr HCnOJIb30BaTbCH CTaIUI.apTHble BOJIHO-
B01(HbIe Ta6JIHU:bI. TIO.up06HbIe paCqeTbI pacnpOCTpaHeHHH BOJIH B SIW npl1Be,n:eHbI
B pa60Te [126]. Pa60TbI no SIS (SIW co meJIHMH) BKJIlOqaIOT B ce6H HCCJIe,n:OBaHHH
npo,n:OJIbHbIX Il(eJIeii [119], aHTeHHbIX perneTOK Ha OCHOBe npo,n:OJIbHbIX meJIei1
[133] H aHTeHHbIX perneTOK Ha OCHOBe HaKJIOHHbIX m:eJIeH ,n:BOHHOH nOJIHpH3aUHH
[92]. HaKOHeQ, aHTeHHaH pellIeTKa SIS BOJlHOBO.n;OB HCnOJIb30BaJIaCb ,lUIH nHTaHHH
pe<pJIeKTOpa [18]. SIW HCnOJlb30BaJIHCb TalOKe B KaqeCTBe <l>a30Bpam:aTeJIei1, r.n;e
,n;orrOJIHHTeJIbHble IIlTblpbKH o6eCneqHBaJIH c.n;BHr <pa3 [19, 113].
5.3. PynopHble TEM M3nY"l8TenM
5.3.1. 3BOnlOL4MSI pynopHblx TEM M3nY'laTeneM
PynOpHbIH TEM H3.rryqaTeJIb C03,n:aeTCH ,n:BYMH HanpaBJIHIOm:HMH, 06pa3yIOIl(HMI1
HenpepbIBHbIi1 HJIH CT)'TIeWIaTbIH pynop C TEM MO.LJ;OH Me)l{JI;Y HHMH. B OTJIHqHe OT
....
BOJIHOBo,n:Horo pynopa, r.ne cy:w:eCTByeT OTCeQKa nHTalOm;eH MO,n:bI, nOJIoca nponyc-
KaHHH TEM pynopa MO)l(eT npeBbIrnaTb OKTaBY. HH3KOQaCTOTHbIe HMne,n:aHCHbIe
xapaKTepHCTHKH onpe,n:eJIHIOTCH, rJIaBHbIM o6pa30M, BXO,n:HbIM OTBepCTHeM pynopa.

 rAoeo 5. 3AeMenmbl onmennou pememKU
06Cy)f(,LI;aeMbIe ,aaJIee pa3JIMqHbIe BM,abI TEM pynOpOB 06pa3yroTc$I M3 6HKOHMQeC-
KOH aHTeHHbI, KaK rrOKa3aHO Ha cxeMe, B3$1TOH H3 pa60TbI [110], 11 npe,aCTaBJIeH-
HOH Ha pMC. 5.24. B p$I,ae pa60T, BbIrrOJIHeHHbIX B rrepl1o,n BTOpOH Ml1pOBOH BOHHbI,
npOH3Bo,aHJIaCb ,ae<J;>opMaUM$I If rrOBopOT V-06pa3Hofo 1.(l1nOJI$I, KaK If306pa)l(eHO Ha
pl1C. 5.25 [2]. B pa60Te [115] 6bIJI H3fOTOBJIeH C)')KalOlUI1HC$I ,aBYMepHbIH TEM py-
nop Ha OCHOBe MeTaJIJII1QeCKI1X nOJIOC (CM. pHC. 5.26). TpexMepHbIe (3D) TEM py-
nopbI C paCIIIl1peHl1eM KaK pacTpy6a, TaK M IlIMpHHbI fOpJIOBHHbI 06eCneQMBalOT
JIytlIllHe MMrre,aaHCHbIe xapaKTepHCTHKH B IIIHpOKOH rrOJIoce QaCTOT [27]. CxeMa
TpeXMepHoro TEM pyrropa nOKa3aHa Ha pHC. 5.27. B [57] HCnOJIb30BaH pynop Ha
OCHOBe rpe6eHQaTOrO BOJIHOBo,na, r,ae rpe6HM I1MelOT npHMepHO 3KcrrOHeHl{:HaJlb-
Hoe C}')KeHMe OT pacTpy6a ,no Bxo,aHoro oTBepCTH$I.
2/ --.
----
--
-
-. 
K
XapaKTepHCTH1JeCKHM Zt
HMTIe,L:(aHC
-
1
/
.)
PHC. 5.24. I1epexo.a OT 611KOHI1QeCKOrO .a11110JUI K JII1HI1I1 IIepe.aaQI1 [110]

(0)
(b)
(c)
s
w
./
, ,
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, /
'/',
;/
PHC. 5.25. npOTOTI1IIbI Ha OCHOBe ,UHIIOJIH B KOaKCHaJIbHOI1 060JIOQKe [2]
BnOCJIe,aCTBHH 6billO 06Hap)')l(eHO, q'f0 60KoBbIe CTeHKH MOryT 6bITb y,aarreHbI, 06-
pa3YSI TEM pynop. BepXHl1e M HJiDKHHe CTeHKH TalOKe OKa3arrHCb HeCYJ.l(eCTBeHHbIMH.
XOpOllIHH pyrrop 06pa3yIDT O,aHH TOJIbKO pe6pa; CJIeJIyIDIUHM llIafOM 6bIJIO YBeJIHQeHHe
llIHpHHbI rrpOBo,aHHKa Ha KIDK,[(OH H3 CTOpOH [115] H H3fOTOBJIeHHe pynopa rryTeM
1]>aBJIeHIDI pyrrOpOBMHOH <J;>OpMbI B <}>OJIbfMpOBaHHbIX ,aH3JIe:KTpHQeCKMX JIHCTaX [97,
33]. B nOCJIe,aHeH pa60Te ORa HOClUla rrpWIYMHBoe Ha3BaHHe «AHTeHHa BHBaJIb,lJ;H»,
RO 3TOT TepMHH rrpe,aCTaBllileTC$I Hey,aaQHbIM, rrOCKOJIbK)' OH 6ecco,n:ep)l(aTeJIeH.

1 ,
PRC. 5.26. 3JIeMeHTapHbIH TEM pyrrop [115]
5.3. Pynopllble TEM U3JlY"lameJlU

1
""
,"
.....
. .:.. .
. .
.- .' . .
" ...'c,';;J "'c.' i \Ii.
'.' , ' .. ;';';"1V";;" 'y", '
...... ,-' '. .-
. .
., .... 
{j,;': " .;J
.... .....-:': . '. ' ,, ' , : . "' . , , .
j: '.,
Cyru;eCTByJOT HeCKonbKO BapMaHToB TaKJ1X
neqaTHbIX TEM pynOpOB. MeTaJIJIMQeCKJ1e npo-
BO,L(HMKH, 06pa3yJOIUMe CTOpOHbI pynopa, MOryr
pacxo,aMTbCH Ha He60nbllIoe paccToHHMe MJIll co-
e,L(HIDITbCH C npoBo,aHMKaMM CMe)f(HbIX pynOpOB.
TIpOBO,aHHKH pynopa MOryr 6bITb BbITHHyTbIMM
HJIM HMeTb <POPMY fna;:(KHX JIeneCTKOB [32, 30].
PacTPy6 pynopa MO)f(eT 113fH6aTbcH npHMepHO
3KcnOHeHQHaJIbHbIM 06pa30M, a MO)f(eT HMeTb
<pHKcMpoBaHHbIH yron paCKpbITIDI (KaK B cnyqae
V-06pa3Hofo ,L(MnonH) HnH 6bITb cTyneHQaTbIM,
KaK B pyrrope Ha 6a3e CTYneHQaTOrO BOJIHOBO,L(a.
BapHaHTbI pynopoB C nOCTOSlHHbIM yrJIOM pac-
KpbITHH H CTYneHqaTble pynOpbI HOCHT Ha3BaHHe
'-'
Il(eneBbIX aHTeHH C «nHHeHHbIM C}')KeHMeM» 11
«nOCTOSlHHOH llIMpMHOth) [136, 137, 53, 108].
3Ta TepMHHonOfIDI HeY,L(OBneTBOpHTeJIbHa, no-
CKonbKY TepMHH «meneBaH aHTeHHa» no.apa3Y-
MeBaeT H3nyqeHHe Qepe3 rn:enb, TOf.aa KaK Bce PRC. 5.27. CxeMa TEM pynopa
3TH aHTeHHbI HBJUlIOTCH pynOpHbIMH TEM aH-
TeHHaMH oceBOfO H3nyqeHMR. ,LI:nH nHTaHMSI py-
nopHOfO H3nyqaTelliI Bcex nepeQHCneHHbIx neqaTHbIX aHTeHH qaCTO 6bIBaeT y,a06HO
Hcnonb30BaTb nonOCKOBbIe H MHKpOnOJIOCKOBble nHHMI1, meJIeByJO JIHHHIO, KOllJIa-
HapHbIH BonHOBO,a H TaK ,L(aJIee. Bo Bcex CJIyqaSlx np" pa3pa60TKe lliMpOKononOCHbIX
-

 Dwea 5. .9JU!MeHmbl aHmeHHou peUlemKU
CMCTeM B036)')K.L1:eHMR, RBJUIIOI.I..(HXCR nepexo,UHbIM 3BeHOM Me)l(,[{Y nepe,UalOIUeH JIH-
HHeM H pynOpOM, npORBJIReTCR MHoro M306peTaTeJIbHOCTI1. CymecTByeT MHoro TH-
v
nOB CMMMeTpHpYIDIUHX YCTPOHCTB B neqaTHOM HCnOJIHeHHH; MHKpOnOJIOCKOBOe
CHMMeTpMpYIDmee YCTPOHCTBO H306pIDKeHO Ha pHC. 5.28 [116].
r---------------------------------------l
 j
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t. .
I: I
t .
· .'. , """'.,.. f
 i t;,.,.,\;",:",,,,,,\..,:,\::,,:..:. .' '".. «
t,'.'- ": t
i ·
t':: \; I
: * \:,:";;\C', ",,"""'-""'"" '. ,,,,,,'...-" """..",.::,,, . ;
i ...',.,.,,"'-.... ,'" :.,(, :
: qeTBepTbBOJIHO-;l  t
I BOll TpaHC- _\:'--,
: <popMaTOp ::!: "j; !
.s-' ,Lbf3JIeKTpHQeCKaH
.
/' l1oMO>KKa
...
...
EoEr
eo
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.
I
t
I
.
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.

t
j
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: :- 3a3eMJIeHHbIH 3KpaH
i l
c_.__ I_______________l
\,
,

"
,
'-.MHKP0I10JIOC-
KOBbIH BXOL\
"

"
\
".
"
"
-0
'- b :
.
i
r
I

s
"
,
s
I
t-.. CBH3aHHbIe
MHKp0I10-
1IOCKOBble 1I11H11H
(HeQeTHaH MOJJ:a)
s-V-LTSA
I

i
i
-t
.
.
-- KOTIJIa-
HapHaH
1101l0CKOBaR
11 11HHR
Pac. 5.28. MHKpOIIOJIOCKOBOe COfJIaCYIOrn;ee YCTPOMCTBO [116]
rIpH KOHCTpYHpOBaHHH aHTeHHbIX pemeTOK Ha 6a3e neqaTHbIX TEM pynOpOB
v
Ba>KHO npOBO,L(MTb pa3JIMQHe Me)l(,[{Y pynopaMH C npOBO,UHMKaMH KOHeqHOH IlIHpH-
v
HbI M pynopaMH, B KOTOpbIX npOBO,UHHKH RBJIRIOTCR QaCTblO npOBO,L(RI.I..(eH nJIaTbI.
B nOCJIe,L(HeM CJIyqae TOKH, 06pa30BaHHbIe B036)')K.L1:eHHeM O,l(HOrO Pynopa, MOryr
6bITb Henocpe,UCTBeHHO CBR3aHbI co CMe)l(HbIMH pynopaMH. C TOqKH 3peHHR corJIa-
COBaHHR liMne,l(aHCa 60JIbllIMX aHTeHHbIX pellieTOK 3TO MO)l(eT MMeTb CBOM npeHMY-
m;eCTBa HJIH He,l(OCTaTKH.
5.3.2. PaC'IeT M KOHCTPYMpOBaHMe pynopHblX M3nY'laTeneM
O,UMHOQHbIe TEM pynOpbI MOryr paCCqHTbIBaTbCR MeTO,l(OM MOMeHTOB C MO,l(eJIH-
pOBaHHeM yqacTKoB nOBepXHOCTH MeT01(OM MOMeHTOB [51], npH KOTOpOM BJIHRHHe
,l(H3JIeKTpHQeCKOrO JIHCTa yqMTbIBaeTCR C nOMOI.l..(blO TeopMH B03MYI.I..(eHHH. I1cnoJIb-
3yIOTCR TaIOKe MeTO,L(bI npOCl'paHCTBeHHbIX ceTOK; FDTD (MeTO,l( KOHeqHbIX pa3-
HOCTeH BO BpeMeHHoH 06JIaCTH), npHMeHeHHbIM B pa60Te [122] K O,nHHOqHbIM
TEM pynopaM M MaJIbIM aHTeHHbIM pellIeTKaM Ha OCHOBe pynopHbIX H3JIyqaTeJIeH.
TIpH 3TOM nOJIyqeHbI xopOIlIHe pe3YJIbTaTbI, HO BbIqMCJIMTeJIbHbIH npouecc He 3$-
<peKTHBeH no 3aTpaTaM. B nO,l(XO,l(ax C HCnOJIb30BaHHeM MeHbllIHX BbIqHCJIHTeJIbHbIX
MOII(HOCTeH KOHTYP pynopa 3aMeHReTCR 60JIbIIIHM qHCJIOM MaJIeHbKHX CTyneHeK,

5.3. PynopH/>le TEM u3I/Y'lameJ/u 
'-' '-'
MCnOJIb3YIDTCR ypaBHeHI1R m:eJIeBOI1 JII1HI1M ,lLJIR Ka)l{,l(OI1 cTyneHbKJ1 11, HaKoHeu;,
ypaBHI1BaeTcR nOTOK MOm:HOCTI1 Me)l(,[(y cTyneHbKaMI1. ,l].JIR nOJIyqeHI1R ,aMarpaMMbI
HanpaBJIeHHOCTM I1CnOJIb3yeTcR pe3YJIbTl1pYIOee anepTypHoe pacnpe,aeJIeHl1e C
npMMeHeHMeM <PYHKUI1I1 rpl1Ha ,lLJIR nOJIyrrJIOCKOCTI1 [25, 52]. llOJIyqaeMble pe3YJIb-
TaTbI He TaK XOpOllIM, KaK Te, KOTopble nOJIyqeHbI MeTo,aOM COrJIaCOBaHMR MO,a Ha
'-'
MaJIbIX cTyneHbKax B BOJIHOBO,aHbIX pynopax, HO npl1 pa3Mepax BXO,aHbIX OTBepCTMM
pynopoB B HeCKOJIbKO ,lLJII1H BOJIH M 60JIee pe3YJIbTaTbI JIyqrne. 113-3a HaJIHqHR
60JIbIIlOrO KOJIHqeCTBa nepeMeHHbIX: IllMpMHbI Bxo,aHoro OTBepCTI1R, ,lLJIMHbI pyrro-
pa, reOMeTpl1H npOBo,aHHKa pynopa, ,aM3JIeKTpHQeCKOH npOHl1uaeMOCTI1 11 TOJIIl{I1-
HbI ,aM3JIeKTpI1QeCKOrO JIMCTa (eCJII1 TaKOBOH MCnOJIb3yeTCR) M TMna nMTaHMR npl1-
BeCTI1 paCQeTHbIe ,l:(aHHble 3J(eCb HeB03MO)l(lfO, oc06eHHO ,lLJUI OTHOCI1TeJIbHO
He60JIbIIll1X pynopoB, npMro,aHbIX ,lLJIR MCnOJIb30BaHMR B aHTeHHbIX peIIleTKax. Pe-
KOMeH,ayeTcR npOH3Bo,aI1Tb paCQeT MeTo,aOM MOMeHTOB M C06JIIO.aaTb nOCJIe.aOBa-
'-'
TeJIbHOCTb npOeKTl1pOBaHI1R, npl1 KOTOpOI1 Haql1HalOT co CJIyqaR OTCyrCTBMR ,aH-
3JIeKTpl1Ka 11 H,L(e3JIbHOrO nI1TaHIDI, a 3aTeM ,a06aBillI1OT COOTBeTCTBYIOl1e nYHKTbI.
TIOJIb30BaTeJIRM HyxaIO I1MeTb B BH,ay, qTO .n.B}'MepHble pynopbI MOryr C03,aaBaTb
CMJIbHyro KpOCC- nOJIRpH3aUHIO B ,aHarOH3JIbHOH llJIOCKOCTI1 [61]. EblcTpoe H3MeHe-
HMe nOJIRpH3aUI1H ,aOCTHraeTCR npOCTO C nOMOIUblO ,aBYX pynopoB, pacnOJIOXeH-
HbIX no,l:( npRMbIM yrJIOM, HJII1 npH OC060H KOH<pHrypaQHH C qeTblpbMR pyrropaMH
H I.(HJIHH.lI:pHqeCKHM pe30HaTopOM no,a HI1MH. 3.n.ecb pyrrOpbI 06pa3YIDT QeTblpeXKO-
HeqHYJO 3Be3,ay C 06pam:eHHbIMH BHyrpb BXO,aHbIMH OTBepCTHRMH [93].
5.3.3. AHTeHHble peweTKM Ha OCHOBe TEM pynopoB
XapaKTepHcTHKH aHTeHHOH peIIleTKH Ha OCHOBe TEM pynOpOB 3aBHCRT OT Toro,
KaK CBR3aHbI OT,aeJIbHble pynOpbI: TOJIbKO l(enblO nHTaHHR HJII1 npRMbIMM TOKOBbI-
MM nyrRMH Me)l(,l(y COCe,l:(HI1MH pynopaMI1. ECJIH OTBepCTHR pynOpOB BbITpaBJIeHbI B
rrpOBo,aRm:eM CJIoe, TO Me)l(,l(y ropnOBHHaMH H BXO.n.HbIMH OTBepCTHRMM Bcex pyno-
pOB HMelOTCR TOKonpOBo,aRm:He yqacTKH. npOBO,aRIUl1e yqacTKH TalOKe CBR3bIBalOT
pynopbI C rOpJIOBI1HaMI1 M BXO,aHbIMH OTBepCTHRMM coceJ(HMX pynopOB. B pe3YJIbTa-
Te HMne,aaHC B 3aBHCHMOCTH OT QaCTOTbI ,LUIR <pI1KCHpOBaHHoro nOJIOXeHHR nyqa
'-' '-'
pellieTKI1 HJIH HMne,aaHC rrpH CKaHl1pOBaHl111 ,lLJIR CKaHMPYIOIUeM aHTeHHOI1 peIlleT-
KM 6y,aeT pa3JIHqHbIM. KOHeqHO, MHoroe y,aaeTCR BbIRCHHTb C nOMOIUblO xapaKTe-
pl1CTHK M KOHCTPYKTMBHbIX oc06eHHOCTeH 6eCKOHeQHbIX aHTeHHbIX peIlleTOK, ,lLJIH
KOTOpbIX B CneKTpaJIbHOM npeJ(CTaBJIeHMH (<I>JIOKe no,axo,a) KOJII1QeCTBO pernaeMbIX
ypaBHeHMH HeBeJIHKO. B pa60Te [22] MeTo,aOM MOMeHTOB np0l13Be,aeH paCQeT 6ec-
KOHeQHOH aHTeHHOM pemeTKI1 JIHHeHHO pacmHpRIOIUMXCR TEM pynopoB, a B [109]
pacnpOCTpaHeH 3TOT no,axo,a Ha KpMBOJIMHeHHble TEM pynopbI. 3TI1 paCQeTbI cno-
C06HbI npe,l:(CKa3bIBaTb Ba)I(Hble RBJIeHHR, Hanpl1Mep, nORBJIeHl1e CJIenbIX yrJIOB npl1
CKaHHpOBaHl111 B E-nJIOCKOCTH. 06e JIHHeHHbIe nOJIRpH3al(HH MOryr 6bITb 06ecrre-
qeHbI rryreM npn,aaHHR ,aBYM neQaTHbIM nJIaTaM pe6pl1CTOM KOH<pl1rypaUHM [46] .
B ,apyroH KOH<pMrypaUHH ,lLJIR nOJIyqeHHR O.n.HOH nOJIRpH3al(HH MCnOJIb3YlOTCR ne-
'-'
qaTHbIe pynOpbI, a ,LUIR ,apyrOI1 nOJIRpH3al(HH - BOJIHOBo,aHaR Mo.aa Me)l(,[(y neqaT-
HbIMI1 llJIOCKOCTRMH [78, 79]. npH Bcex KOH<pl1rypaUI1HX OCH pyrrOpOB CMOTpRT B
'-'
HarrpaBJIeHl111 rJIaBHOrO JIyqa, OHI1 He MOryr JIeXaTb B IlJIOCKOCTI1 aHTeHHOI1 peIIleT-
KM, nOCKonbK)' .n.JIHHbI pynOpOB npeBbIllialOT nOJIOBI1HY ,lLJII1HbI BOJIHhI. AHTeHHhle
pemeTKH Ha OCHOBe TEM pynOpOB no,apo6HO 06Cy)I()laIOTC.H B fJI. 7.

 f/la8a 5. 3/leMeHmbl aHmeHHou peUJemKU
5.3.4. AHTeHHbl MMnnMMeTpoBoro AMana30Ha
B rrOCJIe,nHHe rOL(bI rrpHJIaraJIHCb 60JIbllIHe YCHJII1JI B c<l>epe 06'be,nHHeHIDI TBep,no-
TeJIbHbIX YCTJ)OHCTB C aHTeHHaMH, C03,l(aHHbIMI1, rJIaBHbIM o6pa30M, Ha OCHOBe V-06-
pa3HbIX rrOJIOCKOBbIX ,nHIIOJIeH H TEM pynOpOB [66]. B MHJIJIlfMeTpOBOM ,l(Harra30He
,lUIHH BOJIH 6JIOKH reHepaTopa HJIH rrpe,nYCHJIHTeJI5I-CMeCHTeJI5I MOryr 6bITb BbIrrOJIHe-
HbI Ha TOM )Ke lIJIaTe, qTO H aHTeHHa. B pa60Te [104, 105] rrpHBo,nHTC5I 0630p TaKHX
YC1pOMcTB. Bo MHorHX pa60Tax paCCMaTpHBaIOTC5I, rJIaBHbIM o6pa30M, TBeplXOTeJIb-
HbIe YCTpoHcTBa, a He aHTeHHbI, rr03TOMY OHH 3,l(eCb He 06caIOTC5I. BapHaH-
TOM neqaTHOrO IIJIOCKOrO TEM pynopa 51BJI5IeTCSI pynop C JIHHeHHbIM Cy;KeHHeM If
,aHnOJIbHbIM B036eHHeM; CTeHKH pynopa, KaK H <pH,lI,ep [23], H3rOTOBJIeHbI nyreM
TpaBJIeHH5I H MeTaJIJIH3aU;HH TOJICTOH nO,lUIO)l(J(H [34, 104, 105]. nO,lLTIo)l(J(a H3 HH3KO-
TeMnepaT)'pHOH KepaMHKH LTCC (Low-Temperature Cofired Ceramic) HMeeT,MaJIbIe
nOTepH If COBMeCTHMa C CBq-qHrraMH (MMIC TeXHOJIOrHIf). 06bIqHO B ,l(Harra30e
30 rru; HCrrOJIb3yIOTCSI MHoroypOBHeBbIe rreqaTHbIe aHTeHHbI (stacked patcb) Ha
LTCC [89] H neqaTHbIe pellIeTKM [3]. B rrOCJIe,l(HeH pa60Te H3rH6 llJIeq CJI}')KHT He
,lLTI5I nO,l(aBJIeHHSI aCHMMe1pHqHbIX MO,l( B036eHIDI (CM. pa3,neJI 7.4.3), a, CKopee,
,lIJISi. YBeJIHqeHHR llIHpHHbI .rryqa B E-IIJIOCKOCTH Ha qaCTOTe 20 rru;. B MOHOHMnYJIb-
CHOH aHTeHHOH peIIIeTKe ,l(Hana30Ha 32 rrIJ, HCrrOJIb3yIOTC5I rrpO,l(OJIbHbIe IIJ.eJIH [69].
PynopHbIe TEM HJJIyqaTeJIH TaIOKe SlBJI5IIOTCSI XOpOIIIHMH KamUi,naTaMH B aHTeHHbI
MHJIJIHMeTpOBoro ,l(Hana30Ha [137]. Ha3BaHHe «KOHYCHa51 IIJ.eJIeBaSi aHTeHHa» Hey-
,l(aqHO. 3TH aHTeHHbI npe,l(CTaBJISIIOT C060H He aHTeHHbI 6eryIl.(eH BOJIHbI, KaK qaCTO
yrBep)K,l(aeTCSI, a HaCTOSlIIJ.lfe pynopHbIe H3JIyqaTeJIH. B 60JIee rr03,l(HeH pa60Te rro
TEM pynopaM HCIIOJIb30BaJIaCb LTCC TeXHOJIOrHSI [80].
B HaCTOSlm;ee BpeMR HCnOJIb3yIDTCSI CHCTeMbI CB5I3H C MaJIbIM P3JI:HYCOM n;eHcT-
BH5I Ha 60 rru, nOCKOJIbKY B 3TOM qaCTOTHOM ,l(Harra30He Ha6JIIOn;aeTC5I MHHH-
MYM IIOMex H3-3a CHJIbHOrO 3aTYXaHlf5I B aTMoc<t>epe, COCTaBJI5IIOm;erO rrpHMepHO
15 ,l(E/KM. B ,l(Harra30He 60 rru; HCnOJIb3yIDTCSI, B OCHOBHOI, Te )Ke aHTeHHbI, qTO If
npl1 60JIee HH3KMX qaCTOTax: rreqaTHbIe II pynopHbIe TEM H3JIyqaTeJIH. B pa60Te
[82] M5I C03lXaHH5I CHCTeMbI KOMHaTHOH 6eCrrpOBO,l(HOM JIOKaJIbHOM ceTH HCnOJIb30-
BaHbI neqaTHbIe aHTeHHbI, pacnOJIO)KeHHbIe Ha rpaH5IX qeTbIpexrpaHHoH nlfpaMH,JJ;bI.
B pa60Te [112] HCnOJIb30BaHbI rreqaTHbIe aHTeHHbI C naCClfBHbIMIf 3JIeMeHTaMIf Ha
LTCC. PellIeTKH IIeqaTHbIX aHTeHH Ha LTCC pa3pa6oTaHbI TaIOKe MSI HeJIlfl(eH3H-
pyeMoro qaCTOTHoro .llHana30Ha 57-64 rru; [67]. B pa60Te [62] onHcaHa pynopHaSi
TEM aHTeHHa Ha L TCC C B03,aYllIHbIM pe30HaTopOM. nMpaMHlXaJIbHbIe BOJIHOBO,l(-
. u u
HbIe pyrropbI npHMeHeHbI B nepeKJIIOqaeMOI1 aHTeHHOM CHCTeMe MSI onTHMH3aIJ;HH
OTHOllIeHHR CHrHaJI/llIyM [16]. MOHoHMnYJIbCHaH meJIeBa5I aHTeHHaH perneTKa pa3-
pa60TaHa B [69]).
TEM pynOpbI SlBIDIIOTCSI XOpOllIHM BapHaHTOM H3JIyqaTeJIeM B ,l(Hana30He qaCTOT
BbIllIe 60 rru; B Teparepu;oBoH 06JIaCTH. B pa60Te [66] Ha qaCTOTe 80 rrIJ, HCnOJIb30-
BaH TEM pynop C ,l(BOHHbIM Cy;KeHHeM Ha nO,lLTIO)l(J(e C HH3KHM 3HaqeHHeM ,l(H3JIeKT-
pHqeCKOH npOHHu;aeMOCTH. TEM pynop Ha KpeMHHeBoH nO,lLTIO)l(J(e HCCJIe,l(OBaJICSI B
pa60Te [103] Ha qaCTOTe 90 rrIJ,. nO-BH,LJ;HMOMY, caMbIH BbICOKOqaCTOTHbIM pynop-
RbIM H3JIyqaTeJIb M5I ,l(Hana30Ha 802 rrI.( OI}HCaH B pa60Te [1]. Pynop 6bIJI H3rOTOB-
JIeH Ha TOHKOIIJIeHOqHOM OKMCJIe-HH1pH,LJ;e KpeMHH5I. OnHcaHHe KBa3HOnTHqeC
TeparepU;OBbIX aHTeHH II cBepxnpoBOJUIm;HX SIS aHTeHH [140] BbIXO,nHT 3a paMKH
3TOM KHHrH. B pa60Te .[20] onHcaHa aHTeHHa51 perneTKa Ha OCHOBe npO.1l0JIbHbIX me-

5.4. MUlCpOnOJlOCK06ble namltu u ounoJlu 
JIeH )]}ISI ,n;Hana30Ha 79 rrn:. 3Hr3aro06pa3HbIe MOHOnOJIbHbIe H3JIyqaTeJIH HCnOJIb30-
BaJIHCb [139] Ha qaCTOTe 110 rrn:. HaKoHen:,,lLJISI qaCTOTbI 28.3 rrQ (PJIC no.a;CBeTKH
QeJIH) pa3pa60TaHa aHTeHHaSl perneTKa Ha OCHOBe .a;HnOJIeH C nOCJIe,n;OBaTeJIbHbIM
B036}')K,L(eHHeM [77].
5.4. MMKpononocKoBble naT"IM M AnonM
MHKpOnOJIOCKOBbIe naTq H .a;HnOJIb npe.uCTaBJISlIOT C060H pe30HaHCHYIO MeTaJlJIH-
qecKYIO nJlaCTHHY Ha BepXHeM npOBo.a;HHKe MHKpOnOJlOCKOBOH JIHHHM. MMKpono-
JlOCKOBaSl neqaTHaSl aHTeHHa BnepBbIe npe)]}lO)f(eHa B [23], BepOHTHO, Ha OCHOBe
60JIee paHHeH pa60TbI no aHTeHHaM THna «partial sleeve» (3aKOpOqeHHbIH qeT-
BepTbBOJIHOBbIH H3JIyqaTeJlb). ,L(aJlbHeHllIee pa3BHTHe OHH nOJIyqHJIH B pa60Te [81]
H pa60Tax ,n;PyrMx HCCJIe.a;oBaTeJIeH. 113-3a 0611IHpHOCTH JIHTepaTypbI no MHKpono-
JIOCKOBbIM aHTeHHaM .a;aHHaSl TeMa OXBaqeHa 3,n;eCb JIHllIb nOBepXHOCTHO. EM nOCBR-
lI(eHbI CJIe,n;yroru:He KHHrH: Microstrip Antennas [4], Microstrip Antenna Theory and
Design [49], Handbook of Antenna Design (2 TOMa) [48], Millimeter-Wave Microstrip
and Printed Circuit Antennas [7], Broadband Patch Antennas [141] H Advances
in Microstrip and Printed Antennas [68]. IIOJIe3HbIH 0630p MHKpOnOJIOCKOBbIX
KOHCTpYKJ..(HH H cnoc060B H3rOTOBJIeHHSI .a;aH B pa60Te [31].
IIaT1IH MOryT HMeTb caMylO pa3JIWlHyJO <POPMY, HO B 60JIbllIHHCTBe CJIyqaeB
OHH 6bIBalOT npSlMoyrOJIbHbIMH (nOqTH KBarI:paTHbIMH) HJIH KpyrJIbIMH. IIeqaTHaR
aHTeHHa MO)f(eT B036}')K,L(aTbCR MHKpOnOJlOCKOBOM JIHHHeH, JIe)f(aru:eH B TOH )l(e
nJIOCKOCTII, KaK rrOKa3aHO Ha pliC. 5.29, HJIII KOaKCHaJlbHbIM Ka6eJIeM, nO,LU(JIlOqeH-
.... u v u
HbIM OnJIeTKOH K HH)l(}feH CTopOHe 3KpaHHpyroru:ell nJIOCKOCTH, a u;eHTpaJIbHOH
)l(HJIOH - K MHKpOnOJIOCKOBOMY H3nyqaTeJIIO. TMrrHqHaSl cxeMa no.a;KJIlOqeHIDI
MHKpOrrOJIOCKOBOH JlHHHH, 06eCrreqHBalOru:aSl COrJIaCOBaHHe HMrre,n;aHCOB, rrOKa3aHa
Ha pliC. 5.30. IIeqaTHbIe aHTeHHbI, 06bIqHO HMelOru:lle KBa,n;paTHyro HJIH KpyrJIyro
cl>OPMY, MOryr HMeTb CBSl3aHHbIe C HHMH 3JIeKTpOMarHHTHbIM 06pa30M 3JIeMeHTbI;
rrOCJIe,lJ;HHe 06C}')K,L(aIOTCSI HH)f(e. I1crroJIb3yroTcR TaIOKe KBa.a;paTHbIe H KpyrJIbIe
KOJIbn:eBbIe meJIH B rrOJIOCKOBOH JIHHHH. IIJISlpH3an:HR H ,n;HarpaMMa HarrpaBJIeHHO-
v
CTH rreqaTHOH aHTeHHbI aHaJlOrHqHbI COOTBeTCTBYIOru:IIM xapaKTepHCTHKaM nOJlY-
BOJIHOBbIX .a;HrrOJleH HJIH I.U;eJIeH. )J.HarpaMMa KBarI:paTHOM rreqaTHOH aHTeHHbI
B rrepBOM rrpH6JIH)f(eHHH .a;aeTCSI BbIpIDKeHHeM
. ( kLV J ( kWU J
Ex = Cose slnc 2 cos 2 '
(5.7)
r,ae u = sin e cos <I> H V = sin e sin <1>. )J.mI KpyrJIOH aHTeHHbI C ParI:HYCOM a, H f3 = ka
sin e ,n;HarpaMMa HarrpaBJIeHHOCTH B nepBOM rrpH6JIIDKeHHH HMeeT BH,n;
Ex = cos e [/ 0 «(3) - cos(2<1»/ 2 «(3)],
(5.8)
r.ne 1 0 , 1 2 - cl>YHKIJ;HH BecceJISI COOTBeTCTByroI.U;IIX rrOpSl,L(KOB.
THrrHqHaR H3MepeHHaSl ,lJ;HarpaMMa HarrpaBJIeHHOCTH rrOKa3aHa Ha pHC. 5.31
[58]. Kpocc- nOJISlpH3aUHR (XP) Ha6JIIO.a;aeTcSI B ,n;HarOHaJlbHbIX nJIOCKOCTSlX, ee
MaKCHMaJIbHbIe ypOBHH rrpHBe.a;eHbI B Ta6JI. 5.1 [38]. OTMeTHM, qTO B UHTHpyeMoH
pa60Te <POPMYJIbI BepHbI, 3a HCKJIlOqeHHeM Toro, qTO K03cl><PHUHeHT .LUIR XP H3JIY-

tJ:
rJla6a 5. 3JleMeHmbi aHmeHHou pelUemKu
/'-
w
BH,LJ; cBepxy
-
-
MeTaJIJI )
--_.- ......-..-..- ........................-..........---..
.l!1!3JI<;Kf'p t
MeTaJIJI ./
'" 3J1eKTpHQeCKOe
nOJle
rT T I .
BH.L1 c60KY
PHC. 5.29. feoMeTpHH MHKpOnOJIOCKOBOH neqaTHOH
aHTeHHbI
PHC. 5.30. 110,IIKJIlOqeHHe JIHHHH
B036y)l(,IleHHH, 06eCneQHBalOmee
COrJIaCOBaHHe HMne,IIaHCOB
PHC. 5.31. THnHQHaH ,IIHarpaMMa HanpaBJIeHHOCTH MHKpOnOJIOCKOBOH aHTeHHbI [58]

5.4. Mw,ponoJ/ocKo8ble namlfu U iJunoJ/u d
qeHI1JI KBa,[{paTHoM neqaTHOH aHTeHHbI ,[{OJI)I(eH 6bITb paBeH 2uw a He 4uw. O,n;HaKO,
rrpHBe,n;eHHbIe TaM Ta6JIHUbI 01lIH60qHbI; I1CnpaBJIeHHa5.1 Ta6JIHua HMeeT B1111::
KpOCC-nOJUlpH3aJUlJl KpyrJlOH ne'laTHOH aHTeHHbI
£
Omax (rpa,a) XPOL (,n6)
1 51.956 -17.37
1.5 52.934 -20.36
2 53.404 -22.59
3 53.861 -25.84
4 54.085 - 28.20
5 54.217 -30.36
7 54.367 -32.89
10 54.479 -35.91
15 54.565 -39.38
Ta6J1HQa 5.1. MaKCMMaJIbHbIe ypOBHM KpOCC-nOJUlpM3aUMM
Koa,apaTHaJI ne'laTHaB aHTeHHa KpyrJlaJI ne'laTHaJI aHTelUla
0max.XP (rpa,a) Max. XP (.n6) 0max,XP (rpa.a) Max. XP (,n6)
1 51.51 -17.93 51.96 -17.37
2 54.74 - 23.54 53.40 -22.59
3 54.74 -26.82 53.86 -25.84
5 54.74 -31.07 54.22 -30.36
10 54.74 -36.95 54.48 - 35.91
I1pOCTOM cnoc06 C03,lI.aHMR KpyrOBOH nOJIRpl13aUMH (CP) COCTOHT B I1CnOJIb30-
BaHH" ,lI.BYX JIHHI1M nHTaHM5.I C 90° C,lI.BI1TOM <l>a3bI H nO,lU{JIlOqeHHOH K 3THM JII1HH-
5.lM 90° rH6pl'l.aHOM CXeMbI. npH OTHOCMTeJIbHO IlIMpOKOnOJIOCHOH rH6pH,l(Hoi1 cxe-
Me ,lI.Hana30H qaCTOT ,LUISI KpyroBoM rrOJISlp113a1111 6Y,lI.eT TeM )l(e, qTO Ii ,l(JISI
H3JIyqeHI1S1 C JIHHeHHOM nOJIRpH3a"eM. EOJIee npOCTbIM, HO HeCKOJIbKO 60JIee Y3-
KOnOJIOCHbIM BapMaHTOM 5.lBJI5.leTC5.I 3aMeHa rM6pH,lI.HOM cxeMbI ,lI.eJIHTeJIeM MOIUHO-
CTH C BKJIIOqeHHOM B OL{HO M3 nJIeq TIHTaHH5.I ,l(OnOJIHHTeJIbHOM JIHHHeH ,lI:JIHHOM ')...,/4.
JI5.I nOJIyqeHI1S1 KpyroBoH nOJISlp113a1111 MOryT MCnOJIb30BaTbCSI TaIOKe O,[{I1HOqHbIe
errH B036Y)Kj{eHHSI: OCHOBHOM npHHIJ.Mn COCTOI1T B TaKOH MO,lI.I1<pMKaIJ.HI1 neQaTHOH
aHTeHHbI, qT06bI qaCTOTa ero pe30HaHca no X-HanpaBJIeHHIO JIe)l(aJIa HH)I(e, a Qac-
TOTa pe30HaHca no Y-HanpaBJIeHHIO - BbIllie pa60qero ,l(l1ana30Ha qaCTOT. Kor.aa
pa3JIHqMe <l>a3 ,n;OCTMraeT 90°, B03HI1KaeT KpyroBa51 nonHpH3aIJ.115.1. O,l(HaKO ,[{Hana-
30H qaCTOT, B KOTOpOM HMeeT MeCTO KpyroBaSl nOJI5.lpI13aM5.I, 3HaQMTeJIbHO MeHb-
llIe, qeM c06CTBeHHa5.1 nOJIoca nporrYCKaHI15.1 MHKpOnOJIOCKOBOro H3JIyqaTeJI5.I.
HarrpHMep, rreQaTHa51 aHTeHHa HMeeT rrp5.lMoyrOJIbHyJO <POPMY, f,l(e O,lI.Ha CTOpO-
Ha KOpOqe, a ,npyraH ,lI.JIHHHee pe6pa KBa,npaTa. KpyrJIaH rreQaTHa5.1 aHTeHHa MO)l(eT

 FAa6a 5. 3AeMeHmbl aHmeHHOU peUJemKU
6bITb IIpe06pa30BaHa B 3JIJIHIITHqecKYID. npOCT.bIe <l>oPMYJIbI, CBH3bIBalOIl(He pa3Me-
pbI C IIOJIOCOH npOnYCKaHHH, BbIBe,LJ;eHbI B pa60Te [71]. ,[(PyrHe cxeMbI B036)')K.lJ:e-
HHH KpyrOBOll nOJIHpl13aQHI1 11306pIDKeHbI Ha pHC. 5.32.
a+L!
a
a
a
a
/
a
Puc. 5.32. I1eqaTHbIe aHTeHHbI C KpyroBoH nOJUlpH3aUHeH [58]
MHKpOIIOJIOCKOBbIe ,LJ;HnOJIH, TO eCTb neqaTHbIe aHTeHHhI C MaJIOll llIHpHHOll,
06pa3YIOIl(He nOJIOCKOBbIe ,LJ;HnOJII1, HHTeHCHBHO HCCJIe,LJ;OBaJIHCh B pa60Tax [124].
O,LJ;HaKO npH TOHKI1X nOLLJIO)l(J(ax HX nOJIoca nponYCKaHHH HaMHoro )')Ke, qeM Y ne-
qaTHbIX aHTeHH, pa3MeIl(eHHbIX Ha TaKOll xe nO,LJ;JIO)KKe [94].
5.4. 1. MOAenb B BMAe nMHMM nepeAa'lM
KBa,n;paTHaR neqaTHaH aHTeHHa ,LJ;eHcTByeT KaK JIHHHR nepe,LJ;aqH nOJIYBOJIHOBOH
LLJIHHbI C KOHl(eBbIMH 3a30paMH, C03,LJ;alOIl(HMH H3JIyqaeMoe nOJIe, KaK H306paxeHo
Ha pHC. 5.33. npOcTeHmeH aHaJIl1TWleCKOH MO,LJ;eJIblO RBJIReTCR Mo.neJIh nepe.nalO-
Il(ell JIHHHH [114] C 3<1><I>eKTHBHOH ,LJ;H3JIeKTpHqeCKOH npOHHl(aeMOCTblO, qhH KOH-
l(bI HarpyxeHbI aKTHBHOH II peaKTIIBHOH IIpOBO,LJ;HMOCThlO H3JIyqeHHH. 3<l><I>eKTHB-
HaR .n;H3JIeKTpllqeCKaR npOHHl(aeMOCTb Be MeHReTCH B 3aBHCliMOCTH OT OTHOIIleHHH
TOJIIl(HHhI 1 neqaTHOll aHTeHHhI K ee lliHpHHe W [35]:
1 Br -1
E e = - (E r + 1) + .J ·
. 2 2 1 + 121 / W
(5.9)
B pa60Te [36] nOJIyqeHo 60JIee CJIO)KHoe BbIpaxeHHe, HO ero ynp0Il(eHHaR <pop-
Ma MO)KeT OKa3aThCR .n;ocTaTOqHoH. npOBO.n;HMOCTh H3JIyqeHHH BhIpaxaeTCH Qepe3
3HaqeHHe .n;06POTHOCTH H3JIyqeHHH Q, nOJIyqeHHoe B CJIe.n;YIOIl(eM BH,lJ,e [125]:
Q _ AO _ Bef1L
rad - 41 l'
(5.10)
r.ne tJ,.L - H3MeHeHHe 3<1><I>eKTHBHoH LLJIHHbI, BbI3BaHHoe KpaeBhIMH 3<l><I>eKTaMI1
nOJIR [35]:
f1L = 0,412 (Be + 0,300)(W / t + 0,262) .
1 (Be - O,258)(W / t + 0,813)
(5.11)
DOJIee TOqHaR H B TO xe BpeMR 60JIee CJIO)KHaR <l>opMYJIa .n;aHa B pa60Te [65].
TIpeHMYIl(ecTBOM no.n;xo.n;a, HCnOJIh3YIOIl(erO Mo.n;eJIh JIHHHH nepe.aaqH, HBJIReTCH
JIerKOCTh BhIqHCJIeHIDI HMne.naHca B TOqKe B036)')K.lJ:eHKSI. nOCKOJIhKY nOJIoca npo-
rrycKaHHH aHTeHHhI C MaJIOH nOJIOCOH no KCBH  2 (VSWR - voltage standing

5.4. MUKponOllocKoBbie nam'lu U ounoJlu . 
E- nOJIe
".. 0
, ..(,
,
,
 H3JIeKTpHK
___   rrpO O.l\HHK
PHC. 5.33. M3JIyqeHI1e KpaeBbIX m;eJIeH neqaTHOH aHTeHHbI
wave ratio, KCBH - K03<P<PHll:l'leHT CTOHqeH BOJIHbI no HanpIDKeHHIO) nponopUHO-
HaJIbHa 3HaqeHHIO 1/ ( .J2Q ), OTHOCHTeJIbHaH nOJIoca nponYCKaHHR npH6JIIDKeHHO
paBHa
BW '" 41 .
.J 2E r A O
(5.12)
TaKHM 06pa30M, nOJIoca nponYCKaHHH nponOpUHOHaJIbHa TOJIIUHHe B ,l])IHHaX
BOJIH B BaKYYMe H 06paTHo nponOpUHOHaJIbHa KOpHIO KBa,L(paTHOMY H3 ,n;H3JIeKTpH-
qeCKOH npOHHQaeMOCTH. Ha pHC. 5.34 npe,n;CTaBJIeHa llIHpHHa nOJIOCbI nponYCKa-
HIDI no KCBH < 2 .lL7IH 3HaqeHHH ,n;H3JIeKTpHqeCKOH npOHHuaeMOCTH 2.5, 5.0 H
10.0. He06xo,n;HMO OTMeTHTb, qTO 3TO npH6JIH)I(eHHOe 3HaqeHHe He yqHTbIBaeT 3<1>-
<1>eKToB BJIHRHHR HHLI;YKIlHOHHbIX H l1H3JIeKTpHQeCKHX nOTepb, YBeJIHQHBalOIUMX
llIHPHHY nOJIOCbI nponYCKaHHR.
3<p<peKTbI BJIHHHHR nOBepXHOCTHbIX BOJIH TaIOKe He yqHTbIBaIOTCR, HO 06bIQHO
OHH 6bIBalOT CyrQeCTBeHHbI TOJIbKO .lL7IR 60JIbllIHX aHTeHHbIX pellIeTOK. ,LI:JIR ,n;PyrMx
3HaQeHHH KCBH llIHpHHa nOJIOCbI nponYCKaHHR paCCQHTbIBaeTCR, eCJIH H3BeCTHa
llIHpMHa nOJIOCbI nponYCKaHHR BW 2 no KCBH = 2, no CJIe,n;YIOIUei1 <1>opMYJIe:
BW = BW 2 fi,(VSWR -1) .
. '. .J VSWR
(5.13)
TaK, eCJIH Ha ypOBHe nOJIOBHHHOH MOIII.HOCTH KCBH = 5.828, TO llIHpMHa no-
JIOCbI nponYCKaHHR B 2fi, pa3a 60JIbIIIe, qeM npH KCBH = 2. HCnOJIb30BaHHe no,n;-
JIO)I(KH C HH3KHMH MarHHTHbIMH nOTepRMH MO)l(eT 3HaQHTeJIbHO YBeJIHQHTb llIHpH-
HY nOJIOCbI nponYCKaHHR [42].

 DW6a 5. 3lU!Menmbl anmennou peUJemKU
10
9
,
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I'
,
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,
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2.5
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1',1',1" /
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€, = 10
".
1
I'
,,1'1'1"/
1" "
.,//
"
0 0 . 00 0.01
0.02
0.03 0.04 0.05 0.06 0.07 0.08
T OJIIlJ;lfHa/ .lUIHHa BOJIHbI B BaKYYMe
0.09
0.10
PHC. 5.34. TIOJIoca nponYCKaHHH neqaTHOH aHTeHHbI no KCBH = 2
5.4.2. MOAenb pe30HaTopa M APyrMe MOAenM
B Mo,n:eJIM pe30HaTopa, pa3pa6oTaHHoH B [72, 15], nOJIe Me)l()];Y neqaTHOM aHTeH-
HOH M 3KpaHMPYIOll.(eH nJIOCKOCTbIO npe,n:CTaBJIeHO B BM,n:e pH,n:a no Mo,aaM np5IMO-
yrOJIbHOrO (IDIH KpyrJIOro) pe30HaTopa. 3aTeM npOM3Bo.nMTCH COrJIaCOBaHMe 3TMX
MO,n: C npOBo.nMMOCTbIO 3a30pa Ha Kpa5IX neqaTHOM aHTeHHbI. TIOqTM BCH 3HeprlfH
M3JIyqeHlf5I o6eCneqMBaeTC5I OCHOBHOH TM o1 MO,nOH; OTCIO,aa MO}l(eT 6bITb BbIqlfC-
JIeHO 3HaqeHlfe Qrad' B 3anaceHHYIO 3HeprlfIO BHOCHT BKJIa,IJ; Bce MO,lI.bI. I1cnoJIb3YH
TOK If nOJIe OCHOBHOH MO.nbI, Moryr 6bITb BbIQlfCJIeHbI nOTepM B npOBo,n:HlfKax If
,n:lf3JIeKTplfKax, onpe,n:eJIHIOll.(He Qcond, Qdie/, M 3HaQeHlfe nOJIHOM JJ.06pOTHOCTIf Q,
onpe.neJIHeMOe BbIpa)l(eHlfeM I/Q = I/Qrad + I/Qcond + l/Qdiel' llIMplfHa nOJIOCbI
nponYCKaHliH, KaK Ii paHbllIe, onpe.neJUleTCH 3HaQeHlieM Q, a BXOJJ.HOH liMne.naHC
BbIQlfCJI5IeTCH C yqeToM 3HaQeHMH Q II BeJIHQlfHbI 3arraceHHOM If 1f3JIyqaeMoM
MOll.(HOCTIf. XOTH B Mo,n:eJIIi pe30HaTopa pe30HaHCHaH qaCTOTa BbIqMCJIHeTCH TOq-
Hee, qeM B Mo,n:eJIM rrepe.nalOIl{eM JIlfHlfH, 06blqHO B03HlfKaeT He60JIblllaH norpelll-
HOCTb MJIM C,nBI1T.
L(JIH onpeJJ.eJIeHM5I 3HaQeHlfH TOKOB Ha rrpOBo,nHIl{lfX rrOBepXHOCT5IX MCrrOJIb30-
BaJIlfCb TaIOKe MeTo,n:bI MOMeHTOB. B pa60Te [84] IfCrrOJIb30BaHbI pa3JIO)l(eHMe no
MOJJ.aM rrp5IMoyrOJIbHOrO pe30HaTopa If TeCTOBbIe <PYHKQIfIf B npocTpaHcTBeHHoM
06JIaCTIf. 3TO n03BOJIHeT M36e)l(aTb TPy,n:HocTeH, CB5I3aHHbIX C BbIqMCJIeHMeM cneKT-
paJIbHOrO npe,n:CTaBJIeHM5I <PYHKI..(MM rpMHa; CneKTpaJIbHOe npe,n:CTaBJIeHlfe JIyqIIIe
no,n:xo,n:MT ,lLJI5I paCQeTa 6eCKOHeQHOH aHTeHHOM perneTKM C nOMOIIIblO Teope-
MbI <l>JIOKe. Co BpeMeHM TOH nepBoH pa60TbI n05IBlfJIOCb MHoro ,n:pyrMX, B KOTOpbIX
I
L

r
5.4. MUKponollocKo8ble nam'tu U iJunollu 
HCnOJIb30BaJIHCb pa3JIO)l(eHH5I no MO.LJ:aM pe30HaTopoB .LJ:pyrOH <pOpMbI H .LJ:pyrHe Tec-
TOBbIe <PYHKUHH. ,lLrr5I paCqeTa neqaTHbIX 3JIeMeHTOB HCnOJIb30BaTIC5I TalOKe MeTO,L(
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6bm rrOJIyqeHbI B [118]. B Ta6JI. 5.2 H 5.3 npHBe,l(eHbI 3HaQeHHH 0, b H 6, nonyqeH-
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I
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B 3.8 pa3a.
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BH,nHO, 06ecueHHBaeT ero pe3YJIbTaT. TOQHOe 3HaQeHHe nOJIyqeHo B pa60Te [41]:
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Cl>aHo (3HaQeHHB ,[(JIB 6eCKOHeQHOrO KOJIHQeCTBa CeKl(HH H3 Ta6JI. 5.4).
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conpOTHBJIeHHe HarpY3KH Zo He paBHO conpOTHBJIeHHIO 3JIeMeHTa Ro, a BBO,nHTCB
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npHBOMTCSI OnTHMaJIbHbIe 3HaqeHHSI T H YJlyqIlIeHHbIe 3HaqeHIDI QB. OqeBRIJ;HO,
qTO npH MaJIbIX KCBH YJlyqrneHHe MeHbllIe.
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pa3JIOXeHHe no BceM 06JIaCTH H TeCTOBbIe <PYHKIJ;HH (MO,nbI pe30HaTopa) B npOC1'paH-
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JIHTepaTYPa
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1 - exp[j (N - l)J3d] sin J3d
r == N slnJ3d
3expU2NJ3d) + exp[j(N + l)J3d] sinf3d
N slnJ3d
(6.3)
MHO)l(llTeJIb (sin Nf3d)/(N sin f3d) onHCbIBaeT ,n;HarpaMMY HanpaBJIeHHOCTH
N-3JIeMeHTHoM aHTeHHoM peIIIeTKH H rrOpO:>K,I(aeT OCUHJIJIHUHH BeJIHqHH KCBH H r
rrpH H3MeHeHHH 3HaqeHHH f3d. 3TH OCUHJIJIHUHH rrOKa3aHbI B pa60Te [19], rL(e IIPH-
Be,n;eH rpa<pHK ypaBHeHHH (6.3). C YBeJIHqeHHeM qaCTOTbI KCBH TalOKe paCTeT, ,n;o-
CTHraH IIPH HopMHpoBaHHoM qaCTOTe, MeHbIIIeH 1 + 1/2N, 3HaqeHHH, paBHoro 2, a
3aTeM OCUHJIJIHpyeT OTHOCHTeJIbHO ypOBHH KCBH == 2. MHO)l(J1TeJIb KaqeCTBa co-
CTaBJIHeT NB == 89 ,lI;lIH N == 20. 3TO 3HaqeHHe HBJIHeTCH 60JIee KOHcepBaTHBHoM
oueHKoH MHO)l(HTeJIH KaqeCTBa, qeM rrpe,n;bI,n;yn.J;aH yrrpomeHHaH oueHKa NB == 114.
IIpH 60JIee TOqHOM rro,n;xo,n:e, npHMeHH-
MOM TalOKe B CJIyqae B036)')K,L(eHHH C aMIIJIMTY- 0 1
,n;OH, cna,n;alOmei1 Ha KpaHx paCKpbIBa, MCIIOJIb-
3yeTcH KaCKa,n: MaTpMU A-B-C-D [2]. Ka)K)J;aH 0
v
CeKI..'(HH BOJIHOBo,n:a C HarpY3KOH B BH,II;e IIapaJI-
JIeJIbHOH rrOJIHOH IIPOBOL(HOCTH (eJIblO) PRC. 6.2. Mo.n;eJII1PYlOwaH ceK:QI1R
rrpe,n;cTaBJIeHa Mo,n;eJIHpYIOrn:eH CeKI..'(HeH, KaK
rrOKa3aHO Ha pHC. 6.2. ,lJ;JIH KpaTKOCTH 0603Ha-
qHM C == cos f3d H S == sin f3d. Tor,n;a MaTpHua
ceqeHMM HMeeT BII,I( [2]
( C jS )( 1 0 ) _ ( c + jYnS jS )
jS C Y n 1 - YnC + jS C'
o
y
n
Y =1
o
o
8£
(6.4)
MaTpHl(a pe30HaHcHoM AP B 3TOM cJIyqae rrpe,n:cTaBJIHeT C060H rrpoH3Be,n;eHHe
N MaTpHIJ: CeqeHHM, HaqaJIbHaH MaTpHua KOToporo cooTBeTcTByeT O,lJ;HOMY KOHl(Y
u u
BOJIHOBo,n:a, a KOHeqHaH MaTpMua - 3aKOpOqeHHOH qeTBepTbBOJIHOBOH CeKl(MM.
bOJIbIIIOe 3HaqeHHe  Mo,n;eJIHpyeT 3aKopoTKY, a IIOJIHaH MaTpHua MMeeT BH,II:
( A B ) == [ fI ( C + jYnS jS )]( C 2 + jY 2 S 2
C D n=l YnC + jS C Y 2 C 2 + j S 2
j S 2 )
C 2 .
(6.5)
IlapaMeTp C HCnOJIb3yeTcH II B KaqeCTBe TpHrOHOMeTpllqeCKOrO qJIeHa, M KaK
qaCTb BbIpa)l(eHHH A-B-C-D. HIDKHHM HH,lI;eKC 2 OTHOCHTCH K 3aKOpOQeHHOM ceK-
UHH. BXO,lI;HOH HMne,L(aHC H K03<P<PHUHeHT OTpa)l(eHHH JIerKO onpe,L(eJIHIOTCH
z. == A + B . r == 2 . ( 6.6 )
III C+D' A+B+C+D
Ha pRC. 6.3 H306pa)l(eHa 3aBHCHMOCTb KCBH OT HOpMRpoBaHHoH qaCTOTbI ,II;JIH
20-3JIeMeHTHoM AP C nOCTOHHHbIM aMIIJIHTY,L(HbIM pacnpe,n;eJIeHReM. IloCKOJIbKY
KpMBaH CHMMeTpHqHa OTHOCHTeJIbHO f, rrOKa3aHa TOJIbKO ee nOJIOBHHa. AHTeHHaH
perneTKa C 25 ,L(b pacrrpe,L(eJIeHHeM TeitJIopa ,L(aeT aHaJIOrHqHYIO KPMByIO C 3aTyxaIO-
mHMH KOJIe6aHHHMH. Ha pHC. 6.4 rrOKa3aHbI 3aBHCHMOCTH rpa<pHKoB 3THX KpHBbIX,
pacrrOJIO)l(eHHbIX HIDKe nepBoro IIHKa, OT 3HaqeHIDI NB. 113 3THX ,L(aHHbIX CJIe,L(yeT


FJla6a 6. CucmeMbl numanUR anmennbLX pewemOK
4
N20
3
=:c

U

2
1
1
1.02
1.04
1.06
flfo
1.08
1.10
Puc. 6.3. KCBH pe30HaHcHoH aHTeHHOH perneTKH C O)J;HOP0)J;HbIM B036yx,aeHHeM
3.0
25-.nB pacnpe.neJIeHHe
TeHJIOpa
2.5
nOCTOSlHHoe
pacrrpe.neJleHHe
N 3J1eMeHTOB
B = llIHpHHa -rrOJlOCbI B %
:I::

u 2.0

1.5
1.0
o
20
80
40
NB
60
PUC. 6.4. nOJIOca nponYCKaHH pe30HaHCHOH aHTeHHOH perneTKH

6.1. IIoCJleoo6ameJ/bltble JlUItUU numaltUR d
3HaqeHHe MHo}J(HTeJI$I. KaqeCTBa NB = 66 IIPH IIOCTORHHOM aMIIJIHTy,n;HOM paCIIpe-
,n;eJIeHHH H KCBH = 2, a TaIOKe NB = 50 IIPH KCBH = 2 ,lLJIR 25 ,n;D pacnpe)];eJIeHHR
T eHJIopa.
fpaHHUbI nOJIOCbI IIpOIIYCKaHMR onpe.n;eJIRIOTCR C IIOMOm;blO rpa<J;>MqeCKHX ,n;Ma-
rpaMM CMMTa. TIpH paBHOMepHOM aMIIJIHTy.n;HOM pacnpe)];eJIeHHH Bce 3HaqeHH.SI
CMem;eHH.H IIOJIOCbI paBHbI, HO HeCKOJIbKO rrepBbIX 60JIbllIe, H Ha )];HarpaMMe CMHTa
OHM paCIIOJIO)l(eHbI nOqTH pan;HaJIbHO, KaK IIOKa3aHO Ha pMC. 6.5. OHM CMem;aIOT
3HaqeHHe HMIIe.n;aHca K TOqKe COrJIaCOBaHH.H. ITpM B036y)1(J(eHHH C aMnJIHT)'.n;oH,
CIIan;alOm;eH K Kpa.SlM paCKpbIBa (pMC. 6.6), IIepBbIe CMem;eHH.H Ha .n;HarpaMMe MeHb-
me H3-3a YMeHbIIleHM.H aMIIJIHT)')];bI B036y)1(J(eHM.H. TIoCJIe.n;HHe CMem;eHH.H 60JIbllIe,
M OHM orM6alOT TOqKY COrJIaCOBaHMR MMIIe,n;aHCOB.
,...
" \
,  \
\
,
\
\
--
-
......
PHC. 6.5. npeo6pa30BaHMe MMlIe,n:aHCOB pe30HaHcHoH aHTeHHOH perneTKH 113 qeTbIpex
3JIeMeHTOB C IIOCTOHHHbIM aMIIJIMTY,n:HbIM paClIpen:eJIeHMeM lIP" lifo = 0.96
B 060MX CJIyqaRx npH 60JIbmOM qMCJIe 3JIeMeHTOB npOHCXO)];HT IIOqTM rrOJIHbIH
nOBopOT BOKpyr ueHTpa .n;HarpaMMbI Ha Ka)l()];OM IIlare. JIoKaJIH3aUH.H ueIIH IIHTa-
HHH B6JIH3H CMJIbHO CBH3aHHbix 3JIeMeHTOB 060CTpReT npHBe,n;eHHYIO nOJIOcy IIpO-
nYCKaHH.H.
Ha IIpaKTHKe IIOJIOCa IIponYCKaHMR MeHbllIe BCJIe)];CTBMe 3aBHCHMOCTM IIOJIHOH
IIpOBO,lJ;IfMOCTM rueJIM OT qaCTOTbI. 3aBHCHMOCTb nOJIHOH npOBO,lJ;IfMOCTH OT qaCTOTbI
MO}J(eT 6bITb yqTeHa ,lLJIR Bcex THnOB BOJIHOBO.n;HbIX m;eJIeH C nOMOm;blO MeTO,lJ;a MO-
v v
MeHTOB, HO Mo.n;eJIlfpOBaHHe IIJ;eJIeH B llIHpOKOH CTeHKe BOJIHOBo.n;a OKa3bIBaeTCH
60JIee npOCTbIM H TOqHbIM, qeM IUeJIeH no Y3KOH CTeHKe. )];OIIOJIHHTeJIbHYIO TPy,n;-
HOCTb npe,n;CTaBJIHeT c060H pa3)];BOeHHe JIyqa, KOTopoe MO}J(eT npOMCXO,lJ;MTb, KOf,n;a
,n;Be 6erym;Me BOJIHbI, Bxo,n;RIUHe B COCTaB CTOHqeH BOJIHbI, 06pa3yIOT JIyqM, HanpaB-
JIeHHbIe BJIeBO H BIIpaBO OT ueHTpa [43]. 3TO npOMcxo.n;HT IIPH 3HaqeHMH NB, paB-
HOM npMMepHO y,n;BoeHHOMY 3HaqeHMIO KCBH = 2. TIO,U,l(ep}J(aHHe 3HaqeHlfR
KCBH < 2 YCTpaHHeT TaKHe pa3)];BOeHHble JIyqH.

 DWBa 6. CUCmeMbl numaHUR aHmeHHbIX pewemOK
Poc. 6.6. npeo6pa30BaHlfe HMne.n;aHca pe30HaHcHoH aHTeHHOH perneTKIf H3 qeTbI-
pex 3JIeMeHTOB C 25 .n;E pacrrpe.n;eJIeHlfeM,I/lo = 0.96
6. 1. 1.2. PaclfeT aHTeHHoM peweTKM Ha OCHose
pe30HaHcHwxeneH
H3JIO)l(MM rrop,[(OK paCqeTa AP Ha OCHOBe BOJIHOBO,[(HbIX rn:eJIeH, nOCKOJIbKy Ta-
KMe perneTKM 06JIa,n:a1OT BbICOKOH 3cPcPeKTMBHoCTblO M rr03BOJI5IIOT cPOpMHpoBaTb
ynpaBJI5IeMYIO ,n:MarpaMMY HarrpaBJIeHHOCTM. ECJII1 rnar perneTKM paBeH rrOJIOBMHe
,l(JIMHbI BOJIHbI B BOJIHOBo,n:e, Heo6xo,n:MMO M3MeHeHHe 3HaKa CB3M ,n:JI Ka)l()];OH
BTOpOH Il(eJIM. B perneTKe Ha OCHOBe npo,n:OJIbHbIX m:eJIeH N m;eJIM nOOqepe,n:HO
v v
pacrrOJIaralOTC5I C pa3HbIX CTOpOH OT cpe,n:HeM JIMHHH llIHpOKOM CTeHKll BOJIHOBO-
,n:a. ITpM I1CrrOJIb30BaHMM HaKJIOHHbIX rueJIeH B lllHPOKOH CTeHKe M HaKJIOHHbIX
v v v
KpaeBbIX meJIeH Ha Y3KOM CTeHKe yrOJI HaKJIOHa nOCJIe,[()'IOIQeM m:eJIM HMeeT rrpo-
CTO 06paTHbIM 3HaK. B pe3YJlbTaTe cPPOHTaJIbHOe M3JIyqeHMe Bcex rn:eJIen OKa3bIBa-
eTC CI1HQ:>a3HbIM.
Onpe,[(eJIeHMe ,lLJIMHbI m:eJIeM M MX OTBeTBJIeHI1H IUlM ,l(JIMHbI :rn;eJIeH M yrJIOB,
06eCneqMBalOIl(I1X rrOJIyqeHHe )l(eJIaeMOrO aMIIJII1Ty,n:HO-<pa30Boro pacrrpe.neJIeHHH
v v
no aHTeHHOH pellIeTKe npH y,n:OBJIeTBOpeHHM pe30HaHCHbIX YCJIOBHH, BJIeTC5I
Tpy,n:HOH 3a,n;aqeH. 3Ta 3a,n;aqa OKa3aJIaCb 6bI He CTOJIb CJIO)l(HOH, eCJIH He yqHTbIBaTb
B3aHMHbIM HMne,n:aHC. O,n:HaKO B3al1MHaH CB3b BCIO,n:y npHcyrcTByeT M CyuJ;eCTBeH-
Ha, rr03TOMY ,n:OJI)l(}fa yqMTbIBaTbC. TaKMM 06pa30M, npH paCqeTe AP Heo6xo,n:MMO
yqMTbIBaTb Bce meJIM o,aHOBpeMeHHO. PellIeHHe 06eCneqHBaeTC ,n:B)'M5I COOTHOllIe-
HI1MI1. Bo-rrepBbIX, CYMMa nOJIHbIX rrpOBO,[(MMOCTeH m:eJIeH (B pe30HaHce) ,n:OJDKHa
6bITb paBHa BbI6paHHOH nOJIHOH BXO,n:HOH npOBo,n:HMOCTH, paBHoH 1 + jO ,l(JIR OT-
,n:eJIbHOH JIMHeMHOM pellIeTKll, HO MeHIOm:eMc WI5I JIMHeeK, 06pa3)'1OIQMX IIJIOCK)'IO
AP. BO-BTOpbIX, Mo,aOBbIe HarrpIDKeHHH Bcex meJIeM ,aOJDKHbI 6bITb paBHbI. B ,n:aJIb-
HeHrneM paCCMaTpHBaeTC5I rrpMMep rrpo,n:OJIbHbIX rn;eJIei1: B llIHpOKOH CTeHKe BOJIHO-

6.1. IIOCIleo06ame.nbHble J/UHUU nUmaHUJl 
BO,l1a. B3aMMHbIH HMIIe,l1aHC onpe,l1eJIHeTCH IIYTeM 3aMeHbI meJIeH 3KBHBaJIeHTHbIMH
MMKpOnOJIOCKOBbIMH ,l1HnOJIHMM Ea6HHe, aTe, B CBOIO Oqepe,l1b, ,l10nYCKaIOT 3aMeHY
UHJIJlIUJ:pI1QeCKHMJI ,l1HIIOJIHMH C ,l1HaMeTpOM, paBHbIM nOJIynIJlpJlHe MJlKpOnOJIOC-
KOBoro npOBO,l1HJlKa [61]. TIpe,l1nOJIaraeTCH, qTO CTeHKa BOJIHOBO,l1a IIpe,l1CTaBJIHeT
C060H IIJIOCKHH 3a3eMJIeHHbIH 3KpaH. )];JIH paCQeTa B3aJlMHOrO HMne,lJ;aHCa MOryT
JlCnOJIb30BaTbCH <POPMYJIbI KapTepa; Y,l106HaH nporpaMMa Ha <I>OPTPAHe IIpe.l1JlO-
xeHa B [29]. )];JIH BOJIHOBO,lJ;a C ,lJ;M3JIeKTpHqeCKHM 3anOJIHeHHeM MoxeT HCIIOJIb30-
BaTbCH 60JIee TOqHOe 3HaQeHMe B3al1MHOrO HMne,l(aHCa, yqJlTbIBalOmee KOCI1HYCOI1-
,l(aJIbHOe pacnpe,l1eJIeHHe nOJIH B,l10JIb meJIH [15], O,l(HaKO BbIQHCJIeHHe B3aJlMHOrO
I1Mne,l(aHCa B 3TOM crryqae Tpe6yeT QJlCJIeHHOrO I1HTerpl1pOBaHHH. Onpe,l(eJIeHJle
c06CTBeHHOH IIOJIHOH npOBOLlJlMOCTJI meJIJI, yqHTbIBalOweH 3<p<peKTbI HaKOnJIeHI1H
3Heprl111 BHYTpJl BOJIHOBO,l1a, Tpe6yeT 60JIee TmaTeJIbHbIX BbIQJlCJIeHI1:H IDII1 113Mepe-
HI1H. TIpH 3THX BbIQHCneHHHX I1CnOJIb3yJOTCH BapHaUI10HHble MeTO,l1bI [70] HJII1 Me-
TO,l(bI MOMeHTOB. TIoCJIe,l(HJle, npe.l1JIOXeHHble B pa60Te [40], ycnellIHo pa3BJlTbI B
[14, 16]. EOJIee n0,l1p06HOe paCCMOTpeHHe rrpeLlCTaBJIeHO B rJI. 5.
I1cnoJIb3YH Onl1CaHHble B fJI. 5 pe3ynbTaTbI 11 3HaQeHI1e I1Mne,l(aHCa Zn 06ne,l1M-
u u
HeHHblX meJIel1, IIonyqaeM BblpIDKeHHe ,lLJUI nOJIHOJI npOBO,l1HMOCTJI menH
Y n _ 480(0 / b)C
Go n(J3 / k)Z n
(6.7)
3HaQeHJle K03<P<PHUHeHTa C n rrpl1Be,l1eHO B rJI. 5, a Zn npe,l1CTaBJIHeT C060H 06-
paTHYIO CYMMY 3HaQeHHH c06cTBeHHoH nOJIHOH npOBO,l1HMOCTJI meJII1 H nonHOH
B3al1MHOH npOBO,l(I1MOCTI1. I1cnoJIb3YH ypaBHeHHH ueneM, norryqaeM I1Mne,l1aHC
06ne,l1J1HeHHbIx meJIeH B BI1Lle
Z - 480(0 / b)C L N VmZnm
n - +
o .
n(J3 / k)Y n / Go m=l V n
(6.8)
TIepBbIM QJIeH BKJIIOQaeT c06cTBeHHyJO nOJIHyJO npOBO,l(I1MOCTb meJIJI Yno, a
CYMMa OXBaTbIBaeT Bce B3al1MHbIe QJIeHbI, r,l1e Znm npe,l1CTaBJIHeT C060H nOJIHbIM
B3aMMHbIM I1Mne,l1aHC Me)l():(y n-M 11 m-M n;l1nOJIHMH. HanpHxeHl1e Ha meJIU paBHO
V n . IlpM 3a,IJ;aHHbIX ,l1JIHHaX :r.u;eJIeti 11 OTBeTBJIeHI1M ,l1JIH rrOJIyqeHMH IIOJIHOM npOBO-
,l1MMOCTM meJII1 MOryr HCnOJIb30BaTbCH ypaBHeHMJI (6.7) M (6.8). IIoCKOJIbK)' CYMMa
OrpaHJlQeHa
f Y n =l+jO,
n=l Go
3TO KOMrrJIeKCHOe ypaBHeHl1e n;aeT ,l1Ba ,l1eMCTBJlTeJIbHblx. Tenepb ypaBHMBalOTCH
MOn;OBble Hanpf[)KeHIfH. KaK CJIe,l1yeT 113 rn. 5, B blpaXeHJlH .l1JIH HIfX JlMelOT BI1,l(
. 2 -J 20/ bCnV n
On = J. (6.10)
n(J3 / k)Y n / Go
(6.9)
B pe3YJIbTaTe norryqaeTcH CJlCTeMa 113 2N - 2 ypaBHeHI1M, COCTaBlliIlO:r.u;aH, BMeCTe
C ypaBHeHJleM (6.9), 2N ypaBHeHJlM ,lLJUI 2N HeIf3BeCTHblX (.l1JIJlHbI :r.u;eJIeH If OTBeTBJIe-
HMH). 3TI1 HeJIIfHeMHble TpaHCueIUJ:eHTHbIe ypaBHeH:IDI nefKO pernalOTCH MeTO,UOM,
paCKpbITbIM B [60], r,l(e rpa,IJ;JleHTHaJI MaTpMua COCTOJIT 113 ypaBHeHIfH IIpOM3BO,l(HbIX
no KIDK,I:{OM rrepeMeHHOH. 3a,n:aIOTCH MCXO,l(Hble 3HaQeHJlH MMH If OTBeTBJIeHIfM. IlTe-
u
paUIfOHHbIM rryreM HaXO,l1IfTCH perneHIfe, y,lJ;OBJIeTBopHlOlI(ee 3HaQeHIflO nOJIHOM

 FJ/a8a 6. CucmeMbi nUmaHUJI aHmeHHbIX pewemOK
BXO,n:HOH npoBo,n:lfMOCTIf If ypaBHeHIDIM MO,n:OBbIX HanpIDKeHlfH. 06bIqHO 3TOT MeTO,n:
o6eCneQMBaeT CXO,aHMOCTb 3a 6-10 HTepaQHH, H OH HCnOJIb30BaJICR ,n:JUI paCqeTa
u
MHorHX JIHHeHHbIX H TIJIOCKHX I.IJ;eJIeBbIX aHTeHHblX pemeTOK, BKJIIOQaR pemeTKM C
npo<pHJIHpOBaHHoH orH6alO:rn:eH 60KOBbIX JIeneCTKOB (CM. rJI. 3). CxeMa AP Ha OCHO-
Be npo,n:OJIbHbIX BOJIHOBO,n:HbIX I.IJ;eJIeH nOKa3aHa Ha pHC. 6.7.
Puc. 6.7. n pO.n;OJIbHbIe rnYHTMpYlOllIJle meJIM
6. 1.2. AHTeHHble peweTKM 6erYl1.\eM BonHbl
AHTeHHaR pemeTKa 6eryIIJ:eti BOJIHbI (TW), KaK 11 pe30HaHCHaR aHTeHHaSI pemeTKa,
HMeeT pacnpe,aeJIeHHble B,n:OJIb JIHHHH nepe,n:aQH 113JIyqalOI.IJ;l1e 3JIeMeHTbI. O,n:HaKo
nHTaHl1e 3TOH AP ocyrn:eCTBJIReTCR C o,n:Horo KOHIJ;a, a Ha ,apyroM ee KOHIJ;e BKJIIO-
qeHa HarpY3Ka. IIo Mepe pacnpOCTpaHeHMR BOJIHbI B036y)1(,[(eHI1H no AP qaCTb ee
3Heprl1H H3.rryqaeTCR, a He60JIbllIaR OCTaBmaHCR qaCTb norJIOmaeTCH KOHueBOH Ha-
rpY3Kon. II03TOMY 3JIeMeHTbI, pacnOJIO)l(eHHbIe B6JIH311 nHTalOI.IJ;erO KOHQa, cJIa60
u u
CBR3aHbI C nepe,n:alOI.IJ;eH JIlfHHelf, a 3JIeMeHTbI Ha HarpY30QHOM KOHQe - CMJIbHO.
Bo H36e)l(aHHe nORBJIeHHR cHH<pa3HbIx OTpa)l(eHHM 3JIeMeHTbI He ,n;OJDKHbI pacrrOJIa-
raTbCH C nOJIYBOJIHOBbIM llIarOM, n03TOMY TW-perneTKa HBJIReTCH Hepe30HaHCHOH.
113-3a Hepe30HaHCHoro 3HaQeHlfR rnara pemeTKll OCHOBHOH JIeneCTOK ,n:lfarpaMMbI
HanpaBJIeHHOCTIf HeMHoro nepeMeI.IJ;aeTCH C QaCTOTon. llIar pa3Mell.(eHHH 3JIeMeH-
TOB MO)l(eT 6bITb KaK MeHbrne, TaK If 60JIbme nOJIYBOJIHOBOrO 3HaQeHIDI; 3TH CJIyqaH
06Cy)I(,[(alOTCSI ,n;aJIee. PeaKTHBHaR npOBO.III1MOCTb CBR3aHHbIX 3neMeHTOB MeHbilie
I1JII1 paBHa HYnlO, TaK qTO rrceB,aOCJIyqaHHaH CYMMa ,n;aHHbIX BenHqHH I1MeeT He-
60nbIlloe 3HaqeHHe. npl1 3a,n:aHHOM Tpe6yeMoM aMTIJII11)',n;HOM pacnpe,aeJIeHHH AP
Heo6xo.IlHMO np0l13BeCTH paCqeT JIHHI1H nepe,naql1 11 nOJIyqHTb 3HaqeHIDI CBR311
3JIeMeHTOB.
6. 1.2. 1. "IacToTHoe CMeu.ceHMe MaKcMMYMa ,qJfarpaMMbl
HanpasneHHocTM Jf ycnosJfe e,qJfHCTSeHHOCTJf ny"a
,[(JIH nl1TaHIDI AP HCnOJIb3YlOTCH KaK TEM-nHHlfH, TaK If ,nHcnepCMOHHbIe JIHHMH
nepe,naqM. <I>a30BaR CKOpOCTb BOJIH B HMX MO)l(eT 6bITb BbIllie (BOJIHOBO,n;), paBHa
HJIH HIDKe (KoaKCHaJI C ,nM3JIeKTpHQeCKMM 3anOJIHeHMeM), QeM B BaKYYMe. B KaKOM

6.1. IIoCfleao6ame.nbHble JlUHUU nUmaHUJl d
,D;Jilana30He 3HaqeHllH mara pemeTKll cym:ecTByeT TOJIbKO OllHH JIyq? TIoKa3aTeJIbHbI
L(Ba npHMepa. TIepBbIH - TEM-JIHHH.SI C Me)K3JIeMeHTHbIMH CB.SI3.SIMH, CL(BHHyrbIMH
Ha Jt no <pa3e. He06xoL(HMOCTb HecHH<pa3HoH CB.SI3H 06"bHCHHeTcH HIDKe. ECJIH, KaK
06bIQHO, 8 - yrOJI, H3Mep.SIeMbIH OT HanpaBJIeHHH, nepneH,LJ;HKYJI.SIpHOrO paCKpbIBY
aHTeHHbI, a d - mar pemeTKll, TO Me)K3JIeMeHTHbIH <pa30BbIH c.uBHr, He06xoL(HMbIH
,l.UI.SI nOJIO)KeHH.SI rJIaBHOrO JIyqa nOL( yrJIOM 8 0 , COCTaBJIHeT kd sin 8 0 , 3HaqeHHe <pa3bI
BL(OJIb JIHHHH nllTaHH.SI paBHO kd + Jt, r.ue Jt - HecHH<pa3HbIH qJIeH. TaKllM o6pa-
30M, <pa30Boe ypaBHeHHe llMeeT BH,Q
kd sin 00 + 2nJt = kd - Jt.
(6.11 )
KIDK,LJ;oe 3HaqeHHe n > 0 COOTBeTcTByeT peaJIbHOMY JIyqy, rrpHQeM n-H JIyq B03-
HHKaeT npH d/A = (n + 1/2)/2. Ha pHC. 6.8 nOKa3aHa 3aBllCHMOCTb yrJIOBOrO nOJIO-
lKeHllH JIyqa OT d/A ,LJ;JI.SI nepBbIX Tpex JIyqeH. IIpH d/A <0.25 He cym:eCTByeT nOJIHO-
CTblO a.,zJJJ;HTllBHbIX nyqeH, a rrpH d/A  0.75 HMeeTC.SI .uBa JIyqa. TaKllM o6pa30M,
pa60qHH .uHarra30H 3HaqeHHH d/A COCTaBJI.SIeT 0.25 <d/A <0.75. YroJI Me)l()];y MaKCll-
M)'MOM L(llarpaMMbI HarrpaBJIeHHOCTH H OCblO CHMMeTpHH aHTeHHbI MOlKeT 6bITb
JIH60 OCTpbIM (d/A> 0.5), JIH60 TynbIM (d/A <0.5). 113MeHeHHe 3Toro yrJIa C qaCTO-
TOH nOKa3aHO HaKJIOHOM KpHBOH C n = O. PemeTKa C marOM, paBHbIM 0.5A, npeL(-
CTaBJIHeT C060H QaCTHbIH CJIyqaH AP nOnepeQHOrO ll3JIyqeHHH. O.uHaKo L(aHHOe
3HaQeHHe mara n03BOJI.SIeT CKJla,r(bIBaTb nOJIHble npOBo.uHMOCTll Bcex 3JIeMeHTOB,
qTO npHBO,LJ;HT K Y3KOnOJIOCHbIM pa60QHM xapaKTepllCTHKaM AP CTOHQeH BOJIHbI,
paccMoTpeHHoH B pa3,neJIe 6.1.1.
1.0
 8=k
C"')
0.8 C\:S
::I::
<J)
:s:
::I::
0.6 <J)

C\:S

O.l. t:::
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0.2
(1)0
c
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0.2
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0.6 :s::
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0.8 
C\!

t:::
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1.0 
0 0.2 0.4 0.6 0.8 1.0 1.2 1.' 1.6 1.8 2.0
d/}'
PHC. 6.8. 3aBI1CI1MOCTb IIOJIOXeHI1H JIyqa aHTeHHOH perneTKI1 6eryw:eH BOJIHbI
OT rnara perneTKI1

 Dla6a 6. CUCmeMbl nUmaHUJI aHmeHHblX peUJemOic
Tenepb HCHO, nOqeMY He)l(eJIaTeJIbHO HCrrOJIb30BaTb aHTeHHbIe TW-perneTKH C
cHH<}>a3HoM CBH3blO. <l>a30Boe ypaBHeHHe B 3TOM cJIyqae HMeeT BH,l(
kd sin 8 0 + 2nrc = kd.
(6.12)
JIH n = 0 (sin 8 0 = 1) 3TO ypaBHeHHe npH JII060M 3HaqeHHH rnara ,l(OnycKaeT
HaJIHqHe HarrpaBJ1eHHOrO Brrepe.n; rJIaBHOrO oceBoro JIyqa. XOTH JIyql1, COOTBeTCTBY-
10111;I1e n = 1, 2 H TaK ,l(aJIee, opHeHTHpOBaHbI no,l( Tpe6yeMbIMH yrJIaMH, oceBOH J1yq
npHcyrcTByeT Bcer.n;a.
BTOpOM npHMep - 3TO BOJIHOBO,l(HaH aHTeHHaH perneTKa C npOTI1Bo<pa3HoM
CBH3blO. B CJIyqae CHH<pa3HOH CBH3H, rrpH JII060M 3HaqeHI1H rnara I1MeeTCH J1yq C
sin 8 0 = f3/k. ,LI;JIH CJIyqaH rrpoTHBo<pa3HoM CBH3H <pa30Boe ypaBHeHHe HMeeT BH.n;
kd sin 8 0 + 2nrc = f3d - 3t.
(6.13)
B 3TOM CJIyqae 11 rrOJIO)l(I1TeJIbHbIe, H OTpHuaTeJlbHbIe 3HaqeHHH n COOTBeTCTBY-
lOT pearrbHbIM JIyqaM. Ha pHC. 6.9 nOKa3aHa 3aBHCHMOCTb nOJlO)l(eHHH JIyqa OT d/A
,l(JIH nepBbIX Tpex JIyqeH. fpa<}>HK rrOCTpoeH rrpH 3HaqeHHH (3/k = 0.6. TIpH (3/k = 0.5
o6e MO,l(bI, COOTBeTCTByJOiliHe n = 1, B03HHKalOT IIPH 3HaqeHHH d/A = 1. nOCKOJIbK)'
BOJIHOBO.n;bI 06bIqHO I1CIIOJIb3YlOTCH C 60nee BbICOKHMH 3HaqeHHHMH f3/k, pa60QHH
,ilHana30H COCTaBJ1HeT
0,5 d 1,5 A / k 0 5
<-< , p >,.
1 + (J3 / k) A 1 + (J3 / k)
(6.14)
1.0
0.8 81le = 0.6
0.6
0.1.
0.2
(J:) 0
c 0
,(/)
-0.2
- 0,1.
-0.6
-0.8
-1.0
0 0.2 O.L 0.6 0.8 1-0 1.2 1.[, 1.6 1.8 2.0
d/).
PHC. 6.9. 3aBHCHMOCTb rrOJIOXeHHB nyqa aHTeHHOH perneTKH 6erymeH BOnHbJ
OT rnara perneTKM
.L

6.1. IlOCJleiJoeameJlbHble AUHUU nUmaHUJI d
B BbI6paHHoM npMMepe nyq, cooTBeTcTByrorn;MH 3HaqeHMIO n = -I, B03HMKaeT
npll dl'A = 1.25, Tor.n;a KaK .rryq, cooTBeTcTByroI.UllH n = 1, B03HllKaeT IIpll dl'A =
= 0.9375. He IIOKa3aHHbIH JIyq .runI 3HaqeHllH n = 2 B03HMKaeT npll dl'A = 1.563. 3TOT
PllCYHOK ,UaeT KapTllHY o6pa30BaHllH MO,I(, HO He rO,UllTCH ,l])UI paCqeTa, nOCKOJIbKY
npllMeHllM TOJIbKO ,lJ,JIH 131 k = 0.6. Ha pllC. 6.10 nOKa3aHa 3aBllCllMOCTb yrJIOBOrO no-
JIO)l(eHllH JIyqa OT llIara perneTKll WIH pa3JIllQHbIX 3HaQeHllH I3lk: I3lk = 0.5(0.1)0.9.
C nOMOIUblO 3Toro rpacplfKa 3HaQeHlfH I3lk If dl'A MOryr 6bITb COrJIaCOBaHbJ WIH Toro,
QT06bI 3an;aTb nOJIO)l(eHlle <pI1KclfpoBaHHoro .rryqa.
0.8
0.'
-0.'
0.2
o 0
c
.-
'"
-0.2
-0.6
-0.8
-1.0
o
0.2
0-1.
0.6
d/
0.8
1 0
PUC. 6.10. 3aBHCHMOCTb yrJIOBOrO IIOnO)l(eHHH O,nHHOQHOrO nyqa OT rnara perneTKH
. TIo HaKJIOHY KpllBbIX MO)I(HO Bll,aeTb, QTO M3MeHeHlle nOJIO)l(eHllH JIyqa c QaCTO-
TOM 3HaQMTeJIbHO. TIOJIe3HO llMeTb HBHYIO <}>OPMYJIY MH HaKJIOHa. ,L(H<}><t>epeHI(llpO-
BaHlle sin 8 0 no QaCTOTe C nOCJIe.n;yIOIUllM yMHO)l(eHlleM .anH HOpMllpOBaHllH HaKJIO-
Ha .n;aeT Bblpa)l(eHMe
f d SIDe 0 = ').} / ')...2 c + 1
df r3 I k 2d I A
(6.15)
TIocne,n;Hee BbIpa)l(eHlle co,n;ep)I(HT TPM B3allMOCBR3aHHble nepeMeHHbIe, o,n;HaKO
ero MO)I(HO yrrpOCTlfTb
f d sin eo 1 . e
= - SIn .
df r3 I k 0
(6.16)
3aBMCMMOCTb HOpMRpOBaHHoro HaKJIOHa OT sin 8 0 npRBe,I(eHa Ha pRC. 6.11. KaK
R OaJIOCb, 3HaqeHllR I3lk, 6JIll3Klle K e,n;llHMI(e, paBHO KaK M 60JIbllIlle 3HaQeHll.SI

 f/la8a 6. CUCmeMbl numaltUJI altmeltltbDC peUlemOK
3
2.5
:I:
0 2
Q

::c
'::s::
:a
:I:
:I: ,.5

j:Q
0
c.
::s::

Q..
0
::t 1.0
O.g
0.5
o
-1.0 -0.8 -0.6 -0.1. -0.2 0 0.2 0.1. 0.6 0.8 '.0
sin '0
PUC. 6.11. 113MeHeHHe nOJIO)((eHHjI JIyqa aHTeHHOH perneTKH 6eryrn:eH BOJIHbI
C qaCTOTOH
sin 8 0 , npHBO)J;HT K MeHbIIIHM 3HaqeHIDIM !laKJIOHa. KpHBble 06pbIBalOTCR npH Tex yr-
JIax, r,n;e B03HHKaeT BTOpOH .rryq; TaKHM 06pa30M, .n;aHHble KpMBble )'Ka3bIBa1OT npaK-
TlftleCKHH ,n;l1ana30H paCqeTa. LI:1liI OIITHMH3aIJ;HH paCqeTa, C yqeToM KOHKpeTHoro
rrpWMeHeHIDI, yrJIOBOe nOJIO)l(eHHe JIyqa 8 0 , 3Ha'IeHMe (3/k B BOJIHOBo.n;e, mar pa3Me-
:I,QeHHR 3JIeMeHTOB H HOpMHpoBaHHbIR HaKJIOH MOryr 6bITb B3aHMOCOrJIaCOBaHbI.
6. 1.2.2. Bb''II'ICneHl'le BKTI'IBHOM npoBoJ;tI'lMOCTI'I aneMeHTB
IIpH TO'IHOM BblqHCJIeHHH CBR3H B aHTeHHOR pemeTKe 6eryw;eH BOJIHbI HCrrOJIb3Y-
IOTCR MaTpHUbI A-B-C-D, CBR3bIBalOIUI1e Bce <pparMeHTbI BOJIHOBo.n;a (Me)l():(Y m:eJIR-
MH) H rrOJIHYIO rrpOBo.n;HMOCTb OT.n;eJIbHbIX m:eJIeR C .n;pyrHMI1 <pparMeHTaMH, 'ITO rro-
3BOJIReT orrpe.n;eJIHTb rrOJIHyIO BXO.n;HyIO rrpOBo.n;I1MOCTb, KaK 3TO .n;eJIaeTCR B cnyqae
pe30HaHCHbIX AP. AHTeHHble pemeTKll 6erym:eH BOJIHbI 06bI'IHO MMelOT MHoro 3ne-
MeHTOB, a CBR3b Ka)l(,L(orO H3 HHX Marra, H nOCKOJIbKy rrOJIHble IIpOBO.IJ:WMOCTH 3JIe-
MeHTOB H3-3a HppaIJ;MOHaJIbHOrO 3HaqeHI1R IIIara CKJI3):(bIBaIOTCR rrceB,UOCJIyqaRHbIM
06pa30M, 3Toro 06bIqHO 6bIBaeT .n;OCTaTO'IHO WUI npHHRTMR .n;OrryIl.(eHHR 0 cornaco-
BaHHOCTH AP B nlO6oR TOQKe.
Ha Ka)l()lOM 3neMeHTe rrpOHcxo.n:HT .n:eneHHe MOIUHOCTH: 'IaCTb ee ocyrn:eCTBJIHeT
B036}')K,L1;eHHe 3JIeMeHTa, a OCTaJIbHaR qaCTb, I1CIIbITaB HeKOTopoe 3aTYXaHHe B BOJI-
HOBo,n;e, rrpoxo.n;HT K cne,n;yrom:eMY 3JIeMeHT)'. IIYCTb XeJIaeMOe pacrrpe.n;eJIeHHe
MOIU;OCTI1 B036}')K,L1;eHHH AP npOrrOpIJ;110HaJIbHO En' r.n;e 3HaqeHI1e n H3MeHHeTCH OT

6.1. IIOCJlea08ameJlbHble IlUHUU nUmaHUJI 
n = 1 ,[(0 N. 0603HaQHM ,[(01110 BXO,[(HOU MOIIJ:HOCTH, pacceHBaeMyro Ha KOHQeBoH
HarpY3Ke, KaK L
L= I1 ,
n
( 6.17)
a pacrrpe,[(eneHHe aKTMBHoM npoBo,[(MMOCTH B,[(OJIb BOJIHOBo,[(a KaK G n . IIpM yqeTe
u
IIoTepb B BOJIHOBO)Ie MHO)l(HTeJIb s, OIIMCbIBalOII..I;HH IIoTepH MOlQHOCTM Me)l(,l(Y lQe-
JUIMH, I1MeeT BH,[(:
s = exp( -2ad). (6.18)
liar pa3MemeHHH 3JIeMeHTOB paBeH d, a K03<P<PHUHeHT 3aTyxaHHH a npHBO-
,[(HTCH B CTaH,IJ;apTHbIX yqe6HHKax no 311eKTpoMarHHTHoM TeopHH. MCrrOJIb3YH cxeMY
Ha pHC. 6.12, CHaQarra 3anHIlleM BbIpa)l(eHHe .lUIH rroc1Ie,[(HeM CBH3H, 3aTeM ,[(1IH CJIe-
,[(YIOIII;ei1: H TaK ,[(arree.
G - FN _ FN .
N - P N - 11 '
N
L Fmsn-m + I1sn-N
m=n+ 1
.
,
FN-I .
,
FNIs+Ptl s
G - F I
1-
R -R (
In
(6.19)
G - FN-l
N-I - -
PN-I
On =
Fn
(6.20)
F 1
t
F
2
t
F
N-1
t
F
N
t
G,
G 2
G N - 1
S
5
-.
Pin
-+
P2
-.
P N - 1
--+
PfJ.
PHC. 6.12. 3JIeKTpHQeCKaH cxeMa aHTeHHOH perneTKH 6eryIlIeH BOJIHbI
BXO,[(HaH MOlQHOCTb paBHa MOlQHOCTI1 B HarpY3Ke n1IIOC cYMMapHa.H MOmHOCTb
,LLJISI cBH3ei1:, Ka)l(,l(aH H3 KOTOpbIX YMHO)l(aeTC.H Ha K03<P<PHQHeHT nOTepb lis, COOT-
BeTcTBYIOI..QHM HOMepy <pparMeHTa: .
N
n = L FmsI-m + Sl-N. (6.21)
m=]
1I.H HCKJIIOQeHHH Pin H HaXO)l(,[{eHHH Pt MOryr HCn01Ib30BaTbCH ypaBHeHM.H
(6.20) H (6.21):
= L (;. F n .
1-LsI-Nsn
IIo,[(cTaB1IHH 3TO 3HaqeHHe B BbIpa)l(eHHe .lUIH G n , nOC1Ie HeKOTopOH neperpyrr-
nHpOBKH no.rryqaeM ypaBHeHHe ,LLJIH aKTHBHOH npOBo.nHMOCTH:
Fn I s n
1 N F n F. .
I - LSI-N L S : - L S :
m=] m=I
( 6.22)
G n =
(6.23)

 Dla8a 6. CucmeMbl numaHUR aHmeHHbIX peUlemOiC
ECJIM nOTepH npeHe6pe)l{lfMO MaJIbI, TO S = 1. 06bIqHO rrOTepH yqHTbIBalOTCH
TOJIbKO B TOM CJIyqae, KOr,L(a OHM BeJIMKH, MJIM KOr,L(a Me)l(3JIeMeHTHble nOTepH
CpaBHHMbI C MHHMMaJIbHbIMM nOTepHMll, 06YCJIOBJIeHHbIMM aKTllBHOM rrpOBO,ll;HMO-
CTblO. K03<P<PHIJ;MeHTbI B036)')K,L1;eHM.H Fn 06bIQHO HaXO,L(HTCH M3 pacnpe,L(eJIeHlUI, Ha-
npMMep, OllHorrapaMeTpllQeCKOrO pacrrpeJ],eJIeHllH Teitrropa MJIM pacrrpe,aeJIeHMH
TeMJIOpa C napaMeTpOM n , a HOPMMpYIOIII:Me MHO)l(J1TeJII1 Fn 06eCrreQMBalOT Pin = 1.
OTMeTHM, qTO ,aOJIH OTBO,ll;MMOM MOIII:HOCTM CBH3ll Ha Ka)l(,[(OM IUeJIM paBHa
Gj(1 + G). qacTo BCTpeqaeTCH HerrpepbIBHaH BepCMH ypaBHeHMH (9.169) [44]
G( ) = F(x)
X L /2 x .
1 J [F(y) + R(y)]dy - J [F(y) + R(y)]dy
1 - L -L/2 -L/2
(6.24)
3,lIeCb R(y) - IIOTepM Ha e.lU1HHl\Y ,lLJIHHbI BOJIHOBo,aa. O,aHaKO, KaK MO)I(HO O)l(J1-
u
,[(aTb, .n;I1CKpeTI13al\MH HenpepbIBHbIX pe3YJIbTaTOB ,lIJIH IIOJIyqeHMH 3HaQeHMll CBH3M
m:eJIeii MeHee TOqHa, qeM HCnOJIb30BaHI1e <P0PMYJIbI ,lLJIH CYMMbI (ypaBHeHMe 6.23).
LI:JIH He6oJIbllII1X AP llJIll pellieTOK C HM3K11M ypOBHeM 60KOBbIX JIerreCTKOB Heo6xo-
.n;MMO HCnOJIb30BaTb 60JIee TOQHOe ypaBHeHMe.
Ha pMC. 6.13 nOKa3aHbl 3HaqeHMH aKTMBHOM rrpOBOJ],I1MOCTll 29-3JIeMeHTHoM
AP C rrOCTOHHHbIM aMnJIMTY,L(HbIM pacnpeJ],eJIeHlleM npl1 MOIUHOCTM B HarpY3Ke 5,
10 If 25%. MO)I(Ho Bl1,[(eTb, qTO 5- 11 10%-Hble KplfBbIe BbIXO,L(HT 3a rpaHMl\bl llIKa-
JIbl, a MaKCMMyM 25%-HOM KplfBOM JIHilib HeMHoro npeBbIlliaeT 3HaQeHHe 0.1. 3Ha-
qeHMH aKTMBHOM rrpOBOJ],HMOCTI1 ,L(OJI)I(HbI BCer,L(a rrO.I1.L(ep)Kl1BaTbCH MaJIbIMI1; 0.1 HB-
0.28
0.24
-..
u P, = 0.05
::t
(1)
 0.20 N=29

U
--
toO

u 0.16
0

::s::
t::r
0

0 0.12

J::
0::
ro
::t

 0.08


0.04
o
1
5
9
13 17
HOMep eJUI
21
25
29
PHC. 6.13. AKTHBHaH rrpOBO,lI;HMOCTb I..IJ;enH rrpH rrOCTOHHHOM pacrrpen:eJIeHHH

6.1. IlOC/lea06ameJlbHble IIUHUU numaHUH d
JIReTCR XOpOllIHM 3HaqeHHeM ,lLJIR MaKcHMyMa. llOMHMO Tpy,n;HOCTH peaJIH3aI.J;HH
60JIbllIHX 3HaqeHHH, ,lI)IR HHX HeJIb3R 60nee rrpeHe6peraTb 3<p<peKToM paccorJIaco-
BaHHR HMrre,aaHca. KOHeqHO, y 60JIbllIHX AP BeJIHqHHa aKTHBHoH rrpoBo,aHMOCTII
Ha eJIb HHxe. 3TH KpHBbIe .n:JIR N = 29 MO)I(HO (rrpH6nIDKeHHo) npe06pa30BaTb B
YHHBepCaJIbHbIe KpHBbIe rryreM YMHoxeHH5I COOTBeTcTByrorn;HX 3HaqeHHM Ha N 12 =
= 14.5. 3HaqeHH5I aKTHBHOH rrpOBo,n;HMOCTII rrpH pa3JIHQHbIX N TOf.na 110JIyqaIOTC5I
rryreM ,n;eneHH5I HOBbIX 3HaQeHHM Ha N12. O.nHaKo ,n;JI5I 110JIyqeHllH TOQHbIX pe3YJIb-
TaTOB nOCJIe 3a,n:aHHH KOJIHQeCTBa rn;eJIeH He06xo.LJ:IIMO rrpOBeCTH HOBoe BbIQllCJIe-
HHe, OCHOBaHHoe Ha TOJIbKO qTO Ol1HCaHHOM npH6JIIDKeHHOM MacllITa611poBaHHII.
Ha pHC. 6.14 II 6.15 rrpe,aCTaBJIeHbI 3HaqeHHR aKTHBHOll rrpOBo,aHMOCTI1 ,lLJIH o,a-
HOl1apaMeTpHQeCKOrO pacnpeLJ;eneHHR TeHJIOpa M pacrrpe,neneHH5I TeHJIOpa C rrapa-
MeTpOM n = 5. ,D;JI5I 060HX pIICyJIKOB N =29 H SLR = 25 .n:E. OTMeTMM, QTO O.LJ:HOrra-
paMeTpHQeCKOe paCl1pe,aeJIeHHe C CMJIbHbIM YMeHbIIIeHHeM aM nJIMTYLJ;bI K KpaHM
paCKpbIBa LJ;aeT KpHBble C OLJ;HHM l1HKOM, TOrLJ;a KaK rrpH n -pacnpe,aeJIeHIIH C 60JIee
BbICOKHM l1be,n;eCTaJIOM (CM. rJI. 3) rrp05IBJIHeTCR TeH.aeHI.J;HH K HOBOMY pOCT)' KPM-
BOM B6JIII3H HarpY3KH, oco6eHHo rrpH MaJIOH MOlI.{HOCTH B HarpY3Ke.
0.28
0.24 PI = 0.05
,-..., N=29
u
::c
C1)
 0.20
::s::
U
---
..Q SLR = 25 dB
E-<
u 0.16
0

::s:
I::i
0
I:Q
0 0.12

t::

::c
I:Q 0.08
::s:

0.04
o
1
5
9 13 17
HOMep IIJ;eJIH
21
25
29
PHC. 6.14. AKTHBHaH rrpOBOllHMOCTb meJIH rrpH o,n:HorrapaMeTpHQeCKOM pacrrpe.LJ:eJIe-
HHH TeHJIOpa
llOCKOJIbKY Y Bcex KpIIBbIX IIPII 5- H 10%-HoM MOlI.{HOCTH B HarpY3Ke MMeeTCH
rrMK > 0.1, Ha npaKTHKe He06xo,D:IIMO HJIH YBeJIMqHTb MOlI.{HOCTb B HarpY3Ke, TeM
caMbIM YMeHbllIaH KY, IIJIII YBeJIIIQHTb qHCJIO m:eJIeM. M B 3TOM CJIyqae KpHBbIe MO-
ryr 6bITb npH6JIIDKeHHO MacllITa6HpoBaHbI C rrOMom:bIO MHO)KlITeJI5I N /2.

 DlaBa 6. CUCmeMbl numaHUJ/ aHmeHHblX peUlemOiC
0.24
N=29
,,-.... 0.20
u
::t:: SLR = 25 dB
OJ
::g
:s:
U n =5
-- 0.16

E--
U
0
:g
== 0.12
t::i
0
I:Q
0

t::
 0.08
::t
I:Q
:s:
 0.04
o
1
5
9 13 17
HOMep meJIU
21
25
29
PRC. 6.15. AKTHBHa$l rrpOBo,nHMOCTb rn;eJ1H rrpH pacrrpe,L(eJ1eHHH TeHJ10pa c napaMeT-
pOMn
6. 1.2.3. PaClfeT LLlenesoM aHTeHHoM peweTKH 6eryUleM sonHbl
Be3 yqeTa 3<t><l>eKToB B3aIfMHoti CBR311 paCqeT AP Ha OCHOBe ru;eneBoro BOnHOBO,lI,a
6erym:ei1 BonHbI npOCT: ,lLJUI onpe,lI,eneHI1.H )])II1HbI If nOnO)l(eHIf5I Bcex ru;eneti, o6ec-
neqHBalOru;IfX Tpe6yeMyro pe30HaHCHyID npOBO,LI:I1MOCTb, I1crronb3yeTC.H Ta6nl1u;a aK-
TI1BHbIX rrpOBO,lI,IfMOcTeti (CM. npe.1IbI,lI,ymI1M pa3,lI,en) 11 YHI1BepCaJIbHbIe KpIfBbIe ,lUIR
m;enei1 113 rn. 5. C yqeToM B3al1MHOH CB5I3H ru;enH B3aHMO,lI,eMcTBYIOT Cl1nbHO, rr03-
TOMY Heo6xo,lI,IfMO paCCMaTpIfBaTb BCIO AP cpa3Y. 3TO C,lI,enaHO B [14] ,lI,JI5I llIYHTIf-
pyrom;HX (cMeru;eHHbIx) meneti B llIHpOKOH CTeHKe BOnHOBO,lI,a, npMqeM )]:aHHa.H
rrpou;e,n;ypa C paBHbIM ycnexoM npHMeHI1Ma K nlO6oM AP, B KOTopOti B3aHMHaR
CBR3b Me)K,l(y 3neMeHTaMH BbIQHCn5IeTC5I TOqHO. Cy:w:ecTBeHHoe MCKJIlOqeHHe rrpe,n;-
CTaBmIeT C060H AP Ha OCHOBe HaKJIOHHbIX KpaeBbIX BOnHOBO,lI,HbIX m;eneH, no-
CKonbKY 3aMeHa meneti 3KBHBaJIeHTHbIMH ,LI:HnOn5IMH Ba6HHe ,lI,JIR BbIqHCneHHR B3a-
OJ OJ
HMHoro HMrre,n:aHca He ,lI,OCTaTOqHO TOqHa H3-3a rrepeXO,lI,a meneIf C Y3KOH CTeHKM
Ha llIHpOKylO.
MeTO,lI, paCqeTa AP 6erym:ei1 BonHbI no)]:o6eH TOMY, KOTOpbIH Mcnonb3yeTcR ,lLIT5I
pe30HaHCHbIX AP, HO 60nee CnO)l(eH. KaK II B pe30HaHCHOM cnyqae, MO,lI,OBOe Ha-
OJ
npIDKeHIfe ,lLJUI Ka)K)J;OH menH rrponOpU;IIOHaJIbHO HarrpR)I(eHHIO Ha Il.(enH, ,lI,eneHHO-
MY Ha HMIIe)]:aHC CKaHMpOBaHHR:
2 .J a / bCnV n
v -
n - 1t( / k)Yt / Go .
( 6.25)
B OTnMqHe OT pe30HaHcHoi1 AP, Mo,n:OBbIe HarrpIDKeHH5I He paBHbI, IIOCKonbKY
m;enH paCIIOnO)l(eHbI ,lI,pyr OT ,lI,pyra Ha paCCTORHHRX, paBHbIX MppaUHOHaJIbHOMY
qHCJIY ,[(JIHH BonH B BOnHOBO,lI,e. .I1cIIonb3YlOTCH Te )l(e 0603HaqeHH5I, qTO H B pa3,lI,e-
L

6.1. IIOCJle008ameJlbHble J/UHUU nUmaHUJI 
JIe 6.1.1, 3a HCKJIlOqeHHeM MO,nOBbIX HanpIDKeHHH, HMelOru;HX 3,neCb no,nCTpOqHbIe
HH,neKCbI. <I>aKTHqeCIGI, Mo,nOBoe HanpIDKeHHe n-H ru;eJIH CB.H3aHO C MO,nOBbIM Ha-
rrpIDKeHHeM (n - 1)-H ru;eJIH H ee rrOJIHOH npOBo,nI1MOCTblO, r,ne 3JIeMeHTbI HYMepy-
IOTC.H, HaqHHa.H OT HarpY3K11. 3TO COOTHOllIeHl1e I1MeeT BJU(
V n = cosPd + j Yn-l sinpd. (6.26)
v n-l Go
TIapaMeTp Y n onpe,neJI.HeTC.H HlUKe, a d - mar pa3Meru;eHH.H ru;eneH B,nOJIb BOJI-
HOBo,na. 06"be,nHHIDI 3TO BbIpa)l(eHHe C ypaBHeHl1eM (6.25), nOJIyqaeM ypaBHeHHe
u u
,lUI.H oTHom:eHHH HanpIDKeHHH ,nBYX nocne,nOBaTeJIbHbIX ru;eneH:
V n Cn-lYnl ( A d . Y n - l . A d]
= A cos p + ] slnp.
V n - 1 CnY n Go
(6.27)
TIocKOnbKY HanpIDKeHHe Ha ru;eJI.HX onpe,neneHO, eCJIH H3BeCTHbI napI.(HaJIbHaR
MOru;HOCTb B HarpY3Ke L H Bce MHHbI eJIeH H OTBeTBneHI1H, <l>opMYJIa (6.27)
npe,nCTaBJIHeT C060H CHCTeMY 2N - 2 ypaBHeHHH. TalGlM 06pa30M, HCrrOJIb30BaHHe
COOTBeTCTByIOlI.(HX napaMeTpOB meJIeH n03BonHeT nOJIyqHTb He06xo,[(HMbIe OTHOllIe-
HHH HanpIDKeHHH Ha m;eJIRX. TIpH 3TOM HCnOJIb3yeTcH MeTO,n B03Myrn;eHHH C Ha-
qaJIbHbIMH 3HaqeHHHMM MMH I.IJ;eneH H OTBeTBJIeHMH. )];JI.H AP C N 3JIeMeHTaMM
HMeeTCH 2N HeM3BeCTHbIX; OCTaBllIHeCH ,nBa ypaBHeHMH 6epyrcH M3 YCJIOBHH ,lUIH
nOJIHOH BXOI(HOH npOBO.l{HMOCTH. KaK H B cnyqae pe30HaHcHoH AP, OHa ,nOJI)l(Ha
paBHHTbC.H 1 + jO. O,nHaKo nonHaH BXO,[(Ha.H npOBo,nHMOCTb 3,[(eCb He .HBJI.HeTCR npo-
u v u u
CTOH CYMMOH nOJIHbIX aKTMBHbIX rrpOBo,nHMOCTeH Il(eJIeM; npaBMJIbHee HCnOJIb30-
BaTb KaCKa;:I:Hoe coe,[(HHeHHe JIHHHH nepe,naqH. Qepe3 Y n 0603HaqaeTC.H nonHaSl
npOBo,nHMOCTb BOJIHOBo.aa, M3Mep.HeMa.H B6JIM3M n-H meJIH (BKJIlOqalOma.H nOJIH}'IO
npOBo,nHMOCTb BOJIHOBo,na BHe Il(eJIH M nonHyIO aKTHBHYIO npOBo,nHMOCTb ru;eJII1),
OHa HMeeT BH,LI;:
Y n Yn A Y n - 1 cosPd + jG o sinPd
-=-+ .
Go Go Go cosPd + jY n - 1 sinPd
YpaBHeHMe (6.28) npHMeHHeTC.H nocne,nOBaTenbHO, HaqHHa.H OT meJIH, 6JIlDKaH-
meH K HarpY3Ke, r,ne JI =  A + GO, nOKa He onpe.aeJI.HeTC.H nOJIHaH Bxo,nHa.H npOBO-
,nHMOCTb. TIpH npaBHJIbHOM BbI60pe MI1HbI meneH H OTBeTBJIeHHH OHa ,lJ;OJI)I(HO
6bITb paBHa 1 + jO. 3TH ,nBa ,neHCTBHTeJIbHbIX ypaBHeHIDI BMeCTe C 2N - 2 ypaBHe-
HHHMH wrn MO,nOBbIX HanpIDKeHMH 06pa3yIOT CHCTeMY 2N ,neHcTBHTeJIbHbIX ypaBHe-
HHH, He06xo,lJ;HMbIX M.H perneHH.H 3a):(aQH. 3TH ypaBHeHH.H TaIOKe MOryr pellIaTbCR
HTepaIJ;HOHHbIM nyreM C nOMOI.IJ;blO MeTo,[(a HbIOTOHa- Pa<l>coHa. Ha pHC. 6.16 H306-
pIDKeHa AP 6eryI.I.J;eH BonHbI Ha OCHOBe MHKpOnOJIOCKOBbIX H3JIyqaTeJIeH; OTMeTHM
u
H3MeHeHHe B pa3Mepax H3nyqaTeJIeH C IJ;eJIblO COrJIaCOBaHHR conpOTHBJIeHIDI CB.H3H,
HMelOIl(erO BH,[(, nOKa3aHHbIH Ha pHC. 6.14. Ha pHC 6.17 M306pa)l(eHa AP CHCTeMbI
ABAKC, B KOTOpOH rOpl130HTaJIbHbIe BonHOBO,[(HbIe JIHHeHKH npe,nCTaBJI.HIOT C060H
AP 6eryI.I.J;eH BOJIHbI Ha OCHOBe KpaeBbIX meJIeH. 3Ta AP HMeeT OQeHb HH3KHH ypo-
BeHb 60KOBbIX JIerreCTKOB (-50 ,[(E).
(6.28)
e-{ J.. ,


}
[
J · t: ,J
Iv -j 
PRC. 6.16. AHTeHHaH perneTKa 6eryrn;ei1 BOJIHbI Ha OCHOBe MHKpOnOJIOCKOBbIX 3JIe-
MeHTOB


ffla8a 6. CucmeMbl nUmaHUJl aHmeHHbLX peUlemOK
. . .;.::..;':.;.:".
. ".'. .'
;$;j:!\\\::\\\\.\\;\%\\0m\\\$);\t(;:)\\.
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. .  ":.""-.':.'.,1:\'"","'I':._'
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. .... ' '--,,' .', .' ....- '\'. .' .
.--:' .." ." . .--':.: '::':.f
:..t:;:'\\;\':\:;\"\'
Puc. 6.17. AHTeHHaR perneTKa C HH3KMM ypOBHeM 60KOBbIX nerreCTKOB Ha OCHOBe
HaKJIOHHbIX IIJ;eneH B Y3KMX CTeHKax BOJIHOBO,l(a
Y OIlHcaHHbIX 3L(eCb AP 6eryIIJ;eH BOJIHbI yrJIOBOe rrOJIO)l(eHHe JIyqa H3MeHHeTC5I
C qaCTOTOM BCne,lJ;CTBHe rrOCJIe.n:OBaTenbHoro xapaKTepa rrHTaHHH. 3TO ,lJ;BH)I(eHHe
JIyqa MO)l(eT 6bITb YCTpaHeHo rryreM HCrrOJIb30BaHH5I nHTaHH5I C paBHoH ,lLJIHHOH
TpaKToB, cxeMa KOToporo rrpHBe,neHa Ha pRC. 6.18 [7].
I13JIyqalO1lilfe 3JIeMeHTbI
Bxo,n;
Bxo,n;
ACIfMMeTpl1QHaR cxeMa
Puc. 6.18. CxeMbI ITHTaHMR C paBHoM ,lLJIHHOll TpaKTa
npl1 3TOM, K CO)l(aJIeHlflO, rrpocToTa H .n:erneBH3Ha KOHCTPYKUHI1 nOCJIeL(OBaTeJIb-
Horo rrl1TaHHH perneToK 6eryIIJ;eit BOJIHbI 6bIBalOT B 3HaQl1TeJIbHOH Mepe rroTepRHbI.
I.IJ:eJII1 C rrOCJIe.n:OBaTeJIbHbIM rrHTaHHeM B 3TOH cxeMe He H3JIyqalOT Herrocpe,nCTBeH-
HO, a KIDK,Z:(aH rrHTaeT BOJIHOBO,n. H3JIyqalOID;He 3JIeMeHTbI pa3MeIII.aIOTCH B KOHue
BOJIHOBo,na. CxeMa YCTpoeHa TaKHM 06pa30M, QTO ,lLJIHHa rrpo6era BOJIHbI B BOJIHOBO-

6.1. IloCl/eoo80menbHble flUHUU nUmOHUJI 
,ae OT Bxo.n;Horo oTBepcTHH .n;o Ka)l(,[(OrO H3 H3JIyqalOIllJlx 3JIeMeHTOB o.n;Ha 11 Ta )l(e,
rr03TOMY HMKaKMX 113MeHeHHH rrOJIO)l(eHJ1H nyqa C qaCTOTOM He rrpOMCXO):{MT. ,[(pyroe
rrpeMMym:eCTBO COCTOHT B TOM, qTO M3JIYQaTeJIJ1 J1CnbITbIBaIOT o.n;HHaKOBbIH 3<p<peKT
BJIMHHHH ,l(HCnepCHM B BOJIHOBo.n;e. J13JIyqaIOIUMe BOJIHOBO.n;bI pacnOJIO)l(eHbI B.n;OJIb
HanpaBJIeHHM MaKCI1MYMoB .n;MarpaMMbI HanpaBJIeHHOCTI1 aHTeHHbI TaKI1M 06pa30M,
QT06bI anepTypa 6bIJIa nOrrepeqHO-HanpaBJIeHHoi1. 3TO 3a,uaeT yrOJI Me)l(.l(y nMTalO-
II.:(I1MM 11 M3JIyqaIOIll.HMI1 BOJIHOBo,UaMI1.
6.1.3. "IacToTHoe CKaHpOBaHe
TIPM YBeJIMqeHMM ,lI,nMHbI TpaKTa Me)K)J.y 3JIeMeHTaMH .n;OCTl1raeTCSI BbIl1rpbIlli B 3Ha-
qeHMM yrna OTKJIOHeHI15I JIyqa C qaCTOTOM, npM KOTOpOM CKaHl1pOBaHMe rJIaBHOrO
JIyqa ocymeCTBJIHeTCH He60JIbIllMM M3MeHeHI1eM qaCTOTbI. TaKl1e aHTeHHble perneT-
KI1 HBJISIIOTCSI pa3HOBM,1J:HOCTblO aHTeHHblX pellieTOK 6erymeM BOJIHbI, ):{OCTaTOqHO
Ba)I(HOM, qT06bI rrOCBHTI1Tb eM oT.n;eJIbHbIH pa3.n;eJI.' TIpe.n;nOJIO)l(I1M, qTO 113JIyqalO-
IUl1e 3JIeMeHTbI, pacrrOJIO)l(eHHble C rnarOM d, cBSl3aHbI 1130rH)'TOll (3MeeBH.n;Holl)
JIHHMeM nMTaHM5I C ,lI,JII1HOll S J1 BOJIHOBbIM qMCJIOM (3. <l>poHT BOJIHbI onpe,neJIHeTCSI
BbIpa)l(eHMeM
kd sin 8m = (3s - 2mn (6.29)
(CM. cxeMY Ha pl1C. 6.19). 80 M36e)l(aHMe B03HI1KHOBeHHH oceBoro JIyqa ,lI.OJI)I(HO
BblnOJIHSlTbCH COOTHOlIIeHl1e kd > (3s - 2m'Jt. I1CKJIlOqMTb nOHBJIeHHe 60JIee qeM o,n-
Horo fnaBHoro JIyqa (CM. pa31IeJI 2.1) MO)l(HO, o6eCneQMB YCJIOBl1e
d 1
-<
A 1 + sin8 m
(6.30)
J13J1yqalOll(He
Il{eJUI
Bxo,Q
./
BOJIHOBOlI.
HarpY3Ka
PUC. 6.19. CxeMa 3MeeBM.IJ:HOH nI1HMM IIMTaHJHI
<I>a30Boe ypaBHeHMe qaCTO 3arrHCbIBaeTCSI B BHD,e
sin 8 m
SA
dAg
mA
--
d
(6.31)
OqeBH,IJ;HO, qTO 60JIbllIee 3HaqeHI1e s/"A 11, COOTBeTCTBeHHO, 60JIbIllee m, ,IJ;aeT
60JIee 6bICTpoe M3MeHeHHe yrna OTKJIOHeHI1H JIyqa C qaCTOTOM. Ecnl1 npM qaCTOT-

 DlO6a 6. CUCmeMbl nUmaHUJl aHmeHHblX pememoK
,
I,
HOM cKaHHpoBaHHH H3MeHHeTCH HanpaBJIeHHe, nepneH,L(HK)'n5lpHOe pacKpbIBY aH-
TeHHbI, TO Ha6nlO,n;aeTCH 3HaqHTeJIbHOe Jf3MeHeHHe HMne,n;aHCa BCne,n;CTBHe CJIO)l(e-
HH5I aKTHBHbIX npOBO,n;HMOCTeH BCeX 3neMeHTOB. AKTHBHbIe npOBO,n;HMOCTH
3JIeMeHTOB HnH CBH3eH onpe,n;eJI5IIOTCH Tal< )l(e, KaK H ,lJ)I5I AP 6erymeH BOnHbI. ECJIH
H3rH6bI BOJIHOBo,n;a, ifeo6xo,n;HMbIe .nnH C03,n;aHHH 3MeeBH,I(HOH KOHCTp)'KIJ;HH, He,n;o-
CTaTOqHO cornaCOBaHbI no qaCTOTHOMY ,n;Hana30HY, TO MO)l(eT nOTpe6oBaTbC5I BbI-
qHCJIeHHe nonHOH BXO,n;HOH npOBo,n;HMOCTH C nOMOInblO MeTo,n;OB, pa3pa6oTaHHbIX
)lJIH pe30HaHCHbIX AP. OTpa)l(eHHH OT 3neMeHTOB CB5I3H nOpO)l(,I(alOT 60KOBOH JIene-
CTOK B HaIIpaBJIeHHH conpIDKeHHoro nyqa; YPOBeHb 3Toro 60KOBoro neneCTKa 3aBH-
CHT OT aKTHBHbIX npOBo,n;HMOCTeH 3JIeMeHTOB CBH3H, OH 60JIbllIe npH CKaHHpOBa-
HHH B6JIH3H HanpaBneHHH, nepneH,IJ;HK)'JIHpHOrO paCKpbIBY aHTeHHbI.
IIpH npHMOH JIHHHH nHTaHHH pellIeTKH 6eryIl{eH BonHbI nOTepH 06bIQHO 6bIBalOT
He3HaqHTenbHbI, HO: ,n;onOJIHHTenbHaH ,lUIHHa H3BHJIHCTOH JIHHHH IIHTaHHH qaCTO
BHOCHT CyrIJ;eCTBeHHbIe nOTepH. MaKCHMaJIbHbIH KY HMeeT MeCTO npH as = 1, r.ne
S - IIOJIHaH ,lUIHHa 3MeeBH,Lt;HOH JIHHHH nHTaHHH [4]. CooTBeTcTByroI..QHe nOTepH B
nHHHH nHTaHIDI COCTaBnHIOT 4.3 ,n;D. MaKCHMaJIbHaH TOqHOCTb COnpOBO)l(,[(eHHH uenH
pa;:J;apOM, npe.nCTaBnHIOInaH C060H KOM6HHaUHIO KY H IlIHpHHbI nyqa, )];OCTHraeTC5I
,lWH as = 2 npH 8.6 )];D nOTep5IX B JIHHHH nHTaHHH [4]. )J,HcnepcHH B 3MeeBH,I(HOH nH-
HHH HCKa)l(aeT KopOTKHe HMnynbcbI, ecnH MHTeJIbHOCTb HMnynbca MeHbllIe IDIH
cpaBHHMa co BpeMeHeM ero npOXO)l()];eHHH no nHHHH nHTaHH5I. nO.II:p06HbIe BbIqHC-
neHIDI BbIIIOJIHeHbI B pa60Tax [3, 64]. B KaqeCTBe npHMepa npe)];nOnO)l(llM, qTO MHHa
KIDK,[(OH IIeTJIH 3MeeBH,Lt;HOH JIHHHH paBHa nHTH MHHaM BonHbI B BaKYYMe (s = 5Ao),
OTHOllIeHHe BonHOBbIX qHCen B BonHOBo,n;e Ha u.eHTpaJIbHOH qaCTOTe B/k = 0.6, a llIar
pacnOnO)l(eHIDI IneJIeH COCTaBJIHeT IIonOBHH)' ,lWHHbI BonHbI B BaKYYMe. YrnOBoe no-
nO)l(eHHe nyqa ,n;aeTC5I BbIpa)l(eHHeM
sin8 0 = 10
1_ ( °'8/0 ) 2 _06 /0 .
1 ' 1
(6.32)
3Ta 3aBHCHMOCTb H306pIDKeHa Ha pHC. 6.20, a 10%-Ha51 nonoca IIponYCKaHH5I
OXBaTbIBaeT yron CKaHHpOBaHHH 117 0 . THnHqHa51 H3BHJIHCTa51 JIHHH5I nHTaHH5I C HC-
IIonb30BaHHeM 3neMeHTOB CB5I3H Ha 60KOBOH CTeHKe nOKa3aHa Ha pHC. 6.21. 113BH-
nHCTa51 JIHHH5I nMTaHH5I HcnOnb30BaJIaCb TaIOKe ,lUI5I nHTaHH5I UHJIHH,n:pHqeCKHX
pe<pJIeKTopoB. )J,pyrOH cnoco6 KOMIIOHOBKH 3MeeBH,n;HoH JIHHHH nHTaHH5I - renH-
KOH,I(aJIbHa51 cxeMa. 3,n;ecb H3 IIOJIHOTeJIOrO 6JIOKa <ppe3epyeTcH CIIHpaJIbHbIH BOJIHO-
u u u
BO,n; C OTKpbITOH BHelliHeM CTeHKOH, IIOCJIe qero Ha OTKPbITYIO BepXHlO1O qaCTb Kpe-
nHTC5I KpbIIliKa [10]. DOJIee BbICOKaH ,n;HcnepCHH II, CJIe)];OBaTeJIbHO, 60JIbllIHM
HaKJIOH KpHBOH CKaHHpOBaHH5I B rpa;:J;ycax Ha Merarepu IIOJIyqalOTC5I C IIOMOIIJ:blO
u u
,n;HcnepCHOHHoro BOJIHOBo,n;a C IIepHo,n;HqeCKOH HarpY3KOH, aHaJIOrHqHOrO BOJIHO-
BO)];HbIM JIHHH5IM 3a;:J;ep)KJ(H, HCIIOJIb3yeMbIM B JIaMnaX 6eryIl{eM BOJIHbI [30].
ECJIH pa6oqa51 qaCTOTa CJIHIlIKOM 6JIH3Ka K pe30HaHcHoM qaCTOTe AP, ,n;o6aBJI5I-
IOTC5I OTpIDKeHH5I OT H3rH6oB JIHHHH nHTaHHH H 3JIeMeHTOB CB5I3H, ,n;aBa51 3Ha-
qHTeJIbHbIH OTpa)l(eHHbIH CHrHaJI. B pa60Te [22] pa3pa6oTaHbI COrJIaCOBaHHbIe no
HMIIe,n;aHCY HeHaIIpaBneHHbIe 3JIeMeHTbI CBH3H, KOTopbIe IIOKa3aHbI co CTOpOHbI
JIHHHH IIHTaHH5I. OHH II03BOlliIIOT OCyrIJ;eCTBJIHTb CKaHHpOBaHHe C IIpOXO)l(,I(eHHeM
HanpaBJIeHH5I HOpMaJIH K paCKpbIBY aHTeHHbI C He60JIbllIHM yxy,n;llIeHHeM xapaKTe-
pHCTHK. B 3JIeMeHTe CB5I3H HCnOJIb3yeTc5I np5lMoyrOJIbHbIH BOJIHOBO,n;, paCIIOJIO)l(eH-

6.1. IIoCJleiJoBameJ/bHble J/UHUU nUmaHUJl ' 
90
o

o
::t::
A
0::

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SA
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t::::s
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H

s = 51
IJlk=O.6
d/AO=O.S
-90
0.95
1,0
flfO
1.05
PHC. 6.20. fIpl1Mep xapaKTepl1CTMKI1 qaCTOTHoro CKaHl1pOBaHIHI
v v v
HbIM nepneHllHKYJI5IpHO Y3KOH CTeHKe nMTalOm:ero BOJIHOBon:a, C l(eHTpMpoBaHHoH
rnYHTMPYlOmeM m:eJIblO B 3TOM CTeHKe. HanpOTI1B m:eJIM CBH3II B BOJIHOBo,[(e nMTa-
HIIH HaXO,LI,HTCH pe30HaHcHaH MH,LI,YKTMBHaH ,[(Ha-
cPparMa.
,l],JIH YCTPOMCTB C HM3KHM ypoBHeM 60KOBbIX
v
JIeneCTKOB HCnOJIb3yeTcH ycoBeprneHcTBoBaHHbIH
4-nopToBbIM 3JIeMeHT CBH3M Ha OCHOBe CKpemeH-
HbIX BOJIHOBO,LI,OB C ,LI,ByMH napaMI1 KpeCToo6pa3HbIX
meneM CBH311. HarpY3Ka 3Toro HanpaBJIeHHOrO OT-
v
BeTBMTeJIH pacnOnO)l(eHa B KOHl(e H3JIy;qaIOIl(eM
BOJIHOBO,[(HOM JIHHeMKH [1]. Ha PHG. 6.22 H306pa-
xeHa 30Ha CBH3M OTBeTBMTeJI5I S-,[(Hana30Ha. Ha
pMC. 6.23 nOKa3aHa 3aBI1CMMOCTb CllBMTa <t>a3bI OT
CTeneHH CBH3H ,LI,JIH .n;aHHoro OTBeTBHTeJIH, a Ha
pMC. 6.24 - ero TMnHqHOe HcnonHeHHe [1]. B pa-
60Te [52] I1CnOJIb30BaJIaCb r -o6pa3HaH m:eJIb CBH3M.
Ha pHC. 6.25 nOKa3aHa aHTeHHa 0630pHOH Pa.II:MO-
JlOKal(HOHHOM CTaHUHH a3ponopTa. I1cnoJIb30Ba-
HHe llIMpOKOnOJIOCHbIX HanpaBJIeHHbIX OTBTBHTe-
v
JleM, H3rOTOBJIeHHbIX 113 aJIlOMMHHeBoro npOKaTa
nyreM BbICOKOTOqHOH MeXaHHqeCKOH 06paOTKI1 Ha
CTaHKax C qny, n03BOJI5IeT nOJIyqMTb HI13KHM ypo-
BeHb 60KOBbIX neneCTKOB. PHC. 6.21. 3MeeBM,L(Hafl JII1HMfI
TII1TaHMfI


Filaea 6. CucmeMbl numaHUR aHmeHHblX peUlemOK
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l
1/2 BbICOTbI
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-10 -12 -14 -16 -18 -20 -22 -24 -26 -28
CBH3b (,nE)
Puc. 6.23. <I>a30BbIH c,nBl1r KpecToo6pa3Horo meJIeBOrO 3JIeMeHTa CBR311 [1]

6.1. JIoCJleaOeaml!JlbHble IlUHUU numaHUR 
M3BMJIHCTaR
BOJIHOBO.f(HaH
JUIHMH nHTaHHH
HanpaBJIeHHbIM OTBeTBHTeJIb Ha OCHOBe
CKpelI..{eHHbIX BOJIHOBO.f(OB YMeHbIlleHHoM
M cTaH,n;apTHou BbICOTbI C KpecToo6pa3HbIMM
lI..{eJIeBbIMH 3JIeMeHTaMH CBH3H
COrJIaCOBaHHaR OKOHeQHaH
HarpY3Ka HanpaBJIeHHOrO
OTBeTBHTeJIH
M3JIyqalOlI..{Me
II(eJIH
JIHHe:MHble
aHTeHHble
peIlleTKH
CTyrreHQaTbIM nepeXO.f( C BOJIHOBo,na
YMeHbllIeHHoM BbICOTbI
Ha cTaH,n;apTHbIu BOJIHOBO.f(
PHC. 6.24. 3MeeBM,[(Ha5I JIMHM5I TIMTaHM5I aHTeHHOH perneTKM Ha OCHOBe HaKJIOHHbIX
meJIeH B Y3KMX CTeHKax BOJIHOBo,[(a [1]
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PHC. 6.25. AHTeHHa 0630pHOH PJ1C a3ponopTa

 rJla6a 6. CUCmeMbl numaHUfl aHmeHHblX pelUemOK
6.1.4. CKaHMpoBaHMe c nOMOUJ,blO a30BpaUJ,aTeneM
B JIllHeHHbIX rrOCJIe.uOBaTeJIbHbIX l(err5IX IIllTaHll5I CKaHllpOBaHlle MO)l(eT ocy:ru;e-
CTBJI5ITbC5I C rrOMOll(blO <t>a30Bpall(aTeJIen, BCTpoeHHbIX B JIllHllll rrllTaHll5I llJIll He-
rrocpe,n:CTBeHHO y ll3nyqalOll(llX 3JIeMeHTOB. 3TO, COOTBeTCTBeHHO, cxeMbI C rrOCJIe-
,n:OBaTeJIbHO II rrapaJIJIeJIbHO BKJIlOqeHHbIMll <pa30Bpall(aTeJI5IMll. Ha pllC. 6.26
rrpllBe.ueHbI cxeMbI 3TMX KOH<pMrypal(IIH. npM IICrrOJIb30BaHMM AP Ha OCHOBe BOJI-
HOBO)];HbIX ll(eJIeBbIX JIMHeeK MeCTa ,lLJI5I pa3Mell(eHM5I <pa30Bpall(aTeJIeH He OCTaeTC5I.
MHorlie )];pyrMe KOH<pRfypal(IIM rr03BOJI5IIOT BKJIlOqRTb <pa30Bpall(aTeJIll, HarrpMMep,
B cxeMbI rrMTaHM5I, He ll3MeH5IIOll(lIe yrOJI OTKJIOHeHII5I JIyqa (CM. pllC. 6.18). npe-
llMYll(eCTBO rrapaJIJIeJIbHbIX <t>a30Bpall(aTeJIen COCTOMT B TOM, qTO KIDK,[(bIH <pa30-
Bpall(aTeJIb o6pa6aTbIBaeT TOJIbKO 1/ N qaCTb rrepe,n:aBaeMoH MOll(HOCTM M B TpaKT
Ka)l()];OrO 3JIeMeHTa BHeceHbI nOTepll TOJIbKO O,n:HOfO <pa30Bpall(aTeJI5I. He,n:ocTaT-
KOM 5IBJI5IeTC5I TO, qTO OCHOBHon <pa30BbIn C,n:BMf Me)l()Jy 3JIeMeHTaMM <I> == kd sin 8 0
.uOJI)I(eH YMHO)l(aTbC5I Ha HOMep 3JIeMeHTa. IIoCKOJIbK)' rrOqTM Bce <pa30Bpall(aTeJIM
CeMqaC MMelOT l(M<ppoBoe yrrpaBJIeHlIe, rrOCJIe)];Hee Hey,n:06cTBO He3HaqMTeJIbHO.
COBpeMeHHbIe CMCTeMbI l(1I<PPOBOfO yrrpaBJIeHM5I He,n:opOflie. IIpeliMYll(ecTBo MC-
IIOJIb30BaHII5I rrOCJIe.uOBaTeJIbHbIX <l>a30Bpall(aTeJIeH COCTOIiT B TOM, qTO Bce OHM CO-
3.ua1OT O.uMH M TOT )l(e <pa30BbIM C,n:BMf, paBHbIn <1>. He.uOCTaTKH )l(e 3aKJIIOQaIOTC5I
B TOM, qTO rrepBbIH <t>a30Bpall(aTeJIb )];OJDKeH pa60TaTb nOqTM C rrOJIHbIM YPOB-
HeM MOll(HOCTM M rrOTepM Ha <t>a30Bpall(aTeJI5IX 5IBJI5IIOTC5I rrOCJIe,n:OBaTeJIbHbIMM.
IIpM 06eMx TOrrOJIOfM5IX l(errM MMeIOTC5I CMCTeMaTMqeCKlie OIIIM6KH, 06YCJIOBJIeH-
HbIe paCCOfJIaCOBaHlieM IIMrre.uaHca; OHII 06C)')K,I(aIOTC5I rr03)1(e.
3JIeMeHTbI
<I>a30BpamaTeJIli
Bxo,n;
IIapaJlJIeJIbHble cPa30BpamaTeJIH
IIOCJIe,n;OBaTeJIbHble cPa30BpaIl{aTeJIH
Puc. 6.26. CxeMbI TIMTaHIUI C IIOCJIe.n;OBaTeJIbHbIMM JIMHIUIMM
OTMeTIiM oco6eHHocTH <pa30BpaI.UaTeJIen, XOT5I no.upo6Hoe MX 06C)')K,I(eHMe BbI-
XO,n:IIT 3a paMKH ,l(aHHOH KHMfM. <Da30BpaI.UaTeJIII, qaCTO Ha3bIBaeMbIe <t>a30c,n:BI1-
ralOll(IIMM YCTpoHcTBaMII, 6bIBaIOT, B OCHOBHOM, ,n;BYX TlinOB: Ha KOMMyrlIpyeMbIx
JIMHM5IX II <t>eppMToBbIe. B <pa30BpaI.UaTeJI5IX Ha KOMMyrlIpyeMbIx JIMHM5IX IICnOJIb3Y-
IOTC5I rrOJIyrrpOBO)];HMKOBbIe rrepeKJIlOqaTeJIR, no,n:KJIlOqalOI.UlIe RJIM OTKJIlOqalOll(Me
yqacTKH JIMHMI1 rrepe,n:aqR, KOTOpa5I 06bIqHO 6bIBaeT KOaKClIaJIbHOH, MMKpOnOJIOc-
KOBOM llJII1 rrOJIOCKoBOM. IIpM 3TOM MOfyr llCnOJIb30BaTbC5I ,n:RcKpeTHbIe KOMrrOHeH-
.....

6.1. IIoCJleooeameJlbHble J/UHUU numaHUJ/ 
TbI, HO qam:e rrepeKJIlOqaTeJII1., COrJIaCOBaHHbIe HarpY3KM 11 Cpe,lJ;CTBa ynpaBJIeHMH
u
11.3fOTaBJIMBaIOTC.H B BM,ae MHTerpaJIbHbIX MO,lJ;YJIeM, BCTpaMBaeMbIx B rrOJIOCKoByIO
I1.JIM MHKpOrrOJIOCKoByIO JIMHHIO. Hal160JIee yrroTpe6HTeJIbHbIMI1, oc06eHHo B ,n:l1a-
rra30He > 10 ff1(, HBJI.HIOTCH MOHOJIMTHbIe MHKpOBOJIHOBbIe I1HTerpaJIbHbIe CXeMbI.
KOHeQHO, B ,naHHbIX <pa30Bpam:aTeJIHX I1.CrrOJIb3yIOTCH BpeMeHHbIe 3aJ(ep)l(KH, HO
rrOCKOJIbK)' HaH60JIbIlll1.ll pa3pH,n 113MeHeHI1H <pa3bl 06bIQHO COOTBeTcTByeT 180° ,
OHH KJIaCcH<pI1l(MpyIOTCH KaK $a30Bpam:aTeJIH. B l(H<PPOBbIX $a30Bpam:aTeJIHX I1C-
rrOJIb3yeTcR ,nBOI1QHbIll KO,n:: 5-pa3p.H,LI;HbIH <pa30Bpam:aTeJIb 06eCrreQl1BaeT c,nBl1r
a3bI Ha 180, 90, 45, 22.5 11 11.25°. KOHCTp)'KI.J;MH <pa30Bpam:aTeJIH ,n:OJDKHa 06ecrre-
ql1BaTb COrJIaCOBaHl1e I1Mne,naHCOB rrpH nepeKJIIOQeHl111 pa3pH,lJ;OB, a TaIOKe He3Ha-
ql1TeJIbHbIe nOTepH. ECJIH ,nJI.H KOMneHCal(1111 nOTepb B TpaKT BKJIIOQalOTCR YCWIHTe-
JII1., <pa30BpaIIJ,aTeJII1. CTaHOBRTCH HeB3aHMHbIMH.
<l>eppl1.TOBbIe <pa30BpaIII.aTeJIH TaIOKe 6bIBalOT ,nBYX THnOB, M XOTR OHH, no CyrH,
RBJIHIOTCR aHaJIOfOBbIMH YC'TpOllCTBaMH, COBpeMeHHaH TeXHOJIOflliI rr03BOJIMJIa nepeBe-
CTH yrrpaBJIeHHe <pa30ll B l(H<PPOByIO <t>opMY. <l>eppHToBbIe <pa30BpaIII;aTeJIH nOqTH Bce-
r,na pa3MeIII;a1OTCR B BOJIHOBo,Ue. B TOpOH,I:(aTIbHOM <peppHTOBOM <pa30BpaIII;aTeJIe HC-
rrOJIb3yeTcR O,n:HH MJIM HeCKOJIbKO <t>epPI1.TOBbIX TOpOI1)];OB npHMoyrOJIbHOH <pOpMbI,
pa3Mern;eHHbIX B BOJIHOBO,lJ;e TaKHM 06pa30M, QTO OCb TOpOH,I:(OB HanpaBJIeHa B,nOJIb OCH
BOJIHOBo,na. IIII1.Ha B036)')K,L{eHIDI, npo,n:eTa5I Qepe3 TOpOI1,[{, C03,naeT rrOJIO)l(l1.TeJIbHbIM
IUIH OTpHl(aTeJIbHbIll MMrryJIbC TOKa. I1MrryJIbC BbI3bIBaeT HaCbIIII;eHHe TOpOM,II,a, M TOT
MKCI1PyeTC5I B TOqKe nOJIO)l(J1TeJIbHOll MJIM O'TpI1.u;aTeJIbHOll OCTaTOqHOll HH):(yI(IJ;I1.Il.
C,nBHf <pa3 06eCneQHBaeTCH pa3HOCTblO Me)l()JJ' 3JIeKTIII1'IeCKMMM ,lI)IHHaMM ,nBYX COCTO-
RHHll. KaK rrpaBHJIO, HeCKOJIbKO TOpOH,I:(OB pa3Mem:a1OTCH nOCJIe,lJ;OBaTeJIbHO, rrpH 3TOM
3JIeIcrpWIeCKMe )])IHHbI BbI6HpalOTCH TaKMM 06pa30M, qTo6bI 06eCneQMTb N pa3pMOB
c,nBMra <t>a3bI. IIpeHMyJ.IJ;eCTBa H He,nOCTaTKM KOHC'Tp)'KI.J;MH OQeBI1,L(HbI: 3TH <t>a30Bpa-
maTeJIM RBlliIlOTCR HeB3aHMHbIMH M rrpM pa60Te pa,napa ,n:OIDKHbI nepeYCTaHaBJIHBaTbCH
rrOCJIe KIDK,LJ;OrO MMrryJIbCa; MOIII;HOCTb B036)')K,L{eHIDI MCnOJIb3yeTcR TOJIbKO rrpH rrepe-
KJIIOQeHMM, TaK QTO pacxo,U MOIII;HOCTH M TeIIJIOBbl,[(eJIeHHe MMHMMaJIbHbl.
B <peppHTOBOM cpa30BpaIII.aTeJIe C <t>apa,n;eeBCKHM BpaIII.eHMeM I1.CnOJIb3yeTcSI
pacnOJIO)l(eHHbIH B,nOJIb OCM BOJIHOBO,lJ;a $eppMTOBbIH CTep)l(eHb C QeTBepTbBOJIHO-
BbIMM nJIaCTMHaMll Ha KOHl(ax, CJI)')KaI.IJ;HMM ,lLJIH npeo6pa30BaHI1.R JIMHeHHOH nOJIH-
pH3al(HM B KpyrOBYIO 11. Ha060pOT. Ha rrpaKTI1.Ke <l>eppMToBbIM CTep)l(eHb I1MeeT 30-
JIOTOe MJIM cepe6pHHoe rrOKpbITMe 11. rrpe,nCTaBJI5IeT C060ll He6oJIbllIOll <peppI1.TOBbIH
BOJIHOBO,lJ;. 3aTeM 3TOT <t>eppI1.TOBbIM BOJIHOBO,lJ; YCTaHaBJIMBaeTCH B 06bIQHbIH BOJI-
HOBO,lJ; C C)')KaIOIII;MMMCH rrepexo,nHbIMM CeKl(MRMM 6e3 rarrbBaHI1QeCKOrO rrOKpbITMH
Ha KOHu;ax, rrpe,lJ;Ha3HaQeHHbIMI1 llJI5I COrJIaCOBaHIDI ,UBYX BOJIHOBO,UOB. BHeIIIHMH
COJIeHOH,lJ; BOKpyr BOJIHOBO,lJ;a C03,n:aeT HaMafHI1.QI1.BaHl1.e, ynpaBJIHIOm:ee c,nBHrOM
<pa3. TMnHQHbIe cxeMbI B036)')K,L{eHHSI, B CBOIO OQepe,lJ;b, yrrpaBJISIIOTCSI CHrHaJIOM B
UM<PPOBOll <popMe. 3TH <pa30BpamaTeJIM SIBJIHIOTCH B3aMMHbIMI1 H QaCTO MCnOJIb3Y-
IOTCSI B npMJIO)l(eHMRX (TaKMX KaK paJ(apbI) C BbICOKMM ypOBHeM MOIIJ,HOCTH. )];JIH
uerrell B036)')K,L{eHM5I pa3pa6oTaHbI CJIO)l(HbIe cxeMbI KOMneHCal(HH, KOppeKTl1.pylO-
III;He BbIXO,nHOH CHfHaJI npl1 B03paCTaHMH TeMnepaTYpbI <peppI1Ta; u:enRM B036)')K,L{e-
HHR nOCTORHHO Tpe6yeTcH 3HeprOnHTaHl1e.
TIOJIe3HbIe CCbIJIKH Ha pa60TbI no <pa30BpaIIJ,aTeJIRM rrpl1Be,n:eHbI B CrreUl1.aTIbHOM
BblnYCKe THH3P no yrrpaBJIRlOllJ;:HM YCTpOHCTBaM ,nJI$I aHTeHHbIX peIIIeTOK [68],
npe,nCTaBJIeHbI B rJIaBe no <;l>a30BpaIII;aTeJIHM 11 JII1HI1HM 3a,n;ep)l(KH [34] 11 ,n:BYXTOM-
HOH MOHorpa<pHH [42].

 flla8a 6. CUCmeMbl numaHUfI aHmeHHblX pememOK
6.2. napannenbHble nMHMM nMTaHMR'
6.2.1. 06"beAMHeHHble nMHMM nMTaHMSI
061>e,LJ;MHeHHbIe (KopnopaTMBHbIe) nHHI1H rrl1TaHI1JI lliMpOKO pacrrpOCTpaHeHbI B AP
Ha OCHOBe ,LJ;MnoneM, BOJIHOBO,LJ;OB C OTKpbITbIM KOHIJ;OM If MMKpOrrOJIOCKOBbIX aH-
TeHH. OHH Ha3bIBaIOTC.H TaK B CHJIy KOHQ:>HrypaIJ;HM CTPYKTYPHOH cxeMbI, r,n;e JIHHM.H
rrHTaHHH ,n;enHTC.H Ha ,LJ;Ba HJIH 60JIee TpaKTa, Ka)l(,[(bIM H3 KOTOpbIX 3aTeM ,LJ;eJIHTC.H
,n;anbllie H TaK ,LJ;anee. TaKl1e JIHHHH rrHTaHH.H 06bIQHO 6HHapHbI, HO HHOr,LJ;a ,LJ;peBO-
Blf)];Ha.H CTpYKTYpa BKJIlOqaeT TpeXKaHaJIbHbIe HJIM ,n;a)l(e nHTHKaHaJIbHbIe ,n;eJIHTenM,
B 3aBMCMMOCTH OT qlfCJIa 3JIeMeHTOB aHTeHHoM pellieTKH. Ha pHC. 6.27 rrOKa3aHa
rrpOCTa.H 6HHapHaR napanJIeJIbHaR cxeMa IIHTaHHH C <l>a30BpamaTeJIHMH. KaK H B
CJIyqae MarHCTpaJIbHbIX rrOCJIe,n;OBaTeJIbHbIX cxeM nHTaHH.H, Heo6xo,n;HMbIH c,n;BHr
Q:>a3 rrporpeCCHBHO B03paCTaeT. O,n;HaKo Terrepb Y KIDK,IJ;OrO yqacTKa TpaKTa HMeeTC.H
TonbKO O,LJ;HH <t>a30BpamaTeJIb. B lliHpOKOrrOJIOCHbIX BapHaHTax HcrronHeHHH AP,
r,n;e <t>a30BbIH c,n;BHr no MO,LJ;YJIIO 2n He,n;OCTaTOqeH, MOryr Hcnonb30BaTbCR YCTPOH-
CTBa 3a,n;epXKH. B IIpHHIJ;Hrre, MO,n;YJIb 3a,n:ep)I(KH Heo6xo,LJ;HM Ha KIDK,IJ;OM YPOBHe ,LJ;e-
neHH.H MOmHOCTH. IIpH CKaHHpOBaHHH C 60nblliHM yrJIOM OTKJIOHeHH.H JIyqa YCT-
pOHcTBa C <l>a30BoH 38.,[(ep)I(KOH !. Nkd sin 8 0 YCTaHaBJIHBaIOTC.H rrOCJIe nepBoH
2
 
cTyneHH .n;eJIeHHH MOIUHOCTH, qeTbIpe YCTpOHCTBa C IIOJIOBHHOH 3Toro 3HaqeHHH 3a-
,n;ep)l(KJf - Ha CJIe,n;YlOmeH cTyneHH H, HaKOHeIJ;, BoceMb <t>a30BpaIUaTeJIeH - Ha
ypOBHe 3JIeMeHTOB, r,n:e Bce <t>a30BbIe 3a,n:ep)J(KH paBHbI 2n.
3JIeMeHTbI
<l>a30BpamaTeJIH
,lJ.eJIHTeJIH
MOrn:HOCTH
Bxo,n;
PHC. 6.27. ITapaJIJIeJIbHaH cxeMa rrMTaHMH (rrpoHYMepoBaHbI <!>a30C,lJ;BMraIOII(Me
MO,n;YJIM)
,LJ;JIH 66J1blliHX AP qame rrpMMeHHeTcH KOMnpoMHccHaH cxeMa, HMelOlI(aH O,n;HH
HJIH ,n:Ba ypOBHH YCTPOMCTB 3arra3,n:bIBaHIDI B .n;orrOJIHeHHe K <t>a30BpamaTeJIIO Ha
KIDK,IJ;OM 3JIeMeHTe. Ha pHC. 6.28 rrOKa3aH npHMep TaKOH CXeMbI.
KpMTHqeCKHM KOMIIOHeHTOM 061>e,n:MHeHHoH cxeMbI rrMTaHIDI HBJIHeTCH ,n;eJIH-
TeJIb (CYMMaTop) MOIl(HOCTH; .LLJIH 3Toro MoxeT HCrrOJIb30BaTbC.H pa3BeTBJIeHHbIH
T -o6pa3HbIH BOJIHOBO,n;, HJIH T -o6pa3Ha.H KOaKClfaJIbHa.H pa3B.H3Ka, HJIH rH6plf)];Ha.H

6.2. IlapatlJleJlbHble JlUHUU numaHUR 
3JIeMeHTbI
<l>a30BpamaTeJIH
YCTpOHCTBa
3a,n;ep)l(KH
Bxo,n:
PRC. 6.28. 061>e,lUIHeHHaH cxeMa IIHTaHIUI C 3a,LJ;ep)J(KoH cpa3bI
cxeMa. IIepBbIH BapHaHT npoII.J;e, HO fH6pl1,LI;HbIe COe,L(HHeHHH YMeHbIIIalOT 3<p<peKTbI
paccOrJIaCOBaHHH HMne,L(aHCOB 3JIeMeHTOB. THnHqHbIMH rH6pH,[(HbIMH cxeMaMH HB-
JUllOTCH cxeMbI C KOpOTKOH lI(eJIblO [53, 49], B KOTOpbIX HCnOJIb3YIOTCH ,L(Ba BOJIHO-
BO,L(a co CMe)I(HOH Y3KOH cTeHKoH, rH6pl1,LI;HaH cxeMa C BepXHeH CTeHKOH [23],
):J;BOHHOH BOJIHOBO,nHbIH TpOHHHK [71] H rH6pH,[(Hoe KOJIbl(O [65]. j];eJIHTeJIH MO-
HOCTH H rH6pH,I(HbIe cxeMbI MOryT 6bITb TaIOKe BbInOJIHeHbI Ha MHKpOnOJIOCKOBbIX
HJIlI nOJIOCKOBbIX JIHHHHX [39, 49, 72]. IIIHpOKOnOJIOCHbIH OTBeTBHTeJIb Ha OCHOBe
TEM-JIHHHH pa3pa6oTaH B [54]. IIonYIDIpHbIH ,[(eJIHTeJIb YHJIKHHCOHa [69] ,L(JIH
YJIyqIIIeHHH COrJIaCOBaHHH co,nep)lQfT pe3HCTHBHbIe HarpY3KH; 06bIqHO OH npe,n-
CTaBJIHeT C060R MHKpOnOJIOCKOBbIH ,lJ;eJIHTeJIb C HarpY3KoH, BKJIIOQeHHOH Me)l()]:Y
JIHHHHMH. ,l];PyroR THn MHKpOnOJIOCKOBOro ,neJIHTeJIH - OTBeTBHTeJIb JIaHre [45],
rrpe,nCTaBJIHeT C060R 90° rH6pl1,LI;HYlO cxeMY C HCnOJIb30BaHHeM BCTpeQHO-CTep)I(He-
BOH CTp)'KTypbI CBH3aHHbIX JIHHHH. O,nHaKo BO MHorHX AP Ha OCHOBe MHKpOnOJIOC-
u u u
KOBbIX H3JIyqaTeJIeH HCnOJIb3yeTcH npOCTOH peaKTHBHbIH pa3BeTBHTeJIb MOII.J;HOCTH
.
Me)l()]:Y KaHaJIaMH.
6.2.2. PacnpeAeneHHble aHTeHHbie peweTKM
B pacnpe,neJIeHHOR AP KIDK,[(bIR 3JIeMeHT no,nKJIIOQeH K c06cTBeHHoMY npMeMo-ne-
pe,L(alOII.J;eMY MO,nYJIIO. TaKHe MO,IJyJIH QaCTO co,nep)l{aT ,nynrreKcepbI, llHPKYJIHTOpbI,
«pHJIbTpbI, npe,nYCHJIHTeJIH, YCHITHTeJIH MOII.J;HOCTH, <pa30BpaII.J;aTeJIH H KOMnOHeHTbI
CHCTeMbI ynpaBJIeHHH. MHor,na 3JIeMeHT AP HBIDIeTCH QaCTblO MO,nYJIH. 3TO HMeeT
PM npeHMyru;ecTB. BMecTo O,L(HOrO MOII.J;HOrO JIaMnOBOro reHepaTopa MO)l{eT HCnOJIb-
30BaTbCH MHoro MaJIOMOII.J;HbIX nonyrrpoBo,nHHKOBbIX feHepaTopoB. MHHHMM3HPY-
IOTCH nOTepH B ceTH nHTaHHH, YMeHbIIIalOII.J;He OTHomeHHe CMfHaJIjrnyM (SjN).
B03MO)I(HOCTb yxy,nIIIeHHH xapaKTepHCTHK 6e3 HapymeHHH pa60Tocnoc06HOCTlI no-
3BOJIHeT CHCTeMe <PYHKl(HOHHpOBaTb C He60JIbIIIHMH 113MeHeHIDIMH KY 11 ypOBIDI 60-
KOBbIX JIeneCTKOB npH BbIxo,ne QaCTH Mo,nYJIeH 113 CTpOH. Pe3KO B03paCTaeT cpe,nHee
BpeMH Hapa60TKH Ha OTKa3 [28]. 060pOTHOH CTOpOHOH 3TI1X npeHMyru;eCTB HBJIHeTCH
60JIee BbICOKaH CTOI1MOCTb. CTOHMOCTb Mo,nYJIeif B HeCKOJIbKO COT ,nOJIJIapOB 3a nrry-
KY HBJIHeTCH ,naBHO nOCTaBJIeHHOH :u;eJIblO, HO pa30BbIe TeXHHQeCKHe 3aTPaTbI, OCO-

 DJa6a 6. CucmeMbi nUmaHUJI aHmeHHblX pememOK
6eHHO B cnyqae MOHonHTHbIX MHKpOrrOJIOCKOBbIX HHTerparrbHbIx cxeM, BbICOKM, rro-
3TOMY ,lLIDI ,llOCTIDKeHHH peHTa6enbHocTH MO.L(YJIeM Tpe6yeTcH 60nbIIloe KOJIHQeCTBO
e.L(HHHU rrp0.L(y:KIJ;I1M. TBep,aoTeJIbHbIe 11 naMnOBbIe MO.L(ynl1 06c)')K.I(aIOTCH B pa60Te
[51]; cOBpeMeHHbIM TeXHOJIOfl1QeCKMM ypOBeHb paCCMaTpI1BaeTC5I B pa60Te [8].
MO.L(YJIM MOryr Mcrronb30BaTbCH ,llnH Bcex 3neMeHTOB I1JII1 JII1HeHHbIX AP B co-
CTaBe AP, cKaHl1pYIOIUeH TOJIbKO B O,n:HOH rrJIOCKOCTH. Ha pl1C. 6.29 H306pa)l(eH MO-
,n:YJIb, rrHTalOIUI1H rneCTb rreqaTHbIX ,n:l1rrOJIeM. MO,n:YJII1,L(JIH nJIOCKHX AP 06C)')K.I(aIOT-
C5I B pa3,n:eJIe 6.3.
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.:._... ;_:.:::_........ '. :....:..... ...:::;:.:..:::... :1......;.. ..,:':...
PHC. 6.29. MO.aYJIb aHTCHHOM pCIllCTKH
BbIQHCJIeHl1e OTHOllIeHI1H GfT ,llJHI aKTI1BHOH AP HeCJIO)I(HO rrpl1 YCJIOBHH, qTO
LLJIH 06eCrreQeHHH crran;a aMrrJIHTy,n:bI K KpaHM paCKpbIBa He HCrrOJIb3YIOTCH corrpo-
TI1BJIeHI1H; KOHeQHO, ,n:OJDKHbI 6bITb 113BeCTHbI rrOTepM ,n:JIH Bcex Y3JIOB, K03<P<PHUH-
eHTbI YCHJIeHHH aKTHBHbIX 3JIeMeHTOB H rnYM-<paKTOp. qacTo 6bIBalOT TaIOKe Ba)I(HbI
TOqKa rrepeCeqeHHH TpeTbero nOPMKa H CB060,n:HbIM OT BbI6poCOB ,n:I1HaMHQeCKHH
,n:Harra30H (CM. pa311eJI 6.4.1). B CJIyqae pe311CTHBHoro YMeHbIIleHHH aMITJIHTy,n:bI K
KpaHM paCKpbIBa rrpH BbIQI1CJIeHIDIX GjT He06xo.llHMa OCTOpO)l(HOCTb [46]. CpaBHe-
HHe aKTHBHOH BeCOBOH 06pa60TKH ,n:aHHbIX (,L(JIH YMeHbllIeHHH aMITJIHTy,n:bI K Kpa-
HM) c rroMOIUblO K03<P<PHUHeHTa YCHJIeHHH npe,n:YCI1JIHTeJIeM MOHOJIHTHbIX MHKpO-
rrOJIOCKOBbIX I1HTerparrbHbIX cxeM H rraCCHBHOH BeCOBOH 06pa60TKH C rroMOIUblO
HepaBHOMepHbIX CYMMaTopOB rrpOBo,n:HTCH B pa60Te r 31].

6.3. J{6)lMepHble CXeMbl numaHU5l 
6.3. ABYMepHble cxeMbl nMTaHMR
6.3.1. AHTeHHble peweTKM,C MKcMpoBaHHbIM
nOnO>KeHMeM ny...a
TIJIOCKlIe AP MOryr COCTOHTb H3 JIHHeHHbIX AP HJIH 6bITb co6paHbI H3 OT,l(eJIbHbIX
3JIeMeHTOB, TaKllX KaK, HanpHMep, OTKpbITbIe BOJIHOBO,l(bI. ECJIH HanpaBJIeHHe rJIaB-
Horo JIyqa <pHKcHpoBaHo, COCTaBlliIIDII(He JIHHeHHbIe AP H nHTaIDlI(aH HX rJIaBHaH
JIHHH5J MOryr 6bITb YC1pOHCTBaMH 6eryII(eH BOJIHbI, pe30HaHCHbIMH HJIH Kopnopa-
THBHbIMH YCTpoHcTBaMH. TaK, ITJIOCKaH ,l(B)'MepHaH AP, 3aMeHHBmaH napa60JIHQe-
cKlIe OTpa)l(aTeJIbHbIe aHTeHHbI BO MHorHX PJIC JIeTaTeJIbHbIX annapaTOB H paKeT,
COCTOHT H3 JIHHeeK, HBlliIIDII(HXCH pe30HaHCHbIMH AP Ha OCHOBe npO,l(OJIbHbIX mYH-
 u u
THPYlOIII;HX BOJIHOBO,l(HbIX III;eJIeH, C nHTaHHeM OT pe30HaHCHOH rJIaBHOH JIHHHH.
Ha pHC. 6.30 nOKa3aHa ITJIOCKaH ,l(B)'MepHaH AP, B KOTOpOH Ka)l(,[(aH JIHHeHKa pe-
rneTKlI pa3,l(eJIeHa Ha nO,l(pemeTKlI (,l(JIH I(eHTpaJIbHOH JIHHeHKlI Ha nRTb nO,l(peme-
TOK). 3TO C,l(eJIaHO ,l(JIH YBeJIHQeHIDI mHpHHbI nOJIOCbI QaCTOT, TaK KaK Y Ka)K)J;OH pe-
30HaHCHOH AP Tenepb MeHbme 21 l.I(eJIH. IIoJIHaH AP HMeeT 1368 III;eJIeH. Ha pHC.
6.31 nOKa3aHa o6paTHaH CTopOHa, r,l(e MO)I(HO BH,[(eTb cxeMY nHTaHHH Ha OCHOBe
CKpelI(eHHbIX BOJIHOBO,l(OB. KopnopaTHBHaR BOJIHOBO,l(HaR cxeMa nHTaHHR B036)')K,L(a-
eT cxeMY Ha OCHOBe CKpern:eHHbIX BOJIHOBO,l(OB. ,[(JIR 06eCneQeHMH onTMMH3I1pOBaH-
'-' u u v
HOM C)'MMapHOH a3HMyraJIbHOH ,l(HarpaMMbI HanpaBJIeHHOCTH H pa3HOCTHOH ,I:(Ha-
rpaMMbI HanpaBJIeHHOCTH no yrJIY MeCTa HCnOJIb3yeTcH rH6pH,[(HaH MOHOHMnYJIbCHaR
ceTb nlfTaHlfH. Ha pHC. 6.17 nOKa3aHa AP Ha OCHOBe KpaeBbIX BOJIHOBO,I:(HbIX lI(eJIeH,
06JIa,n:alOlI(aR OQeHb Hlf3Kl1M (-50 ,l(E) ypOBHeM 60KOBbIX JIeneCTKOB, <popMa KOTOpOH
PRC. 6.30. IIJIocKaH )J;B)'MepHaH m;eJIeBaH aHTeHHaH perneTKa


rfla8a 6. CucmeMbl numanu.R. anmennblX pewemOK
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CTHOM ,I1J'farpaMM HanpaBJIeHHOCTI1
COOTBeTcTByeT 06TeKaTeJIIO aHTeHHbI PJIC. 3,neCb JIMHeMKH AP rrpe,l(CTaBJIHIOT C060R
aHTeHHbIe pemeTKM 6eryrn:eti BOJIHbI; npM 3TOM OTKJIOHeHMe JIyqa OT HOpMaJIM JIerKO
u
KOMIIeHcHpyeTcH ,nOBOpOTOM B a3MMyraJIbHOH IIJIOCKOCTH.
,l];ocTIDKeHHe CTOJIb HH3KMX ypOBHell 60KOBbIX JIeIIeCTKOB 1pe6yeT Tm;aTeJIbHOrO
COrJIaCOBaHIUI KpaeBbIX 3cPcPeKTOB H 3cPcPeKTOB B3aMMHOll CBH3M. ,lJ;.Jrn aHTeHH C HM3-
KHM ypOBHeM 60KOBbIX JIeneCTKOB cym:eCTBeHHa TOqHOCTb M3rOTOBJIeHIUI. He,lI,OCTaT-
KOM IIeqaTHbIX aHTeHH C KopnopaTHBHbIMH JII1HI1JIMM nl1TaHIUI B IIJIOCKOCTH aHTeHHbI
HBJIHIOTCH 113JIyqeHHe JIHHl1ll nHTaHlUI M 3cPcPeKTbI B3aHMHOM CBH3H JIHHl1ti nHTaHlliI
[24]. Ha pl1C. 6.32 nOKa3aHa 60JIbIllaH AP M3 neqaTHbIX 113JIyqaTeJIeit C-,nMarra30Ha, B
KOTOpOlll1CnOJIb3yeTcH pe30HaHCHaH cxeMa III1TaHIUI no.n:pemeTOK [21].
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PUC. 6.32. AHTeHHa51 neQaTHa51 perneTKa P 11 C C- ,lU1ana30Ha C CI1HTe311pOBaHHOH
anepTYPOM 11 ,aBOMHOM IIOJI5IpI13aU;Meii

6.3. j/,8)lMepHlJle CXeMbl nUmaHUJI d
6.3.2. AHTeH'Hble peweTKM C nocneAOBaTenbHblM
B036y>KAeHMeM
B IIJIOCKOM AP C JIMHeMHO rrOJIHpM30-
BaHHbIMM 3JIeMeHTaMM rrOCJIe,n;HMe MO-
ryr 6bITb rrOCJIe,n;OBaTeJIbHO opMeHTMpo-
BaHbI M5I rrOJIyqeHlliI M3JIyqeHMH C
KpyrOBOM rrOlliIpM3aIJ;MeM [32, 33, 24].
Ha pMC. 6.33 rrpMBe,n;eHa cxeMa AP Ha
OCHOBe KpyrJIbIX MMKpOrrOJIOCKOBbIX M3-
v
.rryqaTeJIeM, KOTopbIe opMeHTMpOBaHbI M
<pa3MpoBaHbI M5I rro.rryqeHMH M3.rryqeHMH
KpyrOBOM rrOJI5IpM3aIJ;MM. OCHOBHbIM TO-
rrOJIOrMqeCKMM 3JIeMeHTOM HBJI5IeTCH
rro,n;perneTKa 2 x 2 C COOTBeTCTByroru:MM
rrOBopOTOM M <pa3MpoBaHMeM M3JIyqaTe-
JIeM. IIpeMMyru;ecTBaMM KOHCTPYKll;l'lM
HBJI5IIOTC5I .rryqrnee yrrpaBJIeHMe rnMpM-
HOM JIyqa B E-M H-IDIOCKOCTIDC M YMeHb-
rneHMe 3<p<peKToB B3aMMHOH CBH3M [32].
OCHOBHOti He,n;OCTaTOK - 60JIbrnMe
L(Mej;)paKIJ;MOHHbIe JIerreCTKM B ,n;MarOHaJIbHbIX IDIOCKOCTHX. OHM YCTpaH5IIOTCH I1PM MC-
v v v
rrOJIb30BaHMM 3JIeMeHTOB KpyrOBOM nOlliIpM3aIJ;MM C rrOCJIe,n;OBaTeJIbHOM opMeHTaIJ;MeM
M B036)')K,II:eHMeM. TOT}I(e MeTo,n; MO}l(eT npMMeHHTbcH MH YMeHbIIIeHlliI YPOBH5I ,n;Hej;)-
paKl(MOHHbIX JIerreCTKOB B cJIyqae HeH,I(eaJIbHbIX 3JIeMeHTOB RJII1 npH ,n;eej;)eKTax rrHTa-
HM5I [25, 26]. )];JIH YMeHbIIIeHHH ypOBHH 60KOBbIX JIerreCTKOB 60JIbrnHe no,n;perneTKM,
HanpHMep, 4 x 4, MOryr MCIIOJIb30BaTbCH C HOBbIMM IIOCJIe,n;OBaTeJIbHbIMH KOHej;)Hry-
paIJ;H5IMH IIOBopOTa 3JIeMeHTOB [26]. HaKOHeIJ;, JIMHeMHbIe rrOJIHpH30BaHHbIe 3JIeMeH-
TbI C IIOCJIe,n;OBaTeJIbHbIM B036)')K,II:eHl1eM MOryr pa3Meru:aTbC5I KOJIbIJ;eo6pa3Ho [35].
Pa3HOBH,I(HOCTbIO JIMHeMHO IIOJIHpl130BaHHbIX 3JIeMeHTOB HBlliIlOTCH perneTqaTbIe
MMKpOrrOJIOCKOBbIe aHTeHHbI, KIDK,IJ;a5I M3 KOTOpbIX COCTOI1T M3 PMa Y3KMX IIapaJI-
JIeJIbHbIX JIeHT, Opl1eHTaIJ;MH KOTOpbIX, KaK M paHee, COBepIIIaeT IIOBOpOT BOKpyr IIO,n;-
perneTKM 2 x 2. HCrrOJIb30BaHI1e perneTtIaTbIX yqacTKoB YMeHbrnaeT B3al1MHyIO CB5I3b
Me)l(,[I;Y IIOJIHpH3aIJ;MHMM [5].
PHC. 6.33. AHTeHHa51 peIIIeTKa Ha OCHOBe
MHKpOnOJIOCKOBbIX 3JIeMeTOB, pacnOJIO-
xeHHblX C nOCJIe,nOBaTeJIbHbIM nOBopOTOM
6.3.3. 3neKTpoHHoe CKaHMpOBaHMe B OAHOM nnOCKOCTM
C,n;BMr<pa3, onpe,n;eJI5IeMbIM ,n;JIMHOti JIMHMM Me)l(,[(Y 3JIeMeHTaMH M qaCTOTOM I1JIM
c03,n;aHHbIM ej;)a30Bpam:aTeJIHMM, cIIoco6eH 06eCneQl1Tb CKaHl1pOBaHHe B O,n;HOM
IIJIOCKOCTH. EOJIbIIIMHCTBO AP C 3JIeKTpOHHbIM CKaHl1pOBaHMeM OTHOC5ITCH K 3TO-
MY THny BCJIe,n;CTBHe xapaKTepHbIX ,n;JIH HerO 60JIee HM3KI1X IIOTepb M CTOMMOCTM.
CKaHHpoBaHHe BO BTOpOM rrJIOCKOCTM QaCTO o6eCneQMBaeTCH MeXaHMQeCKMM Bpa-
meHMeM. <I>a30BpamaTeJIM MorYT BKJIIOQaTbCH nOCJIe,n;OBaTeJIbHO C JIHHMeM nHTa-
HM5I MJIH IIapaJIJIeJIbHO, pacnOJIaraHCb B6JIH3M 3JIeMeHTOB; 60JIee IIo,n;po6HO 3TO
06C)')K,II:aeTCH B pa3,n;eJIe 6.3.4. Ha pMC. 6.34 IIOKa3aHa QaCTb IIJIOCKOM AP Ha OCHO-
Be MMKpOIIOJIOCKOBbIX M3JIyqaTeJIeM L-,n;Mana30Ha; ropM30HTaJIbHbIe 18-3JIeMeHT-

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QHBalOT cKaHHpoBaHHe no yrJIY MecTa, npH 3TOM MO.l(YJIM 3anMTbIBalOTCH no
06'bellMHeHHoH cxeMe [13].
Ha pMC. 6.25 npe,l(CTaBJIeHa <poTorpa<pMH 0630pHOH PJIC a3ponopTa, HMelOrn:eti
qaCTOTHoe CKaHMpOBaHMe (CM. pa3,l(eJI 6.3.4) no yrJIY MeCTa, M BpamaTeJIbHOe - no
a3MMyry. B aHTeHHOH perneTKe MCnOJIb3YIOTCH KpaeBble meJII1.

6.3. J(<<yMepHble cxeMbl numaHWl 
6.3.4. 3neKTpoHHoe CKaHMpOBaHMe B ABYX nnOCKOCTRX
Y 6O'JIbIIII1HCTBa ,I:(BYMepHbIX AP H3.rryqaIOIl(He 3JIeMeHTbI pacnO'JIO'XeHbI nO' pe-
ryJISIPHO'M ceTKe CTO'JI6u;O'B H CTPO'K, Ii cxeMbI nHTaHH5I CJIe.u;YIOT TO'M )l(e reO'MeTpHH.
B CJIyqae nJIO'CKHX AP C HenO',I:(BIDKHbIM .rryqO'M Ha O'CRO'Be BO'JIHO'BO',I:(HbIX Il(eJIell H3-
JIyqalOrn:He 3JIeMeHTbI 5IBJI5IIOTCSI HeO'TbeMJIeMO'll qaCTblO JIHHHH nHTaHH5I. KaK O'T-
MeqanO'Cb B pa3,I:(eJIaX 6.1 H 6.2, KO'MnO'HeHTbI O'CHO'BHO'll H BTO'PHqHbIX JIHHH:H IIHTa-
HH5I MO'ryr 6bITb pe3O'HaHCHbIMH, O'6'be,I:(HHeHHbIMH IDIH nO'CTPO'eHHbIMH Ha O'CHO'Be
6eryrn:e:H BO'JIHbI. 5I pa3rpaHHqeHHSI TO'nO'JIO'rH:H nHTaHH5I 3,I:(eCb HCnO'JIb3yeTcSI HO'-
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HCCJIe,l(O'BaHa JIHHeHHaSI cxeMa C O'TBeTBJIeHHHMH.
<l>a3O'Bparn:aTeJIH MO'ryr paCIIO'JIaraTbC5I IIO'CJIe,l(O'BaTeJIbHO' HJIH IIapanJIeJIbHO'
O'TBeTBJIeHHSIM, KaK nO'Ka3aHO' Ha pHC. 6.26. ITHTaHHe JIHHH:H O'TBeTBJIeHH:H MO'XeT
6bITb pe3O'HaHCHbIM, O'6'be,I:(HHeHHbIM HJIH Ha O'CHO'Be 6eryru:e:H BOJIHbI. KO'Heq-
HO', IIPH IIHTaHHH IIO' cxeMe 6erYIl(eti BO'JIHbI YCTaHOBKH <}>a3O'BpaIl(aTeJI5I ,l(O'JIXHbI
COO'TBeTCTBO'BaTb H3MeHeHHIO <}>a3bI B,I:(O'JIb MarHcTparrH nHTaHHH 6eryrn:e:H BO'JIHbI.
OCHO'BHaSI MarHCTpanb IIHTaHHH, K KOTO'PO':H IIO',I:(KJIlOqeHbI Bce JIHHHH nHTaHHSI
O'TBeTBJIeHH:H, TaIOKe MO'XeT 6bITb IIO'CJIe,I:(O'BaTeJIbHO:H HJIH napanJIeJIbHO':H. Ta-
KHM O'6pa3O'M, TpeXMepHble AP ,l(OnYCKaIOT MHO'rO' KO'M6HHaU;HM cxeM IIHTa-
HHH; O',l(HaKO' HeKO'TO'Pble KO'M6HHaU;HH 6O'nee TeXHOJIOrHqHbI B H3rO'TO'BJIeHHH, qeM
,L(pyrl1e.
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v u
KO'TO'PO'H KaK JIHHHM OTBeTBJIeHHH, TaK H OCHO'BHa5I MarHCTpanb nHTaHHSI SIBJISIIOTCSI
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TIpeHMyru:eCTBO' ,I:(aHHO'H cxeMbI CO'CTO'HT B TOM, qTO' <}>a3O'BpaIl(aTeJIH BCeX OTBeT-
BJIeHHM HMelOT O',I:(HY H TY xe YCTaHO'BKY 8 = kd sin 8 0 If Bce <}>a3O'BpaIl(aTeJIH O'CHO'B-
HO'M MarHCTpanlf HMelOT O',UHHaKOByK> YCTaHO'BKY <I> = kd sin <Po. B O'6e cPa3bI BBO'-

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,[(MTC5I nonpaBKa Ha cpa30BbIe CL(BMrM B JIMHMI1 nMTaHM5I 6eryII.J:eM BOJIHbI. n pM Bcex
,L(BYMepHbIx reOMeTpMSlx CKaHMpOBaHM5I B03MO)l(HO ynpOlI(eHMe cxeMbI nMTaHHH ,[(0
cxeMbI O,I(HOMepHoro CKaHHpOBaHMH. HanpMMep, JIMHHM OTBeTBJIeHHM Moryr 6bITb
JIMHMSlMI1 IIMTaHMH HenO,I(BH)I(HOrO JIyqa, a rJIaBHaR MarHCTparrb MO)J(eT 6bITb JIH-
HHett nHTaHM5I 6eryII.J:eM BOJIHbI C qaCTOTHbIM CKaHHpOBaHHeM. IlOCJIen:oBaTeJIbHbIe I
JIHHMH IIHTaHHH OTBeTBJIeHHM Moryr 6bITb pe30HaHCHbIMM; 3TO qaCTO HCnOJIb3yeT-
C5I, eCJIH no HHM He npOH3BO,I(HTCR CKaHHpOBaHHe.
Y naparrnenbHO- nOCJIeL(OBaTeJIbHOM cxeMbI nHTaHHR MMeeTC5I PM oTBeTBneHHM
JIMHMM I1I1TaHMH C naparrJIeJIbHbIMH cPa30Bpam:aTenHMM 11 p5I,I( <pa30Bparn:aTeneM
rJIaBHOM nMHMI1 (CM. pMC. 6.36). Tenepb Ha6erH <pa3bI ,I(JIH <pa30BpalUaTeJIeM Ka)l(,L(O-
fO OTBeTBneHHSI KpaTHbI <I>. llpM 3TOM Ka)l()]:bIM naparr.rreJIbHbIM <pa30BpamaTeJIb
orrepllpyeT O,[(HHM II TeM )l(e YPOBHeM MOm:HOCTH, H KIDK,[I;bIM 3JIeMeHT BHOCMT O,[(M-
HaKOBbIe nOTepM (,l(JI5I OTBeTBJIeHMM JIMHMll nMTaHMH). 11 B 3TOM cnyqae JIMHI1M OT-
BeTBJIeHMM M rJIaBHaH JIHHM5I MOryT 6bITb pe30HaHCHoro TMna MJIII JIMHM5IMI1 6ery-
v
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B KopnopaTMBHO-nOCJIe,I(OBaTeJIbHOM cxeMe npe,l(ycMoTpeHo 06'be,[(HHeHHoe nlI-
TaHHe Ka)l():(OfO pH,[(a 3JIeMeHTOB, rrpM 3TOM JIHHMH KopnopaTMBHofO rrHTaHMR no,1];-
KJIIOqeHbI K rrOCne,I(OBaTeJIbHOM rnaBHoM JIMHMM. Ha pMC. 6.37 nOKa3aH 3CKH3 3TOM
TOTIOJIOfIIM. J1 B 3TOM CJIyqae OCHOBHa5I JIHHMR nMTaHHR MO)l(eT 6bITb HeCKonbKMX
TJ1TIOB. C,l(BMfM <pa3bI, C03)],aBaeMbIe cPa30BpaaTeJISlMI1 B JIHHMRX KoprropaTMBHoro
IIHTaHM5I, 11 B 3TOM cnyqae RBJIHIOTCH KpaTHbIMM BeJIMqMHaMM; M3nyqaeMa5I MOII(-
HOCTb ,IJ:enI1TC5I Me)l()]:y <pa30Bpam:aTeJIHMH.
Bce 3TH cxeMbI nMTaHMSI OTBeTBneHMM MorYT I1CnOJIb30BaTbC51 TaIOKe C napaJI-
JIeJIbHbIMM HJIJ1 06'be,l(HHeHHbIMM rJIaBHbIMII JIHHM5IMII IIHTaHH51. Ha pMC. 6.38
H306pa)l(eHa nOCJIe,IJ:OBaTeJIbHO- napaJIJIeJIbHa5I TOnOJIOrMSI C JIMHHSlMM OTBeTBJIeHIIM
6eryII.J:eM BOJIHbI .ILJISI IIOCJIe,I(OBaTenbHbIX q,a30BpamaTeneM H pe30HaHcHoM MarHCT-
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6.3. JJ6JlMepHble cxeMbl numaHUfl d
PUC. 6.37. 06'be,ZUIHeHHO- IIOCJIe,nOBaTeJIbHaR cxeMa IIIITaHIiR
113JIyqaTeJIb
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paJIbHOH JIlfHHeH C rrapaJIJIeJIbHbIMlf MarlfCTpaJIbHbIMH <pa30Bparu;aTeJIHMH. MarMCT-
paJIbHbIe <l>a30Bparu;aTeJIH H B 3TOM CJIyqae lfMelOT KpaTHbIH C,D;BHr <pa3 If IIpOrrYCKa-
lOT O,D;lfHaKOByro MOru;HOCTb (rrpH O,D;HOpO,l(HOM B036)')K,IJ;eHHH AP). Pa3HOBH,II;HOCTb
3TOH TOIIOJIOrHIf IIlfTaHHH HCrrOJIb30BaHa B AP Ha ,D;lfarra30H 20 rru;, IIOKa3aHHOH
Ha pHC. 6.39 [17].
3an;HlfH 6JIOK CO,l(ep)l{JfT BOJIHOBO,l(bI 6eryII(eH BOJIHbI C rrepeXO,lI;HlfKaMIf Ha BOJIHO-
BO,lI;bI KpyrJIOrO CeqeHlfH. B u;eHTpaJIbHOM 6JIOKe HaXO,WITCH MO,lJ;YJIH <l>a30Bparu;aTeJIen
If ,lJ;lfrrOJIbHbIX H3JIyqaTeJIeH; B rrpaBOM 6JIOKe - BOJIHOBO,D;bI C ,lJ;H3JIeKTplfqeCKHMM

b
fflaea 6. CucmeMbl nUmaHU.R. aHmeHHblX peUlemOK
PHC. 6.39. MO,n:YJlM aHTeHHOH perneTKlI c reKCarOHaJIbHOH ceTKOH
PHC. 6.40. IIOCJle.aoBaTeJIbHO-o61>e.aHHeHHaH cxeMa llHTaHMH

6.3. J(BYMepHble cxeMbl numaHUfl 
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BCTaBKaMH (qaCTOTa cpe3a HlDKe, qeM Y BOJIHOBo,n;a C B03,n;ynIHbIM 3anOJIHeHHeM)
H nOJIHpH3aTOpbI.
B nocJIe,n;oBaTeJIbHo-o6'be,[(HHeHHoM cxeMe nHTaHHH KopnopaTHBHoe nHTaHHe
HCnOJIb3yeTcH ,WIH B036y)1()J;eHHH JIHHHM oTBeTBJIeHHM, KaK nOKa3aHO Ha pHC. 6.40.
fJIaBHbIM npeHMyrn;ecTBoM 06'be,n;HHeHHoro nHTaJfHH HBJIHeTCH CBoMcTBeHHaH eMY
60JIbllIa5.1 IIIHpOKOnOJIOCHOCTb; B 3TOM cxeM HeT H3MeHHIOm;erOCH C qaCTOTOM
c,n;BHra <l>a3bI Me)J()J;Y JIHHHHMH OTBeTBJIeHHM HJIM Me)l():tY 3JIeMeHTaMH.
Bce 'KopnopaTHBHbIe 'JIHHHM nHTaHHH HMeIOT"'j;>aBHYK> ,[(JIHHY. ,L(JIH peaJIH3aII;HH
3TOM nOTeHII;HaJIbHOM mHpOKOnOJIOCHOCTH <l>a30Bpam;aTeJII1 3aMeIDIlOT YCTpoMcTBa-
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MH BpeMeHHOH 3a.,n:ep)I(KH, nO,lJJ(ep)I(HBalOm;HMH Hannexam;yro ,WIHHY TpaKTa Ha Bcex

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HaKoHeII;, B nOJIHOC!blO KopnopaTHBHoM cxeMe nHTaHI1H HCnOJIb3yeTcH e,n;H-
OJ OJ
HbIH npHHII;Hn nOCTpoeHHH KaK JlHHH:I{ OTBeTBJIeHHH, TaK H MarHCTpaJIbHbIX JII1-
HHM (CM. pHC. 6.41). Tenepb Y Bcex <l>a30Bpam;aTeJIeM pa3JIHqHbIe 3HaqeHHH <l>a30-
Boro c,n;BHra, HO MOm;HOCTb Me)l(,[(Y HHMH ,n;eJlHTCH paBHOMepHO.
PHC. 6.41. nOJIHOCTblO o6be,D;JfHeHHaH cxeMa I1HTaHHH
3TOT TI1TI nHTaHHH qaCTO HCnOJIb3yeTcH B aHTeHHbIX pemeTKax 113 MHKpOnOJIOC-
KOBbIX 3JIeMeHTOB (CM. pHC. 6.42). KaK OTMeqaJIOCb B npe,n;bl,L(yrn;eM pa3,n;eJIe, npo-
,n;OJDKaeTCH COBepmeHCTBOBaHHe H )'MeHbmeHHe pa3MepOB npHeMo-nepe,n;aIOII(I1X
Mo,n;YJIeif. Ha pHC. 6.43 nOKa3aHbI qeTbIpe nOKOJIeHHH Mo,n;YJIeM X-,n;Hana30Ha ,[(JIH
nHTaHHH BOJIHOBo,n;a KpyrJIOrO CeqeHIDI If PyrropHoro TEM-H3JIyqaTeJIH. Ha pHC.
6.44 rrOKa3aHbI AP, B KOTOpbIX IfCnOJIb3YIOTCH npHeMo-nepe,n;alOm;He MO,n;YJIH; Ha
BepxHeM KapTHHKe - aHTeHHaH pemeTKa MERA (1965 r.), a Ha HIDKHeM KapTHH-
Ke - aHTeHHaH pemeTKa RASSR (1974 r.).

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rfloeo 6. CucmeMbl numonU51 onmennblX peUlemOK
Puc. 6.42. AHTeHHaH perneTKa MMKp0I10JIOCKOBbIX 3JIeMeHTOB C 06'beAMHeHHbIM
I1MTaHMeM
Puc. 6.43. qeTblpe IIOKOJIeHM5I MOAYJIen

6.3. ,l(6YMepHble cxeMbl numOHUR
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 DW6a 6. CUCmeMbl nUmaHUJI aHmeHHbIX peUlemOlC
6.4. OnTMLlecKMe (OToHHble) CMCTeMbl nMT8HMR
TIoTeHIJ;lHUIbHbIe npeHMYI..UeCTBa npHMeHeHHR OnTHqeCKHX (<l>OTOHHbIX) TeXHH-
qeCKHX cpe,L(CTB ,lI;JI5I 06CJI)T)KHBaHHR H B036)')K,L(eHHR <pa3HpoBaHHbIx AP ,lI;BORKHe:
06eCneqeHHe BpeMeHH6M 3a,L(ep)I(I(H 6e3 HCnOJIb30BaHHR 60JIbllIHX, TIDKeJIbIX JIHHHM
nepe,L(aQH C nOTep5IMH H YMeHbllIeHHe Beca, 06'beMa H CTOHMOCTH YCTPOMCTB. 3,lI;eCb
KpaTKO paCCMaTpHBaeTC5I 3Ta 6bICTpO pa3BHBalOI..Ua5ICR 06JIaCTb. IJ;eJIeC006pa3Ho
yrroMRHyrb ,[(Be KHHrH [73, 43] no ,L(aHHOMY Bonpocy. KpoMe Toro, ARPA (YnpaB-
JIeHHe nepcneKTHBHbIX HCCJIe,L(OBaHHM H pa3pa6oToK) cnoHcHpyeT e)KerO,L(HbIe CHM-
n03H)'MbI no <pOTOHHbIM CHCTeMaM ,[(JIR AP, OTKpbITbIe ,[(JIR CnenHaJIH3HpOBaHHbIX
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nepCMOHHbIe 3a;:I:ep)I(I(H. KpoMe Toro, paCCMaTpHBalOTC5I pa3JIHQHbIe HeTpa;:I:HnMOH-
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6.4.1. BonOKOHHo-onTMeCKMe nMHMM 3aAep>KKM
6.4. 1. 1. P'SOM'IHhle nMHMM 3a,qepJKKM
B KaqeCTBe MMKpOBOJIHOBbIX JIHHMM 3a;:I:ep)KKlf qaCTO HCnOJIb3yroTCH OnTMqeCKHe
JII1HMH C nepeKJIIOQaTeJIRMH ,WIg BbI60pa pa3JIHQHbIX TpaKTOB 3a,L(ep)KKlf. TIpM 3TOM,
KOHeqHO, Heo6xo,[(HMbI OIITHqeCKHe MO.LJ:YJIRTOpbI M .neTeKTopbI; OHH paCCMaTpHBa-
.
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Bble OnTHQeCKMe IIepeKJIIOQaTeJIH, BKJIlOqalOI..UHe MJIH OTKJIlOqalOIUHe cerMeHTbI
TpaKTa 3a,L(ep)KKH, C .nJIHHaMM, 6MHapHO KpaTHbIMM MMHMMaJIbHOM ,[(JIHHe, paBHOM,
K npHMepy, lA. KaCKaD: 3a,lI;ep)I(I(M C n ,LI;BOHqHbIMH pa3PMaMH 06eCneQHBaeT JUIHHY
TpaKTa 3a,L(ep)KKH, paBH)'IO lA, 2A, 4A..., 2n-lA. ECJIM MR 3a,L(ep)KeK < 1A He HCrrOJIb-
3YIOTC5I <pa30BpaIUaTeJIH, OnTHqeCKHM KaCKa,L( 3an;ep)I(KH MO)KeT BKJIIOqaTb TaIOKe 11
I1X. Ha pMC. 6.45 nOKa3aHa 6JIOK-CXeMa KaCKan;a 3an;ep)KJ(lf, HHOr,lI;a Ha3bIBaeMoro
611HapHoM OrrTOBOJIOKOHHOM 3auep)KJ(OM [20, 43]. MCnOJIb30BaHHe OnTHQeCKOM 3a-
,L(ep)KKM 3<p<peKTHBHO TOJIbKO M5I no,n;pellIeTOK, r,[(e Ka)l(,l(bIM 3JIeMeHT aHTeHHbI CBR-
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TCTByeT 180° <l>a30BoMY C.nBHry; 3aTeM Ka)l(,[(aR no,n;pellIeTKa nO,L(KJIlOqaeTCR K
OrrTI1QeCKOMY KacKan;y 3an;ep)KJ(H [50, 47].
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,
C paBHOMepHOCTblO, cTa6MJIbHOCTblO, ,n;peM<poM H napaMe'rpOM IP3, Ha3bIBaeMbIM TOQ-
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1 .uE nOpO)l(,[(aeT norpellIHOCTb no CBq B 2 ,n;D. IP3 - TOqKa nepeCeqeHIDI lpeTbero
rrOPMKa, 3TO rrOIDITMe OTHOCHTC5I K YCIDIMTeJUIM, KOMrreHCHp)'lOIUHM nOTepH B JIHHHM
CBR3H. YpoBeH co6CTBeHHbIX myMOB YCIDIHTeIDI M IP3 onpe,n;eIDIeT cBo6o,n;HbIM OT BbI-
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Hoil 3aaaqeH. I1pH ,n:OrryCTHMOH norpelliHOCTH 2° TOqHOCTb nO,ILLJ;ep)l(aHIDI BpeMeHH 3a-
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B ,n:PyroM THne KaCKa,rr;a 3a,aep)I(J(H HCnOJIb3ye1'cR ,n:Ba nOCJIe,n:OBaTeJIbHO YC1'a-
HOBJIeHHbIX Ha60pa nepeKJIlOqaeMbIX cerMeHTOB. TaKaR JIHHHR 3a,rr;ep)l(J(H Ha3bIBa-
eTCR KBa.II:pa1'HqHO-KOpHeBoH [56, 20]. OHa 06eCneql1Bae1' rrOJIyqeHHe pMa 3a.n;ep-
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KOJIHQeCTBO JII1HHH 3a;J:ep)KJ(}f COCTaBJIReT 2m, Tor,n:a KaK KOJIllQeC1'BO nepeKJIIO-
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.aJIR B036y:JKlIeHH5I AP C <pMKcHpoBaHHhIM yrJIOM CKaHllpOBaHHR, HO KBa.n;pa1'HqHO-
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,n:OJDKHbI I1CnOJIb30Ba1'bCR Bce nepecTaHOBKH nepeKJIlOqa1'eJIR. TaK KaK, IIO-BH.l(IlMO-
MY, He cym.eC1'Bye1' cIIoco6a <pHKcaUHH (coxpaHeHHSI) 3HaqeHHM 3a.aep)J(eK, 31'01'
1'Hn KaCKa,L(a 3a,n:ep)l(KH ,n:JIR AP He no,n:xo,n:H1'.
ToqKa nepeCeqeHHSI TpeTbero nopSl,n:Ka nOJIyqaeTcR nYTeM nepe,n:aqH Qepe3 YCH-
JIHTeJIb ,n:BYX qaCTOT nOJIOCbI nponYCKaHHSI fi H 12. Ha qaCTOTe 212 - Ii B03HI1KaeT
CHrHaJI TpeTbero nOPMKa, a IP3 - ypOBeHb MOm.HOCTH, npH KOTOpOM JIHHeHHaR
(3KCTpanOJIHPyeMa5I) aMnJIH1'YAHaSi xapaKTepl1CTMKa nepeceKaeT aMnJIH1'Y,L(HYIO xa-
paKTepHC1'HK)' 1'pe1'bero rropR,n:Ka.
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CeQeHHeM JIHHHH ypOBHR co6C1'BeHHbIX IIIYMOB H JIHHH5IMH.IO H 212 (CM. pHC. 6.46).
IP3 KaCKa.n;a YCHJIlI1'eJIeH BbIqHCJIHe1'CR npOCTO:
1 1 + G 1 (6.33)
IP3 IP3} IP3 2 '

 Ffl060 6. CucmeMbi numOHUJ/ OHmeHHbIX peUiemOK
140
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r,n;e ,nBa YCllJIllTeJI llMelOT IIapaMeTpbI IP3 1 If IP3 2 II K03<P<P M l(lfeHTbI YCllJIeHM5I G 1
M G 2 . 3TO 3HaqeHI1e IP3 IIpMHllMaeTC5I KaK BXO,lI;Hoe. BbIpa)l(eHlIe ,lI;JI5I BbIXO,lI;HOrO
3HaqeHll IP3 llMeeT BM,lI; [47]
1
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1
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1
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(6.34)
Pa3MepHOCTb IIapaMeTpa IP3 - ,lI;DMjfl( 2/3 .
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KM BJIeTC5I N-KaHaJIbHbIH «IIepeKJIlOqaTeJIb» C BbI6opOM O,lI;HOH 113 N JII1HIIH 3a-
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HaJIbHbIH QaCTOTe MHKpOBOJIHOBOrO B036)')K,IJ;eHM5I. 3aTeM OIITMQeCKMH JIyq IIa.n;aeT Ha
O,lI;HO If3 rpyrrIIbI OIITMQeCKI1X BOJIOKOH, MMelOll.(MX KpaTHbIe 611HapHbIe 3HaqeHM 3a-
,n;ep)I(l(J1. BbIXO,lI;HbIe CMrHaJIbI Bcex BOJIOKOH BBO,lI;5ITC5I B OIITWleCKI1M CyMMaTOp MOm-
HOCTeM, KOTOpbIM, B CBOIO OQepe,nb, IIMTaeT <poTO,lI;eTeKTOp [36, 37]. CxeMa TaKoro
YCTpoMcTBa IIpIfBe,lI;eHa Ha pMC. 6.47.

6.4. Onmu'tecKue (rjJomoHHble) CUCmeMbl numaHUfl d
<l>oTo,n;eTeKTOp
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8t" aHTeHHOM pemeTKM
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6.4. 1.3. Mop,ynRTopbl VI C/JoTop,eTeKTOpbl
JIa3epHbIe MOlIYJlRTOpbI CBeTa 6bIBalOT KaK rrpHMbIMI1, TaK 11 BHellIHI1MI1. IIpn
rrpRMoM MOlIYJIRUl111 pa,n:110cnfHaJI IIOlIBO,lJ,HTCR K III1TalOI..IJ;eMY Jla3ep I1CTOqHMKY
nOCTORHHOfO TOKa. IIoJlyqaeMaR OnTl1qeCKaH I1HTeHCI1BHOCTb nponOpUllOHaJIbHa
TOKy MO,n:YJIHUI1H. ,LJ;JlH IIpHMOM MOlIYJlHUl111 06bIQHO I1CrrOJlb3yJOTCH rrOJIynpo-
BO,n:HI1KOBbIe na3epHbIe l(110.n;bI C pacnpe.n;eJIeHHOM o6paTHoll CBH3blO, TaK KaK npl1
xopOllieM .n;MHaMMqeCKOM .n;l1arra30He 11 HI13KOM ypOBHe mYMOB BHOCMMbIe I1MI1
rrOTepl1 MOryT 6bITb HI13KI1MI1. ,l].JII1HbI BOJlHbI 06bIQHO COCTaBJIHIOT 1310 11J111
1515 HM. IIoMI1MO YKa3aHHoro JIa3epa Jla3epHbIM MO,n:YJIb MO)l(eT COlIep)l(aTb Tep-
v v
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rrO;:J;aBJl5IlOmylO OTpa)l(eHl1e CBeTa OT CTeKJIOBOJIOKHa, H KOMrrOHeHTbI ,L(JIH corJIaco-
BaHI1R HMnelIaHca. llIHpl1Ha rrOJIOCbI qaCTOT nOJIynpoBO;:J;HHKOBbIX JIa3epHbIX lIMO-
,nOB C paCnpelIeJIeHHOM o6paTHoH CBR3blO, IIO-BH.n;HMOMY, OrpaHHqeHa 3HaqeHHeM
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66JIbllIyID rrOJIOcy QaCTOT.
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o6eCneQeHHR xopomeM JIHHellHOCTI1) 11 MaJIOllIYMHmHll I1CTOqHI1K CBeTa; B 60JIb-
llIHHCTBe H3 HI1X HCnOJlb3yeTcR TBep.n;OTeJIbHOe YCTPOMCTBO NdYAG C .n;HO.n;HOH Ha-
KaQKOH. BbIXOlI Jla3epa nOlIKJIIOQaeTCR K OrrTHQeCKOMY Ka6eJIIO C YCTaHOBJIeHHbIM
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06YCJIOBJIeHHbIH <pOHOH-<pOHOHHbIM B3aHMo,n:eMcTBlIeM. TaKl1M 06pa30M, OI1TlIqe-
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ITIiH -<pOTO,LIIiOllbI I1CnOJIb3yroTCH, fJIaBHbIM o6pa30M, KaK ,LIeMO.II:YJIRTOPbI MR
BOJIOKOHHOM onTIIKlI, rrpli 3TOM HMeeTCR npoTMBOpeqlIe Me)l()J,Y KBaHToBoM 3<p<peK-
TMBHOCTblO H qaCTOTOH MO.II:ynHll;lllI; 60JIee BbICOKHe qaCTOTbI CHIDKalOT 3<p<peKTHB-
HOCTb. AMI1JIlIry,IJ;HO-qaCTOTHaH xapaKTeplIcTIiKa OrpaHMQeHa BpeMeHeM .II:peH<pa
HocMTeneH H3 06JIaCTI1 o6e)IHeHMH M nocToHHHOM 110 BpeMeHI1 .II:JIR eMKOCTH 06JIac-
TH nepexo,n;a nJIIOC napa311THoH eMKOCTH. DOJIee TOHKMH 06e,n;HeHHbIH cnoM, I1pM-
MeHReMbIM Ha 60nee BbICOKl1X qaCTOTax, nOfJIOlI(aeT MeHbllIe CBeTa 11, cne,n:OBaTenb-
HO, MeHee 3<p<peKTMBeH. Ha qaCTOTe 10 rru 3<p<peKTHBHOCTb 6bIBaeT BbICOKOM, HO
Ha 60 rru OHa CHM)I(aeTCH ,n:o 30% [67]. ,LJ;nR CTOJIb BbICOKOqaCTOTHbIX MMKpOBonH
MCnOJIb3yroTCH BonHOBo,n;HbIe CTPYKTYPbI C opTOrOHaJIbHbIM nepeHOCOM 11 110fJIOlI(e-
HHeM HOCMTeJIeH, YCTpaHHlOlI(He nOTpe6HocTb B TOHKOM o6e,n:HeHHoM CJIoe. AJIH
06eCneqeHHH MaKCMMaJIbHOM 3<p<peKTMBHOCTH c06MpalOII(aR al1epTypa <pOTO,IJ;Mo,n;a
,n;OJDKHa COOTBeTCTBOBaTb )IMaMeTpy OI1TOBOJIOKHa. ,LJ;JIH YMeHbIIleHHR OTpa)l(eHHH
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uenH <J;>OTo,n:lIo,n:a ,n:OJDKeH 6bITb cornaCOBaH C COOTBeTCTByJOlI(HM BonHOBbIM I1M-
ne,n;aHCOM CMCTeMbI. CCbInKH Ha CTaTbl1 no KOMI10HeHTaM MO)l(HO HaMTM B pa6o-
Te [62].
6.4.2. OnTOBonOKOHHble nMHMM 3aAep>KKM
C pa3AeneHMeM no AnMHaM BonH
3a,n;ep}l(J(a MO)l(eT MeHRTbCH l1yreM BbI60pa cooTBeTcTBYlOlI(eH ,IJ;JIHHbI BonHbI CBeTa
6JIarO.IJ:apH I1cnonb30BaHlIIO ,n:HcneprHpyJOrn:Hx OllTHqeCKHX BonOKOH IUIM qaCTOT-
HO-3aBHCIiMbIX ,n;H<ppaKQI10HHbIX perneToK.
6.4.2. 1. RJfHJfJf 3ap,epJKKJf Ha OCHose
p,JfcneprJfpYIOU4JfX OnTJflleCKJfX sonOKOH
Pa.II:IIOqaCTOTHO Mo,n;ynHpoBaHHbIM OnTHqeCKIiM nyq llepe.II:aeTCH 110 yqaCTK)' BbICO-
KO.IJ:IICnepCIIOHHoro OnTOBOJIOKHa; "PH 3TOM ,n;MCKpeTHO perynHpyeMaR 3a.n:ep)I(Ka
nponOpUIiOHaJIbHa C.II:BHry .II:JIHHbI BOJIHbI JIa3epHOM HeCyn.I:eM [57]. THlllIqHOe 3Ha-
qeHMe xpOMaTHqeCKOM .II:HCnepCMM COCTaBJIReT 50 I1C/MM C.II:BHra ,nJIHHbl BOJIHbI Ha
KHJIOMeTp OllTOBOJIOKHa. 3Ta .IJ:HCnepCHR npH6JIH3HTeJIbHO nOCTORHHa no ,nMana-
30HY nepecTpoHKH JIa3epa. IIepeMeHHaR 3a,nep)l(Ka C03,n:aeTCH npOCTO nepeCTpaM-
, OJ
BaHHeM .II:JIHHbI BOJIHbI JIa3epa, "PH 3TOM BpeMH 3a,n;ep)I(KH onpe,nenHeTCH ,nnHHOI1
,nHcneprMpYlOmefO CTeKJIOBOJIOKHa. OpOCTaH (HO ,noporaH) CHCTeMa lllITaHHH AP
HMeeT na3epHbIM reHepaTOp ,nJIH KaJK.nOro 3JIeMeHTa AP, a 113JIyqeHHe KaJK.nOrO na-
3epa npoxo,nHT qepe3 ,nI1ClleprHpyromee OI1TOBOJIOKHO Ha <pOTo,n;eTeKTOp K 3JIe-
MeHTY. ,L(JII1Ha .IJ:I1CneprHpyIOlI(HX onTOBonOKOHHbIX nHHMM COCTaBnHeT llOpH,lJ;Ka
1-10 KM.
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HOCTblO .IJ:O MHHI1MaJIbHOfO pa3pSI,IJ:a <J;>a30Bparn:aTeJIH AP. TIpH 60nee H3HII(HOM pe-
meHMII IICnOJIb3yeTcH O,IJ;HH (Ha llJIOCKOCTh CKaHl1pOBaHHH) nepecTpaHBaeMbIH JIa-

1
6.4. OnmUlieCKUe (rjJomoHHble) cucmeMbl nUmaHUf/ d ,
  
3ep C MOJIHpOBaHHoH BbIXO,1J;HOH MOmHOCTblO, pa3BeTBJIHeMOH Ha rpynrry
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4't, (2N - I)'t, I1PH 3TOM KaJK,II;aH JIHHH.H ynpaBJIHeT O,UHHM 3JIeMeHTOM AP. IIepe-

cTpoHKa JIa3epa H3MeHHeT 3HaqeHHe 't, H TeM caMbIM oCeCTBJIHeTC.H cKaHHpoBa-
HHe JIyqOM (CM. pHC. 6.48). ,LJ;lliI 60JIbllIHX AP HarpY30qHbIe rrOTepH MOryr 6bITb
3HaqHTeJIbHbIMH. npH JI:B)'MepHOM CKaHHpOBaHHH HCrrOJIb3yroTCH JI:Ba rrepeCTpaHBa-
eMbIX JIa3epa, a 3a.,n;ep)f(}(JI 110 a3HMyraJIbHOMY H yrJIOMeCTHOMY KaHaJIaM CKJla.LI:bIBa-
IOTC.H Ha ct>oTorrpHeMHHKax 3JIeMeHTOB [38, 18].
CYMMaTOp
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6.4.2.2. OnTOBonOKOHHb.e nHHHH 3ap,epJKKH C peweTKoH 6p3rra
llyreM ct>OKYCHpOBKH YJIbTpact>HOJIeTOBOfo H3JIyqeHlliI B TOqKaX, l1epHO,D;HQeCKH

paCI10JIO}l(eHHbIX B,D;OJIb OrrTOBOJIOKHa, BbI3bIBalOmeH JIOKaJIbHOe 113MeHeHHe rrOKa-
3aTeJIH I1peJIOMJIeHHH, Ha yqacTKe OITTOBOJIOKHa MO}l(eT 6bITb C03,1J;aHa J(Hct>paKUHoH-
HaH perneTKa. TaKaH ,D;Hct>paKl(HOHHaH perneTKa OTpa)l(aeT OI1TllQecKYJO BOJIHY Ha
pe30HaHcHoH QaCTOTe pellIeTKH. B,D;OJIb OrrTOBOJIOKHa MO)I{HO paCrrOJIO)l(HTb pH,D;
6p3froBcKHx pemeTOK, C03,1J;alOmHX OTpa)l(eHHe OI1THQeCKHX BOJIH pa3JIHQHOH ,WIH-
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BbIXO,D;HOH CHfHaJI U;HpKyJIHTOpa Qepe3 <pOTO,D;HOJI: rrO,D;aeTCH Ha 3JIeMeHT.
B 60JIee CJIO)I{HOH cxeMe HCrrOJIb3yeTcH rrpH3Ma H3 OI1TOBOJIOKOHHbIX ,UH<ppaK-
U;HOHHbIX pemeTOK, I1pe,lJ,CTaBJIHlOmaH C060H Ha60p OrrTHQeCKHX BOJIOKOH C 6p3f-
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 DWBa 6. CucmeMbl numaHUR aHmeHHblX pememOK
C.H CBOI1 LUf<ppaKll;I10HHbIe pelIIeTKJ1, pacnOJIO)l(eHHbIe Ha 60JIbllIeM paCCTO.HHI1I1
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eTC.H Ha OnTWQeCKHM .n;eJII1TeJIb. H B 3TOM cJIyqae Heo6xo.n;HMO yqHTbIBaTb Harpy-
30QHbIe nOTepl1 (CM. pHC. 6.49) [58, 63, 74, 6].
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l{HPKYJHITOp
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,

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Y HHX OqeHb He60JIbllIOe CeqeHHe paCCe.SlHH.SI (CB.SI3H). TIOJIHa.Sl .n:HarpaMMa HanpaB-
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nOCTO.SlHHOH MOm:HOCTH B036)')K,IJ;eHH.SI, B KOTOpbIX HMne,L(aHCHOe paCCOrJIaCOBaHHe
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TIpH CB060,aHOM B036)')K,IJ;eHHH rrpe,L(nOJIaraeTCH, QTO KaJK,IJ;bIH yqacToK I(enH
TIHTaHHH 3KBHBaJIeHTeH HCTOqHHKY HanpH)I(eHHH (TOKa) C nOCJIe.n:OBaTeJIbHO BKJIIO-
qeHHbIM conpOTHBJIeHHeM Ro. TaKHe HCTOqHHKH C nOCTOHHHOH MOIl(HOCTblO naaa-
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S - MaTpHua paCCe.SlHHSI H3 K03<P<PHI(HeHTOB CB.SI3H. K03rjJrjJuueHm ompa:JICellUR npu
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CHnY pa3JIHQHH aMnTIHTY.n: TIpH HCnOJIb30BaHHH KOHeqHOH AP C B036)')K,IJ;eHHeM,
CnaaalOI.UHM K KpaHM paCKpbIBa. XOT.SI MeTO,a pacceHHHH TOQHO Mo,aeJIHpyeT 60JIb-
llIHHCTBO AP H KOHuenTYaJIbHO npocT, OH He ,naeT npHMoro cnoc06a BbIQHCJIeHHH
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HbIM K03cPcPHllHeHTOM YCHJIeHH.H, TaKoe H3MepeHMe 06bIqHO 6bIBaeT ,UOCTaTOQHbIM.
3JIeMeHTbI pe30HaHCHbIX pa3MepOB (,nHnOJIM) HMelOT CB.H3b B H-TIJIOCKOCTM, YMeHb-
maIOIUYIOC.H KaK 3aBJfCHMOCTb 1/r2, Tor,na KaK CB.H3b B E-:TIJIOCKOCTH YMeHbIIIaeTC.H
KaK 1/ r [130].
O,nHaKo, KaK nOKa3aHO B pa60Tax [48, 41, 116], BeJIHQHHa CB.H3M B AP aCHMn-
TOTHqeCKM cna.n.aeT B OTHOllIeHMH l/r 2 . 3TOT BbIBO.a no.aTBep)l(,L(aeTC H3MepeHM.HMH
Ha 60JIblliJfX AP [36, 33]. <I>a30BbIe M3MepeHMH nOKa3bIBaIOT, QTO npM OTCyrCTBHIi
BHellIHeH HarpY3KH 3ReprHH CB.H3H MMeeT <l>a30BYIO CKOpOCTb cBo6o.aHoro npo-
CTpaHCTBa.
Y HeKOTopbIX AP CYIUecTByeT nOJIO)l(eHHe JIyqa (OTJIJfqHOe OT e = 90°), npH KO-
TOpOM OUa2paMMa CKaHup08aHUR 3JleMeHma HMeeT HYJIb HJIH, .apyrMMM CJIOBaMH,
npM KOTOpOM BeJIHqMHa K03cjJrjJuu,ueHma OmpaJICeHUR npu CKaHup08aHUU paBRa e.aH-
HHue. TaKo" yrOJI Ha3bIBaeTCH «yrJIOM OCJIenJIeHMH» «<blind spot»). HH)I(e 6y.aeT
nOKa3aHO, qTO ero nO.HBJIeHHe MO)l(eT 6bITb YCTpaHeHO C nOMOIUblO Harwe)l(aIUerO
BbI60pa napaMeTpOB AP.
.
7.2.3. MMneAaHC CKaHMpOBaHMSI
M AMarpaMMa CKaHMpOBaHMSI 3neMeHTa
HaJf60JIee Ba)J(HbIM H nOJIe3HbIM napaMeTpOM HBJI.HeTCH UMneoaHC CKaHup08aHUfl
(scan impedance), T.e. cPYHKI.J;HOHaJIbHa.H 3aBHCHMOCTb HMne.aaHca 3JIeMeHTa OT
yrJIOB CKaHHpOBaHHH, npH KOTOpOM Bce 3JIeMeHTbI B036y)1(L(alOTCH C HaLUIe)l(aIUeH
aMTIJIHTY.uoH H <pa30H. OTclO.ua HeMe.n;JIeHHO nOJIyqaeTcH K03rjJrjJuu,ueHm OmpaJICeHUfl
npu CKaHup08aHUU. 3aTeM onpe,n:eJIHIOTCH xapaKTepHCTHKH AP nyreM YMHO)l(eHHH
.aHarpaMMbI HanpaBJIeHHOCTJf no MOIIJ;HOCTH MH OT.aeJIbHOrO 3JIeMeHTa (HOpMHpO-
BaHHOH K MaKCHMaJIbHOMY YPOBHIO 0 .aE) Ha MHO)I(HTeJIb pemeTKH H30TponHbIX
3JIeMeHTOB (no MOIUHOCTH) H Ha K03<t>cPliI.J;MeHT paCCOrJIaCOBaHHH HMne.uaHca
(1 -If 12). ,[(HarpaMMa HanpaBJIeHHOCTH H30JIHpOBaHHoro 3JIeMeHTa li3Mep.HeTCH
npH pa3pbIBe ueneH OCTaJIbHbIX 3JIeMeHTOB (pe)I(HM XOJIOCTOrO xo.aa). 3TH pe3YJIb-
TaTbI He BnOJIHe COBna.n.aIOT C nOJIyqaeMbIMH B OTcyrcTBHe Bcex OCTaJIbHbIX 3JIeMeH-
TOB, 3a HCKJIlOqeHHeM CJIyqa KJIaCCHqeCKHX aHTeHH C MHHHMaJIbHbIM paCCe.HHHeM
(CM. pa3,neJI 7.2.3.1). 3.aecb npe,n:nOJIaraeTCH, qTO AP .aOCTaTOQHO BeJIHKa, TaK qTO
KpaeBbIMH 3cPcPeKTaMH MO)I(HO npeHe6peQb, Ii uMneiJaHc CKaHup08aHUR 6Y,lI,eT TaKJ1M
}l(e, KaK H .LUIH 6eCKOHeQHOH AP. 3TO npOCToe BbIpIDKeHHe MH xapaKTepHCTHK no-
3BOJIHeT pa3JIHQHTb BKJIazIbI, 06YCJIOBJIeHHbIe ceTKOH AP, marOM pa3MemeHHH 3JIe-
MeHTOB, TJfnOM 3JIeMeHTOB H 3cP<t>eKTaMH B3aHMHOH CBH3Jf.
3KBHBaJIeHTHOe BbIpIDKeHHe .LUIH pa60QHX xapaKTepHCTJfK AP 06'be,lI,HHHeT .aHa-
rpaMMY HanpaBJIeHHOCTH OT.aeJIbHOrO 3JIeMeHTa M K03<l><PHUHeHT paCCOrJIaCOBaHM
HMne.uaHca B HOBbIH napaMeTp - iJua2paMMY CKaHup08aHUR 3JleMeHma (scan element
pattern - SEP), paHee Hey.aaQHO Ha3bIBaeMYlO .aHarpaMMoH HanpaBJIeHHOCTH aK-
THBHoro 3JIeMeHTa. Tenepb nOJIHaH pa6oqa.H xapaKTepHCTHKa AP npe.aCTaBJIHeT co-
60H npOH3Be,lI,eHHe MHO)l(HTeJIH pemeTKH H30TponHbIX 3JIeMeHTOB H oua2paMMbi
CKaHup08aHUR 3JleMeHma. IIepBbIH MHO)l(HTeJIb onpe.ueJIHeT IIIHPHHY JIyqa AP Ii
CTPYKTYPY 60KOBbIX JIeneCTKOB .LUIH HHTepeCYIOIUero yrJIa CKaHHpOBaHHH; nOCJIe,n;-
HHH, nO.lI06HO .aHarpaMMe HanpaBJIeHHOCTH H30JIHpOBaHHoro 3JIeMeHTa, H3MeHHeT-

Z2. OcH06Hble npUHlJ,Unbl C1CaHUpylOU4UX aHmeHHbIX peWem01C d
CR Me.a.rreHHO H onpe,n:eJIReT 3aBHCHMOCTb K03<P<PHUHeHTa YCllJIeHHR AP OT yrJIa
CKaHMpOBaHllR. BIDKHO OTMeTHTb, qTO SEP ,n:aeT KOHCTPYKTOpy pa.aapa IDIH CBR3-
HOW CllCTeMbI 3aBHCllMOCTb K03<P<PHUHeHTa YCHJIeHMSI. AP B MaKCHMYMe CKaHHpylO-
ero JIyqa OT yrJIOB CKaHHpOBaHHR. ,D,uazpaMMa CKaHUp06aHUR 3JleMeHma MO)l(eT
6bITb onpe,n:eJIeHa HCXOlUI H3 UMneOaHCa CKaHUpOeaHUR H ,n:llarpaMMbI HanpaBJIeHHO-
CTH OT,[(eJIbHOrO 3JIeMeHTa CJIe,[(yrom:HM 06pa30M: B MaKCHMYMe CKaHHpYIOm:erO
JIyqa K03<P<PllUHeHT YCHJIeHllR AP COCTaBJIReT
G(8) = Ng s (8) = 41t 1£(8) P ,
"P avail
(7.10)
r,ne gs - ,n:HarpaMMa cKaHHpoBaHHR 3JIeMeHTa no MOII.J;HOCTH, a P avail - no,n:BO,[(I1-
MaR MOm:HOCTb.
3JIeKTpllQeCKOe nOJIe MO)l(eT 6bITb BbIpa)f(eHO Qepe3 ,[(HarpaMMY HanpaBJIeHHO-
CTH OT,n:eJIbHOrO 3JIeMeHTa pemeTKH, HOpMHpOBaHHYIO TOKOM 3JIeMeHTa npH CKaHI1-
pOBaHHH /s(8):
E(8) = HIs (8) E iso (8) .
liso
(7.11 )
K03<P<PHUHeHT YCIDIeHHR H30JIHpOBaHHoro 3JIeMeHTa BbIpa)l(aeTCR B BJUJ:e OTHO-
rneHHR KBa,n:paTa HanpIDKeHHOCTH nOJIR K MOm:HOCTH:
. li S) _ 4nl E iso (8)1 2
glSO\: - 1 1 2 .
" I iso R iso
(7.12)
MOlI{HOCTb, nOCTYIIalOII.J;aR B AP, BbIpa)l(aeTC.SI qepe3 TOK B 3JIeMeHTax npH CKa-
HHpOBaHHH H HMne,n:aHCbI:
Pavail -
NV 2
4Rg
_ NIIs(8)12IZs(8)+ZgI2
4Rg
(7.13)
06'be,n:HHeHHe 3THX pe3YJIbTaTOB ,n:aeT ouazpaMMY CKaHupoeaHUR 3JleMeHma, BbIpa-
)l(eHHyro Qepe3 K03<P<PHUHeHT YCHJIeHHR OT,n:eJIbHOrO 3JIeMeHTa H llMne,aaHCbI [26]:
4Rg Risogiso (8)
gs (8) = I Zs (8) + Z gl2 ·
(7.14 )
ECJIM ouazpaMMa cKaHupoeaHuR 3JleMeHma npH e = 0 HOpMl1pOBaHa K e,n:I1HMQe,
OHa MO)f(eT 6bITb BbIpa)l(eHa TOJIbKO Qepe3 ,n:HarpaMMY HarrpaBJIeHHOCTH OT,[(eJIbHOrO
3JIeMeHTa no MOlI{HOCTH H uMneoaHC CKaHupoeaHuR:
li S) _ 4Rs (0)giso(8)
gs \: - .
I Z s(8)+Zgj2 giso(O)
(7.15)
B o6ru:eM CJIyqae, eCJIH peaKTHBHoe conpOTHBJIeHHe reHepaTopa He paBHO
HYJIIO, ueJIeC006pa3HO HCIIOJIb30BaTb COnpR)I(eHHbIH K03<P<PHUHeHT OTpa)l(eHHR,
onpe,n:eJUIeMbIW KaK
Z; (8) - Z g
r* = .
Z s (8) + Z g
(7.16)

 Dla8a Z B3aUMHllJI C8R3b
.'
3TO .naeT
1-lr j2 == 4RgRs(8)
* I Z s(8)+ Z g I2'
(7.17)
qTO n03BOJIReT BbIpa3HTb iJuazpaMMY CKaltUp08altUJl 3JleMeltma qepe3 K03rjJrjJuu,ueltm
ompaJICeltUJl npu CKaItUp08aItUU, ,DJlarpaMMY HanpaBJIeHHOCTH OT.aeJIbHOrO 3JIeMeHTa
H conpOmU8JleltUe CKaItUp08aItUJl:
g (8) = Risogiso (8) (1 -I r * 1 2 ).
s Rs (8)
(7.18)
Tenepb conpIDKeHHbIH reHepaTOp (HCTOqHHK), cOrJIaCOBaHHbIH C conpOmU8Jle-
ItUeM CKaltUp08altUJl npH e = 0, n03BonReT nOJIyqHTb BbIpa)l(eHHe ,l])IR SEP B KOHeq-
HOM BH.ae.
gs (8) = Rs (O)giso (8) [1 -I r * (8)1 2 ].
Rs (8)giso (0)
(7.19)
OTMeTHM, qTO B qaCTHOM c.rryqae, Kor.na HMne.naHC reHepaTopa .aeHcTBHTeJIeH,
SEP BbIpIDKaeTCR B CJIe.nYIOIUeM BH.ae:
gs (8) = Risogiso (8) 11 - r(8) 1 2 . (7.20)
Rg
IIpe.arnecTByIOIUHH BapHaHT npe.aIIOqTHTeneH, IIOCKOJIbKY B HeM RBHO BbIpa)l{e-
Ha pOJIb conpOmU8JleltUJl CKaItUp08aItUJl, ,l(HarpaMMbI HarrpaBJIeHHOCTH OT.aeJIbHOrO
3JIeMeHTa H K03rjJrjJuu,ueltma ompaJICeltUJl npu CKaItUp08aItUU.
CTOHT OCTaHOBHTbCR Ha qaCTO U;HTHpyeMoM npH6JIIDKeHHOM pe3YJIbTaTe ,WUI
SEP. Ero CMbICJI B TOM, qTo6bI nOKa3aTb 3aBHCHMOCTb BJL[(a cos e [47]:
4nA
gs (8) - 'At m cos8[1-1 r(8)12], (7.21)
r.ae A elem - llJIOIUMb 3JIeMeHTapHoH RqeHKH AP . B pa3.aeJIe 7.4 IIOKa3aHO, qTO no-
Be.aeHHe iJuazpaMMbl CKaltUp08altUJl 3Jle.Meltma 6JIH)I(e K cos 1,5 e H3-3a .aonOJIHHTeJIb-
HOH MOIUHOCTH, BHeceHHOH BCJIe.aCTBHe paCCOrJIaCOBaHHR HMne.aaHca. IIo3TOMY
,l])IR nOJIyqeHHR TOqHbIX H 3<p<peKTHBHbIX pe3YJIbTaTOB JIyqrne HCnOJIb30BaTb 06bIq-
HYIO cPOPMYJIY, npHMeHHMYIO K SEP (ypaBHeHHe 7.19). 06rnHpHbIe .aaHHbIe no UM-
neiJaltcy CKaltUp08altUJl .aHnOJIbHbIX AP rrpHBe.aeHbI B pa3.aeJIe 7.4.1.
B .apyrOM BapHaHTe ypaBHeHHH, IIpHMeHHMOM ,lUIR KOMrrblOTepHoro aHaJIH3a,
HCrrOJIb3YlOTCR 3HaqeHHR TOKOB:
E(8, cI» == 60F(8, cI» fIn.
r
(7.22)
3.aeCb npOH3Bo.aHTCR CYMMHpOBaHHe no 3JIeMeHTaM AP, H .aHarpaMMa HarrpaBJIeH-
HOCTH F HMeeT BHl(
F(8, cI» == cos kh - cos(kh cos 8) .
sin kh  I - cos 2 8 cos 2 4>
(7.23)
)].HnOJIH HarrpaBJIeHbI B,l(OJIb OCH x II paCIIOJIO)l{eHbI B X- Y IIJIOCKOCTH. TalGlM
06pa30M, OCb aHTeHHOH perneTKH COOTBeTcTByeT <t> = O. IIoJIoBHHa ,l])IIIHbI .aHnOJUI
paBHa h, k = 2n/A.

Z2. OcH08Hble npUHlUnbl CKaHUpylOUJ,UX aHmeHHbIX peWemOK 'd
Mom;HOCTb, nOCTYTIalOm;aSI B AP, 6e3 yqeTa COrJIaCOBaHRSI RJIR RMne,naHCa RC-
TOqHRKa BbIpIDKaeTCSI CJIe,nyrom;HM 06pa30M:
N
P=LInI;Rsn,
(7.24)
f,l(e Rsn - conpomu8AeHue CKaHUp08aHUJl n-ro 3JIeMeHTa. YpaBHeHHe L(JISI K03<P<PH-
IJ;ReHTa YCRJIeHHSI Tenepb npHHHMaeT BH)J;
N N
120F2 (8, <1» L In L I;
G(8, <1» = N .
L1nI;Rsn
(7.25)
nOCKOJIbK}' SEP npe,nCTaB.IDIeT C060H 3HaqeHHe K03<P<l>RIJ;HeHTa YCRJIeHHSI Ha
3JIeMeHT, nOJIyqaeM
N N
120F2 (8,<1» L In L I;
SEP = N .
NLInI;Rsn
(7.26)
3TO MO)l(eT 6bITb BbIpIDKeHO qepe3 K03<P<PHl(HeHT YCRJIeHIDI OT,neJIbHOrO 3JIe-
MeHTa giso' r,ne
. 10 th\ _ 120F2 (8, <1»
g ISO \U, ,+,J - R. ·
ISO
(7.27)
TaKHM o6pa30M, SEP HMeeT BJm
.
N N
Risogiso(8,<I» L In L I;
SEP(8, <1» = N .
NRs LIn I ;
(7.28)
3TO MO)l(eT 6bITb BbIpIDKeHO B BH)J;e:
N N
120R. F2(8,<I» I  1*
SEP(e, «1» = ISO N £.., n £.., n X [1 -I r * (e, «1» 1 2 ],
Rs (8, <1» L I n/;
(7.29)
fe Rs - conpomU8AeHue CKaHup08aHUJl.
E,nHHCTBeHHoe ,nOnyIl(eHHe B ypaBHeHHH (7.29) COCTOHT B TOM, qTO cOnpOmU8-
AeHUJl CKaHUp08aHUJl BCeX 3JIeMeHTOB paBHbI, qTO BJIHSIeT Ha C}'MMapHyro MOm;HOCTb
11 MHO)I(JITeJIb paCCOrJIaCOBaHHR. ,LLrrR He60JIbllIHX AP MHO)I(JITeJIb paCCOrJIaCOBaHHSI
MO)l(eT 6bITb BbIqHCJIeH L(lliI KIDK,Z:I;OrO 3JIeMeHTa, a 3aTeM ycpe,nHeH. 3<l><peKTHBHOCTb
3Toro no,nxo,na nOKa3aHa B pa3,neJIe 7.2.3.1.

 FIla6a Z B3aUMHaJl C6JI3b
7.2.3.1. CpaSHeHlAe p,IASrpaMMhl CKaHlApOSaHHfI aneMeHTS
Ha nplAeM M nepep,s'IY
)].JUI TOqHOrO onpe,n:eJIeHI1R 3aBI1CMMOC:r11 CKaHI1PYIOIIleH .n:l1arpaMMbI HanpaBJIeH-
HOCTH ueHTpaJIbHOrO B036)')K,l];eHHOrO (nepe.n:alOI..Qero) 3JIeMeHTa OT yrJIa 11 qaCTOTbI
B npouecce 113MepeHI1R I1CnOJIb30BaJIaCb nporpaMMa paCqeTa IIJIOCKOH AP Ha OCHO-
Be TOHIGIX .lUinOJIeH, pa3MeI.I..J:eHHbIX Ha KBa.n:paTHOH ceTKe [54]. 3Ta nporpaMMa MO-
.n:eJIHpyeT KOHeqHYIO KBa,LI:paTHYIO AP, HMelOI.I..J:YIO .n:o 100 3JIeMeHTOB no Ka)l()];OH
OCI1, BocnpOH3BO.lI.R, TaKI1M 06pa30M, npOue.lI.YPY H3MepeHI1R. nOCKOJIbKY .n:HnOJIH
v
TOHKHe, a MaKCHMaJIbHbII1 I1X pa3Mep paBeH nOJIOBI1He LUIHHbI BOJIHbI, TOKOBoe pac-
npe.n:eJIeHl1e OqeHb 6JIH3KO K CI1HYCOl1.lI.aJIbHOMY, n03TOM)' npl1MeHeHl1e MeTo.n:a MO-
MeHTOB He Tpe6yeTCR. Ko BceM 3JIeMeHTaM nO.lI.KJIlOqaJIaCb pe311CTI1BHaR HarpY3Ka
11 B036)')K,l];aJICR ueHTpaJIbHbIH 3JIeMeHT.
PerneHl1e MaTpl1qHbIX ypaBHeHl1ti C B3al1MHbIMI1 I1Mne.n:aHcaMH ,UaeT KOMIIJIeKC-
HbIe TOIGI LUIR Bcex 3JIeMeHTOB AP. B3al1MHbIe HMne.n:aHCbI H 06paTHaH MaTpHua
BbIqHCJIRJII1Cb C Y,UBoeHHOH TOqHOCTblO. )].HarpaMMa HanpaBJIeHHOCTH B ,n:aJIbHeH
30He BbIQHCJIIDIaCb nyreM CYMMHpOBaHI1H np0113Be,UeHI1H TOKOB 3JIeMeHTOB Ha CO-
OTBeTCTBYlOlliHe ynpaBJIRIOI.I..J:He $a30Bble MHO)I(HTeJII1 11 Ha ,n:HarpaMMbI HanpaBJIeH-
HOCTI1 3JIeMeHTOB. K03$$I1UHeHT YCHJIeHHH paBeH 120£2 / P* (1 - IfF), r,n:e f -
K03$$HUl1eHT OTpa)l(eHI1H. HCnOJIb30BaJII1Cb ,UBa COrJIaCYIOIIIHX I1Mne,n:aHca: O,n:HH
,UJIR 6eCKOHeQHOH AP B036)')K,l];eHHbIX .n:HnOJIeH, a ,n:pyrOH - TOJIbKO ,UJIH B036yx-
.n:eHHoro ueHTpaJIbHOrO 3JIeMeHTa. BbIQHCJIeHHH BblnOJIHeHbI Ha 64-pa3PMHoH pa-
60Qeti CTaHUHH HP UNIX.
Ha pl1C. 7.3 npHBe,n:eHbI pe3YJIbTaTbI ,UJIH AP, co.n:epxam;eti 50 x 50 3JIeMeHTOB
(2500 HeH3BecTHbIX). 3HaQeHHH SEP (K03$$HUl1eHT YClllIeHHH Ha 3JIeMeHT) HOp-
MRpOBaHbI, QT06bI nOJIyqHTb HOJIb ,n:elJ,H6eJI B HanpaBJIeHHH, nepneH,n:HKYJIHpHOM
paCKpbIBY perneTKH, TaK KaK a6COJIIOTHbIe 3HaQeHIDI HeKoppeKTHbI H3-3a B3aHMHblX
RMne.n:aHCOB naCCRBHbIX 3JIeMeHTOB. A6COJIIOTHbIe 3HaqeHI1H 06c)')K,l];aIOTCH HIDKe.
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60
70
80
90
PHC. 7.3. AHTeHHaH pemeTKa 113 50 x 50 .D:I1IIOJIeH, L == Dx == Dy == O.5A

7.2. OCH06Hble npuHu,Unbl CTCOHUPYIOUI,UX aHmeHHblX peUJemOK d
LJ;JIfI COrJIaCOBaHI1f1 I1CnOJIb30BaJIC5I MMIIe,IJ;aHC CMH<}>a3Hoti AP: 63 + j23 Q. no cpaB-
HeHMIO C 6eCKOHeqHoti AP 3HaqeHI1f1 SEP OT.n:eJIbHOrO M3JIyqalOll.{ero 3JIeMeHTa (Ha-
3bIBaeMoro nepe.n:alOll.{I1M) npl1MepHO Ha 2 ,IJ;D 60JIbllIe B ,IJ;Mana30He e OT 40 ,n;o 80 0
B E-nJIOCKocTI1. D:JIR H-nJIOCKOCTM 3HaqeHM5I HeCKOJIbKO BbIllie. OTKJIOHeHl1e OT
a6COJIIOTHOrO 3HaqeHI1R K03<}><}>l1ltHeHTa YCI1JIeHM5I 3HaQMTeJIbHO 60JIbllIe, qeM BbI-
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Ha$l CBfl3b 3HaQl1TeJIbHO YMeHbllIaeT aMIIJIHl)',IJ;bI TOKOB, YMeHbllIaSl, TeM caMbIM, KO-
3<P<PHUl1eHT YCMJIeHHH Ha 3JIeMeHT. 3HaqHTeJIbHbIe KOJIe6aHI151 SEP B H-IIJIOCKOCTI1
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,n:RmHX CTep)I(HeH nOJIOBHHHOH ,n:JIHHbI, OCTalOlI(HHCR npH pa30MKHyrbIX ,l1HnOJIRX.
COrJIaCHO O)l(J{)1aHHRM nOJIYBOJIHOBble ,n:HnOJIH He RBJUlIOTCR CMS-aHTeHHaMH.
AHaJIOrHqHbIM 06pa30M, eCJIH meJIH B 3KpaHHPYIOII(eH TIJIOCKOCTH lIlYJITHPYJOTCR
BbIBO.ll.aMH nHTaHIDI, OCTaIOII(HeCH meJIH nOJIOBHHHOH )l,JIHHbI BJIHRIOT Ha pacnpe,l(e-
u
JIeHHe TOKa B 3KpaHHPYJOIUeH nJIOCKOCTH.
B pa60Te [125] nOKa3aHO, qTO B3aHMHbIH HMne,n:aHC (aaMHTaHc) ,n:BYX H,[{eHTHq-
HbIX MSA-aHTeHH MoxeT 6bITb BblpaxeH B BH,n;e HHTerparra OT ,n;HarpaMMbI HanpaB-
u
JIeHHOCTH no MOII(HOCTH OT,n;eJIbHOrO 3JIeMeHTa no HeKOTopbIM ,n;eHCTBHTeJIbHbIM H
KOMTIJleKCHbIM yrJIaM (CM  TaIOKe [11]):
Z12 = 2 J exp(-jkdcosw)P(w)dw. (7.31)
path
r,n:e w = u + jv 11 ,l(HarpaMMa HanpaBJIeHHOCTH no MOIUHOCTH onpe.n:eJIReTCR KaK
P(w) = f(w)f(w + 1t), a nyrb HHTerpHpOBaHHR B KOMnJIeKCHOH nnOCKOCTH w npoxo-
lIHT OT (-1t/2, - (0) ,n:o (-1t/2, 0), 3aTeM K (3/2, 0) H K (3/2, (0). HarpaMMa HanpaB-
JIeHHOCTH no MOII(HOCTH HOpMHpOBaHa TaKHM o6pa30M, qTO ee HHTerpaJI no BceM
.neHcTBHTeJIbHbIM yrJIaM paBeH e,l(HHHue. 3TOT HHTerpaJI MO)l(eT 6bITb BblpIDKeH TaK-
)l(e B Koop,n:HHaTax BOJIHOBOrO qHCJIa. HanpHMep, )l,JIR ,n:BYX aHTeHH B xy TIJlOCKOCTH
B3aHMHbIH HMne,n:aHC ,n:aeTCR <POPMYJIOH
2 00 00 ex p[ J ' ( k d + k d )]
Z = - J J - x x Y Y P ( k k ) dk dk
12  x' y x yo
k k 2 - k 2 - k 2
-00 -00 x Y
(7.32)
B3aHMHaR CBH3b B 3TOM c.rryqae onpe,n:ellileTCR ,n:HarpaMMoH HanpaB.ITeHHOCTH
3JIeMeHTa H llIarOM B AP H nOJIHOCTbIO He3aBHCHMa OT cnoco6a C03,n:aHHR 3TOH ,l(Ha-
rpaMMbI HanpaBJIeHHOCTH. 3TOT BbIBO.n: )l,JIH MSA RB.ITReTCR o6061I(eHHeM BbIBo,n;a,
06cyJK,LJ:aeMOrO B pa3,n:eJIe 7.3 npH paCCMOTpeHHH PMa ,l(H<ppaKUHoHHbIX JleneCTKOB.
EOJlbllIHHCTBO MHorOMO,l(OBbIX 3JIeMeHTOB He HMelOT opTorOHarrbHbIX ,n:HarpaMM
HanpaBJIeHHOCTH If, cne,n:OBaTeJlbHO, He HBJIHIOTCR MSA-aHTeHHaMH. O.nHaKO MHO-
rHe O,n:HOMo,n:OBble aHTeHHbI npH6JIHXaIOTCR K MSA. KopOTKHe ,n:HnOJIH, B KOTOpbIX
pacnpe,n:eJIeHHe TOKa no CYlI(eCTBY JIHHeHHO, 6JIH3KH K MSA. Pe30HaHCHbIH (nOqTH
nO.rryBOJIHOBOH) ,n:HnOJlb OqeHb Marroro paaMYca 6JIH30K K MSA; MarrbIH paaHYC

Z3. IlpocmpaHcm6eHHble noiJxoiJbl K 3rjxJJeKmaM 63aUMHOU C6Jl3U d
npIfBO,1I;I1T K nOqTIf CIfHYCOH,L(aJIbHOMY paCnpe,L(eJIeHHIO TOKa. llOKa3aHO, qTO B3aIfM'r'
u
HhIIf IfMne,L(aHC Me)l(,L(Y TOHKHMIf KOJIJIIfHeapHbIMH rrOJIYBOJIHOBbIMH ,LI;HnOlliIMIf CO-
rJIacyeTcR C pe3YJIbTaTaMH KapTepa [125]. B pa60Te [6] nOKa3aHO, qTO CKpemeHHbIe
,n:lfrrOJIH rrpH6JIIDKeHHO RBJIRIOTCR MSA-aHTeHHaMH B O,Ll;HOH IIJIOCKOCTH ,LI;lfarpaM-
u
MbI HanpaBJIeHHOCTIf, a B3aHMHblIf IfMrre,n:aHC XOpOlliO BhIqlfCJIReTCR C nOMOmblO
MSA-TeopIfH, eCJIH l(eHTp O,lJ,HOrO nepeKpeCTbR JIe)I(HT Ha 6HcceKTpHce CTOpOH
,n:Pyroro nepeKpeCTbR. He60JIbllIHe CnHpaJIM TaIOKe npH6JIIDKalOTCR K MSA.
7.3. npOCTpaHCTBeHHble nOAXOAbl
K 3<1><I>eKTaM B3aMMHOM CBR3M
B OCHOBe paCqeTa AP, KpOMe pell1eTOK C MaJIbIM qHCJIOM 3JIeMeHTOB B,l{OJIb KIDK.ZJ:OH
CTOpOHbI, JIelKlfT TeopHR 60JIbllIMX HJIM 6eCKOHeqHbIX AP. OHa npe,l{CKa3bIBaeT rro-
Be,n:eHMe Bcex 3JIeMeHTOB, KpOMe KpaeBbIX; rrOCJIe,n:HHe ,l{aJIee paCCMaTpHBalOTCR OT-
.n:eJIbHO (CM. rJIaBY 8). B rrpocTpaHcTBeHHoH 06JIaCTH AP Mon:eJIMpyeTcR MaTpHl(eH
IfMne,l{aHCOB (a,n;MlfTaHcoB), YCTaHaBJIMBalOmeH CBR3b HanpIDKeHHH (TOKOB), nplf-
JIOlKeHHbIX K ,l{lfnOJIRM (meJIRM), M pe3YJIbTMpyromHX TOKOB (HarrpIDKeHIfH). j:(JUI
60JIbll1MHCTBa ,n:lfana30HOB yrJIOB CKaHMpOBaHMR Y AP )'MepeHHbIX pa3MepOB UMne-
(Jane CKanupoeanUR If iJua2paMMa CKanupoeanUR 3JleMenma nOQTH He 3aBMCRT OT pa3-
Mepa pell1eTKH. TIpe)l()1e qeM nepeHTH K ,n;HHOMY rr03JIeMeHTHOMY rro,L(XO,l{Y, HCCJIe-
,n:yeM B3aHMHbIH HMrre,l{aHC ,l{BYX 3JIeMeHTOB; KaK OTMeqaJIOCb B npe,l{bI,l{YI.U:HX
pa3,l{eJIaX, B3aMMHhIH HMrre,l{aHC RBJIReTCR If npHqHHOH, If 061>RCHeHHeM Bcex RBJIe-
HHM, Ha6JIIO,n:aeMbIX B CKaHHPYlOlI(eH AP. 3TH B3aHMHbIe HMne.uaHCbI RBJIRIOTCR
3JIeMeHTaMH MaTpHUbI HMrre.uaHCOB AP.
7.3. 1. KnacCM"IeCKMe BMAbl CBR3M
7.3.1.1. B3aHMHb/M HMnep,aHC J;lHnOneM H UjeneH
I1MeeTc HeCKOJIbKO IfHTYMTHBHO nOHRTHbIX npaBHJI, KacalOmlfXCR B3alfMHOM CBR-
31f Me)l(,l(Y ,n;BYM 3JIeMeHTaMIf aHTeHHbI. Bo- nepBbIX, BeJIMqHHa B3aHMHoro IfMne-
,naHca YMeHbllIaeTCR C paCCTORHlfeM Me)l(,l(Y 3JIeMeHTaMIf. Bo- BTOpbIX, eCJIIf O,l{Ha
u
aHTeHHa HaXOJIIfTC B MaKCHMYMe ,l{lfarpaMMbI HanpaBJIeHHOCTIf JIpyrOIf, TO CBR3b
CIfJIbHee, qeM B CJIyqae HaXO)l(,l(eHM B npOBaJIe ,l{lfarpaMMbI HanpaBJIeHHOCTM. ECJIM
o,nHa aHTeHHa HaXO,l{IfTC B 6JIIDKHeM nOJIe H3JIyqeHlfR ,l{PyroH, TO IfCnOJIb3yroTC
nOJIR B 6JIHlKHeH 30He. B-TpeTbHX, eCJIIf 3JIeKTpHqeCKHe nOJIR napa.TIJIeJIbHbI, TO
CBR3b CHJIbHee, qeM B CJIyqae HX KOJIJIMHeapHOCTIf. ,lJ;JIR rrpOBOJIOqHbIX aHTeHH 3TO
MOlKHO nepe<popMYJIlfpOBaTb B TepMMHax 3aTeHeHMR: 60JIbllIOe 3aTeHeHlfe KOppeJIM-
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llIyro CBR3b. HanpHMep, y 60JIbllIMX pyrrOpOB MeHbllIlfH B3alfMHbIH IfMne.n:aHC, qeM
Y MaJIeHbKHX pynOpOB. 3TH npaBHJIa, XOTR M nOJIe3HbI, He 3aMeHRIOT MeTo.n:bI onpe-
)];eJIeHHR peaJIbHbIX 3HaqeHlfM B3aHMHoro HMne,naHca HJIH MMIfTaHca. 3,l{eCb no)];-
P06HO paccMaTpHBaeTcR B3aHMHbIH HMne,l(aHc. Me)l(,[{Y ,l{HnOJIRMH, nOCKOJIbKY ,l{lfno-
JIM H meJIH RBJIRIOTCR pacnpOCTpaHeHHbIMH 3JIeMeHTaMIf AP. 3TH IfMne,l{aHCbI
SlBJIRIOTCR THnMqHbIMM B3aHMHbIMH HMne.n:aHcaMH pe30HaHcHblx 3JIeMeHTOB, TalGlX

b FnaBa Z B3aUMllaJl CBR3b
KaK MlfKpOIIOJIOCKOBbIe aHTeHHbI [3]; TaKHM 06pa30M, nOBe,D:eHMe B3aMMHoro HM-
OJ
lIeLIaHca llMIIOJIeM MMeeT YHHBepCaJIbHYIO npMMeHMMOCTb.'
TOHKMe l(MJIMH,n:pMqeCKMe ,D:MnOJIH 3KBMBaJIeHTHbI llJIOCKMM nOJIOCKOBbIM llMno-
JIRM, Y KOTOpbIX llIHpHHa nOJIOCKOBOro npOBo,nHMKa paBHa y,nBoeHHOMY ,nHaMeTPY
OJ OJ
npOBo,na, a ,n:aHHbIe no B3aHMHOM npOBO,D:HMOCTlf ll.{eJIeM BbIBO,aRTCR M3 pe3YJIbTaTOB
,ILJIR nOJIOCKOBbIX ,n:MnOJIei1 C nOMOll.{blO npMHUHna .6a6MHe.
,lLrrR paCqeTa B3aHMHoro MMne,aaHca 06bIqHO npMro,n:eH no,[(Xo,n: HYJIeBOrO nopmI.-
Ka (CMHYCOM,aaJIbHOe pacnpe,n:eJIeHMe TOKa). B 3TOM CJIyqae MOryr MCnOJIb30BaTbCR
<POPMYJIbI [62] . OHM 3an;a1OT BbIpIDKeHMe ,ILJIR B3aMMHoro lfMne,aaHca napaJIJIeJIbHbIX
KOMllJIaHapHbIX ,UMnOJIeH HepaBHOH ,ILJIMHbI, pacnOJIOXeHHbIX C1)'IIeHbKaMM. O,aHaKO
3TM <POPMYJIbI co,aep)l(aT 24 'lJIeHa C MHTerpaJIbHbIMM cMHycaMlf M KocMHycaMM OT
CJIO)I(HbIX M pa3HOTHnHbIX apryMeHTOB. XOTR pe3YJIbTaTbI [62] ,aonYCKaIOT peaJIM3a-
UHIO B Blf.[(e KOMnblOTepHoro aJIrOpMTMa, rrpOIIJ;e BbIBeCTM <POPMYJIY Henocpe,aCTBeH-
OJ
HO, C nOMOIll.blO TOqHbIX BbIpIDKeHMM ,ILJIR
6JIIDKHerO 3JIeKTpHqeCKOrO nOJIR 113 pa60-
TbI [112a]. TOqHOe nOJIe CHHYCO.l1,[(aJIbHOrO
TOKa 3anHCbIBaeTCR B BM,l(e 'Tpex C<pepHqe-
CKMX BOJIH C KOMIIOHeHTaMH IIOJIR B l(M-
JIMH.apHqeCKHX Koop,aI1HaTax. B3aHMHbIH
MMne,aaHC 1I0JIyqaeTcR B pe3YJIbTaTe MHTer-
pMpOBaHIDI 3Toro 3JIeKTpHQeCKOrO IIOJIR
(OT KIDK,[(OH nOJIOBHHbI ,UHIIOJIR), YMHO-
)l(eHHOrO Ha paClIpe,neJIeHHe TOKa B ,apyrOM
,D:HIIOJIe. ,lLrrR reOMeTpHH, npI1Be,aeHHOH Ha
pHC. 7.9, BbIpIDKeHHe ,ILJIR B3al1MHOrO HM- PHC. 7.9. CTyneHQaTOe
ne,D:aHCa HMeeT BM,l( ,lJ;Hnonei1
I
I
2d2 I
! f
I Yo
· ___l_l__ _ ---
I
I
..
....
2 d 1
I
I ..
I
Xo
pacnOJIO)l(eHHe
_ j30 d)
Z = J ['PI - 2'P 2 cos(kd 2 ) + \}'3 + 'P 4 - 2\}'5 cos(kd 2 ) + 'P6] sin [ k(d I - X)] dx, (7.33)
8 1 8 2 Q
r,D:e
8} = sin (kd l ); 8 2 = sin (kd 2 ); \Pi = exp( -jkR i )/ R i .
TIpM 60JIbllIOH TOJIIIJ;HHe 1I0,ILJIO)l(J(H ,ILJIR BbIQHCJIeHHR B3aHMHoro HMlIe,aaHca
MMKpOnOJIOCKOBbIX aHTeHH He06xo,D:HMO yqHTbIBaTb nOBepXHOCTHYIO BOJIHY B no,n-
OJ
JIO)l(I(e, n03ToMY pe3YJIbTaTbI, nOJIyqeHHbIe ,L(JIR ,aMnOJIeM, B 3TOM CJIyqae )')ICe He
BepHbI.
BeJIHQMHbI R MMelOT CJIe,ayIOIIJ;He 3HaQeHHR
Rf = Y6 + (XQ + d 2 - X)2,
Ri = Y6 + (xQ - X)2,
Rj =Y6 +(xQ -d 2 -x)2,
Rl = Y6 + (xQ -d 2 + X)2,
RJ = Y6 + (xQ + x)2,
RJ = Y6 + (xQ + d 2 + x)2 .
(7.34)

Z3. IIpocmpaHcm6eHHble noiJxOabl K 3£jxJJeKmaM 63aUMHOU C6R3U d
HHTerpaJI MO)l(eT 6bITb Bblql1CJIeH QRCJIeHHO (3TOT cIIoco6 IIpe,n:IIOQTI1TeJIeH IIPH
60JIbllIHX paCCTORHIDIX Me)l()Jy ,n:HIIOJUIMR). O,n:HaKO HaH60JIee BIDKHbIH BKJIaa BHOCRT
COCe,n:HRe H 6JIH3JIe)l(aU.(Re ,n:HIIOJIH, R ,l])UI HHX Heo6xo,l{RMO TOqHOe BbIQRCJIeHHe.
TOQHOe pemeHl1e 3aIIRCbIBaeTCR B BR,l{e ,n:BOMHOM CYMMbI [55], r,n:e mar IIpHpa-
l..QeHI1R n paBeH 2:
-15 1 .g
Z = L L C m {expUkU) [E(kA + kU) - E(kB + kV)] +
SlS2 m=-l n=-)
+ exp(-jkU)[E(kA - kU) - E(kB - kV)]}.
(7.35)
K03<P<PHIJ;l1eHTbI HMelOT BH,n:
C_) = C 1 = 1; Co = 2cos kd 2 ,
a E(x) IIpe,n:CTaBJISIeT C060H HHTerpaJI OT 3KCnOHeHIJ;HaJIbHOM <PYHKl.{HH [2a] C apry-
MeHTaMR:
U = d) + n(xo + md 2 ),
V = n(xo + md 2 ), (7.36)
A2 =Y6 +(xo +nd 2 +md 2 )2,
B2 = Y6 + (xo + md 2 )2.
ECJII1 ,n:Ba ,n:HIIOJIR RMelOT o,n:HHaKOByJO MI1HY, <popMYJIa yrrpomaeTCR [51]
15 2 .g
Z=2 L LA m exp[-jkn(xo+md)]E(kf3), (7.37)
S m=-2 n=-l
r,l{e
f3 =  (xo + md)2 + Y6 - n(xo + md).
a K03<P<PHIJ;HeHTbI RMelOT BI1,L(
A_ 2 = A 2 = 1; A-I = Al = -4coskd;
Ao = 2(1 + 2cos 2 kd); S = sinkd.
(7.38)
<l>YHKl.{HR E(x) MO)l(eT 6bITb Bblpa)l(eHa B BH,n:e HHTerpaJIbHbIX KOCI1HYCOB H CH-
HYCOB, Ci H Si. ECJII1 Yo = 0, TO eCTb ,n:HTIOJIH KOJIJII1HeapHbI, Yo 3aMeHReTCSI paal1Y-
COM a ,n:I1TIOJISI. ECJIH ,n:HTIOJIH TIOJIYBOJIHOBble, qJIeHbI C m = 2 H 4 HCQe3aIOT, H 3KC-
nOHeHTbI yrrpomalOTCR. 3Ta <popMYJIa aHaJIOrHqHa IIOJIyqeHHoH B pa60Te [107] ,L(JIR
OJ OJ
n;BYX TOHK.HX J(HTIOJIeH paBHOH ,lI)II1HbI C OCSIMH, paCIIOJIO)l(eHHbIMI1 nOl( yrJIOM.
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HeM BbIQHCJIeHHR TpRrOHOMeTpHQeCKRX <PYHK:QHit B 3THX IIOJ(IIporpaMMax I1CIIOJIb-
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Ha pliC. 7.10 Ha rpa<pRKe RMIIeJ(aHca IIOKa3aHbI 3HaQeHHSI Z;j J(BYX IIapaJIJIeJIb-
HbIX IIOJIYBOJIHOBbIX J(RTIOJIeH. )].aHHaR KpRBaSI C paCCTORHReM B ,lI)II1HaX BOJIH KaK
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JISleTCSI 0.5.
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MeHbIIlero 3aTeHeHHSI, TaK H npOBaJIa B ,LJ;HarpaMMe HanpaBJIeHHOCTH. O,LJ;HaKO B
6JIIDKHeH BOJIHOBOH 30He ,LJ;HnOJISI npH 3TOM HMeeTCSI H aKCHaJIbHOe, H pa.n:HaJIb-
Hoe 3JIeKTpHQeCKHe nOJISI, H, AJlSI nOCJIe,nHero OTcyrcTByeT npOBaJI ,LJ;HarpaMMbI Ha-
npaBJIeHHOCTI1 B,n:OJIb OCH.

Z3. IIpocmpaHcm6eHHble noiJxoobl « 3rjxJJe«mllM 63aUMHOU C6Jl3U 
,L(JIR meJIeif, paCnOJIO)l(eHHbIX Ha IIOBepXHOCTM nOJIOCKOBOH JIMHHH HJIH B
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6bI meJIM 6bIJIM Bblpe3aHbI B 6eCKOHeqHOM 3KpaHe. )];JIH BblqHCJIeHHR MMIIe,naHCa H
B3aMMHOrO HMne,naHCa I.IJ;eJIH MOryr 6bITb 3aMeHeHbI nOJIOCKOBbIMM ,nHnOJIHMH [18],
HCnOJIb3YH npHHUHn Ea6HHe, pa3BHTbIH B [23]. B3aHMHbIH HMne.n:aHC lI..{eJIeH Z12 H
B3aMMHbIH a,nMHTaHC nOJIOCKOBbIX ,nHIIOJIeH Y12 CBR3aHbI COOTHOIIIeHHeM:
2Z 12 = ,,2 Y12, (7.39)
r,ne 11 = 1201t. MHO)l(HTeJIb YMeHbllIeH C 4 ,no 2, nOCKOJIbKY I.IJ;eJIH H3JIyqalOT TOJIbKO
B O,nHY CTOPOHY.
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v v
nOJIRMH C pa,nHYCOM, paBHbIM O,nHOH qeTBepTOH IIlHpHHbI lI..{eJIH HJIH nOJIOCKOBOro
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v
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llpH BbIqMCJIeHHH B3aHMHoro HMIIe,naHca Me)l(,L(Y ,nBYMR MHKpOnOJIOCKOBbIMH H3JIy-
qaTeJIRMH ,nOJDKHbI yqHTbIBaTbCR 3<p<peKTbI BJIHRHHH 3a3eMJIeHHOH (,nH3JIeKTpHqeC-
KOH) nOLLTIO)I(KH, QTO 06bIQHO .neJIaeTCH C nOMOI.IJ;blO <PYHKUHH fpHHa. 3TO TPe6y-
eT BbIqMCJIeHHR o,nHoro, a qaCTO HeCKOJIbKHX MHTerpaJIOB TMna 30MMep<peJIb,na,
v v
YCJIO:>KHeHHbIX OCUMJIJIRl.{HRMH H HeorpaHMqeHHbIM pOCTOM Ha ,neHCTBMTeJIbHOH
OCH, TOqKaMH BeTBJIeHMR, nOBepXHOCTHbIMH BOJIHaMM H .npyrHMH nOJIIOCaMH npH
HHTerpHpOBaHMH B KOMIIJIeKCHOM IIJIOCKOCTH. TIpocTeMIIlHH MeTO,n 6a3HPyeTcH Ha
v v
Mo.neJIH rrepe,nalOI.IJ;eH JIHHMH; o,nHaKO yqeT KpaeBbIX I.IJ;eJIeH MMKpOnOJIOCKOBbIX H3-
JIyqaTeJIeH RBJIReTCR peIIlalOlI..{HM. 06bIqHO 3Ta Mo,neJIb 3aMeHReTCR 60JIee TOqHbI-
MH. CyI.IJ;eCTByroT ,nBa THna TaKHX Mo.neJIeH: Mo.neJIb pe30HaTopa M Mo,neJIb Ha OCHO-
Be MeTo,na MOMeHTOB. B 06eHX HCnOJIb3yeTcR CTporoe Bblpa)l(eHHe <PYHKl.{HH fpHHa
,lUIR CJI OR.
B Mo,neJIH, HCnOJIb3YIOlI..{eH MeTO,l( MOMeHTOB, BBO,l(RTCR <PYHKl.{HH pa3JIO)l(eHHR
TOKa Ha neqaTHOM aHTeHHe: HanpHMep, TpaIIeueH,l(aJIbHbIe <PYHKl.{HH; COBMeCTHO C
TeCTOBbIMH <PYHKl.{HRMM OHM n03BOJIRIOT ,l(HCKpeTH3HpOBaTb HHTerpaJIbHOe ypaBHe-
HHe [100,92]. 06bIQHO He06xo,nHMO HeCKOJIbKO npoue,l(YP HHTerpHpOBaHHH <PYHK-
l{HH fpHHa.
B Mo,neJIH pe30HaTopa aHTeHHa 3aMeHReTCR 3a3eMJIeHHOH ,nH3JIeKTpHqeCKOM
v v v
nJIaCTHHOH C pacnpe,neJIeHHRMH MarHHTHoro TOKa Ha KIDK,[(OH OTKpbITOH CTeHKe pe-
30HaTopa aHTeHHbI. BblqHCJIeHHR [46] BbIRBHJIH OCl.{HJIJIRl.{HH ,neHcTBHTeJIbHOH H
u v V '-I
MHHMOH qaCTeH nOJIHOI1 B3aHMHOH npOBO,l(HMOCTH H 3aTyxaHHe npl1 YBeJIHQeHHH
paCCTORHHR, npHqeM HYJIH O,l(HOH H3 3THX <PYHKl.{HH HaXO,l(RTCR Ha MeCTe nHKOB
,l(PyroH. KpMBbIe 6JIH3KH K KpHBbIM B3aHMHoro HMne.naHca ,l(HnOJIeH. llpeHMyI.IJ;eCT-
BO ,naHHoH Mo,neJIH COCTOHT B TOM, qTO Tpe6yeTcR e,l(HHCTBeHHoe HHTerpHpOBaHHe
<PYHKl{HH fpHHa, H OHO ynpOlI..{aeTCR C rrOMOlI..{blO MeTo.na En <1> [85]. 3TOT IIO,l(XO,l(,
v
BH,nHMO, CTOJIb )l(e TOqeH, KaK H rro,l(XO,l(, HCnOJIb3YIOI.IJ;HH MeTOL( MOMeHTOB, XOTR
OTCyrCTByroT cpaBHHTeJIbHbIe ,l(aHHble ,l(JUI CJIyqaH 60JIee BbICOKoro E. 06e cepHH
pe3YJIbTaTOB XOpOIliO COrJIacyroTCR C H3MepeHHRMH [57]. TOJIbKO He60JIbIIlHe OT-
KJIOHeHHR 6bIJIH 3aMeqeHbI npM Y,l(BOeHHH TOJII.IJ;HHbI.

 rlla6a 7. /J3aUMHaJl C6R3b
3TM M3MepeHMSI 6bIJIM 3aHOBO npoBeL{eHbI B pa60Te [85], M nO.rlyqeHa xopornaR
COrJIaCOBaHHOCTb pe3YJIbTaTOB; npOBe,L(eHbI TaIOKe M3MepeHHH B LlMana30He 5 rru;
Ha neqaTHbIX aHTeHHax 0.282Ao x 0.267Ao C napaMeTpaMM nO,lI,JIO)l(KM £ = 2.55 M t =
= 0.0252AO' pe3YJIbTaTbI cpaBHMBaJIMCb C L{aHHbIMM BbIqMCJIeHMit Ha pMC. 7.12 BM.LJ:-
HO xopOillaSl COrJIaCOBaHHOCTb pe3YJIbTaTOB. ll03TOMY MO)l(HO CLleJIaTb BbIBOL{, qTO
.... ....
CYlUecTByeT OTHOCHTeJIbHO npOCTOM M TOqHbIM MeTO,L( ,l1,J1H BblqMCJIeHMH B3aMMHbIX
MMne,aaHCOB neqaTHbIX aHTeHH.
-10
-20
E nJIOCKOCTb
..-

t::!
--
-
J.;" -30
00
o
-
<=>
N
-t.O
.
...
M3MepeHIUI
PaCqeT
H-nJlOCKOCTb
-
-50
o
0.2
0.1.
0.6
0.8
dlAo
1.0
1.2
1.4
1.6
PUC. 7.12. B3aHMHaH CBH3b MI1KpOrrOJIOCKOBbIX aHTeHH [85]
3a npOilleL{illMe ro,abI 6bIJIO ony6JIMKOBaHO MHoro pa60T, KaCalOIIJ:MXCR oueHKH
HHTerpaJIOB <PYHKI.J:MH [pMHa. npHBeL{eM 3L{eCb HeCKOJIbKO CCbIJIOK: [98, 58, 84, 29,
12, 13, 83, 137,65,99].
7.3. 1.3. B3aHMHhlH HMne,qaHC pynopHhlx H3nYIIBTeneH
npe,aeJIbHbIH CJIyqaH BOJIHOBO,L(HOrO pyrropa - M3JIYQaIOIUMM: BOJIHOBOlI C OTKpbI-
TbIM KOHUOM. npM O,n:HOMO,n:OBOM B036y)1{):{eHIIM o,n:Horo 3JIeMeHTa BO BTOpOM BOJI-
HOBo,n:e, nOMHMO pacnpOCTpaHHlOlUMXCH MO,L(, B036y)1{):{alOTCH TalOKe 3aTyxalOlUHe
MO,n:bI. B 60JIbillllHCTBe pa60T IICnOJIb3yeTcH anepTypHoe MHTerpMpOBaHMe: pa60TbI
[72,20,] no npSlMoyrOJIbHbIM BOJIHOBO,n:HbIM 3JIeMeHTaM, [21] - no npHMoyrOJIb-
HbIM 3JIeMeHTaM pa3JIHQHbIX pa3MepOB II no npHMoyrOJIbHbIM 3JIeMeHTaM C nOBOpo-
TOM, [9,8,] H [19] - no KOJIbueBbIM BOJIHOBO,n:HbIM 3JIeMeHTaM.
CBSl3b Me)l(,l(y CeKTOpaJIbHbIMH pynopaMM B E-nJIOCKOCTM M3MepeHa B pa60Te
[79]. KaK BH,n:HO 113 pHC. 7.13, pynopbI C YCMJIeHMeM 8 ,L(D, pacnOJIO)l(eHHbIe Ha pac-
CTOSlHHII 0.73A, IIMelOT cJIa6ylO CBSl3b. B 3aBHCMMOCTM OT M3MeHeHI1JI yrJIa opMeH-
TaUHH BeJIHqHHbI CBSl3H B E- H H-nJIOCKOCTSlX MeHSlIOT MaKCMMYMbI II MMHHMYMbI.
TIpH 60JIbillllX paCCTORHHSlX CBSl3b C rrapaJIJIeJIbHOH nOJIHpM3aUMeH cnalIaeT KaK
llr 2 , IUIM Ha 12 ,n:6 npH KIDK,lJ;OM y,n:BoeHHH paCCTOHHHSI r, TOr,L(a KaK KOJIJIMHeapHaR
CBH3b cna,n:aeT KaK 1/r. .n:aHHbIe no CBSl3H nHpaMHL{aJIbHbIX pyrropoB, pacnOJIO)l(eH-
HbIX Ha paCCTOSlHHH 5.93A, npe,L(CTaBJIeHbI Ha pRC. 7.14.

7.3. JIpocmpaHcm6eHHble noiJxoobl " 3rjxJJe"mllM 63aUMHOU C6Jl3U 
-'0
CB5J.3b B E-nJIOCKOCTH
CBH3b
B H- nJIOCKOCTH
-

t1
-
..Q -60
M

co
U
-70
a
<I> (rpa.a.)
PHC. 7.13. CBH3b ceKTOpMaJIhHblX pynopoB B E- nnOCKOCTH [79]
-80
-180
-90
90
180
-1.O

qJ
-50
-
LQ

-
..Q - 60
M

a:I
U
-70
o
ct- (rpa.a.)
PHC. 7.14. CBH3b nHpaMH.llaJIbHbIX pynopoB [79]
-80
-Ieo
-90
+ 90
+180
-

 Dla8a 7. B3aUMHaJl C8R3b
B ,n:pyrOM no,n:xo,n:e K BbIqHCJIeHHIO B3aHMHOH CB.SI3H Me)I()J:Y CeKTOparrbHbIMH PY-
nOpaMH C anepTYpaMH 3'A B [45] npHMeHeHa reOMeTpHqeCKa.SI TeOpH.SI ,n:H<ppaKI..J;MH;
3aBHCHMOCTb CB.SI3H OT Me)l(IJ;eHTpOBoro paCCTO.SIHH.SI BbIpa)l(eHa B TMTIMqHOM <pop-
MaTe B BM,n:e nHKOB M HYJIeH C orM6alOlI(ei1, M3MeH.SIlOlI(ei1C.SI npH6JIH3HTeJIbHO KaK
3HaqeHMe CB.SI3H '" (-49 - sj'A) ,n:E.
7.3.2. PaC"IeT Ha OCHOBe MaTpMLI,bl MMneAaHCOB
KOHeqHbIe AP ,IIHTIOJIell, eJIei1 lUlH neqaTHbIX aHTeHH MOryr 6bITb TIpOaHaJIH3MpO-
BaHbI nyreM COCTaBJIeHMSI MaTpHIJ;bI B3aHMHblX HMne,n:aHCOB. 06bIqHO ,LLJI.SI 3Toro
HCnOJIb3yroTC.SI B3aHMHble HMne,n:aHCbI KapTepOBCKoro Tl1na (CM. npe,n:bI,n:YII(Me pa3-
,n:eJIbI). ECJIM B AP MCnOJIb3yroTC.SI ,n:HnOJIH Ha,n; 3KpaHOM, nOCJ1e,ll.HHe 3aMeH.SIIOTC.SI
3epKaJlbHbIM oT06pIDKeHHeM AP, qTO npMBO,ll.l1T K MaTpHue MMne,ll.aHCOB C pa3Mep-
HOCTblO 2N x 2N BMeCTO N x N. TIpH cHMMeTpHqHOll AP B OTcyrcTBl1e CKaHMpOBa-
HH.SI 3Ta MaTpMu;a MO)l(eT 6bITb CBepHyTa, qTO YMeHbllIaeT ee pa3MepHOCTb npMMep-
HO B,lI.BOe (TOqHO B,lI.BOe, eCJ1M N - qeTHOe qHCJIO). YrOJI CKaHMpOBaHH.SI BXO,ll.HT B
MOHOTOHHO B03paCTalOII(yro <t>a3Y BeKTopa ynpaBJIeHH.SI (drive vector), COCTaBJI.SIIO-
II(He KOToporo, paCCqHTaHHbIe ,lI,JI.SI n-p.SI,lI.a H m-cToJI6u;a, MMelOT BH,LJ;
Vi = Anm exp[-j2n(nu + mv)].
(7.40 )
KaK H paHee, BbIpa)l(eHH.SI ,lI,JI.SI KOMnOHeHT BeKTOpa ynpaBJIeHH.SI HMelOT BH,IJ;
u = d x sin8cosq,;
'A
d
v =  sin e sinq,.
'A
(7.41)
B3aHMHbIll HMne,ll.aHC Zij onpe.n;eJI.SIeTCSI Me)l()];Y i-M M j-M 3J1eMeHTaMH. TIpH pe-
....
rneHHH CHCTeMbI KOMTIJIeKCHblX ypaBHeHHI1 HaXO,IJ;lITC.SI BeKTOp TOKa
[Vj] = [] [Zjj]
(7.42)
....
M Ha OCHOBe HaH.n;eHHoro BeKTopa TOKa onpe.n;eJI.SIeTC.SI HMne,ll.aHC CKaHHpOBaHIDI
Ka)l(,L{OrO 3JIeMeHTa AP. ECJIM He06xo,ll.HMO perneHHe ,lI,JI.SI HeCKOJIbKHX yrJIOB CKaHH-
pOBaHH.SI, npH KOTOpbIX H3MeH.SIeTC.SI TOJIbKO BeKTOp ynpaBJIeHH.SI, a He MaTpHIJ;a Z;j'
....
TO MO)l(eT MCnOJIb30BaTbC.SI nporpaMMa perneHHSI CHCTeM ypaBHeHHM C 3anOMHHa-
HHeM ,lI.MarOHaJIM30BaHHOH MaTpHIJ;bI, qTO n03BOJI.SIeT 6bICTpO nOJIyqMTb perneHMe
,lI,JISi HOBbIX BeKTopOB nOCJIe HaXO)I()J:eHH.SI rrepBoro. OTMeTHM, qTO TaKoe perneHHe
CHCTeMbI ypaBHeHMH npOM3Bo,n:MTC.SI npMMepHO B TPH pa3a 6bICTpee, qeM HHBepCHSI
Ma1'pHIJ;bI [128].
C nOMOlI(blO BeKTopa TOKa, KOHeqHO, MOryr 6bITb BbIqMCJIeHbI M ,lI.MarpaMMbI
HanpaBJIeHHOCTH AP. PaCqeT C nOMOlI(blO MaTpHUbI HMne,ll.aHCOB HMeeT CBoe npeH-
MyrueCTBO: cnan;aHMe aMTIJ1HTy,n:bI B036)')K,LJ;eHHSI K KpaSlM paCKpbIBa MO)l(eT 6bITb
BKJIIOqeHO HenOCpe,ll.CTBeHHO B BeKTOp ynpaBJIeHMH, B OTJIHqHe OT paCCMaTpHBae-
MbIX B pa3,l1.eJIe 7.4 MeTo,n:OB ,lI,JISi 6ecKoHeQHoM AP, r,ll.e B036)')K,LJ;eHHe ,lI.OJDKHO 6bITb
O,ll.HOpO,n:HbIM.
Pe3YJIbTaTbI paCqeTa HMne,n;aHca CKaHHpOBaHHH 60JIbrnHX AP, no cyrueCTBY, Ta-
KHe )l(e, KaK M ,lI,JI.SI 6eCKOHeqHbIX AP (CM. pa3,l1.eJI 7.4) 3a MCKJIlOqeHHeM yrJIOB CKa-
HHpOBaHHSI, 6JIH3KHX K 90°. B pa60Te [35] paCCqHTaHa AP Ha OCHOBe 65 x 149 no-
.... ....
JIYBOJIHOBbIX ,n:HnOJIeM C 3KpaHOM; HHKaKHX pa3JIHqHH He OTMeqaJIOCb, nOKa yrOJI

Z3. IlpocmpaHcm8eHHble noOXoObllC 3rJxjJeICmllM 83aUMHOU C8Jl3U  ,
CKaHHpOBaHHH He npeBbICHJI 70°, QTO CBH3aHO, rro BceH BH,[(HMOCTH, C TeM, qTO
rrpH 60JIbllIHX yrJIax CKaHHpOBaHHH 60JIbllIe «KpaeBbIX 3JIeMeHTOB».
KOHeqHyK> AP C MHorOMo.nOBbIM:M 3JIeMeHTaMH, B npHHl(Hrre, MO)I(HO orrHcaTb
nyreM yBeJIHqeHH5I pa3MepHOCTH MaTpHl(bI C N x N ,no NM x NM, r,ne y Ka)l(,L(Oro
3JIeMeHTa HMeeTCH, K npHMepy, M MOLl;. TIOCKOJIbK)' npH pellIeHHH CHCTeMbI ypaB-
HeHHM MallIHHHoe BpeMH B03paCTaeT npOrrOpl(HOHaJIbHO K)'6y pa3MepHOCTH MaTpH-
l(bI, paCqeT 60JIbllIHX AP MoxeT 6bITb 3aTpy,nHHTeJIeH. ArrbTepHaTHBHoe pellIeHHe
npeWIoxeHO B pa60Te [43]. HanpIDKeHHe MO,nbI Ha Ka)l(,L(OM 3JIeMeHTe 3anHCbIBaeT-
CH B BH.ne CYMMbI (no 3JIeMeHTaM) HanpIDKeHHM B036y)K)J;eHHH, YMHoxeHHbIX Ha
K03<P<PHl(HeHTbI CBH3H H <pa30BbIH MHO)KHTeJIb CKaHHpOBaHIDI. K03<P<PHUHeHTbI
CBH3H npaKTHQeCKH He 3aBHCHT OT pa3MepOB AP (3TO cnpaBeWIHBO, CTporo rOBopH,
JIHllIb WIH 3JIeMeHTOB CMS-aHTeHH) H MOryr 6bITb onpe.neJIeHbI ,l(IDI 6eCKOHeQHOH
AP. 3aTeM npOH3Bo,nHTCH paCQeT 6eCKOHeqHOM AP C COOTBeTCTByrollJ;HM llIarOM,
v v
,n:Hana30HOM CKaHHpOBaHHR H nOJIOCOH rrponYCKaHHH, onHcaHHbIH B ,npyrOM pa3,ne-
JIe 3TOM fJIaBbI. B pe3YJIbTaTe nOJIyqaeTcR 3aBHCHMOCTb HanpIDKeHHM MOLl: H K03rjJ-
cjJuu,ueHma OmpaJICeHUR npu CKaHup08aHUU OT 3HaqeHHH U. JUI rrOJIyqeHHR K03<p-
<pHl(HeHTOB CBR3H HCnOJIb3yeTcR 06paTHoe npe06pa30BaHHe <l>YPbe, 3aTeM
K03cP<PHl(HeHTbI CBR3H CYMMHPYIOTCR, ,naBaR pR,IJ; HarrpIDKeHHH MO,IJ; H K03<P<PHUH-
eHT OTpaxeHIDI ,l(IDI Ka)K)]:orO 3JIeMeHTa AP. TIOJIHaH BeJIHqHHa CBR3H peaJIH3yeTcR,
no ceCTBY, TOJIbKO WIH ueHTpaJIbHbIX 3JIeMeHTOB 60JIbllIOH AP; K03<P<PHl(HeHTbI
CBR3H 3JIeMeHTOB, HaxoIDIIIIHxCR Ha KpalO HJIH B6JIH3H KpaH AP MeHbllIe, TaK KaK
OHH 6bICTpO YMeHbllIalOTCR C YBeJIHqeHHeM MeX3JIeMeHTHoro paCCTORHHR, 3a HCK-
JIlOqeHHeM 06JIaCTH, 6JIH3KOM K nOJIOXeHHIO ,nH<ppaKII:HOHHOro JIerreCTKa. 3<p<peK-
TbI crra,n:aHIDI aMIIJIHTY,nbI K KpaHM paCKpbIBa MOryr 6bITb npOCTO yqTeHbI rryreM
BBe.neHHR B KIDK.UYJO CYMMY aMIIJIHTY,nHbIX K03<P<PHUHeHTOB. HMneoaHC CKaHup08a-
HUll MOJICem 6bITb 3arrHcaH HCXO,lUl H3 K03<P<PlfQHeHTa 01'pIDKeHHR Ka)l(,L(OrO 3JIe-
MeHTa, a ,nHarpaMMa HanpaBJIeHHOCTH AP HaXOLl:HTCH nyreM CYMMHpOBaHHR MO-
Ll:aJIbHbIX ,LJ;HarpaMM HanpaBJIeHHOCTH AP, B KOTOpbIX HCrrOJIb3yroTCH MO,QaJIbHbIe
LJ;HarpaMMbI HarrpaBJIeHHOCTH 3JIeMeHTOB H HanpIDKeHHR MO,LJ;.
Y 60JIbllIHX AP uMneoaHC CKaHup08aHUll H OUa2paMMa CKaHup08aHUR 3JleMeHma
TaKHe xe, KaK H y 6eCKOHeQHbIX AP (CM. pa3,neJI 7.4), HO C He60JIbllIHMH OCl(HJIlliI-
l(HHMH; Y 60JIee KpynHbIX perneTOK OCl(HJIJIHUHH 60JIbllIe, H OHH HMelOT MeHbllIyIO
aMIIJIHTY.ny. ,[(aHHbIe )UlH MaJIbIX AP rrpHBO,LJ;HTCR B rJIaBe 8.
7 .3.3. AMcI>paKMoHHble neneCTKM
I1HT}'HTHBHoe nOHHMaHHe pOJIH B3aHMHOH CBH3H npH CKaHHpOBaHHH AP 06JIerqaeT-
CR npHBJIeqeHHeM rrOIDITIDI Ll:H<ppaKUHoHHbIX JIeneCTKOB, CBR3bIBalOllJ;erO paCCMOT-
peHHyro 3.neCb KOHIlenl(HIO TOKOBoro JIHCTKa C rrOLl;XOLIOM PMa <l>JIOKe, onHcaHHoro B
CJIeLl:YIOrn:eM pa3,n;eJIe. ,[(aHHbIM MeTO,LJ; MoxeT 06Cy)K)J;aTbCH BMeCTe C KOHl(enUHeH rre-
pHO,LJ;HqeCKOM HqeMKH, KaHaJIa <l>JIOKe, HO Cyrb MeTOLl:a Ll:H<ppaKl(HOHHbIX JIeneCTKOB
CBR3aHa C 3JIeMeHTOM AP; n03TOM)' ero onHcaHHe rrpHBO,lU.fTCR 3,neCb. -
B pa60Te [132] nOKa3aHO, qTO Ka)l(,lIbIH q)leH D:BOMHOro pH,ZJ;a B BbIpaxeHHH )UlR
uMneoaHca CKaHup08aHUR ,lI.HnOJIR CBR3aH C TOqKOM u,v CeTKM Ll:H<ppaKl(HOHHbIX
JIeneCTKOB (HanpHMep, Ha pHC. 7.15). 3TO BepHO WIH Bcex THnOB 3JIeMeHTOB, pac-
nOJIOXeHHbIX Ha peryIDIpHoM ceTKe, HO HaH60JIee HarJIR,nHO oT06paxaeTcR npH
paCCMOTpeHHH KOpOTKMX ,lI.HnOJIeH. B CJIyqae KOpOTKHX ,IJ;HnOJIeH <POPMYJIbI, BbIBe-

b Dza6a 7. B3aUMHllJI C6R3b
1)
Z-06JIaCTb
/
u
U1 = }'Id x 1)1 = Ald y
PHC. 7.15. CeTKa ,lI;If<ppa:KIJ;HOHHhIX nerreCTKOB
u u .
,aeHHbIe .lLJIH ,aHnOJIeH npOH3BOJIbHOH .lLJIHHbI, ynpomalOTcR, nOToMY qTO SIDC- If
COSC-MHO)I(JITeJIH CTaHOBRTCH paBHbIMIf e,aHHHu;e. ECJIH Tenepb BbIpIDKeHIDI (7.41) If
(7.42) (BbIBe,aeHHbIe paHee B pa3,aeJIe 7.4) pa3,aeJIHTb Ha conpOmU6JleHUe CKaHup06a-
u
HUJl B HanpaBJIeHHH, nepneIUJ:HKyJIHpHOM paCKpbIBY, HOpMHpOBaHHbIH HMne.aaHC
OKa3bIBaeTCR paBeH
t
I
R'uv\ k 2 -k 2
\! , J H xO
= 00 =
R(O,O) k  k2 - k 2 - k 2 '
xO yO
X(u, v) = _ '" '" Hnm = '" '" k 2 - kin
R(O,O) L., L., L., L., k  k;" + k;m _ k 2 .
(7.43)
'*
3,aeCb BbIpa)ICeHHH .lUllI Hoo H Hnm Te )ICe, qTO H B ypaBHeHHH (7.40). YIDIJIep CKOp-
peJIHpOBaJI 3TH qJIeHbI C TOqKaMH U,V ,aH<ppaKI.J:HOHHbIX JIeneCTKOB H H,I(eHTH<pHU;H-
pOBaJI KIDK,[(bIH qJIeH KaK HMne,aaHCHyID 06JIaCTb (KpaTep), nOHRTHe KOTOpOM npe,a-
JIO)ICeHO B pa60Te [106]. HOpMHpoBaHHbIll HMne,aaHC HMeeT BH,I(
Zs(u,v) = LL Zc(u-n/dx,v-m/dy) .
Rs (0,0) Rs (0,0)
(7.44 )
t
3.ueCb Zsl Rs - HMne,aaHC 06JIaCTH [40], rrpe.acTaBJIHIOIl{HIl C060H KpHByro HOpMIf-
pOBaHHoro HMrre,aaHca 3JIeMeHTa B u,v rrpOCTpaHCTBe. Ha pHC. 7.16 IIOKa3aHa HM-
rre,aaHCHaH 06JIaCTb KopOTKoro ,aHnOlliI, a Ha pHC. 7.17 - HMne.naHCHaH 06JIaCTb
nOJIYBOJIHOBOH Il{eJIH Ha llJIOCKOCTH BOJIHOBbIX qHCeJI. BbUlBJIeHO, qTO 3<p<peKTbI
B3aHMHOH CBH3H rrpH CKaHHpOBaHHH H 3<P<l>eKTbI, CBR3aHHbIe C B03HHKHOBeHHeM
)J;H<ppaKU;HoHHbIX JIerreCTKOB, MOryT 6bITb BH3yarrH3HpoBaHbI nyreM pa3Mern;eHIDI
t

-
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PUC. 7.16. 06JIaCTb HMTIe,n;aHca KopOTKoro ,n;HTIOJIR [132]
ky
I.k
'It
o
kx
Pac. 7.17. 06JIaCTb rrpOBo,n;HMOCTH TIOJIYBOJIHOBOH I..I.J;eJIH [106]

 rJ/OBO Z B30UMHaJl CBJI3b
MMne,aaHCHOM 06JIaCTH B Ka)l()J;OM Y3JIe CeTKH B U,V-TIJIOCKOCTM. TepMMH «KpaTep»
MCnOJIb3yeTcR B CHJIY TOrO, 'ITO COnpOTHBJIeHHe BOCnpOM3BO,il.MT TOnOJIOrH'IeCKyIO
CPOPMY KpaTepa. TaKHM 06pa30M, CeMeMCTBO ,aM<ppaKIIHOHHbIX JIeneCTKOB YCTaHaB-
JIHBaeT CBR3b Me)l()J;y 06C)')K.lJ:aBlIIeMCR paHee KOHIJ;enUl1eM TOKOBOrO JIHCTKa M nOll-
XOllOM C n03HIIMI1 nepHOJIHqeCKHX CTPYKTYp.
CeMeMCTBO JIH<ppaKIIHOHHbIX JIeneCTKOB MOXeT 6bITb TaIOKe BbIpaXeHO B Tep-
MHHaX npe06pa30BaHH$! nOJIR anepTYPbI [25]. /IOJllia5l npo8oiJuMocmb npu CKaliUpo-
8aliUU (aiJMumalic) AP C npRMoyrOJIbHOM ceTKOM 3anHCbIBaeTC5J KaK MHTerpan B
npOCTpaHCTBe BOJIHOBbIX 1.JHCeJI npeo6pa30BaHH$! <l>YPbe anepTypHoro nOAA, )'MHO-
}KeHHOrO Ha <l>YPbe-06pa3 conpIDKeHHoro nOJI$! Ka)l()];OrO 3JIeMeHTa.
,L(BoMHaR 6eCKOHe1.JHaR CYMMa, onHCbIBaIOIl(aR <pa3bI 3JIeMeHTOB, MoxeT 6bITb
BbIpa}KeHa B BH,ae ,aBYMepHO nepHo,aH1.JeCKOM ,n;eJIbTa-<PYHKIIHH, 'ITO CBOllHT HHTer-
panbI K BbIpaxeHHIO
,
Y s
41tJ) 00 00 [ k2 * * ]
L L - EpEp + wE\jJE\jJ ,
kTldxd y -00 -00 w
(7.45)
r,ae w = -j -J u 2 + v 2 - k 2 , a nOJI$! onpe,aeJIRIOTCR B U,V TOqKaX ,il.II<ppaKIIHoHHbIX
JIeneCTKOB. AHanorHqHbIM o6pa30M B3aHMHbIM HMnellaHC llBYX 3JIeMeHTOB MoxeT
6bITb 3anHcaH B Bl1,[(e HHTerpana B npOCTpaHCTBe BOJIHOBbIX qHCeJI npeo6pa30BaHHR
<l>YPbe anepTYpHoro pacnpe,n;eJIeHH$!, 'ITO MO)I(HO CBeCTH K KOMnJIeKCHbIM ypaBHe-
HHRM ,lL1IR MOIUHOCTH anepTYpHoro nOJI$!, npe,lL1l0lKeHHbIM B pa60Tax [24,105].
,
7.4. nOAXOAbl B cneKTpanbHOM 06naCTM
t
7.4. 1. AMnonM M enM
KaK CJIe,ayeT H3 TeopeMbI <l>JIOKe ,lL1IR AP, nOJIR B Ka)l()];OM RqeMKe 6eCKOHe'IHOM pe-
v v
ryIDIpHOH nepHo,aH'IeCKOH CTPYKTYpbI pa3JIII'IaIOTCR JIHlIIb MOHOTOHHO B03paCTaIO-
IUHM 3KcnOHeHIIHanbHbIM MHO)l(l1TeJIeM [5, 28]. LI.anee nOIDI MOryT onHCbIBaTbC$! B
BH,lIe pRlla opTorOHanbHbIX MOJI. no CYIUeCTBY, B 06JIaCTH onpe,aeneHIDI <l>YPbe-06-
pa3a rpaHH'IHbIe ycnoBHR cornaCOBaHbI, 'ITO B HeKOTopbIX cnyqaRx rrpHBo,n;HT K CBe-
,aeHHIO HHTerpanbHoro ypaBHeHH$! K arrre6paH'IeCKoMY.
YHJInep [129]) 6brn, BepO$!THO, nepBbIM, KTO pa3pa6oTaJI MeTO,a e,aHHH'IHOH
R'IeMKH HJIH nepHOllH'IeCKOM ceTKH $!1.JeeK ,lL1IR AP C Heno,aBIDKHbIM nyqOM, B KOTO-
v
pbIX Bce 3JIeMeHTbI Haxo,aRTCR B o,aHHaKOBbIX npHJIeraIOIUHX ,apyr K ,apyry R'IeHKax.
B [37, 97] pacnpOCTpaHeH no,n;xo,a nepHo,aH'IeCKHX CTPYKTYP Ha CKaHHPYJOIUHe AP.
OH OKa3anCR HaH60nee MOIUHbIM M <pM3M'IeCKH HarJIR,[(HbIM MeTo,aOM MR HCCJIe,n;o-
BaHH$! M npoeKTHpOBaHM$! CJIOXHbIX AP. AHanorHqHbIe MCCJIe,aOBaHHR npOBe,aeHbI B
[35, 115]. Bcne,acTBHe CHMMeTpHH <l>JIOKe OT.aeJIbHaR e.aHHl1qHa$! R1.JeMKa BbI$!BnReT
Bce xapaKTepHCTHKH nOJIHOM npOBo,aHMOCTH Ka)K,[(OrO 3JIeMeHTa AP. E,aI1HI1'IHble
R1.JeMKH pacnOJIOXeHbI nepneH,aHK)'JIRpHO nOBepXHOCTH AP, IIeHTpHpOBaHbI OTHO-'
CHTeJIbHO 3JIeMeHTOB II npIIneraIOT ,n;pyr K ,n;pyry (CM. pHC. 7.18). TIpl1 H3nyqeHHM,
HopManbHOM K paCKpbIBY aHTeHHbI, II OTCyrCTBHI1 ,il.H<ppaKIlI10HHbIX JIeneCTKOB B
e,n;I1HH1.JHOM $!'IeHKe C TEM-MO,aOM HMeIOTCR ,aBe npOTHBOJIeXaIUI1X 3neKTpH1.JeCKHX
CTeHKH (c HyneBbIM 3JIeKTpH1.JeCKHM nOJIeM) H ,aBe MarHIITHbIX CTeHKH (c HYJIeBbIM
MarHHTHbIM nOJIeM). O,aHaKo rrpH CKaHHpOBaHHH nyqa TaKaR eJIHHH1.JHaR WIeMKa

Z 4. /JOOxOObl B cnelCmpllllbHou o61lacmu 
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.u;OJDKHa HaKJIOH5ITbC5I BMeCTe C nyqoM, 11 ,L(JUI KIDK,[(OrO .u;H<ppaKl{HOHHOro JIerreCTKa
.u;OJDKHa J(06aBn5ITbC5I ew:e OJ(Ha e,lJ;HHHqHa5I 5IQeHKa. B cHJIy 3THX TPy.n;HocTeH OJIH-
Hep HcrrOnb30BaJI <pI1KCl1pOBaHHyIO, HOpMaJIbHO pacrrOnO)l(eHHYIO eJ(HHWIHyIO
5IQeHKY, a.n;arrTHpOBaHHYIO K JII060MY yrny cKaHHpOBaHH5I H nlO6oMY KOnHQeCTBY
.u;H<ppaHoHHbIX JIerreCTKOB. CTeHKH e.u;I1HHQHOH 5IQeMKH, B l(enOM, He SlBJISIIOTCSI
3JIeKTpHqeCKHMH HJII1 MarHHTHbIMH, a MOJ(bI BHyTpH 5IBlliIIOTC5I MOJ(aMH LSE (rrpo-
J(onbHO-3JIeKTpHQeCKHe) H/HJIH LSM (npOJ(OJIbHO-MarHHTHble) B 3aBHCHMOCTH OT
nnOCKOCTH CKaHHpOBaHIDI. IIOJIH Ha rrpOTHBOrrOJIO)I(HbIX CTeHKax pa3nHQalOTCSI
C,IJ;BHrOM <pa3 <l>noKe. Ka)K)].bIH OCHOBHOH JIyq HJIH ,IJ;H<ppaKIJ;HOHHbIH nerreCTOK
ou ou
rrpeJ(CTaBJIeHbI pacrrpOCTPaHSlIOw:eHCR MO,IJ;OH, a 3a1)'XalOrn;He MO,IJ;bI BHOCRT BKJIa;:( B
aKKYMynl1pOBaHHe 3HeprHH (peaKTHBHYIO rrpOBo.u;HMOCTb) Ha rrOBepXHOCTI1 AP.
XOTR MeTOJ(OM nepHO,ll,WIeCKJ1X HQeeK npoll(e aHaJIH3HpOBaTb KopOTKHe rn;eJII1
1111M ,IJ;MnOJIH, 60JIbIIIee 3HaQeHHe HMeeT pe30HaHCHbIH ,lI,HrrOJIb; rr03TOM)' 3TOT CJIY-
qai1: 6y,n:eT paCCMOTpeH ,lI,OCTaTOQHO no.u;po6HO. Donee rrpOCTbIM HBnHeTCH TaIOKe
cnyqaH CKaHHpOBaHH5I B rJIaBHOH nnOCKOCTH, HO 3,n:eCb 6Y,IJ;eT paCCMaTpHBaTbCSI
npOH3BonbHoe CKaHHpOBaHHe. IIpH 3TOM Bce QeTblpe CTeHKH e,ll,HHI11{HOH SlQeHKH C
Ez- H Hz-KoMnoHeHTaMH nOJIH 3aBI1CHT OT rrapaMeTpOB CKaHl1pOBaHHH. Heo6xo,IJ;l1-
MO Hcrronb30BaTb cyneprr03Hl(HIO OCHOBHOM LSE-MO,n:bI II OCHOBHOH LSM-MO,n:bI.
BOJIHOBOe QHCnO B Z-HarrpaB1IeH IIII paBHO
k z =  k2 -ko -k;o = kcos8 0 , (7.46)
r,n:e
k xO = k sin 8 0 COO; kyO = k sin 8 0 sin <1>0.
Pa3MepbI e.n;HHWIHoH WleHKH COCTaB1IHIOT Dx = dxf'A II Dy = dy/'A, r,n:e 3HaQeHI1R
IIIara ceTKH pa3Mern;eHlI5I 3JIeMeHTOB - d x H d y . 0606meHHble BOJIHOBble QIICJIa HMe-
lOT BIf)];
k xn = k(Sin8 o coscl>o + d: )
k ym = k( sin8 0 sincl>o +  )
(7.47)

 rAa6a Z /J3aUMHWI C6Jl3b
a o606IIJ.eHHbIH MHO)lQfTeJIb CKaHlipOBaHli51 COCTaBJI.HeT
(Sine o cos4>o + t J -1
(Sine o cos4> 0 +  J + (Sin 2 eo sin 2 4>0 +  J -1
1 - sin 2 So cos 2 <1>0
Hoo == .
cosSo
Hnm
,
(7.48)
npH pacnOJIO)KeHl111 BbIBO.n;OB l1nOJIbHOrO H3JIyqaTeJUI B neHTpe ,LIJlnOJI.H peaK-
OJ OJ
TI1BHOe conpOTHBJIeHHe BKJIlOqeHO rrapaJIJIeJIbHO BOJIHOBO.n:y eJ,J:I1HHqHOI1 SlQeHKM,
HO nOCJIeJJ:OBaTeJIbHO C BbIBOJ,J:aMM nHTaHMSI. O.lI.HO 113 npeI1MYIIJ.eCTB nOJ,J:xoJ,J:a, I1C-
nOJIb3YIOIIIero eJJ:I1HMQHYIO SlQeHKY, BbIHBJIHeTC.H npH paCCMOTpeHHH 3KpaHa. YQM-
TbIBaeM, qTO J,J:l1nOJIbHa.H AP B CBo6oJ,J:HOM npOCTpaHCTBe MO)KeT 6bITb npe,nCTaBJIeHa
B BH,LJ;e AP 113 eJ,J:HHMQHbIX .HlIeeK, HaxOMIIJ.HXCH C Ka)l(,[{OH 113 CTOpOH J,J:MnOJI.H, npH-
lIeM o6e en:MHHqHble HqetiIrn: HMelOT ITOJIy6ecKOHeqHyIO ,lLJIMHY, a 3KpaH M306pa)Ka-
eTC.H npOCTO B Bl1,[{e 3aKopOTKH, rrpoxoJJ:.HIII.ei1 Qepe3 OJ,J:HY M3 eJ,J:MHWlHbIX .HqeeK Ha
BbICOTe h OT J,J:I1ITOJUI. ITOCKOJIbKY paCCTO.HHHe OT 3KpaHa J,J:O ,nHnOJI.H 06bIQHO 6bIBa-
eT nOPMKa "-./4, 3aTYXalOIIJ.Me MO,n:bI BbICllIero nOPMKa B e.n;HHHqHOH .SJqeMKe nOCJIe
npOXO)l(,l(eHIDI OT n:HrrOJI.H J,J:O 3KpaHa Ii o6paTHo 6bIBalOT 3HaqHTeJIbHO rro,naBJIeHbI, ,
TaK QTO MMH MO)KHO rrpeHe6peQb. O,[(HaKo 3KpaH OKa3bIBaeT BJIliHHHe KaK Ha aK-
TI1BHOe, TaK M Ha peaKTHBHOe conpOTHBJIeHHe Qepe3 OCHOBHYIO MOn:y. 0603HaQe-
HID! pa3MepOB rrpHBeJ,J:eHbI Ha pHC. 7.19. IlpeJ,J:noJIaraeTcH, lITO TOK J,J:HnOJISI TeqeT
TOJIbKO B HanpaBneHHH OCM x, a B HanpaBJIeHI1H OCI1 y OH nOCTO.HHeH. PacnpeJ,J:ene-
HMe BllOJIb OCM x npMHHMaeTCR KaK KOCHHYCOlUl:aJIbHoe. 3aTeM B llJIOCKOCTH J,J:Mno-
OJ OJ
neM np0I13Bo.n;MTCH cornaCOBaHHe 3neKTpMQeCKHX nOJIeM, nOp0)l([laeMbIX ,UMnoneM M
Ha6opOM BOJIHOBO,[(HbIX MO.n; eJ,J:HHHqHOH .H:qeHKH. OTCIOJ,J:a nonyqaeTC.H: PM JJ:lI.H pe-
y
I I I * b s
<4 as .
I f I I
x
I - I J I
Dy - dy/A
-
, I J - , [ a 1
..... Dx ....
Ox = dxlA
PUC. 7.19. feOMeTPHH nOJIOCKOBOH ,n:HnOJIbHOH aHTeHHOH perneTKH

7.4. IloiJxoiJbl 6 CneKmpl1JlbHOU ofinacmu 
aKTMBHOfO COnpOTMBneHlliI CKaHMpOBaHMH. ,D:nH HaXO}l{,L(eHMH aKmU6H020 cOnpOmU6-
lleHUR CKaHUp06aHUJI 3KpaH 3aMeHHeTCH 3epKaJIbHbIM .l(MnOJIeM, paCnOJIOXeHHbIM Ha
paCCTOHHI1M 2h. AKmU6HOe cOnpOmU6JleHUe CKaHUp06aHUR MMeeT BM,L(
R 4800; 2 kxoos . 2 k yobs . 2 (k h)H
s = COSC SInc SIn zo 00.
nd x d y A2 2 2
(7.49)
B OTcyrcTBl1e 3KpaHa MHO)l(lfTenb sin 2 kzOh 3aMeHHeTCH Ha O.f(HY BTOpyro. BbIpa-
)l(eHMe .f(J1H peaKTMBHOfO conpOTMBneHMH MMeeT BM,L(
240a 2 [ k oa. kyob s .
X s = s cosc 2 x s sInc 2 sIn 2 (k zoh)H 00 -
nd x d y A2 2 2
"" k a kymb s ]
-  LJ cosc 2 xn s sinc 2 Hnm .
2 2
(7.50)
MHO)l(lfTenM sinc If cosc MO)I(HO M.f(eHTM<pMllJlpOBaTb KaK o6pa3bI npeo6pa30Ba-
HI1H Cl>YPbe O.l(HOpO.l(HOrO H KOCHHYCOM.l(aJIbHOfO pacnpe.l(eneHMH TOKa.
rpa<pMKM uMneiJaHca CKaHupOBaHUR II iJua2paMMbl CKaHupOBaHUfl 3JleMeHma ,QalOT
nOHHMaHl1e Toro, KaK pa60TaeT AP npM M3MeHeHMM YfJIa CKaHMpOBaHMH M llIafa ceT-
KM. Ha pMC. 7.20-7.22 M306paxeHbI iJua2paMMbl CKaHupOBaHUR 3JleMeHma SEP M UM-
neiJaHcbl CKaHupOBaHUR .lLIDI TOHKMX nOJIyBOJIHOBbIX ,QMnOJIeH, pacnOJIOXeHHbIX Ha no-
nYBOJIHOBOH KBan;paTHoH ceTKe. KaK M CJIe.f(OBaJIO O)l{Jf,QaTb, aKmU6Hoe M peaKmUBHoe
conpOmU6JleHUR CKaHupOBaHUR B H-nnocKocTM B03paCTalOT C yrJIOM CKaHlfpOBaHlliI,
TOr.f(a KaK B E-llJIOCKOCTM OHM YMeHbllIaIOTCH. B .l(MarOHaJIbHOH nnOCKOCTM Ha6JIIO.f(a-
eTCH CMellIaHHoe nOBe.f(eHMe. C YBenMqeHMeM yrJIa CKaHMpOBaHMH B E-nnOCKOCTM
SEP HMeeT 60JIbllIMH cnan. BCJIelICTBlfe YCMJIeHMH paCCOfJlaCOBaHMH. CpaBHeHMe BHlIa
300
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u
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Q)

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00
10
20
30
40 50
e (rpa.n;.)
60
70
80
90
PHC. 7.20. AHTIOJIbHa5I aHTeHHa5I perneTKa, Dx = Dy = 0.5, L = 0.5A


ffla6a Z B3aUMHaJl C6Jl3b
250
'.
-.
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tI:: 200
::s::
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t:Q
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c..>
Q,) H-nJIOCKOCTb
::s:: -
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Q,) 100

::s::
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0
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t::
0 50
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Q,)
0
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t:Q D
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Cd E
Q,)

-50
o
10
20
30
40 50
e (rpa,n;.)
60
70
80
90
PUC. 7.21. ,LJ;lfTIOJIbHaH aHTeHHaH perneTKa, Dx = Dy = 0.5, L = 0.5A
o
-20
o
10
20
-. E- TIJIOCKOCTb

t:::[
--
Cd
E-< -5
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(T)
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Cd

c..>
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Cd -15
0..

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t=:[
30
40 50
e (rpa,n;.)
60
70
80
90
PUC. 7.22. ,LJ;lfTIOJIbHaH aHTeHHaH perneTKa, Dx = Dy = 0.5, L = 0.51..

7.4. IloiJxoiJbl 6 CneICmpOJlbHOU 06Aacmu \,
SEP CO CTeneHblO cos 8, nOKa3bIBaeT, qTO HaH.JIy1IllIee COOTBeTCTBHe ,nOCTHraeTC npH
cos1,58; 3Ta ,nHarpaMMa no MOW:HOCTH npoxo,nHT npH6JIH3HTeJIbHO Mex,ny KpHBbIMH
,lIJI H- 11 E-llJIOCKOcTeit OTMeTHM, qTO napaMeTpbI ,lUI w:eJIeH nonyqalOTc rryreM
YMHoxeHIDI Ha KOHCTaHTY ,l(HnOJIbHbIX napaMe1])OB [97]. ,[(o6aBJIeHHe 3KpaHa nOBbI-
llIaeT aKmU81l0e conpOmU8Jle1lUe CKa1lUp08a1lWl B HanpaBJIeHHH, nepneH,l(HKyIDIpHOM
paCKpbIBY aHTeHHbI, HO, qTO 60JIee BIDKHO, npHBo,n:HT K CMew:eHHIO 3HaqeHHH .lLIDI
H-IIJIOCKOCTH B 6eCKOHeQHYJO 06JIaCTb (CM. pHC. 7.23-7.25). Ha 3TOT pe3YJIbTaT
BJIIDIeT MHO)I(HTeJIb ,nHarpaMMbI HanpaBJIeHHOCTH 3KpaHa, TaK qTO B HTore 3HaQeHHe
SEP C1])yKTypbI «,nHnOJIH/3KpaH» (pHC. 7.25) OKa3bIBaeTC ,lI)UI Bcex llJIOCKOCTeH
xyxe cooTBeTCTByIOw:eH ,l(HarpaMMbI ,lI)UI ,l(HnOJIbHOH AP (pHC. 7.22).
250
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Puc. 7.23. ,D;HllOJIbHaSl aHTeHHaSl perneTKa C 3KpaHOM, Dx = Dy = 0.5, L = 0.5A,
H = 0.25A
10
20
30
60
70
80
90
M B 3TOM c.rryqae ,lJ,HarpaMMa HanpaBJIeHHOCTH no MOW:HOCTH B:u,.aa cosl. 5 ,naeT
TaK xe xopornee COOTBeTCTBHe npH cKaHHpoBaHHH B npe,neJIax yrJIa -50°; BHe 3TO-
ro ,n:Hana30Ha 3HaQeHHe SEP 6bICTpO nan;aeT H3-3a MHO)I(HTeJISI 3KpaHa.
TIoKa3aTeJIbHO nOBe,n:eHHe HMne,naHca npH B03HHKHOBeHHH ,nH«}>paKl(HOHHOro
JIeneCTKa. TOJIbKO qTO o6cyx,naBllIHec CJIyqaH nOBTopSIIOTCSI ,lI)UI KB8JJ:paTHOH ceT-
KH co CTOpOHOH 0.7'A, ,nonycKalOw:eH B03HHKHOBeHHe ,nH«}>paKl(HOHHOro JIeneCTKa
IIPH 8 = 25.38°. Ha pHC. 7.26-7.28 nOKa3aHbI uMneiJallC CKa1lUp08a1lUJl H SEP ,lJ,H-
IIOJIbHOH AP; y 06eHX KOMnOHeHT UMneiJallCa CKa1lUp08a1lUJl HMeeTCSI 6eCKOHeqHaSI
CHHryJIpHOCTb npH yrJIe ,nH«}>paKl(HOHHOro JIeneCTKa. B 3TOM CJIyqae SEP HMeeT
yrOJI OCJIellJIeHIDI npH CKaHHpOBaHHH B H-IIJIOCKOCTH. XapaKTepHCTHKH ,lI)UI
E-llJIOCKOCTH 11 ,lJ,HarOHaJIbHOH IIJIOCKOCTH CKaHHpOBaHHSI 3a1])arHBaIOTCSI He3HaqH-
TeJIbHO. ,[(o6aBJIeHHe 3KpaHa npHBo,nHT K 3aMeHe 6eCKOHeQHbIX cHHryJISIpHOCTeH
....
KpyrbIM, HO KOHeQHbIM CKaqKOM aKmU81l0Z0 conpOmU8Jle1lUJl CKa1lUp08a1lUJl H TOQKOIi
neperH6a KpHBOH peaKmU81l0Z0 conpOmU8Jle1lUfl CKaHUp08a1lUJl (CM. pHC. 7.29-7.31).

b
rJlaea Z B3aUMHafl Cefl3b
250
H- TIJIOCKOCTb
..-
C
--

 200
ro

o

:s:
::c
ro

u 150
«1)
::s::
::c
«1)


:s:
E-<
o 100
Q;
t::
o
u
«1)
o
::c

::s:: 50

ro
«1)

D
E
0 0 10 20 30 40 50 60 70 80 90
e (rpa,n;.)
PUC. 7.24. )];IIITOJIbHa51 aHTeHHa5.1 perneTKa C 3KpaHOM, Dx Dy 0.5, L - 0.5A,
-
H = 0.25A
o
-20
o
10
20
30
E- IDIOCKOCTb
..-

I=:(
--
ro
 -5
::c
«1)

«1)

(I')
c::
::s:
::c
ro

o
Q;
::s::
::c
ro

u
ro


ro -15


ro
::s::

40 50
e (rpa.,n;.)
60
70
80
90
PUC. 7.25. )];IIITOJIbHa51 aHTeHHa51 perneTKa C 3KpaHOM, Dx
L = 0.5A, H = 0.25A
Dy
0.5, L
0.5,

I
I
7.4. IIoiJxoabl 6 CneKmp{JJlbHOU o611acmu 
300
--
a
--
 250
:s:
:I:
t'd

0

:s:
:I:
t'd

U
C1) H- TIJIOCKOCTb
:s:
:I:
C1)


::so:
E--
 0

t:: 100
0
u
C1)
0
:I:

::so:
 50 E
o
o
10
20
30
40 50
e (rpa,L(.)
60
70
80
90
PUC. 7.26. ,D;JiIllOJIbHaR aHTeHHaR perneTKa, Dx == Dy == 0.7, L == 0.5"-
300
--
a
-- 250
tJ:::
:s:
:I:
t'd

0 200

:s:
:I: H- TIJIOCKOCTb
t'd

U
C1) 150
:s:
:I:
C1)


:s:
E-- 100
0
Po.
t::
0
u
C1) 50
0 E
:I:

:s:

t'd 0
C1)

-50
o
10
20
30
40 50
e (rpa):(.)
60
70
80
90
PHC. 7.27. ,D;JiIllOJIbHaR aHTeHHa51 perneTKa, Dx == Dy == 0.7, L == 0.5"-


FJlaea Z B3aUMHaJl CeJl3b
o
.-

!::!:
--
ro
f-< -5
:I:
Q)
:E
Q)
t::
('T')

::so::
:I:
ro
j:Q -10
0
0..
::s:
::t
ro

u
ro
::E
:E
ro -15
0..

ro
::so::
I::f
-20
o
10
20
30
40 50
e (rpa,n:.)
70
90
60
80
PHC. 7.28. L(HTIOJIbHa51 aHTeHHa51 perneTKa, Dx = Dy = 0.7, L = O.5A
200
.-
C
--

::so::
::t
ro 150
j:Q
0
0..
::so::
::t
ro

u
Q)
::so::
::t 100
Q)
t::
j:Q
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f-<
0
0..

0
u E
Q) 50
0
:I:
c::I
::so::
f-<

a
o
10
20
30
60
90
40 50
e (rpa,n:.)
70
80
PHC. 7.29. L(HTIOJIbHa51 aHTeHHa51 perneTKa C 3KpaHOM, Dx - Dy
H = O.25A
0.7, L
O.5A,

Z4. IIooxoobl 6 CneKmpaJIbHOU: 06Aacmu 
200
,,-.,
C
--
e;:
:s::

c:oa
 150

:s::

c:oa

u
cu
:s::

cu 100


:s::

o


o
u
cu
 50

:s::

c:oa
cu

H-nJIOCKOCTb
E
0 0 10 20 30 40 50 60 70 80 90
e (rp.)
Pac. 7.30. ,l1;HTIOJIbHa51 aHTeHHa51 pellIeTKa C 3KpaHOM, Dx - Dy - 0.7, L 0.5"-,
H = 0.25"-
o
-..

t=:t:
--
c:oa
 -5

cu

cu


e;:
:s::

c:oa
 -10

:s::

c:oa

u
c:oa


c:oa -15


cd
:s::

-20
0 10 20 30 40 50 60 70 80 90
e (rp.)
Pac. 7.31. ,l1;HTIOJIbHaH aHTeHHaH pellIeTKa C 3KpaHOM, Dx =D 0.7, L = 0.5"-,
H = 0.25"- y

 rl1060 Z B30UMHllfl C6JI3b
Y SEP HMeeTCR npHMepHO 3 ,L(D-MHHHMYM npH B03HHKHOBeHHH ,L(H<ppaKU:HOHHOro
JIerreCTKa, HO .upyrHe IIJIOCKOCTM 3aTparHBalOTCR He3HaqMTeJIbHO. .HCHO, qTO ,L(JIR
llIHpOKOnOJIOCHbIX npMMeHeHMM 3KpaH CYIl(eCTBeHeH. IIpH ,L(pyrMX 3HaqeHMRX llIara
ceTKlI B 06JIaCTM yrJIOB ,L(M<ppaKll;IloHHbIX JIeneCTKOB Ha6JIIO,L(aeTCR aHaJIOrHQHOe IIO-
Be,L(eHHe. YrOJI OCJIellJIeHIDI B03HllKaeT nOTOMY, QTO K03<P<PHl(HeHT OTpIDKeHHR B
3TOM CJIyqae paBeH e,L(HHMl(e. 3TH ,L(aHHbIe CpaBHHBaJIHCb C BbIQHCJIeHIDIMH, BbI-
IIOJIHeHHbIMM ,lIJIR 60JIbllIOH AP B npOCTpaHCTBeHHOM 06JIaCTH, B KOTOpbIX HCnOJIb-
30BaJIllCb ,L(aHHbIe B3allMHoro HMne,L(aHCa KapTepa, npH 3TOM ,L(OCTHrHYTO TOQHOe
COrJIaClle [97]. 06bIQHO npH BbIQMCJIeHHM peaKTllBHoro conpOTHBJIeHHR yqHTbIBa-
JIMCb 900 (10 x 90) qrreHOB p.H.II:a. Bce npe,L(CTaBJIeHHbIe KpHBbIe nOJIyqeHbI ,lLJIR pa-
,L{Myca ,L(HnOJIR 0.001),,; 60JIee TOJICTbIe ,L(HnOJIH HMelOT MeHbllIee 3HaQeHHe UMneiJaH-
ca CKaHupOeaHUJl B HarrpaBJIeHHH, rrepneH,II;HK)'JIRpHOM paCKpbIBY aHTeHHbI, HO C
B03paCTaHHeM yrJIa CKaHHpOBaHMR H3MeHeHHR YMeHbllIaIOTCR.
,LJ:JIR CneIcrpaJIbHOM 06JIaCTM 3TM pe3YJIbTaTbI MOryT 6bITb BbIBe,L(eHbI HenOCpe,L(-
CTBeHHO H3 B3aHMHbIX HMIIe,L(aHCOB ,L(MllOJIeH KapTepa. PaccMoTpHM AP KOJIJIHHe-
apHbIX KOMllJIaHapHbIX TOHKlIX ,L(MIIOJIeM, paCllOJIO)l(eHHbIX B,L(OJIb OCM Y C llIarOM d x
H d y . HMneiJaHc CKaHUpOeaHUJl HaXO,L(HTCR KaK CYMMa B3aHMHbIX MMlle,L(aHCOB Me)l(,L(Y
,L(HnOlliIMM B AP, paCllOJIO)l(eHHbIMM Ha paCCTORHHH Xo H Yo ,L(pyr OT ,L(pyra, OT,L(eJIb-
HOrO ,L(HnOlliI H ,L(HIIOJIR B COCTaBe AP
IlpOCTpaHCTBeHHbIM uMneiJaHc CKaHUpOeaHUJl paBeH
Z == LLexp[jk(nu + mv)]Znm, (7.51)
r,L(e Znm CO,L(ep)l(J1T 'rpH c<l>epHqeCKllX BOJIHOBbIX qrreHa, KaK YCTaHOBJIeHO KapTepoM
[10]. IIpH pa;:I;Hyce a lUfllOJIR H YTpoeHHbIX paCCTORHIDIX OT KOHl(OB H u;eHTpa ,L(MnOJI5.I
r 1 2 =(xo +a+nd x )2 +(Y+YO +md y _ 1 J,
rl == (xo + a + nd x )2 + (y + Yo + md y )2, (7.52)
rl = (xo + a + nd x )2 + (Y + Yo + md y + I J '
r,L(e ,lJ)IHHbI OT,L(eJIbHOrO ,L(lIllOlliI II ,L(MllOJIH B COCTaBe AP paBHbI fs H ft. B3aHMHbIM
IIMlle,L(aHC Me)l(L(Y ,L(HnOJIRMH CTaHOBIITCR paBeH
Znm = j30 If [ eXp(-jkr 1 ) -2Cs exp(-jkro) + e X p (-jkr 2 ) ] sink(lt/ 2 _IYl)d Y , (7.53)
Ss Sf -/,/2 rl ro r2
r,L(e Ss == sin k1s/2, St == sin k1t/2, C s == cos k1s/2. 3,L(eCb npHBe,L(eHa O,L(Ha H3 Tpex KOM-
IIOHeHT B3aHMHoro HMlle.naHca:
Zl = j30 LexpUnkdxu) J sin[k(/tf2-lyl)] LexpUmkdyv) exp(-jkr 1 ) . (7.54)
S s S t n n r]
MCIIOJIb3YR <POPMYny CYMMHpOBaHHR IIyaccoHa II TeopeMY C,L(Bllra llpOCTpaHCT-
....
BeHHOH qaCTOTbI, IlOJIyqaeM
L expUmkd y v) exp(- jkrl) = j1t L exp[jkf3(y + Yo - Is /2)] x
m  d y m
x H62)[k -J l _p2 (xo + a + nd x )],
(7.55)

Z4. IloiJxoiJbl 6 Cne1CmpllllbHOii ofinacmu d
... -;.
r.n:e [3 == v + mAl dye 3TO rr03BOJIReT co6paTb H rrpOHHTerpHpOBaTb ueJIOqHCJIeHHbIe
qJIeHbI B Bblpa)l(eHHM ,lLJIR Zl'
Z\ = -30n LexpUnkdxu) Lexp[-jk!3(Yo -/s/2)] x
S s S t d y n m
/,/2
x Ha 2 >[k .J I -13 2 (XO + a + nd x )] J expUkJ3y) sin[k(lt 12 -I y/)]dy.
-/,/2
(7.56)
HHTerpaJI rrpe.n:CTaBJIHeT C060H o606eHHyID .n:HarpaMMY HarrpaBJIeHHOCTH:
2[ cos(kJ31 t 12) - cos(kl t 12) ]
k(J32 -1)
(7.57)
,[(JlR .n:BYX .n:pyrHX BOJIHOBbIX qJIeHOB KapTepa COBeprnaeTCR Ta )l(e rrpoue.llYpa.
K03<P<l>HUHeHTbI H HHTerpaJIbI OT 3KCrrOHeHl(HaJIhHOH <l>YHKIJ:HH rrpHHHMalOT BIf,[(
exp(jk[3IJ2) - 2C s + exp( -jk[3ls12) == 2[( cos (k[3ls/2) - cos(kIJ2)]
(7.58)
TaKHM o6pa30M, ,nBe o606eHHbIe ,nHarpaMMbI HarrpaBJIeHHOCTH rrepeMHO)l(a-
IOTCH, ,naBaR B pe3YJIbTaTe
P. P. == [cos(kJ31 s /2) - cos(kl s /2)] [cos(kJ31 t /2) - cos(kJ31 t /2)]
s t 1 -13 2 .
(7.59)
B pe3YJIbTaTe HMrre,naHC CKaHHpOBaHHR rrpHHHMaeT BIf,[(
Z = -120n L expUnkdxu) L.Ps p, expUk!3yo) x
SsSt kdy n m
X Ha 2 }[k .J l -13 2 (Xo + a + nd x )].
(7.60)
,l(JIR rrpeo6pa30BaHHR CYMMhI C <PYHKIJ:Hei1 faHKeJIH B CneKTpaJIbHyro CyMMY MO-
)l(eT HCrrOJIb30BaTbCH rrpe,nhUJ;yu:(ee npeo6pa30BaHHe nyaccoHa:
z = 2110 L.PsP, expUk!3yo) x
SsSt k2d X d y m
. exp(- jka .J l - a 2 -(3 2 )
x LexpUkaxo) .J '
n l-a 2 -13 2
(7.61)
r.n:e a == U + nAI d x . 3Ta CHMMeTpHQHaH <popMYJIa rronyqeHa B pe3ynbTaTe rrpHMeHe-
HUH CneKTpaJIbHOrO rro.n:xo.n:a K UMneoaHCY CKaHupOBaHUR B pa60Tax [76, 77, 88, 90].
AHaJIOrHqHbIe MeTo.n:hI MOryr Hcnonb30BaTbCH ,lLJIH napaJIJlenbHbIX .n:HrroneH (AP MO-
HorroneH) HJlM ,lLJISI l{HnOJIe:n, CKpemeHHbIX rro,ll, nlO6bIM TpeXMepHbIM yrnoM [90,
88]. JIerKo TaIOKe paCCMal'pHBaIOTCH menH [77]. Pa3nHQHbIe peaJIH3aUHH MeTo.n:a
MOMeHTOB MOryr Mcrronh30BaTb 3TY MeTo.n:onorMIO, nOCKOJIbKY OHa Henocpe,nCTBeH-
HO npHMeHHMa K BbICOK03<p<peKTHBHOMY KYCOqHO-CHHYCOlf,[(aJIbHOMY pa3JIO)l(eHHIO
M TeCTOBbIM <PYHKUHHM [66]. llIHpoKoe pacnpOCTpaHeHHe HallIJIH pa3pa6oTaHHbIe B
3TOH CBH3H KOMrrblOTepHbIe rrporpaMMbI (HarrpHMep, nepuOOutteCKuU Memoo MOMeH-
mOB). D:aHHbIH CneKTpaJIbHbIH MeTO.n: rrpMMeHHM TaIOKe K KOHeQHO-6eCKOHeQHbIM
AP (CM. rJIaBY 8).

 Dza6a 7. JJ3aUMHllJI C6R3b
7.4.2. MMKpononocKoBble aHTeHHbie peweTKM
DOJIbiliHe (H 6eCKOHeqHble) AP 113JIyqalOII(HX 3JIeMeHTOB (rreqaTHbIX 3JIeMeHToB) TaK-
)l(e rrOMaIOTC aHaJIH3Y Ha OCHOBe PMa <1>JIOKe ,l(.JUI rrepHO,l(WIeCIGIX WIeeK. 3TO
BrrepBble c.n:eJIaHO B pa60Te [73] .1UI 6eCKOHeQHOH AP MHKpOrrOJIOCKOBbIX H3.rryqaTe-
JIeH co CKaHHpOBaHHeM B E- IIJIOCKOCTH; MeTO.n; MOMeHTOB HCrrOJIb30BaJIC B cneKT-
paJIbHOH 06JIaCTI1 C CHHYCOH.n;aJIbHbIMI1 cl>YHKIJ;JfMH B pa3JIO)l(eHHH TOKa. 06c}')K.LI:e-
u
HHe npl1MeHeHI1H CrreKTpaJIbHbIX MeTO,l(OB MOMeHTa ,lLJ1 CJIOHCTbIX cpe.n: npHBo.n:I1TC
B pa60Te [73]. Hey.n:HBI1TeJIbHO, qTO 3aBI1CI1MOCTb UMneOallCa CKa1lUp06a1lUR OT yrJIa
6JIH3Ka K COOTBeTCTByJOlI(HM xapaKTepHCTHKaM .n:lfrrOJIbHbIX AP (CM. pa3.n:eJI 7.4.1).
KOMrrblOTepHoe Mo.n:eJIlfpOBaHHe BbIBJfJIO pe30HaHC BbITeKalOIllHX BOJIH, nopO)l()];alO-
II(HH rrHK B 3aBI1ClfMOCTlf aKmU61l020 conpOmU6Jle1lUJl CKa1lUp06a1lUJl OT yrJIa; rrpH YBe-
JIHQeHHI1. TOJIlI(lfHbI IIO)])lO)l(l(lf nlfK rrOBJIeTC npH MeHbIIIeM yrJIe CKaHIfpOBaHIDI H
CTaHOBI1TC 60JIee OCTpbIM H BbICOKHM. 3TOT no,l(XO,l( 6bIJI pacnpOCT}JaHeH Ha rreQaT-
HbIe ,l(l1nOJIbHble AP, a 3aTeM Ha AP IIpMoyrOJIbHbIX IIeqaTHbIX aHTeHH B pa60Te
[10 I]. TpHroHOMeTpHQeCKHe <PYHKUlfH pa3JIO)l(eHIf no IIOJIHOH 06JIaCTIf 6bIJIIf IfC-
rrOJIb30BaHbI B MeTO,l(e MOMeHTOB B CIIeKTpaJIbHOH 06JIaCTI1. 06HapyxeHbI yrJIbI
OCJIeIIJIeHIDI, 06YCJIOBJIeHHbIe KaK 3<P<l>eKToM B03,l(eHcTBH ,l(lfcPpaKUlfoHHbIX JIeneCT-
KOB, TaK H B036}')K.L1:eHlfeM nOBepXHocTHoH BOJIHbI. TOHKa (0.02AO) IIO.l(JlO)l(J(a C £r =
2.55 H rnarOM Ao/2 06eCneqHBaeT xopOlIlee 3HaQeHHe aKmU61l020 conpOmU6Jle1lUfl CKa-
llupoeallUJl 3a HCKJIIOQeHlfeM yrJIa OCJIeIIJIeHH B E-IIJIOCKOCTH npH e = 82.9°, COOT-
BeTCTByJOIIIero nOBepXHocTHOH BOJIHe P/k = 1.0076, r.n;e sin e = kiP. npH 60JIee TOJI-
CTOH nOJ])IO)I(Ke (0.06AO) B03HHKaeT IIOBepXHOCTHaSl BOJIHa P/k = 1.028 C yrJIOM
OCJIerrJIeHHR 68.8° B E-IIJIOCKOCTIf, KaK nOKa3aHO Ha pHC. 7.32.
B .n:aHHOM paCQeTe IfCrrOJIb3yeTc 3HaqeHIfe mara pa3MelI(eHIf 3JIeMeHTOB B
E-IIJIOCKOCTH, paBHoe 0.5IAO, rr03TOM)' .n;IfcPpaKUHoHHbIH JIerreCTOK B03HHKaeT npl1
yrJIe 73.9°. npIf HCIIOJIb30BaHHIf 60JIee BbICOKoro 3HaQeHIf ,l(H3JIeKTpHQeCKOH no-
CTOHHOR (£ = 12.8) .1UI TOJICTOH no,l(-
'-' u
JIO)f(J(lf C rrOJIYBOJIHOBOH ceTKOIf yrOJI
OCJIelIJIeHH COCTaBJIReT 45.6°, KaK nOKa-
3aHO Ha pHC. 7.33. B 3TOM paCQeTe, BbI-
IIOJIHeHHOM B pa60Te [102], He yqIfTbIBa-
JIHCb TOKOBbIe MO,l(bI mTbIp, IIpMoe
H3JIyqeHHe lIlTbIp H KpaeBoe YCJIOBHe B
cPYHKUHX pa3JIO)l(eHH. TIoCJIe.n:Hee
BJIHeT Ha CXO)lHMOCTb, HO H3JIyqeHHe
lliTbIpR B 3TOM c.rryqae MO)l(eT rropO)f()IaTb
HCKYCCTBeHHbIe yrJIbI OCJIenrreHH B
H-nrrOCKOCTH. TI03TOMY Ha plfC. 7.32 If
7.33 OHH YCTpaHeHbI.
B pa60Te [72] rrpHMeHeH nO)lXo,l(,
HCIIOJIb3yJOII.{HH MeTO,l( MOMeHTa C .n;06a-
90 BOQHbIMH Mo.n;aMIf llITblp If CIfHryJIp-
HOCTblO KpaeBoro YCJIOBH, CorJIacyJO-
lI(eHCSI C <PYHKUIfMH pa3JIO)l(eHIf. KaK
nOKa3aHO Ha pHC. 7 .34, J(JI KBa,n:paTHbIX
neQaTHbIX 3JIeMeHTOB Ha KBaIJ:paTHOH
1.0
0.9
0.8
E- ITJIOCKOCTb
0.7
0.8
_ o.
a:
-
E = 2.55
O
0.2
0.1
o
o
30 60
YrOJI CKaHHpOBaHHR
PRC. 7.32. K03<l><lnfI..UieHT OTpa)f(eHIHI pe-
rneTKI1 MI1KpOnOJIOCKOBbIX 3JIeMeHTOB npl1
CKaHl1pOBaHl111 [102]


Z4. IIoiJxoobl 6 CneKmpatlbHOU o6J/acmu d
1.0
.',:i 1
0.9 E- TIJIOCKOCTb /j
0.8
I,
0.1 II
I,
OS t
1
- 0.5 /,
cr: D/ / /
-
0.4 / I
/ IH
/
0.3 /
/ I
0.2 / /
/
0.1 / ,,/
/ ./ £ = 12.8
-" ..."" ""
0 ---'
0 30 60 90
YrOJI CKaHHpOBaHHR
80
IIIA-O.I
x"..O.21
y,I..O.&
80 ,,-2.&
hIA-O.1
Ra
(OM)
40
20
hfA-o. '5
o
0.1' 0.'1 0.2 0.22 0.24 0.28 0.28 0.3
a/A
PHC. 7.33. K03<P<PHUHeHT 01'pa)l(eHIUI perneT-
KH MHKpononOCKOBbIX 3neMeHTOB npl1 CKa-
HHpOBaHI1H [102]
I
PHC. 7.34. AKTI1BHOe COnpOTI1BneHl1e B
MI1KpOnOnOCKOBOH perneTKe npM CKaHI1-
pOBaHHI1 [73]
ceTKe npH 60JIee TOJICTbIX rrO,lUIO)l{l(ax KpHBa5I QKmU8H020 conpOmU8JleHUR CKQHUPO-
8QHUR CTaHOBHTC5I 60JIee rJIMKOH H rrpOXOJ1HT HIDKe. 3TM pe30HaHCHble nMKM o6y-
CJIOBJIeHbI <pa30BbIM COrJIaCOBaHHeM Me)l(,[(Y ,JJ;H<ppaKUHOHHbIM JIeneCTKOM 11 BbITe-
OJ OJ
KalOI..IJ;eH BOJIHOH:
sin e Iw =  - 
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M YCTpaHeHMe yrnoB ocnenneHMR
7.5.1. Yrnbl ocnenneHMSI
HeKOTopble AP He H3JIyqalOT non; onpe,neJIeHHbIM yrJIOM; 3TOT yrOJI Ha3bIBaeTC5I
yrJIOM OCJIeIIJIeHH5I. 3TO 51BJIeHHe, KaK M xapaKTepHCTHKH AP B u:eJIOM, MO)J(eT 6bITb
paCCMOTpeHO C TOqKH 3peHHH JIM60 K03fjJfjJuu,ueHma Ompa:JICeHUR npu CKaHupoeaHUU,
JIH60 iJuazpaMMbl CKaHupoeaHUR 3JleMeHma. K03fjJfjJuu,ueHm Ompa:JICeHUfl npu CKaHUpo-
eaHUU MO)l(eT HMeTb BeJIHqHHY, 6JIH3KYIO MJIM paBHyro eJ(MHMue, MJIM iJuazpaMMa
CKaHupoeaHUR 3JleMeHma MO)J(eT 6bITb paBHOM HJII1 6JIH3KOM K HYJIIO B onpeJ(eJIeH-
HOM HanpaBJIeHMH. B nepBOM c.rryqae, T.e. B CJIyqae K03fjJfjJUlI,UeHma ompa:JICel-lUR om
3JleMeHma npu CKaHupoeaHUU, yrOJI OCJIenrreHMg B03HHKaeT, eCJIM BbICIllaH MOJ(a
nOJI5I 3JIeMeHTa raCHT OCHOBHyro. nOCKOJIbK)' OTHOCHTeJIbHaH <t>a3a 6bICTpO H3MeH5I-
eTCH C H3MeHeHHeM yrJIa CKaHHpOBaHMH, 3TH ,nBe MO,n:bI 06pa3YlOT pe30HaHC, H yrOJI
pe30HaHca <pa3bI MO)l(}{O onpe,n:eJIHTb no YMeHbIlleHHIO I riB 3aBHCHMOCTH OT yrJIa
CKaHMpOBaHHH. BbICIllaH Mo,n:a MO)ICeT 6bITb 06YCJIOBJIeHa BHellIHeH HJIH BHyrpeH-
HeM CTPYKTYPOH. IIpHMepaMM BHeIIIHeH CTPYKTypbI, nOpO)l()].alOll(eH yrOJI OCJIeTIJIe-
HH5I, 51BJI5IIOTC5I ,n:H3JIeKTpHQeCKHH 06TeKaTeJIb, nOKpbIBalOII.1HH Ka)l(,ll,bIH 3JIeMeHT
I1JIH PM 3JIeMeHTOB [67], ,n:H3JIeKTpMQeCKMM JIHCT, HaJIO)l(eHHbIH Ha nOBepXHOCTb
aHTeHHOM peIlleTKH [14, 26, 136, 44], 1'1 .I1H3JIeKTpHqeCKaH BCTaBKa, BbICTYITalOrn:a5I
113 anepTypbI Ka)l(,I(OrO BOJIHOBo,nHoro 3JIeMeHTa [49]. Bo Bcex CJIyqa5IX aKTMBHa5I
COCTaBJI5IIOII.1a5I BOJIHOBOrO HMne,naHca Ha nOBepXHOCTH AP BH,nOH3MeH5IeTC5I 11.3-3a
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JIOKaJlH3yeTC5I B OCHOBHOM BHe nOBepXHOCTM.
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CJIe.n;HRR cxeMaTWIeCKH H306pIDKeHa Ha
pHC. 7.42. B 3THX pa3JIHqHbIX cTPYKTYPax
BOJIHOBO.n;HbIM 3JIeMeHT nO,lI,L(ep)I(HBaeT
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lIlliI yrJIa OCJIellJIeHIDI. B AP C 1peyrOJIb-
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HIDKe qaCTOTbI OTCeqKH BBH,[(y 60JIbIIIHX pa3MepOB BOJIHOBo.n;a. B pa60Tax [95, 64] lIlliI
onpe.n;eJIeHlUI nOBe.n;eHlUI K03<P<PHI(HeHTa OTj)IDKeHIDI HCnOJIb30BaJIaCb 3KBHBaJIeHT-
HaR cxeMa ,!])IR 3THX llBYX MOD:. C.rryqaM nOJIHOrO otpa)l(eHlUI COOTBeTcTByeT HYJIeBOH
aKTHBHOH rrpOBO,l{HMOCTH. B npOI(eCce npoeKTHpOBaHHR ,[(JIR KOHTj)OJIH HaJIHqIUI yr-
JIOB OCJIellJIeHlUI H HX YC1paHeHHR HCnOJIb30BaJIHCb HMHTaTopbI (CM. pa3.n;eJI 7.4).
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Ha nOBepXHOCTH AP, yqHTbIBalOru:HM BJIHRHHe BHemHeM IUIH BHYTpeHHeM CTPYKTY-
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AP yrOJI OCJIellJIeHHR 06bIQHO OTCYTCTByeT, HJIH HMeeTCH JIHmb He6oJIbIIIOM MHHH-
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IIIe, nOCKOJIbK)' B HHX JIerqe B036y)1(,l{aeTCR BbITeKalOru:aR BOJIHa. Y BbITeKalOru:eH
BOJIHbI BOJIHOBOe qHCJIO KOMllJIeKCHOe, qTO aHaJIOrHQHO CJIyqalO aHOMaJIHH By.n;a
lIlliI OnTHQeCKOll OTpIDKalOII.J;eM .n;H<ppaKI.J;HOHHOM pemeTKH [56]. I1pH COOTBeTCTBYJO-
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BaeT xapaKTep rrpeKparu:eHIUI H3JIyqeHHR B 06JIaCTH yrJIa OCJIellJIeHH5I, r.ne r (K03<p-
<pHUHeHT oTpIDKeHHR) pa3JIaraeTCR B p5I,L( TeMJIOpa B6JIH3H rrOJIlOca. Ha pHC. 7.44
nOKa3aH K03rjJrjJuu,uellm ompa:JICellUR npu CKa1lUp06a1lUU AP Ha OCHOBe Y3KHX meJIeM,
U U U
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nJIaCTHHOM ,lI.JIR CJIyqaR CKaHHpOBaHH5I B E- IIJIOCKOCTH. 3Ta KpHBaR BbIQHCJIeHa c
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,l{a - 0.3"A, a llJIaCTHHa HMeJIa 3HaqeHHe £ = 2.56 H TOJIII.J;HHY 0.2"A. B pa60Te [64]
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npaBJIeHHH TaIOKe paBeH e.n;HHHI(e. B .n:pyrOM npHMepe HCnOJIb3yeTC5I AP H3 npRMO-
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,[(aHHOM rrpHMepe OH nOJIHOCTblO HaXO,[(HTCH BHyrpH [96].

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60JIee TeCHOM (B e,n:HHHuax ,l]JIHH BOJIH) ynaKoBKe 3JIeMeHTOB. Pe3YJlbTaTbI pa3,n:e-
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Z5. KOMneHcaqUJI 3ifxjJelCmoB ClCaHUpOBaHUJI U ycmpaHeHUe Y2JIOB OCJIefUleHUJI d
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MeHeHHOM BHyrpeHHeM cpe.n:OM HJIH BHelllHHM OKpyxeHHeM BOJIHOBona. B pa60Tax
[ 118, 134] I1CTIOJIb3yIOTCH .n:113neKTpHQeCKaH BCTaBKa B paCKpbIBe npSlMoyrOJIbROrO
BOJIHOBo,na H cornacyIOlI(HH IlITblpb, a B [119] HCnOJIb3yeTc$I np$lMoyrOJIbHbIM BOJI-
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3neKTpHqeCKHe BCTaBKH B paCKpbIBe BonHOBo.n:a, a B [135] npMMeHeHbl BCTaBKH B
KpyrJIbIX BOJIHOBO.n:HbIX 3neMeHTax. Heo6xo.n:HMaSl KOM6MHauHSI MO)], 3aBHCHT OT
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,lJ)ISI TE 20 MO.n:bI Ha Bxo.n:e B cornacyIOlI(yro uelIb. 3aTeM ,lJ)ISI COrJIaCOBaHIDI MMrre,lI,aHCa
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BOJIHOBo,n:a; LVUI COrJIaCOBaHH$I MOryT Hcnonb30BaTbCH TaIOKe .n:OIIOJIHHTeJIbHbIe .n:H3-
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BOJIHOBO,lI,a, BKJIIOqalOlI(a$l ABe IIJIaCTHHbI, HaXOM:rn:l1ecSI Ha IIOBepXHOCTI1 AP. Bce
3TH 3JIeMeHTbI paCCQHTbIBaIOTCH MeToAoM COfJIaCOBaHI1.H MOA, IIPH KOTOpOM pacnpo-
cTpaH.HIO:rn:l1eC.H 11 3al)'XaIO:rn:l1e MO.n:bI BOJIHOBo,n:a cOrJIacyIOTcH Ha Ka)l(1IOM rpaHlfue
pa3LIeJIa. 3TO YLI06HO ocyrn:ecTBJI$leTCR B CrreKT}JaJIbHOH 06JIaCTI1. ITOCKOJIbKY e,n:l1-
HHQHa$l SlQeMKa rrpH yrJIax cKaHHpOBaHI1$1, OTJII1QHbIX OT HOpMaJIH K AP, I1MeeT I1M-
rre,lI,aHCHbIe CTeHKI1, pa60Ql1MI1 Mo,naMI1 6y.n:YT LSE H LSM, a He TE H TM. L(JIJJ Ha-
Qarra WTepallHOHHoro npouecca He06xO,llHMO 3a,n:aTb 3HaQeHI1S1 Bcex <p113I1QeCKlfX
napaMeTpOB: .L{H3JIeKTpHQeCKl1e IIOCTOHHHbIe H TOJIIIlHHY IIJIaCTHH, ,n:H3JIeKTpM'-IeCKHe
nOCTOSlHHbIe If ,lJ)IHHY BCTaBOK, BbICOTY W llIHPHHY BOJIHOBO,L(OB H, KOHeQHO, pa3MepbI
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CeTKM pacnOJIO)l(eHIDI 3JIeMeHTOB. 3aTeM YCTaHaBJII1BaeTC.H Ha60p MOn: BOJIHOBOJ{Horo
3JIeMeHTa. BbI60p nOlIxo;un.u;ero Ha60pa Bcex 3TI1X rrapaMe'TpoB Tpe6yeT 3HaqHTeJIb-
Horo orrbITa, rrpHo6peTaeMoro, rJIaBHbIM o6pa30M, rryreM ql1CJIeHHOrO nporoHa pa3-
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paMeTpoB BbIQl1CJI5IeTCH nOJIHa.H npOBO.IJ:MMOCTb e.IJ:I1HMqHOM 5PIeHKM .lLIDI KaJK.II.OM
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v v
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pHQeCKI1e nJIaCTHHbI H 3aTeM 06'belIHH.HIOT C )lpyrHMH MO)laMH e)lHHHQHOH 5IqeMKJ1.
KOJIHQeCTBO MOn: 06blQHO COCTaBJ1.HeT 100-300.
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)l(HbI 6bITb npe06pa30BaHbI B TE M TM MO.ll.bI. 3aTeM BbIQHCJI5IeTCR anepTypHa5I
nOJIHaSl npOBOlIMMOCTb Ka)l([[OM BOJIHOBOD;HOH MO,abI, HaQHHaH C nHTalO:I.QeH BOJIHO-
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.lI.MIvIOCTI1. TaKHM 06pa30M, np0I13BOL(MTCR pellIeHMe CHCTeMbI ypaBHeHI1H - no OL(-
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TpeyrOJIbHOH ceTKe, rrpHBO,lIJITCR Ha pHC. 7.49 [121]. I1oJIoca nponYCKaHIDI .lUIR
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OHI1 .n:OIDKHbI 6hITh KaK MO)I(HO 60JIhIIIerO pa3Mepa, KOTOphIH .n;orrycKaeT pemeTKa.
,[LITH O.n;HOH nOJIRpl13aUHH nonyqeHa nOJIOca nporrYCKaHMR > 50% C KCBH < 4 H
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TaTbI. KaK COCTaBHaR qaCTb npou;e,nypbI COrJIaCOBaHI1H MOl( Ha rrOBepXHOCTH AP
MOryr YCTaHaBJIHBaThCR o.n:Ha IUIH 60JIee ,n113JIeKTpMQeCKHX IIJIaCTMH [135].
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pa3HbIMH OTBo.n:aMI1, pa3pa60TaHHaSl B [31]. MOH0110JII1 YMeHhmaIOT IIll1pMHY JIyqa
B E-rrnocKocTM M n:06aBJIRIOT MO,ny 3JIeKTpMQeCKOrO TMna, n:orrOJIIDIIOIl(yJO IIJ;eneByro
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HO c,UenaTh 01U1HaKOBbIMH [52]. MeX3JIeMeHTHaR CBH3b YMeHbIIlaeTCH Ha 14 .n:E, If
3HaQHTeJIbHO YMeHbIIlalOTCH 60KOBhIe nerreCTKM 11 3a.LI:HI1H nerreCTOK aHTeHHOH pe-
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CKaHMpOBaHMR .n:o 80° [88]. ,l],pyrHe nOJIe3HbIe CCbIJIKM Ha pa60TbI no CJIOMCTbIM BOJI-
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JIuTepaT)'pa
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KOHeqHOM perneTKIf; perneTKa 101 x 101 Ha pHC. 8.4 JIyqrne. Pa3Mep perneTKH B
rrOrrepeqHOM HanpaBJIeHlf1f HBJIHeTCH MeHee KPHTHqHbIM; IIOJIyqeHHe rJIy6oKoro
,L(H<ppaK:QHOHHOro MaKCHMYMa rrpH yrJIax OCJIerrJIeHHH Tpe6yeT 41 HJIH 60JIee 3JIe-
MeHTOB.
o
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ca

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ca


ca
0.. -15

ca
:s:
t1
-20
o
10
20
30
40 50
e (rpa,n;.)
60
70
80
90
PHC. 8.3. ,L(11IIOJIbHaH perneTKa, annpOKCHMaU;I1H MeTo.n;OM 60JIbrnOH perneTKH,
41 x 41, d x = d y = 0,7 'A, L = 0,5'A
06aBJIeHHe 3KpaHa rrpOHBJIHeTCH B rrpHBHeceHHH :QHKJIHqeCKOrO xapaKTepa
nOBe,L(eHHH corrpOTHBJIeHHH Me)l(,I(y ,L(HrrOJIHMH, B pe3YJIbTaTe qero arrrrpoKcHMa:QH5I
60JIbllIOM pellieTKIf ,l(aeT OqeHb He60JIblIIHe KOJIe6aHHH. Ha pHC. 8.5 rrOKa3aHO, qTO
OqeHb XOpOllIa5I KOppeJIH:QHH C pe3YJIbTaTaMH ,l(lliI 6eCKOHeqHOM pellIeTKH If MeeT
MeCTO ,l(JI5I pellieTKIf C qHCJIOM 3JIeMeHTOB 41 x 41. ,L(mI pellIeTKH 21 x 21 OC:QHJIJUI-
QIfIf < IrrD. MeTorr 60JIbllIOM perneTKH OKa3bIBaeTCH nOJIe3HbIM lUI5I pellieTOK, r,L(e
OJ
,l(HarpaMMOIf 3JIeMeHTa HBJIHeTCH ,l(HarpaMMa THna «llHnOJIb-3KpaH».

8.1. MemoObl aHaJlU3a \
o
H- TIJIOCKOCTb
",......,

-5
(':j
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CI)

CI)
r:::
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0::
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o -10
0.
:s:
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(':j

C,)
(':j


(':j
0. -15


:s:
r::t:
-20
o
10
20
30
40 50
e (rpa,n;.)
60
70
80
90
Pac. 8.4. )];HrrOJIbHaR perneTKa, arrrrpOKCHMaIJ;HH MeTo,nOM 60JIbrnOH perneTKH,
101 x 101, d x = d y = 0,7 'A, L = 0,5'A
(':j
 -5
CI)

CI)
r:::
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0::
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o -10
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(':j
 -15
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---
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"
"" E- IIJIOCKOCTb
"-
"
"
"
-.

I=:t:
---
"
"
"
"
"
\
\
\
\
\
\
\
\
\
\
\
\
-20
o
10
20
30
40 50
e (rpa,n;.)
60
70
80
90
Pac. 8.5. )];HrrOJIbHaH perneTKa Ha,n 3KpaHOM, arrrrpOKCHMaIJ;HR MeTo,nOM 60JIbIDOH
pemeTKH, 41 x 41, d x = d y = 0,7 'A, L = 0,5'A, H = 0,25'A

 DW6a 8. KOHe'lHble aHmeHHble peUlemlCU
8. 1.2. KOHe"lHO-6eCKOHe"lHble peweTKM
3aTpaTbI Ha paCqeTbI COKparuaIOTCR, KOr,L(a paCCMaTpHBalOTCR KOHeqHO-6eCKOHeq-
v v
Hble pemeTKH co CKaHHpOBaHHeM B rrJIOCKOCTH, rrepneH.IIHK)'IDIpHOH KOHeqHOH
mHpHHe pemeTKJI [9]. B 3TOM CJIyqae ,L(OnYCKaeTCR CKaHHpOBaHHe TOJIbKO B rJIaB-
HOM nrrOCKOCTH. ,[(IDKe rrpH rrpHMeHeHHH MeTO,L(a MOMeHTOB MOryr 6bITb rrpOMOJ(e-
JIHpOBaHbI OTHOCHTeJIbHO 60JIbllIHe perneTKJI. EJIarO,L(apR TaKOMY crroco6y MO,L(eJIH-
pOBaHIDI MHoroe MO)I(HO rrOHRTb 0 rrOBe,L(eHHH KpaHHHx 3JIeMeHTOB B pemeTKe. KaK
6bIJlO MHorOKpaTHO nOKa3aHO, nOJIyBOJIHOBble pemeTKH TOHKJIX ,L(HnOJleM npOHBJlH-
lOT BCe XapaKTepHble OC06eHHOCTH B3aHMHOH CBH3H. TaKJIM 06pa30M, Ha ,n;aHHOM
3Tane He Tpe6YIOTCR CJlO)l(}fble 3JIeMeHTbI pemeTKJI H pemeHHH MeTO,L(OM MOMeHTOB.
PaCCMaTpHBaH KOJIJIHHeapHbIe HJIH napaJIJIeJIbHble ,L(HrrOJlI1, MO)KHO yqecTb CKaHH-
pOBaHHe KaK B H-, TaK H B E-rrJIOCKOCTRX. BbIqHCJlHTeJlbHaH MOJ(eJlb TOr,L(a COCTOI1T
H3 N 6eCKOHeqHbIX JIHHeHHbIX perneTOK, KaK H306pa)l(eHO Ha pHC. 8.6 H 8.7.
00
r
---
"
/ / / / /
-- ---- - - - -----
/ / /
/ / /
/ /
/ / / / /
I I I I /
IIIII
\.
---

00
PHC. 8.6. KOHeQHO-6eCKOHeQHaH perneTKa J(MIIoneH co CKaHMpOBaHMeM B H-lIJIoc-
KOCTI1
KaJK.IJ:aH 6eCKOHeQHa5I perneTKa (JllfHeHKa) COCTOHT H3 rrOJIYBOJIHOBbIX TOHKHX
J(l1rrOJleH. TaKJIM 06pa30M paCCQHTbIBaeTcH B3aHMHoe corrpOTHBJIeHHe Me)l()];Y Me)l(-
L{Y OTL{eJlbHbIM .nl1rrOJIeM H BCeMI1 L{HnOIDIMH B OL{HOH 6eCKOHeQHOH «JII1HeHKe». Co-
BOKYTIHOCTb H3 HHX lLIDI Bcex JIHHeeK HCrrOJIb3yeTcH ,l(JIH <pOpMl1pOBaHHH 06bPIHOH
v
MaTpHUbI COnpOTI1BJIeHHH, npl1 3TOM pemeHHe rr03BOJIReT rrOJIyqHTb conpomu8ileHue
aUnOilR npu cKaHupo8aHuu ailR KaJlCaOU ilUlleUKu.
3aBHcHMoCTb conpomu8ileHuR npu cKaHupo8aHuu ,l(JIH 6eCKOHeQHOH pemeTKH rro-
JlyqeHa BnepBble B [29] pemeHHeM B cneKTparrbHoH 06JIaCTH. 3.necb 3HaQeHHe co-
npomU6ileHUR L{aeTC$I B Bl1,L(e npOCToro qJIeHa L{JIH Ka)l()];OrO rJIaBHOrO JIerreCTKa RJIH
L{11Q>paKUHoHHoro JIeneCTKa B Bl1,L(e cneKTparrbHoro CYMMHpOBaHIDI <PYHKUHH Tpl1-
rOHOMeTpHqeCKOrO Tl1na ,lUIR peaKmU6H020 conpomU6ileHUJl. IDI mara B pemeTKe,
6JIH3KOrO K 3HaqeHHIO A/2, <popMYJIa 06eCrreQHBaeT KpaHHe 6bICTpyIO CXO.nHMOCTb.

8.1. MemoiJbl aHaJlU3a ;,,
. i
00
\..


00
PRC. 8.7. KOHeQHO-6eCKOHeQHaH pemeTKa )J;HTIoJIeH co CKaHHpOBaHHeM B E-TIJIOC-
KOCTH
,[(JI5I 060RX CJIyqacB cKaHHpOBaHH5I B H- H E-nJIOCKOCT5IX nOJIHbIC conpOTHBJIC-
HH5I ,n:HnOJI5I B JIHHCHKC 6bIJIH paCCqHTaHbI KaK B npocTpaHcTBcHHOH, TaK H B cnCK-
TpaJIbHOH 06JIaCT5Ix. B npocTpaHcTBcHHOH 06JIaCTH M5I paCqCTa conpOTHBJICHH5I Za
MC)I()Iy ,n:HnOJI5IMH HCnOJIb3ycTC5I no,n:nporpaMMa Ha OCHOBe B3aHMHoro HMnclIaHca
KapTcpa Me)l(,L(Y ,n:B)'M5I TOHKHMH npOBOJIOqHbIMH ,n:HnOJI5IMH [16]. OHa BKJUOqaCT
u u
CHHYCHbIe H KOCHHYCHbIe HHTCrpaJIbI, KOTopbIe paCCQHTbIBaIOTC5I C ,l(BOHHOH TOQHO-
CTblO, QTo6bI MO)KHO 6 bill 0 CYMMHpOBaTb MHOrOqHCJIeHHbIe IUIeHbI. ,[{.JuI JIHHeeK
KOJIJIHHCapHbIX JJ:HnOJIeH (CKaHHpOBaHHe B H-nJIOCKOCTH) HMnel(aHC llHnOJUI B JIH-
u u
HCHHOH perneTKe npe,n:CTaBJIeH CJIe,n:yroII(HM BbIpIDKCHHeM:
Z = LZa(XO + nd, .J a 2 + y2).
(8.3)
KaK nOKa3aHO Ha pHC. 8.8, CMern:eHHe OT,l(eJIbHOrO ,l(HITOJI5.l COCTaBJI5IeT a, na-
u u
paJIJIeJIbHbIH c.n;BHr paBIDIeTC5I xo, nepneH.n;HKYJI5IpHbIH HHTepBaJI - Yo, HHTepBaJI
perneTKH COCTaJI5IeT d x , H nOJIOBHHa MHHbI ,l(HnOJI5I - h. ,[(JI5I JIHHCeK napaJIJIeJIb-
HbIX ,l(HnOJIeH (cKaHHpoBaHHe B E-nJIOCKocTH) HMne.n;aHC ,l(HnOJI5I B JIHHeHHOH pe-
rnCTKe COCTaBJI5IeT
z = LZa ( (Xo +nd)2 +a 2 ,yo).
(8.4)
Pa3MepbI YKa3aHbI Ha pHC. 8.9. CJIO)KHOCTb B03HHKaeT B CB5I3H C TeM, qTO C)'MMbI
KOJIe6JIIOTC5I, npH 3TOM CHTYaUIDI YXY,l(rnaeTC5I no Mepe YMCHbIIleHIDI paCCT05.lHH5I
Me)l()Iy JJ:HnOJUIMH. IIoCKOJIbK)' nepHO,n: KOJIe6aHHH CYMMbI H3MeIDIeTC5I B 3aBHCH-
u
MOCTH OT pa3MepOB, HH O,l(HH npOCTOH MeTO,n: KOMneHcaUHH He ,l(aeT YlIOBJIeTBOpH-
TCJIbHbIX pe3YJIbTaTOB. CXO,n:HMOCTb He 6bIJIa ,n:OCTHrH)'Ta rrpl1 CYMMHpOBaHHH 60JIee
1000 qrreHOB. I1pHeMbI y.rryqIIleHH5.l CXO.n;HMOCTH BKJIIOQalOT CneUHaJIbHbIe npHeMbI
[35, 25]. 06a rrpHeMa HCnOJIb30BaJIHCb, HO npHeM B [25] JIyqrne, ITOCKOJIbK)' OH He

 Dla8a 8. KOHertHble aHmeHHble peUJemKU
C
z
z
a
y
y
x
x
Puc. 8.8. KOJIJIIiHeapHa}l reOMel'pHH
PHC. 8.9. TIapaJIJIeJIbHa}l reOMel'pH}I
Oe,l{HHSIeT B uenoqKY IIorpelliHocTH oKpyrJIeHHSI. TpaHc<popMaUIDI B [25] npe,l{CTaB-
JUIeT C060H nepeCTaHOBKY qaCTHqHbIX CYMM B [37, 38]:
f ( -l)i ( "! )( n + j ) m-l S n+l
Sn = i=O I n + m Sn+i+l - Sn+l
L , .m =0 (-1)i ( 7 )( :: ) m-] 1
Sn+i+l - Sn+l
(8.5)
3TO .n:aeT rrpe06pa30BaHMe rrOPMKa m, r.n:e ( 7 ) - 6MHOMMHaJIbHbIH K03cPQml{MeHT.
KaK npaBRJIO, 21 l{HKJI ,l{aeT OTJIHqHYJO TOqHOCTb .LUISI Bcex c.rryqaeB [25], no-
u u
CKOJIbKY B3aHMHbIH HMne,l{aHC napaJI.JleJIbHbIX ,l{HnOJIeH }'MeHbllIaeTCSI aCHMnTOTH-
qeCKH, KaK l/r, B TO BpeMSI KaK .LUIH KOJillHHeapHbIX ,l{HnOJIeH 3aBHCHMOCTb 1/,.1,
H Tpe6yeTcSI 60JIbllIe l{HKJIOB ,l])ISI ,l{OCTIDKeHHSI CXO,l{HMOCTH. ,[lrrSI o6eHX IIJIOCKOCTeH
CKaHHpOBaHHSI 60JIbllIee Me)K3JIeMeHTHoe paCCTOSIHHe ,l{aeT 60JIee 6bICTpyIO CXO,l{H-
MOCTb.
TaIOKe HCnOJIb30BaJIC5.I pa3pa6oTaHHbIH B [34] MeTO,l{ C}'MMHpOBaHIDI B cneKT-
paJIbHOH 06JIaCTH, QTO ynpoaeT HCnOJIb30BaHHe MeTO,l{a MOMeHTOB ,l])UI nepHO,l{Hqe-
CKHX CTpyKTyp. B3aHMHbIH HMne,l{aHC 3anHCbIBaeTCSI KaK cneIcrpaJIbHOe CYMMHpOBa-
HHe (<I>JIOKe) no BOJIHOBOMY qHC.ny, r,l{e BOJIHOBOe qHCJIO BKJIlOqaeT paCCTOSIHHe
Me)l{J{y 3JIeMeHTaMH. ,[lrr5.1 pemeTKH, cKaHHpyIOeH B H-IIJIOCKOCTH, CYMMHpOBaHHe
CO,l{ep:>KHT <PYHKUHH XaHKeJUI H o606eHHbIe MHOlKHTeJIH ,l{HarpaMMbI:
Zi = ?O Lp2 expUkxou)H2)(k  (a2 + y)O -u 2 »
d sln 2 kh
(8.6)
npH
p - coskhu -coskh . u = sin8 0 .
- k .J l-u 2 '
(8.7)

8.2. XapalcmepUCmuKu CKaHupo8aHUfl ManbIX pewemOK 
,LJ;JIH 3Toro c.rryqaR H-IIJIOCKOCTH 401 qJIeH ,Z:(aeT TOqHOCTb BbIqHCJIeHHR B3aHM-
Horo HMne,Z:(aHca, paBH)'IO 0,01 OM. DOnbllIee Me)l{3neMeHTHOe paCCTORHHe Tpe6yeT
60JIbllIerO KOJIHqeCTBa qneHOB.
Cyn..I:eCTByeT 3HaqHTeJIbHOe OTJIHqHe napaJIJIeJIbHOrO cnyqaR (llJIOCKOCTb E) OT
KOJIJIHHeapHOrO C.rryqaR: <PYHKl(IDI XaHKenH Tenepb HaXO,Z:(HTCH BH)'TpH 0606:rn:eH-
HOH HHTerpaJIbHOM ,Z:(HarpaMMHOM <PYHKIJ;HH, KaK nOKa3aHO B [39, 40], H HHTerpaJI
He MO:>KeT 6bITb npOHHTerpHpOBaH B 3aMKHYTOM <popMe. <I>opMYJIa C onyn..I:eHHbIMH
no,Z:(po6HOCTSlMH ee BbIBo,Z:(a cne,Z:()'IOIUaR:
h
Zj=- 02 LexpUkxou)fsin[k(h-lyl)]x
d x sm kh -h
x H2) (k  a2 + (y + Yo - h)2 .J l - u 2 )dy.
ECJIH d x He ,Z:(onYCKaeT ,Z:(H<ppaKIJ;HOHHOro JIeneCTKa, apryMeHT Hci 2 ) RBJIReTCSI
MHHMbIM, 3a HCKJIIOqeHHeM cnyqaH n = 0; HJ2) 3aMeHReTCH Ha (2/:rr)K o (arg). qHC-
neHHoe HHTerpHpOBaHHe 6bIJIO npHMeHeHO ,L(JIH BbIqHCJIeHHR KIDK.IJ;OrO qJIeHa BbI-
llIenpHBe,[(eHHoro pHlIa. ,LJ;JIR Yo > 1 6bIJIa HCnOJIb30BaHa CJIO)l{}{aR 32-TOqeqHaR <t>op-
MYJIa faycca H 128-ToqeqHaR <poPMYJIa ,L(JIR 60nee 6JIH3KHX HHTepBaJIOB B [44].
OTJIHqHaR CXO,Z:(HMOCTb 6blJIa ,Z:(OCTHrHYTa C yqeToM 501 qJIeHa, HO B pe3YJIbTaTe no-
JIyqHJIaCb Me,L(JIeHHaR nporpaMMa.
TIpH COOTBeTCTB)'IOIUeM BbI60pe npe,[(eJIOB KaK CneKTpaJIbHOrO, TaK H npo-
CTpaHCTBeHHoro C)'MMHpOBaHHR KpHBbIe uMneiJaHca CKaHup08aHUJl B paMKax 3THX
,[(BYX MeTO,[(OB COBnan:aJIH. B I.(eJIOM, CneKTpaJIbHOe C)'MMHpOBaHHe 6bIJIO Me,[(JIeH-
Hee H MeHee Y,Z:(OBJIeTBOpHTeJIbHbIM. Pe3YJIbTaTbI npHBe,Z:(eHbI B pa3,[(eJIe 8.3.1.
(8.8)
8.2. XapaKTepMCTMKM CKaHMpOBaHMR ManblX peweTOK
I1cnoJIb3YSI HMneaHCHbIH MaTpHqHbIH no,[(xo,Z:(, B [11] paCCqHTaHbI uMneiJaHc
CKaHup08aHUJl (H3MeHeHHe HMne,Z:(aHca 3JIeMeHTa npH cKaHHpoBaHHH) H iJua2paMMa
CKaHup08aHUJl 3JleMeHma (3aBHcHMoCTb K03<P<PHUHeHTa YCHneHHH 3JIeMeHTa AP OT
yrna cKaHHpoBaHHH) MR pSl,na MaJIbIX pellieTOK ,Z:(HnOJIeM. Ha pHC. 8.10 nOKa3aHO
aKTHBHoe conpOTHBJIeHHe B 3aBHCHMOCTH OT yrJIa CKaHHpOBaHHR MH ueHTpaJIbHO-
ro 3JIeMeHTa pellIeTKH H3 nonYBOJIHOBbIX HnOJIeM pa3MepOM 7 x 9 C KBa,u.paTHoH
SlqeMKOH A/2 BMeCTe C pe3ynbTaTaMH ,L(JIR 6eCKOHeqHOM pellIeTKH, KOTopaR nOKa3a-
Ha IlITpHXOBOH JIHHHeM MH cpaBHeHHR. Ha pHC. 8.11 Ta )l{e caMaSl pellIeTKa Haxo-
,Z:(HTCR Ha,u. 3KpaHOM Ha BbICOTe A/4. 3KpaH CHHMaeT BbICOKHe 3HaqeHHR conpOTHB-
JIeHIDI B H-nJIOCKOCTH H ,l(HarOHaJIbHOH llJIOCKOCTH. XapaKTepHcTHKH He6oJIbllIOH
pellIeTKH OTJIHqalOTCH KOJIe6aHHRMH OTHOCHTeJIbHO 3HaqeHHH 60JIbllIOH pellIeTKH.
AHaJIOrHqHble OCUHJIJIHUHH HMelOT MeCTO H npH BbPIHCJIeHHH peaKmU8H020 conpo-
mU8JleHUJl npu CKaHup08aHUU y He60JIbIlIHX pellieTOK. Bo06:rn:e, KaK MO:>KHO O:>KH,naTb,
KpynHbIe pellieTIGI HMelOT 60nbIlIe OCUHJLnRUHH, HO MeHbllI}'IO aMnnHT)',UY.
, ,l(ua2paMMbl Hanpa8JleHHOCmu 3JleMeHm08 P npeCTaBJIRIOT HHTepec ,[(JIR He6oJIb-
llIHX pellIeTOK, TaK KaK B ,UaHHOM cnyqae He npe,UCTaBJIReTCH npaBOMepHbIM YMHO-
:>KaTb MHO)l(J1Tenb pellIeTKH Ha O,l(HY ,l(HarpaMMY 3neMeHTa ,l(JUI no.rryqeHHSI 06:rn:eH
,l(HarpaMMbI HanpaBJIeHHOCTH perneTIGI. Ha pRC. 8.12 nOKa3aHbI paCCqHTaHHbIe H H3-
MepeHHbIe SEP-,nHarpaMMbI ueHTpaJIbHOrO ,l(HnOnR B pellIeTKe 5 x 5 nOJIyBOJIHOBbIX

 DW8a 8. KOHeHble aHmeHHble pewemKU
200 200
80
---
"
H ,
,
\
\
\
160
80
160
120
120
R
R
40 40
7 x 9 7 x 9
---- EeCKOHeQHag AP ""
...... --- EeCKOHeQHIDI AP
......
.......
0 0
0 30 60 90 0 20 40 60 80
e 8
PHc.8.10.AKTHBHoe COnpOTHBlleHHe ueH-
TpaJIbHOrO 3lleMeHTa nOllYBOllHOBOM ,QH-
nOllbHOM perneTKH npH CKaHHpOBaHHH [11]
PHC. 8.11. AKTHBHoe conpOTHBlleHHe ueH-
TPaJIbHOrO 3lleMeHTa nOnyBOnHOBOH ,QH-
nonbHOH perneTKH C 3KpaHOM npH CKaHH-
pOBaHHH [11]
OTHOCI1TeJIbHaH
MOIIIHOCTb (.nE)
20
E-nJIOCKOCTb
113MepeHHaH
10
30'-
oe
30.
60-
90.
10
OTHOCI1TeJIbHaH
MOm;HOCTb (.nE)
20
H - TIJIOCKOCTb
90. 60. 30- O. 30. 60. 90-
PHC. 8.12. ,LJ;HarpaMMbI CKaHHpOBaHHR ueHl'paJIbHOrO 3neMeHTa perneTKH H3 5 x 5
,QHIIolleH C 3KpaHOM

8.2. XapaKmepucmuKu CKaHup06aHUR MllIlblX peUJemoK 
u.. '-' u
LU1TIOJIelI C nOJIyBOJIHOBhIM paccToHHlIeM II qeTBepThBOJIHOBOI1 BhICOTOlI HaLI: 3Kpa-
HOM. 3aMeTHo pacllIlIpeHlIe 11 ynnOIIJ;eHlIe L{lIarpaMMbI B E-IIJIOCKOCTlI. Ha plIC. 8.13
II 8.14 lI306pa)KeHhI S EP - .IIlIarpaMMbI u:eH1paJIbHOrO 3JIeMeHTa pemeTKH 7 x 9 L{lITIO-
JIeM ,WUl pa3JIlIQHbIX Me)K3JIeMeHTHblX paCCT05lHlIM. M3 3THX KpHBbIX OqeBJUJ:HO, QTO
SEP-.IIHarpaMMa orpaHHQHBaeT L{Hana30H yrJIOB CKaHHpOBaHlIH. ITo Mepe L{06aBJIe-
HHH 60JIhrnerO KOJIHQeCTBa 3JIeMeHTOB K perneTKe KOJIHQeCTBO KOJIe6aHHM B L{Ha-
rpaMMe yBeJIMQHBaeTCH M KpMBhle CTaHOB5ITC5I 60JIee ITJIaBHbIMH. TaIOKe cna.n. CTaHO-
BHTCH 60JIee KpyrbIM. Ha pHC. 8.15 H 8.16 cpaBHHBaIOTC5I SEP-.IIHarpaMMbI
 1130JUIpOBaHHbIH ,[(HTIOJIb
C .lI)IHHOH A/2 . .
.
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.
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.
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. .
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20
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PRC. 8.13. L{l1arpaMMhI CKaHlipOBaHIiR B H-nJIOCKOCTH ueH1'paJIhHOrO 3JIeMeHTa
LI:I1ITOJIhHOM perneTKH 7 x 9 [11]
to
---
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D:I1ITOJIhHOM perneTKH 7 x 9 HaLI: 3KpaHOM [11]

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,D;HIIOJIei1: C 3KpaHOM [11]
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.LJ:HIIOJIei1: C 3KpaHOM [11]

8.2. XapaKmepucmw<-u CKaHupoeaHUR Ml1JlblX pewemOK 
....
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MeTpllll, H yrJIOBOrO 3JIeMeHTa perneTKH 113 9 x 11 ,aMrrOJIen. LJ:lIR yrlIOBbIX 3neMeHTOB
He Ha61I1O,aaeTCR CHMMe1pHR 3<P<l>eKTOB B3aMMHOH CBH3ll, KOTOpa5.1 rrpMBo,aHT K BbI-
paBHllBaHMIO SEP-,allarpaMMbI. ECJIH MeCTa ,aOCTaTOqHO, MOryr 6bITb ,ao6aBlIeHbI
naCCHBHbIe 3JIeMeHTbI Ha KpaRX perneTKH, qTo6bI y.rryqrnllTb xapaKTepHCTMKH CKaHM-
pOBaHHR.
I1HTepeCHbIH rrpMMep KpaeBbIX 3<P<l>eKTOB B JIHHeMHOM perneTKe n:aH B [14] lIJIR
nOJIyBOJIHOBbIX ,aHIIOJIeM C 3KpaHOM H 6e3 3KpaHa. MeX3JIeMeHTHoe paCCTORHl1e co-
CTaBlliIeT 0,586A, QTO o6eCrreQHBaeT e,aBa BH,IJ;llMbIM ,aH<ppaKIJ:llOHHbIM JIelIeCTOK Ha
e = 90° IIPH CKaHHpOBaHMH Ha yrOJI 45°; opHeHTaUIDI ,aHrrOJIeM RBlliIeTCR KaK naparr-
JIeJIbHOH, TaK M KOJIJIHHeapHoM. IJ;eHTparrbHbIH 3JIeMeHT cornaCOBaH,WIR yrJIa CKaHM-
pOBaHIDI 0°, npH 3TOM BO Bcex 3JIeMeHTax rrpMMeHeHa o,aHa M Ta )l(e cxeMa corJIaco-
BaHIDI. PerneTKa COCTOMT H3 51 3JIeMeHTa, a paCCTORHMe ,ao 3KpaHa paBHO 0,25 A.
KOJIJIMHeapHbIe perneTKM Be,ayr ce6R xoporno ,JIaxe B 06JIaCTH ,aH<ppaKIIMoHHoro JIe-
neCTKa; rraparrJIeJIbHble perneTKlf Be,JIyr ce6R HeCKOJIbKO X)')Ke ,ao 06JIaCTH ,aHcPpaK-
UHOHHoro JIerreCTKa, a B caMOH 06JIaCTH OTMeQarrCR 3aMeTHbIH KpaeBoH 3cPcPeKT, B
oco6eHHOCTH,WIR perneTKH 6e3 3KpaHa. Ha pHC. 8.17 M 8.18 rrOKa3aH MMne,aaHC 3JIe-
",
3
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16
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56
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104
120
PHC. 8.17. I1Mne.aaHc 3JIeMeHTOB JIM-
HeMHOM perneTKM napaJIJIeJIbHbIX .aM-
nOJIeR .aJI5I pa3JIMQHbIX yrJIOB CKaHH-
pOBaHM5I [14]
PHC. 8.18. I1Mne.aaHc 3JIeMeHTOB JIMHeMHOM pe-
rneTKM napaJIJIeJIbHbIX .aHnOJIeM C 3KpaHOM .aJIR
pa3JIMQHbIX yrJIOB CKaHMpOBaHI1R [14]

 TJ/a6a 8. KOHe'lHf>le aHmeHHble peUlemKU
MeHTOB C pa3JIHqHbIM HOMepoM, C 3KpaHoM H 6e3 3KpaHa, L(lliI yrJIOB cKaHHpoBaHHfI
0, 40, H 45° L(lliI napaJIJIeJIbHbIX ,LIJlnOJIew. OKa3bIBaeTcR, qTO KpaeBbIe 3neMeHTbI,
pacnOJIO)l(eHHbIe B HanpaBJIeHHH CKaHHpOBaHHfI, nO,lI;BepralOTCR 60JIbllIeM)' BJIHflHHIO
no cpaBHeHHIO C KpaeBbIMM 3JIeMeHTaMH, JIe)KaIUMMM B 06paTHoM HanpaBJIeHHI1. On:-
HaKO KCBH nOCJIe,UHHX 3JIeMeHTOB BbIllIe, TaK KaK ,lI;H<ppaMoHHbIM JIeneCTOK pac-
nOJIO)KeH B 3TOM HanpaBJIeHMM. TIpM6JIIDKeHHOe Ta6YJIMpOBaHHe QMCJIa KpaeBbIX 3JIe-
v
MeRTOB, MMnen:aHC KOTOpbIX Raxo.aMTCfI 3a npe.aeJIaMM I(eH1'paJIbHOM rpynnbI,
OTpa)KeHO B Ta6JI. 8.1. He CJIe.ayeT npe,nnOJlaraTb, QTO 3TM pe3YJIbTaTbI OTHOCflTCR K
IIJIOCKH1 perneTKaM, HO 3HaHHe TeH,neHI(HH ,lI;OJDKHO 6bITb nOJIe3HO.
LIJUI TEM-pynOpHbIX pellieTOK .aOKa3aHO, QTO pa3Mep pellieTOK .aOIDKeH COCTaB-
JIHTb, no KpaMHeM Mepe, 5A x 5A ,UJI.H MHHHMH3aI(HH KpaeBbIX 3<p<peKTOB [23].
Ta6J1HQa 8.1. qHCJIO «KpaeBbIX 3JIeMeHTOB». ,n;M<ppaMoHHhIH JIeneCTOK nOHBJI5IeTCH
npM CKaHMpOBaHHH Ha 45°
)J,IfllQJIH npOTHBOBCC (3KpaH) HanpaBJICHHC CKaHHpOBaHIDI 06paTHoe HanpaBJICHHC
TIapaJIJIeJIbHble HeT 1-5-30 1-2-3
napaJIJIeJIbHbIe ,[(a 1-3-6 1-2-3
KOJIJIlfHeapHbIe HeT 1-2-2 1-]-1
KOJUIHHeapHble JJ:a 1-1-2 1-1-2
8.3. MOAenb rM66ca KOHe"lHO-6eCKOHe"lHOM peweTKM
8.3.1. Oco6eHHocTM nOBeAeHMR MMneAaHca
npM CKaHMpOBaHMM
I;
Mon:eJIM KOHeQHO-6eCKOHeQHOM perneTKH, onMcaHHbIe B pa3,UeJle 8.1.2, 6bIJII1 MC-
nOJIb30BaHW ,l(JIR paCqeTa uMneoaHca 3JIeMeHTOB pellleTKH npu CKaHup06aHUU n:JIH
HeCKOJIbKMX pellieTOK - OT 60JlbIIIHX .ao MaJIbIX. Pe3ynbTaTbI npll CKaHHpOBaHHM
B H-nJIOCKOCTM ,nJIfI pellieTOK, COCTORI.U;HX H3 201 nHHeMKJf pe30HaHCHbIX n:Mno-
JIe", nOKa3aHbI CnJIOIIIHbIMM nHHl1RMM Ha pMC. 8.19-8.21. YrJIbI CKaHHpOBaHHfI
CJIe,UyIOIUlle: 0, 45 II 60°. KpMBbIe, nOKa3aHHbIe nyJIKTHpHOM nHHMeM, COOTBeTCT-
BYIOT Mon:eJIH fH66ca, paccMaTpHBaeMoH HH)Ke. ,lJ;JIHHa n:MlloneM perynHpOBaJIaCb
LUISI nOJIyqeHHfI pe30HaHCHoro 3HaQeHllR HMne,lI;aHCa B 6eCKOHeqHOM peIIIeTKe C
IIOnepeQHbIM H3nyqeHHeM. J[QeWKa perneTKH HMena pa3Mep A/2 x A/2, a pa.aHYCbI
LU1110JIeM COCTaBnRnH 0,005A [19]. 3HaQeHHR uMneoaHca HOpMHpOBaHbI K 3HaqeHH-
HM B 6eCKOHeQHOM peIIIeTKe npH Ka)I()XOM yrne CKaHMpOBaHHH. JIHHeHKH npOHY-
MepOBaHbI OT 1 ,QO 201, Haql1Hafl OT KpaR, npM 3TOM Jlyq HanpaBJleH B CTOPOHY
3JIeMeHTa 1. Ha 3TMX pl1CyJIKax IIOKa3aHbI HenpepbIBHbIe KpHBbIe, HO 06paTHTe
BHllMaHHe Ha TO, QTO OHM 6bIJlII nOCTpoeHbI Ha OCHOBe 201 TOQKH. Ha pHC. 8.19
ll306pa)l(eHa TOJIbKO nOJIOBllHa pellleTKH; npH rrOnepeQHOM H3JIyqeHllH KpHBbIe
CI1MMeTplf4HbI.
Ha pHC. 8.22 II 8.23 H306pa)KeHbI 3aBHCI1MOCTM uMneoaHca 3JleMeHm06
npu CKaHupoeaHUU B MeHbIIleM peIIleTKe, COCTORI.U;eti 113 51 nHHeHKI1, n:JIfI yrJIOB

8.3. MOOeJlb ru66ca lCoHe'tHo-6eclCoHe'tHou pememlCu d
1.2
1.1
8
N
""'"
N
(OJ
 1
E-4
::s::
a

0.9 -
0.8
1
11
21
31
41 51 61
HOMep 3JIeMeHTa
71
81
91
101
PHC. 8.19. PemeTKa H3 201 JIHHeHKH pe30HaHCHbIX .l1HIIOJIei1 (MO.l1eJIb KOHeQHO-
6eCKOHeQHOH pemeTKH), CKaHHpOBaHl1e B H-IIJIOCKOCTH .l1JUI 0°
1.2
1.1
8
N
""'"
N
(OJ


::s::
r:;
t::

<:
1
.... ". .. -.
0.9
0.8
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201
HOMep 3JIeMeHTa
PHC. 8.20. PemeTKa 113 201 JIHHeHKH pe30HaHCHbIX .l1HIIOJIeH (MO.l1eJIb KOHeQHO-
6eCKOHeQHOH pemeTKH), CKaHHpOBaHHe B H-IIJIOCKOCTH .l11UI 45°


fflaea 8. KOHeltHbie aHmeHHble pewemKU
1.2
1.1 -
B
N
............
N

 1
Eo-
::s:

t:::

0.9 -
0.8
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201
HOMep 3J1eMeHTa
PHC. 8.21. PerneTKa H3 201 JIHHeHKH pe30HaHCHbIX .n;HllOJIeH (Mo.neJIb KOHeqHO-
6eCKOHeQHOH perneTKH), CKaHHpOBaHHe B H-TIJIOCKOCTH ,lLJUI 60 0
1.2.
1.1
8
N
............
N

 1
Eo-
:s:
r=:
t::

0.9 -
0.8
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
HOMep 3J1eMeHTa
PHC. 8.22. PerneTKa H3 51 JIHHeHKH pe30HaHCHhIX .nHTIOJIeH (Mo.neJIb KOHeQHO-
6eCKOHeQHOH perneTKH), CKaHHpOBaHHe B H-nnOCKOCTH .aJUI 0 0

8.3. MOOeJlb Iu66ca KOHe'tHo-6ecKoHe'tHou pewemKU 
1.2
1.1
B :
.,
N .,
...........
N : ;
; :

 1

:s:
r:::
t::

0.9
0.8
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
HOMep 3JIeMeHTa
PHC. 8.23. PerneTKa H3 51 JIHHeMKH pe30HaHCHbIX ,nHllOJIeii (Mo.n;eJIb KOHeQHO-
6eCKOHeQHOH perneTKH), CKaHHpOBaHHe B H-llJIOCKOCTH ,lLJUI 60°
1.2 :
1.1
B
N
...........
N

 1
:s:
a

0.9 -
0.8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
HOMep 3JIeMeHTa
PHC. 8.24. PerneTKa H3 21 JIHHeHKH pe30HaHCHbIX .n;HllOJIeH (Mo.n:eJIb KOHeQHO-
6eCKOHeQHOH perneTKH), CKaHHpOBaHHe B H-llJIOCKOCTH ,lLJHI 0°

 Dla6a 8. KOHe'lHble aHmeHHble pelUemKu
CKaHI1pOBaHI15I 0 11 60°. Ha pl1C. 8.24 nOKa3aH uMneoanc JIJI5I perneTKM H3 21 JII1-
HeHKI1, 113JIyqalOIUeti no HOpMaJIl1. 06paTI1Te BHHMaHHe Ha TO, qTO Y MaJIbIX pe-
rneTOK ,n:l1arpaMMa TaKa5I )l(e, KaK 11 y 60JIbrnl1x. OCUl1illIRUHH uMneoanca 3HaqH-
TeJIbHO MeHbrne B ueHTpe perneTKH npl1 HOpMaJIbHOM H3JIyqeHHH H CTaHOBRTCR
60JIbrne no Mepe YBeJIHqeHH5I yrJIa cKaHHpOBaHH5I. 3HaqeHHR Ha KpaRx 60JIbIIIe
.LLJIR Bcex yrJIOB cKaHHpOBaHI15I, KaK npaBHJIO, Ha 20%.
3TH pe3YJIbTaTbI ,[(JIR ,n:l1nOJIbHbIX perneTOK HanpRMyIO npHMeHHMbI K IUeJIeBbIM
perneTKaM Ha MeTaJIJIl1qeCKOM 3KpaHe B CRJIY rrpHHUHna ,n:BOHCTBeHHOCTI1 Ea611He.
LLrrR IUeJIeM B BOJIHOBO,n:HOM CTeHKe K npOBo,n:I1MOCTI1 IUeJIH lIOJI)l(Ha 6bITb 1I06aBJIe-
Ha BHyTpeHHIDI peaKTHBHaR npOBo,n:HMOCTb.
Pl1c. 8.25-8.27 OTHOCRTC5I K TOM xe caMOM perneTKe 113 201 JIHHeHKH, HO pac-
nOJIO)KeHHoti Ha,[( 3KpaHOM Ha BbICOTe "-/4. OnRTb-TaKH .LLJII1Ha ,n:l1nOJIeH oTperyJII1-
pOBaHa ,[(0 ,[(OCTIDKeHI1R pe30HaHca B 6eCKOHeQHOM nOnepeQHO 113JIyqalOII.J.eH pe-
rneTKe. Ha 3TI1X rpa<pHKax OCUHJIJIRUI1H 3aTYXalOT 6bIcTpee B HanpaBJIeHI1H ueHTpa
perneTKH, XOT5I KpaeBbIe 3HaQeHI1R Bce ern:e 60JIbrnHe. ,[(JIR He60JIbrnHX perneTOK H3
51 11 21 JIHHeeK pe3YJIbTaTbI ,l(JIR HOpMaJIbHOrO H3JIyqeHHR npHBe,[(eHbI Ha pHC. 8.28
H 8.29. 3,n:ecb CHOBa aHaJIH3HpyeTcR ,n:HarpaMMa 201-3JIeMeHTHoti perneTKH.
1.2
1.1
8
N
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 1 i\;"A'
 Vvv y
t:::
t::

0.9
0.8 1
.
,
I
,
11
21
31
41 51 61
HOMep 3JIeMeHTa
71
81
91
101
PRC. 8.25. PerneTKa H3 201 nHHetiKH pe30HaHCHbIX ,n:Hnoneti Ha,n: 3KpaHOM (Mo,n;eJIh
KOHeQHO-6eCKOHeQHoti perneTKH), CKaHHpOBaHHe B H-nnocKocTH ,n;JIII 0°
Ha OCHOBaHHll 3THX KpHBbIX CTaHOBRTCR OQeBll,[(HbIMH HeCKOJIbKO MOMeHTOB.
Bo- nepBbIx, nceB,[(OCT05IQa51 BOJIHa B 3HaQeHHRX uMneoanca cKanupOeanuJl cyruecT-
ByeT Ha anepType perneTKlf ,[(a)l(e .LJ:JIR nOnepeQHOrO H3JIyqeHIDI. Bo- BTOpbIX, nepHo.n:
nceB,n:ocTORQeH BOJIHbI 5IBJIReTCR <PYHKIJ;Heil yrJIa cKaHHpOBaHH5I, QTO H MO)KHO
6bIJIO O)I(M,[(aTb. 11 B-TpeTbHx, ,L(Be nceB,n:06eryI.I.J:He BOJIHbI, 06pa3yIOIUHe C060R
nceB,n:ocToRqyJO BOJIHY, 3aTyxaIOT C paCCTORHl1eM OT cooTBeTcTByIOIUHX KpaeB.

8.3. MoiJeJlb Fu66ca KOHe'tHo-6eCKOHe'tHOU pewemKU 
1.2
, . .
1.1
8
N
............
N

 1

::s::

t::

0.9 -
0.8
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201
HOMep 3JIeMeHTa
Puc. 8.26. PerneTKa 113 201 JIHHeHKI1 pe30HaHCHbIX .nHllOJIeH Ha,n 3KpaHOM (Mo.neJIb
KOHeQHO-6eCKOHeQHOH perneTKw), CKaHHpOBaHl1e B H-IIJIOCKOCTH
.LUISI 45 0
1.2
1.1 .
8
N
............
N



::s::

t::

1
0.9
0.8
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201
HOMep 3JIeMeHTa
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KOHeQHO-6eCKOHeQHOH perneTKH), CKaHHpOBaHHe B H-nrrocKocTH
.LUUI 60 0

r.b
rJlG6G 8. KOHer.tHble GHmeHHble pewemKU
1.2
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.
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1.1
8
N
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N
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:s::

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...
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0.9   ..I
0.8
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
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KOHeQHO-6eCKOHeQHOH perneTKI1), CKaHl1pOBaHl1e B H-llJIOCKOCTI1 ,l(JlSI 0°
1.2
1.1
8
N
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 1
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:s::
t::::
t::

<:
0.9 -
0.8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
HOMep 3neMeHTa
. PUC. 8.29. PerneTKa 113 21 HHeHIGI pe30HaHCHbIX .nl1nOneH H3,[( 3KpaHOM (Mo.nenb
KOHeQHO-6eCKOHeQHOH perneTIrn), CKaHHpOBaHHe B H-llJIOCKOCTI1 M.H. 0°
- . . :. 1:. .

8.3. MoiJenb ru66ca lWHe'lHO-6eCKOHe'tHOU peUJemKU d
ITepHO,n: Ha anepTYpe perneTKH HBJIHeTCH rrOqTH rrOCTOHHHbIM H orrpe,n:eJIBeTCB
CJIe.n}'IOIUeH rrpH6nIDKeHHoH <l>OPMYJIOH
05
TIepHo.n = ' (B .n.rrHHax BOJIHbI),
1- sine o
f.ne eo - yrOJI CKaHHpOBaHHB OT HOpMaJIH. 3TOT pe3YJIbTaT MoxeT HHTeprrpeTHpo-
BaTbCB rro,n:06HO <l>opMyne .n.rrB ,n:H<l>paKUHoHHoro nerreCTKa OT ,n:BYX rrceB,n:OBOJIH,
f.ne o.nHa CBB3aHa C yrJIOM CKaHHpOBaHHR, a BTopaH H.D:eT B,n:OJIb perneTKH B HarrpaB-
JIeHHH KpaR.
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8. 1 pe3YJIbTaTbI ,l.UUI perneTKH H3 201 JIHHeHKH rrapaJIJIeJIbHbIX ,n:HrrOJIeH CHOBa C
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JIHpOBaJIaCb ,n:o pe30HaHCHbIX 3HaqeHHH B 6eCKOHeqHOH pemeTKe. Terrepb 3aT}'Xa-
HHe OCI.{HJIJIRI.{HH OT KpaH K ueHTpy Me,lLJIeHHee. B l.{eJIOM, pa3Max 60JIbme, qeM .lVIB
CKaHHpOBaHHR B H-WIOCKOCTH. ITpH HOpMaJIbHOM H3nyqeHHH 3HaqeHHe Ha KpalO
npH CKaHHpOBaHHH B E-IIJIOCKOCTH HIDKe, B TO BpeMB KaK ,lLJIR H-IIJIOCKOCTH OHO
BbIwe e.nHHHUbI; OTKJIOHeHIDI RBJIRIOTCR conOCTaBHMbIMH [20]. Ha pHC. 8.32 npH-
Be.neHbI ,n:aHHbIe .lVIR 51-3JIeMeHTHoH pemeTKH npH HYJIeBOM CKaHHpOBaHHH.
(8.9)
1.2
1.1 .
B
N

=
 1
E-o
:s:
a

0.9
- 0.8
. 1
11
21
31
41 51 61
HOMep 3JIeMeHTa
71
81
91
101
PRC. 8.30. PerneTKa H3 201 JIHHeHKH pe30HaHCHbIX .n;HnOJIeH (Mo.n;eJIb KOHetJHo-6ec-
KOHetJHOH perneTKH), CKaHHpOBaHHe B E-nJIOCKOCTH ,WUI 0°
KOf.na ,n:06aBJUleTCR 3KpaH, npH cKaHHpoBaHHH B E-IIJIOCKOCTH, 06Hap}')KHBaeTCR
HOBoe BBJIeHHe. ITpH HOpMaJIbHOM H3JIyqeHHH O)l(Jf,1J;aeMbIe nOJIyBOJIHOBbIe rrpo-
c1])aHcTBeHHbIe OCI.{HJl.IDIUHH MO,n:YJIHPYIOTCR KOJIe6aHHeM 60JIbrnerO rrepHo.na, Ha-
nOMHHalOIUHM reTepo,n:HHHbIH npouecc. PHC. 8.33 OTHOCHTCR K pemeTKe H3 201 JIH-
HeHKH pe30HaHCHbIX ,n:HrrOJIeH C .D:JIHHOH 0,484IA, panHYCOM 0,005A, BbICOTOH
Han; 3KpaHOM O,25A H pa3MepOM HqeHKH A/2 x A/2. llpe,n:bmymHe HCCJIe,n:OBaHIDI

b
FADea 8. KOHe'tHble aHmeHHble pezuemKU
1.2
1.1
B
N
.............
N
co
 1

:s:
a
 :
:
0.9
. .
. .
, '
.'
0.8
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201
HOMep 3JIeMeHTa
Pac. 8.31. PemeTKa H3 201 JIHHeihrn pe30HaHCHbIX ,lUIIIOJIeH (Mo.n:eJIb KOHeqHO-
6eCKOHeQHOH pemeTKH), CKaHHpOBaHHe B E-nnOCKOCTH ,lLJUI 60°
1.2
1.1
B
N
.............
N :
:
co
 1

::s::
t::::
t:::

0.9
0.8
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
HOMep 3JIeMeHTa
Pac. 8.32. PerneTKa H3 51 JIHHeHKH pe30HaHCHbIX .nHTIOJIeH (Mo.neJIb KOHeQHO-
6eCKOHeQHOH perneTKH), CKaHHpOBaHHe B E-TIJIOCKOCTH .nJUI 0°
-

8.3. MOOeAb fu66ca 1CoHe'tlw-6ec1CoHe'lHou pezuem1CU d
1.4 '
1.2
8
N
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0.6 : ::
1
11
21
31
71
81
91
101
41 51 61
HOMep 3JIeMeHTa
PUC. 8.33. PerneTKa H3 201 JIHHeMKH pe30HaHCHbIX ,DJIITOJIeH Ha,a 3KpaHOM (Mon:eJIb
KOHeQHO-6eCKOHeQHOM perneTKH), CKaHHpOBaHHe B E-nJIOCKOCTH .D.JIH 0°
CKaHMpOBaHH5I B H-IIJIOCKOCTH ,1])I5I ,aHIIoneH H ,l(HrrOneH H3,[( 3KpaHoM, a TaIOKe B
E-IIJIOCKOCTH .lUUI ,aHrroneH He BbI5IBHnO 3HaQHTenbHoro H3MeHeHlUI 3aBHCHMOCTeH
OT p3J(H)'ca ,aHrronR, rrOKa OH OCTaBaJIC5I MaJIbIM. B cnyqae C E-rrnocKocTblO, a TaK-
OJ
)l(e B cnyqae ,aHIIoneH Ha;:J; 3KpaHOM, rrpHao,aHMOM 3,[(eCb, Pau.Hyc BJIlUIeT Ha rrepHO,Q
MO,[(YJI5IUHH. ;J;orrycKa51 reTepO,lJ;HHHbIH rrpouecc C pa60QeH «pa3HocTHOH qaCToToH»,
rrepHO,a P BbIpIDKaeTCR rrpOCTO KaK 1/ P = 1/ PI - 1/ P 2 , r,ae PI - OCHOBHOH nepHO,a
HMne,lJ;aHCa B ,1])IHHaX BonH (HyneBoe CKaHHpOBaHHe), a P2 - 3TO P b MO,[(H<l>HUHpO-
BaHHbIH K03<l>cl>HUHeHTOM P 2 = PI (1 + ). Ha pHC. 8.34 nOKa3aH napaMe1p  )J)UI
rrRTH P3,[(HYCOB OT 0,001')....,lJ;0 0,02').... [22]. 3TO nHHeHHO-JIOrapH<l>MWIecKoe COOTHorne-
HHe, 06ycnoBneHHoe H3MeHeHHeM B3aHMHbIX HMne,aaHCOB npH H3MeHeHHH paaH)'ca,
rrOJIHOCTblO BbIpIDKaeTCR Qepe3 06pameHIfYIO Mal'pHIJy HMne,l(aHCOB. nOQeMY 3TO rrpo-
RBlliIeTCR TOJIbKO B E-nrrocKocTH )J)UI ,lJ;HnOneH C 3KpaHOM, OCTaeTCR HeH3BeCTHbIM.
B03HHKaeT OqeBH,[(HbIH Borrpoc: KaK 3TO RBneHHe H3MeHReTCR B 3aBHCHMOCTH
OT yrna cKaHHpoBaHHR? TIpH 30° Mo.nynRUHR He npORBnReTCR. TIpH 15° MO.nyJIRUHR
npHcyrcTByeT, HO J(HarpaMMa OCTaeTCR HeRCHoit 3TO HOBoe SlBJIeHHe npe,aCTaBJIReT
C060H BbI30B B Mo,aenHpOBaHHH perneTOK.
B 6eCKOHeQHOH perneTKe H3 nOJIyBonHOBbIX ,aHnOJIeM C Me)l(3JIeMeHTHbIM paCCTO-
RHHeM, ,lJ;OCTaTOqHO 60JIbrnHM )J)UI Toro, qT06bI cym;ecTBOBaJI ,[(H<l>paKUHoHHbIH JIene-
CTOK, nORBJIReTCR yrOJI OCJIerrneHIDI, T.e. conpomU8fleHue U peaKmU8Hocmb npu CKaHU-
poeaHUU CTaHOBRTCH 6eCKOHeQHbIMH (CM. rnaBY 7). YroJI OCJIerrneHlUI COOTBeTcTByeT
yrJIY CKaHHpOBaHIDI, npH KOTOpOM nOHBlliIeTCR ,[(H<l>paKl(HOHHbIH JIeneCTOK. B pe-
3YJIbTaTe aMllJIH1)',Qa K03<l><PHIJ.HeHTa OTpIDKeHHH paBHa e,lJ;HHHue, H MOIUHOCTb He
H3JIyqaeTCR. B03HHKaeT OqeBH,[(HbIH Borrpoc: QTO npOHcxo,nHT C UMneoallCOM B KOHeQ-
HOM perneTKe B 06JIaCTH rnaBHoro neneCTKa? Dbma Hcnonb30BaHa Mo,aenb ,[(Hnonb-
HOM perneTKH B H-llJIOCKOCTH C Me)l(3neMeHTHbIM paCCTOHHHeM 0,5858')...., KOTOpIDI ,[(0-
rrycKaJIa rrORBJIeHHe ,[(H<l>paKUHoHHoro JIerreCTKa npH 45°. Ha pHC. 8.35 nOKa3aHa

b
fllaea 8. KOHellHble anmenHble pelUemlCu
0.06
0.05
0.02
0.01
o
0.005
0.010
a/>..
0.015
0.020
Pac. 8.34. 3aBHCHMOCTb K03<P<PH«HeHTa MO,aYJUI«HH 11 OT pa.nHyca ,aHTIOJUI
1.8
1.6
1.4
...
-
c
(.)
N 1.2
...........
N

 1
:s:

I::
 0.8 -
0.6
0.4
0.2
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201
HOMep 3JIeMeHTa
Pac. 8.35. PemeTKa H3 201 JlHHeHKH pe30HaHcHblx ,aHTIOJleH (Mo,aeJlb KOHe'lHO-
6eCKOHe'lHOH pemeTKH), cKaHHpoBaHHe B H-TIJlOCKOCTH ILJUI 45 0
-

8.3. MOiJeJlb' fu66ca lCoHe'tHo-6eclCoHe'tHoii peUlemlCU  ,:
aMIIJIHTy.n;a uMnedaHca cKaHup08anUJl .n;JIH peIIIeTKH H3 201 JIHHeHKH IIpl1 CKaHHpo-
BaHHH Ha 45°; OHa paBHOMepHO YBeJIHqHBaeTCH OT 3HaqeHHH, 6JIH3KI1X K HYJIIO,
.n;o IIpH6JIH3HTeJIbHO 1,4 C HeCKOJIbKHMH KOJIe6aHHHMH B KOHI.J;e. MeHbIIIHe pe-
rneTKH .neMOHCTpHpyroT aHaJIOrHqHOe rrOBe.n;eHHe, HO C MeHbIIIHMI1 OCI.J;HJIJIH-
I.J;HHMH.
HOpMHpyroII.J;HH MHO)I(HTeJIb, npe.n;cTaBJIHIOII.J;HH C060H 3HaqeHHe I1Mrre.n;aHca
3JIeMeHTa B ueHTPe peIIIeTKH, rrpOHBIDIeT JIOrapH<pMHqecKoe rrOBe.n;eHHe no 06eHM
OCHM B <PYHKI.J;HH qHCJIa 3JIeMeHTOB (pHC. 8.36). MOXHO BH,l(eTb, qTO OqeHb 60JIb-
llIHe perneTKH rrpH6JIIDKalOTCH K yrJIY OCJIeIIJIeHHH C 6eCKOHeqHbIM HMne.n;aHCOM.
Cl>a3a uMnedaHca rrpH6JIH3HTeJIbHO paBHHeTCH 45°.
3000
1000
-

0
--
N /'


:s:

t:: 400

2000
200
100
10
20
40
100
200
300
NEL-1
PHC. 8.36. 3HaqeHHe HMne.n:aHca ueHTparrbHoro 3JIeMeHTa, COOTBeTCTBYIOIUee yrJIY
rrOHBJIeHHH .D:H<ppaKQHoHHOro JIerreCTKa
Ta xe caMaH perneTKa npH .n;pyrHx yrJIax cKaHHpoBaHHH xapaKTepH3yeTcH Tpa-
.n;HU;HOHHbIM IIoBe.n;eHHeM; paBHoMepHbIH xapaKTep uMneiJaHca no perneTKe HMeeT
MeCTO TOJIbKO MH Y3Koro .n;Hana30Ha yrJIOB BOKpyr rJIaBHOrO JIeneCTKa. npl1 n:pyrHX
yrJIax cKaHHpoBaHHH cyw;ecTByeT He3HaqHTeJIbHaH rrOJIYBOJIHOBaH MO.n;YJI$lIJ;J1$1.

 Tlzaea 8. KOHe'tHbLe aHmeHHbLe peUJemKU
8.3.2. MOAenM rM66ca KOHeLlHblX peweToK
Xopomo H3BeCTHO, qTO BOJIHa B Bl1,L(e HMnYJIbCa npHMoyrOJIbHOH cPOpMbI (square
wave) C KOHeqHOH nOJIOCOH HMeeT OCUHJIJIHllJIH, KOTopbIe Ha3bIBalOTCH HBJIeHHeM
fH66ca. TaKHM o6pa30M, npeo6pa30BaHHe <l>YPbe C KOHeqHbIMH npe,neJIaMII OT
sinc-CneKTpa rapMOHHK C03,naeT BOJIHY C TaKHMH OCUHJIJIHI.{HHMH y KpaeB. Pac-
CMOTpeHHe pe3YJIbTaTOB pa3JIllqHbIX paCqeTOB nOKa3bIBaeT, qTO nHKM II npOBaJIbI
KOJIe6aHHH HMelOT peryJIHpHbIe HHTepBaJIbI, II qTO aMnJIHTY,nbI nepBoro, BToporo,
TpeTbero H T.,n. nHKOB He 3aBHCHT OT BepXHeH rpaHHUbI nOJIOCbI. TaK, nepBbIH nllK
BOJIHbI HMeeT MeCTO Ha Ka)l(,[(OM Kpae BOJIHbI B Bl1,L(e npHMoyrOJIbHOrO HMnYJIbCa,
npH 3TOM BTOpOH IIHK RBJIHeTCR CMe)I(HbIM H T.,n. no Mepe Toro. KaK BepXHRR rpa-
HHl.{a IIOJIOCbJ )'BeJIllqHBaeTCR, )'BeJIHqHBaeTCR II o6IUee KOJIHqeCTBO nHKoB, OCTaBa-
HCb npM6JIM3MTeJIbHO paBHbIM BepxHeMY IIpe,n;eJIY, ,neJIeHHoMY Ha j[, H, KOHeqHO,
M3MeHHeTCH HHTepBaJI, HO aMIIJIMTY,l(bI OCTalOTCR TeMH )l(e. B JIHTepaType cO,l(ep-
)l(lfTCR MaJIO ynoMMHaHHH 0 TOM, KaK paCCqHTbIBaTb 3TH IIHKM ,l(JIH BOJIHbI npHMO-
yrOJIbHOH cPOpMbI, HO B [15] npHBo,nRTCR pe3YJIbTaTbI, BbIBe,n:eHHbIe B [5]. OpHrH-
HaJIbHbIH IIpHeM HCnOJIb3yeTcR B nOCJIe,n;HeH pa60Te .LUIR onpe.n:eJIeHHR nOJIO)l(eHHH
3KCTpeMYMOB. KOHeqHbIH PM, npe,nCTaBJIHIOIUMH npHMoyrOJIbHyro BOJIHY, ,nHQ:>Q:>e-
v
peHUHpyeTcR, II npe,l(nOJIaraeTCR, qTO 3Ta cYMMa HMeeT pe3YJIbTaT, BbIpIDKeHHbIH B
3aMKHyroM Bl1,L(e. 113 paBeHCTBa HYJIIO onpe,neJIRIOTCR KOpHH, KOTopble ,l(alOT TOqKH
HaXO)l(,[(eHHR 3KCTpeMyMOB. 3TO m'Jtj2n, r,ne m - 3TO HOMep 3KCTpeMYMa, a n -
3TO BepXHHH npe,n:eJI CYMMIIpOBaHMR. AMIIJIHTY,l(bI B 3THX TOqKaX Bblpa)l(alOTCR B
BH,ne HHTerpana, KOTOpbIH ,l(JIR 60JIbIIIHX n MO)l(eT 6bITb BblpIDKeH B BH,n:e HHTer-
panbHoro cHHyca; pe3YJIbTaT - (2j'Jt)Si(m'Jt). TaK, ,WIH 60JIbllIHX 3HaqeHHH nOJIOCbI
aMIIJIHTY.n:bI nMKOB JIerKO OIIpe,n;eJIHIOTCH II paBHbI 1,1790, 0,9028, 1,0062, 0,9499
If T.,n.
MO)l(HO O)l(H)];aTb, qTO O.n:HHOqHbIH HMnYJIbC C JIHHeHHOH Q:>a30H B 3KcnOHeHTe
6y,n;eT JIyqmHM o6pa30M npe,nCTaBJIRTb CKaHHpyroIUyro KOHeqIfYlO pemeTKY. Anep-
TypHoe pacnpe,n;eJIeHHe ,n:OJDKHO 6bITb CJIe,n;yroIUHM: exp( -jtU sin8 0 ) ,l])lH I t I  1 H
paBHbIM HYJIIO,lLJIR I t I > 1. npe06pa30BaHHe 3Toro anepTYpHoro pacnpe,neJIeHHR
HMeeT cneKTp, KOTOpbIH paBeH [42]
If.!) = Si1ic[<OO - a) ; 1
(8.10)
3,neCb a = U sin 8 0 . 3TOT cneKTp 3aTeM TpaHcQ:>opMHpyeTcR K KOHeqHbIM npe,l(e-
JIaM, qTo6bI IIO.JIyqHTb HMnYJIbC co CKaHHpOBaHHeM C OCURJIJIRUIDIMH fM66ca. npe-
o6pa30BaHHe CJIe,nyroIIJ.ee
If.!) = l.sine [<00 - a) ; }XPUOYt)dW.
(8.11 )

BbIqMCJIeHHe HHTerpaJIa RBJIReTCR CJIO)I(HbIM npoueCCOM H ,naeT .neHcTBHTeJIb-
Hyro qaCTb C HHTerpanbHbIMH cMHycaMM H MHHMyro qaCTb C HHTerparrbHbIMH KOCH-
HycaMH. IIocJIe,nHRR, rJIaBHbIM o6pa30M, npe.n:CTaBJIReT C060H BKJIa,n: .neJIbTao6pa3-
HbIX cPYHKII:HH Ha KpaRX HMnYJIbCa, a nepBaR qaCTb 06YCJIOBJIeHa KOJIe6aHHRMH
-

8.3. MoiJeJlb ru66ca lWHeltHo-6eclCoHe'1II0U peUJemlCU d
aMnJIHTy,n:bI HMnyJIbca. TIocJIe pMa npeo6pa30BaHHH nepeMeHHbIx ,n:eHcTBHTeJIbHaH
qaCTb CTaHOBHTCR paBHoM [21]
1(1) = Si[((J + a) (1 + T)] + Si[((J -a) (1 + T)] +
+ Si[((J + a) (1 - T)] + Si[((J - a)(1- T)].
(8.12)
TOqKH 3KcTpeMYMoB Haxo,n:HTCH H3 paBeHCTBa HYJIIO rrpoH3Bo,n:HOH f no T C HC-
nOJIb30BaHHeM rrpe,n:bl,[(YlUero 3HaqeHHR U. TIpH CHIDKeHHH 3HaqeHIDI <);>a30Boro
qJIeHa HMeeM:
f = sin[((J + a)(l + T)] + sin[((J - a)(l + T)] _
l+T l+T
_ sin[((J + a)(l - T)] _ sin[((J - a)(l - T)] = o.
1-T 1-T
(8.13)
113-3a KOJIe6aHHH Ka)l(J];OrO H3 qeTbIpex CJIaraeMbIX HMeeTCH MHoxeCTBO BeTBeM
KopHeM. TIOJIe3HOH HBJIHeTCH annpOKCHMaIJ;HH, npe,n:nOJIaralOlUaH, qTO nepBble 1])H
CJIaraeMbIX HMelOT 60JIblIlHe apryMeHTbI, H, COOTBeTCTBeHHO, '"'-J n/2. Tor,n:a
I ' '"'-J sin[ ((J - a)(l - T)] = 0
I-T '
(8.14 )
qTO ,LIaeT
T '"'-J 1 _ 1pt = 1 _ T)1t
U - a U(l- sine o )
(8.15)
TaKHM 06pa30M, nepHO.LI. YBeJIHqHBaeTCH H3-3a MHO)I(HTeJIH nCeB.LI.O.LI.H<ppaKIJ;H-
OHHoro JIeneCTKa 1/(1 - sin 8 0 ). YMeHbIIIeHHe qHCJIa OCIJ;HJIlliIIJ;HM npH YBeJIHqeHHH
yrJIa CKaHHpOBaHIDI TOqHO COBna,n:aeT C pe3YJIbTaTaMH, nOJIyqeHHbIMH npH KOMnb-
IOTepHOM Mo,n:eJIHpOBaHHH. )];arree 6Y.LI.eT nOCTpoeHa Mo,n:eJIb .1UUI BbPIHCJIeHHH UMne-
iJaHca CKaHup06aHUR [18].
HCnOJIb3yeMbIM 3.LI.eCb MeTO,n: 6blJI Ha3BaH «napaMeTpH3aIJ;HeH, OCHOBaHHOM Ha
Ha6JIIO,n:eHHHx» [4], npH KOTOpOH Ha6JIIO,n:aeMble (npH Mo,n:eJIHpOBaHHH) .LI.aHHble co-
rrOCTaBIDIIOTCH C COOTBeTCTByJOlUHMH <popMYJIaMH, B ,n:aHHOM CJIyqae C OCIJ;HJIJIHIJ;H-
HMH fH66ca. MHO)I(HTeJIb fH66ca (2/n) [Si(n) - 1] n03BOJIReT HaMTH 3KCTpeMYM
-- nL/'A (npH  = n), KOTOpbIH OTCqHTblBaeTCH OT KpaH pemeTKH K IJ;eHTpy. ,D;JUI .LI.H-
nOJIbHOM peIIIeTKH, cKaHHpyJOlUeM B H-nJIOCKOCTH, MHO)I(HTeJIb [Si(n) - 1] npH-
MeHHeTCH HanpHMyJO. Kor,n:a .LI.06aBJIHeTCH 3KpaH, 3aTyxaHlle OT KpaH K IJ;eHTpy CTa-
HOBHTCH 3HaqHTeJIbHO 60JIee 6bICTpbIM; OHO npOHcxo,n:HT .n.o rrpe06pa30BaHHH
MHO)I(HTeJIH B [Si(n) - 1] 1.5. 3TO 06YCJIOBJIeHO ,lI;II<I><l>epeHIJ;HarrbHbIM YMeHbmeHH-
eM B3aHMHOH CBH3H C 3KpaHOM. ,D;HnOJIbHaH pemeTKa, CKaHHpyJOlUaH B E-llJIOCKO-
CTH, .n.eMOHC1])HPyeT MeHbmee 3aTyxaHHe; nOKa3aTeJIb CTeneHH 0,75. 3TH Mo,n:eJIH
fH66ca xopomo COfJIaCyJOTCR C .n.aHHbIMH Mo.n.eJIHpOBaHHH, 3a HCKJIIOQeHHeM Kpae-
Boro 3JIeMeHTa. ,D;JIH 3a,n:Hero KpaeBoro 3JIeMeHTa 6blJIO .LI.OCTHrH)'TO nOJIHHOMH-
HarrbHoe COOTBeTCTBHe C .n.aHHbIMH MO.LI.eJIHpOBaHHH.
)];arree pe3YJIbTaTbI MO.LI.eJIH fH66ca 6y.LI.YT cpaBHHBaTbCH C pe3YJIbTaTaMH MO.LI.e-
JIHpOBaHHH ,lLJIH peIIIeTOK H3 201 3JIeMeHTa. Pe3YJIbTaTbI ,lLJIH ,n:HnOJIbHOM pemeTKH
co cKaHHpoBaHHeM B H-nJIOCKOCTH nOKa3aHbl Ha pHC. 8.19-8.21 .1UUI yrJIOB CKaHll-
pOBaHHH 0, 45 H 60°. ,LJ:aHHble Mo.n.eJIH H306paxeHbI npepbIBHCTbIMH JIHHHHMH, B TO
BpeMH KaK ,n:aHHble KOMTIblOTepHoro Mo.n:eJIHpOBaHIDI - HenpepblBHbIMH. MO)I(HO
BH.n.eTb, QTO COBn3)];eHHe npeBocxo,n:Hoe. 3aMeTHM, qTO COrJIaCOBaHHOCTb Me)l()J;Y TO-

 FIla6a 8. KOHe'tHble aHmeHHble pe/UemKU
qeqHOH H CTIJIOlliHOH KpHBbIMH, HanpHMep, Ha pl1c. 8.20; Ba)l(Hee, qeM cOBnMeHHe
nHKOB 3THX KpHBbIX. Ha pHc.8.22 H 8.23 npI1BO,DJITCH cpaBHeHIDI ,lLillI pellIeTKH C 51 t
3JIeMeHTOM rrpH 0 H 60°, B TO BpeM5I KaK pHC. 8.24 OTHOCHTC5I K pellIeTKe C 21 3ne-
MeHToM npl1 nOnepeqHOM H3JIyqeHI1H. On5lTb-TaKH Ha6JIIO,l1.aeTCH OTJIHqHaH corJIa-
COBaHHOCTb.
113MeHeHIDI uMneoaHca CKaHup08aHUR .LUI5I .n;HnOJIbHbIX pemeTOK 113 201 3neMeH-
Ta C 3KpaHOM npH CKaHHpOBaHHH B H-nJIOCKOCTH rrOKa3aHbI Ha pHC. 8.25-8.27,
r.n;e CHOBa nyHKTHpHbIMH nHHHHMH 0603HaqeHa Mo.aenb fH66ca, a HenpepblBHbIMH
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JIHTepaT)'pa
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TY,LI;HbIM pacnpe,aeJIeHHeM COCTaBJUleT 3,64. 06pam;aeM BHHMaHHe Ha TO, qTO <l>a3a
qaCTH H3.rryqaTeJIeH OTJIHqaeTCH OT .npyrHX Ha 180 0 .
Ta6J1Hu;a 9.1. CBepxHanpaBJIeHHaB CeMH3JIeMeHTHaB pemeTKa, d = ').../4
qHCJlO 3J1eMemOB AMruurry,n,a AImmHoe cOnpOTHBJIeHHe (OM)
1 1,443 0,13299
2 -3,933 -0,04879
3 7,122 0,02694
4 -8,264 -0,02322
5 7,122 0,02694
6 -3,933 -0,04879
7 1,443 0,13299

 rlla6a 9. C6epXHanpa6lleHHllle aHmeHHllle pewemKU
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(J
Puc. 9.2. PerneTKa C MaKCHMaJIbHOH HanpaBJIeHHOCTblO, N = 7, d = O,25A
9.2.2. HanpaBneHHOCTb AP npM CTpeMneHMM
Me>K3neMeHTHoro paCCTORHMR K HynlO
B pa60Te [42] rrOJIyqeH rrpe,neJI MaKCHMaJIbHOH HarrpaBJIeHHOCTH MR perneTKH B
c.rryqaRX, Kor,na Me)K3JIeMeHTHoe paCCTORHHe CTpeMHTCR K HYJIIO, rrpH 3TOM rrpe,neJI
rrpe,nCTaBJIReTCH B BH,lJ;e CYMMbI MHOrOqrreHOB JIe)KaH.npa. Pe3YJIbTaT MH perneTKH
H3 N 3JIeMeHTOB paBHHeTCH
N-I
G = L(2n+l)[Pn(cos8)]2,
n=O
(9.3)
r,ne e - yrOJI OTKJIOHeHHH rJIaBHOrO JIyqa OT HarrpaBJIeHHH, HOpMaJIbHOrO K pac-
KPbIBY aHTeHHbI. B [40] He3aBHCHMO rrOJIyqeHbI aHaJIOrHqHbIe pe3YJIbTaTbI MH AP
rrOrrepeQHOrO H3JIyqeHHH, r,ne cos e = 1. nOCKOJIbK)' MHOrOQJIeH JIe)l(aH.npa apry-
MeHTa 1 MO)KeT 6bITb 3arrHcaH B BH,lJ;e rrpOH3Be,neHHH K03<P<PHU;HeHToB, pe3YJIbTaT
MaKCHMaJIbHOH HarrpaBJIeHHOCTH paBeH
G  ( 1 . 3 . 5 .. . M ) r,ne M = 2AINT ( N + 1 ) - 1.
2 . 4 . 6 .. . (M - 1) 2
(9.4)
3,neCb M - qHCJIO HeqeTHbIX 3JIeMeHTOB, HJIH qHCJIO qeTHbIX 3JIeMeHTOB MHHYC 1.
TaKHM o6pa30M, Ba)KHbIH pe3YJIbTaT 3aKJIIOQaeTCH B TOM, qTO Tpex- H qeTbI-
peX3JIeMeHTHbIe perneTKH HMelOT O,nHO H TO )Ke rrpe,neJIbHOe 3HaqeHHe, rr5ITH- H
rneCTH3J1eMeHTHbIe perneTKH HMelOT TO )Ke caMoe 3HaqeHHe H T.,n. IIpHXO.IJ;HM K 3a-
KJIlOqeHHIO, qTO 3TO 06'bHCHHMO, rrOCKOJIbK)' Tpex- H qeTbIpeX3J1eMeHTHbIe perneTKH
HMelOT .IJ;Be rrepeMeHHbIe, paBHO KaK rrHTH- H rneCTH3JIeMeHTHbIe HMelOT .TpH rrepe-
MeHHbIe H T.,n. 3Ta MaKCHMaJIbHaH HarrpaBJIeHHOCTb rrpe,nCTaBJleHa Ha pHC. 9.3.


9.2. MaKCUMaJlbHaJI Hanpa8l/eHHOCmb aHmeHHOU peUlemKU 
10
8
6
,-.

t::t:
--
0
,
o I/yBJI = 10 CuB)
o l/yEJI = 20 Cn;l»
2
o
1
2
3 l.
5
6
7
8
9 10 11 12 13
N
Pac. 9.3. MaKCHMaJIbHa.H HarrpaBJIeHHOCTb pemeTOK rrOnepeQHOrO H3JIyqeHH.H
npH CTpeMJIeHHH Me)l(3JIeMeHTHoro paCCTOHHHH K HYJIIO
KpyxKaMH 0603HaqeHa npe,l(enbHaH HarrpaBJIeHHOCTb ,ILJUI AP qe6bIllieBa C OTHO-
llIeHHeM 60KOBbIX neneCTKOB IjY1)JI (B aHrnOH3bIQHOM T}JaHcKpHnl(1111 SLR - Side-
lobe ratio) 10 ,l(o, a KBMpaTHbIM 3HaQKaM COOTBeTCTByIOT 3HaQeHHH SLR = 2 ,l(o.
HanpaBneHHocTb AP qe6bIweBa MeHbllIe, nOCKonbK)' ,n:l1arpaMMa C MaKCHMaJIbHOM
HarrpaBITeHHOCTblO He I1MeeT 60KOBbIX nerreCTKOB paBHoro YPOBHH. ,[(a)Ke B cnyqae
TOJIbKO o,n:Horo 60KOBoro neneCTKa (3MHHM nerreCTOK) pe3ynbTaT qe6bIllieBa 6y,n:eT
paBIDITbCH MaKCHMaJIbHOMY 3HaQeHHIO, TonbKO ecnH COOTBeTCTBYIOlI.J;HM 06pa30M
BbI6paH ypOBeHb SLR. CM. pa3,n:en 9.2.4, f,n:e npI1Bo,n:HTCH paCCMOTpeHHe AP qe6bI-
llIeBa.
,[LITH AP rrpo,aonbHoro (oceBoro) H3nyqeHHH MaKCHMaJIbHaH HanpaBneHHOCTb B
npe,n:ene npH CTpeMJIeHHH llIara pellieTKI1 K HYnlO paBHa
N-l N-I
G L(2n+l)[Pn(O)]2 = L(2n+l)=N2.
n=O n=O
(9.5)
9.2.3. HanpaBneHHOCTb aHTeHHblX peweTOK
npOAonbHoro (oceBoro) M3nY'leHMSI
B pa60Te [22] Hccne,aOBaH JII1HeMHbIH I1CTOQHI1K npo,n;onbHoro (oceBoro) H3nyqe-
HHH C He6oJIbllIOM CBepXHanpaBJIeHHOCTblO. 3TOT pe3ynbTaT rrpe,n:CTaBlliIeT HHTepec,
TaK KaK pacrrpe,n;eJIeHHe MoxeT 6bITb ,n;I1CKpeTH3HpOBaHO ,ILJUI nOJIyqeHIDI B036YlK.D.e-
HHH pellIeTKH. TaK KaK aMrrnl1TY,n:a rrpH 3TOM HBJIHeTCH rrocToHHHOM, 3Ta oco6eH-


rJla8a 9. C8epxHanpa8JleHHble aHmeHHble pewemKU 1.,;\
\ :
HOCTb HBJIHeTCH npHBJIeKaTeJIbHOH WIH pemeToK. )];HarpaMMa pemeTKH npo,n:OlIbHO-
ro (oceBoro) H3JIyqeHHH )])IH HCTOqHHKa WIHHOH L HMeT"'BH.n .
I(S) = sinc (L (k sinS - (3»,
2
(9.6)
r,n:e (3 - 3TO BOJIHOBOe qHCJIO Ha paCKpbIBe.
BeJIHqHHa, 06paTHaH HanpaBJIeHHOCTH, nponOpUHOHaJIbHa BbIpaxeHHIO
 ex: ( 1 ) f sinc 2 ( L (k sine -13) }osede =
sinc2 L (k - (3) 2
2 (9.7)
1 ( 1t S . cos <p - 1 }
= - + 1<P +
sinc 2 (<p / 2) 2 <p
I.:
3n:eCb Si - 3TO HHTerpaJIbHbIH CHHYC, a cp '- L (k - (3) - ,nonOJIHHTeJIbHaH <l>a3a
B,nOJIb paCKpbIBa (,nonOJIHHTeJIbHO K JIHHeHHoMY Ha6ery <l>a3bI npH npo,n:OJIbHOM H3-
JIyqeHHH). EbIJIO YCTaHOBJIeHO, qTO MaKCHMaJIbHaH HanpaBJIeHHOCTb HMeeT MeCTO
WI5I cp = 2,922 pan:. Bo MHorHX pa60Tax ,n;eJIaeTCH CKOpOnaJIHTeJIbHbIH BbIBO.n: 0 He-
06XO,nHMOCTH ,IJ;OnOJIHHTeJIbHbIX 1t pan:HaH <l>a3bI, HO 3TO He HMeeT <l>H3HqeCKOrO
CMbICJIa; 60JIee OnTHMaJIbHbIM oKpyrJIeHHeM 2,92 HBJIHeTCH 3. YBeJIHqeHHe HanpaB-
JIeHHOCTH no cpaBHeHHIO C HOpMaJIbHbIM npo.n:OJIbHbIM H3.rryqeHHeM COCTaBJIHeT
2,56 .n:E, H SLR = I/yEJI paBHO 9,92 n:E. Pacnpe.ZIeJIeHHe 5IBJI5IeTC5I nO,IJ;Xo,n:HI.I..(HM
)])IH WIHHHbIX pemeTOK; WI5I KOpOTKHX pemeTOK peKOMeH.nyeTC5I KOMnblOTepHa5I
onTHMH3aUH5I <l>a30Boro pacnpe.n:eJIeHIDI (CM. [21]). .
Pacnpe.n:eJIeHHe XaHceHa-BYJn>5Ip,na <l>opMHpyeT npo,nOJIbHOe H3JiyqeHHe, H,
KaK npaBHlIO, MaKCHMaJIbHOH HanpaBJIeHHOCTH He B03HHKaeT. HaH60JIee 061.I..(ee
pemeHHe WI5I paBHoMepHoro pacnpe.n:eJIeHH5I n03BOIDIeT HCnOJIb30BaTb JII06bIe 3Ha-
qeHH5I <l>a3bI ,lLJI5I MaKCHMH3aUHH HanpaBJIeHHocTH. TaKoe pemeHHe MOrJIO 6bI 6bITb
I
<l>OpMaJIbHO peaJIH30BaHo WI5I 3an:aHHoro KOJIHqeCTBa 3JIeMeHTOB H paccToHHHH
Me)l()];y HHMH, HO WI5I ypaBHeHIDI nOTpe6yeTC5I QHCJIeHHOe pemeHHe. HeCKOJIbKO
60JIee npOCTa5I 3an:aqa 6bIJIa pemeHa [1]; 6a30H 5IBJIHeTCH paBHOaMTIJIH1)',nHaH AP,
KOTOpa5I 6bIJIa c<l>a3HpoBaHa B HanpaBJIeHHH 8 0 . MeX3JIeMeHTHbIH <l>a30BbIH MHO-
)l{HTeJIb 6 = kd sin 8 0 , a HanpaBJIeHHOCTb (CM. rJIaBY 2) paBH5IeTC5I
G = N (9.8)
1 +  r.. :/ (N - n)sinc(nkd)cos(n8)
PaCqeTbI 6bIJIH BbInOJIHeHbI WI5I 2-, 3-, 4- H 10-3JIeMeHTHbIx pemetoK ,lLJIH Bcex
yrJIOB OTKJIOHeHH5I JIyqa H WI5I MeX3JIeMeHTHbIX paccToHHHH .n:o A. Ha pHC. 9.4 no:"
Ka3aHbI pe3YJIbTaTbI ,IJ;JI5I 2- H 3-3JIeMeHTHbIX pemeTOK, a Ha pHC. 9.5 - )])IH"4-"H'
10-3JIeMeHTHbIx pemeTOK. PHC. 9.5b He noxox Ha ,IJ;pyrHe TeM, qTO 3HaqeHIDI BbICO-'1
KOH HanpaBJIeHHOCTH pacnOJIOXeHbI B,IJ;OJIb HanpaBJIeHHR, npH6JIH3HTeJIbHO COOT-
. '
BeTCTByJOl.I..(eMY kd + 6 = 0, HJIH8 0 = - 1t/2. npH 3TOM nHKOBaH HanpaBJIeHHOCT:b
06eCneqHBaeTCH npH npaKTHqeCKH npO,IJ;OJIbHOM H3JIyqeHHH C MeX3JIeMeHTHbIM HH-
TepBaJIOM A. B,IJ;OJIb 3Toro HanpaBJIeHIDI 3HaqeHHR HanpaBJIeHHOCTH 6bIcTpo'MeHH  .
eTCH, B03MO)I{HO, B CHlIY nOHBJIeHIDI em:e o,nHoro JIeneCTKa. 3HaqeHH5I HanpaBJIeH-
HOCTH nOKa3aHbI npH 8 0 , HO B HeKOTopbIX CJIyqaHx «60KOBOH JIeneCTOK» MO)KeT
HMeTb 60JIee BbICOKYID aMTIJIHTY.n:y.

9.2. MalCCUMOJIbHaJI Hanpa6JleHHOCmb aHmeHHOU pelUemlCu 
(8)
o
w/2
."
31(/2
k O d:21T
-1(12
1.50
1-75
20
N=2
8:-11"
2,0
I
(b)
o
-rr/2
7r
3w12
kOd: 27r
-1('/2
2.5
30
3,0
2S
N=3
 = _oK
Pac. 9.4. HanpaBJIeHHOCTb pemeTKH npH paBHOMepHOM B036yx,n;eHHH [1]
9.2.4. WMpMHa nonOCbl, 3cj)cj)eKTMBHOCTb M AonYCKM
nepBaOH H3 TPex OCHOBHbIX TPY.D:HOCTeH, CBR3aHHblX co CBepXHanpaBJIeHHbIMH pe-
meTKaMH, HBIDIeTCH IIIHpHHa nOJIOCbI, KOTopaH 6bICTpO YMeHbIIIaeTCH no Mepe
yMeHbllIeHIDI HHTepBaJIa 3JIeMeHTOB < A/2. PaCcMOTPHM, K rrpHMepy, .D:06pOTHOCTb
Q. ,a;rn Y3KOnOJIOCHbIX aHTeHH llIHpHHa nOJIOCbI qaCTOT  l1Q, a nOJIoca COrJIaCOBa-
HHB == 21Q. COOTHomeHHe Me)K)];Y 3anaceHHOH H pacceHHHoH 3HeprHeH, Q, MOXHO
aHaJIOrnQHbIM o6pa30M 3aIIHcaTb C TOqKH 3peHHH K03<1><PHUHeHToB B036y)K)]:eHIDI
v
pemeTKH Ii B3aHMHOH CBH3H, H ,l(JIH H30TPonHbIX 3JIeMeHTOB nOJIyqaeTcH CJIe,lJ;yIO-
lI.{ee BbIpIDKeHHe
"'\" N A 2
Q =  n=l n
N N .
Ln=lLm=l AnAmsinc(n -m)2nd I 'A]
(9.9)

 FAa8a 9. C8epXHanpa8AeHHble aHmeHHble pewemKU
(a)
o
n/2
n
3n /2
k O d=2rr
-1r /2
4
N=4
d =-1C
-1r /2
1C/2
1C
31C/2
k O d=2rr
(b)
3
10
N= 10
b = -1C
PHC. 9.5. HarrpaBJIeHHOCTb perneTKH rrpH paBHOMepHOM B036)')K.lJ:eHHH [1]
PaCqeTbI nOKa3aJIH [17], qTO ,WUl perneTOK <t>HKcHpoBaHHoH ,lUIHHbI, H3.rryqalO-
IUMX no HOpMaJIH, KaK HanpaBJIeHHOCTb, TaK H Q YBenHqHBalOTCH B 3aBHCHMOCTH
OT KOnHqeCTBa 3neMeHTOB. PerneTKa C qeTHbIM qHCnOM 3neMeHTOB HMeeT HeCKonb-
KO 60nee BbICOKoe Q, qeM perneTKa co cne.ayK>IUHM no BeJIHqHHe HeqeTHbIM KonH-
qeCTBOM 3neMeHTOB, B03MO)l(JfO, IIOTOMY, QTO ,nHCKpeTH3aUHH paCIIpe,neneHIDI ,nJUI
HeqeTHOrO KOnHQeCTBa 3neMeHTOB HBnHeTCH 60nee 3<t><t>eKTHBHoH. ,[(Jrn Bcex pac-
CqHTaHHbIX c.rryqaeB log Q H3MeHIDICH IIpH6nH3HTenbHo nHHeHHO B 3aBHCHMOCTH OT
HanpaBJIeHHOCTH. Ha pHC. 9.6 nOKa3aHa 3aBHCHMOCTb log Q OT HanpaBneHHOCTH
,nn perneTOK C HeqeTHbIM KOnHqeCTBOM 3neMeHTOB co 3HaqeHIDIMH ,nnHHbI lA, 2A
M 5A. Kpyxx:aMH 0603HaqeHbI TOqKH, paCCqHTaHHbIe C ,nBOHHOH TO'lllOCTblO; nOBbI-
rneHHaH TOqHOCTb Tpe6yeTcH ,nnH perneTOK C 60nbrnHM KOJIWleCTBOM 3JIeMeHTOB.
TIpHMble JIHHHH IIpOBe,neHbI Qepe3 TOqKH co 3HaQeHHHMH HanpaBneHHOCTH npH
paBHOMepHOM B036)')K.I(eHHH (paBHbIe Go) C HaKJIOHOM :Tt, r,ne Go - 3TO YClUIeHHe
-'

9.2. MaKCUMOJIbHWl HanpaBAeHHOCmb aHmeHHOU peUJemKU 
10
2
LaA
2,1
5A
o
3
5
7
9
13
11
11
19
8
11
Log Q
17
6
4
15
13
15
PHC. 9.6. fpa<}JHK 3aBHCHMOCTH Q OT MaKCHMaJIbHOM HanpaBJIeHHOCTH perneTKH
C HeqeTHbIM qHCJIOM 3JIeMeHTOB
peIIleTKH TaKoH )l(e L(JIllHbI C nOJIYBOJIHOBbIM llHTepBaJIOM: Go = 1 + 2L/A. B lIaHHbIH
MOMeHT HeT HllKaKoro <pll3HqeCKOrO CMbICJIa HCnOJIb30BaTb 3TY BeJIMQI1HY HaKJIOHa,
HO Ha 31)' MbICJIb HaBo,n:RT paCqeTbI [34] no CBepXHanpaBJIeHHbIM JII1HeHHbIM HCTOq-
HHKaM. I1pH BbInOJIHeHHH HaHJIyqIIleH annpOKCHMal(HH np.HMOH JIHHHeH Ha60pa
TOQeK lIJI.H Ka)l(,[{oi1: ll3 Tpex perneTOK HaKJIOHbI <paKTllQeCKM KOHl(eH1pllpOBaI1Cb BO-
Kpyr 3HaqeHHR 3,14. O,n:HaKo HeJIerKO BbInOJIHI1Tb TaKYIO annpOKCI1Mal(lllO TOqHO,
rrOTOMY qTO, KaK no,n:qepKHyro B [34], Kpl1BaR 3aBHCHMOCTH log Q OT HanpaBJIeHHO-
CTl1llMeeT KOJIe6aTeJIbHbIH xapaKTep npH HH3KHX 3HaqeHH.HX Q. ECJIH BbIllleyxa3aH-
HbIe ,lI.Onyrn;eHIDI .HBJI.HIOTC.H HCTHHHbIMH, TO xapaKTepHCTHKa CBepXHanpaBJIeHHOH
perneTKH C 60KOBbIM ll3JIyqeHHeM 3an;aeTC.H CJIe,n;yroII.J;HM ypaBHeHHeM.
log Q = 'Jt(G - Go).
(9.10)
TaKHM o6pa30M, peaJIH3an;HR cBepxHanpaBJIeHHOH pellleTKH, 6e3YCJIOBHO, BnH-
CbIBaeTCR B KaTeropllIO cPYJI,lI;aMeHTaJIbHbIX orpaHllqeHHH, HaJIO)KeHHbIX Ha xapaKTe-
pHCTHKM aHTeHH [16],
O)l(H)J;aeMOe 3HaqeHI1e Q ,lIJUI pemeTKH H30TponHbIX 3JIeMeHTOB npll6JIH3HTeJIb-
HO .HBJIReTCR <PYHKUl1eH qHCJIa 3JIeMeHTOB, ,n:eJIeHHOrO Ha d/"A. Ha pRC. 9.7 3TO co-
OTHomeHHe nOKa3aHO ,[(JUI pMa pemeTOK; KaJKlIa.H perneTKa npelICTaBJIeHa OKPYX:-
HOCTbIO. Me)K3JIeMeHTHbIe llHTepBaJIbI > 0,3"A He nOKa3aHbI, nOCKOJIbKY BeJIHqHHa
,n:OCTllraeMOH CBepXHanpaBJIeHHOCTH .ruUI HHX HBJI.HeTCSI MaJIOH. TIoKa3aTeJIb log Q

b r/la8a 9. C8epXHanpa8/1eHHble aHmeHHble pememlCu
6
5
4
logQ
3
2
1
10
20
30
40
50
60
NAld
PHC. 9.7. fpacpHK 3HaqeHHH Q ,lLJISI CBepXHanpaBJIeHHbIX JIHHeHHbIX peweTOK
nOnepeQHOrO H3JIyqeHHH
RBJIReTCR npH6JIH3HTeJIbHO JIHHeHHbIM npH NA/ d; annpoKcHMaUHR TOqeK npRMoH
u
JIHHHeH Ha pHcYHKe BbIpaxaeTcR B cJIe,nyJOrueM BH,l];e
logQ - 0, 1604{  ) - 1,53476.
(9.11)
3TH ,naHHbIe rr03BOJlSIIOT KOHCTPYKTOPY pemeTKH oueHHTb CTerreHb CBepXHan-
paBJIeHHOCTH (Q) .lUIH 3arI:aHHOH reOMeTPHH perneTKH.
EblJIH npOBe,neHbI paCqeTbI pa60qHX xapaKTepHCTHK CBepXHanpaBJIeHHbIX nHHeH-
HbIX perneTOK H3 rrapaJIJIeJIbHbIX ,nHnOJIeH. KOJIJlMHeapHbIe ,nHllOJIH He paCCMaTPHBa-
IOTCH, TaK KaK OHM HaKJIarI:bIBaJIHCb 6bI Ha coce,nHHe. Ha pHC. 9.8 nOKa3aHa 3aBHCH-
MOCTb log Q OT HanpaBJIeHHOCTH ,lLJUI perneTOK ,l(JIHHOH B 2A. MCrrOJIb3yJOTcR KaK
I(HnOJIH ,lJ)IHHOH 0, lA, TaK H O,5A. OIDITh 3aBHCHMOCTb log Q OT G npeI(CTaBJlSleT npR-
MyJO JIHHHIO. KaK H O)l(H,l{aJIOCb, nO.rryBOJIHOBaSI .D:HnOJIbHaH pemeTKa HMeeT 60nee
BbICOKoe Q, qeM COOTBeTCTByK>ruaH perneTKa H30TponHbIX H3JIyqaTeJIeH, B CHJIy co-
xpaHeHHH 3HeprHH B 6JIIDKHeM nOJIe ,nHnOJUl. B CJIyqae KOpOTKHX ,nHIIOJIeH (O,IA) 3TO
HaKonrreHHe 3HeprHH ropa3,no 60JIbllIe, B pe3YJIbTaTe qero nOJIyqaeTcR ropa3ll0 60JIb-
rnee Q.
,[{.TUI JIHHeHHbIX napaJIJIeJIbHbIX ,nHnOJIbHbIX pellieTOK npo,nOJIbHOrO H3JIyqeHHR
H3MeHeHHe log Q B 3aBHCHMOCTH OT HanpaBJIeHHOCTH onRTb HBJUleTCH JIHHeHHbIM,
HO HaKJIOH H3MeIDIeTCH no Mepe H3MeHeHHH .lUIHHbI pellIeTKH. Ha pHC. 9.9 npHBe-
,neHbI ,Z:(aHHbIe .lUIH pemeTOK co 3HaqeHHRMH ,lLJIHHbI lA, 2A H 5A; KOJIHqeCTBO 3ne-
MeHTOB B KaJK,[(OH pemeTKe rrOKa3aHO Ha pHCyJIKe [19].

. '
,
8
6
logQ
4
2
o
6
9.2. MaKCUMQJlbHllJl Hanpa6JleHHOCmb aHmeHHOU pememKU , 
," ,
"J.
11
£=0.5A
8
10
14
16
18
12
G
Puc. 9.8. fpaqnIK 3HaqeHHH Q JIHHeHHOH perneTKM rrOnepeQHOrO H3JIyqeHHR
LUIHHOH 2A H3 napaJIJIeJIbHbIX ,[(HnOJIeH
logQ
.:
! '
8
2,1
6
A
4
1- O.l
o
. 0
20
40
.60
80
loa
G
PUC. 9.9. fpaij)MK 3HaqeHHH Q,WIR peJlIeTOK npO,[(OJIbHOrO H3JIyqeHHR H3 rrapaJIJIeJIb-
OJ
HbIX ,[(HnOJIeH

,  DlaBa 9. CBepXHanpaBJIeHHble aHmeHHble pewemKU
BTOPOll He)l(eJlaTeJlbHOll oc06eHHocTblO cBepxHanpaBJleHHbIX perneToK RBJIReTCR
HH3KaR 3<p<peKTHBHOCTb, CBR3aHHaR KaK C nOTepRMH B corJlaCyIOmell uenH (CM. pa3-
,n:eJl 9.4.1), TaK H C nOTepRMH B 3J1eMeHTax aHTeHHbI. 11 TO, H ,n:pyroe BbI3bIBaeTCR
HH3KHMH COnpOTHBJIeHHRMH H3.rryqeHHR 3THX perneTOK. KaK npaBHJIO, 3J1eMeHTbI B
ueHTjJe perneTKH HMelOT CaMOe HH3KOe COnpOTHBJIeHHe H3JIyqeHHR; paCqeTbI .lI)UI
MHO)l(eCTBa MaJIbIX perneTOK H3 H30TpOnHbIX 3J1eMeHTOB noi<a3bIBaIOT, qTO Rrad ex: /.JQ.
Ha pHC. 9.10 nOKa3aHbI 3TH ,n:aHHbIe. AnnpoKcHMaUHR npRMOll JlHHHeH npH Jlora-
pH<pMHqeCKOM MaClIlTa6e no 06eHM OCRM BbIpIDKaeTCR CJle,n:YlOmeH <pOPMYJlOH
8,058
Rrad - .JQ'
(9.12)
1
,-....

o
'-" 0.1
"0
e
C(
0.01 2
10
5 X 10 4
10 3
10 4
Q
PHC. 9.10. fpa<):>MK 3aBMCMMOCTM COilpOTMBneHM M3nyqeHM ueHTpanbHoro 3neMeH-
Ta perneTOK rrOrrepeQHOrO M3nyqeHM OT Q
AHaJIOrHqHbIe ,n:aHHbIe MR pelIleToK npo,n:OJlbHOrO H3J1yqeHHR npHBo,n:RTCR Ha
pHC. 9.11. Ha6J1IO,n:aeTcR npaKTWIeCKH JlorapH<pMHqeCKaR 3aBHCHMOCTb conpOTHB-
neHHH H3JIyqeHHR OT Q.
ConpOTHBJIeHHe nOTepb UIUIHH,n:pHqeCKHX IUIH nOJlOCKOBbIX ,n:HnOJleH paCCqH-
TbIBaeTCR nerKO: ,n:Hnonb JUlHHbI 1 PMHyca a, H3rOTOBJIeHHbIH H3 MaTepHaJIa C no-
BepXHOCTHbIM conpOTHBJleHHeM Rs, HMeeT conpOTHBneHHe IIOTepb R10s s
R - Rs 1(1 - sinckl) (9 .13 )
ls - 1.
4rca sin 2 - kl
2
,[(JIR nOJIYBOJIHOBbIX IDIH pe30HaHCHbIX ,n:HnOJIeH R10s s = Rs 1/431: a. nOJIOCKOBbIe
 u
,n:HnOJIH 3KBHBaJIeHTHbI UIUIHH.LI:pHqeCKHM ,n:HnOJIRM C rnHpHHOH IIOJIOCKH, paBHOH
4a. Me,n:HaH npOBOJIOKa HMeeT H,LJ:eaJIbHOe nOBepxHocTHoe conpOTHBJIeHHe
Rs :: 0,000261  f MHz.
(9.14)

9.2. MaKcUMaJ/bHOJI Hanpa8JleHHOCmb aHmeHHOU pewemKU 
0.3
0.1
R
(n)
0.04
0.01
0.006
30
100
400
Q
10 3
4xl0 3
10"
PHC. 9.11. fpa<t>HK 3aBHCHMOCTH corrpOTHBJIeHHR H3JIyqeHHR n;eHTparrbHoro 3JICMeH-
Ta CBcpXHarrpaBJICHHbIX pcrnCTOK rrpo,aOJIbHOrO H3JIyqeHHR OT Q
B rrpe,[(eJIax ,[(llarra30Ha OT 10 ,[(0 1000 Mu Rs ll3MeHReTCR OT 0,000825 )10
0,00825 OM/e,n:llHllUY rrJIoru;a,n;ll. IIpll llCrrOJIb30BaHllll 3HaqeHllH l/a = 25 ,[(JIH He-
3HaqllTeJIbHO )'TOJIru;eHHoro CllMMe1pllqHOrO Bll6paTopa (.n;llrrOJIH), corrpOTllBJIeHlle
rrOTepb ll3MeHHeTCH OT 0,0066 Q rrpll 10 Mru .n;o 0,066 Q rrpll 1 rru. Kor)1a 3Tll Tll-
rrllqHbIe 3HaqeHllH corrpOTllBJIeHIfH rrOTepb cpaBHllBalOTCH co 3HaqeHllHMll corrpo-
TllBJIeHllH ll3JIyqeHllH pllC. 9.10 II 9.11, CTaHOBllTCH HCHO, QTO 3<l><l>eKTllBHoCTb
cBepXHarrpaBJIeHHOll perneTKH MO)l{eT 6bITb cyrueCTBeHHO OrpaHllQllBalOru;llM co06-
pa)l(eHlfeM. llcrroJIb30BaHlle BbICOKOTeMrrepaT)'pHbIX MaTepllaJIOB co cBepxnpoBo,n:ll-
MOCTblO B perneTKe II pacrrpe)1eJIllTeJIbHOll CllCTeMe MoxeT 06eCrreQHBaTb BbICOKHe
3HaQeHllH 3<l><l>eKTllBHoCTll, HO ,n:OCTIDKllMaH B HaCTOHru;ee BpeMH .n;06pOTHOCTb Q -
3TO Ta, QTO rrpllBe.n;eHa Ha pRC. 9.7-9.9.
TpeTbH cyrueCTBeHHaH rrp06JIeMa, CBH3aHHaH co CBepXHarrpaBJIeHHbIMll perneTKa-
Mll, - 3TO )l(eCTKlle Tpe60BaHIDI K ,n:orrYCKaM. IIoCKOJIbKY CBepXHarrpaBJIeHHOCTb
rrpe,n:rrOJIaraeT QaCTllqHOe raIIIeHlle BJIIDIHIDI 3JIeMeHTOB Ha rJIaBHbIll JIyq, TO ,n:OrryCK
Ha K03<l><l>HUlleHTbI B036y)1(,[(eHIDI KIDK,l(Oro 3JIeMeHTa CTaHOBllTCH 60JIee )l(eCTKHM
rrpll YBeJIllQeHllll CBepXHarrpaBJIeHHOCTll [42]. EbIJI BbIrrOJIHeH rrpocToll paCqeT 3TllX
3<l><peKTOB ,[(JI5I perneTOK ,lJ;oJIb<l>a-Qe6bIIIIeBa rryTeM B036y)1(,[(eHllH ueHTpaJIbHOrO
3JIeMeHTa HeQeTHOll perneTKll II HaXO)l(,L(eHIDI ,[(orrycKa ,[(JI5I YMeHbrneHllH HarrpaBJIeH-
HOCTll Ha 0,5 ,n:E. IIpe,[(rroJIaraeTcH, qTO qyBCTBllTeJIbHOCTb K ypOBHIO SLR = IjYEJI
OTC)'TCTByeT. llcrroJIb30BaJIOCb 3HaQeHHe 20,n:E. EbIJIH BbIrrOJIHeHbI paCQeTbI ,[(JI5I N =
= 3 If 5 KaK <PYHKUHll RHTepBaJIa; pe3YJIbTaTbI rrOKa3aHbI Ha pHC. 9.12. 06paTRTe
BHHMaHlle Ha TO, qTO KpHBaH 3aBHCHMOCTH rrpOl.{eHTa OIIIH6KH OT d/A HBIDIeTCH JIH-
HellHOH ,[(0 Me)l(3JIeMeHTHoro paCCTOHHIDI rrpH6JIH3HTeJIbHO O,IA. ,lLrrH N = 3 HaKJIOH
COCTaBIDIeT 2:1, a ,[(JIH N = 5 HaKJIOH COCTaBIDIeT 4:1. TaKHM 06pa30M, ,[(JI5I N = 3,
eCJIH Me)l(3JIeMeHTHoe paCCTOHHHe 6y,[(eT YMeHbIIIeHO B ,n:Ba pa3a, ,[(orrYCKll ,n:OJDKHbI

 Dlaea 9. CeepXHanpa6JleHHble aHmeHHble pewemICu
10- 1
10- 2
'bl
10- 3
10- 4
10- 5
10- 4
10- 3 10 2
)];OnYCK B npOueHTaX
10- 1
1
PHC. 9.12. Ll.onycK Ha K03<P<PHUJleHT B036)')K.L{eHHH ueHTpaJIbHOrO 3JIeMeHTa npH na-
.aeHHH HanpaBJIeHHOCTH Ha 0,5 .aE
6bITb B qeTbIpe pa3a )KecTtIe. ,[(orrycK B rrpoueHTax ,lI)IH ueHTPaJIbHOfO 3JIeMeHTa .wrn
coxpaHeHH 3HaqeHHH HarrpaBJIeHHOCTH, 6JIH3KOfO K O)l(lf)];aeMoMY (B rrpe,neJIax
0,5 .aD), rrpH6JIH311TeJIbHO BbIpIDKaeTCH CJIeLJYlOIUlfM o6pa30M
100
JQ.
(9.15)
HO rrOCTOHHa 1f3MeHeTCR B 3aBHCHMOCTH OT qlfCJIa 3JIeMeHTOB.
TaKI1M o6pa30M, rrpH Q = 1000 ,norryCK COCTaBJIHeT 3,2%. IIIlfplfHa IIOJIOCbI H
COrrpOTI1BJIeHHe H3JIyqeHHR RBlliIIOTCR 60JIee cepbe3HbIMH orpaHHqeHHHMH CBepx-
HarrpaBJIeHHbIX pemeTOK.
9.3. OnTMMM3aMR C OrpaHM'IeHMRMM
HanpaBJIeHHOCTb MO)KeT MaKCHMlf3lfpOBaTbCR C yqeToM orpaHlfQeHI1R, KOTOpbIM
MO)KeT RBJIHTbCR orpaHHQeHHe 60KOBbIX JIerreCTKOB ,UHarpaMMbI, mHpHHbI rrOJIOCbI
HJIM Q, pa3pemeHHbIX ,norrYCKOB, COOTHOIIIeHMH CHfHaJI/myM (SIN) If T.,n. TIo
,[(OJIb<pY 11 Qe6bImeBY, caMoe rrpOCToe - 3TO orpaHMQeHMe 60KOBbIX JIerreCTKOB.
9.3.1. CBepxHanpaBneHHocTb Aonbcl>a-'-Ie6blweBa
IIpl1HQl1rrbI 11 paCQeTHbIe COOTHOIIIeHIDI ,lI)IR pemeTOK C 60KOBbIMH JIerreCTKaMH paB-
HOfO ypOBIDI, pemeTOK ,[(OJIb<pa-Qe6bIllieBa, 6bIJIM paCCMOTpeHbI IIo,npo6HO B fJIa-
Be 3. O,nHaKo BbIKJIarIKH If <pOPMYJIbI B pa60Tax [9, 39] orpaHWIeHbI d  A/2. B [35]
nOKa3aHO, qTO 3TO orpaH:uqeHHe MO)KeT 6bITb CIDITO, HO TOJIbKO JUUI N HeQeTHoro.

9.3. OnmUMU3al(UH C OZpaHU'leHWlMU d
,LJ:n MeX3neMeHTHoro paccToHH MeHee nonOBHHbI ,LI)IHHbI BonHbI npo-
cTpaHcTBeHHa ,n:HarpaMMa H!lnpaBneHHocTH <l>opMHPyeTc, HaqHHa C TOqKH p-
,n:OM C KOHIJ;OM o6nacTH + 1 qe6bImeBa, ,n:aJIee <l>opMHpyeTc no Kone6aTenbHoMY
paHoHY ,n:o ,n:pyroro KOHIJ;a o6nacTH. 3aTeM B03Bparu:aeTc, K HaqaJIbHOMY KOHIJ;Y IiI
BBepx no MOHOTOHHOH qaCTIiI ,lUI o6pa30BaHH nonOBHHbI rnaBHoro neneCTKa
(nyqa). ITocKOnbKY nonHHOM qe6bImeBa M-ro nopMKa HMeeT M - 1 Kone6aHHn,
KOTopbIe npOXO)lTC ,[(Ba)l()];bI, H IIOCKonbKY cne,n: OT 0 ,[(0 1 If 06paTHo o6pa3yeT
u:eHTpaJIbHbIH 60KOBOH neneCTOK, npOCTpaHCTBeHHa ,n:HarpaMMa HanpaBneHHO-
CTIf Bcer,n:a IiIMeeT HeqeTHOe qHCnO 60KOBbIX neneCTKOB C Ka)l()J;On CTOpOHbI, IDIIiI
qeTHOe qHCnO Hynen. OTclO,n:a TonbKO HeqeTHOe qHCnO 3neMeHTOB MoxeT o6pa30-
BbIBaTb pemeTKY qe6bImeBa ,lUI d < A/2. ,[(lfarpaMMa BbIpaxaeTC B cne,[(yJOru:eM
BIf,n:e:
T M (a cos \}' + b)
Zo + 1
a=
l-coskd
b = Zo coskd + 1
,
coskd -1
(9.16)
r,[(e, KaK If paHbme, W = kd sin O. 3HaqeHHe Zo paBHO
h arccoshSLR
Z 0 = cos .
M
(9.17)
OTHomeHlfe 60KOBbIX neneCTKOB SRL = IjYEJI onpe,[(eneTC H3 ypaBHeHH
SL R T M(ZO).
(9.18)
<DopMynbI 6bIJIIf pa3pa60TaHbI [5, 6, 36, 10-12]. 3,n:ecb 6y,[(yr IiICnOnb30BaHbI
<l>OPMYJIbI ,LJ:peHHa [10], nOCKonbKY OHH no.n:xOJ(T )lJI KOMnblOTepHoro paCqeTa
CBepXHanpaBneHHbIX pemeTOK. K03<P<PHIJ;HeHTbI B036y;K,l];eHIf 3neMeHTOB pemeTOK
CJIe.n:yrom:liIe:
E 
An = n LEmEM2-mTn(xn)[TM(axn + b) + (-I)nT M (b -ax n )],
4M m=O
(9.19)
r,[(e £i = 1 ,lUI i = 0, If paBHO 2 ,lUI i > 0; X n = cos n 'Jtl M. I.J.eJIbIe M 1 If M 2 - 3TO,
COOTBeTCTBeHHO, IJ;eJIbIe qaCTH MI2 If (M +1)/2. 3TOT pe3ynbTaT BneTC ,n:eHcTBH-
TeJIbHbIM .lUI d  A/2. IIpH MaJIOM MeX3neMeHTHOM paCCTOHHH (BbIcoKocBepx-
HanpaBJIeHHbIe pemeTKH) MOryr Tpe6oBaTbc 60nbmHe TOqHOCTH B CIDIY BbIqH-
TaHH qneHOB. MHorHe pemeTKM HMelOT nOn)'BOJIHOBOH HHTepBaJI Me)l()J;y
3neMeHTaMH; ,lUI HHX a IiI b CBO.n:TC K CJIe,nyrom:eMY BH,[(Y
1 1
a = -(zo + 1); b = -(zo -1).
2 2
(9.20)
,LJ;IDI nOJIyBOJIHOBOrO mara 3TOT IIO.n:XO,n: H no,n:xoJ( rnaBbI 2 J(alOT o,n:HHaKOBbIe
pe3YJIbTaTbI! B Cym:HOCTH, B CHJIy CBOHCTB MHOrOqneHa qe6bImeBa J(Be npOCTpaHCT-

 FJ/a6a 9. C6epXHanpa6J/eHHble aHmeHHble peLUemKU
BeHHble .lIllarpaMMbI HarrpaBJIeHHOCTH B HacToHIUeH II npe,llJlIecTByroIUllX cPopMax
paBHbl
( N-l 'P ) ( Zr (cos'P + 1) + cos'P -1 )
TN-I Zo cos- = TM
2 2
N -1 = 2M,
(9.21)
v v
r.lIe BepXHHe llH.n:eKCbI Zo nOKa3bIBaIOT, QTO KIDK)10ll pellIeTKe COOTBeTcTByeT CBOll
llOJIMHOM. TIOCKOJIbKY MHorHe KOMnblOTepbI He llMelOT 06paTHblX rHrrep6onWlec-
KMX <PYHKll;I1M, y.n:06HO rrepenMcaTb Zo CJIe.lIYIOIUIIM 06pa30M:
Zo = l[SLR+ -J SLR2 -l]l/Af + l[SLR- -J SLR2 -l]1/M.
2 2
(9.22)
HanpaBJIeHHOCTb perneTOK H3 3, 5, 7 H 9 3JIeMeHTOB 6blna paCCqllTaHa .lIJIH
ypOBHH SLR 10 H 20 .n:n. PaCqeTHble 3HaqeHMR CBepXHanpaBJIeHHOCTH rrpe.n:CTaBJIe-
RbI Ha pllC. 9.13 11 9.14 MH Me)l(3JIeMeHTHoro llIara < 0,5A-, nOCKOJIbKy 06bIQHaji
HarrpaBJIeHHOCTb (c HCnOJIb30BaHlleM K03<P<Plll(lleHTOB Qe6bIllIeBa, KOTopble OT llH-
TepBaJIa He 3aBHCHT) ITJ1aBHO CTpeMHTCH K 0 )1:6 rrpH HyneBoM mare. Ha pHCyHKax
oTo6pa)f(aeTCH 3aBI1CMMOCTb 3TllX paCQeTHbIX 3HaQeHllM HarrpaBJIeHHOCTll OT llHTep-
BaJIa lVle)K)1Y 3JIeMeHTaMll. TaKHM 06pa30M, TpeX3JIeMeHTHaH perneTKa 06eCrreQllBa-
eT HanpaBJIeHHOCTb rrpM6JIH3HTeJIbHO 3 .n:n )1JUl MaJIbIX llHTepBaJIOB, perneTKa 113
IIHTH 3JIeMeHTOB 06eCrreQl1BaeT rrpH6JIH3HTeJIbHO 5 .lIE. HlDKe 6y.n:Yf paCCMOTpeHbl
Hen:OCTaTKH CBepXHarrpaBJIeHHOCTll.
12
8
10
--..

-5 6
o
4
2
o
o
0.1
0.2 0.3
0.4 0.5
dll
0.6
0.7 0.8
0.9
1.0
Poc. 9.13. HarrpaBJIeHHOCTb perneTKH Qe6bIrneBa, SLR = IjYEn = 10 lIE
TIapaMeTp .n:06pOTHOCTH Q, KOTopaH o6paTHo npOrrOpl(HOHaJIbHa llIllpHHe rro-
JIOCbl qaCTOT, BbIpa)l(eH B [27] CJIe.lIyroIUHM o6pa30M
I'
""f\'N A2
Q=  n=l n
L:l L:=1 AnAm sinc[ (n - m)kd]
(9.23)
...J

9.3. OnmUMU3aqUJI C OZpaHU"IeHUJlMU 
14
12
10
-- 8

t::{
--
o
6
4
2
o
o
0.1
0.2 0.3
0.4 0.5
d/).
0.6
0.7
0.8
0.9
1.0
Puc. 9.14. HanpaBJIeHHOCTb perneTKH Qe6bIIlleBa, SLR = l/YEJ1 = 20 .aE
H oTo6pa)l(aeTC5I B BH,[(e rpa<pHKa 3aBHCHMOCTH JUI5I perneToK ,[J;oJIb<pa-Qe6bIIlleBa
OT d/"A Ha pHC. 9.15. 3aBHCHMOCTb Q OT Illara peIlleTKH B JIOrapH<pMHqecKoM Mac-
IllTa6e IIpl1 N = 3 HfeeT HaKJIOH 4:1, npHQeM peIlleTKa H3 N = 5 I1MeeT HaKJIOH 8:1.
PeIlleTKH N = 7 11 9 HMelOT elUe 60JIee BbICOKMe HaKJIOHbI. )];JI5I MaJIbIX 3HaqeHHll Q
Kpl1Ba51 He RBlliIeTC5I CTOJIb TOqHOll.
10 7
10
10 6
10 5
10 4
Q
10 3
10 2
1
0.01
0.2 (). (J.E)
0.1
0.2
o.
0.6
dlA
Puc. 9.15. rpaq)J1K .n:06POTHOCH Q ,lLJUI perneTOK nOnepeQHOrO H3JIyqeHHR

 FilO80 9. C8epXHOnp08JleHHble OHmeHHble pewemKU
llIHpHHa nOJIOCbI qaCTOT HaKJIazIbIBaeT 66nbllIHe orpaHl1qeHIDI no cpaBHeHl110 C
.aonycKaMI1; perneTKa N = 3 B uenSIX npaKTHqHOCTI1 Tpe6yeT MeX3JIeMeHTHoro mara
nopMKa O,IA Hnl1 60JIbIlle. ,[(nH pellIeTKH C N> 3 orpaHHqeHMH eme 60JIee C1porMe.
HanpaBneHHocTb BbIpaxaeTCH CJIe.ayromMM o6pa30M:
G = (L:l An)2
N N. ·
Ln=l Lm=l AnAmsmc[(n - m)kd]
(9.24)
CJIeJJ.yeT 06paTI1Tb BHMMaHHe Ha cxoxeCTb pe3ynbTaToB )UlH Q. EbIJIO paCCqHTa-
HO JJ.Ba CJIyqaH CBepXHanpaBJIeHHbIX pellieTOK qe6blrneBa .nnH KJIJIIOCTpaUHM 113Me-
HeHI1H Q B 3aBI1CMMOCTH OT YBeJIMqeHHH HanpaBneHHOCTM. llepBbIH - 3TO pemeTKa
.lLTIMHOH 2A 113 1130TponHbIX 3JIeMeHTOB, KOTopaH npl1 rrOJIyBOJIHOBOM Illare MMeeT
MI1HI1MaJIbHyIO HanpaBJIeHHOCTb, paBHyro 5. Ha pa3Mepe B .nBe ,lIJII1HbI BOJIHbI pa3-
MemaJIMCb 7, 9, 11 11 13 3JIeMeHTOB. B Ta6n. 9.2 nOKa3aH MeX3JIeMeHTHbIH mar, Ha-
npaBJIeHHOCTb M Q ,LI,JIH Tpe6yeMoro ypOBHH SLR, paBHoro 20 JJ.D. 3HaqeHMH Q yx:a-
3bIBaIOTCH Ha pRC. 9.16 .naHHbIe npe.nCTaBJIeHbI Ha npHMOH nMHMH, paCCqHTaHHOH
CJIe.ayroIIJ;HM 06pa30M:
log Q  3,3175(G -5).
(9.25)
Ta6J1Hna 9.2. PerneTKa MHHOM 2A, SLR = I/YEJI = 20 ,lJ.D
N dll.. G Q
5 0.500 4.69 1.7
7 0.333 5.18 7.0
9 0.250 6.21 1.2 x 10 4
11 0.200 7.36 5.8 x 10 7
13 0.167 8.54 5.5 x lOll
<DopMa ypaBHeHI1H rrOCJIe BbIqHTaHMH HOpMaJIbHOH HanpaBJIeHHOCTH (Go = 5)
6bIJIa npe)UlOxeHa B [33, 34], r.ne MaKCMMH311pOBaHa HanpaBneHHOCTb JIHHeHHOro
HCTOqHI1Ka C yqeToM OrpaHHqeHI1H Ha Q C HCnOJIb30BaHI1eM co6cTBeHHbIX cPyHKUMH
I1CTOqHMKa - BbITHHyrbIX ccPepOl1,L{aJIbHbIX cPyHKUI1H. OHM oc06eHHO rro.nXO,lUIT AJUI
paCqeTOB, TaK KaK n03BOJIHIOT 6paTb npocTyIO npOH3BO,lJ;Hyro, nOCKOJIbK)' HMelOT
.nBOHHYIO opTOrOHaJIbHOCTb: B 6eCKOHeQHbIX npe.nenax, QTO COOTBeTcTByeT HHTerpa-
JIY 06meH 3HeprMH BO BceH 06naCTH yrnoB, 11 B paMKax KOHeqHbIX npe.nenOB, QTO
COOTBeTcTByeT HHTerpaJIY H3.rryqaeMOH 3Heprl1H B 06JIaCTH peaJIbHbIX yrJIOB. YCTa-
HOBJIeHO npH6JIH3HTeJIbHO JIHHeHHOe COOTHOllIeHHe Me)I{)IY log Q H HarrpaBJIeHHO-
CTblO C K03<P<PHUHeHToM, paBHbIM -2. 3TO nOJJ.TBep)I{)IaeT no.a03peHHe OTHOCHTeJIb-
HO Toro, qTO BapHaHT qe6bIllieBa MoxeT B pe3YJIbTaTe lIaBaTb Q 60nee BbICOKoe,
QeM He06xo.nHMO ,[(JIH .naHHoH HanpaBJIeHHOCTH, nOCKOJIbKY K03cPcPHUHeHTbI 113
Ta6n. 9.2 Ii 9.3 HaXO,lJ;HTCH B .nHana30He 3-4.
L(JIH Toro, QT06bI nOKa3aTb BJIHHHHe H3MeHeHHH YPOBHH SLR, B Ta6JI. 9.3
npHBe.aeHbI ,naHHbIe npH SLR = 10 n:E, a Ha pHC. 9.17 nOKa3aHa JIHHeHHaH 3aBH-

,
9.3. OnmUMU3au,UJI C Oi!paHU'1eHUflMU 
14
, 10 :'
. \
. .
10 8
d
N=13, = 0.167
10 12
10 10
Q
d
N=ll, x= O. 200
10 6
10 4
d
N=9 J = O. 250
10 2
d
N-J, ):'=-0.333
1 5
6
7
G
8
9
PHC. 9.16. rpa<pMK 3aBJ1CJ1MOCTJ1 Q OT HanpaBJIeHHOCTM, SLR = l/YDJI = 20 .aD
Ta6JIHna 9.3. PerneTKa .aJU1HOM 2A, SLR = l/YEJI = 10 n;D
N d/A G Q
5 0.500 4.89 1.8
7 0.333 5.40 37
9 0.250 6.19 7.6 x 10 4
11 0.200 6.99 3.5 x 10 8
13 0.167 7.74 3.3 x 10 10
CMMOCTb C K03<P<PMI.{MeHTOM 4,1475. fioJIee BbICOKMe 3HaqeHMH 60KOBbIX JIerreCT-
KOB YBeJIMQMBaIOT HarrpaBJIeHHOCTb 11 Q. PaCCqMTaHHbIe TOqKM ,LJ)IH N = 13 HBJIH-
K?TCH HeTOQHbIMI1, .LJ:BOMHa51 TOqHOCTb Ha 32-pa3PMHoM MaIlIHHe HBJIHeTCH
H.LJ:OCTaTOqHoii. TaKHM o6pa30M, Q YBeJIMQMBaeTCH npH6JIM3HTeJIbHO 3KcrrOHeH-

 DW8a 9. C8epXHanpa8JleHHble aHmeHHble peUJemKU
10 14
10 8
N-11. 1- 0.200
N-13, -0.167
10 12
10 10
Q
10 6
10 4
d
N-9. X. 0.250
10 2
N-7. 1- 0 . 333
6
7
G
8
9
1 S
PHC. 9.17. fpa<pMK 3aBMCMMOCTM Q OT HanpaBJIeHHOCTM, SLR = IjYEn = 10.n:E
IJ:HaJIbHO OTHOCHTeJIbHO HanpaBJleHHOCTH BblIIIe HOpMaJIbHOrO 3HaqeHHH. ,il;JISI
60JlbIllHHCTBa 3HaqeHH:M: YBeJIHqeHHe BblIIIe HOpMaJIbHO:M: HanpaBJleHHOCTH 03Ha-
qaeT, qTO KpHBaH Q HMeeT He3HaqHTeJlbHble KOJle6aHHH. CJIe,nyeT o6paTHTb BHH-
MaHHe Ha OqeHb 6blcTpoe YBeJIHqeHHe Q B 3aBHCHMOCTH OT HanpaBJIeHHOCTH;
,aa)l(e YBeJIHqeHMe Ha 10% OrpaHMqMBaeT IIIJilpJilHY nOJIOCbI qaCTOT HeCKOJIblGlMH
npoueHTaMH. O,l(HaKO BapHaHT qe6blIIIeBa MoxeT He ,l(aBaTb caMoe HM3Koe 3Haqe-
HHe Q, no BCe:M: BH,l(HMOCTH, Heo6xo,l(HM OrpaHHqeHHbIH CHHTe3 .IUIH nOJIyqeHHH
caMoro HH3Koro 3HaqeHHH Q ,lIJIH ,aaHHOH HanpaBJIeHHOCTH. B [29] npOBe,l(eHO Ta-
Koe HCCJIe,l(OBaHHe ,l(JIH peIIIeTOK npO,l(OJIbHOrO (oceBoro) H3JIyqeHIUI, HO TOJIbKO
)UIJI ,l(BYX CJIyqae B.
BTOpO:M: cJIyqaii - 3TO peIlleTKa C pa3MepOM B nOJIOBHHY ,l(JIHHbI BOJlHbI, nepBO-
HaqaJIbHO paCCqMTaHHaH B [44], KOTOpaH npH HCnOJIb30BaHHH ,l(BYX H301ponHbIX
3JIeMeHTOB ,l(aeT MaKCHMaJIbHYID HanpaBJIeHHOCTb 2. B 3TOT paCKpbIB nOMemalOTCSI
1])H, IIHTb, ceMb HJIH .aeBHTb 3J1eMeHTOB. B Ta6J1. 9.4 npHBO,l(HTCH COOTBeTCTBYIDIUHe
napaMeTpbI, OIIHTb-TalGl LLIDI ypOBHH SLR, paBHoro 20.aB. HCIIOJIb3YIDTCH 0603Ha-
-

9.3. OnmUMU3a14UJ1 C 02paHU'IeHUJlMU 
Ta6JIHua 9.4. PemeTKa .nJIHHOH 0,5"-, SLR = I/YEJI = 20 .nE
N d/l G Q
3 0.25 2.11 2.6
5 0.125 3.17 8.7 x 10 3
7 0.0833 4.40 5.7 x 10 8
9 0.0625 5.66 1.7 x 10 14
qeHI1H Toro )l(e Tl1na - log Q = a(G - 2), HO B .naHHOM CJIyqae TOqHOCTb He CTOJIb
BbICOKaH. HeI13BeCTHO, BbI3BaHO JII1 3TO OIIIH6KaMI1 B paCqeTaX I1JII1 MaJIbIM pa3Me-
pOM paCKpbIBa B ,l])IHHaX BOJIH.
B [12] pacrrpOCTpaHeH rrpl1HHn qe6bIllieBa Ha peIIIeTKH npo,nOJIbHOrO 113JIyqe-
HI1$I, HO TOJIbKO ,nJUI d < A/2. Bo H36e)l(aHHe nOHBJIeHHH 3a.n;Hero JIeneCTKa IIIar pe-
IIIeTKH 06bIQHO 6epeTC$I < "-/4. ArrH JII06oro yrJIa CKaHl1pOBaHl1$I '" npeo6pa3yeTcH,
KaK 06bIqHO, B cJIe,nYIOII(I1M BM,[(:
'V = kd(sine - sine o ),
(9.26)
r.ne 8 0 - 3TO yrOJI CKaHl1pOBaHIDI (rJIaBHbIM nyq), a Me)l(3JIeMeHTHbIM c,nBl1r no
<pa3e paBIDIeTCR kd sin 8 0 . K03<P<PHI.(HeHT bI a 11 b CTaHOB$ITCR paBHbIMI1
3 + Zo + 2 .J 2(zo + 1) cos kd
a=- .
2 sin 2 kd '
b = (.Jzo + 1 +.J2 coskd) .
2 sin 2 kd
(9.27)
9.3.2. OrpaHMeHMe Q MnM AonYCKOB
HanpaBJIeHHOCTb MO)l(eT MaKCI1MI1311pOBaTbCH C yqeToM orpaHI1QeHHH no IIIl1pl1He
rrOJIOCbI (Q) MH .norrYCKaM. Ea30BbIe paMKH orpaHWleHHoH OrrTI1MH3a1111 6bIJII1 pa3-
pa60TaHbI [15, 42]. B [7] rrpe,nCTaBJIeHa o630pHa$I pa60Ta no .naHHoM TeMe. MCrrOJIb-
30BaHI1e 3anl1CH co cKo6KaMH, BBe.neHHoe ,lJ.HpaKoM [14], n03BOJIReT ynpOCTI1Tb
npe,nCTaBJIeHl1e. llYCTb (AI 6y,n;eT BeKTOpOM-CTpOKOH, a I A) - BeKTOpOM-CTOJI6OM.
CKaJIHpHOe np0l13Be,neHl1e 3aTeM npHHHMaeT CJIe.nyIOlI(HM BH,LI;:
(AIA*) = LIAI,
(9.28)
r,n;e * 03HaQaeT KOMnJIeKCHO-conpIDKeHHyIO BeJIHQI1HY. Ha30BeM BeKTop-CTpOK)'
KOMITJIeKCHblX B036)')K,[(eHI1M peIIIeTKH J 11 BeKTOp-CTOJI6e <pa30BbIX Ha6erOB F:
exp(- jkrl sine)
F = : ,
exp(- jkr n sine)
(9.29)
r,ne r n - 3TO paCCTO$IHl1e OT TOQKH OTCQeTa .no n- ro 3JIeMeHTa. ,L1;JI$I peIIIeTKH C paB-
HbIM HHTepBaJIOM r n (n - l)d.'

b rlla8a 9. C8epXHanpa8lleHHble aHmeHHble pememKU
Terrepb orrpe.u;enHM MaTpHIJ.bI A H B, flIe A II 3neMeHTbI.B paBHbI
IAI =I F*)(FI.
Bnm =  f /;(8,<p)exp[-jkd(n -m)sin8]dn.
41t
(9.30)
(9.31)
,lJ.l1arpaMMa i-fo 3JIeMeHTa - fi. 1130l'pOnHbIe 3neMeHTbI 11 3KBH.nHCTaHTHaR pe-
llIeTKa .u;orrYCKaIOT ynpoIUeHHR A H B. 3neMeHTbI CTaHOBRTCR paBHbIMH
Anm = exp[ - jkd(n - m) sin 8],
Bnm = sinc[(n -m)kd].
(9.32)
Tenepb HanpaBneHHOCTb MoxeT 6bITb 3arrl1CaHa B cOKpameHHoH <popMe:
G = (J1AIJ*) .
(J1  J*)
(9.33)
'lIyncTBHTenbHOCTb .u;onYCKa S onpe.u;eIDIeTC5I KaK Benl1qHHa H3MeHeHH5I MaKCH-
MaJIbHOfO 3HaqeHH5I HarrpRxeHHOCTH rron5l, C03.u;aBaeMOfO norpemHOCT5IMH H3Me-
HeHHR cr} (H3MeHeHHeM 3JIeMeHTOB MaTpHl(bI J) [42]:
(8.£)2 cr). <J1 J)
cr 2 £2 <J1 AI J*)
S=--'£= -
cr} cr}. cr}.
_ (J1 I)
- <J1AIJ*).
(9.34)
TaKHM 06pa30M, QYBCTBHTenbHOCTb TaIOKe 3anHCbIBaeTC5I B cOKparueHHOM
Bl1.lJ:e. TIapaMeTp Q y.u;06HO Haxo.u;HTC5I H3 Q = SG, WIH
(J1 J*)
Q= <JlBlJ*) .
(9.35)
HanpaBJIeHHOCTb - 3TO COOTHomeHHe .u;BYX 3pMHTOBbIX KBMpaTHqHbIX <pOPM,
npH 3TOM B HBIDIeTCH nOJIO)l(J{TenbHO onpe.n:eneHHoH, a A RBn5leTCR, no KpaHHei1
Mepe, nOnO)l(J{TenbHO nOJlyonpe.n:eJleHHoH. TalGlM o6pa30M, Bce c06cTBeHHbIe 3Ha-
qeHH5I conpIDKeHHoro ypaBHeHIDI
IAII) =GmaxlJ)
(9.36)
51BIDIIOTC5I HYn5lMH HJIII nOJIO)l(J{TeJIbHO .u;eHcTBHTeJIbHbIMH 3HaqeHIDIMH. TIOCKOJIbKY
A - 3TO o.n:HOqrreHHaR ,[(Han;a, TO IIMeeTC5I O,[(HO HeHyneBoe c06CTBeHHoe 3HaqeHHe.
C06CTBeHHbIH BeKTOp paBeH
I J max) =I -l F).
(9.37)
COOTBeTCTByIOIUaH MaKCHMaJIbHaR HanpaBneHHOCTb npe.u;CTaBlliIeTC5I B BH,D;e
G max = (FI -l F*).
(9.38)
Bo MHOfHX rrpHnoxeHHHX BIDKHO MaKCHMH3HpOBaTb G/T (oTHomeHHe HanpaB-
JIeHHOCTH K myMY H myMoBOH TeMnepaType), qTO 3KBHBaneHTHO MaKCHMH3aIJ.HH
SIN (cHfHaJI/myM). QT06bI 3TO c,[(eJIaTb, .u;HarpaMMa 3neMeHTa B HHTerpane ,[(JIR Bnm
yMHoxaeTCR Ha myMOByIO TeMnepaTYPY aHTeHHbI T(8, <p). ,lJ.aJIee BeKTOp B036yx,ne-
HHR, KOTOpbIH MaKCHMI13HpyeT SjN IUIH GIT, HBJIReTC5I qaCTblO ypaBHeHHR (9.37).
1_

9.4. C02J/OC060Hue C6epXHOnp06JleHHbIX peUJemOK d
JJ:pyroe CooTHollIeHHe, KOTopoe MO)KeT 6bITb Hanp.HMyIO MHHHMH3HpoBaHo, -
3TO 3CP<l>eKTHBHOCTb rnaBHoro JIeneCTKa: ,UOllil MOll{HOCTH, cOJJ:ep)l(all{ellC.H BHyrpH
rnaBHoro nyqa no HYJIeBoMY ypOBHIO. To eCTb
(J] AI J*)
llb = (J] B1 J*)'
(9.39)
npH 3TOM HHTerpHpOBaHHe B (9.31) ocym:eCTBn.HeTC.H no o6nacTI1, 3aH.HTOll fJIaB-
HbIM JIeneCTKOM.
TaIOKe B03MO)I(Ha onTHMH3aUH.H nyreM perynHpoBKH TonbKO <l>a3 [43]. 3TOT Ba-
pHaHT MO)l(eT 6bITb npl1BneKaTeJIbHbIM .l{JIH pellieTOK C aKTHBHbIMI1 MOJJ:ynHMH, rJJ:e
)l(eJIaTeJIbHO paBHOMepHoe aMnJIHTYJJ:Hoe pacnpeJJ:eJIeHHe. K CO}J(aJIeHHIO, nOJIOBHHa
CTeneHeH cBo6oJJ:bI TepHeTCH, H aMnJIHTy.ua HrpaeT ropa3JJ:O 60JIee CHJIbHyIO pOJIb B
cl>opMHpoBaHHH JJ:HarpaMMbI.
Ha npaKTHKe, H3-3a HMeBllIerOCH paHee OrpaHHqeHHOrO aHCaM6JIH BapHaHTOB
CBepXHanpaBJIeHHbIX pellIeTOK npOll{e paCCIIHTaTb Q, Rrad H G .l{JI.H HeCKOJIbKHX pe-
llIeTOK HanpHM)'IO. 3TO n03BOJIHeT IUl:TH Ha npHeMneMble KOMnpOMHCCbI npH pa3-
pa60TKe 6e3 CnO)I(HOH onTHMH3aUHH C orpaHHIIeHIDIMH.
9.4. CornaCOBaHMe CBepXHanpaBneHHblX peweTOK
CBepXHanpaBJIeHHble pellIeTKH, KaK 3JIeKTpHIIeCKH MaJIbIe pellIeTKH, 06JI3JI:a1OT 3Ha-
lIeHIDIMH conpOTHBJIeHHH H3JIyqeHHH MHoro MeHbllIe 50 OM H peaKTHBHoro conpo-
THBJIeHHR MHoro 60JIbllIe 50 OM. B 060HX cnyqaHx cornac)'IOlI(He u;enH npen;CTaB-
JIHIOT C060H cepbe3HyIO npo6neMY: co6cTBeHHbIe nOTepH 3HaqHTenbHO
yneJIHQHBaIOTCH, KaK 6YJJ:eT nOKa3aHO HlDKe.
9.4.1. YBenMeHMe nOTepb pacnpeAenMTenbHoM CMCTeMbl
COrnaCyIOIUHe uenH .l{JIH cBepxHanpaBJIeHHOll pellIeTKH L(OJDKHbI KOMneHCHpOBaTb
60JIbllIOe peaKTHBHoe conpOTHBneHHe H npeo6pa30BbIBaTb He6oJIbllIOe conpOTHB-
JIeHHe H3JIyqeHH.H nnlOc corrpOTHBJIeHHe rrOTepb B HOMHHaJIbHyIO BeJIHqHHY, 06bIQ-
HO 50 OM. KaK npaBHJIO, Ka)l(,l(OMY 3JIeMeH1)' Heo6xon;HMa CBO.H COrJIaC)'IOlliaH
uenb, XOTH CHMMeTpHqHbIM pellIeTKaM (c nOnepeIIHbIM H3JIyqeHHeM) Tpe6yeTcH
MeHbllIe TaKHX uenell. ECJIH corJIaC)'IOIUaH uenb COCTOHT H3 JJ:HCKpeTHbIX KOMno-
HeHTOB L H C, TO HH3Koe 3HaIIeHHe R H BbICOKoe X 6YJJ:YT C03JJ:aBaTb OqeHb 60JIb-
llIHe UHpKYnHpYIDll{He TOKH B 06ll{eH uenH, COCTOHll{en H3 3JIeMeHTa pellIeTKH, CO-
rJIaCYIOIUeH uenH H reHepaTopa. 3TH TOKH 6y)IyT YBeJIHQHBaTb c06CTBeHHbIe
rrOTepH. AHaJIOrHqHbIM 06pa30M, pacnpeJJ:eJIeHHaH COrJIaCYIOIUaH u;enb npH YCJIOBH-
HX HH3Koro R H BbICOKoro X 6YJJ:eT HMeTb OQeHb 60nbllIHe CTOHQHe BOJIHbI BL(OJIb
llIJIeHcpOB H TpaHC<pOpMMPYIDIUHX OTpe3KOB. OnHTb-TaKH c06CTBeHHbIe nOTepH )'Be-
JIHQHBaIOTCH. B 060HX CJIyqaHx 60JIbIIlHe nOTepM CBH3aHbI C TeM, QTO MOll{HOCTb
rrponOpU;HOHaJIbHa KB3JI:pa1)' HanpIDKeHIDI (HJIH TOKa); UHpKYnHpYIOIIJ;He TOKH HJIH
CTOWIHe BOJIHbI HBJIHIOTC.H 60JIbllIHMH.

 rlla6a 9. C6epXHanpa6lleHHble aHmeHHble peUlemKU
TpaHc<popMaTOp JIMHMM nepe,[(aqM RBJIReTCR TMnMqHbIM. 0603HaqMM nOTepM
COrJIaCOBaHMR KaK L, a K03CP<PMUMeHT CT05IQei1 BOJIHbI no HanpIDKeHMIO aHTeHHbI
KaK KCBH (VSWR). Tor.n:a cpaKTMqeCKlle nOTepM La COCTaBJIReT [28]:
(VSWR + 1)2 L2 - (VSWR -1)2
La = .
4 . L . VSWR
(9.40 )
,LJ;JIR KCBH » 1, cpaKTMQeCKMe nOTepH COCTaBJIRIOT:
VSWR . (L2 - 1)
La  .
4L
(9.41)
Ha pMC. 9.18 nOKa3aHa 3aBHCHMOCTb cpaKTHQeCKllX IIOTepb OT KCBH npM nOTe-
pRX COrJIaCOBaHMR, paBHbIX 0,1, 0,2, 03, 0,5, 1, 2, 3 M 5 ,[(E. ,LJ;JIR R < < Ro, KCBH
paBeH KCBH ::: (R2 0 +XZ)/RR o , a JI]lR X» Ro KCBH  X2/RRo. TIoCJIe,[(Hee TaIOKe
cnpaBeLUIMBO ,[(lliI R < < Ro M X > > Ro. HeKoTopbIe TMnMqHble 3HaqeHIDI npMBO,lIRT-
CR B Ta6JI. 9.5. HarrpMMep, cJIyqaH RjRo = 0,1 M X/Ro = 10 ,[(aeT KCBH = 1010. 00-
TepM COfJIaCOBaHMR 0,01 ,[(1) cpaKTMqeCKM CTaHOB5ITCR IIOTepRMM 3,35 .lIE; nOTepH
COfJIaCOBaHMR 0,1 ,[(D cpaKTHqeCKH CTaHOBRTCR nOTepRMH 11,01 .n:E. Donee BepORT-
HbIM cnyqaeM, nOCKOJIbKY OTHOllIeHMe peaKTHBHoro corrpOTMBJIeHMR K aKTMBHOMY
06bIqHO BbIllIe, RBJIReTCH R/Ro = 0,1 If X/Ro = 30, B pe3YJIbTaTe KCBH = 9010. no-
TepM COrJIaCOBaHlfR 0,01 ,[(1) Tenepb ,[(alOT cpaKTlfQeCKHe nOTepH 10,56 .n:E; nOTepH
cornaCOBaHIDI 0,] ,[(D ,[(alOT cpaKTMIIecKHe nOTepM 20,2 ,[(1). 3TH <paKTHqeCKHe nOTe-
pM nOPMKa 10 ,[(1) corJIaCYIOTCR C H3MepeHMHMM Ha uenRX (BbIcoKoTeMnepaTYPHbIX
CBepxnpOBO.LJ;RIUMX 11 Me,aHbIX COfJIacyJOIUl1x) [23-25].
1
IloTepl1
CTORQei1
BOJIHbI
10
0.1
1
10
KCBH
100
1000
PHC. 9.18. KpMBble nOTepb B <PYHKUMM KCBH cBepxHanpaBJIeHHOH aHTeHHbI

JIumepamypa d
Ta6JIHua 9.5. 3aBHcHMoCTb KCBH OT paccOrJIaCOBaHHH MMne,n:aHca aHTeHHbI
R/Ro X/Ro
1 3 10 30 100
1 1.000 10.91 102.0 902.0 1.000 x 10 4
0.3 6.820 33.60 337.0 3004.0 3.334 x 10 4
0.1 20.05 100.1 1010.0 9010.0 1.000 X 10 5
0.03 66.68 333.4 3367.0 3.003 x 10 4 3.334 x 10 5
0.01 200.0 1000.0 1.010 X 10 4 9.010 X 10 4 1.000 x 10 6
9.4.2. PeweTKM C Mcnonb30BaHMeM BblcoKoTeMnepaTypHblx
CBepxnpOBOAHMKOB (High-Temperature
Superconductors - HTS)
TIOCKOJIbK)' conpOTllBJIeHMe 113JIyqeHIl5I cBepxHanpaBJIeHHOM pellIeTKM yMeHbllIaeT-
CH npll6JIM3HTeJIbHO o6paTHo rrponOPQMOHaJIbHO JQ, JIerKO cnpoeKTHpOBaTb pe-
llIeTKY, rn;e Rrad conOCTaBllMO HJIM < R1os s , B pe3YJIbTaTe qero 3<t><t>eKTHBHoCTb co-
CTaBJIHeT 50% HJIH MeHbllIe. KpoMe Toro, MMelOT MeCTO nOTepH corJIaC)'IOll.{MX
u;enei1, KaK 3TO TOJIbKO qTO 6blJIO onllcaHO B [20]. Ha npaKTllKe npllMeHHMOCTb
3TMX pellIeTOK orpaHMqHBaeTCH Q HJIH llIHpHHOH nOJIOCbI qaCTOT; MoxeT HCnOJIb30-
BaTbCS{ aHTeHHa C Q B HeCKOJIbKO COTeH, HO aHTeHHa C Q B HeCKOJIbKO TbICHq, KaK
npaBHJIO, HCnOJIb30BaTbCH He MoxeT. ,[(axe eCJIll llIllpHHa rrOJIOCbI CllrHaJIa < < 1%,
HeCTa611JIbHOCTb napaMeTpOB oKpyxaIOll.{ei1: Cpen;bI LUI5I aHTeHH C OqeHb BbICOKHM Q
3aTpyn;HHeT HX HCrrOJIb30BaHHe. AuanTHBHa5I HacTpoHKa B03MO)I(Ha, HO llMeeT CBOH
co6cTBeHHbIe Hen;OCTaTKH. ,n;JISI 3THX HeCKOJIbKMX c.rryqaeB, r,n:e Q aHTeHHbI HBJIHeTCSI
yrrpaBJIHeMbIM, HO CHIDKaeTCH 3cl><l>eKTHBHoCTb, MoxeT 6bITb u;eJIeC006pa3HoH pea-
JIH3aUHSI perneTKM B BapHaHTe HTS [8].
JIHTepaT)'pa
1. Bach, H., «Directivity of Basic Linear Arrays», Trans. IEEE, Vol. AP-18, Jan. 1970, pp.
107-110.
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.....

JIumepamypa 
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1081-1085.

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OnTHMH3all.H5I MaTpHUbI EaTJIepa BKJIlOqaeT y.rryqIlIeHHe nOJIOCbI nponYCKaHM5I
(24%) C npHMeHeHHeM ,aonOJIHHTeJIbHOrO cPa3HpOBaHH5I, HCnOJIb3Y51 pa30MKHYTbIe
IlIJIeHcPbJ Ha JII1HHH 3a,IJ,ep)l(J(l1, a TaIOKe 60JIee IlIHpOKOnOJIOCHbIe IIOCJIe,aOBaTeJIb-
HbIe rM6pl1,LI:HbIe YCTpoHcTBa [72]. B pa60Te [17] HCnOJIb3yeTc5I TeXHOJIOfM5I
ll(eJIeBOH JIHHHM ,lJ)I5I I1CKJllOqeHHH nepeCeqeHM5I JIHHHH. bOKoBbIe JIeneCTKM 6bIJIH
yMeHbllIeHbI nYTeM I1CnOJIb30BaHH5I 8 3JIeMeHTOB C HepaBHOMepHbIMH HanpaBJIeH-
HbIMH .ueJIMTeJI5IMH [70].
10.2.1.3. MaTplfLlhl 5nacca If HoneHa
B MaTpHlI.e EJIacca llCnOJIb3yeTc5I Ha60p JIHHHll nepe,aaQI1 K 3JIeMeHTaM pemeTKH,
KOTopbIe nepeceKalOT Ha60p JII1HMH rropTOB .rryqeti, C HarrpaBJIeHHbIM OTBeTBMTeJIeM
B Ka)I()J:OH TOQKe nepeCeqeHH5I [8] (CM. 3CKH3 Ha pllC. 10.6).
HanpaBJIeHHbI:H
OTBeTBllTeJIb
TIOpTbI
JIyqeif
PRC. 10.6. CxeMa MaTpl1I.J;bI Enacca
BepXH5I5I cPM,aepHa51 JIMHM5I BbID.eJI5IeT JIyq, HarrpaBJIeHHbIH no HOpMaJIH K pac-
KPbIBY, II OTHOCMTeJIbHO He3aBllCllMa OT ,n:pyrHx <pl1,LI:epHbIX JIHHllH. BTopa51 qHUlep-
Ha51 JIMHll51 cTpeMHTC5I BbI,n:eJIHTb JIyq, HanpaBJIeHHbIM no,n: yrJIOM K HOpMaJIl1, HO Ha
CB5I3b OKa3bIBaeT B03,n:eHCTBl1e BepxHHI JII1HM5I. LI.lliI ycnemHoro aHaJIll3a Heo6xOlll1-
MO paCCMaTpl1BaTb JIllHl110 nopTa Ka)I()J:OfO JIyqa KaK perneTK:y (oTBeTBHTeJIeH) 6ery-
ll(eH BOJIHbI C yqeToM B3allMo,n:eHCTBI151 HeCKOJIbKHX TaKHX perneToK. B pa60Te [12]
npHBo,n:HTC5I aHaJIll3 MaTpMlI.bI EJIacca. MOLleJIl1pOBaHHe MO)l(eT 6bITb BbInOJIHeHO
Ha KOMnblOTepe, QTo6bI o6eCneQHTb y,n:aQHbIH KOMnpOMI1CC Me)I()J:y 3<P<I>eKTHBHo-
CTblO cxeMbI II CB5I3blO JIyqell. On:HaKO 3TH perneTKH Tpy,n:HO KOHCTpyJ1pyIDTCH, no-
u v
CKOJIbKy B3allMo,n:eI1CTBMe Me)l(,[(y OTBeTBI1TeJI5IMI1 3aTpY,JJ;H5IeT HaCTpOI1K:y OTBeTBMTe-
JIell 11 KOppeJI5IlI.l1lO C H3MepeHHbIMI1 xapaKTepllCTI1KaMM. B pa60Te [12]
HCCJIe,aOBaHbI TalOKe llIMpOKOnOJIOCHbIe BepCHH MaTpHlI.bI bJIaCCa, BKJIIOQalOIlI.He
,
BpeMeHHyIO 3a.aep)l(}()'.
MaTpllua HOJIeHa [41] - 3TO o606rn:eHlle MaTpllU EJIacca 11 EaTJIepa, npe,a-
CTaBJI5IIOll(aH C060M KaHOHHQecK:y1O KOH<pl1rypaQHIO cxeMbI ,l],OY. OHa HCXO,QllT 113

 rA060 10. MH020A)l'Ie6ble OHmeHHbl
t
<t>aKTa, orrpe,neJIeHHOrO HIDKe, KOTOpbIH COCTOHT B TOM, qTO OpTOrOHaJIbHbIM .rryqaM
1pe6yeTcH yHHTapHaR MaTpHl.(a CBH3H, r,ne 3JIeMeHTbI MaTpHl.(bI eCTb CBR3b n-fO 3JIe-
MeHTa aHTeHHbI C nopTOM m-ro JIyqa. YHHTapHbIe MaTpHl.(bI MOryr 6bITb pa3JIOXe-
HbI Ha rrpOH3Be,neHHe 3JIeMeHTapHbIX yHHTapHbIX MaTpHI.(, H3 KOTOpbIX 3,L(eCb rrpe,L(-
v
CTaBJIReT HHTepec CJIe,nYK>W;HH THrr:
jcosaexpj(3 -jsina 0
j sin a exp j(3 j cosa 1
o 1 I
(10.5)
3TO rrpe,ncTaBJIeHHe rrOJIe3HO, TaK KaK OHO rrpe,ncTaBJIReT C060H rrpocTyIO uenb,
CO,L(epxalI.{ylO ct>a30Bpaw;aTeJIb Ii HarrpaBJIeHHbIH OTBeTBHTeJIb, KaK BH.D:HO Ha
pHC. 10.7. COe,L(HHeHHe 3THX rrpOTOTHrrHbIX CeKIJ;HH I(enH o6pa3yeT MaTpHl.(y HOJIe-
Ha, nOKa3aHHYlO Ha pHC. 10.8. ,L(oKa3aHo, tJTO MaTpHI(a HOJIeHa MoxeT 6bITb CBe,L(e-
Ha K MaTpHue EaTJIepa. KaK H B CJIyqae MaTpHI(bI bJIaCCa, MaTpHl.(a HOJIeHa MoxeT
v
HMeTb KOJIHqeCTBO rropTOB JIyqeH, OTJIHqalOw;eeCB OT KOJIHQeCTBa 3JIeMeHTOB aH-
TeHHbI, XOTH TOJIbKO tJTO npe,L(CTaBJIeHHaH KOHI(errTyarrbHaH pa3pa6oTKa 1'pe6yeT,
qTo6bI 3TH KOJIHqeCTBa 6bIJIH paBHbIMH. PerneTKa HOJIeHa rrpe,ncTaBJIHeT C060R pe-
Pac. 10.7. Qenb YHHTapHoH MaTPHbI CBR3H
f
cJ>a30BpaIQaTeJlb
nOpTbI
.nyqei1
I'
fH6pH.nHIDI
cxeMa
Pac. 10.8. CxeMa MaTPHUbI HOJIeHa

10.2. YcmpoucmBa rjJopMupoBaHUR JI)l'teu 
aJII13aljJ11O o6I.I.J;ero aJIrOpMTMa ,lI.I1CKpeTHoro rrpeo6pa30BaHI15I <1>YPbe M rrpl1MeHI1Ma
WI5I JII06oro ql1CJIa 3JIeMCHTOB, BKJIIOQa5I rrpocTbIe QI1CJ1a. no Mepe YBeJII1QeHI15I
QI1CJIa K03<P<PI1IJ:l1eHTOB B QHCJIe 3JIeMeHTOB pemeTKJ1 MaTpHIJ:a HOJIeHa MO)l(eT 6bITb
rrpl1Be,lleHa K GOJIee rrpocTbIM <popMaM, B pe3YJIbTaTe qero B KOHeqHOM HTore rro.rry-
QaeTC5I aHMor 6bICTporo rrpeo6pa30BaHI15I <1>YPhe- EaTJIepa, KOr,l1a N:= 2 n . B CH.rry
u..... u '-'
BbICOKoro qHCJIa COCTaBHbIX qaCTeH 11 TPY,l1HOCTeH, CBH3aHHhIX C HaCTpOHKOH IJ:errH,
cxeMa <pOpMHpOBaHH5I JIyqa HOJIeHa HCrrOJIb3yeTC5I pe,l1KO.
!.t
--
10.2.1.4. p'sYMepHhle /1,HarpaMMoo6pa3YIOUlHe YCTpoMcTsa
HeCKOJIbKO nyqeH B o6el1x IIJIOCKOCTHX MOryT 06eCrreQHBaTbC5I rryreM rrepeKpeCTHo-
ro COe,l1I1HeHKH ,l1BYX MaTpHIJ: EaTJIepa HJIH JIHH3 POTMaHa (CM. pa3,l1eJI 10.2.2.1). Ha
pl1C. 10.9 rrOKa3aHO 3TO pacrrOJIO)l(eHHe [57]. Ha pHC. 10.10 11306pa)l(eHa ctorrKa JIHH3
POTMaHa Ge3 COe,l1HHHTeJIhHbIX Ka6eJIeH [4]. MaTpMIJ:a reKCarOHaJIbHOH pemeTKH
MaK<1>apJIeH.na 113 cJIe,l1yIOI.I.J;ero pa3,l1eJIa RBlliIeTC5I 60JIee 3cPcPeKTHBHbIM (MeHbmee
KOJIIIQeCTBO KOMrroHeHToB) AOY. EI.I.J;e B O,l1HOH ,l1BYMepHOH CHCTeMe HCrrOJIb3yIOTC5I
,[{Be CTorrKH 8-rropToBbIX MaTpMIJ: BaTJIepa, KaK rrOKa3aHO Ha pRC. 10.11 [18]. TIyqOK
JIyqeH 3TOH pemeTKH rrOKa3aH Ha pRC. 10.12. CJIO)l(HaR aHTeHHa, B KOTOpOi1 rrpMMe-
IDIIOTC5I rrepeceKalOrn;lIeCR MaTpHIJ:bI EaTJIepa, rrpe,l1Ha3HaqeHa WI5I CrryrHMKOB «l1pM-
,l1HYM». llIeCTHaaIJ:aTI13JIeMeHTHbIe MaTpMIJ:bI rrO,l1COe,l1I1HeHbI K 3JIeMeHTaM AP, rrpl1
3TOM 8-3JIeMeHTHbIe MaTpWIJ:bI I1MelOT rrepeKpeCTHoe COe,l1RHeHl1e [486]. I10CKOJIbKY
30Ha rrOKpbITIDl KOi1 pemeTKlf rrpH6JII13RTeJIhHO WMeeT <POPMY ceKTopa, He06xo-
,l1HMa TOJIbKO nOJIOBI1Ha HOpMaJIbHbIX 256 MaTpHIJ:, 11 HeKOTophIe nopTbI JIyqei1 HeHC-
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KOJIHqeCTBO KOMTIOHeHToB) 2-MepHa5I MaTpHIJ:a.
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I KaJIbHble
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10.2.1.5. p'sYMepHafl MaTpHLla MaKtPapneHp,a
M,l1eR 2-MepHoro Ma1pHHoro A9Y C I1CnOJIb30BaHHeM rneCTHrpaHHbIX perneTOK H3-
.rryqalOlI.(11X 3JIeMeHTOB, BH,l1HMO, B03HI1KJIa B HaqaJIe 60-x r0,l10B 20-ro BeKa; 3aTeM
pa60Ta rrp0,l10JDKaJIaCb B [65]. B pa60Te [36] rrOKa3aHO, KaK CI1HTe3HpOBaTh uenb ,l1e-
JII1TeJIeH MOrn:HOCTI1 H <pa30C,l1Bl1ralOlI.(I1X WIeeK WIH 2-MepHoi1 pemeTKH .rryqei1. 3TO
)J.OY OCHOBaHO Ha HeqeTHOH reKCarOHaJIbHOH (meCTl1rpaHHoi1:) AP, rlIe u:eHTpOM 5IB-
lliIeTCR He O,l1I1H 3JIeMeHT, a, CKopee, TpHaaa 3JIeMeHTOB, KaK rrOKa3aHO Ha pRC. 10.13.

 Dla6a 10. MH02OJl}"le6ble aHmeHHbl
I
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PHC. 10.10. CToIIKa JII1H3
POTMaHa
PHC. 10.11. )J;BYMepHbIe MaTpMUbI EaTJIepa [18]
PHC. 10.12. )J;BYMepHa5I p03eTKa JIyqei1: MaT-
PMUbI EaTJIepa [18]
PHC. 10.13. Tpna.nbI rpYIIIIbI PYIIOPOB
3M2 ,L(JI5I M = 4, N = 48
3TO nplfBO.IUfT K TOMY, qTO KaJK,LJ;aH BTopaH cTopoHa rnecTlfrpaHHlfKa 3JIeMeHTOB
I1MeeT Ha O.l(I1H 3JIeMeHT 60JIbIIle, qeM CMe)KHbIe CTOpOHbI. ECJIlf M - nOJIOBlfHa
ql1CJIa 3JIeMeHTOB B Hal160JIbIIleH .l(HarOHaJIl1, TO o6m;ee ql1CJIO 3JIeMeHTOB N paBHH-
eTCH 3M2. OKa3bIBaeTC5I, QTO 3Ta HeQeTHaH peIlIeTKa MoxeT 6bITb pa3.l(eJIeHa Ha TpH
CHMMeTpl1QHbIX Ha60pa 3JIeMeHTOB, KaK IIOKa3aHO Ha pl1CyHKe, H Ka)J()];bIll Ha60p
MoxeT 6hITb nO.l(COe.l(lfHeH K cl>opMlfpOBaTeJIIO .rryqeH. Tplf Coe.l(I1HeHHbIX Me)l([(Y co-
60ll cl>opMHpOBaTeJIH JIyqeH Tor,na o6eCneqlfBalOT reKCarOHaJIbHyJO (rneCTl1yrOJIb-

10.2. Ycmpoucm6a rjJopMupo6aHUR Ilyrteu 
BbIXO,ll;HbIe IIOpTbI
TIJIOCKOCTb
pacnOJIOXeHIDI
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(BXO.ilHbIe nopTbI)
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PHC. 10.14. TpHa.aa ,[(oy rnecTMrpaHHoM perneTKM
BbIXO,ll;bI N2 BbIXOD:bI N2
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KOH 3JIeMeHTOB. 3TH <}>OpMlfpOBaTeJIH JIyqeH, KOHeqHO, 60JIee CJIO)l(Hble, qeM
o,n:HOMepHaR MaTplfu;a. OHM BKJIIOqalOT B ce6R ,n:eJIIfTeJIM MOII.J;HOCTIf C HeCKOJIbKHMIf
IIJIeqaMH, B qaCTHOCTH, TaKHe KaK TpeXKaHaJIbHble ,n:eJIHTeJIH Ii <}>a30c,n:BHraIOWHe
RqeHKH [14]. ,
Ha pHC. 10.14 If 10.15 IIOKa3aHbI ,n:Be cxeMbI no,n:coe,n:IfHeHHR 3JIeMeHTOB K
rropTaM JIyqeH. Ha pHC. 10.14 TpHaaa 3JIeMeHTOB perneTKH no,n:coen:HHeHa K Ha60-
py Mo,n:YJIeH ,n:eJIHTeJIb-<}>a30BpawaTeJIb C BbIxo,n:aMH, npe,n:OCTaBJIRIOII.J;IfMH C060M
TpHaabI nopTOB JIyqeH. Ha pHC. 10.15 nOKa3aHO 06paTHoe no,n:KJIlOqeHMe (K MaT-
pHu;e) - TpHa.aa 3JIeMeHTOB H TpHaaa nopTOB .rryqeit Ha 3TOM THne pellIeTKH BbI-
nOJIHeH OTHOCIfTeJIbHO He60JIbllIOH 06'beM pa60T, M 06IIJ;He MeTo.n;bI ClfHTe3a nOKa
HeH3BeCTHbI. <l>aKTlfqeCKIf BCR 3Ta TeMaTIfKa, no BceR BIf,n:HMOCTIf, OCTaHOBHJIaCb,
HeCMOTpR Ha CBOID nepcneKTIfBHOCTb. JJ:BYMepHbIll <pOpMHpOBaTeJIb JIyqeH HMeeT
HeCKOJIbKO npeHMyru;eCTB. Bo-nepBbIx, 3,n:eCb MeHbrne qaCTeH, qeM B KaCKaae 01I-
HOMepHbIX perneTOK EaTJIepa. Bo- BTOpbIX, npe.n;CTaBJIReTC.H B03MO)l(HOH CHHep-
reTlfqeCKaSl IfHTerpaU;IfSl <}>OpMHpOBaTeJISI JIyqeH C nepeKJIlOqalOmeM MaTplf-
ueH. HaKoHeu;, ero reOMeTplf.H 60JIee 3<}><}>eKTIfBHO no.n;xo,n:HT KaK MR lIBYMepHOM
perneTKIf npH6JIlf3lfTeJIbHO KpyrJIOH <}>OPMbI, TaK If ,n:JIR npOCTpaHCTBeHHoro
0630pa.
10.2.2. nMH3bl
10.2.2.1. p,HarpaMMoo6pa3YlOlLlee YCTPOMCTBO -
nHH3a POTMaHa
<l>IUI:epHaR (Ka6eJIbHaR) JIlfH3a (bootlace lens - rnHypOBaR JIHH3a) - 3TO orpaHJlqeH-
HaSl JIIfH3a, B KOTOpOH HCnOJIb3yroTCSI pa3JIJlqHble JIHHIfIf nepe,n:aq CBq, a DJlIfHbI IIY-
TeH OT BbIXO,n:HbIX nopTOB JIMH3bI K nopTaM M3.rryqalOIIJ;IfX 3JIeMeHTOB rrpe,n:onpe,n:eJIe-
HbI. PaHee B KaqeCTBe H30rH)'TOH JIlfH3bI HCnOJIb30BarraCb JIHH3a -2R [10, 11], rlIe
BHYTPeHHIDI H BHemH.H.H rrOBepXHOCTIf JIHH3bI 6bIJIH 06pa30BaHbI ,n:yraMIf OKp)')KHO-
CTeH C Hap)')KHbIM paaMYCOM B ,n:Ba pa3a 60JIbllIe BHY1]JeHHero. 3TO JIHH3a C e,rtIfHcT-
BeHHOH MMHOH n)'T1f C l1,[(earrbHOH KOJIJIHMaU;MeM B TOqKe B036y)K):(eHMSI B JII060H
TOqKe Ha <}>OKaJIbHOH .uyre [29]. O,n:HaKo aCHMMe1]lIDI aMllJIHTy,n:bI M.H BHeoceBoro
IIOJIO)l(eHHR .rryqeM nOBbIllIaeT ypOBeHb 60KOBbIX JIeneCTKOB. 3TO BMeCTe C KpyrJIOH
<}>OpMOH perneTKH orpaHHql1JIO nOJIe3HOCTb R-2R. IIepBoHaqaJIbHo OHa 6bIJIa BbIIIOJI-
HeHa B reo,n:e3lfqeCKOH <popMe (,n:e<}>opMHpOBaHHbIe rrapaJIJIeJIbHbIe IIJIaCTIfHbI).
06maSl TeopHSI cplf,n:epHbIX JIHH3 6bIJIa npeMoxeHa B [25]. ,lJ;pyra.H OlIHOMepHaR
JIHH3a (Ha3bIBaeMa5.1 «o,n:HoMepHOH», nOTOMY qTO OHa C03,n:aeT JIyqH B O,n:HOH nJIOC-
KOCTH), npe.n;Ha3HaqeHHaSl .aJISI IIepeMem:alOm:erocSI B036y)K):(eHHSI (rrHTaHH5.I) H JIM-
HeMHOH 113JIyqalOIIJ;eM perneTKIf, 6bma pa3pa60TaHa B [46]. BCKope 3TO IIplfBeJIO K
C03,n:aHHIO JIHH3bI POTMaHa C perneTKoH <}>HKcHpoBaHHblx TOqeK B036y)K):(eHH5I MSI
IIOpTOB JIyqeH. Ha plfC. 10.16 H306pIDKeHa JIlfH3a POTMaHa; nOKa3aH TOJIbKO O.n;IfH
IIOpT JIyqa. B rrepBOHaqarrbHOH JIHH3e IiCnOJIb30BaJIlfCb BOJIHOBO.ll. 1f3 rrapaJIJIeJIbHbIX
rrJIaCTHH JUISI B036y)K):(alOm:eH qaCTIf If KOaKClfaJIbHble Ka6eJIIf M5.I cpl1,[(epHoif qaCTIf.
B HaCTOSll.l{ee BpeMSI <popMaT IfCnOJIHeHHSI, KaK npaBRJIO, rrpe,n:CTaBJISleT C060H MIfK-
pOrrOJIOCKOByIO IfJIIf rrOJIOCKOBYJO JIHHHID JUI.H B036y)K):(alOm:eH qaCTIf, If JIH60 KoaK-
CHaJIbHbIe Ka6eJIu, JIu60 JIIfHHIf Ha rreqaTHOH n.rraTe lUIR <}>lflIepHoM qaCTU [4].
-

10.2. Ycmpoiicm6a r/JopMupo6aHUR JlY'Ieii d
IIOpTbI
3JIeMeHTOB
M3.rryqaIOIIJ.aR
perneTKa
I
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....... <pPOHT
I
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PHC. 10.16. ,n;OY Ha OCHOBe JUfH3bI POTMaHa
CT}Joro rOBopR, JIHH3a - 3TO cl>HJJ:epHaR (Ka6eJIbHaR) qaCTb, HO o6IUenpHHHTaR
npaKTHKa 3aKJIIOqaeTCR B TOM, QT06bI Ha3bIBaTb JIHH30H BeCb Y3eJI. 3TH JIHH3bI
HMelOT T}JH (HJJ:eaJIbHbIe) <POKaJIbHbIe TOqKH, 06bIqHO B ueHTpe pemeTKJI B036y)1(,[(e-
HHH H B ,nBYX CHMMeTpHqHbIX TOqKaX Me)f{)J;Y QeHTpOM H KpaeM ,nyrH B036y)1(,[(eHHH
(,nyrH KaqaHHR 06.rryqaTeJIR). OHH, TaKJIM 06pa30M, Cyru;eCTBeHHO YJIyqmalOT KOH-
CT}JYKI..J:HIO Py3e [48a].
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MHCCbI, TaK H 3<l>cl>eKTbI B3aHMHOH CBR3H Me)f{)J;Y nOpTaMH JIHH3bI. llOCJIe,nHee OT-
HOCHTeJIbHO TPy,nHO nO,lJ)];aeTCR KOHTpOJIIO, HO nepBOe RBJIReTCH pemalOIUHM MR
BbIITOJIHeHHR 3<t>cl>eKTHBHOH H KOMnaKTHOH JIHH3bI. TaKHM 06pa30M, B nepByK>
OQepe,n:b, Heo6xo,n:HMO TIUaTeJIbHO pa3pa6oTaTb reOMeTpHqeCKyK> onTHKY; 3a-
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CBH3H.
3,neCb OITHCaHbI KOMnpOMHCCbI reOMeTp:UQeCKOrO pemeHHR. JIHH3a POTMaHa
HMeeT meCTb OCHOBHbIX napaMeTpOB KOHCTpYK1l.I1H: <pOKaJIbHbIH yrOJI a, <pOKaJIb-
Hoe OTHomeHHe f3, OTHomeHHe yrJIa paCTBopa JIyqa K yrJIY opHeHTaQHH JIyqa y,
MaKCHMaJIbHbIH yrOJI paCTBopa JIyqa W m , <pOK)'CHOe paCCTORHHe /1 H mar pemeT-
KH d. llOCJIe,nHl1e ,nBa BbIpaxeHbI B MHHax BOJIHbI, a y - OTHomeHHe CHHYCOB.
Ce,n:bMoH napaMeTp KOHCTPYKQHH n03BOJIReT ,nyre nopToB JIyqeH 6bITb 3JIJIHITTI1-
QeCKOH, a He KpyrOBOlt. TIOCKOJIbK)' ypaBHeHHH KOHCTPYKl(HH HOCHT HeRBHbIH H
u u
TpaHCQeH,I:{eHTHbIH xapaKTep C e,nHHCTBeHHOH ITOCJIe,nOBaTeJIbHOCTblO pemeHHR,
Tpy.n;HO BbIRBHTb B3aI1Mo,n;eHCTBHe napaMeTpOB KOHCTPYK1l.I1H. ,l];JIR .n;eMOHCTpaUHH

b rAaea 10. Mn020A)l'I.eeble anmennbl
i
3<p<peKTOB Ka)l()J;orO IIapaMeTpa HCIIOJIb3yeTcR cepHR rpa<pHKoB JIHH3bl. OmH6-
KIf reOMeTpHqeCKOH <pa3bI H aMIIJIHTy,n;bI Ha ,n;yre IIOpTOB 3JIeMeHTOB, rnaBHbIM 06-
pa30M, H3MeHRIOTCR B 3aBHCHMOCTH OT a H (3 H B 3aBHCHMOCTH OT HeRBHoro
  
IIapaMeTpa, KOTOpbIH HBJIReTCR HOpMHpOBaHHOH BbICOTOH ,n;yrH IIOpTOB 3JIeMeH-
TOB. HarnMHble rpa<pHKH ,n;eMOHCTpHpyroT, KaK 3TH OIIIH6KH 3aBHCRT OT IIapa-
MeTpOB.
)];JIR JIHH3, r,ne ,LJ;yra IIOpTOB .rryqeH H ,n;yra IIOpTOB B036)')K.LI:eHHR (IIHTaHHH) HB-

JlHIOTCR l1,[(eHTHqHbIMH, qTO IIpHBO,n;HT K IIOJIHOH CHMMeTpHqHOCTH JIHH3bI, ypaB-
HeHHH KOHCTPYKJJ;HH 3HaQHTeJIbHO yrrpom;alOTCR [52]. O,n;HaKo 3TH nHH3bI pe,n;KO
HCIIOJIb3YIOTCR, nOCKOJIbK:y HX BapHaHTbI KOHCTpYKJ..(HH ropa3,n0 60JIee orpaHH-
QeHbI.
YpaBHeHHR JIHH3bI YCTaHaBJIHBalOT paBeHCTBO ,l(JIHH ITYTeiI OT <pOK:yCOB ,n;o 3JIe-
MeHTOB pemeTKH [46]. MCIIOJIb3YH 0603HaQeHIDI pHC. 10.17, y,n;06HO HOpMHpOBaTb
Bce pa3MepbI K OCHOBHOMY <pOK:yCHOM)' paCCTOHHHIO fi. 3TO TalOKe HB.illIeTC5I TOJI-
m;HHOH JIHH3bI B l(eHTpe. <I>OKaJIbHbIH yrOJI a CTHrHBaeTC5I BepXHHM H HIDKHHM <po-
K:ycaMH B l(eHTpe KpHBOH IIopTa 3JIeMeHTa. 3,n;eCb npe,LJ;IIOnaraeTCR, QTO <pOK:yCbI
CHMMelpHQHO paCIIOJIOXeHbI OTHOCHTeJIbHO OCH H QTO JIHH3a TalOKe 5IB.illIeTC5I CHM-
)
'I
y
13
Y2
<1>OKYC
(fl-f2Cf) .1 2
x
.£1
13
. (f 1 -£2 C '-£2$)
o
<1>OKYc
(xz,lv
Puc. 10.17. feoMeTplHI JIyqa
-

10.2. Ycmpoiicm6a fjJopMupooaHUJ/ J/)l'teii 
MeTPHqHoit JJ;3JIee, napaMe1]J f3 eCTb oTHollIeH:ue l BepxHero (H HH)KHero) <pOK)'CHO-
ro paCCTORHIDI /2 K fi :
J3= h .
/1
(10.6)
JICHO, qTO rn:up:UHa JIHH3bI, BbIpIDKeHHaR B ,lLJIHHaX BOJIHbI, filA, - 3TO eI..I.J:e
O,aHH napaMeTp. Tenepb yrOJI paCTBopa (m:up:UHbI) JIyqa, 1f3JIyqaeMoro perneTKoH,
paBeH llJ, If eCJIH B036)')Kl1:aeTCR O,aHH 113 <pOKYCOB, HaXOlUlI..I.J:IIXCR BHe OCII, OTHOllIe-
H:ue yrJIa paCTBopa JIyqa a K yrJIY oplleHTaIJ;1I11 JIyqa JIlfH3bI llJ eCTb Y:
sin 'II
y = . (10.7)
sma
KocBeHHbIH nOJIe3HbIH napaMeTp - 3TO napaMeTp , KOTOpbIH CBR3bIBaeT pac-
CTORHIIR Y3 JII060H TOqKH Ha perneTKe OT ee OCII co 3HaqeHHeM fi. 3TOT napaMeTp
KOHTpOJIlfpyeT qaCTb KpHBbIX omH6oK <l>a3bI II aMnJIlfTY,abI, KOTopaR npHXOJIHTCR Ha
JIlfH3Y. 3TO BbIpa)KaeTCR KaK:
 = Y3Y .
/1
(10.8)
06paTHM BHHMaHHe Ha TO, qTO 3HaqeHlfR MHH JIHHHH W Ha pHC. 10.16, 10.17
RBJIRIOTCR HeOTheMJIeMOM If CyIl(eCTBeHHoH qaCTblO JIIIH3bI. MaKCIIM3JIbHbIH yrOJI
paCTBopa JIyqa llJ m - 3TO BIDKHbIH napaMeTp, TaK xe KaK mar perneTKH, BbIpIDKeH-
HbIH B MHHax BOJIHbI diA. CooTBeTcTByrowlIH max BbIpaxaeTCR KaK:
r _ (NE - l)yd
max - 2/ 1 '
1.0
(10.9)
r,ae NE - qllCJIO 3JIeMeHTOB B JIIIHeH-
HOH AP, nOCKOJIbK)' Ymax = (NE -
- 1)/2. BepxHHH npe,aeJI  If MeeT Mec-
v
TO, Kor,aa KaCaTeJIbHaR K KplfBOII no-
pTOB 3JIeMeHTOB RBnReTCR BepTIIK3JIb-
HOH; 3TO TaIOKe .n:aeT W = O. JJ;aHHoe
3HaqeHHe  BbIpaxaeTCR CJIe,ayroI..I.J:HM
ypaBHeHlleM:
(10.10)
0.4
0.8
0.6

 _ _ 2  1-f3C I-f3C
O 1-.
w= S S
Ha pHC. 10.18 npHBe,aeHa 3aBHCII-
MOCTb 3Toro orpaHHQeHHOrO 3HaQe-
HlfR OT f3 LlJllI HeCKOJIbKHX 3HaqeHHH
a. IIoCKOJIbK)' nOJIe3HbIH ,aHana30H 
BKJIIOQaeT npH6JIII3HTeJIbHO 3HaQeHIIR
OT 0,5 ,ao 0,8, MoxeT 6bITb BbIBe,aeH
,aHana30H f3, cooTBeTcTBYIOI..I.J:HH ,aaH-
HOMY a.
0.2
o
0.80
0.84
0.88
P
0.92
0.96
PUC. 10.18. BepXHMH npe,n;eJI napaMe'Tpa 
1 CJIeJJYeT 06paTMTb BHMMaHMe Ha TO, qTO 13 - 3TO 06paTHOe 3HaqeHMe K03<t>HUHeHTa g,
HCnOJIb3yeMoro B [46] M [37]; f3 RBJUleTCR 60JIee y,n;06HbIM npM HOpMMpOBaHMH Kfi.

J Dla6a 10. MHo201lYlfe6ble aHmeHHbl
YpaBHeHHe reOMeTpHqeCKOH JIHH3bI RBJIReTCR KBa,apaTHbIM ypaBHeHHeM OTHO-
OJ
CHTeJIbHO ,lU[HHbI JIHHHH w, coe,n;HHRlOmeH nopT 3JIeMeHTa C cooTBeTcTByIOWHM
3JIeMeHTOM AP:
( J 2
W bw
a fi + fi +c=O,
(10.11)
r,n;e K03<P<PHUHeHTbI BKJIlOqalOT rrapaMeTpbI a, (3 H Y
(1 - J3)2 l;2
a = 1- --
(1-J3C)2 J32
2l;2 2(1 - J3) l;2 8 2 (1 - J3)
b = -2 + + -
J3 1 - J3C (1 - J3C)2
l; 2 8 2 l; 48 4
C = -(? + I-J3C - 4(1_J3C)2
(10.12)
H C = cos a, S = sin a.
06bIqHO qHCJIO JIyqeH H 3JIeMeHTOB, MaKCHMaJIbHbIH yrOJI paCTBopa JIyqa H mar
pemeTKH 3a,aaIOTCR H3 Tpe60BaHHH CHCTeMbI. TaKHM 06pa30M, 3an;aqa 3aKJIIOqaeTCR
B TOM, qT06bI BbI6paTb OnTHMaJIbHbIe a, (3, Y H filA.
I1MeeT 3HaqeHHe <popMa JIHH3bI KaK ,lU[R coxpaHeHHR ra6apHToB, TaK H .lUIR
YMeHbIIleHHR rrOTepb. HanpHMep, 60JIee rrJIOCKaR JIHH3a xapaKTepH3yeTcR TeH.lI.eH-
UHeM HMeTb )I,JlHHbI rryreH, KOTopbIe SIBJIRIOTCR B 60JIbI11eH CTerreHH paBHbIMH H no-
u u u
3BOJISIIOT KpHBOH rropTOB JIyqelf H KpHBOH rropTOB 3JIeMeHTOB HMeTb pa3Hble 3Haqe-
HHR BbICOTbI H ,n;IDKe pa3HbIe 3HaqeHHR KPHBH3HbI. KaK BH,lI;HO H3 pHC. 10.17,
TOJIlI.(HHa - 3TO TOJIIUHHa B,n;OJIb OCH JIHH3bI. TOJICTbIe JIHH3bI HMelOT 60JIbI11He rro-
TepH 3a CqeT nepeJIHBaHHR 3HeprHH (aHaJIOrHqHO TOMY, Kor,n;a MOWHOCTb o6JIyqa-
Tellil He rrepeXBaTbIBaeTCSI 3epKaJIOM) H 60JIee BbICOKHe nOTepH B JIHHHH rrepe.naqH.
KOMnaKTHaR JIHH3a HMeeT TeH.lI.eHUHIO MHHHMH3HpoBaTb rrOTepH 3a CqeT nepeJIH-
BaHHR 3HeprHH; 3,n;eCb BO H36exaHHe CHJIbHOrO aCHMMeTpHqHOrO YMeHbllIeHHR aM-
llJIH'fY,L(bI H 60JIbllIHX <pa30BbIx 0llIH60K CTaHOBRTCSI BaXHbIMH rrpH6JIH3HTeJIbHO
paBHbIe BbICOTbI KpHBbIX rropToB. KpHBH3Ha ,n;ByxnOpTOBbIX rpa<pHKoB MoxeT 6bITb
pa3JIHqHOH; HCrrOJIb30BaHHe llIara pellIeTKH, 60JIbllIerO, qeM rrOJIOBHHa ,l(JIHHbI BOJI-
HbI, rr03BOJIHeT HCrrOJIb30BaTb 60JIbIIIe rropTOB nyqei1, qeM rropToB 3JIeMeHTOB.
B 3TOM CJIyqae KpHBaR nopTOB JIyqeH MoxeT 6bITb 60JIee HCKpHBJIeHHOH, a KpHBaR
nopTOB 3JIeMeHTOB 60JIee IIJIOCKOH.
3cJ:><peKTbI ceMH napaMeTpoB 6yJJYT nOKa3aHbI qepe3 cepHIO rpa<pHKoB [26].
llIecTb rpa<pHKoB rrpHBO,L(SITCSI Ha pHC. 10.19-10.24. ITOpTbI .rryqeH, KOTopbIe OTMe-
qeHbI raJIOqKOH, Haxo,n;RTCSI CJIeBa. ITOpTbI 3JIeMeHTOB, TaIOKe OTMeqeHHbIe raJIoq-
KaMH, HaXO,lUITCH cnpaBa. <l>OKYCbI YKa3bIBalOTCR 3Be3,n;OQKaMH. <l>OKYCHOe paCCTOR-
HHe rrpOHopMHpOBaHO K e,n;HHHue, KIDK,L(aH MeTKa-raJIOqKa Ha OCH (H Ha op,n;HHaTe)
paBHSIeTCR 0,05. 113 IIIKaJIbI op,n;HHaT MOryT 6bITb BbIBe,n;eHbI napaMeTpbI nOJIoxe-
HHSI 3JIeMeHTOB. Ka)K)]:aSI KpHBaR JIHH3bI npOCTHpaeTCR 3a BHellIHHH KpaHHHH nopT
Ha rrOJIllIHpHHbI 3Toro nopTa. B 3THX npHMepax HMeeTCSI 9 nopTOB .rryqeH H 11 nop-
TOB 3JIeMeHTOB H, KOHeQHO, 11 3JIeMeHTOB B JIHHeMHOH AP C nOCTORHHbIM llIarOM.
ITpH Bcex ,n;pyrHX <pHKcHpoBaHHbIX rrepeMeHHbIX yJ3eJIHqeHHe a OTKpbIBaeT KPH-
ByJO rropTOB JIyqei1 H 3aKpbIBaeT KPHByIO rropTOB 3JIeMeHTOB. ITOJIOXeHHSI nopToB
HBJISIIOTCSI rrpH6JIH3HTeJIbHO HeH3MeHHbIMH. Ho rrOJIO)l(eHHR BHellIHHX <pOKYCOB,

30
a=40
PHC. 10.19. 3cpcpeKT Q;>oKaJIbHOrO yrJIa: (3 =
= 0,9, y = 1,1, 1fJ m = 50,/1 = 4"-, d= 0,5"-
10.2. Ycmpoucm8a qmpMupo8aHUR JlY'Ieu d
0.86
P=0.92 088
0.90 0 . 9 .
.88
0.86 0.92
PHC. 10.20. 3Q;>cpeKT cpoKaJIbHOrO K03<PCPM-
UMeHTa: a = 40, y = 1,1, 1fJ m = 50,11 = 4"-,
d = 0,5"-
KaK 11 O)KM,lJ;CUlOCb, 3aMeTHO MeHHIOTCH. Ha pMC. 10.19 Tpl1 Kpl1BbIe IUIJIIOCTpl1pyroT
3TI1 3<pcpeKTbI. 06paTMTe BHI1MaHl1e Ha TO, qTO 3HaqeHI1e a MO)l(eT 6bITb BbI6paHO
TaK, qTo6bI npM6JII1311TeJIbHO BbIpOBH.HTb BbICOTbI ,aBYX KpI1BbIX. KOHeqHO, a ,aOJI-
)l(HO BbI6MpaTbC.H COBMeCTHO C ,apyrl1MI1 nepeMeHHbIMM ,lLJI.H MI1HI1MI13al.{I1M OIIIlf6oK
<pa3bI B paCKpbIBe. HapyxHbIe cpOKYCbI ,aOJDKHbI 6bITb nOJIHOCTblO BHyrplf KplfBOH
u
nopTOB JIyqelf.
YBeJIlfqeHlfe (3 OKa3bIBaeT B03,aeHCTBlfe, cxo,aHoe YBeJIlfqeHlf10 a; KplfBa.H nop-
TOB JIyqeH OTKpbIBaeTCH, a KpHBaH nopTOB 3JIeMeHTOB 3aKpbIBaeTCH. Ha plfC. 10.20
rrpHBen:eHhI Tplf KpHBbIe JIIfH3bI, H3 KOTOpbIX 3TO BJI,lJ:HO. Orr.HTb-TaKH, nOJIO)l(eHHH
rropTOB OCTalOTCH npaKTHqeCKH 6e3 H3MeHeHI1H. TIOJIOXeHH.H cpoKYca TaK )l(e 113Me-
H.HIOTC.H OTHOCI1TeJIbHO He3HaqIfTeJIbHO. OnHTb-TaKI1, MoxeT 6bITb BbI6paHo TaKoe
3HaqeHHe (3, KOTopoe npH6JIlf3lfTeJIbHO ypaBHI1BaeT BbICOTbI KpHBbIX.
I1MeIOTC.H rrapbI a M (3, KOTopbIe C03,aaIOT npl16JIH3HTeJIbHO TY xe caMyIO CPOPMY
JII1H3bI H IIOJIOXeHI1H nopTOB. O,aHaKo cpOKYCbI 113MeH.HIOTCH B 3aBI1CI1MOCTH OT a, II
coe,aHHHTeJIbHbIe JIHHHH (OT rropTOB 3JIeMeHTOB ,ao 3JIeMeHToB) OTJIHQaIOTCH.
 Ta6JI. 10.2 nOKa3aHbI TPH napbI JII1H3 a-f3, HMelOIIJ;HX 06IIJ;He Kpl1BbIe JIlfH3 II
nopTbI - Bce npH Y = 1,1, 1JJ m = 50, filA = 4, H d = A/2. TaKHM o6pa30M, MO)l(J{O
c,aeJIaTb BbIBO]J., qTO ollI116Ka cpa3bI B paCKpbIBe ,lLJIH Ka)l([(OrO JIyqa 6Y1(eT OTJIIfQaTb-
C.H B 3aBlfCI1MOCTIf OT a. 3TO 6y,aeT nOKa3aHO B CJIe,ayroIIJ;eM pa3,l(eJIe. ,LLrr.H JII06oro

 Dlaea 10. MHOi!Olly'teeble aHmeHHbl
Puc. 10.21. 3<}><}>eKT K03<}><}>I1I.UfeHTa yr-
JIa JIyqa: a = 40, f3 = 0,9, W m = 50, /1 =
= 4A, d = 0,5A.
5S
PRC. 10.22. 3<l><l>eKT MaKCI1MaJIbHOrO yr-
JIa JIyqa: a = 35, f3 = 0,92, y = 1,1'/1 = 4A,
d = 0,5A.
Ta6JIRna 10.2. IIapbI a-f3 Ha60pa .n;pyrHX qeTbIpex napaMeTPoB,
BepoHTHo, cymecTByJOT HeIGIe napbI
a-(3, Be.n;ymHe ce6H aHaJIOrHqHbIM 06-
pa30M.
YBenHqeHHe y OCTaBnHeT 06e KPH-
BbIe nHH3bI 6e3 H3MeHeHHH, HO nopTbI
nyqeH CXO,1UITCH 6nIDKe .n;pyr K .n;pyry,
npH 3TOM nopTbI 3neMeHTOB pacxo.n;HTCH.
Ha60p napaMeTpOB .l(nH TPex nHH3 Ha
pHC. 10.21 .n;eMOHcTpHpyeT 3TY TeHlIeHUHIO. XOTH <pOKYCbI OCTalOTCH <PHKcHpoBaH-
HbIMH, KOHUbI KpHBbIX H3MeHHIOTCH, TaK qTO H OTHOCHTenbHoe nonoxeHHe <pOKY-
COB MeHSIeTCH. 3HaqeHHe Y TaIOKe MoxeT OKa3bIBaTb B03.n;eHCTBHe Ha OTHOCHTenb-
HbIe BbICOTbI .n;BYX KpHBbIX.
3HaqeHHH Y 3I(eCb paBHHIOTCH 1 HJIH 60nbIIIe, nOCKonbKY Bce HCnOJIb30BaHHbIe
CJIyqaH - 3TO CJIyqaH 60JIbIIIHX yrJIOB pacTBopa (IIIHpHHbI) JIyqa. Kor.n;a nyqoK JIY-
qeH CTHrHBaeT MeHbIIIHH yron (HanpHMep, 30°), 3HaqeHHH Y < 1 HBJUIIOTCH no.[(Xo-
.n;HIUHMH, TaK KaK OHH .n;onYCKaIOT «)l(HPHYIO» HJIH H30rHyryIO nHH3Y.
C H3MeHeHHeM 1JJ m MeHHIOTCH TonbKO paCCTOHHHH Me)l(,[(y nopTaMH .rryqeH. YBe-
JIWIeHHe 1JJ m pa3Bo.n;HT nopTbI JIyqeH H paCIIIHpHeT KPHBYIO nopTOB, TaK qTO 3TOT
napaMeTp nOMoraeT C03.n;aTb nHH3Y C npH6JIH3HTeJIbHO paBHbIMH BbICOTaMH KpHBbIX
nopTOB JIyqeH H 3JIeMeHTOB. Ha pHC. 10.22 KpHBbIe .n;JIH Tpex napaMeTpOB JIHH3bI
oT06paxalOT 3TOT THn nOBe.n;eHHH.
mar peIIIeTIGI HBnHeTCH KpHTHqeCIGIM napaMeTpOM, nOCKonbKY OH KOHTPOJIH-
pyeT B03HHKHOBeHHe .n;H<ppaKIJ;HOHHbIX JIeneCTKOB (CM. rn. 2). ,LI:JIH MaKCHMaJIbHOrO
HOMep a: Ii
1 30 0,94
2 35 0,92
3 40 0,90


0.50
a I -. I'
PHC. 10.23. 3<p<peKT rnara Me)l(,[(Y 3JIe-
MeHTaMI1 perneTKI1: a == 40, f3 == 0,88, y ==
== 1,1, 'W m == 50,/1 == 4"-
10.2. Ycmpoucm8a rjJOpMupo8aHUR ily'teu ' d
3.5
PHC. 10.24. 3<p<peKT <pOK)'CHOrO paCCTOR-
HI1R: a == 40, [3 == 0,9, 'W m == 50, d == 0,5"-
yrJIa pacTBopa (IlIMpMHbI) JIyqa W m llIar pellIeTKM, L(OnycKalOmMll rr05IBJIeHHe ,[(Mcp-
paKllMoHHoro JIeneCTKa, paBeH:
d 1
A 1 + sin \}1m
(10.13)
KaK npaBMJIO, llIar pellIeTKM rrO,JI,LJ;ep}I{HBaeTC5I HIDKe 3Toro 3HaqeHM5I. I1pM M3-
MeHeHMM 3HaqeHH5I d MeH5IIOTC5I TOJIbKO paCCT05IHH5I Me)l()];Y nopTaMH 3JIeMeHTOB H
CTerreHb KpHBOll rropTOB aHanOrHQHO TOMY, KaK W m M3MeH5IeT llIar rropTOB JIyqell.
Ha pHC. 10.23 ,[(JI5I L(eMOHCTpaUMM 3Toro npHBO.l15ITCR KpHBbIe ,[(JI5I ,[(BYX rrapaMeTpOB
JIMH3bI.
YBeJIHQeHHe cpOK)'CHOrO paCCT05IHM5I (llIHpHHbI) JIHH3bI, B ueJIOM, YBeJIlfqHBaeT
TaIOKe pa3B5I3K)' Me)l()];Y KOHeqHbIMH nopTaMH. Ho H3MeHeHHe filA TaIOKe npHBOlU1T
K 1f3MeHeHHIO Bcex paCCTORHHH, nOCKOJIbK)' ypaBHeHH5I JIlfH3 HOpMMpOBaHbI K fi .
TaKHM 06pa30M, KaK BH,[(HO H3 ,[(BYX KpHBbIX Ha pHC. 10.24, H3MeHeHlfe filA TaIOKe
H3MeH5IeT ,[(yry nopTOB 3JIeMeHTOB H mar nopTOB 3JIeMeHTOB. MlfHHManbHoe 3HaQe-
Hlfe fi MeHbllIe ,[(JI5I JIHH3 POTMaHa, qeM .lUIR L(pyrlfX THIIOB JIHH3 [54]. )].anee 6y,[(yr
paCCMOTpeHbI OllIH6KH <pa3bI Ii aMIIJIH'fYL(bI.
OIII1I6KH paCKpbIBa 3aBHC5IT OT a H (3, 3KcueH1'pHQHOCTH If JIHllIb KOCBeHHO -
OT ,[(pyrHX napaMeTpOB. TaKHM o6pa30M, HaH60JIee HH<popMaTHBHbIM 5IBJI5IeTC5I no-
CTpoeHHe rpacpHKa 3aBHCHMOCTH OIIIH6oK <l>a3bI Ii aMIIJIH'fYL(bI OT HOpMlfpOBaHHoro
rrapaMeTpa  (CM. ypaBHeHHe (10.8». TIOCKOJIbKY OIIIli6KH <l>a3bI paBHbI HYJIIO npH

b FJla8a 10. MnOCOJlY'le8ble anmenH/>l
yrJIax, cooTBeTcTBYJOIlJJIX TpeM <:];>OKYCaM, YLI;OBJIeTBbpiIt(JIbHbIM rrOLI;XOLI;OM 5IBJI5I-
u
eTC5I TaKolf, B KOTOpOM IfCrrOJIb3yeTC5I OLI;HO rrOJIO:>KeHlfe JIyqa B cepeLI;IfHe Me)l(,[(Y
u:eHTpaJIbHbIM II KpaeBbIM <:];>OKYCaMIf, a BTopoe rrOJIO:>KeHlle JIyqa HaXOlIIfTC5I 3a rrpe-
lIeJIaMll KpaeBoro <:];>oKYca. OllIll6K1f aMIIJIIfTYLI;bI rrpOIfCXOLI;5IT BO Bcex rropTax JIyqeH,
rro3ToMY LI;JI5I oTo6pa)l(eHIf5I rrOBeLI;eHIf5I OllIlf6K1f aMIIJIllTYLI;bI Tpe6yeTC5I 60JIbllIe
rrplfMepoB.
Ha pllC. 10.25-10.28 rrOKa3aHa 3aBlfClfMOCTb OllIII6Kll <:];>a3bI OT  ,WI5I JIlfH3 C
a = 35, 40 II 45° lIJI5I pa3JIllqHbIX 3HaqeHlfH (3. 06paTlfTe BHIfMaHlfe Ha TO, qTO ,WI5I
rrOJIyqeHIf5I OllIlf6K1f <:];>a3bI 3HaqHIf5I 113 PllCYHKOB LI;OJDKHbI 6bITb YMHO:>KeHbI Ha KO-
3<:];><:];>IfUlleHT filA. Ll,JI5I cpeLI;He<:];>OKYCHbIX .rryqeH ollIlf6Ka <}>a3bI 5IBJI5IeTC5I MaJIeHbKoH,
3a llCKJIIOQeHlleM OQeHb 60JIbllIlfX JIIfH3. OllIII6Kll <:];>a3bI L(JI5I JIyqeH C 60JIee llIlfpO-
KllM yrJIOM rro- rrpe)l(HeMY 5IBJI5IIOTC5I He3HaQlfTeJIbHbIMIf If He 6YLI;)'T cym:eCTBeHHbI-
Mll, 3a llCKJIIOQeHlleM 60JI bllI If X JIIIH3 IDIII KOHCTPYKUIfH C  > 0,75. B u:eJIOM,
OllIll6K1f cPa3bI YBeJIIfQIfBaIOTC5I rro Mepe YBeJIllqeHIf5I a LI;JI5I Bcex rrOJIO)l(eHIfH JIyqa.
2.0
"
1.5
1.0
-
I:::!

0.. 0.5
'-'
--


to 
::s:: - 0.0
a -
......
0
0:::
 -0.5
£:Q
0
M

e
-1.0
-1.5
-2.° 0
- .8.
-0.6
-0.4
-0.2
0.0

0.2
0.4
0.6
0.8
PHC. 10.25. JI:HH3a POTMaHa, a = 35°, yrOJI opHeHTaII;HH JIyqa = 17,5°
XOT5I B [46] YK:a3aHa OrrTIfMaJIbHa5I BeJIlfqlfHa (3, KOTOpa5I COCTaBJIIDIa 2/(2 + a)2,
paCCMOTpeHlfe pllC. 10.25-JO..28.rroKa3b»aeT, qTO OrrTtlMaJJbH;oe (3 cym:eCTByeT TOJIb-
KO iLrr5I OLI;Horo LI;llarra30Ha  II OLI;Horo yrJIa oplfeHTaUIfH JIyqa. HaRJIyqllIlle 3HaqeHlf5I
(3 pa3Hble ,WI5I JIyqeH Me)l(,[(Y <:];>OKYCaMIf II .rryqeH 3a IIpeLI;eJIaMII cPOKYCOB. IIoCKOJIbKY
IIOCJIeLI;Hlfe 06bJ1IHO HMelOT <:];>a30ByIO OllIlf6KY 60JIbllIe" pa3pa6oT1IIIK MO:>KeT ee orrTll-
Mll3llpOBaTb, HO 3HaqeHlfe 6YLI;eT ll3MeH5ITbC5I B 3aBlfCIIMOCTll KaK OT yrJIa oplfeHTa-
UIfIf .rryqa, TaK II OT max' 3TO CTapoe 3HaqeHlfe TaIOKe ,n;aeT IIJIOXlle <:];>OpMbI JIIfH3bI,
KorLI;a QIfCJIO IIOpTOB JIyqeH II qlfCJIO IIOpTOB 3JIeMeHTOB rrplfMepHO paBHbI.
Pe3YJIbTaTbI llCrrOJIb30BaHIDI 3JIJIIIIITIIQeCKOH KplfBoH IIOpTOB JIyqeH IIOKa3aHbI Ha
pllC. 10.29, rLI;e <l>a30Bble OIIIII6K1f ypaBHIfBaIOTC5I rrplf  = + 0,7 ,[(JI5I yrJIa JIyqa 45°.

10.2. Ycmpoiicm8o rPoPMUP080HUR Ily'teii 
2.0
-
1.5
'"'
\
\
\
\ p = 0.9
\
\
,
"-
"-
.......
........-
---



--
0.5
co;:S

\0
::s::
3
o
c::
co;:S
j:Q
o
M
co;:S
e
.",-
,.,.-
/"
/"
/"
, \, -94
---
-1.0
-0.6
-0.4
-0.2
0.0
t
0.2
0.4
0.6
0.8
Puc. 10.26. nHH3a POTMaHa, a = 35 0 , yroJl opHeHTaUHH Jlyqa = 45 0
2
1
-


'-'
--
c!j

\.0
::s: """'< 0
3 -..
..:- ---.-
0
c::
c!j
j:Q
0
M
c!j
e
-1
-2
-0.8
-O.B
-0.4
-0.2
0.0
t
0.2
0.4
0.6
0.8
PUC. 10.27. nHH3a POTMaHa, a = 40 0 , yrOJl opHeHTaI.J.HH Jlyqa = 20 0

b
Ffl060 10. MHo2oflY"'le6ble OHmeHHbl
1
-...
.

0.

--
(Ij


;:s::  0
S -
.-
.....
0
t::I::
ro
::c
0
M
Cd
e
-1
2
f
,
f3 = 0.9
:;;;---- ------.:. ----
....
..-
//;
.7'1' 0,86
" I
//
,
-2
-0.8
-0.6
-0.4
0.6
0.8
-0.2
0.0

0.2
0.4
Poc. 10.28. JIMH3a POTMaHa, a = 45°, yrOJI opMeHTall.MI1 JIyqa = 22,5°
-...
t::{
Cd
0.

--
Cd


:s: 
3  0
o .....
0:::
Cd
::Q
o
M
Cd
e
4
2
17.5
YrOJI opueHTaUIU1 JIyqa = 45
-2
-O.8
-0.6
-0.4
-0.2
0.0

0.2
0.4
0.6
0.8
Poc. 10.29. JII1H3a POTMaHa, a = 35°, J3 = 0,92

10.2. Ycmpoucmea fjJopMupOeaHUJl J/Y'leu 
06paTMM BHHMaHMe Ha TO, qTO 3JlJIHIITMqeCKaH KpHBaH IIOpTOB JIyqell - 3TO
IIpOCTOM CIIoco6 peaJIH3an;HM OIITHMaJIbHOM KpHBOM [30]. 3THM .l(OCTMraeTC5I
I
13%-Hoe YMeHbIIleHMe <pa30BoH OIIlH6KH; <pa30BbIe OllIH6KH .l(JIH cpe.l(He<pOK)'CHbIX
JIyqeM IIpM 17,5° CTaHOB5ITC5I HeCKOJIbKO 60JIee aCHMMeTpHQHbIMH, HO HaXO.l(5ITC5I
nO-IIpe)l(HeMY Ha ypOBHe 3HaqeHHM HIDKe OllIH6oK .rryqell 45°. 06paTHTe BHHMaHHe
Ha TO, QTO 3JlJIHIITMQHOCTb -0,3 If3MeH5IeT OCHOBHOll pa.n;HYC Bcero Ha 5%, II03TO-
MY aMIIJIMTY.l(bI OCTalOTC5I IIpaKTMQeCKH HeH3MeHHbIMH. fJIaBHaH OCb 3JlJIHIICa IIOp-
u u
TOB JIyqeH IIPOXO.l(MT B.l(OJIb OCM JIHH3bI .l(JIH 3TOH 3JlJIHIITHqHOCTH.
AMIIJIHTY.l(HbIe OIIIH6KH paCCQHTbIBalOTC5I C nOMOll(blO ,lU1arpaMM IIOpTOB JIyqeM
H IIOpTOB pynOpHbIX 3JIeMeHTOB C .l(HarpaMMoH sine 1tU, r.l(e Bce 3HaqeHHR IIlHpMHbI
pynOpOB YCTaHOBJIeHbI Ha HOMMHaJIbHOe 3HaQeHHe A/2. Pynop Ka)l(}J;OrO IIOpTa HMe-
eT CBOIO OCb, HOpMaJIbHyro IIO OTHOIIIeHHIO K KpHBOH nopTOB. Ha pHC. 10.30 nOKa-
3aHa aMnJIHTY.l(HaR oIIIM6Ka, HOpMHpOBaHHaR K 0 .l(D .l(JIR oceBoro JIyqa JIHH3bI C a ==
== 35, J3 == 0,92. IlpMBe.l(eHbI KpMBbIe .l(lliI yrJIOB JIyqa 0, 17,5 H 45°. AHaJIOrHQHO, Ha
pHC. 10.31 IIOKa3aHbI 3aBMCMMOCTM .l(JIR JIHH3bI C napaMeTpaMH a == 40°, J3 == 0,9,
.l(JI5I yrJIOB opHeHTan;MM JIyqa 0, 20 If 50°.
2.0
I
\
,
\
,
\
'\
"
..
YrOJI Opl1eHTal(1111 .rryqa = 0
-- 0.0

t:1
-
Cd
::.::
\0
:s::
:3
0
-- -2.0
c:: .....
Cd
:I:


:s::

t::

< -4.0
--
__ -- 17.5
--.-'
--
----
-- ..
- -- """"... ---
--.. ----
------ 45
-6.0
-0.8
-0.6
-0.4
-0.2
0.0

0.2
0.4
0.6
0.8
PHC. 10.30. JIHH3a POTMaHa, a = 35°, (3 = 0,92
3TO .l(Ba IIpHMepa H3 nap a-J3 Ta6JI. 10.2 IIOKa3bIBaIOT, QTO OIIIH6KM aMIIJIHTY-
.l(bI 5IBlliIIOTCH O.l(MHaKOBbIMM. KaK H O)l(H.l(aJIOCb, B CJIyqae IIIHpOKHX yrJIOB opMeH-
Tan;HM JIyqa 6JIIDKHMM M .l(aJIbHMM KOH:U;bI KpHBOH IIOpTOB 3JIeMeHTOB MClIbITbIBalOT
He3HaQMTeJIbHbIe M3MeHeHH5I aMIIJIMTY.l(bI. ITo cpaBHeHHIO C y6bIBaHMeM aMIIJIMTY-
.l(bI, Heo6xo.l(MMbIM LUIR YPOBHR 60KOBbIX JIelIeCTKOB 25 .l(E, 3TH OllIH6KH aMIIJIHTY-
.l(bI RBJIHIOTCR He6oJIbIlIHMH. PeaJIbHbIe JIMH3bI MOryr MMeTb 3HaQeHM5I IIlMpMHbI
rropTa > A/2, II03TOMY MO)l(}lO O)l(H.l(aTb, QTO CIIa.n;aHHe aMIIJIHTY.l(bI 6Y,l(eT YBeJIMQH-
BaTbC5I, B oco6eHHOCTM, .l(JI5I KpaeBbIX .rryqeit

b D/a6a 10. MHo2olly'te6b1e aHmeHHbI
2
\
-..

I::[
---
o
\
YrOJI oplIeHTaUlI1I .rryqa = 0
t'\S

\.0
:s:
S
o
.-
c:: .....
t'\S
:I:

E-
:s:
r=:
r::
::?1
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-,..--
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.....
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, ....
'. ........  ....
.. ..-
.. ------
----
- -,, -
-
-2
----
- -
-- - -
50
,
-4
-6
-0.8
-0.6
-0.4
-0.2
0.0

0.2
0.4
0.6
0.8
PHC. 10.31. JIMH3a POTMaHa, a = 40°, (3 = 0,9
ACHMMeTpH aMllJIHTY,lI.bI ,lI.JI BHeoceBbIX JIyqen MO)l(eT 6bITb YMeHbllIeHa nyreM
HanpaBJIeHH pynopa Ka)l(,[(OrO nopTa Ha npoTHBOrrOJIO)I(HyJO BepllIHHY BMeCTO Ha-
rrpaBneHH, HOpMaJIbHOrO K KpHBon nopTOB [40]. HanpHMep, 9-.rryqeBa 11-3JIe-
MeHTHa JIHH3a C a = 40°, f3 = 0,9, y = 1,1, 'W m = 50, d = 0,5A 11 fi = 4A HMeeT y6bI-
BaHHe aMnJIHTy.n:bI .n:JI BHelliHero JIyqa, KaK nOKa3aHO B Ta6JI. 10.3. TalOKe
nOKa3aHO y6bIBaHHe ,lI.JUI pynOpOB, HanpaBJIeHHbIX Ha BepllIMHY. I1cnoJIb30BaHHe
opHeHTal(HH Ha BepllIHHY C03.naeT 3aMeTHoe ynyqrneHMe. TaIOKe HeCKOJIbKO YJIyq-
llIaeTC YCHJIeHHe.
Ta6JIHQa 10.3. Y6bIBaHMe aMllJlMT)'JJ:bI .ruHI BHelliHero Jlyqa; 11 = 4A
HOMep 3JIeMeHTa OCH, HOpMaJILHbIe .nyre (.lJ.I) OCH '1epe3 oepmHHY (.lJ.I)
1 -8,49 -226
,
2 -703 -1 84
, ,
3 -550 -1 46
, ,
4 -4,29 -1 31
,
5 -333 -1 37
, ,
6 -258 -1.63
,
7 -204 -208
, ,
8 -1 70 -273
, ,
9 -1 57 -360
, ,
10 -1 68 -471
, ,
11 -208 -5,95
,

10.2. Ycmpoucm6a rPoPMup06aHUJI ilY'leU 
IIepeJIHBaHHe H3JIyqeHH.SI rropToB 3JIeMeHTOB H .rryqeH, <pa30BbIe H aMIIJIHTy.n;-
HbIe 01lIH6KH, HeCOOTBeTCTBH.SI HMrre.n;aHCOB rropToB 11 rroTepH B JIHHHH rrepe,l(a-
qH, - Bce 3TO crroc06cTByeT YMeHbllIeHHIO K03<P<PHIJ;HeHTa YCHJIeHIDI JIHH3bI. 06-
paTHTe BHHMaHHe Ha TO, qTO, KaK H B cJIyqae pyrropa, paCrrOJIOXeHHOrO B <pOKYCe H
rrHTalOlI(erO 3epKaJIbHYID aHTeHHY, HeT rrOTepb paCrrpOCTpaHeHH.SI pyrropHoro H3JIY-
qaTeJI.SI, qTO CB.SI3aHO CO CBOHCTBOM paBHOrO rryrH. He60JIbllIOe HepaBeHCTBO ,l(pyrHX
rr)'TeH OTHeCeHO K <pa30BbIM H aMIIJIHTy,l(HbIM 01lIH6KaM rr)'TH. K03<l><PHIJ;HeHT YCI1-
JIeHH.SI 6Y,l(eT paCCqHTbIBaTbC.SI 3,l(eCb Ha OCHOBe rrepeJIHBaHH.SIH3JIyqeHH.SI rrOpTa H
01lIH60K B arrepType. IIOCKOJIbKY paCqeT aMIIJIHTy,l(HOH 01lIH6KH BKJIlOqaeT .n;l1a-
rpaMM)' KaK rrOpTa JIyqa, TaK 11 rrOpTa pyrropHoro 3JIeMeHTa, TO rrepeJIHBaHHe 3Hep-
rHH yqHTbIBaeTC.SI [55]. <l>a30BbIe H aMIIJIHTy,l(HbIe 01lIH6KH B rropTax 3JIeMeHTOB rre-
pe,l(alOTC.SI Ha pellieTKY H30TporrHbIX 3JIeMeHTOB. ,lJ;aJIee rrp06JIeMa CBOJJ:HTC.SI K
rrp06JIeMe paCqeTa YCHJIeHH.SI cHMMeTpHqHOH JIHHeHHOH pellIeTKH H30TporrHbIX 3JIe-
MeHTOB C KOMlIJIeKCHbIMH K03<P<PHIJ;HeHTaMH C I1CrrOJIb30BaHHeM <POPMYJIbI H3 rJI. 2.
<l>aKTHqeCKOe YCHJIeHHe Tor,n;a paBH.SIeTC.SI MHO)I(HTeJIIO H30TporrHoH pellIeTKH, YM-
HoxeHHOMY Ha K03<P<PHIJ;HeHT YCHJIeHH.SI 3JIeMeHTa H Ha K03<P<PHIJ;HeHTbI paCCorJIa-
COBaHH.SI HMrre,l(aHca.
KOJIe6aHHe YCHJIeHH.SI B 3aBHCHMOCTH OT rrapaMeTpOB .SIBJI.SIeTC.SI He3HaqHTeJIb-
HbIM. HarrpHMep, ,l(JIR THrrHqHOM MaJIOH JIHH3bI rrpOHCXO,l(HT H3MeHeHHe TOJIbKO Ha
0,2 ,l(D OT IJ;eHTpaJIbHOrO ,n;o KpaeBoro JIyqa. 3HaqeHIDI YCHJIeHH.SI rrOqTH He3aBHCI1-
MbI OT a, (3, y H T.,l(. B cJIyqae 60JIbllIeH pellIeTKH YCHJIeHHe paCTeT KaK pa3 TaK, KaK
O)l(H)::{aJIOCb. ECJII1 B3.SITb TOT xe caMbIH rrpHMep C 9 JIyqaMH, 11 3JIeMeHTaMH H3 pa3-
,n:eJIa 10.2.1.5, ,l(Harra30H YCHJIeHH.SI Haxo,n;HTC.SI B rrpe,l(eJIax OT 10,2 ,l(0 10, 4 ,n:E; rro-
CJIe,l(H.SI.SI BeJIHqHHa ,l(JI.SI IJ;eHTpaJIbHOrO JIyqa HaXO,l(HTC.SI B rrpe,n;eJIax YCHJIeHH.SI 0, 1 .n;E
,l(JI.SI aHaJIOrHQHOH O,n:HOpO,n:HO B036y)1(,l(aeMOH pellIeTKH. .LJ;JI.SI ,n;aHHoH JIHH3bI .n;Harra-
30H  paBH.SIeTC.SI + 0,756.
3<P<l>eKTbI rrepeJIHBaHH.SI 3HeprHH pyrropHoro 06JIyqaTeJI.SI H BHyrpeHHHe OTpa-
XeHH.SI JIHH3bI MOryr 6bITb YMeHbllIeHbI JIM60 rryreM HCrrOJIb30BaHH.SI JIO)I(HbIX (3a-
rJIym:eHHbIX COrJIaCOBaHHOH HarpY3KoH) pyrrOpHbIX H3JIyqaTeJIeH, CMe)I(HbIX Kpae-
BbIM pyrropaM, JIH60 rrocpe,n:CTBOM HCrrOJIb30BaHM.SI rrOrJIOTHTeJI.SI Me:>K,IJ;Y KOHIJ;aMM
,n:yrH rropTOB JIyqeH M ,l(yrOH rropTOB 3JIeMeHTOB [40].
ilpoIJ;ecc rrpoeKTHpOBaHM.SI HaqHHaeTC.SI C BbI60pa IJ;eHTpaJIbHOH qaCTOTbI, rrpH
KOTOpOH paCCqMTbIBalOTC.SI Bce pa3MepbI. .LJ;aJIee BbI6HpaeTC.SI HaqaJIbHOe 3HaqeHMe
II/A, ,l(JI.SI Toro qT06bI coxpaHHTb max 3HaqHTeJIbHO HIDKe 0,8. <l>OKYCHOe paCCTO.SI-
HHe 6Y,l(eT HeCKOJIbKO MeHbIlle ,l(JIHHbI pellIeTKH. ,lJ;aJIee, HCrrOJIb3Y.SI yKa3aHH.SI, BbI-
6HpalOTC.SI 3HaqeHH.SI a, (3, y, ,l(JI.SI Toro qT06bI: (1) paCrrOJIO)I(HTb rropT BHelliHero
JIyqa Ha He3HaqHTeJIbHyIO BeJIHqHHY 3a BHellIHHH <pOKYC; (2) C03,l(aTb ,LIyrH rropTOB
JIyqeH H rropTOB 3JIeMeHTOB corrOCTaBHMOH BbICOTbI H (3) ,n;06HTbC.SI rrpHeMJIeMbIX
<l>a30Bblx H aMIIJIHTy,n;HbIX 01lIH60K Ha Ka:>K,IJ;OM BXO,l(e. ,lJ;ocTHxeHHe 3Toro MoxeT
rroTpe60BaTb peryJIHpoBKH/I/A I1JIH d/A, a TaIOKe a, (3, y. I1crroJIb30BaHHe 3JIJIHrrTH-
qeCKOH ,l(yrH rropTOB JIyqeH 06bIqHO He OrrpaB,l(aHO, 3a HCKJIlOqeHHeM 60JIbllIHX
JIHH3.
Kor,n;a Y,l(OBJIeTBOpHTeJIbHa.SI KOHCTPYKI.J:H.SI 6y,n;eT BbIrrOJIHeHa Ha u;eHTpaJIbHOH
qaCTOTe, Ha KOHTpOJIbHbIX qaCTOTax paCCqHTbIBalOTC.SI <pa30BbIe H aMIIJIHTy,l(HbIe
OIIlH6KH ,l(JI.SI Ka:>K,IJ;OrO rropTa ,l(JI.SI ou;eHKH pa60Tocrroc06HOCTH BO BceM ,l(Harra30He
qaCTOT. KOHeqHO xe, HCrrOJIb3yIOTC.SI 3HaqeHH.SI <paKTHqeCKOH llIHpHHbI JIyqa H llIH-
pHHa pyrropHoro rropTa 3JIeMeHTa. Ha 3TOM 3Tarre IJ;eJIeC006pa3HO paCCqHTaTb pO-

 FJla6a 10. MHo2011Ylfe6b1e aHmeHHbI
%r .'
'¥'f:1
PHC. 10.32. MMKpOnOJIOCKOBa}l JIMH3a POTMaHa
3eTKY JIyqeH (Ha60p ,UMarpaMM .rryqeH) Ha Ka)l()J;oH no,Uxo,UHru;eH qaCTOTe. MoxeT
nOHa,n:06MTbCH HeKoTopbIH KOMnpoMMcc M MHoroKpaTHaH peryJIMpOBKa napaMeTpoB
v v
)])lH nOJIyqeHM.H xopollIeM llIMpOKOnOJIOCHOCTM, a TaIOKe ,UJI.H JIyqllIeM aKKOMo,UaI(MM
3<P<l>eKToB B3aMMHoH CBH3M.
XOTR IIlMpMHa JIMH3bI II MeHbllIe .lJ)IMHbI peIIleTKM, BbICOTa JIMH3bI Bcer,Ua 60JIbllIe
.lJ)IMHbI pellIeTKJI. Pa3MepbI JIMH3bI YMeHbllIalOTCH 06paTHO npOnOpI(MOHaJIbHO KBa,n:-
paTHOMY KOpHIO M3 3<l><peKTMBHoH ,UM3JIeKTpMqeCKOM npOHMu;aeMOCTM .LLJUI peaJIM3a-
UMM KaK B BillIe nOJIOCKOBOH, TaK M MMKpOnOJIOCKOBOM JIMHMM (CM. npMMepbI Y [5]).
KOHCTpyKUMM C HM3KMM ypOBHeM 60KOBbIX JIeneCTKOB paCCMa1pMBaIOTCli B pa3-
,UeJIe 10.3. Ha pMC. 10.32 nOKa3aHa TMnMqHaH MMKpOnOJIOCKOBaH JIMH3a POTMaHa.
10.2.2.2. p,sYMepHble cpMp,epHble nMH3bl
XOT.H JIMH3a POTMaHa - 3TO <pM,L{epHaH JIMH3a, HacToHru;MM pa3,UeJI nOCBHru;eH ,UBY-
MepHbIM JIMH3aM; HeCKOJIbKO JIyqeti <POpMMPYIOTC.H B ,UBYX M3MepeHM.HX. K COXaJIe-
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JIMH3a HMeeT ,[(0 qeTbIpex ,[(MCKpeTHbIX illIeaJIbHbIX <pOKaJIbHbIX TOqeK, HO OHM He
MOryr 6bITb pa3Meru;eHbI nocpe,UCTBOM qeTBepTHoH CI1MMeTpI1H, KaK BillIHO M3 pac-
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OT BbI60pa <pOKaJIbHbIX TOqeK [16]. Ha npaKTMKe <pM,[(epHbIe M lIpyrHe JIHH3bI He
KOHCTPYJ1PyIOTCH C ,[(MCKpeTHbIMM <pOKYcaMH; OnTMMaJIbHaH KOHCTPYKU;MH rrpe,lJ,-
CTaBJI.HeT co60H perneHMe MMHMMaKc-HoH 3a,[(aqM M.H OKpyxHOCTeH, KOTopoe HBlliI-
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10.2. YcmpoucmBa rPoPMupoBaHUR JlYlfeu 
<pOKYCOB, o,n:HaKo, n03BOJlSIeT pa3,n:eJIHTb JIHH3bI Ha KJIaCCbI H ,n:aeT npe,n:cTaBJIeHHe 0
TOM, KaK 01lIH6KH 3aBHCHT OT reOMeTpHH JIHH3bI.
IIpOCTeHllIaH <pH.n:epHaR JIHH3a HMeeT nJIOc:r<yIO nOBepXHOCTb pellIeTKH H nJIOC-
:r<yIO nOBepXHOCTb JIHH3bI, a TaIOKe ,n:Ba <pOKYca, pacnOJIO)l(eHHbIX CHMMeTpWIHO OT-
HOCHTeJIbHO OCH B nn,OCKOCTH, co,n:ep)l(am:eH OCb. <I>OKYCbI Moryr 6bITb 06'ben:HHeHbI
Ha OCH, B pe3YJIbTaTe qero nOBepXHOCTH JIHH3bI HBJIHIOTCH KpyroBbIMH H CHMMeT-
PHqHbIMH [42]. O,n:HaKo 3Ta cxeMa ,n:aeT HaH60JIbllIHe 01lIH6KM npM CKaHMpOBaHHH.
Kor,n:a nOBepXHOCTb JIHH3bI CTaHOBHTCH 3JIJIHnCOH,JJ:aJIbHOH, HO no-npe)I(HeMY C
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3BOJUIeT ,lLJIHHaM nyreH B nOnepeqHOH llJIOCKOCTH 6bITb nOqTM TaKMMH )l(e, KaK
LLJIHHbI nyreH B OCHOBHOH llJIOCKOCTH OT JII060ro <pOKYca.
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Tpy,n:HO H3rOTOBHTb.
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KH) B rrepeceKalOm:eH rrJIOCKOCTH. B pe3YJIbTaTe 3Toro KOHTYP rrOBepXHOCTH JIMH3bI
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qTO no Mepe YBeJIlfqeHHH OIlIH6KH <pa3bI (HJIH ,lLJIHHbI rryrlf) nepBbIH 60KOBOH JIene-
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cxeMaMM c nOTepflMM
CooTHollIeHHe Me)KJJ,Y ypOBHeM OTHOllIeHHH 60KOBoro JIeneCTKa SLR H ypOBHeM
nepeCeqeHHH ,l],JIH ,LI,HarpaMMoo6pa3YIOI..I.J;eH ueIIH 6e3 IIOTeph He npHMeHHMO K ue-
n5lM C rrOTepHMH. Ba)I(HhIM BOIIpOC 3aKJIIOQaeTCH B TOM, KaKHe IIOTepH ,lJ.OJDKHbI
CQHTaTbC5I npHeMneMbIMH ,l],JIH nOBbIllIeHHH ypOBHH IIepeCeqeHHH. Ha ,naHHhIM MO-
MeHT onpe,lJ.eJIeHHOrO OTBeTa He Cyr.I.{eCTByeT, HO HeKOTopbIe OCHOBHbIe pe3YJIbTaTbI
npHBeCTH MO)I(HO. B pa60Te [66] nOKa3aHO, qTO KOCHHYCOH,LI,aJIbHbIe opTOrOHaJIh-

 rfla6a 10. MHo20flY'le6l>le aHmeHHbl
HbIe JIyqM MOryr <pOpMMpoBaTbcH H3 ,lJ;BYX Ha6opoB CMern;eHHbIX O,lJ,MHaKOBbIX JIyqeH
(CM. pa3,aeJI 10.4). 3TO MO)f(eT ocyrueCTBlliITbCH C nOMOrn;blO ,l.I,OnOJIHRTeJIbHOH ceTH
fw6pH,l.I,HbIX COe,lJ,HHeHHti, KaK nOKa3aHO Ha pRC. 10.43. PH,II:bI rH6pH,aHbIX coe,aHHe-
HHti 06'be,l.I,HHHIOT O,l.I,HHaKOBbIe JIyqH .rum <POpMHpOBaHI1H KOCHHYCOH,L(aJIbHbIX .rry-
qeti, H, KaK BH,L(HO 113 pHCyJiKa, BbIXO,lJ;bI N-JIyqeBoti ,l.I,HarpaMMOo6pa3yIOmeti cxeMbI
C03,l.I,aIOT N - 1 KOCHHYCOH,lUUlbHbIX .rryqeti. JJ.pyroti cnoco6 paccMoTpeHIDI pa60TbI
cxeMbI 3aKJIIOQaeTCH B TOM, QTO fH6pH,l.I,Hble COe,l.I,HHeHHH H30JIHpyIOT nopTbI .rryqeti
,l.I,pyr OT ,l.I,pyra. OTCJIe)I(MBaHHe CHrHaJIa OT o,nHoro nopTa JIyqa nOKa3bIBaeT, qTO no-
JIOBHHa MOrn;HOCTH YXO,nHT B HarpY3KH rH6pH,lJ;HbIX COe,l.I,HHeHHM, TaK QTO 3<p<p eK -
THBHOCTb COCTaBJIHeT -3,01 ,lJ,D, a SLR = 23,0 .nD.
..
.,
.'
,
,
.
.
.
,n:Oy
fM6pH.aHOe
I YCTPOHCTBO
nOpTbI KOCMHYCOH):{aJIbHbIX J1yqeH
PRC. 10.43. <I>opMHpoBaHlIe opTOrOHaJIbHbIX KOCHHYCOM.LJ:aJIbHbIX J1yqeti.
DOJIee HH3KHe 6oKoBbIe neneCTKH MOryr 6bITb ,nocTHrHyrbI nyreM COQeTaHIDI
Tpex Ha6opoB o,nHHaKOBbIX .rryqeti, KaK nOKa3aHO B pa3,neJIe 10.4, C u:eJIblO nOJIyqe-
HIDI JIyqeti pacnpe.neJIeHIDI KOCHHYC KBaL(paT. Ha pHC. 10.44 npe.nCTaBJIeHa 3Ta KOH-
<pHrypaUHH, o6eCneQHBalOlUaH N-2 JIyqeti OT N BbIXO,l.I,OB ,lJ;HarpaMMoo6pa3YlOmeti
CXeMbI. SLR = 31,5 ,nD, a 3<p<peKTHBHOCTb COCTaBJIHeT 3/8, HJIH - 4,26 ,lJ;E.
B Ta6JI. 10.6. npe,nCTaBJIeHbJ ,nOCTIDKHMbIe o:u;eHKR ,lJ;JIH opTOrOHaJIbHbIX anep-
TYPHbIX pacnpe,l.I,eneHHti cos M . Ha pHC. 10.45 nOKa3aHa 3aBMCHMOCTb 3<p<peKTHBHO-
CTH OT YPOBIDI 60KOBbIX JIeneCTKOB.
Ta6J1Rua 10.6. CxeMbI C nOTepHMII ,lLJUI cpOpMMpOBaHMH opTOrOHaJIbHbIX J1yqeH C BbI-
COKlIMH ypOBH.HMH nepeCeqeHllSJ
Pacnpe,neJIeHHe (YB.JIt 1 (,n6) YpOBeHb nepeCeIJeHIfJI (,n6) 1] (,n6)
PaBHOMepHoe 13,26 -3,92 0
KOCHH)'C 23,00 -2 10 -3 01
, ,
KOCHHYC KBa,apaT 31,47 -327 -426
, ,
KOCHHYC KY6 39,30 -444 -505
, ,
,

10.3. HU3Kue 6oKo6ble lleneCmKU U uHmepnOf/fllJ,UJllly'teu d
.
.
.
,L(Oy
fH6pl1,lJ;HOe
/ YCTpOHCTBO
ITOPTbI .rryqeH pacnpe.aeJIeHHH KOCHHYC KBa.n;paT
PHC. 10.44. <I>opMHpoBaHHe opTOrOHaJIbHbIX JIyqei1: C pacrrpelleJIeHl1eM KOCHHYC
KBa,npaT
-10
-20
-..
LQ
t:{
--

LQ
 -30
-.. .....
-- .....
O,nHopo,nHoe -.............
""
"
'"
"
os
"
"
,
"
,
. cos 2
,
,
,
,
cos 3
-40
o
1
2
3
IloTepH (.an)
4
5
6
PHC. 10.45. YpOBHH 60KOBbIX JIeneCTKOB opTOrOHaJIbHOrO pacrrpe.aeJIeHI151
3<l><l>eKTHBHOCTb cxeMbI paBHReTCR
1
11 = J Cos2M (rcp / 2)dp = 1 .3.5... (2M -1) .
o 2 M M!
(10.16)
XOTR cxeMa 6y,neT C03,naBaTb XeJIaeMbIe opTOrOHaJIbHbIe JIyqH C HH3KHM ypOB-
HeM 60KOBbIX JIeneCTKOB If BbICOKHM ypOBHeM nepeCeQeHH5I, HeRCHO, B03MO)I{HO JIM

 Dla8a 10. MHo2oJlY'le8ble aHmeHHbl
C03)(aHHe 60JIee 3<p<peKTHBHbIX ceTeit B paHHHx pa60Tax [59, 2, 51] npHBO,l(RTCR
TOJIbKO 06IIJ:He pe3YJIbTaTbI. B pa60Te [63] HCnOJIb3yeTcR cxeMa <pOpMHpoBaHHR ny-
qeH C JIHH30H POTMaHa, HO nOTepH cxeMbI HeOT,l(eJIHMbI OT nOTepb nHH3bI (CM. TaK-
xe [68, 69]). TaKlfM 06pa30M, Ha ,l(aHHbIH MOMeHT, no BceH BI1,[(HMOCTH, HeT ,l(aH-
HbIX, yKa3bIBalOIIJ:HX Ha TO, qTO MOryT )(OCTHfaTbCR 60JIee Hlf3K1fe nOTepH, HO TaIOKe
M HeT ,l(OKa3aTenbCTBa TOfO, qTO 60JIee HH3Kl1e nOTepH HeB03MO)I(HbI.
10.3.1.4. Cynepn03ML4MfI nYlleif
Hlf3Kl1e 60KOBble JIerreCTKIf MOryT C03,l(aBaTbCR 3a CqeT cooTBeTcTByJOIIJ:ei1 cynepno-
31fU;HH JIyqeH C nOMOI.I.(blO n -pacnpe,l(eneHHR Teiffiopa, onHcaHHOfO B fJIaBe 3. 3TO
pacnpe.n:eJIeHlfe 06eCneQHBaeT rrOqTH OnTHMaJIbHyJO HanpaBJIeHHOCTb H IlIHPHHY
JIyqa ,l{JIR )(aHHOfO 3HaqeHHH SLR, C03)(aBaH rrepBble n 60KOBbIX JIeneCTKOB paBHoH
BeJIIfQHHbI, a OCTaJIbHble 60KOBble JIeneCTKH - y6bIBalOmHMH no 3aKOHY Iju, r,l(e
u = L (sinS - sin8 m ),
A
(10.17)
rrpH 3TOM 8m - HarrpaBJIeHHe m-fO nyqa. B6nH3H n Cyn.J;eCTByeT nepeXO)(HaR 06-
JIaCTb, rr03TOMY n 60KOBbIX JIeneCTKOB He HaXO)(RTCH TOqHO Ha ypOBHe npoeKTHOfO
SLR, a paBHOMepHO y6bIBalOT B OfH6alOmyIO Iju. Y6bIBaHHe orH6alOmeH Iju Heo6-
XO)(HMO ,lI.JUI 06eCneqeHHH YCTOHqHBOrO K norpelliHOCTRM paCKpbIBa (HH3K11H Q).
Bblpa)KeHHe ,[(JIR n -pacnpe,l(eJIeHIfH TeitJIopa If MeeT BIf)(
n -I
g(P) = 1 + 2 L F(n, A, n) cos nnp,
n=I
(10.18)
r.n:e K03<P<PIfU;HeHTbI H 1IJIeHbI orrpe.n:eJIeHbI COfJIaCHO rrOJIOXeHHRM fJI. 3. BbI6paH-
Hoe n -pacrrpe.n:eneHHe Teiffiopa rrpe,l(CTaBJIReT MHTepec 6JIaro.n:ap5I B03MO)I(HOCTH
anrrpOKCHMaU;HH g(p) C nOMOIUblO HeCKOJIbKlfX 1IJIeHOB.
3a HCKJIIOQeHHeM OQeHb MaJIOrO 3HaQeHIDI n , e)(HHCTBeHHbIM 3HaQHMbIM 1ffieHOM
B PMe g(p) RBJI5IeTCR nepBbIH (n = 1). HarrpHMep, paCCMOTpHM 30 .n:E rrpOCTpaHCT-
BeHHbIH MHO)J(lfTeJIb npH HaH60JIbmeM n , B pe3YJIbTaTe npHBOJUlrn:eM K MOHOTOHHO-
MY pacnpe.n:eJIeHHIO. K03<P<P H UHeHTbI npHBO.IDITC5I B Ta6JI. 10.7, H3 KOTOpOH BH,aHO,
QTO He06xo.n:IfMbIMM 5IBJIRIOTCR TOJIbKO .n:Ba K03<l><PHI.I:lfeHTa.
Ta6J1Hu;a 10.7. K03<l><PHHeHTbI pacnpe.n;eJIe-
HID! .lL7UI SLR == 30 .n;E, n = 7
Fo = 1
F I == 0,28266
F 2 = -0,01313
F3 = -0,00164
F4 = 0,00468
) = -0,00414
F(., = 0,00225

]0.3. HU3KUe 60K08ble lleneCmKU U UHmepnOJ/R14UJlIlY'teU 
3TO pacnpe.n.eJIeHl1e HBJIHeTCH paCrrpeJIeJIeHl1eM Tl1rra «KOCMHYC Ha nbe.n.eCTaJIe»,
a He 06bIQHbIM pacnpe.n.eJIeHMeM, nOCKOJIbK)' 31IeCb KOCMHYC MMeeT 3HaqeHMe -1
Ha KOHuax paCKpbIBa. IIapaMeTp n MO)l(eT paCTH .n.o 3HaqeHMR, .n.alOI.I.J.ero MaKCMMa-
JIbHYIO 3<p<peKTHBHOCTb paCKpbIBa ( n = 23 JIIDI 3Toro CJIyqa5I), He CHIDKaH KaqeCTBa
3TOM JIBYXK03<P<PMUl1eHTHOM annpOKCI1MaUI1I1. IIoCKOJIbK)' 113MeHeHI1e 3<p<peKTI1B-
HOCTM OT MaKCMMaJIbHOrO MOHOTOHHoro n JIO MaKCI1MaJIbHOM 3<P<PeKTI1BHOCTH n
COCTaBJIReT < 2% ):(JUI SLR  40 ,l(E, MOHOTOHHoe n HBJIHeTCH XOpOIIIHM BbI60pOM.
TeMJIOp nOKa3aJI, QTO npocTpaHcTBeHHbIM MHO)l(MTeJIb (K03<P<PMUl1eHT 3anOJIHe-
HI1R) MO)l(eT 6bITb 3anl1CaH CJIe.n.yJOll.{I1M 06pa30M (CM. rJI. 3)
n+l
F(u) = LEn F(n, A, i1)sinc[ n(u + n)].
n=-n-l
(10.19)
TaKlfM 06pa30M, rrpOCTpaHCTBeHHbIM MHO)l(JfTeJIb BKJIlOqaeT u.eHTpaJIbHbIM JIyq
C n+ 1 .rryqaMI1, pacrrOJIO)l(eHHbIMI1 no 06e CTOpOHbI OT Hero 11 OTCTOHll.{MMH ,l(pyr OT
JIpyra Ha paCCTOHHMHX, paBHbIX ueJIbIM 3HaqeHlfHM u. 3Tlf COCTaBJIHIOIUlfe .rryq11 RB-
JIHIOTCH pe3YJIbTaTOM O,l(HOpo,n:Horo B036)')K.L1:eHMH. IIOCKOJIbK)' TOJIbKO n = + 1 Tpe6y-
eTCH .lIJ1H arrrrpOKCHMaUl111 n -pacrrpe.n.eJIeHMH TeMJIOpa, He06xo,n:HMO TOJIbKO T}Jlf
JIyqa .lIJ1R annpOKclfMaUlfM npocTpaHcTBeHHoro MHO)l(l1TeJIH TeMJIOpa. ,lJ;lfarpaMMO-
06pa3yJOiliaR cxeMa Tor):(a .n.OJI)f(Ha CJIO)l(lfTb Tplf CMe)l(HbIX JIyqa C Tpe6yeMbIMH Be-
COBbIMM K03<P<PMUlfeHTaMlf ,l(JIH nOJIyqeHlfH o.n.Horo JIyqa C HI13KHM 60KOBbIM JIerre-
CTKOM. QT06bI rrOJIyqllTb N JIyqeM C HI13KHMH 60KOBbIMI1 JIerreCTKaMH, ,lJ;OY,
KOHeqHO, 1I0JDKHO HMeTb N + 2 O,l(HOpO.n.HO B036)')K.L1:eHHbIX JIyqeM. B rrpOCTOM Ba-
u
pMaHTe BbIIIOJIHeHllH MO)l(HO HCnOJIb30BaTb TpeXKaHaJIbHbII1 ,l(eJII1TeJIb MOrn;HOCTH B
Ka)J()]:OM nopTY O,n:HopO):(Horo JIyqa: C JIBYMH KaHaJIaMlf IIPH 2F (1, A, n ) 11 OlIHlfM
KaHaJIOM IIpl1 1. ,LJ;Ba KaHaJIa Ka)J()]:oro KpaMHero IIopTa JIyqeM 3aKaHqlfBalOTCH Ha-
rpY3KoM, paBHO KaK If O,l(I1H KaHaJI Ka)J()]:oro H3 coce,n:HI1X rropTOB JIyqa. 3<p<peKTI1B-
HOCTb B 3TOM CJIyqae BbIQMCJIReTCR KaK <pyHKlI.MR QI1CJIa nopTOB JIyqeM:
N-2
1']=
N
M
M +2'
(10.20)
rJIe MMeeTCH N O,l(HOPO,l(HbIX nopTOB JIyqeM 11 M JIyqeM C HH3KlfMM 60KOBbIMM JIe-
rreCTKaMI1. Hanpl1Mep, .lIJ1H 8 JIyqeM IIOTepl1 COCTaBRT 0,97 ,n:E, a .lIJ1R 16-0,51 JIE.
3TI1 nOTepM paCCeI1BaHI1H, KOHeQHO, He CBH3aHbI C 3<p<peKTMBHOCTblO paCKpbIBa,
KacalOIUeMCR JIyqeM C HI13K11MM 60KOBbIMI1 JIerreCTKaMM. EOKOBbIe JIeneCTKI1 HIDKe
YPOBHH -32 JIE 6bIJII1 ,n:OCTHrHYTbI B [63], r,n:e I1CnOJIb30BaHO ,l],OY B Bl1,[(e JII1H3bI
POTMaHa C 60KOBbIMM JIeneCTKaMM -28 ,lI.I> B nOJIoce qaCTOT 60JIee 10%. KorJIa ,LJ;OY
IIpen:CTaBJIHeT C060M JIMH3Y POTMaHa HJIlf MHyJO <pJ1.IJ:epHYIO JIHH3Y, cynepn03HUHH
JIyqeM MHOr,lI.a Ha3bIBaeTCH «061>e):(I1HeHHbIM rrMTaHMeM».
1 0.3.2. CxeMbl MHTepnOnSlLJ.MM nY'Ia
Kor,n:a JIyqM HMelOT HH3KHe YPOBHH rrepeCeqeHHR, HJIH KOr,l(a He06xo,n:lfMO TOqHO
orrpeJIeJIHTb yrJIa rrpHXOJIa, )l(eJIaTeJIbHO MMeTb B03MO)I(HOCTb rrepeMemaTb rryqOK
JIyqeM B npOCTpaHCTBe lfJII1 <pOpMl1pOBaTb MHTepIIOJIl1pOBaHHbIe JIyqH, KOTopble
MO)l(HO nepeMern;aTb. OrrMIIIeM OJIMH rrpocToM crroc06 BbIrrOJIHeHMR nOCJIeJIHero.
PaccMoTpMM ,lI.Ba CMe)I(HbIX JIyqa OT MHoro.rryqeBoM AP C O,L(HOpO):(HO B036)')K.L1:aeMbI-

 Dla6a 10. MH020Jly'te6ble aHmeHHbl
MM 3JIeMeHTaMM, HaXO.l1RIUHMHCR Ha paccToRHHH, paBHOM IIOJIOBHHe BOJIHbI, ,n:pyr
OT ,n:pyra. ITHKoBbIe yrJIbI JIyqa nOJIyqalOTcR npH
. e mj
SIn. =-
I N'
(10.21)
r,n:e m j - 3TO HeqeTHOe l(eJIoe qHCJIO  nOJIOBHHe qHCJIa 3JIeMeHTOB pemeTKI1 N.
KIDK,II;bIH.rryq MMeeT <Pa3Y (rot - kd sinS j ), KOTOpall ,n:aeT m j 1r./ N npM oT6paCbIBaHHH
rot. Tenepb ,n:Ba CMe)KHbIX nopTa JIyqeH COe.l1HHeHbI qepe3 <t>a30Bpaw:aTeJIH C rH6-
PH.l1HbIM Y3JIOM, KaK nOKa3aHO Ha pHC. 10.46.
ej;j
ej;j
I
6
rH6pH.LJ:HbIH Y3en
Puc. 10.46. I.J;enb HHTepnOJUIl(HH .rryqa
Ha ,n:aHHOM pHcYHKe <pa3bI JIyqa cJIe,n;YIOru;He: <Pj = m j 1[/ N, npH 3TOM <pa30Bpa-
Il{aTeJIH - <Pj M <P2' BbIXO.l1HbIe CI1THaJIbI CyMMbI M pa3HOCTH M3 Y3JIa:
L = 2 Co{  (<p t - <P j + <P 1 - <P 2) }x p [ ; (<p t + <P j + <P 1 + <P 2) }
11 = 2 s  (<p t - <P j + <P 1 - <P2) }x p [ ; (<p t + <P j + <P 1 + <P2) J.
(10.22)
BHaqaJIe B03bMeM cYMMapHbIH BbIXO,n;. ECJIH HCnOJIb3yeTcH TOJIbKO OJJ;HH <pa30-
BpaIl{aTeJIb, 3aBHCHMOCTb <pa3bI .rryqa OT 3HaqeHHlI <l>a30BpaIl{aTeJIR )'Ka3bIBaeTCR
HIDKe HapMY C aMIIJIHTYJJ;HbIMH nOTepRMH. IToTepRHHaH MOIl{HOCTb I1,[(eT B nJIeqo
pa3HOCTM.
<l>a3a .rryqa
<pj
1
2 (q> i + <P j)
<Pj
<l>a30Bpam;aTeJIb <P 1
<pj -<P j
o
AMnrrMTYJJ;a
COS(<p i - q> j)
Co { (<p j - <P j) J
o
(10.23)
<Pj -<pj
ITOCKOJIbKY <Pj - <Pj = 2/ N, B He60JIbllIHX pemeTKax cymeCTByJOT 3aMeTHbIe no-
TepH, Kor,n:a JIyq npM6JIH)KaeTClI K nOJIO)KeHMIO <pj. 3TH nOTepH MO)I(HO YMeHbIIIHTb
nyreM MCnOJIb30BaHMlI 060HX <l>a30BpamaTeJIeH; KOCHHYCOH,n:aJIbHbIH K03<P<PHUHeHT
MO)I(HO coxpaHHTb OKOJIO eJJ;HHHl(bI. TorJJ;a
<l>a3a nyqa <l>a30Bpam;aTeJIb <P 1
<Pi 0
1 1
2 (<p i + <P j) 2 (<p j - cP j)
<Pj <pj -CPj
<l>a30Bparn;aTeJIb <p 2
<Pi -<P j
1
2 (<p i - <p j)
o
(10.24)
XOTlI BbIllie IIOKa3aHbI TOJIbKO 1pH IIOJIO)KeHHR .rryqa, JJ;Ba <pa30BpaIl{aTeJIH MO)K-
HO OTperyJIHpOBaTb TaK, QTo6bI paCIIOJIO)f(J{Tb CyMMapHbIH JIyq B JII060M MeCTe OT

10.4. Opmo2oHaJ/bHocmb JlY'Ieu d
rrOJIOXeHIDI JIyqa <P j ,ao rrOJIOXeHHH JIyqa <Pi + 1 6e3 rrOTepb. <I>aKTHqeCKOe rrOJIOXe-
HHe JIyqa HaXO,lJ.HTCH H3 Q>a3bI JIyqa KaK
n sin 8. = <P .
I I ,
(10.25)
Pa3HOCTHaH ,lJ.HarpaMMa HarrpaBJIeHHOCTI1, KOTopaH MO)l(eT 6bITb I1CrrOJIb30BaHa,
QTo6bI ynpaBJIHTb HYJIeBbIM rrpOBaJIOM MOHOI1MrrYJIbCHOrO THrra MH TOqHOrO yrJIO-
Boro cOrrpOBO)l()]:eHHH, Be,aeT ce6H aHaJIOrWIHbIM o6pa30M:
<I>a3a nyqa <I>a30Bpalll.aTeJIb <P I <I>a30Bpalll.aTeJIb <P 2
<Pi nl2 nI2+<pj-<pj
1 1 1 (10.26)
2 (<p j + <p j) 2 (n - <P i + <P j) 2 (n + <P i - <P j)
<Pj nI2-<Pi+<pj nl2
OrrHTb-TaKl1, K03<P<PI1l(HeHT aMrrJIHTY,lJ.bI paBeH e,lJ.HHHl(e, HO 3HaqeHHH <pa30-
BpamaTeJIH Ha nl2 rrpeBbIllialOT 3HaqeHIDI, Heo6xo,aHMbIe ,lJ.JIH c,aBHra rrHKa CyMMap-
Horo JIyqa. nOJIb3YHCb COOTBeTCTByIDmHMH <pa30BpamaTeJIHMH, MO)I(HO BbIC1])OHTb
KOHTYP corrpOBO)l()]:eHHH, KOTOpbIH 6Y,lJ.eT pa60TaTb ,ao Tex rrop, rrOKa CHrHaJI Haxo-
,lJ.HTCH Me)l()]:Y yrJIaMI1 JIyqa <Pi H <Pi+l [34]. C,aBHr .rryqa H HYJIH MO)l(eT TaKJKe conpo-
BO)l()]:aTbCH Ha npOMeOqHOH qaCTOTe C nOMOmblO o,aHoro rrpHeMHoro KaHaJIa Ha
O,aHH nopT JIyqa [33].
10.4. OpToroHanbHoCTb nY"IeM
1 0.4. 1. OpToroHanbHble nYLIM
10.4. 1. 1. nOHflTVle opToroHanbHocTVI
Kor,aa JIyqH B MHOrOJIyqeBO:H AP opTOrOHaJIbHbI, CHrHaJI, rrO,LJ;aBaeMbIH B ,aaHHbI:H
rropT .rryqa, npOHBJIHeTCH TOJIbKO B ,aHarpaMMe HanpaBJIeHHOCTH, CBO:HCTBeHHOH
3TOMY rropTY, npH OTCyrCTBHH CHrHaJIa B ,apyrHX nopTax. IIpH HCrrOJIb30BaHHH
rrpe,aCTaBJIeHHH peIlleTKH B BlI,[{e MaTpHl(bI pacceHHHH (113 N M30TporrHbIX 3JIeMeH-
TOB) H ,aHarpaMMoo6pa3YlOllI.ei1 cxeMbI He3aBHCHMOCTb M nopTOB Tpe6yeT, QTo6bI
rro,aMaTpHl(a, npe,aCTaBJIHlOmaH rropTbI JIyqeH, HMeJIa HYJIeBbIe 3JIeMeHTbI. B3aHM-
HbIe ,[(OY rrpe,lJ.nOJIaralOT CHMMeTpHQHYIO Ma1])HU:Y, a cxeMa 6e3 rrOTepb Tpe6yroT
...
HaJIHqHH e,aHHHqHOH MaTpHl(bI:
N+M
L Sn;Sj = 8).
n=1
(10.27)
I1crroJIb3YH 3TO COOTHOIlleHHe, B [2] nOKa3aHO, qTO Tpe60BaHHe He3aBHCHMOCTH
JIyqeH (H nopToB) npHBo,aHT K TOMY, qTO
1/2
J F;(nu)F/(1tu)du = 8), (10.28)
-1/2
r,ae u = (dl"A) sin e npH e, H3MepHeMOM B HarrpaBJIeHHH, HOpMaJIbHOM K paCKpbIBY
aHTeHHbI, a npocTpaHcTBeHHbIM MHO)l(J1TeJIb paBeH
F j (1tu) = L S ni expU2nnu). (10.29)

b fl1080 10. MHOi!Olly'te8ble OHmeHHbl
TaKHM 06pa30M, npocTpaHcTBeHHbIH MHO}l(MTeJIb n;OJDKeH 6bITb opTOrOHaJIb-
HbIM B yrJIOBOM n;Mana30He
. A e .'A
-arCSIn - < < arCSIn -
2d 2d'
(10.30)
,lLJI$I Toro qT06bI rrOJIyqHTb He3aBMCMMbIe JIyqM H HeCB$l3aHHbIe nopTbI [286]. Korn;a
dj'A == 1/2 (MJIH dj'A == 1, TaK KaK rrpen;eJIbI MHTerpHpOBaHH$I MOrJIH 6bI 6bITb == 1),
JIyqM $IBJI$lIOTC5I opTOrOHaJIbHbIMM BO BceM BHlIMMOM rrpOCTpaHCTBe. TaKI1M 06pa-
30M, JL]UI paCCTO$lHHH, KpaTHbIX 'Aj2, JIyqH H nopTbI $IBJI5IIOTC5I HeCB$l3aHHbIMH .lI.JI5I
xapaKTepHbIX paCCTO$lHHH Me)l(,[(Y JIyqaMH.
PacnpOCTpaHHB MaTpHQHbIH non;Xon: Ha MHOrOJIyqeBoH aHaJIl13, B [3] ,nOKa3aHO,
QTO pa3B$l3Ka JIyqeH 11 YCTpaHeHHe CB5I3M Me)l()lY rropTaMH Tpe6YIOT, QT06bI B3aHM-
HbIe conpOTHBJIeHH5I perneTKI1 paBH$lJIHCb HYJIIO. )),JI$I M30TporrHbIX 3JIeMeHTOB
B3aHMHoe corrpOTHBJIeHHe nponopU:HOHaJIbHO sinc mkd H paBHO HYJIIO .lI.JI$I nOJIY-
BOJIHOBbIX paCCTO$lHHH. 3TO He06xon:HMO, HO He,nOCTaTOQHO, nOCKOJIbKY 3TO npe.n-
nOJIaraeT pa3B$l3KY JIyqeH (opTOrOHaJIbHOCTb) lUI$I Bcex paCCTO$lHI1H Me)l(J].Y JIyqaMH.
OpTOrOHaJIbHOCTb JIyqeH Tpe6yeT JIH60 B3aHMHoro HMnen;aHca, paBHoro HYJIIO ,1I,JI5I
npOH3BOJIbHOrO rnara perneTKH - a 3TO HHKorn;a He $IBJI5IeTC$I CnpaBe.lI.JlHBbIM, .na}l(e
,lLJI$I H30TponHbIX aHTeHH HJIH aHTeHH C MHHHMaJIbHbIM pacceHBaHHeM [65], -
JIH60 qT06bI HanpaBJI5I1OI.I..J;He BeKTopbI perneTKI1 6bIJIH c06CTBeHHbIMH BeKTopaMM
06paTHoH MaTpHI.J;bI B3aHMHbIX HMne,n:aHCOB. CooTHollIeHHe c06CTBeHHbIX BeJIl1ql1H
npen:CTaBJUIeTC$I cnpaBen;JIHBbIM TOJIbKO JL]UI aMnJIHTYn:HbIX pacnpen:eJIeHI1H, COCT05I-
IUHX H3 cosMx, npH COOTBeTCTBYlOlUMX paCCTO$lHHHX Me)l(,[(Y JIyqaMH. TaKMM 06pa-
30M, D;HarpaMMbI M ypOBHM nepeCeqeHH5I He $IBJI$lIOTC$I He3aBHCHMbIMM.
10.4.1.2. OpToroHanhHocTh pacnpep,eneHVlM
B TO BpeM$I KaK MHOrOJIyqeBa$l aHTeHHa JIM60 caMa HBJI$leTC$I perneTKOH, JIH60 B
HeM HCnOJIb3yeTC$I perneTKa B KaqeCTBe OCHOBHoro 06JIyqaTeJISl, MHoroe MO}l(HO
Y3HaTb, H3yqHB HenpepbIBHbIe (JIMHeHHbIe) HCTOqHHKH. O)J;HOP0)J;HbIH JIHHeMHbIM
u
MCTOqHMK MMeeT rrpocTpaHCTBeHHbIH MHO}I(HTeJIb BH,IJ;a
F(u) == sinc[n(u - u})], (10.31)
r.ne u == (Lj'A) sin 8, ul == (Lj'A) sin 8 1 , 8 1 - rrHK JIyqa. ArrepTYPHoe pacnpe,n:eJIeHHe B
.nHana30He OT p == -1 .no + 1 eCTb
g(P) == exp(- jpnu).
(10.32)
OpTOrOHaJIbHOCTb npOCTpaHCTBeHHbIX ,n:HarpaMM HanpaBJIeHHOCTH MO)l(HO rrpo-
CTO 3anHcaTb (Lewin, 1975) KaK
00
J sinc[n(u - u})]sinc[n(u - u2)]du == sinc[n(ul - U2)] == 8,
(10.33)
-00
r,n:e ,lLJIHHa JIHHeHHOro HCTOQHHKa 6bIJIa npHHHTa 60JIbrnOH C TeM, QT06bI npe.neJIbI
MOrJIH 6bITb arrnpOKCHMMpOBaHbI }IO 00. OpTOrOHaJIbHbIe JIyqH MO)I(HO 3aTeM pacno-
JIO}l(}lTb Ha paCCTO$lHHH )J;pyr OT ,n:pyra B e.nHHHu:ax u/). == + 1, + 2,..., HO TOJIpKO U/). == 1
rr03BOJI$leT CMe)I(HbIM rJIaBHbIM nyqaM nepeceKaTbC$I. 3TO npOMCXO}IMT npM u == u I +
+ Ij2 H .naeT YPOBeHb nepeCeqeHH$I 2jn == -3,92 .nE. I1JIH )J(e HHTerpaJI opTOrOHaJIbHO-
CTM MO)I(HO 6bIJIO 6bI 3anHcaTb no paCKpbIBY, nOCKOJIbKY npe06pa30BaHM5I <DYPbe op-

10.4. Opm020Hll./lbHOCmb Il)l'teu d
TOrOHaJIbHbIX <l>YHKUHH TaIOKe 5IBJIHIOTC5I opTOrOHaJIbHbIMH rrpH 1paHcrroHHpoBaHHH
OJJ:HOH H3 HHX [28a]. ,[Lrr5I O,.a:Hopo,.a:Horo pacKpbIBa 3TO ,.a:aeT
1
J exp[jp1t(u - ul)]exp[jp1t(u - u2)]du = sinc[1t(ul - U2)] = sinc( 1tU ll)' (10.34)
-I
06I.I.{HH KJIacc opTOrOHaJIbHbIX Crra;:I;alOI.I.(HX aMrrJIHTY,.a:HbIX pacnpe,.a:eJIeHHH -
3TO cosM(p'1t/2). TIOCKOJIbKY rrpOC1'paHCTBeHHbIH MHO)KHTenb H HHTerpaJIbI opToro-
H3JIbHOCTH MOryr 6bITb BbIqHCJIeHbI B 5IBHOM BMe, JIerKO CpaBHHTb 3TH pacrrpe,.a:e-
JIeHIDI. B KaqeCTBe rrpHMepa 6YJJ:eT HCnOJIb30BaHO KOCHHYCHOe pacnpeJJ:eJIeHHe.
TIpOCTpaHCTBeHHbIH MHO)KHTenb MO)KeT 6bITb 3arrHCaH OJJ:HHM H3 ,lJ,BYX crrOC060B,
rrpHqeM B 060HX CJIyqaHx F(O) = 1:
F(u) = ; {Sine[ 7t G - u )] + Sine[ 7t G + u )]} = lCS;: · (10.35)
HYJIH npOCTpaHCTBeHHoro MHOXHTeJUI HMelOT MeCTO npH U = 3/2, 5/2, 7/2,...
TIHK nepBoro 60KoBoro JIerreCTKa 6Y,lJ,eT 3a<}>HKcHpoBaH npH U = 1,8894 H SLR =
= 23 JJ:B. IIoJIoBHHa IIIHpHHbI JIyqa B U COCTaBJI5IeT U3 = 0,5945, npH 3TOM 3<P<l>eK-
THBHOCTb paCKphIBa (HanpaBJIeHHOCTb no cpaBHeHHIO C paBHOMepHbIM B036y)K)J.e-
HHeM) COCTaBJUIeT 0,8106. I1HTerpaJI opTOrOHaJIhHOCTH CBO,.a:HTC5I K CJIeJJ:YIDI.I.(eMY:
2sinc(1tuL\) + sinc[1t(1 - Ull)] + sinc[1t(1 + Ull)] = 0, (10.36)
qTO MO)I(HO ynpOCTHTb ,.a:o:
.
sm 1tU L\
Ull (1- UL\)2
= o.
(10.37)
3HaqeHH5I pa3,lJ,eJIeHH5I JIyqeH, JJ:alOI.I.(He opTOrOHaJIbHOCTh nyqa, TorJJ:a 5IBlliIIOTC5I
peIIIeHHHMH 3Toro ypaBHeHHH:
u A = 2, 3, 4,... (10.38)
Bo Bcex c.rryqaRX MHHYC U MO:>KHO 3aMeHHTb Ha TIJlIOC u. B Ta6JI. 10.8 npHBOJJ:RT-
...
CR COOTBeTCTByroI.I.(He napaMeTpbI wrn qeTbIpex pacnpeJJ:eJIeHHH paCKpbIBa.
Ta6JIHua 10.8. OpTOrOHaJIbHbIe npOC'TpaHCTBeHHbIe ,lJ:HarpaMMbI HarrpaBJIeHHOCTH
Pacnpe,neJIeHHe HYJIH U SL SLR (.n;6) 1/2 U 3 1) U x Ex (,n6)
O,ZJ;Hop0,ZJ;Hoe 1, 2, 3 1,4303 13,26 0,4429 1 0,5 -3,94
KOCHHYC 1,5; 2,5; 3 1,8894 23,00 0,5945 0,8106 1 -9,54
KOCHHYC KBa,n:paT 2, 3, 4 2,3619 31,47 0,7203 0,6667 1,5 -15,40
KOCHHYC KY6 2,5; 3,5; 4,5 2,8420 39,30 0,8292 0,5764 2 - 21 ,34
llIHpHHa nyqa H 3<l><l>eKTHBHoCTb B036y)K)J.eHHH pacKpbIBa - 3TO u3 H 11 1 , B TO
BpeMR KaK yron nHKa 60KOBoro JIeneCTKa paBeH USL' Yron H ypOBeHb nepeCeqeHIDI
paBHRIOTCR U x H Fx.
MHorJJ:a YTBep)l{,[(aeTCR, qTO nHHeHHbIe KOM6HHaUHH opTOrOHaJIbHbIX npOCTpaH-
CTBeHHbIX MHO)l(lfTeJIeH MOryr TaIOKe 6hITb opTOrOHaJIbHhIMH, HanpHMep, pacnpe-

 rAa6a 10. MnOZOA)l'Ie6ble anmennbl
,l(eJIeHHH THna KocHHyca Ha nbe.ueCTaJIe. KaK nOKIDKeT npoBepKa, 3TOT BbIBOn: HeBe-
peH. MHTerpaJI opTOrOHaJIbHOCTM no pacKpbIBY, f,l(e u = ul - u2, paBIDIeTcH:
1 1 ( 1 ) 2 ( 1 )
2 L a + bcos 2 1tp expUp1tU"Jdp = a 2 + 2 b 2 SinC(1tUL'> +
+  ab { Sinc[ 1t G - u" )] + SinC[ 1t G + u" )]} +
(10.39)
+ !b 2 {sinc[1t(l - u)] + sinc[1t(1 + u)].
4
3TO CBO,l(MTCH K CJIe.n:YIOru;eMY:
( 2 1 b 2 ) . 2abcos 1tU
a + - SlnC1tU +
2 1t(1 - 4u)2
+ b2u sin 1tU = o.
21t(1 - ui)
(10.40)
AnH OC06bIX CJIyqaeB paBHOMepHoro B036)')K,I(eHHH (b = 0) H KOCHHYCHoro B03-
6)')K,I(eHIDI (a = 0) nO.HBJI.HIOTC.H rrpaBHJIbHbIe 3HaqeHMH u. B o6ru;eM c.rryqae HMeIOT-
CH 3HaqeHHH u, .n:eJIalOru;He .rryqH opTOrOHaJIbHbIMH, HO paCCTOHHHH Me)K)]:y.rryqaMH
He o.nHHaKOBbI. HanpHMep, eCJIH B3.HTb pacnpe,aeJIeHHe C nbe,I(eCTaJIOM 10 ,I(D (B03-
6)')K,I(eHHe KpaH -10 ,l(D), Y KOTOpOfO a = 0,46248, b = 1, 3HaqeHHH u paBH.HIOTCH
u = 1.648; 2.271; 3.143; 4.097; 5.074; 6.060,...
(10.41)
nOCJIe,l(CTBHeM .n:aHHoM HepaBHoMepHoH nOCJIe,aOBaTeJIbHOCTH HBJIHeTCR TO, qTO
Bce CMe)KJIbIe JIyqH HBJIHIOTCH OpTOfOHaJIbHbIMH (u = 1,648), HO HH O,I(HH JIyq HC
.HBJIHeTCH opTOrOHaJIbHbIM JII06bIM .rryqaM .n:aJIbllIe COCC,I(HCro, nOCKOJIbKY
2 x 1.648 = 3.143,3 x 1.648 = 5.074 H T.,l(. HanpoTHB, qHCTO KOCHHYCHOC pacnpc.n:e-
JICHHe HMeeT u = 2, 3, 4,..., TaK qTO, CCJIH CMC)l(HbIC .rryqH OTCTOHT ,l(pyr OT ,I(pyra
Ha 2, TO BCC JIyqH OTCTOHT ,l(pyr OT ,l(pyra Ha paCCTOHHHe, KpaTHOC 2, CJIcn:OBaTCJIb-
HO, OHH opTOrOHaJIbHbI. TOT <l>aKT, qTO pacrrpC,l(eJICHHC «KOCHHYC Ha nbC,l(eCTaJIe»
HC opTOrOHaJIbHO, HC .HBJIHCTC.H HeO)l(Jf)]:aHHbIM, nOCKOJIbKY 3aBHCHMOCTb HHTerpaJIa
opTOrOHaJIbHOCTH OT U CB.H3aHa C npocTpaHcTBcHHbIM MHO)KHTCJICM: CCJIH HYJIH
npocTpaHcTBeHHoro MHO)IGITeJIH pacnOJIo)J(eHbI paBHoMepHo (c nOCTOHHHbIM llIa-
rOM), a nHKH JIyqeH pacnOJIO)J(eHbI B n03HIJ;HHX HYJIeU ,l(pyrHX JIyqeit, JIyqH MOryr
6bITb opTOrOHaJIbHbIMH. 31)' xapaKTepHCTHKY HMeIOT TOJIbKO pacnpe,l(eJIeHHH cosMo
K CO)J(aJIeHHIO, 3TH pacnpe.n;eJIeHHH HBJI.HIOTCH He3<l><peKTHBHbIMH no cpaBHeHHIO C
npOC1'paHCTBeHHbIM MHO)IGITeJIeM TcitJIopa. TaKMe COBpeMeHHbIe npOCTpaHCTBCH-
HbIe ,l(HarpaMMbI HanpaBJIeHHOCTI1 npOeKTHpyroTCH nyreM pa3Meru;eHIDI 6JIIDKHHX
HYJIeit ,l(JIH no.rryqeHIDI 3an;aHHoro ypOBHH 60KOBbIX JIenCCTKOB, a 3aTCM n03BOIDIIOT
HYJIHM nCpeMeIl{aTbCH K ueJIOqHCJICHHbIM paCCTOHHHHM .lLTIH 60JIbllIOrO u. B pe3YJIb-
TaTe HepaBHOMepHoe pacnOJIO)J(eHHC n:eJIaeT npOCTpaHCTBeHHbIe MHO)IGITCJIH Heop-
TOrOHaJIbHbIMH.
OpTOrOHaJIbHOCTb TOf,I(a ,aOCTHraeTCH C TPy,aOM no HeCKOJIbKMM npHqHHaM:
paCKpbIBbI B ,l(JIHHaX BOJIHbI .n:OJDKHbI 6bITb 60JIbllIHMH, H pacnpe,I(eJIeHHH cos M HB-
lliIlOTCH He3<l><l>eKTHBHbIMH; AP ,lIOJDKHbI HMeTb llIar B I10JIOBHHY ,l(JIHHbI BOJIHbI.
MO)J(HO MO.n:H<pHIJ;HpOBaTb 3TH OrpaHHQeHHH I1)'TeM BBo.n;a nOTcpb B ,L(HarpaMMoo6-
pa3YIDIl{yIO cxeMY. 3TO, KOHeqHO, TaIOKe CHH3HT 3<l><peKTHBHOCTb. TIpe)K,I(e qeM 3TO
6y.n:eT paCCM01'peHO, Heo6xo,l(HMO onpe,I(eJIHTb 3<l><l>eKTbI HeopTOrOHaJIbHbIX .rryqei1.

10.4. OpmOZOHatlbHOCmb JI)l'teu d
10.4.1.3. OpToroHanbHocTb peweTOK
B rrpe,n:bl,[{yrueH pa60Te paCCMaTpHBaJIHCb HerrpepbIBHbIe arrepTypHbIe pacrrpe,n:eJIe-
HHH, rrOCKOJIbK)' OHH JIerqe rrO,1J..[(aIOTCR o6pa6oTKe. XOpOlliO H3BeCTHO, qTO pe-
rneTKH, COCTOHII{He H3 MHorHX 3JIeMeHTOB, MOryT TOqHO arrrrpOKCHMHpOBaTb He-
rrpepbIBHoe pacrrpe,n:eJIeHHe, ,n:eJIaR BbI60pKH H3 Hero B MeCTax pacrrOJIOXeHHH
3JIeMeHTOB perneTKH. ,LJ;JIH peaJIH3al{HH 3a,z:J:aHHoro rrpOCTpaHCTBeHHoro MHO)l{}lTeJIH
C perneTKOH H3 HeCKOJIbKHX 3JIeMeHTOB 06bIqHO Heo6xo,lJ;HMO oTperyJIHpOBaTb rro-
JIHHOMHHaJIbHbIe HYJIH perneTKH [23]. K CO)l{aJIeHHIO, 3Ta peryJIHpOBKa RYJIeH pa3-
pyrnaeT opTOrOHaJIbHOCTb JIyqeH. ,LJ;JIH Toro qTo6bI orrpe,lJ;eJIHTb, MOryT JIll opToro-
HaJIbHbIe JIyqH <pOpMHpoBaTbcH H3 MaJIeHbKHX perneTOK, MO)J(HO Herrocpe.n:CTBeHHO
paCCMOTpeTb HHTerpaJI opTOrOHaJIbHOCTH. HarrpHMep,
,
.,
J sin (Nnu j ) sin(Nnu j )
. du
N sin(nuj) N sin(nu j)
( 10.42)
rrpe,n:CTaBJIReT C060H ,n:Ba O.n:HOpO,n:HO B036y)1(,[{eHHbIX JIyqa, C03,n:aBaeMblX perneT-
KOH H3 N 3JIeMeHTOB. MHTerpaJIbI 3Toro THrra He BbIQHCJIHIOTC5I B HBHOM BH,ZJ:e.
KpOMe Toro, OTC)'TCTByeT TeopeMa .n:JI5I ,n;HCKpeTHbIX <PYHKl{HH, rrOKa3bBa1OIUaR
opTOrOHaJIbHOCTb ,n:HCKpeTHoro rrpeo6pa30BaHHH <l>YPbe opTOrOHaJIbHbIX <PYHK-
l{HH. Tor,n:a Y Hac OCTaeTCH TOJIbKO rrpaKTHqeCKOe perneHHe Ol{eHKH HOMHHaJIbHO
opTOrOHaJIbHbIX perneTOK KaK <PYHKIJ;HH QHCJIa 3JIeMeHTOB. DOJIbrnOe KOJIHqeCT-
BO 3JIeMeHTOB ,n:OJI)I{HO ,n:aTb 60KOBbIe JIerreCTKH HerrpepbIBHoro pacrrpe,n;eJIe-
HHH, B TO BpeMR KaK MeHbrnee qHCJIO 3JIeMeHTOB MoxeT ,n;aTb rrOBbIrneHHe 60KO-
BbIX JIerreCTKOB H3-3a MeHee TOqHOrO rrpe.rrcTaBJIeHHH. 3TOT paCqeT rrpHBo,n;HTCH
HH)I{e.
10.4.2. 3c1>cI>eKTbi HeopTorOHanbHOCTM
10.4.2.1. nOTepM 3C/JC/JeKTMBHoCTM
IIpH HCrrOJIb30BaHHH arrepTypHblX pacnpe,n;eJIeHHH, HBJI5I1Om;HXC5I opTOrOHaJIbHbIMH,
HO C HeopTOrOHaJIbHbIMH paCCTOHHHHMH Me)l()];Y JIyqaMH, 3<p<peKTHBHoCTb L(OY Te-
pH eTCH H3-3a CJIHHHHH JIyqeH. B pa60Te [59] rro.rryqeHbI rrpe.rreJIbI CJIIDIHHH JIyqeH H
pe3YJIbTHpyIOm;a5I 3<p<peKTHBHoCTb. IIycTb rrapaMeTp rrepeKpbITH5I nyqeH .n:HarpaM-
Moo6pa3yIOII{eH cxeMbI (3 6y,n;eT
13 ij == J E j (8, <p)E j (8, <p)dQ,
( 10.43)
rrpH 3TOM f3 u ==1. MaKCHMaJIbHa5I 3<p<peKTHBHoCTb Terrepb CTaHOBHTCH paBHoH:
1
llmax == 1 + 13 2 .
(10.44)
MHTerpaJI rr03BOJI5IeT JIerKO orrpe.rreJIHTb 3<p<peKTHBHoCTb ,LJ;OY. B pa60Te [21]
,n;OKa3aHO, qTO 3<p<peKTHBHoCTb ,LJ;OY TaIOKe paBHReTCH OTHorneHHIO Cpe,lJ;HerO H rrH-
KOBoro pacrrpe.n:eJIeHHH MOII(HOCTH paCKpbIBa (perneTKH). TaKHM o6pa30M, ,lLJIR o,n;-
....
Hopo,n;Horo, KOCHHYCHoro H KOCHHYC-KBa,apaTHoro pacrrpe,lJ;eJIeHHH MaKCHMaJIbHa5I

 DWBa 10. MHo2oAy'teBble aHmeHHbl
3<p<peKTHBHOCTb oY COCTaBJIHeT 0 .an, -3,01 .an H -4,26 .an COOTBeTCTBeHHO.
)];HcKpeTHaH 3<P<l>eKTHBHOCTb .aHarpaMMoo6pa3yJOIUeH cxeMbI BhIpIDKaeTCH:
1 + 2:L B
TJBFN = (1 + 2:L B n)2 '
(10.45)
r.ae (3n, HanpHMep, 3TO K03<P<PHUHeHTbI Teitrropa n . PacnpeJJ:eJIeHHe Teitrropa C
SLR = 25 JJ:n H fi = 5 HMeeT 3<p<peKTHBHOCTb oY, paBHyJO -1,75 JJ:n, T.e. ropa3JJ:O
JIyqIIIe 3<l><peKTHBHoCTH ,n;OY KOCHHYCHoro pacnpeJJ:eJIeHIDI, HMelOIUero conOCTaBH-
MbIH YPOBeHb 60KOBbIX JIeneCTKOB. )J)IH 60JIbIIIHX ,n;OY napaMeTp nepeKphITHH .rryqeH
BbIpIDKaeTCH KaK
00
J3 =! J sincxsinc(x + 1tU /1)dx = sinc1tU /1 .
1t
-00
(10.46)
3TOT napaMeTp II COOTBeTCTByJOIUaH 3<p<peKTHBHOCTb nepeKphITIDI JIyqeH nOKa-
3aHbI B BH,ZJ;e rpacpHKa Ha pHC. 10.47. AHaJIOrHqHOe ypaBHeHHe ,lUIH KOCHHYC-KBarr;-
v
paTHoro pacnpeJJ:eJIeHHH HMeeT CJIeJJ:yJOIUHH BH,ZJ;:
00
J3 =! J sinc 2 xsinc 2 (x + 1tuo)dx =
1t -00 (10.47)
= i {2sinc1tu  + sinc[ 1t(1 + U )] + sinc[ 1t(1 - U )].
1t
3TOT napaMeTp Hero 3<p<peKTHBHOCTh TaIOKe nOKa3aHhI B BH,ZJ;e rpacpHKa Ha
pHC. 10.47, 113 KOToporo BHJJ:HO, qTO KOCHHYC-KBMpaTHaH 3<p<peKTI1BHOCTb 3HaqH-
TeJIbHO HH)I(e. 3aMeTbTe, OJJ:HaKO, qTO n -pacnpeJJ:eJIeHMe Teitrropa, KaK MO}I(HO O}l{Jf-
n:aTh, ,n;aCT ropa3,n;o JIyqIIlHe pe3YJIhTaTbI, qeM ,aa)l(e KOCMHYCHoe pacnpeJJ:eJIeHMe.
1
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0.2
0.4
0.6
1
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0.8
1.2
1.4
1.6
1.8
2
Pac. 10.47. K03<l><l>lfU;HCHT ncpCKpbITHR JIyqcif If 3<l><l>CKTlfBHOCTb ):{OY

10.4. Opmo2oHanbHocmb lI)l'teu 
10.4.2.2. U3MeHeHHR 60KOBblX neneCTKOB
B3aMMOBJIMHHMe JIyqeM B '<paKTMqeCKOM aHTeHHe 06eCrreqMBaeTCH 3a CqeT B3aMMHbIX
cBH3eM, M3MeHHIOIII;MX aMrrJIMTY,I:(Y M <pa3Y B036y)1():(eHMH perneTKM. Bo Bcex paHee
rrpMBe.n:eHHbIX CJIyqaHx opTOrOHaJIbHOCTM, a TaIOKe COOTBeTCTB)'IOIII;MX paCqeTaX ,I:(e-
JIaJIOCb .n:orrYlI(eHMe 06 M30TporrHOCTM 3JIeMeHTOB perneTKI1. JIH 3TllX rMrrOTeTllqeC-
KI1X 3JIeMeHTOB HeKoTopoe y6bIBaHlle aMrrJIllTY,IIbI II COOTBeTCTBYlOmMe pacrrOJIO)Ke-
HMH JIyqeM C03,I:(aBaJIll opTOrOHaJIbHbIe JIyqM. Ho B <paKTMqeCKI1 rrpMMeHHeMbIX
perneTKax MCrrOJIb3)'IOTCH meJIll, ,I:(MrrOJIM, rreTJIM, rreqaTHbIe 3JIeMeHTbI M T.,I:(., KOr,I:(a
Tpe6)'IOTCH 3JIeMeHTbI HM3Koro YCMJIeHllH, HJIH pyrrOpbI, IIJIOCKHe CrrMpaJIH, KOHH-
qeCKMe CIIMpaJIH, JIOrOrrepMo.n:llqeCKHe YCTpOMCTBa II T ..n:., Kor.n;a He06xo.n:MMbI 3JIe-
MeHTbI C )'MepeHHbIM YCllJIeHlleM. HM Y O,I:(HOrO ll3 HllX llMrre,I:(aHCbI He rrpM6JIM)Ka-
IOTCH' K c06CTBeHHbIM M B3allMHbIM HMrre,n:aHcaM M30TporrHbIX 3JIeMeHTOB, r.n:e
Z = 120 sinc kd, H, CJIe.n:OBaTeJIbHO, OT perneTOK, B KOTOpbIX MCIIOJIb3)'IOTCH peaJIb-
Hble 3JIeMeHTbI. MTaK, B03HMKaeT Ba)I(HbIM Borrpoc: KaKOBO YXY,I:(rneHHe 60KOBbIX
JIerreCTKOB (B3aHMOBJIHHHHe JIyqeM) M3-3a HeopTOrOHaJIbHOC!H JIyqeM? OTBeT Ha TY
  
qaCTb Borrpoca, KOTopaH CBH3aHa C B3aHMHOM CBH3blO, B03,IIeHCTB)'IOmeM Ha pac-
rrpe.n:eJIeHMe perneTKI1, ,I:(aeTCH HIDKe.
B KaqeCTBe rrpHMepa 6yn;eT llCrrOJIb30BaHa .n:MrrOJIbHaH perneTKa, HO pe3YJIbTaTbI
,lLJIH meJIeBbIX aHTeHH aHaJIOrllqHbIe. ,lJ;llrrOJIbHaH perneTKa 6e3 3a3eMJIeHHOrO 3Kpa-
Ha 3KBllBaJIeHTHa meJIeBOM perneTKe B qaCTH ll3MeHeHllH K03<P<PMI.J;lleHTa OTpaxe-
HMH. Ha30BeM 3HaqeHllH HarrpIDKeHllH B036y)1():(eHMH V n , a pe3YJIbTllp)'IOlI(lle TOKH
In' OHM CBH3aHbI Me)l(,lIY C060M rrOCpe.n:CTBOM MaTpMUbI llMrre.n;aHCa:
[VJ = [1] [ZJ,
(10.48)
r.n:e 3JIeMeHT MaTpMU:bI j - B3allMHbIM MMrre.n:aHC Me)l()J;Y ;-M II j-M 3JIeMeHTaMll.
,lJ;MarpaMMa HarrpaBJIeHHOCTll m-ro JIyqa perneTKH BblpaxaeTCH KaK
N
Fm(S) = L In exp{Jlnkd(sinS - sinS m )]},
n=l
(10.49)
r.n:e d - rnar 3JIeMeHTOB perneTKH. TaKHM o6pa30M, YXY,I:(rneHlle 60KOBbIX JIerreCT-
KOB paCCqMTbIBaeTCH rryreM rrOMemeHllH JIyqa rro,I:( XeJIaeMbIM yrJIOM M BbIqllCJIeHIDI
,IIllarpaMMbI HarrpaBJIeHHOCTll. )J;JIH 3Toro BHaqaJIe pernaeTCH CJIO)I(HaH CllCTeMa
ypaBHeHMM, npl1 3TOM BeKTOp HarrpIDKeHllH B036y)1():(eHMH COn;epXllT KaK y6bIBaHlle
aMrrJIMTy.n:bI, TaK II <pa3llpoBaHlle ,[(JUI rr03MUllOHMpOBaHllH m- ro JIyqa. Pe3ynbTllPY-

lOlI(ee perneHMe - 3TO BeKTOp TOKa, KOTOpbIll llCrrOJIb3yeTcH B C)'MMe BbIrne ,[(JUI
paCqeTa BnO)KeHHOM ,I:(llarpaMMbI m-ro JIyqa. 3HaqeHllH B3al1MHOrO MMne,I:(aHCa pac-
CqMTbIBaIOTCH MCXO,I:(H ll3 TeopMll HYJIeBOrO rrOpH,I:(Ka KapTepa C IIOMOmbIO BepCHll,
c03.n:aHHoM ,lLJIH 3<p<peKTllBHoro paCqeTa [27]. KaK nOKa3aHO B pa3,I:(eJIe 3.1, nyqM
npM O.n:HOpO.n:HOM B036y)1():(eHI1ll I.J;eHTp)'IOTCH no,I:( yrJIaMM, BblpaxaeMbIMll KaK
. 2; - 1
sinS t = ; = 1,2,3, ..., N / 2.
2Nd / A
(10.50)
)J;nH O.n:HopO,I:(HOrO cnyqaH Bce In = 1. Hll3KHe 60KOBbIe nerreCTKH rronyqalOTcH
IIyreM I1crronb30BaHMH n -pacrrpe,n:eneHMH Teitrropa (CM. rJI. 3). 3TO BbICOK03<p<peK-
THBHoe pacrrpen;eneHlle oco6eHHO rrOn;XO.n:llT ,[(JUI MHoronyqeBblx aHTeHH. Bce lllla-
rpaMMbI HarrpaBJIeHHOCTll HOpMMpOBaHbI K e,I:(MHMI.J;e rrpM HOMllHaJIbHOM yrJIe JIyqa.

 rllll6a 10. MH020Jl)"te6ble aHmeHHbl
EbIJII1 BblnOJIHeHbI paCqeTbI ,lLJll[ nOJIYBOJIHOBbIX ,JJ;HnOJIen KaK naparr.rreJIbHOn,
TaK 11 KOJIJII1HeapHOn KOH<pl1rypaUl1n. CaMbln BbICOKl1n 6oKoBon JIeneCTOK Haxo-
,JJ;I1TCH PMOM C rJIaBHbIM JIyqOM, HO MO)l(eT 6bITb KaK C Ton, TaK 11 C ,JJ;pyron CTO-
pOHbI; ,JJ;l1arpaMMbI HanpaBJIeHHOCTI1 aCI1MMeTpl1qHbI. )];JIH onpe,JJ;eJIeHI1H JII06oro
3<p<peKTa pa3MelI(eHI1H JIyqen B npe,JJ;nl1CaHHbIX n0311UHHX (LU1H perneTKI1 C O,JJ;HO-
pO,JJ;HbIM B036y)K)]:eHl1eM) JIyql1 pacnOJIaraJIl1Cb B HanpaBJIeHI1HX, HOpMaJIbHOM K
paCKpbIBY AP, PMOM C HanpaBJIeHl1eM, HOpMaJIbHOM K paCKpbIBY aHTeHHbI, B
OJ OJ
Kpal1HeM IIOJIO)l(eHl111 OTHOCI1TeJIbHO HOpMaJIbHOrO 11 PMOM C Kpal1HI1M nOJIO)l(eHI1-
eM. ,[LITH 66JIbrnl1X paCCTOHHl1n Me)l()]y 3JIeMeHTaMI1 6y,JJ;yr B03HI1KaTb ,JJ;11<ppaKUI10H-
OJ OJ
HbIe JIeneCTKI1, HO BO Bcex CJIyqaHx Kpal1Hl111 JIyq SlBJIHeTCSI qaCTbIO nepBOHaqaJIb-
Horo Ha60pa JIyqen. )];JIH qeTbIpex JIyqen ypOBeHb 60KOBbIX JIeneCTKOB nOKa3aH B
Ta6JI. 10.9 LU1H napaJIJIeJIbHbIX ,JJ;l1nOJIbHbIX 3JIeMeHTOB.
Ta6JIHua 10.9. YpoBeHb 60KOBbIX JIeneCTKOB 8-3JIeMeHTHOH perneTKH napaJIJIeJIbHbIX
,I(MnOJIeW
d/l, YpoBeHb 60KOBbIX J1eneCTKOB (.n;6)
-
JIY'I 0,5 0,6 0,7 0,8 0,9 1,0
HanpaBJIeHMe, HOpMaJIbHOe pacKpbIBY aHTeHHbI -13 3 -13 3 -13 5 -15 0 -12 8 -11 5
, , , , , ,
P5I,I(OM c HarrpaBJIeHMeM, HOpMaJIbHbIM pac- -12,9 -12,9 -13 0 -13 2 -12 3 -10,9
, , ,
KPbIBY aHTeHHbI
P5I,I(OM C KpawHMM -104 -10 0 -9,8 -12 6 -12 7 -12,8
, , , ,
KpawHee -10 0 -9,4 -11 1 -12 7 -12 8 -12 8
, , , , ,
YpOBeHb 60KOBbIX JIeneCTKOB 113MeHHeTCH UI1KJIl1qeCKI1 B 3aBI1CI1MOCTI1 OT rnara
3JIeMeHTOB, Me,JJ;JIeHHO YBeJIl1ql1BaHCb, a 3aTeM 6bICTpO nan;aH, TaKl1M )l(e o6pa30M,
KaK MeHHeTCH HanpaBJIeHHOCTb perneTKI1 B 3aBHCHMOCTH OT rnara perneTKI1. 3TO
HeY,JJ;HBI1TeJIbHO, nOCKOJIbKY o6a 3<p<peKTa BbI3bIBaIOTCH B3aHMHbIMH CBH3HMH. no
Mepe H3MeHeHHH nOJIO)l(eHI1S1 .rryqa nepeJIOMHaSl TOqKa YPOBHH 60KOBbIX JIeneCTKOB
nepeMelI(aeTCH K MeHbrneMY 3HaqeHHIO djA, H, KaK MO)l(HO O)KJf):(aTb, 3<p<peKTHB-
HOCTb KpanHHx JIyqeH YXYllrnaeTcH. KaKaH-JIH60 cyru:ecTBeHHa5I pa3HHua B 3<p<peK-
THBHOCTH npH nepeMelI(eHHH .rryqa no npe,JJ;nHcaHHbIM n0311UI1HM oTcyrcTByeT; no
OJ
BceH BI1,[(HMOCTH, nOJIYBOJIHOBbIe ,JJ;HnOJII1 ,JJ;OCTaTOqHO OTJIHqalOTCSI OT aHTeHH C MH-
HHMaJIbHbIM pacceHBaHHeM LU1H Toro, QTo6bI npeo,JJ;OJIeBaTb JII06ble 3<p<peKTbI nOJIO-
)l(eHHH JIyqa. B Ta6JI. 10.10 npHBOllHTCH pe3YJIbTaTbI llJI5I KOJIJIHHeapHbIX .n;HnOJIeH,
HO TOJIbKO LU1H ueHTpaJIbHOrO JIyqa H Hap)')KHoro JIyqa. KpoMe 3HaqHTeJIbHbIX 3<p-
<peKTOB CBH311 npH nOJIYBOJIHOBOM HHTepBaJIe .n;JISI KpanHero JIyqa KOJIJIHHeapHble
perneTKI1 06Hap)')Kl1BalOT MeHbrne KOJIe6aHHH ypOBHH 6oKoBoro JIeneCTKa B 3aBHCH-
MOCTH OT I1HTepBaJIa 11 OT JIyqa K JIyqy. ,lJ,JIH KOJIJII1HeapHbIX perneTOK Bce YPOBHI1
60KOBbIX JIeneCTKOB npI1BO,JJ;HTCH OTHOCI1TeJIbHO nl1Ka 3Toro JIyqa. B 3TI1X paCqeTaX
6bIJIH HCnOJIb30BaHbI 8 3JIeMeHTOB, nOCKOJIbKY 3TO qaCTO I1CnOJIb3yeMbIn pa3Mep
....
MHoro.rryqeBOH perneTKI1.
B Ta6JI. 10.11 .n;aIOTCSI YPOBHI1 60KOBbIX JIeneCTKOB llJIH perneTOK H3 16 napan-
JIeJIbHbIX .n;HnOJIen. EbIJIO paCCqHTaHO TOJIbKO KpaHHee nOJIO)l(eHHe .rryqa, TaK KaK

10.4. Opmo2oHllIlbHocmb JI)"teu 
Ta6J1Hua 10.10. YpoBeHb 60KOBbIX JIerreCTKOB 8-3JIeMeHTHoH perneTKH KOJIJIHHeap-
v
. HhIX ,D;HrrOJIeH
..;. -
dji., YpoBeHb OOKOBhIX JleneCTKOB (.nB)
JIyq 0,5 0,6 0,7 0,8 0,9 1,0
UeHTPaJIbHbIH -12 8 -12,9 -12,8 -12,9 -13 0 -13 1
, , ,
KpaHHHH -17 5 -13 7 -124 -124 -12 5 -126
, , , , , ,
Ta6J1Hua 10.11. YpoBeHb 60KOBbIX JIerreCTKOB 16-3JIeMeHTHoH perneTKH napaJIJIeJIb-
HbIX ,D;HrrOJIeH
dj)., YpoBeHb 6oKOBhIX JleneCTKOB (.n;B)
JIyq 0,5 0,6 0,7 0,8 0,9 1,0
KpaHHHH -10 8 -11,6 -13 1 -13 1 -13 1 -13 2
, , , , ,
3TO rrpe,L{CTaBJIHeT C060H HaHXYJJ;IIIHH cnyqaH. 3aMeTbTe, qTO ,L{JlSl 60nee KpyrrHbIX
perneToK Kone6aHHe HeCKonbKO MeHbIIIe, qeM MOXHO 6bIJIO OXH,IJ;aTb; L(.JUI 32-3JIe-
MeHTHbIX perneToK peaJIH30BaHHbIe 6oKoBbIe JIerreCTKH OqeHb 6nH3KH K rrpOeKTHbIM
3HaqeHH5IM.
OXH,lIaJIOCb, QTO BbICOKlfe 6oKoBbIe nerreCTKH O,n:HOpO,n:HO B036y)I()IaeMbIX perne-
TOK 6yJJYT B MeHbrneH CTerreHM rro,n;BepraTbcH B03,n;eHcTBMIO, B TO BpeMH KaK perneT-
KIf C HH3K1fMH 60KOBbIMM JIerreCTKaMM HaXO,lI;5ITC5I rro,n: Cepbe3HbIM B03,n;eHCTBMeM.
IIpH paCqeTe perneTOK C HM3KHM YPOBHeM 60KOBbIX JIerreCTKOB MCrrOJIb30BaJIOCb
n -paCrrpel1eJleHMe TeHJlOpa. 3HaqeHMe n L(.JUI Ka)l(,l{OH BeJlMqMHbI YPOBH5I 60KOBOrO
JlerreCTKa BbI6MparrOCb KaK CaMOe 60JlbmOe 3HaqeHMe, ,n;aBmee MOHOTOHHOe pacrrpe-
,n;eJleHMe. B Ta6J1. 10.12 rrOKa3aH ypOBeHb 60KOBbIX nerreCTKOB ,lUI.H pemeTOK Teitrro-
pa, I1MelOlI{HX OTHOIIIeHl1e 6oKoBoro JlerreCTKa SLR = 25 ,n;E rrpM n = 5. IIJlome pe-
3YJlbTaTbI ,lUI5I 8-3J1eMeHTHoH pemeTKH B HarrpaBJIeHMM, rreprreH,IJ;MK)'lliIpHOM
paCKpbIBY, BbI3BaHbI BbI6opKOH pacrrpe,n;eneHIDI Teitrropa, He COOTBeTCTByrom:eH
TOMY, qTO ,n;orrYCKaeT 8-3J1eMeHTHa5I pemeTKa (npM TaKOM MarrOM N cne,n:OBaJIO MC-
rrOJlb30BaTb n -pacrrpe,n:eJleHMe BIDIJIbHeBa, a He Teitrropa (CM. rJl. 3».
Ta6J1Hua 10.12. YpoBeHb 60KOBbIX JIerreCTKOB perneTKH rrapaJIJIeJIbHbIX .n:HrrOJIeH,
SLR = 25 .n:E
YpoBHH 60KOBbIX JleneCTKOB (.n;B)
JIyq dj). = 0,5 djl =1,0
N=8 N=8
HarrpaBJIeHHe, HOpMaJIbHOe pacKpbIBY aHTeHHbI -240 -202
, ,
KpaHHee -20,3 -22 7
,
N= 16
HarrpaBJIeHHe, HOpMaJIbHOe paCKpbIBY aHTeHHbI -25 1
,
KpaHHee -21 1
,

 Dla6a 10. MHo2oAy'te6ble aHmeHHbl
MOXHO oTMeTHTb, qTO ypoBeHb 6oKoBoro JIeneCTKa ,16'3JIeMeHTHoH pellIeTKM
5IBlliIeTC5I y,n;oBJIeTBOpMTeJIbHbIM B HanpaBJIeHHH, HOPMaJIbHt?¥ pacKpbIBY AP. KaK
O)l(H,[(aJIOCb, HMeeT MeCTO YXY,luneHHe YPOBH5I 60KOBbIX JIeneCTKOB npM 60JIbllIHX yr-
JIax JIyqa. 3TO yxy,n;llIeHMe MO)J(HO )'MeHbllIHTb nocpe,acTBoM cOrJIaCOBaHH5I HMne-
,n:aHca 3JIeMeHTOB npM npoMe)I()'TOqHOM yrJIe TaK, QTo6bI JIyq HanpaBJIeHH5I, HOp-
MaJIbHOrO pacKpbIBY aHTeHHbI, M KpaMHMH JIyq 6bIJIM o,n;MHaKOBO paCCOrJIaCOBaHbl.
113 3THX paCqeTOB MOXHO C,n;eJIaTb ,n;Ba BbIBO,n;a. Bo- nepBbIX, MaJIbIe pellIeTKH He3<p-
<peKTHBHO <pOpMHpyroT ,n;HarpaMMbI HanpaBJIeHHOCTM C HH3KHMM 60KOBbIMH JIene-"
CTKaMM; 32 3JIeMeHTa 6JIM3KO npM6JIMXalOTC5I K 3<p<peKTMBHoMY HenpepbIBHOMY
pacnpe,n;eJIeHHIO, B TO BpeM5I KaK 16 3JIeMeHTOB - 3TO OTHOCHTeJIbHO XOpOllIa5I an-
npOKCHMaUH5I. BO-BTOpbIX, ypOBHI1 60KOBbIX JIeneCTKOB 6y,n:yr yxy,n;IIIaTbC5I B Kpai1-
HHX nOJIOXeHH5IX JIyqa, n03TOMY pellIeTKa ,n;OJDKHa npe,aYCMaTpHBaTb npoeKTHYIO
H36bITOqHOCTb, TO eCTb npOeKTHbIM K03<P<PHUHeHT SLR ,n;OJI)I(eH 6bITb 60JIblIIe
OJ
O)l(H,[(aeMOH BeJIHqI1HhI.
Yxy,arneHHe ypOBH5I 60KOBbIX JIeneCTKOB .LLJUI KpaMHHX JIyqei1: MO)l(eT 6bITb MC-
npaBJIeHO rryreM KOMneHcaUHH 3aBHCMMOCTH UMneOallCa CKallUpOeallUR. OT yrJIa CKa-
HHpOBaHM5I (CM. rJI. 7).
BbIpWKaeM npH3HaTeJlbHOCTb
<l>oTorpa<pHH ny6JIHK)'IOTC5I C pa3perneHM5I Ph.D William Kreutel, Ph.D Dave
Thomas, Ph.D J. J. Lee, Pat Valentino, H Ph.D A. Dion.
JIHTepaTYPa
1. Ajioka, J. S. and McFarland, J. L., «Beam-Forming Feeds», in Antenna Handbook: The-
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}[umepamypa 
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8 0 = 45° ,L(illI URJIHHJJ:pa .aHaMeTpOM 52,6"-, co.aep)l(aI.Qero 128 oceBblX IUeJIeH [85].
Pacnpe.aeJIeHHe COOTBeTcTByeT .aHarpaMMe qe6bIllieBa C YEJI -50.aE, n03TOMY TO-
JIbKO <popMa rnaBHoro .rryqa nOKa3aHa Ha rpa<pHKe (Bce 6oKoBbIe JIeneCTKH paB-
HbI -50 .aE ,lLJIR 8 = 8 0 ). EOJIbllIOe paCllIHpeHHe JIyqa (3a npe.aenbI K03<P<PHUHeHTa
(cos 8 0 )-1) H nOTepR YCRJIeHHR ,lLJIR 8 ;#:. 8 0 BbI3BaHbI OTKJIOHeHHeM cpa3bI OT onTHM-
MaJIbHOH, paBHoH -jk cos 8 0 cos f3p). Ha pHC. 11.3 nOKa3aHbI yrJIOMeCTHble .aHa-
rpaMMbI no HanpaBJIeHHIO .rryqa ,lLJIR cp = 0 .lUIR a3HMyraJIbHOH .LJ:HarpaMMbI, onTHMH-
0
-- -5
r.Q
t:t:
'-"
..CI -10
E-<
u
0
::r:: -15
S
0
::E
0:: -20
ro
::r::
..CI -25
r:::
G.>
E-<
:s:
u -30
0
::r::
E-<
0 -35
-40
0 10 20 30 40 SO 60
cp (rpa,n;.)
PRC. 11.1. ,LJ;HarpaMMa KOJIbueBOH perneTKH .LUISI eo = 0 0
0
-s
--
r.Q -10
t:t:
'-"
..CI
E-<
U
 -15
S
0
::E -20
0::
ro
::r::
..CI -25
r:::
G.> 45°
E-<
:s:
U
0 -30
::r::
E-<
0
-35
-40
o
10
20
cp (rpa,a.)
30
4Q
PHC. 11.2. ,aHarpaMMa KOJIbueBOH perneTKH .LUISI eo = 45 0

b DlO6a 11. KOHrPoPMHble aHmeHHble peUlemKu
C
-2
-4
--

t::1 -6
--
e.. 45"/
8.: 60 0
8.;- Oi:l
..CI
E-<
g -8
:::c
3"
o -10

0:::
C'j -12
:::c
..CI
r:::
 -1.
::s:
u
 -16
E-<
o
-18
7
8. = 30°
-20
o
10
20
30 «).
cp (rpa,n:.)
50
60
PHC. 11.3. YrJIOMeCTHbIe .lUiarpaMMbI KOJIbueBOH peweTKH MR a3HMYTaJIbHOH
.lUiarpaMMbI, OTITHMH3HpoBaHHoH IIPH pa3JIH1JHbIX eo
311pOBaHHOll npM pa3JII1qHbIX 8 0 ,' OHI1 CpaBHI1BalOTCR C yrJIOMeCTHoll ,aMarpaMMoH
3JIeMeHTa. ,[{JIH JIMHeHHOH perneTKI1 Bce Kpl1BbIe COOTBeTCTBOBaJIl1 6bI yrJIOMeCTHoH
.nl1arpaMMe 3JIeMeHTa. ,L(JIH KOJIbueBOH perneTKI1 OHI1 COOTBeTCTBYIOT yrJIOMeCTHoH
.LIl1arpaMMe 3JIeMeHTa TOJIbKO npl1 8 0 , f):(e Bce 3JIeMeHTbI CKJIa,abIBaIOTCH no <pa3e 11
06pa3YlOT JIyq. 1lII1pMHa nOJIOCbI 3THX perneTOK, COCTOHIUI1X 113 1130TpOTIHbIX 3JIe-
MeHTOB, OrpaHI1QeHa H3MeHeHHRMI1 K03<P<PI1Ul1eHTa EeCCeJIR; 113MeHeHMe <pa3bI Ha
n/8 .naeT rnHpHHY nOJIOCbI, paBHYIO IDI32A [31], r,ae D - ,al1aMeTp KOJIbua. O.LIHaKO
I1CnOJIb30BaHHe HanpaBJIeHHbIX 3JIeMeHTOB 3HaQl1TeJIbHO YBeJIHQI1BaeT 1lII1pHHY no-
JIOCbI nponYCKaHHR [97].
11.2.2. AMcKpeTHaH Konbu.eBaH peweTKa
HenpepbIBHoe pacnpe,aeJIeHl1e annpOKcl1Ml1pyeTcR M 3JIeMeHTaMI1, pacnOJIOXeH-
HbIMH B TOQKaX
21t(p + f)
J3 p = p = 0, 1, 2, . . ., M - 1,
M
( 11.9)
f.LIe f - ,aP06b, )'Ka3bIBalOmaR nOJIOXeHl1e JIyqa OTHOCI1TeJIbHO nepBoro 3JIeMeHTa.
MO)l(HO .nOKa3aTb [47], QTO
N 1 { 00 }
£(<p,8) = M!;o;;/:o Fn (8)cos n<p + FrM-n(8)COS[(rM -n)<p -2wf] . (11.10)
YpaBHeHl1e (11.10) - 3TO )l(eJIaeMaR .nl1arpaMMa n.rrIOC CJIaraeMOe OIIIH6KI1. ):LITH
HHTepBaJIa s = 2npjm, paBHoro MeHee nOJIOBHHe ,lUII1HbI BOJIHbI, 3Haql1MbIM HBMeT-
CH TOJIbKO QJIeH r = O. ,L(JIH HHTepBaJIa < 1 WIHHbI BOJIHbI BKJIa,a BHOCHTCR TOJIbKO

-

-
11.2. KOAbl{e6ble peUJemKU \,
npH r = 0 H r = 1 H T.J].. OCHOBHOH BKJIa,I( cnaraeMoro ollII16KH B J].l1arpaMMY - 3TO
BKJIa,n: B rnaBHbIR JIeneCTOK.
Y.n:06HbIM cnoco60M Ol(eHKH H3MeHeHI1JI rJIaBHOrO JIeneCTKa HBJUleTCH npen.-
CTaBJIeHl1e 1ffieHOB B ypaBHeHHI1 (11.9) nocpe,n;CTBOM HHTerpanOB If Ol(eHKa C nOMO-
ll(blO MeTo,n;a CTal(HOHapHoR <pa3bI [11]. PaHHHH annpOKCHMal(HH 6bIJIa .n:aHa B
[129]. ,lJ;l1arpaMMa .L(JIH .n:yrOBOR pellIeTKH, COCTOHll(eH H3 2P + 1 aKTI1BHbIX 3JIeMeH-
TOB, I1MeeT CJIe.n:yIOIIII1R BI1.a:
p
E(cp,8) = L I pG(cp - 13, 8).
p=-P
(11.11)
3TO MO)l(eT 6bITb 3anHcaHO KaK pH,L( I1HTerpanOB B COOTBeTCTBI1H C cPOPMYJIOR
CYMMl1pOBaHI1H llyaccoHa:
,
00 p
E(cp, 8) = L L l (J3 p )G(cp -13, 8) exp(j21t1p)dp.
r=-oo
(11.12)
B pe3YJIbTaTe 113MeHeHHH nepeMeHHoH [3 = 2npiM HMeeM
E(cp,8) = M L f I (J3)G(cp -13,8) exp(jMrI3)dl3,
2n r
E(cp,8) = M L E r f I (J3)G(cp -13,8) cos(MrI3)dl3,
2n r
(11.13)
(11.14)
r.n:e 2[3(P) - 3TO aKTI1BHbIR cerMeHT KOJIbl(a, M - qHCJIO 3JIeMeHTOB Ha nOJIHOM
KOJIbl(e 11 1([3) - 3TO HenpepbIBHoe npe,L(CTaBJIeHHe pacnpe.n:eJIeHMH I([3p).
,lJ;anee no.n:cTaHoBKoH (11.10) M (11.6) B (11.12) H nOJIaraH [3(P) = n, nOJIyqaeM,
tITO r-H qJIeH (11.12) l1.aeHTHQeH r-MY qJIeHY (11.10). qJIeH r = 0 - 3TO npOCTO .n:Ha-
rpaMMa .LU1JI HenpepbIBHoro pacnpe.n:eJIeHHH 1([3), a 60JIee BbICOKHe qJIeHbI - 3TO
norpelliHOCTb, BBOJ].HMaH l(OnYI.l.(eHHeM [3 = 2n(p+j)/ M.
MeTO,l1 cTaUHoHapHoR <l>a3bI MO)l(eT npl1MeHHTbCH .L(JIH npH6JIH3HTeJIbHOH Ol(eH-
KH HHTerpanOB B (11.12) - B qaCTHOCTH, .L(JIH onpe.n:eJIeHHH BKJIa,n:a B .n:H<ppaKl(HOH-
HbIR JIeneCTOK. 113 (11.32) H (11.36) CJIe.n:yeT npe.n:CTaBJIeHHe .L(JIH r-ro HHTerpana
(11.12):
f3(p)
I r (cp, 8) = f I I <J3)H G(cp - 13, 8)1 expUkpJ3u)dJ3,
-f3(p)
( 11.15)
r.n:e
u<J3) = cos8cos(cp -(3) -cos8 0 cosJ3 + rf3
s
( 11.16)
11 S = kp/M - 3TO Me)l(3JIeMeHTHbIR I1HTepBaJI.
I1HTerpan Ol(eHHBaeTCH HCXO,l1H H3 ,l10nym;eHHH, qTO HaH60JIbllIHR BKJIa,n: HCXO-
J].HT 113 OKpeCTHOCTH TOqKH (TOqeK) [30' r,l1e qJIeH <l>a3bI u([3) HBJIHeTCH rrOCTOHHHOH
BeJIHqHHOR. 3TO .n:orrym;eHHe .rryqIIIe Bcero rrpHMeHHMO .L(JIH 60JIbllIerO kp. YCJIOBHe
.L(JIH (30 Terrepb rrpe.n:CTaBJIHeT C060H U' «(3) = 0 MJIH
cos8 sin(cp - (3) + cos8 0 sinJ3 + r = O.
s
( 11.17)

b FJla6a 11. KOH(jJopMHble aHmeHHble pelUemKu
B 06JIaCTIf (30' nOCKOJIbK)' u'«(30) = 0,
u(j3) :=:; u(j3 0) + l(p - P 0)2 U" (p 0).
2
(11.18)
,L(a.rree, eCJIIf (30 HaXO.nHTCR BHyrpH .nHana30Ha OT -(3(P) ,no (3(P), npe.neJIbI MOryr
6bITb paClIIHpeHbI ,no -00 If 00. HaKOHeIJ;, nOJIaraR /«(3) If G(<p - (3, 8) nOCTORHHbIMH
B 06JIaCTH, 6JIH3KOM K (30' nOJIyqaeM HHTerpa.rr B 3aMKHyTOM BH.ae:
I r (<p, e) -U <J3)ij G(<p - /3, e)1 kpj :'<J3 0)1
(11.19)
npl1
u" (p 0) = -Cose COS(<p - P) + Cose o cosl3.
(11.20)
,L(JI npOCTOTbI paCCMOTpHM CJIyqaH 8 = 8 0 , Tenepb u"«(3o) = 0 ,LVI <Po = 2 13 0 ,
QTO ):(aeT MaKCI1MYM (11.16), cooTBeTcTBYJOllU'[H ):(H<ppaKIJ;HOHHOMY JIeneCTK)' (,L(JI).
IloJIo)l(eHl1e ,lJ.JI Tenepb BbIpaxaeTcR (11.14) M onpe,neJIeTC BbIpa)l(eHl1eM
. <Po r e
Sln- = --cos 0
2 2s '
(11.21)
r):(e 3Hat.JeHl1e r = 0 ,llaeT rJIaBHbIM nyq rrpH q>o = 0, B TO BpeM KaK nOJIO)l(l1TeJIbHbIe
11 OTpMIJ;aTeJIbHbIe r ,nalOT )];JI npH nOJIO)l(lfTeJIbHOM 11 OTpHIJ;aTeJIbHOM yrJIax <Po npl1
YCJIOBMM
r
-Cose < 1.
2s
(11.22)
O,nHaKO (11.16) He BJIReTCR ,neHCTBHTeJIbHbIM npe,nCTaBJIeHMeM HHTerpa.rra rrpH
u'(J3 o ) = u"«(3o) = 0, nOCKonbK)' (11.15) .n;onXHO 6bITb 3aMeHeHO Ha
. u(P) = u(J3 0) + !. (J3 -13 0)3 u'" (J3 0)' (11.23)
6
OueHHBa HHTerpa.rr, nOJIyqeHHbIM TaKHM o6pa30M npH <Po = 2(30' HMeeM
1 I. e ) -.J lIP.. ) I GI. _ A e ) . ( 6 ) 1/3 r(1 / 3)expUkpp ou)
n \<P, I 'P 0 \<P 0 ,... 0, 0 kpl um(p 0)1 .J3
I I r (<po,eo)1 = { <P 2 0 )o( <P 2 0 ,eo) r 3) e f3 ec:e o )1/3
( 11.24 )
YpaBHeHl1e (11.20) no.n;nan;aeT no.n; orpaHH'IeHHR, 'ITO /(13) H G(<p - 13, 8) BJI-
IOTC Me,LVIeHHO H3MeHRIOI.UHMHCR BeJIHt.JHHaMH, nOCKOJIbK)' kp - 60JIblIIaR BeJIH-
'IHHa, a (30 He RBJIReTCR 6JIH3KOM K HYJIIO, HO Haxo,nHTCR BHyrpH ,nHarra30Ha OT -(3(P)
lIO +J3(P). QTo6bI BbIQI1CJIHTb BeJIH'IHHY M no cpaBHeHHIO C rJIaBHbIM nyqOM, cpaB-
HHM J].JI, paCC'IHTaHHbIM 113 (11.20), C rJIaBHbIM .rryqOM, paCC'IHTaHHbIM H3
J3(p)
10 = J I /(J3)H G(J3, e)1 dl3. (11.25)
-J3(p)
Ha pHC. 11.4 nOKa3aHa BeJIH'IHHa M OTHOCHTeJIbHO rJIaBHOrO KaK <PYHKUHR
HHTepBa.rra (s cos 8 0 ) ,LVIR pa3JIHQHbIX pacnpe.n;eJIeHHM aMnJIHT)',nbI cos n npH p = 26A
,-=-.

11.2. KO/lb/.{e8ble peUlemKU t
-8
-10
-12
-1
..............
 -'4

E-o
u-
o -18
t:::t:::f
0-
r::;: -20
e
or::;:
Xo -22
x cos 2
00
:s:x -24
::fCQ

r::;: -26
p.
-9
:s:::r:
t:::f:s: -28
::re
x::S::
:s::r::;: -30 cos 4
::reo
:s::
r::;: -32
0
CQ
-"
-36
-38
-.to
0.5
CTal.UfOHapHaH <t>a3a
- - PaCCqHTaHHOe 3HaqeHHe
0.6 0.1 0..8 0.9
I1HTepBaJI (B ,WIHHaX BOJIHbI)
I.G
PUC. 11.4. BeJIl1ql1Ha )J.11<ppaKUI10HHOrO JIeneCTKa KaK <PYHKIU1H I1HTepBaJIa
H G(<p - (3, 0 0 ) = cos (<p - (3) [84]. YpaBHeHHe (3(P) = n/2 6bIJIO HCnOJIb30BaHO .lUI
Toro, QT06bI 06eCneQl1Tb YCJIOBl1e 0 < (30 < (3(P). ,l],JI5I cpaBHeHI15I <l>aKTI1QeCKl1e ,n:l1a-
rpaMMbI 6bIJII1 paCCQI1TaHbI 113 (11.10). MaKCI1MaJIbHOe pa3JII1Ql1e Me)I(.QY <l>aKTI1Qe-
CKI1M ,lLJI 11 JIeneCTKOM, paCCQI1TaHHbIM 113 (11.20), COCTaBlliIeT 2 ,n:D. IloCKOJIbKY
annpOKCI1MaIJ:l1 (11.20) npe,n:CTaBJI5IeT C060H HaHxy,n:IIIHH CJIyqaH, C03,n:aeTC5I Bne-
QaTJIeHl1e, QTO 3TO nOJIe3HOe PYKOBO,n:CTBO M5I KOHTpOJll1pOBaHI1 ,n:I1<1>paKIJ:110HHO-
ro JIeneCTKa KaK <l>YHHH I1HTepBaJIa, pacnpe,n:eJleHI15I TOKa, ,n:l1arpaMMbI 3J1eMeH-
TOB, pa,n:l1yca H MI1HbI ,n:yrl1. IIoJIo)l(eHl1e ,il;JI (AJI5I r = -1 11 0 0 = 0), 06YCJIOBJleHHOe
(11.18), nOKa3aHO Ha pl1C. 11.5 B cpaBHeHHH C <l>aKTHQeCKHM nOJlO)l(eHHeM.
11.2.3. CMHa3Hoe B036y>KAeHMe nY'Ia
npMOH cnoco6 ,n:06I1TbC5I Y3Koro Jlyqa OT KOJlbIJ:eBOH peIIIeTKH 3aKJIIOQaeTC5I B
TOM, QT06bI c<l>a3l1poBaTb Bce 3JIeMeHTbI TaKHM 06pa30M, QTo6bI BKJIa,n: 3J1eMeHTOB
COBna,n:aJI B ,n:aJIbHeH 30He no <l>a3e npH yrJIe <Po. 3TO Ha3bIBaeTC5I CI1H<l>a3HbIM B03-
6y)K.LJ:eHHeM JIyqa H Tpe6yeT pacnpe,n:eJIeHI15I <l>a3bI no KOJIbIJ:Y pa,n:WYCOM ro, paBHoro
exp [-jkro cos (<p- <Po)].
(11.26)
,LI;HcKpeTHa5I pemeTKa BbInOJIHHeT ,n:HCKpeTHyro peaJIl13al.{HIO 3Toro HenpepbIB-
Horo pacnpe,n:eJIeHH5I <}>a3bI. ECJlI1 I1HTepBaJI 3JIeMeHTOB COCTaBJIeT nOJIOBI1HY )1)111-

b DlO6a 11. KOH£popMHble aHmeHHble peUiemKU
120
110
70
100
-. 90

p.
-=- 80
9-
CTaUMOHapHaR <l>a3a
60
50
0..5
PaCC1JMTaHHOe 3Ha1JeHMe
0.6
0,.7
0.8
0.9
'.0
I1HTepBaJI (B ,WIMHaX BOJIHbI)
Puc. 11.5. nOJIO)l(eHl1e fJIaBHOrO JIerreCTKa KaK YHKQI1 I1HTepBaJla
HbJ BOJIHbI 11JIM MeHbllIe, a qMCJIO 3JIeMeHTOB 60JIb1lIOe, TO ,L{MarpaMMa 6JIH3Ka K
,L{MarpaMMe HenpepbIBHoro KOJIbIJ;eBOrO HCTOqHHKa (11.1).
OpMMeHeHMe a3HMYTaJIbHoti MO,L{aJlbHOH TeopMM K KOJIbIJ;eBbIM pellIeTKaM 6bIJIO
BnepBbIe npe,L{JIO)l(eHO B [121] H pa3BHTO B [30]. B npMHIJ;Mne, <pa30Boe M aMnJIH-
TY,L{HOe pacnpel(eJIeHHe BOKpyr KOJIbII.eBOH pellIeTKH MO)l(eT 6bITb BbIpa)l(eHO PR.aOM
a311MyraJIbHbIX MOl(, r,ne ,nHCKpeTHoe npe06pa30BaHHe <l>ypbe Ka)l()::{oti MO,nbI ,naeT
,L{HarpaMMY MO,L{bI (KapTHHY nOJIH MO,L{bI). MO)l(HO TalOKe nOJIyql1Tb c06CTBeHHbIH M
B3aHMHbIe HMne,L{aHCbI ,lLJIH Ka)I()J:OH MO,L{bI [119]. 3TH MO,nbI n03BOJIHIOT BbInOJIHHTb
CHHTe3 Tpe6yeMoH ,L{HarpaMMbI, a TalOKe onpe,neJIHTb HMne,L{aHCbI, HanpaBJIeHHOCTb
H T.n.
OYCTb B036}')1<.aeHMe m-ti MO,L{bI Ha KOJIbIJ;eBOH perneTKe ,nHaMeTpa D paBHO
N
gm (13) = LAn expUkdmcos(3), (11.27)
n=l
f,L{e d = 2nD/ N, a (3 - a3HMyraJIbHbIH yrOJI KOJIbII.eBOH perneTKH. ,[(HarpaMMa TaKOH
MO,L{bI BbIpa)l(aeTCH ,QHCKpeTHbIM npe06pa30BaHHeM <l>YPbe:
1m (cp) = J o ( 2kro sin  }o[kr o (1- cos8)], (11.28)
r,L{e nepBaH <PYHKII.HH EeCCeJIH ,L{aeT a3HMyraJIbHyro ,QHarpaMMY, a BTopaH 06eCneqH-
BaeT yrJIOMeCTHyro ,L{HarpaMMY HanpaBJIeHHOCTH. ,LJ;HarpaMMa /0 06eCneQHBaeT BbI-
COKHH ypOBeHb 60KOBoro JIeneCTKa, paBHbIH 7,9 ,nE, II Me,L{JIeHHO YMeHbllIalOIIJ;YIOCR
OfH6alOIIJ;YIO 60KOBbIX JIeneCTKOB, KaK nOKa3aHO Ha pllC. 11.6. A6cIJ;lIcca - 3TO
YHHBepCaJIbHaH nepeMeHHaH, B ,L{aHHOM CJIyqae u = 2kro sin (<p/2).
OqeBH,nHo, qTO ,QJIH YMeHbllIeHII5I YEJI 'rpe6yeTcH BbIKJIlOqeHHe 3aL{HHX 3JIeMeH-
TOB H B3BeIlIIIBaHMe aMnJIIITY,L{HOrO pacnpe,L{eJIeHHH 60KOBbIX 3JIeMeHTOB. TaKHM
06pa30M, BBO,QHTCH y6bIBaHHe aMnJIHTY,QbI C TeM, qT06bI B036}')1<.aeHlle 3JIeMeHTOB
npOHCXO,QI1JIO no,n yrJIOM < 180°, KaK npaBHJIO, 120°. ,L:LrrH CKaHHpOBaHHH JIyqa 3TO
u-==.. _
-

11.2. KOJ/bl(e8b1e pememKU d
o
-5
-..


-
(Ij
 -10
:s:
t=:
t::

-15
.
-20
o
2
4
6
8
10
12
14
16
18
u
PHC. 11.6. 3aBHcHMoCTb aMIIJIHTy,lJ;bI <PYHKIJ;HI1 EecceJul J o OT aprYMeHTa
y6bIBaHHe aMllJIHTY,[(bI (H cooTBeTcTBYIOIl(aSI <pa3a) ,[(OJDKHbI nepeMemaTbcSI no a311-
MYTY. MHorHe ,[(eCSlTRJIeTJUI Hcnonb3YIOTcSI perneTKI1 BynneHBe6epa (Wullenweber)
,[(JISI KOpOTKOBOJIHOBOrO neJIeHfaTOpa; KaK npaBHJIO, B036}')K.aalOmHe Ka6enH 3J1e-
u u u
MeHTOB nO,[(BO,[(SlTCSI K ueHTpaJIbHOH KOHTpOJIbHOI1 TOqKe, f,[(e BpamalOIUl1l1CSI rOHI1-
oMeTp 06eCneqHBaeT Hy)KHbIe <l>a3Y H aMTIJIHTY,[(Y [40]. DbIJIH nOCTpoeHbI 60JIbllll1e
AP BeJIJIeHBe6epa: aHTeHHa YHHBepcHTeTa rnTaTa I1JIJIHHOHC OXBaTbIBaeT ,[(l1ana30H
4-16 Mfu, H B HeH HCnOJIb3YIOTCSI 120 MOHononlOCHbIX 3neMeHTOB (40 O,[(HOBpe-
MeHHo) Ha KOJIbue ,[(HaMeTpOM 955 <l>yrOB [49]. IlocKonbKY KOJIbueBbIe perneTKI1,
KaK npaBRJIO, Hcnonb3yIOTCSI npH 60J1brnHX ,[(JIHHaX BOJIH C COOTBeTCTBYIOIUI1MH OT-
HOCHTeJIbHO Y3KHMH nOJIOCaMH nponYCKaHHSI, 06pa60TKa ,[(HCKpeTHbIM npe06pa30-
BaHHeM <l>ypbe HHOf,[(a MoxeT OC)'I.QeCTBJISlTbCSI UH<PPOBbIM 06pa30M ,[(JISI npHeMHbIX
perneTOK C nOMOIl(blO aHaJIOfOBO-IJ;H<PPOBbIX npe06pa30BaTeJIeti. 3JIeKTpOHHbIe
KOMMyraTopbI 6bIJIH onHcaHbI B [36, 80, 13, 63 ]. B KonbueBbIX AP ,[(JISI pa,Il110-
HaBl1raUHOHHoH CHCTeMbI 6JIIDKHerO .neHCTBI1S1 T AKAH TaIOKe Hcnonb3yIOTCSI
BpaIUalOIl(HeCSI pacnpe,[(eneHHSI [26]. TIpoTHBoBpaIUeHHe aHTeHHbI KOCMHqeCKO-
fO Kopa6nSl OIlHCbIBaeTCSI B [44]. A3HMyraJIbHOe aMIlJIHTY,[(Hoe y6bIBaHHe 6y,[(eT
HeCKonbKO YBeJIHqHBaTb llIHpl1HY JIyqa B TIJIOCKOCTH yrna MeCTa. B COBpeMeHHbIX
KonbueBbIX perneTKax 60JIee qaIl(e Hcnonb3yIOTC.H ,[(HarpaMMo06pa3yIOIl(l1e YCTPOH-
CTBa. IlpHMeHeHHe HanpaBJIeHHbIX 3JIeMeHTOB BMeCTO H30TponHbIX MoxeT YJIyq-
IIIHTb xapaKTepHCTHKH, eCJIH B036}')K.aeHHbIH a3HM)'TaJIbHbIH ceKTOp He CJIHllIKOM
60JIbllIOH. ,L(Jrn ceKTopa 90° MO:>KHO O)l(H,[(aTb HeKOTopoe ynyqIIIeHHe, O,[(HaKO ynyq-
IIIeHHe MeHbllIe ,lJ)IR ceKTopa 120°. OCHoBHoe YJIyqIIIeHHe OT HanpaBJIeHHbIX 3J1e-
MeHTOB COCTOHT B IlOTeHUHaJIbHOM }'MeHbIIIeHHH 3<p<peKTOB B3aHMHOH CBR3H.
BcnoMHHM H3 fJI. 10, qTO MaTpHua EaTJIepa peaJIH3yeT ,[(HCKpeTHoe npe06pa30-
BaHHe <l>YPbe OTHOCHTenbHO Bxo,[(a, n03TOMY JIOrHqHO, qTO MaTpHua EaTnepa MO-
xeT Hcnonb30BaTbCR C KOJIbueBOH perneTKoH ,[(JIH <pOpMHpoBaHHSI Y3Koro nyqa H

b Dla8a 11. KOllfjJopMllble allmellllble peUlemKU
ero BpaIl(eHMR. 3,1J,eCb MaTpMua EaTJIepa N x N no,ncoe,n;MHReTCR C nOMOIl(blO JIMHMH
paBHOH MMHbI K KOJIbueBOH perneTKe M3 N 3JIeMeHTOB; Ha pMC. 11.7 3TO nOKa3aHO
MR N = 16. KIDK,IJ;bIH nopT BaTJIepa 6y,neT B036yx,aaTb O.nHY a3MMyraJIbHyIO MO,ny,
n03TOMY cooTBeTCTByIOIl(MM BbI60p aMnJIMTY,n M <pa3 Ha nopTax 6y,n:eT CMHTe3Mpo-
BaTh HyxHyIO ,n:MarpaMMy C nOMOIl(blO TaKMX MO,n:. EIl(e O,1J,HO npeMMym:eCTBO 3a-
KJIlOqaeTCR B TOM, qTO ,1J,06aBJIeHMe nporpeCCMBHOH <pa3bI n<po K nopTaM, r,1J,e n = 0,
1, ..., N-l, 6y,n:eT npMBo,n:MTb K BpalI(eHMIO JIyqa ,no a3MMyraJIbHOrO yrJIa <Po [30, 31,
107, 108, 112]. ,[(onOJIHMTeJIbHOe npeMMym:eCTBO MaTpHUbI EaTJIepa KaK ,n:MarpaM-
Mo06pa30BaTeJIR KOJIbueBOH perneTKM 3aKJIIOqaeTCR B TOM, qTO B TO BpeMR KaK MO-
,n:aJIbHble B3aMMHble MMne,naHCbI OTJIMQaIOTCR, 3<p<peKTbI KIDK,IJ;OM MO,n:bI nORBJIRIOTCR
TOJIbKO Ha COOTBeTCTByIOIl(eM nopTY EaTJIepa, M, COOTBeTCTBeHHO, 3,n:eCb MoxeT
npOMCXO,1J,MTb HX KOMneHCaIJ;HR.
3JIeMeHTbI
pemeTKH
MaTpHua EaTJIepa 16 x 16
q> 2<p 3<p
16<p
PHC. 11.7. CKaHHpoBaHHe nyqa no a3HMyry
,[(yroBble AP, r.ne H3JIyqalOIUHe 3JIeMeHTbI RBJIRIOTCR <pMKcMpoBaHHbIMH, TaIOKe
06JI3)la1OT 60JIee BbICOKMM YPoBHeM orH6alOIUeM 60KOBbIX JIeneCTKOB npM IlIHpOKMX
yrJIax. Ha pHC. 11.8 nOKa3aHa nOJIHaR ,n:HarpaMMa ,n:yrOBOH perneTKM, OXBaTbIBalO-
lI(aH yrOJI, paBHbIH 63°, C PMHYCOM 12,7A H yrJIOM CKaHHpOBaHMH 15°. 06paTMM
BHHMaHMe Ha TO, qTO ypOBeHb 60KOBoro JIeneCTKa MH 60JIbrnHX 3HaqeHMH yrJIOB
COCTaBJUIeT npM6JIH3HTeJIbHO -30 ,n:n.
..........
.......

11.2. KOllbll,e6ble peUlemKU d
o
- -10

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-50
-60 . J
-90 -80 -70 -60 -SO -'f0 -30 -20 -10 0 10 20 30 1.iO SO 60 70 80 90
A3HMYTaJIbHbIH yrOJI (rpa,a.)
PHC. 11.8. ,[(HarpaMMa ,nyroBoH perneTKH
Kor.n;a MHTepBaJI Me)l(,[(Y 3neMeHTaMM perynHpyeTcR MSI Toro, QTo6bI .u06MTbCSI
paBHoro llIara 3neMeHTOB npoeU;HpyeMoH BHPTYaJIbHOH pellIeTKM, 6oKoBbIe nene-
CTKM npM -90 0 COCTaBJIRIOT TOJIbKO -20 .n;E, (KaK rrOKa3aHO Ha pMC. 11.9) [47].
3TO BbI3bIBaeTCSI aCHMMeTpMSlMM <l>a3bI, KOTopbIe nOSlBJISlIOTCSI Ha CKaHMpYIO:w:eM
JIyqe; MX MO)l(HO YMeHbllIHTb 3a CqeT <l>opMHpoBaHHSI COQeTaHMSI .n;onOJIHI1TeJIbHOH
u u
pa3HOCTH0l1 .n;HarpaMMbI HanpaBJIeHHOCTl111 H CYMMapHOI1 .n;l1arpaMMbI HanpaBJIeH-
HOCT" [1].
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A3HMYTaJIbHbIH yrOJI (rpa,a.)
PHC. 11.9. ,[(HarpaMMa ,nyroBoH pemeTKM c paBHbIM npoeU;HpyeMbIM HHTepBaJIOM

r
 DW6a 11. KOHrpOpMHble aHmeHHble peUlemKu
11.3. AHTeHHble peweTKM
Ha u.MnMHAPM"IeCKOM nOBepxHocTM
.
B .naHHOM pa3.nene paCCMaTpMBaIOTC5I AP Ha l.(MnMH,L(pI1QeCKO:M: nOBepXHOCTM, 3ne-
....
MeHTbl KOTOpblX pacnOnO)l(eHbl no BceM ,L(nMHe OKp)')KHOCTI1 11 no OCM Ha paCCT05l-
HI1I1 L. 3.aeCb npl1MeHI1M MO.aaJIbHbl:M: aHaJII13 pa3,L(ena 11.3.3.1, a TaIOKe I1CnOnb-
30BaHMe .nl1arpaMMo06pa3YIOI..I.(Mx YCTpO:M:CTB C MaTpMl(e:M: EaTnepa. O.aHaKo
CYI..I.(eCTByeT HeCKonbKO CYI..I.(eCTBeHHbIX pa3nl1qH:M:. OCeBO:M: pa3Mep pellIeTKM n03BO-
n5leT nonyqaTb KOHTponb HaLI: yrJIOMeCTHO:M: .nMarpaMMO:M:, a TaIOKe 60nee BbICOK)'JO
HanpaBneHHOCTb. 113-3a MeTaJIJIl1qeCKOrO Ul1nHH.npa .nHarpaMMbl 3neMeHTOB 51BJI5I-
IOTC5I 60nee np5lMb1MH. 3HaqMTenbHa51 Tpy.nHOCTb B03HMKaeT npM paCqeTe B3aMM-
HbIX HMne.naHCOB. B KOnbl(eBO:M: pellleTKe Mcnonb3YIOTC5I npOCTble MeTo.nbI, TaKMe
KaK no.nxo.n. KapTepa, paCCMaTpl1BaeMbI:M: B rn. 7. O.nHaKo npM HaJIl1qMM M30rHYTblX
....
MeTaJInMqeCKMX nOBepXHOCTeM Bblpa)l(eHM5I B3aHMHoro MMne.naHca C03.na1OT TPY.n-
HOpaCCqHTblBaeMble HHTerpaJIbI. BHaqaJIe paCCMaTpMBaeTC5I BJIH5IHHe M30rHyroM
nOBepXHOCTM Ha .nHarpaMMY 3neMeHTOB.
11.3. 1. AMarpaMMbl w,eneBblX 3neMeHTOB
rpaHWlHa5I 3Maqa HeHIDI I..I.(eJIe:M: (c CHHYCOaJIbHbIM pacnpe.n.eneHHeM) Ha Kpyr-
JIOM MeTaJIJ1W1eCKOM IJ.lUIHH.LI:pe 6blJIa peIlleHa HeCKOJIbKO .neC5ITl1JIeTM:M: TOM)' Ha3a,IJ. [23,
48, 70]. PellIeHMe npe.nCTaBJI5IeT C060M rapMOHMqeCKMM PM UHJIHH.LI:pHqeCKHX <PYHK-
QMM, cOOTBeTCTBYJOIUHX <PYHKIJ.I151M Eeccen51 M XaHKen5l. KOHeqHa51 llIMpMHa rueJIM
OKa3bIBaeT He60JIbllIOe B03.n.eMcTBMe Ha ,L(HarpaMMbl, HO, eCJIM He06xo.aMMO, MO)I(HO
BKJllOqMTb COOTBeTCTBYIOIlJJ1:M: K03<PcPl1l(HeHT [27]. npl1 HanpIDKeHI1M rueJIH V H PaII.HY-
ce l(HJIHH.npa a none ,lI)UI oceBOM (npo.nOJIbHOM) nOJIYBOnHOBOM I..I.(enl1 [128] Eo = 0 M
V Co c {! n cose J
E = \ 2 L Emjmcosmcp . (11.29)
cp 2n 2 ka sin 2 e m=O H (ka sine)
3Ta .nMarpaMMa npe.nCTaBn5leT C060H ,L(l1arpaMMY nOJIYBOJIHOBOrO .n.HnOJI5I, MO-
,L(11<pMUHpoBaHHoro CYMMHpOBaHHeM. )];JI5I nOnepeqHOM nOJIyBOJIHOBO:M: TOHKOM
rueJIM non51 CJIe.n.YIOI..I.(l1e:
E - 2kaV LEmjm+lcosmcpcos(m1t/2ka)
9 - 1t 2 sin8cos8 m=O (k2a2 -m 2 )H m (kasin8) , (11.30)
E = 2V cos8 f. mjm+1 sinmcp cos(m1t /2ka) .
<P n2 sin2 e m=O (k 2 a 2 -m2)H(kasine)
(11.31)
CXO,L(HMOCTb 3TI1X PMOB KOHTponHpyeTc5I BbI60pOM ka. Me)I(,QY ka H 2ka, KaK
npaBHJIO, T}Je6yeTc5I aKKYPaTHO .n.onOJIH5ITb cnaraeMble. bOJIbllIHe 1(I1JIHHJI.pbI, TaKMM
o6pa30M, 'rpe6YJOT MHoro CJIaraeMbIX, HO npH HaJIHqHI1 KOMnblOTepHbIX B03MO)I(HO-
CTe:M: MO)I(HO BKJIlOqaTb ,L(eC5ITIq1 cnaraeMbIX. O,L(HaKO ,[(IDI 60JIbIlll1X 1(I1JIHHJI.pOB .rum
npe06pa30BaHI151 BbIllIeYKa3aHHbIX rapMOHWIeCKHX PMOB 6blno Hcnonb30BaHO npe-
06pa30BaHI1e BaTcoHa, KOTopoe ,L(aeT OCHOBHoe CJIaraeMOe H OCTaTOqHbIM PM <PYHK-
UHH XaHKeJUl. AmI 60nbllll1X l(HJIHH,L(POB OCTaTOQHbIH PM, aHaJIOrHqHbIH nOnIOCHO-
MY PMY Perre B KBaHTOBO:M: MeXaHHKe, CXO,L(MTC5I ,lLJI5I HeCKOJIbKI1X qneHOB [27, 74].
B03BpaIUa5lCb K rapMOHHqHOMY PMY, B [128] paCCqHTaHa CYMMa a3HMYTaJIbHbIX ,L(Ha-
---=--
A.

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rpaMM, npe,n:cTaBJHIIOIUI1X OCHOBHOH HHTepec: Ecp MR oceBoM meJII1 11 Ee lLlIR none-
peqHOH meJII1. 3TI1 pe3YJIbTaTbl npIlBO,LJ,RTCR Ha pIlC. 11.10 11 11.11. l1HTepecHo 3aMe-
TI1Tb, qTO 3JIeKTjJI11..feCKOe nOJIe oceBOM Il(eJII1 C03,LJ,aeT I1HTep<pepeHII:111O ,ilIl<ppaKl.{IIII
3a II:IDII1H,UpOM, B TO BpeMR KaK ,[{IIarpaMMa rrOrrepeqHOH meJIII ,UeMOHcTpl1pyeT paB-
HOMepHoe 3aryxaHl1e. 3TII ,Ul1arpaMMbI MCnOJIb3yK>TCR C MHO)lillTeJIeM AP 11 K03rjJrjJU-
u,uenmOM Ompa:JICeHUfl npl1 CKaHl1pOBaHl111 MR rrOJIyqeHI1R [JOJIHOtt ,Ul1arpaMMbI.
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PHC. 11.10. ,L(MarpaMMbI nOnepeqHOM lI(eJIH; x = ka [128]

f
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to
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A3HMyraJIbHbIH yrOJI (q»
PHC. 11.11. ,LJ;l1arpaMMbI oceBoH meJII1; x = ka [128]
11.3.2. AMarpaMMa HanpaBneHHocTM aHTeHHoM peweTKM
UHJIHH,n;pI1QeCKYID perneTKY MO)I(.HO paCCMaTpMBaTb KaK COCTORIl.(YIO 113 CTonKH
H,n;eHTHQHbIX KOJIbu;eBbIX perneTOK. 0603HaQHM CJIO)I(.Hoe B036}')K.l1:eHI1e p- fO 3JIe-
MeHTa B q-M KOJIbu;e nocpe,n;CTBOM Ipq = I (f3 p ' Zq), r,n;e f3 p - yrJIOBOe pacnOJIO)l(eHHe
p-ro, a Zq - pacnOJIOXeHHe no OCH Z q-ro KOJIbua. CHcTeMa Koop,nHHaT nOKa3aHa
Ha pHC. 11.12. I1pI1HHMaeTcH, QTO JIyq HMeeT HanpaBJIeHHe <p = 0 OTHOCHTeJIbHO Ha-
=-

4
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npaBJIeHHR pacnOJIO:>KeHHR 3JIeMeHTa. JIyq M3MeHReT opMeHTauJ'11O BOKpyr QMJII1H-
,apa n}'TeM nOBTopHoro 33)]:aHHR 6a3bI (3 = 0 B Heo6xo,aMMoe nOJIO)J(eHHe.
Bce 3JIeMeHTbI npHHHMalOTcR M,aeHTMqHbIMM, cMMMeTpMqHbIMM, paBHo OTCTOR-
ll.{HMH ,apyr OT ,apyra H HanpaBJIeHHbIMH B,aOJIb BeKTopa pMMyca. TaKI1M o6pa30M,
a3HM}'TaJIbHaR ,aHarpaMMa HanpaBJIeHHOCTH 3JIeMeHTOB MO:>KeT 6bITb BbIpa)J(eHa KaK
<l>YHKUHR I q> - 13  B n:eJIOM, a3HM}'TaJIbHaH ,aMarpaMMa 3aBHCI1T OT yrJIa MeCTa 8.
KOMnJIeKCHaR ,aHarpaMMa 3JIeMeHTOB 0603HaqaeTCR KaK G (q> - (3, 8), npMQeM <l>a3a
cpaBHHBaeTCH C n:eHTpOM KOJIbn:a. TaKHM o6pa30M, eCJII1 ,aeJIaeTCR ,aonymeHMe 0
TOM, QTO QeH1p <}>a3bI Haxo,aHTCR Ha 3JIeMeHTe, TO
G(q> - 13,8) = 1 G(q> - 13,8)1 exp[jkp cos 8 cos(<p -)].
(11.32)
,lJ;aJIbHee nOJIe paBHO
"
,
E(q>,8) = L L I pqG(q> -  p' 8) expUqu), (11.33)
p q
rL{e u = kd sin 8, a d - HHTepBaJI Me)l(,I(Y 3JIeMeHTaMH B oceBOM HanpaBJIeHHM.
JIyq MO:>KeT $OpMMpoBaTbcR B HanpaBJIeHMM q> = 0, 8 = 8 0 nyreM B036}')K.IIeHMR
Bcex 3JIeMeHTOB C ,ao6aBJIeHHeM <}>a3bI B ,aaHHOM HanpaBJIeHHI1 JIyqa. TaKJ1M o6pa-
30M, C yqeToM (11.32) H (11.33):
Ipq = 1 Ipqlexp[jkpcos80 cosa p - jquo],
(11.34)
r,ae Uo = kd sin 8 0 ,
[

 Dla6a 11. KOHfJJOpMHble aHmeHHble pelUemKU
I!
B (11.34) COCTaBJIHIOIl.{He <pa3bI pa3.lIeJIeHbI B r3 p 11 Zq' r,n:e Zq = qd. 3TO n03BOJIH-
eT C.lIeJIaTb .lIOnYIlI.eHl1e 0 pacnpe,n;eJIeHHH TOKa B CJIe,n;yIDIlI.eM BH,n;e:
/ (13 p , Z q) = I a (13 p) / e (z q) = / ff I 
(11.35)
rrpH 3TOM
Iff = /; exp(-jkpcos8 0 cosf3p)
(11.36)
11
/ =I /3I ex p(- jquo).
(11.37)
BepXHHe I1H,n;eKCbI a H e YKa3bIBalOT Ha a3HMyraJIbHOe Ii yrJIOMeCTHoe pacnpe-
,n;eJIeHliH COOTBeTCTBeHHO. 06paTHM BHHMaHHe Ha TO, qTO a3lfMyraJIbHOe pacnpe,n;e-
JIeHHe 3aBHCHT OT yrJIa opHeHTaIJ;Hlf JIytIa KaK no a3HMyry, TaK 11 no yrJIY MeCTa, B
TO BpeMH KaK /3 3aBHCI1T TOJIbKO OT eo. ECJII1 3anl1CaTb pacnpe.lIeJIeHHe TOKa B BI1,n:e
(1] .35), 3TO n03BOJII1T 3anl1CaTb ,n:l1arpaMMY (11.33) B BI1,n:e
E(<p,8) = Ea (<p,8) Ee (e),
(11.38)
r.lIe
Ea(<p,8) = L/;G(<p -f3p,8) (11.39)
H P
Ee(8) = Ll3 expUqu), (11.40)
q
r,L(e Ea(<p, e) - 3TO npOCTO ,n;l1arpaMMa o,n:Horo KOJIbIJ;a, B036y)K,L(aeMaH nOCpe.llCTBOM
lap; Ee(e) - rrpOCTpaHCTBeHHaH .lll1arpaMMa HanpaBJIeHHOCTI1 O.llHOrO BepTI1KaJIbHO-
fO cToJI6u:a 3JIeMeHTOB, B036y)K,L(aeMaH nOCpe.llCTBOM 13.
TaKHM 06pa30M, aHaJII13 MO)l(eT 6bITb ynpOIIJ;eH nyreM yqeTa pa3.lleJIbHOrO arrep-
TypHoro pacrrpe.lIeJIeHI1H Ii paCCMOTpeHI1SJ .lll1arpaMMbI U:I1JII1H.llpI1QeCKO:H AP KaK
u u u
np0l13Be.lleHI1H .lll1arpaMMbI KOJIbu:eBOI1 peIlleTKI1 11 .lIl1arpaMMbI JII1HelfHOlf peIlleTKH.
KapaH.llaIllHbI:H JIyq MO)l(eT 06pa30BbIBaTbCH B pe3YJIbTaTe BbI60pa I: JI)lH <pOpMl1pO-
BaHI1H JIyqa rrpl1 <p = 0 B a3lfMyraJIbHOM KOHyce 8 = eo 11 B pe3YJIbTaTe BbI60pa I 3 ,lI)iH
06pa30BaHI1H JIyqa np" <p = 0 B a311MyraJIbHOM KOHyce e = eo, a TalOKe B pe3YJIbTaTe
BbI60pa 13 JI)lH 06pa30BaHHH JIyqa nplf 8 0 B Meplf,L(HaHaJIbHO:H TIJIOCKOCTH <p = O. IIo-
u .....
CKOJIbKY KapaH.lIallIHbIlf JIytI HBJIHeTCH np0l13Be.lleHlfeM .llBYX BeepHbIX JIytIelf, rJIaBHbIe
60KOBbIe JIerreCTKM 6y.llYT JIeXaTb Ha KOHyce 11 B TIJIOCKOCTI1, B KOTOpOH 6billlf c<pop-
Ml1pOBaHbI BeepHbIe JIyqM.
,LJ.HarpaMMbI He BKJIlOqalOT 3<p<peKTbI B3alfMHOH CBH311. J(uazpaMMbl CKaHupoea-
HUR 3JleMeHma, KOTopbIe BKJIlOqalOT 3<p<peKTbI B3alfMHOH CBH311, a TalOKe COOTBeTCT-
BYIOIIJ;lfe 3HaQeHI1H 3<p<peKTlfBHOCTI1 3JIeMeHTa, 6bIJIlf paCCQI1TaHbI B [102, 65].
11.3.2. 1. p,JfcppaKLf,JfOHHb.e neneCTKJf
IJ;lfJIHH.llP MoxeT 6bITb nOKpbIT peryJIHpHOH ceTKoH, HO rrpoeU:l1pOBaHlfe B JII060M
HarrpaBJIeHHH C03,L(aeT HepaBHbIH HHTepBaJI no a3HMyry. O.llHaKO rro yrJIY MeCTa I1H-
TepBaJIbJ rrpoeU:HpyeMbIx 3JIeMeHTOB O.llI1HaKOBbI, TaK QTO JI.JIH yrJIa MeCTa MO)l(eT
HCnOJIb30BaTbCH 06bIqHaH TeopHH ,n;lf<ppaKIJ;HOHHbIX JIeneCTKOB. B CIDIY a3HMyraJIb-
Horo HHTepBarra pe3KO onpe.lleJIeHHbIX, BbICOKOaMTIJIHTY.llHbIX ,n:H<ppaKIJ:HOHHbIX JIe-
rreCTKOB HeT, HO 60KoBbIe JIeneCTKlf C HH3KHM YPOBHeM MOryr )'BeJIHQHBaTbCH,
eCJIH MeX3JIeMeHTHbIH IIIar CJIHIllKOM 60JIbllIOit IIOCKOJIbKY IJ;HJIHH.llP .llOJDKeH
HMeTb 3JIeMeHTbI «no BceH OKp)')KHOCTlf» .llJIH Toro, QT06bI 06eCneQHBaTb a3HMY-
TaJIbHOe CKaHlfpOBaHHe 360 0 , B paCQeTaX .llH<ppaKIJ:lfOHHOro JIeneCTKa cyrueCTByIDT
,L(Be nepeMeHHbIe: llIar 3JIeMeHTOB H pa,II;I'lYC U:HJIHH.llpa. KpoMe Toro, Y Ka)l(,[(O:H .ll11-

,
11.3. Anmennble peUlemKU no l{UIlunopu'IecKoii n06epxnocmu \
1 .
arpaMMbI 3JIeMeHTOB OCb 06bIQHO opMeHTMpoBaHa B pa.n:MaJIbHOM HanpaBJIeHHH C
TeM, QT06bI ,lIl1arpaMMY 3JIeMeHTOB MO}J(HO 6bIJIO yqecTb B paCqeTax. Y6bIBaHHe aM-
nJIMTY,QbI, KaK npaBMJIO, HCnOJIb3yeTcH ,lLJIH nOJIyqeHHH YMepeHHO HH3Koro YEJI C
TeM, QT06bI JII060ti 3HaqHMbIti paCqeT ,IJ;HarpaMMbI BKJIIOqaJI HHTepBaJI Me)l{,lJ;Y 3JIe-
MeHTaMH, pa,QI1Yc UHJII1H,lIpa, ,QHarpaMMY 3JIeMeHTOB H y6bIBaHHe aMllJIHTY.lIbI. TIo
3TOti npl1QHHe ,lIJUI UHJIHH,QpI1QeCKoti AP npocTbIX pe3YJIbTaTOB ,QJUI oueHKH ,IJ;H<p-
paKl.{HOHHOro JIeneCTKa HeT. U,MJIHli,[(pHqeCKMe pellIeTKM, cP a 3MpoBaHHbIe ,l])IH <t>op-
MMpOBaHI1H Y3KHX JIyqeti, I1MelOT TeH,IJ;eHUMIO 6bITb 60JIee nO,QBep)f(eHHbIMH npo-
6JIeMaM ,Ql1cPpaKUMoHHoro JIeneCTKa, qeM conOCTaBHMbIe nJIOCIGIe AP, B cHJIy .lIBYX
cpaKTopoB: 1) Ha CTopOHax aKTMBHOH qaCTH pellIeTKH JJ;HarpaMMbI 3JIeMeHTOB He
opMeHTHpOBaHbI B HanpaBJIeHMM JIyqa; 2) B 3TOH )Ke caMOH 06JIaCTH Heo6xo,IJ;HMO
BBO,IJ;HTb 60JIbllIOH Me}J(3JIeMeHTHbIH C,IJ;BMr no cPa3e Me)l{,lJ;Y 3JIeMeHTaMH ,LUIH KOM-
.
neHcaUHM H30rHyroCTI1 UHJIHH,Qpa. TIoCJIe.lIHH:H <l;>aKTop 3KBHBaJIeHTeH CKaHHpOBa-
HI1IO 60KOBOM QaCTH pellIeTKH no,IJ; onpe,n:eJIeHHbIM yrJIOM K HanpaBJIeHHIO, HOp-
MaJIbHOMY K UHJIHH,QPY B 3TOH TOqKe. CJIe,QoBaTeJIbHO, MeX3JIeMeHTHbIH llIar
,QOJI}J(eH rrO.lIJ]:ep}J(MBaTbCH He60JIbllIMM .lI1IH npe.lIOTBparn:eHHH 06pa30BaHHH ,lJ.JI.
YrJIOMeCTHoe CKaHMpOBaHHe rro,Q yrJIOM eo .lIOCTHraeTCH nyreM .lI06aBJIeHHH <l;>a-
3bI - qkd sin eo K q-MY KOJIbUY. 3<l>cPeKTMBHOCTb ,n:HarpaMMbI pemeTKH B llJIOCKO-
CTH q> = 0 Tenepb TaKaH )Ke, KaK 11 .lIJIH JIHHeMHOH pemeTKH C «3JIeMeHTaMH» KOJIb-
ueBOM pellieTKI1 H .lIHarpaMMaMH, KaK Ha pHC. 11.3. B qaCTHOCTM, .lIH<l;>paKUHOHHbIH.
neneCTOK rrOHBJIHeTCH npH e, Kor,n:a
d (sin 8 - sin 8 0) = + m, m= 1, 2, ...
A
(11.41)
J
J1errecToK B03HMKaeT npH q> = 0 B a3MMyre, nOCKOJIbK)' Ea (q>, e) HMeeT CBOH
MaKCHMYM npl1 q> = 0 (HJII1 npH6JIH311TeJIbHO TaK) ,lLJIH Bcex e. ,lJ.HcPpaKI.{HOHHbIM JIe-
neCTOK no Mepe ero nOHBJIeHMH M3 Ee(e) HMeeT BeJIHqHHY e,n:HHHUbI (paBHyJO rJIaB-
HOMY JIyqy), HO yMeHbllIaeTCH Ha Ea (q> = 0, e).
PacrrOJIO)l(eHl1e B llIaXMaTHOM nOpH.lIKe qepe.lIYIOI.I.(HXCH CTOJI6UOB 3JIeMeHTOB Ha
lI,HJIHH,n:pe - 3TO 3cPcPeKTHBHoe cpe,n:CTBO paCllIHpeHHH yrJIa CKaHHpOBaHHH no yrJIY
MeCTa lIJIH ,QaHHoro Me}J(KOJIbueBOro HHTepBarra d H rrO,LJ.,LJ:ep)l(aHHH He6oJIbllIOrO ,[(JI.
PaCCMOTpl1M pacrrOJIO)l(eHHyIO B llIaXMaTHOM IIOpH.lIKe pemeTKY KaK HaJIOXeHHe
.lIBYX 06bIQHbIX pellieTOK, Ka)l(J],aH C HOpMaJIbHbIM qHCJIOM KOJIeu Q, HO TOJIbKO C
nOJIOBHHOM KOJIHqeCTBa 3JIeMeHTOB B Ka)l()];OM KOJIbue, M12. TIO.lIpemeTKH HBJIHIOT-
CH H.lIeHTHQHbIMH, 3a I1CKJIIOQeHHeM Toro, qTO O.lIHa nOBepHyra Ha nOJIOBHHY mara
rro a311Myry 11 rrO,QHHTa Ha nOJIOBHHY mara B BepTHKaJIbHOM HanpaBJIeHHH, npHqeM
<l>a3a KOMneHcMpyeT 3TO CMern:eHHe.
,lJ;MarpaMMbI KOJIbu;eBbIX perneTOK ,L(JIH rrO.lIperneTOK MO)KHO 3anHcaTb CJIe,n:yIO-
mMM 06pa30M:
PewemKa I. JIyq B HanpaBJIeHHH nepBoro 3JIeMeHTa; T.e. f = 0;
E 1 = [(8)L,In(80)Fn(8)cosn<p + [(8)L,In(80)FM/2-n(8) x
n n
xcos[(M I 2 - n)<p] + [(8) L, In (8 0 )F M-n (8)cos[(M - n)<p].
n
( 11.42)
qJIeH r = 2, KOTOpbIH 06bIqHO He BHOCHT BKJIa,L( B pa60TY pemeTKH (,L(JIH S < A),
3,L(eCb BKJIIOQeH, nOCKOJIbKY mar Tenepb paBeH .lIBYM HOpMaJIbHbIM HHTepBaJIaM.

b Dla6a 11. KOHfjJopMHble aHmeHHble peUlemKU
PeUlemKa II. JIyq B HanpaBJIeHli1i nOJInyrli Mex.ny .aBYMR 3neMeHTaMIi; T.e.
1 = 0,5:
En = 1(8) L In (80)Fn (8)cos(nq» - 1(8) L In (8 0 )F Mj2-n (8)cos[(M / 2 - n)q>] +
n n (11.43)
+ 1(8) L In (8 0 )F M-n (8)cos[(M - n)q>].
n
ECJIH perneTKa He HMeJIa 6bI maXMaTHbIH nOPMOK, Kax.noe KOJIbUO HMeJIO 6bI
M 3JIeMeHTOB Ii .aliarpaMMY
Ea (q>, 8) = 1(8) L In (80)Fn(8)cos(nq» +
n
+ 1(8) L I n(8 0 )F M-n (8)cos[(M - n)q>].
( 11.44 )
n
qneH ,[(JI, B03HI1KalOIlU1H B pe3YJIbTaTe y,nBoeHHR I1HTepaJIa, paBeH
E gl (q>, 8) = L In (8 o)F M j2-n (8) cos[ (M / 2 - n)q>].
( 11.45)
n
,[(onycTliM, qTO perneTKa II no,nHRTa OTHOCliTeJIbHO pemeTKI1 I Ha d/2 11 nOMHO-
xeHa Ha exp Uk(d/2) (sin 8 - sin 8 0 )] ,[(JIR Toro, QTo6bI yqecTb cpa3Y. Tor.aa .aHa-
rpaMMbI UliJIHH.apHqeCKHX pemeTOK I H II:
E, (cp, e) = t II q I[ E a (cp, e) + E g/ (cp, e)] exp[jqkd (sin e - sin eo)].
q=l
( 11.46)
H
Ell (cp,e) = ex, j (sine - Sineo)]x
x tlI ql[Ea(cp, e) - Eg/(cp, e)]exp[jqkd(sine - sineo)].
q=l
(11.47)
CYMMa E I Ii Ell - 3TO ,nHarpaMMa maXMaTHOH pemeTKH. OHa MO)l(eT 6bITb 3a-
nHcaHa B CJIe.ayJOIUeM BlU(e:
II
 ( .kd )
E(q>,8) = Ea(q>,8)2..,lIqlexp Jq (sin8 - sin8 0 ) +
q=l 2 (11.48)
+ Eg/(cp, e{l - ex{ j (sine - sine 0»)] x II qlexp[jqkd(sine - sin eo)].
nepBbIH qJIeH (11.48) - 3TO ,nHarpaMMa pemeTKH, COCTORII.J.eH H3 2Q KOJIeu,
OTCTORI.UHX ,npyr OT .apyra C marOM, paBHbIM nOJIOBHHe HOpMaJIbHOrO, C M 3ne-
MeHTaMH Ha Kax.nOM KOJIbue, T.e. 3TO maXMaTHaR pemeTKa C 3anOJIHeHHbIMH «OT-
BepCTHRMH». 3TOT qJIeH He ;:J;OJDKeH .aaBaTb HHKaKoro .aHcppaKUHOHHoro neneCTKa
B CBR3H C nOJIOBHHHbIM marOM no yrJIY MeCTa H HOpMaJIbHbIM marOM no a3HMyry.
Bo BTOpOM qJIeHe yqHTbIBaeTCR .aHcppaKUHOHHbIH JIeneCTOK. <l>aKTop
tlI qlexp[jqkd(sine - sine o )] -
q=l
( 11.49)
L_

11.3. AHmennble peUJemlCu no l{UJ/unopu'teclCou n06epxnocmu d
'V .....
3TO .lI:HarpaMMa JIHHeHHOH perneTKH ,aJIg HOpMaJIbHOrO HHTepBaJIa no yrJIY MecTa,
KOTOpag ,naeT M npH
d (sine - sin eo) = + 1.
A
(11.50)
CJIe.n:OBaTeJIbHO, nOJIyqaeM
l-ex{ j (sine - sin eo) ) = 2.
(11.51)
TaKHM 06pa30M, ,[(JI :QHJIHH.npHqeCKOH rnaXMaTHOH AP paBeH ,[(JI JIHHeHHOH
pemeTKH C marOM d, nOMHO)l(eHHOMY Ha ,[(JI KOJIb:QeBOH perneTKH C marOM 2s. TIo-
.....
JIO:>KeHHe no yrJIY MeCTa H a3HMYTY JIeneCTKa gBJIgeTCg nepeCeqeHHeM nOJIO)l(eHHH
JIeneCTKOB JIHHeHHOH 11 KOJIb:QeBOH pemeTKH COOTBeTCTBeHHO. JIenecToK max-
MaTHOH perneTKH B03HHKaeT no,lJ, TeM )l(e yrJIOM MeCTa, KaK 11 JIeneCTOK 06bIQHOH
perneTKH, HO nepeHOCHTCR C <p = 0 B nOJIO)l(eHHe <P = <Pgb KaK 3TO onpe,aeJIReTCR H3
KOJIb:QeBOH perneTKH npH y,aaJIeHHH Ka)l(,l(OrO BToporo 3JIeMeHTa. TIOJIyqaeMoe npe-
HMYI..l.(eCTBO 3aKJIIOqaeTCR B TOM, qTO BeJIHqHHa JIeneCTKa KOJIbu:eBbIX no,apemeTOK
CHH)I(aeTCR OTHOCHTeJIbHO rJIaBHOrO JIyq:a. Ha pHC. 11.13 nOKa3aHO 3HaqeHHe rJIaB-
Horo JIeneCTKa KaK <PYHKU:HH yrJIa CKaHHpOBaHHR ,[(JIR 06blqHOM H rnaXMaTHOH KOH-
cPHrypaU:HH, a TaIOKe nOJIO)l(eHHe no yrJIY MeCTa H a3HMYTY JIeneCTKa rnaXMaTHOH
perneTKH. TIapaMeTpbI CJIe.n:yIOWHe: No = 128, eo = 0° 11 pacnpe.n:eJIeHHe qe6bIrne-
Ba - 50.n:E [47].
TIpH nOJIyqeHHH (11.48) ypaBHeHHe (11.9) 6bIJIO HaqaJIbHbIM MOMeHTOM. O.n:Ha-
KO TaKHM HaqanOM paBHbIM o6pa30M MOrJIO 6bI CTaTb (11.13) C HCnOJIb30BaHHeM
(3 = 231: (p + 1)/ M. TaIOKe 6bIJIO c.n:eJIaHO ,n;onyweHHe, qTO f = 0 ,[(JIR pemeTKH I, H
d = O,72A
u
06bIQHajl
...--. -2 perneTKa

t:::::{
--
ro
 -6
I=:
0

0
:t -10

ro
E
0
:t -1.
,.Q
I=:
Q)
E-t
:s:
u
0 -'I
:t
E-t
0
,.Q lllaXMaTHaH perneTKa
E-t
u -22
0
:t
S
0 lllar: O,65A a3l1Myr,
::E ....26
0,75 A yrOJI MeCTa
CJO
10
10
...--.
'60


--
9- so
....
CD
40
30
20
20
3D
 .50
eo (rpa,a.)
60
70
-30
20 30 40 50 60 1C
nOJIOXeHHe JIyqa no yrJIY MeCTa (rpa,a.)
PUC. 11.13. 3aBHCHMOCTb rrOnO)KeHHe JJ;H<ppaK:QHOHHoro JIerreCTKa Hero MOIUHOCTb
OT yrJIa CKaHHpOBaHH

 Dla6a 11. KOH(jJopMHble aHmeHHble pelUemKU
f = 0,5 ,lLJIR perneTKH II. YpaBHeHHe (11.48) 3aBHCHT TOJIbKO OT Toro, qTO Egl (<p, 8)
.lUUI perneTKH I paBHO -E g1 (<p, 8) ,l(JIR pemeTKII II, qTO CnpaBe,lLJIHBO ,lLJIR JII060H
opHeHTaUHH nepBoro 3JIeMeHTa B OTHomeHHH rJIaBHOrO JIyqa. TaKIIM o6pa30M,
(11.48) HBJIReTCR ,l(eHCTBHTeJIbHbIM .lUIR UHJIHH.apHqeCKHX .nyroBbIx AP B ueJIOM. ,L(a-
JIee Egl (<p,8) MO)l(HO JIerKO orrpe,lIeJIHTb H3 ,lIHarpaMM, paCCQI1TaHHbIX HenOCpe.lICT-
BeHHO H3 (11.10) C B036y)1()]:eHHeM qepe,l(yJOrn:HXCR 3JIeMeHTOB.
Ha pHC. 11.14 nOKa3aHbI ,l(HarpaMMbI Ea (<p, 8) + Egl (<p, 8) ,l(JUI pa3JIHQHbIX 8 0 .
3TH ,l(HarpaMMbI paCCQHTaHbI H3 (11.11), H BKJIa,l( OT Egl (<p,8) JIerKO onpe,l(eJIReTCR.
BH,l(eH 3<p<peKT OT pacnOJIO)l(eHHR 3JIeMeHTOB B maXMaTHOM nOPMKe. Hanpl1Mep,
eCJIH KOJIbu;a pacnOJIaralOTCR C HHTepBaJIOM d = 0, 72"A, JIyq npH 8 0 = 30° .naeT )];JI
npl16JIH3HTeJIbHO npl1 -60°. PeryJIRpHaR pemeTKa ,l(aeT BeJII1QI1HY L(JI -11 ,l(E, QTO
npe.nCTaBJIReT C060H pa3HHU;y Me:>K,[(y JIyqaMH rrpH 8 = 30° H 8 = 60°. ,[(JIR rnaXMaT-
HOH AP 3HaQeHHe ,L(JJ npe,lICTaBJIReT C060H pa3HHUY Me)l([{y JIyqOM npl1 8 = 30° 11
,L(JI npl1 8 = 60°, I1JII1 npl16JIH311TeJIbHO -28 .nE.
(8)
£(0) + £8.1.
eo =0
o
0:: -.

:t t::t -10
,.Q --
r:::,.Q
Q)E-< 20
E-< U -
::S::o
Ux
 S -30
5
20 40
60
311A1h 80
C1.J]b/t L 100 120
blJj YroJ] 140
(rpCi.4.) 160 180
60 10
so
30  {"Q
c't'3. 
 {oJ\ e
(b)
£(0) + £g.1.
eo = 30°
o
t:J::-.
:g  -10
,.Q --
r:::,.Q
 E-< -20
::s::U
u O
x
gs-30
E-<O
O-40
o
20 «)
311A1 60 80
h<iJ[b/fbJIi 100 120
YroJ] 
l'pCi.4. )
IAO 160
180
60 70
50
30.0 l{"Q
10 20 ec't'3.
{oJ\
Pac. 11.14. a - .lU1arpaMMbI qe6bIllieBa 30 ,[{E ,lLIDI e = 0; b - ,[{HarpaMMbI qe6bIllieBa
30 ,[{E lLJUI e = 30°
3.....

1
11.3. AHmeHHble peUJemlCu Ha lI,U//uHOpU'1eCICOU noeepXHocmu t
(c)
£(0) + £g.l.
eo = 60°
o
0::-

:I: r::t -10
-

  -20
::s::U
u O
0:I:
:I: S -30
o
O_AO
o
20 40
3 60 80
1t At Yr Cl.J] 100
bl[b1ii 120
YI'O.l] 140
(I'PCl4.) 160 180
60 70
so
30 40 \.{
20 c'3-
10 '1{oS\ e
Pac. 11.14 (npO.ll.OJUKeHHe). C - ,LJ;flarpaMMbI qe6blIIIeBa 30 .n6 lUI e = 60°
11.3.2.2. OCHoBHble neneCTKM
,L(JI.H 06bIqHOM perneTKH JIeneCTKM 6y,nyr JIe)l(aTb B IIJIOCKOCTH <P = 0 H Ha KOHyce
8 = 8 0 , nOCKOJIbKY .lJ.HarpaMMa TPa.rI.HI(HOHHOll pemeTKH ,l(JUI pa3.lJ.eJI.HeMOrO pacnpe-
v
,neJIeHH.H MO)l(eT paCCMaTpHBaTbC.H KaK npOH3Be.aeHHe .aBYX BeepHbIX JIyqeH.
,L(JI.H rnaXMaTHOH perneTKH MbI MO)l(eM paCCMOTpeTb (11.48). TIepBbIH qJIeH -
v v v
3TO npOH3Be.aeHHe BeepHoro JIyqa JIHHeHHOH perneTKIf If BeepHoro JIyqa KOJIbIJ.eBOIf
perneTKH, ,nalOmee OCHOBHbIe JIeneCTKH B <popMaTe 06blqHOll perneTKH Ha nrrOCKO-
CTH <p = 0 li Ha KOHyce 8 = 8 0 , O.n:HaKo BO BTOpOM qJIeHe .aaeTCH .apyroH Ha60p
oceH. nepBbIe .aBa K03<P<PHIJ.HeHTa BToporo qJIeHa .aalOT ,L(JI JIHHeHHOH perneTKH
(6e3 rJIaBHOrO JIyqa); TpeTHH K03<P<PHI(HeHT .aaeT ,L(J1 KOJIbI(eBOH perneTKH (c .aBOH-
HbIM liHTepBaJIOM). TaKHM 06pa30M, eme O,nHH H3 OCHOBHbIX JIeneCTKOB JIe)l(HT Ha
nepeCeqeHliH KOHyca 8 = 8g/ If HCKpHBJIeHHoi1 nJIOCKOCTH <p = 8 g /(8), r.ae 8g/ 3a.rI.aeT-
C.H H3 (11.41), a 8 g /(8) COOTBeTcTByeT MaKCHMaJIbHOMY 3HaqeHHIO Eg/ (<p, 8).
T or.n:a ,lLTIH 06bIQHOH perneTKH nOJIHa.H .aHarpaMMa IJ;HJIHH,n:pHqeCKOH perneTKH
xoporno npe.aCTaBJI.HeTC.H .aB)'M.H KOHTypaMH qepe3 npOCTpaHCTBO <p, 8: (<p, 8 0 ) H
(0, 8). )];JI.H rnaXMaTHOH perneTKli nOJIHaH ,nliarpaMMa xoporno rrpe.uCTaBJIHeTC.H no-
cpe,nCTBOM qeTblpex KOHTYPOB (<p, 8 0 ), (0, 8), (<p, 8 g /) H (<pg/ (8), 8). Ha pHC. 11.15
npe,nCTaBJIeHbI .lJ.liarpaMMbI ,lLTI.H 06bIQHbIX li rnaXMaTHblX perneTOK rrpH pa3JIHQHbIX
8 0 , npHHliMaIOTC.H Te )l(e caMble napaMeTpbI o,nHoro KOJIbI(a, KaK 11 ,lLTI.H pHC. 11.14;
KpOMe Toro, 32 KOJIbIJ;a C HHTepBaJIOM 0,72A HCrrOJIb3YIOTC.H C pacrrpe.n:eJIeHHeM qe-
6blmeBa 30 .uD lUI.H Iq(e). KOHTYP (<pg/ (8), 8) 6bIJI onpe.ueJIeH H3 .aHarpaMM
pHC. 11.14 npli HHTepnOJIHIJ;HH Me)l(,lI;Y MaKCHMaJIbHOH TOqKOH Ha ,L(JI.
,[(H<ppaKll.HOHHbIH JIerreCTOK MoxeT 6bITb )'MeHbllIeH, H yrJIOMeCTHoe CKaHHpo-
BaHlie MO)l(eT 6bITb pacmHpeHO nyreM )'MeHbllIeHli.H a3HM)'TaJIbHOrO H/HJIH yrJIOMe-
CTHoro llIara llIaXMaTHOH pellIeTKH. HanpHMep, eCJIH )'MeHbllIHTb a3HMyraJIbHbIM
llIar C 0,65A .lJ.0 0,5A (rrpH d = 0,72A), TO rrpe.lJ.eJI yrJIa CKaHHpOBaHH.H YBeJIHQMTC.H
C 30 .ao -40 0 ,lLTI.H nOMep)l(aHH.H ,L(JI Ha ypOBHe 30 ,no, a .lJ.aJIbHeHllIee YMeHbIlleHHe
.n:o 0,4A rr03BOJI.HeT CKaHHpOBaTb >750 npH )J,JI <40 .n:E. YMeHbllIeHHe yrJIOMeCTHoro

b Dloeo 11. KOHrjJopMHble OHmeHHble peUlemKU
(a)
-20
-30
Peryn.HpHa.H perneTKa
8 0 = 0°
o
-10
20 «>
3JtA1h 60 80
Cl.J]b/fA ... 100 120
ill Yll 1 
OJ] ( -.v 160
Pll4.) 180
60
20 40
-20 0  l:)
-40 ec1:
-60 oJ\
(b)
o
-to
-20
-30
IIIaxMaTHa.H perneTKa
8 0 = 0°
20 40
60
3JtA1h 80 100
Cl.J]Al/AJ/i 120
YroJ] (. 1«) 160
rpCl.!(.) 180
.to 60
o 20 :)
-20 c1: l \Q
-40 -rt e
 OJ
(c)
Peryn.HpHa.H perneTKa
8 0 = 30°
o
-1°1
'-»1
-
20
40
3JtAt.h 60 80
Cl.J]A/fAI/i 100 120
YroJ] (.
l'p1l4. )
140 160
180
40 60
o 20 :)
-20 l.
-40 ec1:
oJ\
>
80
Pac. 11.15. ,llHarpaMMbI qe6bIIIIeBa 30 ,n,E
......

11.3. AHmeHHble peUlemlCU Hll lI,UJlUHiJpU'IeCICOU n08epXHocmu 
o
-1(,
-20
-30
IIIaxMaTHaH pemeTKa
8 0 = 0°
(d)
40 60
43ltAth 80 100
Cl.J]b/fblij 120
Yl'oJ[ (J 140
/1JEl4. )
40 60
20
-20 0 t<''3.l(QJ
ec; "
toJ\
o
-10
-20
-30
PeryJIHpHaH pemeTKa
8 0 = 0°
(e)
20 40
3 60
1f At Yr ClJ[ 80 100
b/fblij 120
Yl'oJ[ (l' 140 160
.) 180
40 60
20
-20 0 l(QJ
-40 ec't'3.
 toJ\
(0
-
lllaxMaTHaH pemeTKa
8 0 = 30°
20 40
43ltAt.Yr. 60 80
Cl.J]b/fblij 100 120
Yl'oJ[ f 140
\ I'PEl4.) 160 180
40 60
o 20 9Jl J
-20 t<''3. l(Q
-40 ec;"
-60 toJ\
PHC. 11.15 (npo.n;OJDKeHHe). L(lfarpaMMbI qe6bIIIIeBa 30 .nE

b Dla6a 11. KomJ}()pMHbJe aHmeHHbJe peU1emKu
llIara (rrpM S = 0,65",) C 0,72 ,n:o 0,6", n03BOJUleT CKaHMpOBaTb CBbIllie 50° npM
M < 40 ,n:E. B pearrM3yeMoM pellIeTKe, o,n:HaKO, yrJIOMeCTHbIM llIar OrpaHllqllBaeTC.SI
MMHMMYMOM 0,72", M3-3a pa3Mepa 3JIeMeHTOB.
11.3.2.3. LlHnHH,qpH'IeCKBfI ,qenonflpH3BLlHfI
UMJIMH,n:pllqeCKa.Sl nOBepXHOCTb, KaK JII06a.Sl M30rHyra.Sl rrOBepXHOCTb, ,n:enOJI.SIpIl3Y-
eT rra,aalOIUYID BOJIHY. HarrpHMep, eCJIM JIMHeMHO nOJI.SIpIl30BaHHa.Sl BOJIHa na,n:aeT
B rrJIOCKOCTM na,L(eHM.SI (rrJIOCKOCTM, co,n:ep)l(all.{eM OCb IJ;RTIMH,n:pa M HarrpaBJIeHMe
na,n:eHM.SI), TO nOJI.SIpIl3aIJ;lIl1, .SIBJIRIOll.{lIeCR rrapaJIJIeJIbHbIMM MJIM HOpMaJIbHbIMM K
3TOH rrJIOCKOCTM, Be,n:yr Ce6R rrO-pa3HOMY. Kor,n:a 3JIeKTpMQeCKOe nOJIe napaJIJIeJIb-
u
HO nJIOCKOCTIi rra,aeHMR, oceBaR COCTaBJIRIOll.{aR nOJIR Ha UIIJIMHJJ:pllqeCKOM nOBepx-
HOCTM opMeHTMpOBaHa B TOM )l(e caMOM HanpaBJIeHIIII, HO KpyroBbIe KOMnOHeHTbI
npOTMBOnOJIO)I(HbI. KOHeqHO, npll HOpMaJIbHOM na,L(eHMM nOCJIe.LJ:HMe paBHbI HYJIIO.
,L(JIR HOpMaJIbHOM nOJIRpll3aUMH oceBbIe COCTaBJIRIOll.{Me opMeHTllpOBaHbI B TOM )l(e
caMOM HanpaBJIeHI1M; KpyroBbIe COCTaBJIRIOll.{Me TaIOKe opMeHTHpOBaHbI B KpyrOBOM
HanpaBJIeHIIM.
TaKMM 06pa30M, na,aalOll.{aR BOJIHa C KpyroBoM nOJISlpM3aUMeM C03,n:aeT nOJISI,
u
MMelOll.{Me OCM nOJIRpM3aUMII, opMeHTllpOBaHHbIe BnpaBO C O.LJ:HOII CTOpOHbI H BJIeBO
C ,n:pyroH CTOpOHbI, npM 3TOM nOJIHaR nOJIRpl13aUMR RBJUleTCR 3JIJIllnTMqeCKOH. Co-
u
OTBeTCTBeHHO, B UI1JII1H,n:pHqeCKOI1 perneTKe .LJ:OJDKHbI MCnOJIb30BaTbCR 3JIeMeHTbI,
113JIyqalOll.{Me KaK oceBble, TaK II KOJIbueBble KOMnOHeHTbI. KpOMe Toro, COOTHOllle-
HMe 3TIIX KOMnOHeHTOB, B ueJIOM, ,n:JIR JII060ro ,n:aHHoro 3JIeMeHTa 6y,n:eT 113MeHRTb-
CR no Mepe M3MeHeHMSI yrJIa na,aeHMR (M3JIyqeHM.SI). PellIeTKM Ha 60JIblllMX (OTHO-
CMTeJIbHO ,1J.JIMHbI BOJIHbI) UMJIMH.LJ:paX co Cna,L(alOll.{MMM pacnpe,n:eJIeHMRMM Ha
nepM<pepHM 6y,n:yr I1cnbITbIBaTb 60JIee HI13KMH M, B03MO)I(HO, He3HaqHTeJIbHbIH ypO-
BeHb ,n:enOJIRpIl3aUMI1, nOCKOJIbKY aMnJIMTy,n:a Ha 3JIeMeHTax, 3aMeTHO Y.LJ:aneHHbIX
OT npoeUMpyeMoM nJIOCKOCTM paCKpbIBa, MO)l(eT 6bITb MaJIeHbKoM. KOHMQeCKI1M
u
pellIeTKaM 3TO npeMMYll.{eCTBO He CBOMCTBeHHO, eCJIM TOJIbKO He MCnOJIb3yeTcR
qaCTb nOBepXHOCTM C 60JIbllIHM ,n:MaMeTpOM.
11.3.3. B3BHMHBfI npOBo,qHMOCTb LLlenH
B KOHCTpYJ<l.(MM KOH<pOpMHOMll.{eJIeBoi1 AP Ha nOBepXHOCTI1 npOBO,lUlll.{erO URTIMH,a-
pa paCqeT B3aMMHOH npOBo,n:MMOCTM Y12 RBJIReTCR KpMTllqeCKMM 3TanOM, KOTOpbIH B
nOCJIe,n:HMe rOlIbI IlIMpOKO M3yqarrCR. ECJIH o6paTMTbcR K pl1C. 11.16, TO Ha HeM .llBe
111IeHTMqHbIe ll.{eJIM - nOnepeqHbIe (KOJIbueBbIe) 11 npOlIOJIbHbIe (oceBbIe), - pacno-
JIO)l(eHHHble Ha nOBepXHOCTM 6eCKOHeqHO ,1J.JIMHHOrO UMJIMH,n:pa. feOMeTpMqeCKlle
napaMeTpbI CJIe,n:yJOll.{lIe:
R = pauMYC UMJIMH,n:pa,
(a, b) = ra6apMTbI ll.{eJIM no HanpaBJIeHMSIM (q>, z),
(a - JL]IMHa .LJ:yrll B,n:OJIb UIlJIMH.LJ:pa),
(zo, Rq>o) = Me)l(ueH TpOBbIe paCCTORHMR Me)l(,[(Y ru:eJIRMM,
So =  zJ + (Rq>0)2 ,
8 0 = arctan( Zo / Rq>o).
3a.n:aqa 3aKJIIOQaeTCR B TOM, QTo6bI onpe,n:eJIIITb B3aMMHyJO npOBO.LJ:IIMOCTb Me)l(-
,n:y 3TMMM .llBYMR ll.{eJIRMM, Kor,n:a 3JIeKTpMQeCKMM pa3Mep kR RBJIReTCR 60JIbllIMM.

j
11.3. AHmeHHble pememKU Ha II,UAUHapu'tecKou n08epXHocmu t
z
z
R
R
'------__ ., f
 Zo
t-.-a-." i -L
'. I "
.:::t:tlb - -r'"
. .
r- -  O- 
'"
'.....
......
...----
"
(0)
(b)
PHC. 11.16. reoMeTpHH meJIH: a - nOnepeqHbIe meJIH; b - npo.nOJIbHbIe meJIH
B paMKax 3TOM pa60TbI ,neJIaIOTC$I CJIe,nYlOmHe ,[(onymeHJ1$1: 1) meJI" $IBJI$lIOTC$I TOH-
KHMJ1, H 2) HX lUIHHa npH6JIH3HTeJIbHO COCTaBJI$leT nOJIOBHHY .LJ)IJ1HbI BOJIHbI. Tor,n:a
...
nOJIe B paCKpbIBe B Ka)l(,[(OH meJII1 MO}l{eT a,aeKBaTHO annpOKCHMl1pOBaTbCSJ nocpe,a-
CTBOM npOCToro KOCHHYCOH,[(aJIbHOrO pacnpe,neJIeHH$I, KOTopoe $IBJI$leTC$I TaK Ha-
3bIBaeMbIM «O,[(HOMO,[(HbIM» npH6JIIDKeHl1eM. HanpHMep, eCJIH meJIb 1 $IBJI$leTC$I. no-
nepeQHOM, ee nOJIe B paCKpbIBe npH «O,nHOMO,[(HOM» npl16JIH)I(eHI1H BbIpa}l{aeTC$I
CJIe.uylO IIlI1M 06pa30M:
E = VI eI H = Ilh.,
(11.52)
r,ne
- ( " 2 1t Y )
el = Z-COS-
ab a
hI = X . e],
f,[(e (VI' II) - 3TO, COOTBeTCTBeHHO, MO,naJIbHbIe 3HaQeHH$I (Hanp$l)l(eHHe, TOK)
meJII1 1. B3al1MHa$l npOBo,nHMOCTb Yl2 3an;aeTC$I nocpe,[(CTBOM
1 21
YI2 = Y2I = -, (11.54)
VI
r,ne 1 21 - HH.IIYllJfpOBaHHbIH TOK B meJIH 2, Kor,n:a meJIb 1 B036)')KlJ:aeTC$I Hanp$l)l(e-
Hl1eM VI' a meJIb 2 3aKOpOQeHa.
Cyrn;ecTByeT aJIbTepHaTI1BHOe onpe,n:eJIeHHe B3al1MHOM npOBo,n:J1MOCTI1. BMecTo
(11.52) Mo,n:aJIbHOe HanpIDKeHHe Vi (c no,n:1JepKHBaHHeM) MO)l(eT 3a,[(aBaTbC$I Qepe3
BbIpa}l{eHl1e nOJI$I B paCKpbIBe meJII1 1 CJIe,n:yromHM 06pa30M:
- V I 1tl'
E = Z-=-cos2 (11.55)
b a
y = Rcp,
(11.53)

b Dla8a 11. KOHrjJOpMHble aHmeHHble pewemKU
HJIH 3KBHBaJIeHTHO
b/2
V I = J (Z. E) y=odz,
-b/2
( 11.56)
3aTeM 3a.n:aeTCR ,n:pyraR B3aHMHaR rrpOBO,n:HMOCTb Y1 2 rrOCJIe 3aMeHbI (VI' V 2 ) Ha
( VI ' V 2 ). MO)KHO JIerKO ,n;OKa3aTb, qTO
Y _Oy;
- 12 - 2b 12,
( 11.57)
3.n:eCb YMeCTHO C.n:eJIaTb TPH 3aMeqaHHR: 1) B orpaHHqeHHOM CJIyqae, Kor,n;a
b  0, Y 12 rrepexo,n;HT B HYJIb, KaK H b, B TO BpeMR KaK Y 1 2 rrpH6JIIDKaeTCR K rrOCTO-
RHHOH, He3aBHCHMO OT b; 2) MR Crrel(HaJIbHOrO CJIyqaR 0 = A/2 H R  00 HMeHHO
Y 1 2 ll,n;eHTllqHO B3allMHOMY llMrre,n;aHCY Z12 Me)K)];Y ,n;BYMR COOTBeTCTByIDIUllMll ,n;ll-
rrOJIRMll, paCCqHTaHHbIMH rrocpe,n;CTBOM KJIaCCllqeCKOrO MeTo,n;a KapTepa [46];
3) Kor,n:a lUeJIH B036y)K,[(aIOTCR nocpe,n;CTBOM BOJIHOBO,n;OB (JIllHllH rrepe.n:aqH), qaCTO
llCrrOJIb3yeTcR Y 12 . 3.n:ecb 11 ,n;aJIee BHHMaHHe 6y,n;eT y,n;eJUITbCR Y 12 , a He Y 1 2 .
B3aHMHaR rrpOBo,n;llMOCTb, 3a,L(aHHaR B (11.54), BKJIIOQaeT co6CTBeHHyID rrpOBO-
,n;llMOCTb Y ll B KaqeCTBe Crrel(llaJIbHOrO CJIyqaR, KOTOpbIH llMeeT MeCTO rrpH COBrra-
v
,n:eHI1H ,n;BYX IUeJIell.
11.3.3.1. Mo,qanbHb.e pfl,qb'
MO,n;aJIbHbIH pR.n: 6bIJI pa3pa6oTaH B [42] C llCnOJIb30BaHHeM pR,n;a MR a3llMyraJIb-
HbIX nOJIIOCOB B <PYHKl(llll fpllHa H llHTerpaJIa MR HerrpepbIBHoro cneKTpa no Z
(CM. TaIOKe pa60TbI [43, 11,3, 3]). 3TOT PM llIllpOKO llCrrOJIb30BaJICR rrpH IIOJIyqe-
Hllll Y 12 MR IUeJIeH Ha I(llJIHH.LI:pe [7, 8]. EeCKOHeqHbIH HHTerpaJI Heo6xo,n;llMO arr-
rrpOKCllMllpOBaTb, H 3TO 06JIerqaeTCR 3a CqeT ,aorrYlUeHHR MaJIbIX rrOTepb B cpe,n;e
BBe.n:eHlleM MaJIOH OTpHl(aTeJIbHOM MHllMOH qaCTll k. 3TO rrpll6JIIDKeHlle CTaHOBllT-
CR Bce MeHee rrpHeMJIeMbIM rro Mepe Toro, KaK Z B03paCTaeT, HO MO,all<pllI.{HpOBaH-
Hoe pemeHlle .lUIR 3Toro peXllMa 6y,aeT 06Cy)K,[(aTbCR rr03,n;Hee. <1>OPMYJIbI B3allMHOH
rrpo BO.n:llM OCTll CJIe.n:ylOlUll e:
IlonepettHble w,eflU
00 00
Y12 = J dk z L'V(m,kz)G(m,kz)exp[-j(mcpo + kzz o )],
m=-oo
(11.58)
-00
r,ae
'JI (m, k z) = ab sinc 2 k zb [ Sinc ( mcp a + 1t J + sine ( mcp a - 1t J] 2 ,
81t 2 R 2 2 2
o
cp a = 2R '
. (2 )' ( k ) 2 (2 )
G(m, k ) = YO JkH m (ktR> + m z kt H m (ktR>
z kt H }/;) (kt kl R jkH}/;)' (kt'
 k2_k k > k z
kt =
-j  k -k 2 k < k z
(11.59)

11.3. AHmeHHble pewemKU HO ijUAUHopu'tecKou n06epxHocmu 
IIpoiJoflbHble U{eflu
00 00
Yl2 = J dk z L<P(m,kz)F(m,kz)exp[-j(m<PO + kzZ o )],
-<1J m=-oo
(11.60)
f.n;e
2
, k ) _ ab. cos(k zb / 2)
<p,m, z - - slncm<p a 2 '
8R ( kt ) -( ; r
F(m, k ) = Yo ktHlj; > (ktR) .
z jkH};)' (k 1 R)
JIH Ii MHTIpa (CM. [47]) pa3pa6oTaJlH qepe,nyroIIJ;HHCR MO.n;aJlbHbIH pSl.n;, no.n;xo-
.n;SlIIJ;HH ,L{JISI 60JIbllIOrO Z. BHaqaJIe paCCMOTpHM rrOrrepeqHbIe IIJ;eJIH. TIepenHIIIeM Y l2
c TOqKH 3peHHSI ero peaJIbHOH H MHHMOH qaCTeH: Yl2 = G + jB. MO)l(HO .n;OKa3aTb,
qTO .n;HarpaMMa nOnepeqHOH IUeJIH G BbIpa)l(aeTCR CJIe.n;}'IOIUHM 06pa30M:
ko 00 1
G = J dk z L<P-cos(m<po)cos(kzZo)\V(m,kz)R(m,k z )' (11.62)
o m=O Em
(11.61)
f.n;e
R(m,k,) = 2o 2 1 + ( mkz ) 2 2 1 ,
nkt R Mm(ktR> kOkt R Nm(ktR)
M (x) = J (x) + Y (x),
N (x) = J (x) + Y,; (x).
06paTHM BHHMaHHe Ha TO, qTO G CO.n;epXHT KOHeqHbIH HHTerpaJI M MO)l(eT BbI-
qMCJISlTbC5I 06bIqHbIM 06pa30M nOCpe.n;CTBOM CTaH,L(apTHbIX npHeMOB qHCJIeHHOrO
I1HTerpHpOBaHI1S1. MHI1MaR qaCTb Y 12 BbIpIDKaeTC5I CJIe.nyroIUHM 06pa30M:
(11.63)
00 1
B = J dk z L -cos(m<po)cos(kzzo)W(m,kz)W(m,k z )'
c m=OEm
I
( 11.64)
r.n;e KOHTYP I1HTerpl1pOBaHH5I C 1 nOKa3aH Ha pHC. 11.17 11
( ) 2
ko J J' y Y' 1 mk z 1
kt ( m m + m m) M(ktR) - kokt R N(ktR)
ko > k Z'
Wm(m,k z ) =
-ko K;" (I ktl R) ( mk z ) 2 K m (I ktf R)
Iktl Km(lktlR) kolktlR K;"(lktlR)
( 11.65)
ko < k Z.
PaCqeT B, npOBe.n;eHHbIH c nOMOIIJ;blO (11.64), MoxeT 6bITb BeCbMa Tpy.n;oeMKHM,
nOCKOJIbK)', Bo-nepBbIX, HHTerpHpOBaHl1e OTHOCHTeJIbHO k z HMeeT 6eCKOHeQHbIH
llHana30H, H K03<P<PI1UHeHT cos kzzo xapaKTepH3yeTC5I BbICOKHMH KOJIe6aHI1S1MH npH
60JIbIIIOM kOZo. BO-BTOpbIX, <PYHKl{HSI W(m, k z ) HMeeT HeHHTerpHpyeMbIe oco6eHHO-
CTH npOTHBOnOnO)K}{oro 3HaKa no o6e CTOpOHbI k z = ko, a W(m, k z ) MeJlJleHHO y6bIBa-

b DW8a 11. KOHfJJOpMHble aHmeHHble pewemlCu
eT OTHOCHTeJIbHO m H kz- J(JUI Toro qTo6bI 060MT" BbIllIeYKa3aHHbIe Tpy,n:HOCTH lIP"
BbPlHCJIeHHH B, 6bIJI npHH.HT MeTo,n:, BHe,n:peHHbIM B [33] npH H3yqeHHH np06JIeM UH-
JIHH,L(pWIeCKOH aHTeHHbI. IIepenHllIeM (11.64) CJIe,n:yroIUHM o6pa30M:
00 1
B=lm L-cosm<po -jJ F(m,kz)sin(kzZo)dk z + J F(m,kz)expUkzZo)dk z , (11.66)
m=OEm c)
r,n:e
F(m, k z) = [R(m, k z) + jW(m, k z)]\V(m, k z). (11.67)
MHHMa.H qaCTb rrepBoro qJIeHa BHYTP" CKo6oK (11.66) COCTaBJI.HeT:
ko
1m - j J F(m, k z) sin(k zzo)dk z = - J R(m, k z)\V(m, k z) sin(k zzo)dk z' (11.68)
c) 0
)::LIT.H Toro qTo6bI BbIqHCJIHTb MHHMYIO qaCTb BToporo qJIeHa (11.66), KOHTYP HH-
TerpHpOBaHH.H C 1 ,n:e<l>opMHPyeTcH B C 2 (pHC. 11.17) B COOTBeTCTBHH C TeopHeH
KOMITJIeKCHbIX nepeMeHHbIX. 3Ta MaHHnYJIHQHH npHBo,n:HT K CJIelI.YIOI.l.{eMY:
1m J F(m,kz)expUkzZo)dk z = 1m J F(m,kz)expUkzZo)dk z . (11.69)
c. C 2
113MeHHM nepeMeHHYIO k z = jll B (11.69). llOlI.CTaHOBKa pe3YJIhTHpYIOI.l.{erO
ypaBHeHHH (11.68) B (11.66) ,n:aeT CJIe,n:YIOIUee:
00 1 ( k
B = L -cos(m<po) -Jo 0 R(m, k z)\jI(m, k z) sin(k zzo)dk z +
m=OE m
00
+ J R(m, IrY\V (m, jrV exp( -llZ 0 )dll
o
(11.70)
1m Ic z
C I Re k z
OKOHqaTeJIbHOe BbIpa)l(eHHe Yl2
nOJIyqaeTcH H3 pearrbHoM qaCTH G B.
(11.62) H MHHMOM qaCTI1 B B (11.70).
YMecTHo c,n:eJIaTb HeCKOJIbKO 3aMe-
qaHI1M: 1) He TOJIbKO G, HO TaIOKe B
OlIpe,n:eJIHIOTCH IIOCpe,n:CTBOM R(m, k z ),
QTO ropa3,n:o npOI.l.{e W(m, k z ), 3an;aHHO-
ro B (11.65); 2) napaMeTp G COlI.ep)l(l1T
TOJIbKO KOHeQHbIM I1HTerparr; 3) 6eCKO-
HeqHbIH I1HTerparr B B, T.e. BTOpOM I1H-
Terparr B (11.58), co,n:ep)l(HT 3KCIIOHeH-
QHarrbHO y6bIBalOI.l.{HM K03<l><Pl1l.{HeHT
exp [-(zo - a)ll] B ero nOlI.HHTerpaJIb-
HOM BbIpIDKeHHH. TaKHM o6pa30M, qeM
60JIbllIe zo, TeM 6bIC'Tpee CXO,n:HMOCTb
B BbIQI1CJIeHHH B. 3TO OTJIHQHe OT
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pacrrOJIO)l(eHHbIX rro BceMY UHJIHH,L(PY. B [1] 5-117, 53, 54, 5]] rrOJIyqeHbJ auazpaM-
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B pe3YJIbTaTe BbI,aeJIeHa KOMrrOHeHTa, CBR3aHHaR C HHTerpHpOBaHHeM Ce.lUIOBOH
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b Dla6a 11. KompopMHble aHmeHHble pewemKU
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pOHbI KaCaTeJIbHOH JIHHHH, nponOpUl10HaJIbHYID (krO)-1/3. nOJIe B ,n:aJIbHeH 30He
npo,n:OJIbHOM rn:eJII1 (3JIeKTpHQeCKOe nOJIe nOnepeQHoe) HBJI5IeTC5I npH6JIH3HTeJIbHO
nOCT05IHHbIM, HO nan:aeT .ao -0,7 nplf cp = 90 0 , He3aBHCHMO OT .aHaMeTpa l(IUIHH,IJ;pa,
eCJIH TOJIbKO OH 60JIbllIOH. TIOJIe nOnepeQHOH IlleJIH (npOlI.OJIbHOe 3JIeKTpl1QeCKOe
nOJIe), Ha060poT, nan:aeT npH6JIH3HTeJIbHO ,n:o 0,4(2/kro)1/3. CYJ.l.(eCTByeT MeMeHHaH
3aBHCHMOCTb OT ,n:HaMeTpa URJIHH,IJ.pa. IJ;I1JIHH,l(p ,n:l1aMeTpOM 20A .aaeT nOJIe
-17,9 .an, B TO BpeMH KaK l(RJIHH,l(P ,l(HaMeTpOM 40A .aaeT -19,9 ,n:n. flpH aHaJIH3e
MeTo,n:OM fT,lJ. HCnOJIb30BaJIHCb <PYHKl.{HM Cl>oKa, [37, 18]. CJIO)I(HOCTb BbIBo,n:a <pop-

b Flla6a J 1. KOm!JOpMHble aHmeHHble peUlemKU
........
OCBemeHHaR
06JIaCTb
....-
--
-...

--
....-
-- ."".


__ "'" nepeXO,UHaSi
06JIaCTb
........
-...
---
-...

npO.nOJIbHaSi
meJIb
TeHeBaSi
06JIaCTb
PUC. 11.27. 06JIaCTH nOJIR
MYJI TpaHc<t>opMaUMI1 BaTCOHa nOJI3ym;l1x BOJIH CTaBMT MX 3a npe,UeJIbl TeMaTMKM
HaCT05lmeti KHl1rl1 [130, 22, 34].
Hepa3,UeJIMMOCTb yrJIOMeCTHbIX M a3MMYTaJIbHbIX <t>aKTopOB B BblpIDKeHl111 ,Ul1a-
rpaMMbI 03HaqaeT, QTO ,L1,JUI <pI1KCMpOBaHHoro y6bIBalOmero aMnJIMT)',UHoro pacnpe,Ue-
JIeHI151 yrJIOMeCTHbIe 11 a311MyraJIbHbIe ,UMarpaMMbI M3MeH5IIOTC5I B 3aBI1CMMOCTM OT CKa-
HMpyromero yrJIa B03BbIllIeHM5I 8 0 , OnbIT npaKTMqeCKOrO MCnOJIb30BaHI151 npI1BOl!I1T K
BbIBO,UY, QTO )1)151 nOMep)l(aHM5I HI13KI1X 60KOBbIX JIeneCTKOB B a3MMyre no Mepe 113Me-
HeHIDI CKaHMpyromero yrJIa B03BbIrneHI151 CJIe,l(yeT M3MeH5ITb B036)')K,LI.eHMe perneTKI1.
KpoMe KOMMyrMpYlOmMX M <pa3MpYlOlUMX KOH<pMrypaUMti LI.JI5I nOBopOTa JIyqa
v v
no a3l1Myry, ynOM5IHyrbIX BbIllIe, ,l(JI5I M3JIyqaTeJIeM UMJIMH,l(pMQeCKOI1 perneTKH MC-
nOJIb30BaJII1Cb JII1H3bI [19,61].
11.4.2. CpaBHeHMe nnaHapHblX (nnocKMx)
M ceKTopHblX peweTOK
qacTo B03HMKaeT Bonpoc 0 TOM, 3<p<peKTI1BHO JIM MCnOJIb3yroTC5I paCKpbIB M anna-
v
paTHa51 QaCTb B UMJIMH,UpI1QeCKOM pellIeTKe - B QaCTHOCTM, no cpaBHeHMIO C npMH-
UMnOM CTaH,l(apTHOH nJIOCKOH perneTKM. )];JI5I a3MMyraJIbHOrO nOKpbITM5I 360 0 , KaK
npaBMJIO, Mcnonb3yroTCR qeTblpe nJIOCKMe perneTKI1, Ka)l(JlaR M3 KOTOpbIX cKaHl1pyeT
B ceKTope + 45 0 , n03TOMY UMJIMH,Up cpaBHMBaeTCR C QeTblpexcTopoHHeM nJIOCKoti
KOH<pMrypaUMeti. )];eJIaeTC5I ,UonyweHMe 06 M,UeHTMqHOCTM 3neMeHTOB. ,lI;nR yrno-
MeCTHoro cKaHMpOBaHM5I M yrnoMecTHoM ,UMarpaMMbI YKa3aHHbIe ,UBe KOH<pMrypa-
UMM 06eCneQMBalOT nOQTM M,l(eHTMQHble pe3ynbTaTbI npM ,UonymeHMM 0 TOM, qTO
M B TOM, M B ,UpyroH Mcnonb3yroTCR pa3,UeJI5IeMOe CI1H<pa3Hoe pacnpe,UeneHMe
M l1,UeHTI1QHble pacnpe,UeneHMR no yrJIY MeCTa. YrnoMecTHaR ,UMarpaMMa nnocKOH
perneTKM - 3TO MHOXMTeJIb AP, nOMHO)l(eHHbIM Ha yrJIOMeCTHYIO ,UMarpaMMY 3ne-
MeHTOB. TIpM 3TOM yrnoMecTHaR ,UHarpaMMa UHJIHH,UpHqeCKOH perneTKM npe,UCTaB-
n5leT C060M MHO)l(lfTenb AP, nOMHoxeHHbIH Ha yrnoMeCTHyIO ,UMarpaMMY «3neMeH-
Ta KonbueBoH perneTKH».
--

11.4. CelCmOpnble peUlemlCU no IJ,UJ/unapax 
Ha pHC. ] 1.3, HanpHMep, nOKa3aHbI yrJIOMeCTHbIe ,lJJlarpaMMbI «3JIeMeHTa
KOJIbueBoM perneTKM» B cpaBHeHMH C yrJIoMecTHoM ,nHarpaMMoM 3JIeMeHTa. TIpeH-
MymecTBo [(HJIMH.n:pa 3aKJIIOQaeTCR B TOM, qTO yrJIOMeCTHbIe .n:HarpaMMbI 3JIeMeHTa
B COCTaBe KOJIbu:eBoM perneTKH HMelOT TeH.n:eHUHIO no,naBJIRTb 60KoBbIe JIerreCTKH
B 60JIbllIeM CTeneHM, qeM H30JIHpOBaHHaR .n:HarpaMMa 3JIeMeHTa. B TaKOM CJIyqae
cpaBHeHHe nepBoro nopR.n:Ka MO)l(eT 6bITb c,neHO J( cpaBHeHMIO a3MMyranbHoM
u v. u u u
,nHarpaMMbI KOJIbueBOM pemeTKH C a3HMyranbHoH ,nHarpaMMoH nMHeMHOH pe-
meTKH.
,D;onycTHM, qTO ,nyra He 60JIee 180 0 6y,neT B036yx;n:aTbcR Ha KOJIbu:e. Tor.n:a aMn-
JIH1)',nHoe B036Y)(([leHMe nMHeMHoM perneTKH MO)l(eT npoeUHpOBaTbCR Ha ,nyry, Xop-
,l(a KOTopoM paBHa ,lJJIMHe JIHHeMHOM perneTKH, npH KOppeK.IJ;HH <t>a3bI 3JIeMeHTOB Ha
,nyre ,lJJIR 06eCneQeHMR JIHHeMHoro <t>poHTa <t>a3bI. ,L{JIR He60JIbllIHX yrJIOB OTKJIOHe-
HHR OT HopManM <}>opMa rJIaBHOrO JIyqa M nepBbIX HeCKOJlbKMX 60KOBbIX JIeneCTKOB
,lJJIR ,nyroBoM pellIeTKM 6y.n:yr npH6JIH3MTeJIbHO Te )l(e, qTO ,l(JIH JIMHeMHOH pellIeTKH,
nOCKOJIbKY ,l(JIR ManbIX yrJIOB KpHBM3Ha MMeeT He3HaQHTeJlbHoe .n:eMcTBHe Ha <t>a30-
Boe pacnpe,UeJIeHHe Ka)K,[{OrO 3J1eMeHTa. KpoMe Toro, 3 <l>cPeKTbI Me)l(3JIeMeHTHoro
llIara rrpORBJIRIOTCR TOJIbKO npM 66JIbllIHX yrJIax. rIpM nO,l(06HOM cnoc06e paccY)l(-
,l(eHMR npoeKUMR, CKa)l(eM, pacnpe,aeJIeHMR qe6bIrneBa RBJIReTCR y,a06HbIM Cpe,lJ.CT-
BOM <pOpMHpOBaHMR )l(eJIaeMOM llIHPMHb! JIyqa ,H KOHTpOJIR BHyrpeHHHx 60KOBbIX
JIeneCTKOB ,ayroBoH perneTKM. 3TO TaIOKe no,aTBep:>K,L(aeTCR paCqeTaMM. npH 3TOM
60JIee y,aaneHHbIe Ha BHellIHlO1O CTOPOHY OTKJIOHeHMR OCHOBHoro JIyqa 60KOBbIe
JIeneCTKH, eCTeCTBeHHO, I1MelOT TeH,aeHUMIO K CHM)I(eHMIO, 3a I1CKJIIOQeHl1eM ,U11<}>-
paK.IJ;HOHHOro neneCTKa. PaCqeTbI nOKa3bIBaIOT, qTO eCJIH ypOBeHb LUA<ppaK.IJ;MOHHO-
ro neneCTKa KOHTpOnl1pyeTcR, Bce 60KOBbIe JIeneCTKI1 6y,l(yr Haxo,aMTbCR HM)I(e
BHyrpeHHI1X neneCTKOB.
OTHOCMTenbHaR pa60Tocnoc06HOCTb JIHHeMHbIX H ,ayrOBbIX perneTOK MO)l(eT
6bITb oueHeHa no qMCJIY 3JIeMeHTOB 11 He06xo,nMMOMY 06I.UeMY pa3Mepy aHTeHHbI.
PaCCMOTpHM pMC. 11.28. AIcrI1BHbIe paCKpbIBbI 0603HaqeHbI TeMHbIMM nMHMRMM 11
MMelOT O,aHY M TY )l(e npoeUHpOBaHHYIO ,l(JIMHY. Illar 3JIeMeHTOB Ha JIMHeMHOM pe-
rneTKe MO)l(eT 6bITb 3a<}>MKcllpoBaH Ha d = 0,586"-, 1JTO npe,l(CTaBJIReT c060M MHTep-
Ban, He06xo,aI1MbIM ,l(JIR CKaHl1pOBaHHR B ceKTope + 45 0 , npH 3TOM ,l(llcPpaKIJJIOHHbIM
JIeneCTOK rrORBJIReTCR npH + 90 0 . ,L{nR CJIyqaR C ,nyroM KOHTpOJIb YPOBHR ,nM<ppaK-
UMOHHoro JIeneCTKa B03MO)l(eH, eCJIM nOMeCTI1Tb CTaUI10HapHyID TOqKY 3a npe,nenbI
aKTI1BHOM ,l(yrH, CKa)l(eM, npl1 ao = a (P) + 6.
Tor,na 113 (11.21), Kor,na 8 0 = 0 11 r = -1, nOCKOJIbKY 6 Mano, CJIe,l(yeT
'A
s=
2 sin(a(p) + B)
'A
,....,
,....,
2[sina(P) + B cosa(p)]
(11.73)
06mee QllCJIO 3JIeMeHTOB Ha QeTbIpexcTopoHHeM pemeTKe COCTaBJIReT rrpH6JII1-
3 I1TeJIbHO
8p sina(p)
0.586'A
(11.74)
06I.Uee 1JHCJIO Ha KOJIbue paBH.HeTCR
2np 4np .
= [slna(f) + B cosa(p)].
s 'A .
(11.75)

b DW8a 11. KOIUpopMHble aHmeHHble peUJemKU
..
2p sin a(P)
.
PHC. 11.28. qeTbIpexcTopoHHHI perneTKa B cpaBHeHHH c KpyrJIOH perneTKoH
B pe3YJIbTaTe MMeeM cJIe,n:YIOll.{ee COOTHOllIeHHe:
qHCJIO KOJIbIJ;eBbIX 3JIeMeHTOB = 0,920 [1 + 8 cot a (P)].
l.JHCJIO JIMHeMHbIx 3JIeMeHTOB
I1cxo,n:R H3 3Toro MO)l(HO c,n:eJIaTb BbIBO,n: 0 TOM, qTO '"W 92-100% 3JIeMeHTOB,
He06xo,n:MMbIX J],JIR qeTblpexcTopoHHeM JII1HeHHOH pellIeTKH, Tpe6YIOTcR ,lLJIR nOJIY-
..... .....
qeHMSI 3KBMBaJleHTHOH KOJIbIJ;eBOH pellieTKI1.
Pe3YJIbTaTbI [47] nOKa3bIBaIOT, qTO KpyrOByK> AP C pa3MepOM 11 ql1CJIOM 3JIe-
..... ..........
MeHTOB, 3KBliBaJIeHTHbIMli QeTblpeXCTopOHHeli JII1Hel1HOIi pellIeTKe, MO)l(}lO c,n:eJIaTb
npl16JIM311TeJIbHO 3KBHBaJIeHTHOH no pa60Tocnoc06HoCTli 11 BHe HanpaBJIeHHR,
HOpMaJIbHOrO paCKpbIBY nOJIHOM pellIeTKM. O,n:HaKo, nOCKOJIbK)' JIyq JIHHeHHOM pe-
llIeTKH paCllIMpReTCR ,lI,JIR CKaHHpOBaHHR B HanpaBJIeHHH, HOpMaJIbHOM paCKpbIBY,
06ll.{aR pa60Tocnoc06HoCTb KOJIbIJ;eBOH pellleTKH npeBocxo,n:HT pa60Tocnoc06HoCTb
JII1HeMHOH. KpoMe Toro, cywecTByeT pR,n: HelIOCTaTKOB IIJIOCKOM perneTKI1, KOTopble
I1CKJIlOqalOTCR caMHM npMHIJ;HnOM npHMeHeHHR IJ;HJIHH,n:pHQeCKOH pellieTKI1. JIyq
.....
KOJIbIJ;eBOI1 pemeTKH RBJIReTCR H,lJ,eHTHqHbIM BO Bcex nOJIO)l(eHHRX, B TO BpeM5I KaK
.....
JIyq nJIOCKOH pellleTKH llIHpe npH CKaHHpOBaHHH OT HOpMaJIli K paCKpbIBY aHTeH-
HbI. TIOCKOJIbK)' JIyq KOJIbIJ;eBOH pemeTKH cKaHHpyeTcH <l>aKTI1QeCKH nocpe,n:CTBOM
KOMMyrHpoBaHIDI pacnpe,n:eJIeHHH, OH Bcer,n:a <l>opMHPyeTcR pacnpe,n:eJIeHHeM, CHM-
MeTpMQHbIM no <l>a3e H aMIIJIHTy.n.e. B pe3YJIbTaTe nOJIyqaeTcR npeBocxo,n:HaR TOq-
HOCTb HaBe,n:eHHSI JIyqa, He 3aBHCRll.{aR OT H3MeHeHHR qaCTOTbI. HaKOHeIJ;, IJ;HJIHH,J::(-
pHQeCKaR pemeTKa 06eCneQHBaeT OXBaT 360 0 no a3HMYTY 6e3 KaKl1X-JIH60 np06JIeM,
CBH3aHHbIX C nepeKJIIOQeHHeM, 06YCJIOBJIeHHbIM npHMeHeHHeM HeCKOJIbKHX nJIOC-
KI1X perneTOK. B HeKOTopbIX CJIyqaRx npMMeHeHMR 3TH npel1MymecTBa MOryr OKa-
3aTbCR OQeHb Ba)l(HbIMM.
-
I

11.4. CeKmOpHlJle peUJemKU no u,U//unopax t
O,UHaKO ll;JIJIllH,UpllqeCKaH AP llMeeT pH,U He,UOCTaTKOB. ,LLrrH CKaHllpOBaHllH aM-
IIJIllTYL(a, paBHO KaK II Q:>a3a, ,UOJDKHbI rrepeKJIlOqaTbCH no a3HMyry, a rrOJIyqaeMa5.1 B
pe3YJIbTaTe CllCTeMa nllTaHHH 6y,n;eT 60JIee CnO)I(HOH no cpaBHeHHIO C CllcTeMoi1:
IIJIOCKOi1: perneTKH. TeM He MeHee, ynpaBJIeHHe rrpH CKaHHpOBaHllll HllKaKoi1: CJIO)l(-
HOCTll He npe,n;CTaBJIHeT BBHl(y pa3,UeJIHeMOrO aMnJIllT)',n;Ho-<t;>a30Boro pacnpe,Uene-
HllH. OCHOBHOH He,n;OCTaTOK 3aKJIlOqaeTC5.I B TOM, qTO l(HJIHH,[(pHqeCKaH perneTKa He
MO)l(eT <t;>1I3HQeCKH pa3,n;eJIHTbCH, KaK qeTblpe IIJIOCKHe perneTKH. 3TO 03HaQaeT, qTO
l(IIJIIIH,n;p ,n;OJI)I(eH o6eCneQHBaTb 0630p 360°, B TO BpeMH KaK Ka)l(,[(OH IIJIOCKOH pe-
llleTKe Tpe6yeTc5.I BII,n;eTb TOJIbKO ceKTOp 90°. BOJIee Ba)l(HO, qTO l(HJIIIH,[(P He MO)l(eT
M3MeHHTb CBoe nOJIO)l(eHHe B BepTHKaJIbffOH IIJIOCKOCTH ,[(JIH yBeJIHqeHHH 0630pa
u u
no yrJIY MeCTa, qTO HBJIHeTCH pacnpOCTpaHeHHOH npaKTHKOH B CJIyqae IIJIOCKHX
perneTOK. no 3TOH npHQHHe MOXHO paCCMOTpeTb B03MO:>KHOCTb HCnOJIb30BaHM5.I
yceqeHHOrO KOHyca ,l(JIH pacrnHpeHHH 0630pa no yrJIY MeCTa C o,n;HOBpeMeHHbIM
coxpaHeHHeM npeHMyn.(eCTB KpyrOBOH CHMMCTpHH. CpaBHeHHe C IIJIOCKHMH AP,
KOTopbIe MOryr MeXaHHqeCKH H3MeHHTb HaKJIOH anepTYPbI, HBJIHeTCH 60JIee CJIO)l(-
HbIM [66, 28].
11 .4.3. AnnapaTYPHaSi peanM3au.MSI Konbu.eBoM
-
M u.MnMHAPM'IeCKOM peweTOK
npMBe,UeM HeCKOJIbKO npHMepOB 3KcnepHMeHTaJIbHbIX perneTOK. Ha pllC. 11.29
nOKa3aHa KOJIbl(eBa5.1 AP, COCTOHI.IJ:aH 113 128 ceKTOpllaJIbHbIX pynOpOB, rrpeL(Ha3-
:;)\) .'
:t\\
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, .2' 'Y':i
:".: "J-.-- - 
- .1'_.'.- - __
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;;' ' ,- ' /*':,:,;i
if '.
PHC. 11.29. KOJIbu:eBaH perneTKa
,


Ffla8a J 1. KOHtjJopMHbie aHmeHHble pewemKU
-':":.' - "\. '..":" -.
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Puc. 11.30. CKaHMPYIOIUa51 perneTKa Ha OCHOBe IUeJIei1, npope3aHHbIX B Y3KOH
CTeHKe np5lMoyrOJIbHbIX BOJIHOBO,lJ,OB
HaqeHHbIX ,l(JIH 06JIyqeHJlHI KpyrJIOH JIHH3bI H3 rraparrJIeJIbHbIX IIJIaCTHH. .LJ:HaMeTp
KOJIbIJ;a: 26,4A; pynopbI 1/2 x 3/2 x 3A [20,21]. Ha pHC. 11.30 nOKa3aHa ,l(OnJIepOB-
CKaH CKaHHpYIOlI.(aH MHKpOBOJIHOBaR pellIeTKa a3pO,LI;pOMHOH CI1CTeMbI nOCa,lJ,KI1 Ha
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.aaR KOJIOHKa B036)')K,L(aeTCR <pa30BpalUaTeJIeM [38]. .LJ:pyraR KOJ1bIJ;eBaR pellIeTKa
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)l(eH TaKI1M 06pa30M 6bITb < 0,5 Ao.
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llIaXMaTHOM nOp.lIKe CHMMeTpHqHbIM 06pa30M, CeTKa nOBOpaqHBaeTC Ha 45°, KaK
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pM3aUHH E- non IIJ;eJIM B ,aarrbHeH 30He Bcer,aa nepneH,aMKyJIpHa npOeKl(HH
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pOBaHHbIe .IL1IH pa60Tbl B,aOJIb OCH, no,a ,apyrHMH yrnaMM B npOCTpaHCTBe, 6blJI M3-
rOTOBJIeH 6YMa)l(HblH KOHYC C pWJ;OM IIJ;eneH, HapHCOBaHHbIX Ha HeM (pHC. 11.42).
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nepeKpeCTHa nOJIpH3aUH He npe,n:CTaBnIDIa 6bl C060H 60JIbllIYlO np06JIeMY. O,a-
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nOJIO)l(eHHH IIJ;eneH C)'Il.I.eCTBeHHaH ,n:OJIH MOIIJ;HOCTH 6y,n:eT pacxo,n:OBaTbC$I Ha
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C)'Il.I.eCTByeT HeCKOJIbKO cnoc060B, C nOMOIIJ;blO KOTOpbIX H3JIyqaTeJIM, o6ecne-
qHBalOIIJ;He ynpaBJIHeMYIO nOJIHpH3al.(HIO, MOryr YCTaHaBJIHBaTbC Ha KOHyce, HO
nOJIHa CHMMe1'pHH He MoxeT 6bITb coxpaHeHa C MHHHMaJIbHbIM qHCJIOM 3JIeMeH-
TOB HJIH C npOCTbIMH <l>YHKI.J;HHMH ynpaBJIeHHH ,aJUI <l>opMHpoBaHH H ynpaBJIeHHH

J
1
11.5. PewemlCu Ha ICOHYCax U cl/Jepax d
 
_ -::::::3=:::
". :::::5::::
'"L _ 
,  .:- 
:  
'  
...... ..... ;:::::... ...'
.. ".... WJIt
... -
.,
.....",..... !Ittt.'  

--'-:-  -.
-- ...... ....... - .
...-"" ::..,
 _.... -:. ,
 - "'-
 ::: "-
 - -
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-
I
I
I I
, I ,
I I I
I I I I
, I I ,
I I I J
IIIII
I I I J I
I I I I I J
, " II' ,
I I I I
, , I r r ' J
I I I f I I
I I I I J
-\
/-\
1-\
1/-\\
1/_\\
11-\\
 1 /-\ \ 
11/_\\\
/ 1 /-\\1
,1/-\ \\
,1/_\\\
,'/-\ \\
,'/-\\\
'/-\\\
(a)
(b)
(c)
PUC. 11.42. KOHH1JeCKa$I pemeTKa, npe,nHa3HaQeHHa$I .LUISI H3JIyqeHM$I B,nOJIb OCM
nyqoM. CXeMa, ynpOI.I.J;alOI.I.J;aR 3a;J;aQy yrrpaBJIeHliR, npe.n:YCMaTpliBaeT pacnono)l(e-
Hlie I.I.J;eJIeH Ha KOJIbQaX C <pliKClipOBaHHbIM Me)l(3neMeHTHbIM rnarOM no Ka)K):(OMY
KOJIbQY Ii oplieHTaQlieii KaK B.n:OJIb 06pa3YIOI.I.J;liX, TaK Ii BL(OJIb OKp)')KHOCTeH (CM.
pliC. 11.43). PaCCQliTbIBaTbcR L(OJI)I(HbI TonbKO pa;J;l1aJIbHbIe 11 KpyroBbIe KOMnOHeH-
TbI B036y)1(.lJ:eHI1R [71].
Heo6bIQHaR reOMeTpl15.1 KOHyca Tpe6yeT oco6oro yqeTa CI1CTeMbI Koop.n:I1HaT,
I1CrrOJIb3yeMoH .LUIR rrpe.n:CTaBJIeHI1R L(l1arpaMM. DbIno YCTaHOBneHO, QTO B HeKOTO-
pbIX Koop.n:I1HaTHbIX CI1CTeMaX HeB03MO)l(HO COOTBeTCTBYIOlI.{I1M o6pa30M 33):(aTb .n:Be
rnaBHbIe nnOCKOCTI1 nyqa, KOrL(a rrpOI1CXOL(I1T CKaHl1pOBaHl1e B oceBOM HarrpaBne-
.f
+
+
+
++
++
++
++.f
'+-++-+
+++
++++
4-++4-
i--+ + +....
.....+ + + +.r
i-+++-+-,"
+++++
i--++++i-
i-+++-r.r
PHC. 11.43. KOHYC C 3JIeMeHTaMH Ha KOJIbuaX

 Dzaea 11. KOm!JOpMHble aHmeHHble peUJemlCu
HHH [62]. CooTBeTcTBeHHo, 6bIJIa pa3pa60TaHa CneUHaJIbHaSl CHCTeMa Koop,aHHaT,
KOTopaSl CJIe,ayeT 3a rrHKOM JIyqa rrpH ero cKaHHpoBaHHH [62]. fJIaBHOe Tpe60BaHHe
Koop,aI1HaTHOH CI1CTeMbI 3aKJIIOQaeTCSI B TOM, qTO ,aBe <pHKCMpOBaHHbIe IIJIOCKOCTM
v
,aOJDKHbI rrepeceKaTb rJIaBHbIH JIyq ,IJ;HarpaMMbI aHTeHHbI rro,a rrpSlMbIMM yrJIaMM.
3TO Tpe60BaHHe y,aoBJIeTBOpSleTcSI rrepeMeHHoH c<pepHqeCKOM cHcTeMoM C yrJIo-
BbIMI1 Koop,aHHaTaMH <P' M 8'. CHcTeMa pa3MelI(aeTCSI TaKHM o6pa30M, qTo6bI <P' = 0
M 8' = 90° COOTBeTCTBOBaJIH HarrpaBJIeHHIO rJIaBHOrO JIyqa <P = <PI' 8 = 8 1 . 3Ta rrepe-
MeHHaSl CHCTeMa Koop,aHHaT MO)l(eT COOTHOCHTbCSI C <pHKcHpoBaHHoM 06bIQHOM KO-
op,aHHaTHOM cHcTeMoH Qepe3 rrpe06pa30BaHHSI, orrHcaHHbIe B pa60Te [71]. CBSl3b
..
YCTaHaBJIHBaeTCSI COOTHOllIeHHRMH
cos e = cos e' sin e 1 + sin e' cos <P' cos e 1 ,
sine =  sin2 e'sin 2 <p'+(sine' cos<p' sine ( + cose' Cose 1)2 ,
(11.76)
(11.77)
. sin e' sin <p'
SIn <p = . ,
SIne
(11.78)
sin e' cos<p' sin e 1 - cose' cos<p 1
cos<p = .
sine
(11.79)
TpaHc<popMaUMH He3HaQMTeJIbHO BJIMRIOT Ha rrpe,aCTaBJIeHMR ,aMarpaMMbI ,LUISI
rrOrrepeQHbIX HanpaBJIeHHM CKaHHpOBaHHR JIyqa (8(, 6JIM3KOe, 90°), HO rrpM 3TOM
v
OKa3bIBalOT C)'Il.(eCTBeHHoe B03,aeHCTBHe Ha npo,aOJIbHbIX HanpaBJIeHMSlX CKaHMpOBa-
HHSI JIyqa (8 1 , 6JIM3KOe 0°).
Heo6xo,IJ;MMa ,lI,pyraSl TpaHc<popMaUHSI ,lLJISI coxpaHeHMSI nOJISlpM3aUMM TecToBoM
TOqKH, HCnOJIb3yeMoM ,LUISI nocTpoeHHR rpa<pHKoB ,aHarpaMM. nOJISlpH3aUHSI TeCTO-
BOM TOqKM ,IJ;OJDKHa 6bITb <pMKCHpoBaHHoM B ,IJ;eKapTOBoM CMCTeMe Koop,aHHaT <pH3M-
QeCKOrO KOHyca aHTeHHbl. B pa60Te [71] rrOJIyqeHa CBSl3b HOBbIX nOJISlpH3aUMM co
CTapbIMM nOCpe,lI,CTBOM BbIpa)KeHHSI
I _ [a ( cos e cos <p cos e 1 + sin e sin e 1) -[ <p sin <p cos e 1
-a' - sine' ,
(11.80)
[<p' -
[a cos e 1 sin <p + [<p (cos e cos <p cos e 1 + sin e sin e 1)
sin e'
(11.81)
,LLrrSl y,lI,06CTBa HOBbIe Koop,aMHaTbI 6bIJII1 3aHOBO HOpMHpOBaHbI KaK <p = <p' M
8 = 8'-90° TaK, qT06bI rrHK rJIaBHOrO JIyqa Bcer,aa 6bIJI ueHTpOBaH npH <p = 0°, 8 = 0°.
MCXO,lI,R 113 3TMX MO,lI,M<pHKaUI1M CHCTeMbI KOOp,IJ;HHaT 6bIJI paCCqHTaH pSl,lI, ,aMa-
rpaMM ,lLJIR KOH<pMrypaUI1H C KpeCTo06pa3HbIMH meJISlMH, KOTopbIe QaCTHqHO 3a-
nOJIHSlJIH KOH)'C. CxeMa pellIeTKH COCTOSlJIa H3 llIeCTH KOJIeu KpeCTo06pa3HbIX m:e-
JIeM C 24 m:eJISlMM Ha OD:HO KOJIbUO. TIJIeqH KIDK,aOH KpecTo06pa3HoH m:eJIH
B036y;K.IJ:aJIHCb TaKOM aMnJIHT)',aoM H <l>a30ii, qTO B MaKCHM)'Me JIyqa B pe3YJIbTaTe
<l;>opMHpOBaJIaCb JIMHeHHaSl nOJISlpM3aUHSI cooTBeTcTBYIOru:eM opHeHTaUHH. TOJIb-
KO 60JIbllIOH Topeu KOHyca 6bIJI 3anOJIHeH 3JIeMeHTaMH, a 6JIH)I(aHllIee K BepllIMHe
KOJIbl.{O HaXO.lUUIOCb OT Hero B 10 ,lLJIHHaX BOJIHbI. 06m:aSllUlHHa KOHyca COCTaBJIIDIa
12,2Ao, a OCHOBaHMe HMeJIO ,aHaMeTp 4,4 Ao. 3JIeMeHTbI, TaKMM 06pa30M, pa3Mem:e-
HbI TOJIbKO Ha -- 20% paCCTORHHSI OT OCHOBaHHSI KOHyca ,ao BepllIHHbI, a ,aHarpaM-
MbI npe,aCTaBJISlIOT C060R JIMllIb npM6JIIDKeHHOe H306pIDKeHHe ,aHarpaMM nOJIHO-
CTblO nOKpbIToro KOHyca [5, 7, 8].

-,
11.5. PewemKu Ha KOHYCax U apepax 
B paCqeTaX KIDK,il,hIH 3JIeMeHT B3BemMBaJICH no YCRJIeHMIO, KOTopoe OH MMeeT B
HanpaBJIeHMH nHKa .rryqa. DhIJIO YCTaHOBJIeHO, qTO 3TO B3BemHBaHHe ,[(aeT HaHBhIC-
mee COOTHomeHHe CHrHaJIa K myMy, KOr,ll,a pemeTKa pa60TaeT B npMeMHoM pe)l(}lMe.
Ha pHC. 11.44 rrpe,[(cTaBJIeH PM ,lI,l1arpaMM, paCCqHTaHHhIX,l])IH JIyqa, HanpaBJIeHHOrO
Ha 20° OT OCH (8. = 20°). 3TH ,lI,MarpaMMhI npe,ll,CTaBJIHIOT C060H TOJIhKO rJIaBHYIO
KOMnOHeHTY nOJIHpH3aUHH. TIplf HeKOTophIX yrJIax I1MeeTC.H 3HaqHTeJIhHaH KOMno-
HeHTa C nepeKpeCTHOH nOJI.HpH3aUlfeH. AClfMMeTplf.H KOHWleCKOH reoMeT}JHH Mema-
eT npOCTOMY rrpe,ll,CTaBJIeHHIO ,lI,MarpaMM aHTeHHhI, KaK BH,[(HO M3 CJIO)l(HOrO Ha60pa
rpaij)HKoB ,lI,MarpaMM, npe,ll,CTaBJIeHHOrO Ha pMC. 11.44. AaJIee 6hIJIM C,lI,eJIaHhI pacqe-
TbI ,lI,HarpaMM ,lLJUI 3JIeMeHTOB, pacnOJIO)l(eHHbIX B maXMaTHOH KOH<pMrypal(lfM, aHa-
JIOrMqHOH TOH, KOTopaH nOKa3aHa Ha pMC. 11.45. ,LLrrH nepBOHaqaJIbHOrO paCqeTa
npMHMMaJIOCb ,lI,OneHMe, qTO MMeeTCH meCTHa.,L(l(aTb 3JIeMeHTOB Ha KOJIbl(e. TIpM
TaKOM KOJIHQeCTBe 3JIeMeHTOB B KIDK,il,OM KOJIbue Ha KOHyce YMeCTMTCH 10 KOJIel(. Ta-
KHM 06pa30M, B 06ru;eH CJIO)I(HOCTH 160 3JIeMeHTOB «3anOJIHRTII1» 60JIbmOH TOpel(
KOHyca. MaJIbIH TOpel{ KOHyca B 3TOM CJIyqae OCTaBaJICH «nYCTbIM». AMaMeTp OCHO-
BaHHH KOHyca COCTaBJUIJI 4,724A, a ero 06ru;aH ,lI,JIHHa 13,335A. I1HTepBaJI Me)l()];Y
KOJIbuaMM 6bIJI paBeH 0,45Ao ,l])IH npe,ll,OTBparu;eHI1H nOHBJIeHMR ,lI,M<ppaKl(MOHHbIX JIe-
neCTKOB. AeCHTb KOJIeu, TaKHM 06pa30M, nOKpbIBaJIH qeTbIpe HM)l(HMe ,l])IMHbI BOJIHbI
KOHyca. B npO,ll,OJIbHOM HanpaBJIeHMH npOel(HpyeMbIH pa.n:MYC nYCTOH 30HbI 60JIee
....
qeM B ,lI,Ba pa3a npeBbImaJI rrpoeUl1pyeMYIO TOJIru;MHY KOJIbl(a 3anOJIHeHHOM 30HbI.
,[(HarpaMMbI HanpaBJIeHHOCTH rrOnepeqHOrO H3JIyqeHI1H perneTKM ,[(aHHoro Tl1na
6y,ll,yr BnOJIHe rrpMeMJIeMbIMM, nOCKOJIbKY BM,lI,MMaR nOBepXHOCTb pellIeTKM B JII060M
HanpaBJIeHMI1 RBJIHeTCH rrpM6JII1311TeJIbHO npRMoyrOJIbHOH. KpOMe Toro, 60JIbmlfH-
CTBO ru;eJIeH «BH,[(HbI» no,ll, 6JIarOnpMHTHbIMM yrJIaMM OTHOCMTeJIhHO <popMMpyeMoH
IIOJIRpH3al(MH. O,aHaKO nOHBJIReTCR 3aMeTHoe pa3JIMQMe B 3HaqeHMRX lllMpMHbI JIyqa
,lI,JISI )];BYX rJIaBHbIX nJIOCKOCTeH, KaK BM,aHO 113 pMC. 11.44. DhIJIO BhIHBJIeHO Tpl1
IIPMqMHbI 3Toro pa3JIMqMSI.
1. B3BelliMBaHMe B036}')K,lJ:eHMSI 3JIeMeHTOB MMeeT TeH,[(eHl(MIO «BbIKJIIOQaTb»
3JIeMeHTbI, paCCMaTpHBaeMbIe no)]; He6JIarOnpM.HTHbIM yrJIOM. meJIH B ,aBYX
30Hax KOJIbl(a B036}')K,lJ:aIOTCSI npH 3HaQMTeJIbHO MeHbllIeM ypOBHe. 3TO HHoe
B036}')K,lJ:eHHe MMeeT TeH,[(eHUHIO C03,[(aBaTb 3<p<peKT I1HTep<pepoMeTpa B 0,[(-
HOH rJIaBHOH IIJIOCKOCTM, B TO BpeMH KaK 3<p<peKTI1BHaH llIHpl1Ha nOJIe3HOrO
paCKpbIBa B ,[(pyrOH TIJIOCKOCTM YMeHhllIaeTCH ,ao 3HaqeHHH MeHbllIero, qeM
....
nOJIHbIH ,aHaMeTp OCHOBaHHH.
2. feoMeTpMH KOHyca TaKOBa, qTO Kor.n:a ru;eJIH opMeHTHpOBaHbI B nOJIO)l(eHMM
,lI,JISI OIITHMM3aUMM rrOJISlpM3aUMM CMrHaJIa B;::r;OJIb OCM, OHM He HBJISIIOTCR on-
TMMaJIbHbIMM npM JII060M ,lI,pyrOM yrJIe. B rrpOl(eCce paCqeTa ,aMarpaMMbI He-
06XO,aMMO 3a<pMKCMpOBaTh nOJIRpM3al(MM I..UeJIeH TaKMM 06pa30M, qT06bI Ha
nMKe JIyqa He 6bIJIO KOMnOHeHTbI C nepeKpeCTHOM rrOJIRpM3al(MeH. TIpM .n:py-
rMX yrJIax B 3TY KOMnOHeHTY 6y;::r;eT rrepeKaqMBaTbCH 60JIbllIe I1JIH MeHbllIe
3HeprMM B 3aBMCMMOCTM OT KpyrM3HbI KOHyca M HanpaBJIeHM.H JIyqa. 3TH ,lI,Ba
<paKTopa CBR3aHbI C 6bICTpbIM H3MeHeHHeM yrJIa nOJUlpH3aUHM ,lI,HarpaMMbI
HanpaBJIeHHOCTI1 M3JIyqeHMR IUeJIH npM Ha6JIIO,[(eHMM C HanpaBJIeHHR, 6JIH3-
Koro K Cna.,L(aM ,aMarpaMMbI ,lI,JIH OCHOBHoro JIyqa.
3. DOJIbllIaR nYCTaH 30Ha B ueHTpe «pa60Qero» KOJIbua B CHOCTH HBJIHeTCH
3aTeHeHHeM paCKpbIBa, cnoc06cTByro:W;MM TaIOKe 3<p<peKTY HHTep<pepoMeTpa,
ycyry6JIIDI nepBbIe ,aBe npl1qMHhI.

 rAa6a 11. KOHfjJOpMHble aHmeHHble peUJemKU
'.
J
IJ = O.
---
",,- ..... ,
I ,
I 
,
I I )
-.
() ZI! _5 D
filii"'"
-'"

...
(J = +5 0
CYMMapHa
- .IJ;HarpaMMa
I
, I
, I
,
"
...
- - A3HMYTaJIhHa
pa3HOCTHaH
.IJ;HarpaMMa
-.
j:.Q
t::r
--
,.Q

u
o
:z::
S
o


::I:
,.Q
r:::
C1)

=
u
o
':Z::
<5
fJ = -10 0
IJ = +10 0
, ,
, I
, I
o = -15 0
6 ::: + 15°
,
,
--
o
IJ == -20 0
-40
"",....
--.....
'-
iJ = -20.
-20
,
I
I
I
%40 0
:t 20°
O.
:t20°
t:40°
..
t/J
PHC. 11.44. ,lJ;HarpaMMbI aHTeHHbI, onTHMM3MpOBaHHble ,lLJUI e == 20°

11.5. PewemKu Ha KOHYCax U crjJepax \
o
,
I
,\,
"
---+
...
 -10
E-<
0_
O
:I: I::!
s--
OQ)
=
c::::I:
  *20

t:::
Q)
E-<t::::

00
:I::I:
5
-30
/
I
-40
-too --600
....,,.-
\
I
_30 0
0 0
)00
61)0
9fI'
8' (rpa,n;.)
PUC. 11.45. ,LJ;HarpaMMbI ,lI;JHI perneTKH 3J1eMeHTOB C rnaXMaTHbIM pacnOJlO)l{eHHeM.
11.5. 1.3. npoeKLlHOHHblM CHHTe3
l'I3-3a B03,l(eMCTBI1M KOHl1qeCKOM nOBepXHOCTM Ha ,l(MarpaMMbI 3JIeMeHTOB MeTO,l(
np}lMOrO CMHTe3a }lBJI}leTC Hel(eJIeco06pa3HbIM. TIpl1 113yqeHI1M ,l(enOJI}lpM3al(HH B
pa3,l(eJIe 11.5.1.2 I1CnOJIb30BaJIC}I npOeKl(110HHbIM MeTO,l(. 3TOT MeTO,l( npe,l(CTaBJI}I-
eTC}I nOJIe3HbIM B CJIyqae CHHTe3a KOHHqeCKOM peII1eTKM. BHpTYaJIbHa}l TIJIOCKa}l
perneTKa C )l(eJIaeMbIM pa3MepOM H y6bIBaHM}lMM aMnJIHTY,l(bI nOMemaeTCH nepneH-
,l(HKyJI}lpHO K )l(eJIaeMOMY JIyqy KOHMqeCKOM perneTKM. 3aTeM JIHHeMHO nOJI}lpH30-
u 
BaHHbIH 3JIeMeHT TIJIOCKOH perneTKM npOel(MpyeTc}I Ha KOHHqecKyIO nOBepXHOCTb,
BKJIIOqa}l TpaHc<popMal(HIO nOJI}lpM3al(HH, aMnJIHTY,l(bI M <pa3bI [73, 8]. Pe3YJIbTaT
npOeK..UHOHHOro CHHTe3a MO)l(eT npM He06xo,l(MMOCTH 6bITb YJIyqrneH nOCpe,l(CTBOM
 u
HTepal(HOHHOro MeTO,l(a, KOTOpbIH BKJIlOqaeT TOqHbIH paCqeT ,l(MarpaMM 3JIeMeHTOB
Ha KOHyce. 3TM paCqeTbI BKpaTl(e paCCMaTpHBaIOTC}I B pa3,l(eJIe 11.5.1.4. ,LJ;JI}I nOBbI-
rneHH}I 3<P<t>eKTMBHOCTM perneTKM ,l(HarpaMMbI 3JIeMeHTOB MOryT 6bITb pacrnMpeHbI,
HCnOJIb3Y}l ,l(H3JIeKTpl1qeCKMe HarpY3KM [126, 127].
DbIJIM M3yqeHbI 3<p<peKTbI KBaHTOBaHMH l(M<PPOBbIX <pa30BpamaTeJIeM H l(M<PPO-
BbIX BpamaTeJIei1 rrJIOCKOCTM rrOJI}lpM3al(MM [8]. Pe3YJIbTaTbI aHaJIOrMqHbI TeM, KOTO-
pbIe 6bIJIM rrOJIyqeHbI ,[(JI}I IIJIOCKMX peII1eTOK C <pa30Bpam;aTeJIHMH. QeTbIpex6MTO-
BbIe Bpam:aTeJIM IIJIOCKOCTM rrOJUIpM3aUMH HBJI}lIOTC}I an;eKBaTHbIMH, eCJIH HeT
He06xo,l(MMOCTH B OqeHb HM3KMX YPOBHHX nepeKpeCTHOH nOJIHpM3aUHH MJIM 3Haqe-
HH}lX rJIy6HHbI npOBaJIa pa3HOCTHOM ,l(HarpaMMbI HanpaBJIeHHOCTH.
11.5. 1.4. p,HarpaMMbl HanpasneHHOCTH H S3aHMHafl CSfl3b
KaK H B c.rryqae perneTOK 3JIeMeHTOB Ha UMJIMH,l(pe, perneTKM 3JIeMeHTOB Ha KOHyce
MOryT rrO,l(BepraTbC}I aHaJIH3Y nOCpe,l(CTBOM MeTO,l(a rapMOHMqeCKOrO pH.I1a MJIM
 
aCHMnTOTHqeCKOrO MeTO,l(a, npH 3TOM nOCJIe,l(HMM rrpe,l(Ha3HaqaeTCH ,l])UI qaCTeM KO-
Hyca, r,l(e pa..n;HYC HBJIHeTCH 60JIbII1HM no OTHOII1eHHIO K ,[(JIMHe BOJIHbI. llepBhIe pa-
60ThI no pacqeTY 6JIJDKHHX rrOJIeH m;eJIeH Ha KOHycax 6hIJIM BhInOJIHeHhI B [2];

 rAa8a 11. KOHqmpMHble aHmeHH/lle peUlemlCU
pR,LI;bI BKJIIOqalOT npMcOe,LI;MHeHHbIe <l>YHKUMM JIe)l(aH,LI;pa M c<l>epMqeCKHe <l>YHKUMM
EeCCeJIR. 3HaqMTeJIbHbIe YCMJIHR 6bIJIM nOTpaqeHbI Ha 3TH paCqeTbI, nOCKOJIbKY OHM
u
nOJIe3HbI C TOqKH 3peHHR nOCTpOeHHR ,LJ;MarpaMM M M3yqeHMR B3aMMHOH npOBO,LJ;M-
MOCTM [93, 95]. QMTaTeJIR, B03MO)l(HO, TaIOKe 3aHHTepecyeT pa60Ta no aCHMnTOTH-
qeCKHM aHaJIM3aM 3JIeMeHTOB Ha KOHycax [94, 25]. B [29] MCnOJIb3yeTcR naKeT npo-
rpaMM BbIqHCJIMTeJIbHOll aJIre6pbI ,WIR paCqeTa HYJIett rapMOHMqeCKHX <l>YHKl(I[H.
11.5. 1.5. 3KcnepHMeHTbi C KOHHlfeCKHMH peweTKaMH
BblnOJIHeHbI 3KcnepMMeHTbI C pemeTKaMM Ha KOH)'cax, BKJIlOqaR 60JIbllI}'lO [87] H
MaJIeHbKYIO perneTKM [118]. B nepBMqHbIX 3KcnepMMeHTax MCn0J1b30BaJIaCb JIMHett-
HaR AP B,n:OJ1b o6pa3YIOIUett [9]. TIoCJ1e 3Toro 6bIJIa CKOHCTpYMpOBaHa H no,n:po6HO
McnbITaHa 3KcnepMMeHTaJIbHaR pemeTKa C HCn0J1b30BaHMeM KpecToo6pa3HbIx meJIeii
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liam Gabriel, Boris Sheleg, Ph.D Wolfgang Kummer H Dean Paschen.
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eT MeHbllIHH HHTepec, B OTJIHqHe OT Q;>OPMbI.
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ll{HXCR IIHKOB, 6e3 OCna6JIeHHR KITH KpaeBbIX 3Q;>Q;>eKTOB. npH CKaHHpOBaHHH Ha
30° Ka)l(,lJ;aR qeTBepTaR CeH.H A/2 npOBO,l(a MMeeT He6oJIbllIOH TOK. IIHKH Terrepb
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1-6, 6-12, ..., 234-239, I1MelOT npl16JIH3HTeJIbHO CHHYCOl1.L(aJIbHOe pacnpe.n;eJIeHHe,
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peaKTMBHOrO conpOTMBneHMR
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no B03MOXHOH TpaHCKOHTHHeHTaJIbHYIO Tene<l>oHHIO, H OHH IIIHpOKO Hcrronb30Ba-
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THQeCKOe He<l>ocTepcKoe COrJIaCOBaHHe aHTeHHoro I1Mrre,aaHca 6bIJIO HaQaTO B [21].
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rneTKY 6bIJIO npe,lLJIO)KeHO 11 113yqeHo B [11, 13]. TaKl1e CBH311 coxpaHHIOT pa60To-
cnoc06HoCTb CBH3aHHOM perneTKI1 Ha cpe,aHeH H HIDKHeM QaCTOTe, a TaIOKe BOCCTa-
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rrOKa3aHa 3aBMCMMOCTb SEP (K03<1><I>HU;HeHTa YCI1JIeHI1H 3neMeHTa) ,aJIH perneTKM
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nJIOcK)'JO pemeTKY napaJIJIeJIbHbIX Il.(eJIeH. Ka)l(,I(aH meJIb B036y)1(,[(aeTCR pelIleTKOH
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 rl1060 12. C6J/30HHble peUJemKU
JlHTepaTYP3
1. Baum, C. E., «Some Characteristics of Planar Distributed Sources for Radiating Transient
Pulses», Sensor and Simulation Note 100, AF Weapons Lab., March 1970, pp. 1-31.
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Baum, C. E., Carin, L., and Stone, A. P., Eds., Plenum Press, 1997.
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7. Hansen, R. C., «Finite Array Scan Impedance Gibbsian Models», Radio Sci., Vol. 31,
Nov.-Dec. 1996b, pp. 1631-1637.
8. Hansen, R. C., «Anomalous Edge Effects in Finite Arrays», Trans. IEEE, Vol. AP-47,
Mar. 1999, pp. 549-554.
9. Hansen, R. C., «Effects of a High-Impedance Screen on a Dipole Antenna», IEEE
AWPL,Vol. 1,2002, pp. 46-49.
10.Hansen, R. C., «Current Induced on aWire: Implications for Connected Arrays», IEEE
Antennas Wireless Propagation Lett., Vol. 2, 2003a, pp. 288-289.
11. Hansen, R. C., «Wideband Dipole Arrays Using Non-Foster Coupling», Microw. Opt.
Tech. Lett., Vol. 38, 20 Sept. 2003b, pp. 453-455.
12. Hansen, R. C., «Linear Connected Arrays», IEEE Antennas Wireless Propagation Lett.,
Vol. 3, 2004a, pp. 154-156.
13. Hansen, R. C., «Non-Foster and Connected Planar Arrays», Radio Sci., Vol. 29, 24 July
2004b, pp. 30-43.
14. Hansen, R. C. and Gammon, D., «Standing Waves in Scan Impedance of Finite Scanned
Arrays», Microw. Opt. Tech. Lett., Vol. 8, Mar. 1995, pp. 175-179.
15. Hansen, R. C. and Gammon, D., «A Gibbsian Model for Finite Scanned Arrays», Trans.
IEEE, Vol. AP-44, Feb. 1996, pp. 243-248.
16. Inagaki, N. et aI., <<Ichimatsu Moyou Antenna-Self-Complementary Antenna with Perio-
dic Feeding Points», Electronics Commun. Jpn., Vol. 62-B, 1979, pp. 52-60.
17. Lee, J. J. et aI., «Compact LightWeight UHF Arrays Using Long Slot Apertures», Trans.
IEEE, Vol. AP-54, July 2006, pp. 2009-2015.
18. McGrath, D. T. and Baum, C. E., «Scanning and Impedance Properties of TEM Horn
Arrays for Transient Radiation», Trans. IEEE, Vol. AP-47, Mar. 1999, pp. 469-473.
19. Munk, B. A., Frequency Selective Surfaces-Theory and Design, Wiley, 2000, Section
6.4.
20. Mushiake, Y., Self-Complementary Antennas-Principle of Self-Complementarity for
Constant Impedance, Springer-Verlag, 1996.
21. Poggio, A. J. and Mayes, P. E., «Bandwidth Extension for Dipole Antennas by Conjugate
Reactance Loading», Trans. IEEE, Vol. AP-19, July 1971, pp. 544-547.
22. Neto, A. and Lee, J. J., «'Infinite Bandwidth' Long Slot Array Antenna», IEEE Antennas
Wireless Propagation Lett. Vol. 4, 2005, pp. 75-78.
23. Neto, A. and Lee, J. J., «Ultrawide-Band Properties of Long Slot Arrays», Trans. IEEE,
Vol. AP-54, Feb. 2006, pp. 534-543.
24. Skahill, G., Rudish, R. M., and Piero, J., «Electrically Small, Efficient, Wide- Band,
Low-Noise Antenna Elements», Proc. 1998, Antenna Applications Symp., Allerton, IL,
pp. 214-231.
--.

rllABA 13
OTPA>KA TElIbHblE
H nEPEH3I1Y'-lAIOHE
AHTEHHblE PEWETKH
OTpa)l(aTeJIbHbIe pemeTKH HHor,[{a HBJIHIOTCH 3aMeHOH cpa3HpOBaHHbIX pemeTOK H
MaJIbIX 3epKaJIbHbIX aHTeHH; OHH 06eCneqHBalOT 60JIee KOMnaKTHbIe ra6apHTbI H
60JIee npOCTYID cxeMY B036y)1()];eHHH. B HaCTOHlI(eH rJIaBe ,[{aeTCH KpaTKHll 0630p
OTpa)l(aTeJIbHbIX aHTeHHbIX pemeTOK (AP); 60JIee no,np06HbIe ,naHHbIe MO)KHO Hall-
TI1 y [31,4]. B nOCJIe,[{Hee BpeMH I1HTepec CTaJIH npe,nCTaBJIHTb nepeH3JIyqalOmHe
AP - KaK naCCHBHbIe, TaK H aKTHBHbIe; OHH TaIOKe 3,neCb paCCMaTpHBaIOTCSI.
13. 1. OTpa>KaTenbHble aHTeHHbie peweTKM
13.1.1. I,1CTOPMSI OTpa)l(aTenbHblx aHTeHHblX peweToK
OTpa)l(aTeJIbHa.H pemeTKa 6bIJIa 11306peTeHa MaJIeXOM H ,[{p. [46, 47], XOTSI paHee B
naTeHTe 0 JIHH30BbIX pemeTKax BKpaTue ynoMHHaeTCH OTpIDKaTeJIbHaH pemeTKa
[36]. TIepBaSl OTpa)l(aTeJIbHa.H pemeTKa COCTOHJIa H3 nJIOTHO ynaKoBaHHoll nJIOCKOll
u
pemeTKH, COCTOSlmel1 H3 BOJIHOBO,lJ,OB C OTKpbITbIMH KOHQaMH, nHTaeMbIX pynopoM,
pacnOJIO)l(eHHbIM nepe,n; BOJIHOBO,n;HOH pemeTKoH. KIDK,l.(bIll BOJIHOBO,[{ 6bIJI 3aKOpo-
qeH, a ,lLJIHHa BOJIHOBO,lJ,a BbI6HpaJIaCb TaK, qT06bI KOMneHCHpOBaTb nyrb OT 06JIyqa-
TeJIH ,[{O BOJIHOBo,[{a; OTpIDKeHHaR BOJIHa 6y,neT ITJIOCKOll. Ha pHC. 13.1 nOKa3aHa
o,n;Ha H3 TaKHX 3KcnepHMeHTaJIbHbIX OTpIDKaTeJIbHbIX AP. CJIe,nYlOmHll mar npOH30-
meJI B HaqaJIe 70-x ro,n;OB 20-ro BeKa C H306peTeHHeM cnHpacpa3HbIx OTpIDKaTeJIb-
HbIX pemeTOK. I1ccJIe,[{oBaHHH <l>HJIaHa onHcaHbI B cepHH pa60T H3 qeTbIpex qaCTell,
ony6JIHKOBaHHbIx B Microwave Journal [54], B KOTOpbIX pemeTKa BOJIHOBO,[{OB 3aMe-
HeHa pemeTKoll H3 CnMpaJIbHbIX aHTeHH C qeTbIpbMH nJIeqaMH. 3a CqeT KOHTpOJIH
TOqeK B036y)1()];eHHSI rrocpe,n;CTBOM ,n;HO,nOB MO)l(HO H3MeHHTb <l>a3Y OTpa)l(eHHOrO
nOJIH. 3TOll CHCTeMe CBOllCTBeHHa mHpOKaJI nOJIOca, HO pa60qHe xapaKTepHCTHKH
,[{l1o,[{a OrpaHI1QHBalOT B03MO)l(HOCTI1. CKaQOK OT BOJIHOBO,[{OB K nOJIOCKOBbIM H3JIy-
QaTeJI.HM 6bIJI COBepmeH B 1977 ro,n;y B pa60Te [45], B KOTOpOll ynpaBJIeHHe <l>a3aMH
u u
oTpaeHHR 113JIyqaTeJIel1 npOHcxo,n;HJIO 3a CqeT ,n;HO,n;OB Ha KpaHX H3JIyqaTeJIeH; ,[{HO-
,n;bI 06eCneQHBaJIH B03MO)KHOCTb 3JIeKTpOHHoro CKaHHpOBaHHH.
3Ta pa60Ta 6bIJIa npOl(OJI)I(eHa B [52]. CJIe,nYIDII(Hll mar 6bIJI c,[{eJIaH B 1987 ro-
,[{y, - pa60Ta [53], B KOTOpOll pa3pa6oTaHa OTpIDKaTeJIbHaH pemeTKa neqaTHbIX
u u
3JIeMeHTOB, B KOTOpOH Ka)l{,lJ:bIH 3JIeMeHT HMeJI yKopOqeHHYID JIHHHIO nHTaHIDI, npH
3TOM 3HaqeHH.H ,lLJIHHbI JIHHHH nHTaHHH peryJIHpOBaJIHCb ,lLJIH KOJIJIHMaUHH nepeM3-
JIyqeHHoro JIyqa. Pa60Ta HaD: OTpIDKaTeJIbHbIMH pemeTKaMH rrpo,[{OJDKaJIaCb ,[{O cepe-
,[{HHbI 90-x rO,[{OB. HaH60JIee nOJIe3HbIe H3 3THX pa60T paCCMaTpMBalOTCH B nOCJIe-
,[{YIDmHX pa3,[{eJIax.

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Puc. 13.1. BOJIHOBo.aHaSl OTpa)l(aTeJIhHaSl pernCTKa
13. 1.2. reOMeTpM"ieCKMe COOTHoweHMSI
.
,[(JIH ITJIOCKOM OTpa)l(aTenbHoi1 pemeTKH C yrJIOM paCKpbIBa 06JIyqaTenH 28 0 OTHO-
rneHHe flD if - <t>OKyC, D -,nHaMeTp pemeTKH) COCTaBnHeT
f / D = 0,5 . ( 13.1 )
tan8 0
06JIyqaTeIDIMM 06bJtIHO HBIDIIOTCH pynOpbI, M J(HarpaMMa HanpaBJIeHHOCTH no Ha-
npIDKeHHOCTIf 3JIeIcrpWlecKoro nOIDI annpOKcHMHpyeTcH nocpe,nCTBOM <l>YHKUHH cos n 8.
3<t><I>eKTHBHOCTb 06JIyqaTeJIH (spillover efficiency), T.e. 6eCnOJIe3HaH nOTepH MOlll.HO-
CTM 06JIyqaTenH, He nepeXBaTbIBaeMaH 3epKaJIOM, BbIpa)l(aeTCH cne,nYJOlll.HM 06pa30M:
lls = 1 - cos2 n+ I 8 0 , ( 13.2)
AnepTYPHa51 3<t><t>eKTHBHOCTb (aperture taper efficiency), 06ycnOBJIeHHaH cna,aa-
HMeM nonH K Kpa5lM paCKpbIBa, COCTaBJIHeT [59]:
111 = 4n[1- cos n - 1 8 0 ]2 . (13.3)
(n -1)2 tan 2 8 0 [1 - cos2n 8 0 ]
HaKoHeu, 06lll.aH 3<t><t>eKTHBHoCTb COCTaBJIHeT
11 = 11 s '11 t. ( 13.4 )
Ha pHC. 13.2 nOKa3aHa 3aBHCHMOCTb OT flD 06lll.eM 3<l><l>eKTHBHOCTH 11 H nOKa3a-
TeJIH N annpoKcHMHpyeMoM ,nHarpaMMbI HanpaBJIeHHOCTH 06JIyqaTeJIH. OqeBH.aHO,
qTO,llJIH IlIHpOKoro llHana30HaflD, OT 0,5 llO 1,5, 3<t><t>eKTHBHOCTb H3MeH5IeTCH Bcero
JIHmb He3HaQHTenbHO, OT 0,78 ,no 0,81. 3TO n03BOIDIeT KOHCTPYKTOPy OTpIDKaTeJIb-
HOM AP BbI6HpaTbflD Ha OCHOBe ,nHarpaMMbI HanpaBJIeHHOCTH 06JIyqaTeJIH (cos n 8 0 )
Ii KOHCTPYKTHBHbIX y,n06CTB. BepoHTHo, He60nbllIoe flD H HH3Koe 3HaqeHHe 11 HBJUI-
IOTC5I Haw.rryqmHM BbI60pOM.

13.1. Ompa:JICame.nbHble aHmeHHble peUJemKU d
0.9
22
20
18
16
14
1]
17 0.8 12
N
10
N
8
6
4
0.7
0.5
0.7
0.9
1.1
1.3
2
1.5
flD
PHC. 13.2. 3<l><peKTMBHoCTb Ii nOKa3aTenb JJ:MarpaMMbI HanpaBJIeHHOCTM o6nyqaTenH
13. 1.3. 3neMeHTbi OTpa>KaTenbHblX peweTOK
nepBOHaqaJIbHO 3JIeMeHTaMI1 OTpa)l(aTeJIbHOH AP, KOHeqHO, 6bIJIM BOJIHOBOllbI C
OTKpbITbIMI1 KOHl(aMI1. I1x, B OCHOBHOM, BbITeCHHJIH neqaTHbIe 3JIeMeHTbI. PaHee
MR qaCTOTHO-CeJIeKTHBHbIX CTPYKTYP (Frequency Selective Surface - FSS) 6bIJIH
pa3pa60TaHbI KOHueHTpMqeCKHe KpyroBbIe KOJIbQeBble 3JIeMeHTbI [33]. nOTpe60Ba-
JIOCb MHoro JIeT LIJIR Toro, QT06bI KOJIbueBbIe 3JIeMeHTbI nepellIJIl1 Ha ypOBeHb OTpa-
)l(aTeJIbHbIX AP. B pa60Tax [13, 14] HCn0J1b3YIOTCR Ll:BOHHbIe KpyroBbIe KOJIbl(eBbIe
v
3JIeMeHTbI H Ll:BOMHbIe CKpemeHHble paMKH; TaIOKe HCnOJIb3YlOTCR neqaTHble nOJIOC-
KOBble Ll:HnOJIH [10]. n0J10CKOBbIe H3JIyqaTeJIH If nOJIOCKOBble Ll:HnOJIH KOM6HHHPY-
IOTCR B [63] ,lI)IR 06eCneQeHI1R Ll:Byxn0J10CHOH pa60TbI.
13. 1.4. Cba3MpoBaHMe 3neMeHTOB
npRMOH cnoc06 <pa3HpOBaHI1R OTpa)l(aTeJIbHOH perneTKH C neqaTHbIMI1 3JIeMeHTaMI1
HaqHHaeTCR C paCqeTa H36bITOqHOH ,lI,J1HHbI nyrH Kpa:HHerO 3JIeMeHTa no cpaBHe-
HHIO C 3JIeMeHTOM Ha paCCTORHHH r. KpaHHHH H3JIyqaTeJIb 6y,neT HMeTb OIlUHY IlU-
HUU nUmaHUJI = 0; a l(eHTpaJIbHbIM - MHHY JIHHHH nHTaHHR
1 / 2[ -J D2 / 4 + 1 2 - I],
(13.5)

 Dla8a 13. OmpaJICameJlbl/ble u nepeU3JlJ1'f.aIOUI,ue al/mel/I/ble peUJemKU
B TO BpeMH KaK 3JIeMeHT Ha paCCTOHHI1M r OT u;eHTpa OTpa)l{aTeJIbHOM perneTKH Tpe-
6yeT ,l(JII1HY JIMHMM nMTaHMH
1 / 2[ .J r 2 + 1 2 - I].
( 13.6)
I,
MHO)I(HTeJIb 1/2 nOHBIDIeTCH B CJIyqae KOpoTKo3aMKHyroM JIHHHM nepe.aaqH.
npM npocTeMrneM BapMaHTe I1CnOJIHeHHH Bce 3HaqeHHH ,l(JIMHbI JIMHHM nMTaHM5I
YMeHbrnaIOTC$I Ha KpaTHbIe 3HaqeHMH A .ao Tex nop, nOKa ,l(JIMHa JIMHHI1 He 6y.aeT
< A. 3Ta <l>a3MpoBKa .aaeT rnMpMHY nOJIOCbI nponYCKaHMH (BW), KaK nOKa3aHO Ha
pHC. 13.3.
50
10
OJ)" = 25
40
30
-
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CD
20
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0.7
0.9
1.1
1.3
1.5
lID
Pac. 13.3. lllHpHHa nOJIOCbI npH HCnOJIb30BaHHH c,aBHra no cpa3e
Ha pHC. 13.4 M306pa)l{eHa neqaTHaH OTpaXaTeJIbHa$l perneTKa, <l>a3MpoBaHHaH
nocpe.aCTBOM 3aKOpaQMBaHMH JIMHI1H nMTaHMH. C nOMOIIlblO BToporo npMeMa OTpa-
)l{aTeJIbHaH perneTKa <l>a3MpyeTcH Bpam;eHMeM M3JIyqaTeJIeH aHaJIOrMqHO cnMpa<l>a3-
HOM oTpaXaTeJIbHOH perneTKe [32, 11]. Ha pMC. 13.5 M306paxeH 3TOT npMMep.
TIpl1 TpeTbeM nOL{Xo.ae MCnOJIb3yeTcH pa3Mep neqaTHOrO 3JIeMeHTa ,lUI$I M3MeHe-
HM$I <l>a3bI [23]. 3.lIeCb 3JIeMeHTbI He MMelOT JIMHMH nMTaHMH; <l>a3a nOIDI OTpaxeHHOH
BOJIHbI CBH3aHa C pa3MepOM 3JIeMeHTa. OTpIDKaTeJIbHaH perneTKa C nepeMeHHbIM pa3-
MepOM 3JIeMeHTa M306pIDKeHa Ha pMC. 13.6. 3aBMcMMoCTb <l>a3bI OT pa3Mepa 3JIeMeHTa
npe.aCTaBJIeHa B [57]. AHaJIH3 6eCKOHeqHOH oTpaXaTeJIbHOH perneTKH H3 neQaTHbIX
3JIeMeHTOB, MCnOJIb3yIOIIlMH M.aelO e,lU1HMQHOH HQeHKM <l>JIOKe, npOBe.aeH B [69]; xa-
paKTepHCTMKH <l>a3bI 6bIJIM H3yqeHbI B [5]. B HOBOM TeXHMqeCKOM npMeMe MCnOJIb3Y-
IOTC.H M3.rryqaTeJII1 paBHoro pa3Mepa, r.ae KIDK,lJ,bIH M3.rryqaTeJIb 06JIyqaeTC5I m;eJIblO B
3KpaHe [12]; M3MeHeHMe 3HaqeHMH ,lUIMHbI llI.eJIH M3MeH.HeT <l>a3Y CBH3H.
--.

13.1. Ompa:»cameJ/bHble aHmeHHble pewemKU t
DO.
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Pac. 13.5. <I>a3HpoBaHHe, HCrrOJlb3YIOII(ee BpalI(eHHe (rroBopoT) 3J1eMeHTa

 Dza8a 13. OmpaJICameJ/bHble U nepeU3Jl)l'1.aIOUI,ue aHmeHHble peUJemKU
DD
DDDD
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DDDDDD
DDDD
DD
PHC. 13.6. <l>a3MpoBaHMe, MCnOJIb3YlOIUee pa3Mep M3JIYQalOIUerO 3JIeMeHTa
ECJIM 1III1pl1Ha nonOCbI pl1C. 13.3 He 60nbllle 111l1pl1HbI nonOCbI 3JIeMeHTa, Cne.l(yeT
MCnOJIb30BaTb BpeMeHH)'JO 3anep)l(KY. TIpl1 3TOM K(l)I(,l(bIH neqaTHbIH 3JIeMeHT I1MeeT
u u u
YKopOqeHHYIO nl1Hl11O nlfTaHI1H .l(JII1HOlf, paBHOlf nOJIOBlfHe, onpeJIellileMOlf ypaBHe-
Hl1eM (13.6). 3TO ypaBHeHMe 06eCneqlfBaeT KOJIJIMMaUlflO nyqa He3aBI1CMMO OT qac-
TOTbI. KpoCC-nOJIHpI13aUlfH MO)l(eT 6bITb 3HaQMTenbHO YMeHbllleHa 3a CQeT ClfMMeT-
pMqHOrO pa3MemeHIDI nl1HMH nlfTaHMR M KOpoTK03aMbIKaTeneH [16]. TIonRpl13aUlfR
MO)l(eT 6bITb lf3MeHeHa nOCpeJICTBOM BpameHlfR 06JIyqaTeJIR pellleTKI1 [73].
13. 1.5. WMpMHa nonOCbl
,[(Ba <paKTopa BJIlfRIOT Ha llllfPMHY nOJIOCbI nponYCKaHMR (BW) OTpa)l(aTenbHoH pe-
llIeTKI1: 111l1plfHa nOJIOCbI nponYCKaHMH 3J1eMeHTa 11 .l(JIlfHa nyrlf. B CJIyqae llJIOCKOll
OlpaJKaTeJIbHOH pellleTKlf .LJ.JII1Ha nyrM OT <l>a30Boro ueHTpa JIO K(l)I(,l(OrO 3JIeMeHTa lf3-
MeHReTCR (,l])IR M3JIyqeHMR B HanpaBneHlfl1, HOpMaJIbHOM K pacKpbIBY). OllIM6Ka <l>a-
3bI COCTaBJIReT (k - ko)(R - 1), fJIe k - BOJIHOBOe QlfCJIO. ECJIM JIOrryCTlfTb 01lllf6KY
<l>a3bI jt KaK Ha BepXHell, TaK If Ha HlDKHeH qaCTOTax, TO nOJIyqlfM [56]:
1t = (k - ko)(r - 1) = (k o - kl)(r - 1).
3JIeCb r =  D2 / 4 + /2 . Tor,na IlIlfpl1Ha nOJIOCbI nponycKaHlfH paBHa:
BW = 1 .
D [ .J f2 / D2 + 1 / 4 - f / D]
A
( 13. 7)
( 13.8)
--

13.1. Ompa:JICameJlbHble aHmeHHble peUlemKU d
Ha pHC. 13.3 rrOKa3aHa 3Q6UCUMOcmb lUUPUltbl nOJlOCbl nponYCKQltUR OT flD ,l])UI
D/A = 25, 50 H 100. HanpHMep, npHflD = 0,5 WIH D/A = 25 IIIHpHHa nonOCbI COCTaB-
MeT 19%. OqeBH.II:HO, qTO B 60nbIIIHHCTBe cnyqaeB 3TO 60nbllIe IIIHpHHbI nonOCbI
nponYCKaHHH neqaTHOrO 3neMeHTa. EonbIIIHe 01pa)KaTenbHbIe peIIIeTKM (60nb-
1lI0e D/A) MOryr He 06eCneqHBaTb ,nOCTaTOqH)'IO IIIHPHHY nonOCbI npH HC-
nonb30BaHHH <t>a30Boro ynpaBneHIDI; npOCToe peIIIeHHe 3aKJIIOqaeTCH B TOM, qTo6bI
Hcnonb30BaTb ,l1)IHHbI nHHHH nepe,naqH ,l1)IH no,nKJIIOqeHHH 3neMeHTOB. 3TO, KaK H B
cnyqae <t>a3HpoBaHHoH peIIIeTKM, YCTpaHHeT OrpaHHqeHH5I no IIIHpRHe nOnOCbI.
llIHpHHa rronOCbI oTpIDKaTenbHoH pellIeTKH C neqaTHbIMR H3nyqaTen5IMH 06bIQ-
HO OrpaHHQHBaeTCH llIHpHHOH nonOCbI 3neMeHTa. )];nH pe30HacHoro H3nyqaTen5I Ha
.n;H3neKTpHQecKoH IIJIaCTHHe Tonrn;HHoH t H .n;H3neKTpHQeCKoH nocT05IHHOH £,r llIH-
pHHa nonOCbI npH6nH3HTenbHO paBH5IeTcH:
BW  41 .
A 0 jii:;
( 13.9)
)];n5I YBenHQeHHH IIIHpHHbI nonOCbI cyrn;ecTByeT HeCKonbKO MeTo.n;OB. B caMOM
npocToM Hcnonb3yeTC5I MarHHTHa5I nO,l1)IO)KKa C ManbIMH nOTepRMH BMeCTO .n;H3neK-
TpHQecKoH rrnaCTHHbI. B [29] .n;OKa3aHO, QTO nOWIO)KKa C YMepeHHbIM f..l H HH3KHM E
06eCrreQHBaeT 3HaQHTenbHoe YBenHQeHHe IIIHpHHbI rronOCbI no cpaBHeHHIO C .n;H-
3neKTpHQecKoH nnacTHHoH. HanpHMep, H3nyqaTenb C £, = 1, f..l = 20 o6eCrreQHBaeT B
TPH pa3a 6onbIIIyro llIHPHHY nonOCbI, QeM H3nyqaTenb C £, = 1, f..l = 1. MarHHTHbIM
MaTepHanOM C HH3KHMH nOTepHMH 5IBnHeTCR MeTa<t>epPHT, KOTOpbIll BKJIIOQaeT B
ce65I KOMnneKT OqeHb TOHKHX JIaMHHHpOBaHHbIX nnaCTHH co CBOHMH xapaKTepH-
CTHKaMH MarHHTHbIX MaTepHanOB (<t>HpMeHHbIH npo.n;YKT Metamaterials LLC).
B ern;e O.n;HOM MeTo.n;e YBenHQeHH5I IIIHpHHbI nonOCbI Hcrronb3YIOTCR H3nyqaTenH
C O.n;HHM HnH .n;BYM5I .n;ononHHTenbHbIMH neqaTHbIMH 3neMeHTaMH Ha,n: OCHOBHbIMH
[3]. 3Ta pa6oTa, KaK npe.n;CTaBnReTC5I, RBnReTCR nepBoH pa60ToM no OTpa)KaTenb-
HbIM peIIIeTKaM C .n;ByxcnoMHbIM H3nyqaTeneM. KOHeqHO, .n;ByxcnoMHbIe H3nyqaTenH
.n;nR np5IMbIX H3nyqalOrn;HX AP H3BeCTHbI MHoro neT. Pa60TbI, B KOTOpbIX paCCMaT-
pHBalOTCR KOHCTPYKUHH C .n;ononHHTenbHbIMH rreqaTHbIMH 3neMeHTaMH, BKJIlOqalOT
cne.n;YIOrn;He: [35, 75, 62, 39,72, 38]. Cpe.n;H pa60T no 3TOM TeMe MO)KHO TaIOKe Ha-
3BaTb pa60TbI [33, 23, 69, 24].
13.1.6. Pa3BMTMe OTpa>KalOUJ,Mx peweTOK
AHanorHQHO CKaHHpOBaHRIO <t>a3HpoBaHHoM peIIIeTKH, OTpIDKalOma5I AP cKaHHpyeT
nocpe.n;CTBOM BKJIIOQeHH5I <t>a30BpamaTeneH (<t>a3Hpyrorn;Hx YCTPOMCTB) MJIH
YCTPOMCTB BpeMeHH6M 3a,n:ep)l(l(l{ B JIHHHH nHTaHHH 3JIeMeHTOB. KaK npaBHno, ,l1)IR
BbI60pa o.n;Horo H3 HeCKOnbKMX 3HaQeHRM ,l1)IRHbI nRHRR R 06eCrreQeHHH He06xoJ(H-
Moro <t>a30Boro CJ(BHra Rcnonb3yroTCH ,nHOJ(HbIe nepeKJIIOQaTenR [48] HJIR MEMS
(MIfKp03JIeKTpOMeXaHIfQeCKMe cIfcTeMbI) [40]). 3Ta CnO)KHaR CTpYKTypa If nOTepR
JIHllIaIOT OTpa)KaTenbHyro peIIIeTKy MHorHX npeHMymeCTB. B J(pyrOM KOH<t>HrypanHH
HCnOJIb3yroTCH napaMeTpRQeCKHe (BapaKTopHbIe) J(HOJ(bI WIH coeJ(HHeHHR pa3HbIX
3JIeMeHTOB H3.rryqaTeJIH, TaKHM o6pa30M o6eCneQHBaH ynpaBneHHe <t>a30H [34].
B 3K30THQeCKOM cxeMe HCnOJIb3yeTcH BbICOKope3MCTHBHa5I KpeMHHeBa5I ITJIaCTHHa
no.n; 3JIeMeHTaMH H3.rryqaTeJIH; OnTHQeCKOe B036)')KJ(eHHe nnaCTHHbI peryJIHpyeT <t>o-
II

 FIla8a 13. Ompa;)ICamellbHble U nepeU3/ly'talOUf,ue aHmeHHble peLUemKU
II
il
TOHH,L(yI.J:HpyeMYID TIJIa3MY H TaKHM 06pa30M 06eCrreqHBaeT peryJlHpoBKy cPa3bI [15].
B eIUe O,aHOH cxeMe HCrrOJlb3yroTCH rH6pH,aHbIe H ,aHo,aHbIe CMeCHTeJlH MH yrrpaB-
JleHHH JlyqOM [8].
113BecTHa KOHCTPYKUHH, B KOTOpOH HCrrOJlb3yroTCH rreqaTHbIe 3J1eMeHTbI, KIDK-
v
,abIH H3 KOTOpbIX co,aep)I{HT IUeJlb, KOTopaH coe,aHHHeTCH C JlHHHHMH 3a,aep)I(KH,
pacrrOJlOXeHHbIMH rro,n 3TOH IUeJlblO [9]. Kor,aa B oTpIDKaTeJlbHOH pellIeTKe HCrrOJlb-
v v v
3yroTCH 3J1eMeHTbI C ,aBOHHOH nOJlHpH3aU;HeH H OT,aeJlbHbIMH JlHHHHMH nHTaHHH, B
Ka)l(,[{OM 3J1eMeHTe MOryT rrpHMeHHTbCH MaJIOMOIUHbIe YCHJIHTeJlH, rrpHHHMalOIUHe
CHrHaJI B O.aHOM rropTY (rrOJlHpH3aUHH), YCHJlHBalOWHe ero H rrepe.aalOWHe ero H3
BToporo nopTa (KpoCCnOJlHpH3aU;HH) [60, 20].
TaIOKe HCnOJlb30BaJIHCb OTpIDKalOIUHe pellIeTKH KaccerpeHa [59]. KpoMe 3Toro,
MO)KHO npHMeHHTb CHCTeMY, r,ae BcnOMOraTeJlbHOe 3epKaJIO HBJlHeTCH rHnep60JlH-
qeCKHM, a He napa60JlHqeCKHM. 113-3a 3aTeHeHHH paCKpbIBa 06J1yqaTeJIH HHor.aa
CMerualOTCSI C nOMOIUblO BcnOMOraTeJlbHbIX 3epKaJI KaccerpeHa, HJIH rpHropHaH-
CKHX BcnOMOraTeJlbHbIX 3epKaJI, HJIH ,aa)l(e C nOMorublO npHMoro CMeIUeHHSI 06J1Y-
qaTeJUl. Ko BceM 3THM reOMeTpHqeCKHM cxeMaM npHMeHHMbI 06bIQHbIe KOHCTpyK-
l.{HOHHbIe orpaHHqeHHH. llpHMoe cMerueHHe 06JIyqaTeJUI ycyry6JU1eT np06JIeMY,
CBSl3aHHYlO C llIHpHHOM nOJlOCbI npH cPa3HpOBaHHH, HO MH He60JlbllIHX DIA llIHpH-
Ha nOJlOCbI MoxeT OrpaHHqHBaTbCH llIHpHHOM nOJIOCbI 3J1eMeHTa (CM. rJI. 5).
CJIO)KHbIe 06J1yqaTeJlH MOryr ,aaBaTb MHoxeCTBeHHbIe JlyqH HJIH npocPHJIHpO-
BaHHbIM Jlyq MH Cnel.{HaJIbHOrO ceKTopa 0630pa 3eMJIH [58, 74, 25, 9]. CeKTop 06-
30pa npo<pHJIHpOBaHHbIM JlyqOM MO)KeT 06eCneQHBaTbCH 3a CQeT peryJlHpOBaHHSI
cPa3 3JIeMeHTOB [25], a 3aTeM, Ha BTOpOM 3Tane, - peryJlHpOBaHHeM pa3Mepa 3J1e-
MeHTOB MSI YBeJlHQeHHH llIHpHHbI nOJlOCbI TIpH nO)JJ{ep)l(aHHH He06xo,aHMOH <pa3bI
B K(l)I()];OM H3J1yqaTeJle.
13.2. nepeM3nY'lalOLQMe aHTeHHbie peweTKM
13.2. 1. MCTOpMR nepeM3nY'lalOMx aHTeHHblX peweTOK
nepeH3JIyqalOIUaH AP (pHC. 13.7) 6bIJIa H306peTeHa BaH ArroM [71]. K(l)I()];bIH 3J1e-
v
MeHT pellIeTKH no,acoe,aHHeH K ,npyrOMY 3J1eMeHTY JIHHHHMH nepe.aaqH paBHOH MH-
HbI. llOQTH cpa3Y )Ke B03HHKJIa TPy,nHOCTb, Kor.aa B [64] 6bIJlO TIOKa3aHO, qTO
06paTHaH 3cPcPeKTHBHaH nOBepXHOCTb pacceHHHH (3llP) conOCTaBHMa C nepeH3JIY-
qaeMOH BOJIHOM. 3Ta TPy,aHOCTb JlerKO npeO,[(OJleBaeTCH TI)'TeM H3MeHeHHSI nOJlHpH-
3aUHH, QaCTOTbI HJIH MO,[(YJlHUHH JlH60 TI)'TeM ,[(onOJlHHTeJlbHOrO YCHJIeHHH. Hec-
KOJlbKO TaKHX CHCTeM MH cn)'THHKOB CBH3H H3yqeHo B [28]. PellIeTKH BaH Ana
HHor.aa Ha3bIBalOTCH «caM0<p0KyCHpyroWHMHCH»; 60Jlee y,naQHbIM TepMHHOM 6bIn
6bI TepMHH «caMOKOJlJlHMaUHpYIOIUHe pellIeTKH». B pa60Te [65] paCCMaTpHBaeTCSI
pellIeTKa co CMeIUeHHeM QaCTOTbI:
ECTecTBeHHo, npH JlI060M H3MeHeHHH QaCTOTbI CJle.nyeT yqHTbIBaTb llIHPHHY
nOJlOCbI QaCTOT. B pa60Te [1] paCCMOTpeHa rrepeH3JIyqalOlliaH pellIeTKa lIJISI cn)'THH-
KOBoro HCnOJIb30BaHHH; yqHTbIBalOTCH KaK CMeIUeHHe QaCTOTbI, TaK H H3MeHeHHe
nOJlHpH3al.{HH. 3TO Tpe6yeT HaJIHQHH 3J1eMeHTOB, KOTopbIe pa60TalOT Ha 06eHx rro-
JlHpH3aUHHX.


,
,
13.2. IIepeU3JlY'lalOU{ue aHmeHHble peUJemKU d
12
PHC. 13.7. llepeH3JIyqalOma$l perneTKa BaH ATTa
DOJIee pacnpocTpaHeHHbIH nplIeM, B KOTOpOM lIHBepClI}I nepe1I3JIyqae¥oro
nOJISI C nOMOlI(blO CJIO)l(HOH uenlI, CBO,L(lITCSI K 1II;IBepcMlI <t>a3bI B Ka)l()]:OM 3JIeMeHTe
aHTeHHbI. 3Ta lIHBepclISI n03BOJISleT nepeM3JIYQalOIlleH pellIeTKe <pOpMlIpoBaTb npo-
1I3BOJIbHyIO <t>OPMY ,[(H. B pa60Te [26] lICnOJIb30BaH C6aJIaHClIpOBaHHbIH CMeClI-
TeJIb, r,L(e QaCTOTa reTepO,l(lIHa 6JI1I3Ka K qaCTOTe ClIrHaJIa. BTopaSl rapMOHlIKa reTe-
pOLIlIHa 1I qaCTOTa ClIrHaJIa CMellIlIBaIOTCSI; HIDKHSISI qaCTOTa 60KOBOH nOJIOCbI
lIMeeT lIHBepTlfpOBaHHYIO <t>a3Y (CM. TaIOKe [55]). TaIOKe lICnOJIh30BaJIlICb TYHHeJIh-
HbIH ,L(1f0,L( BMeCTO CMeClITeJISI [61] 1I ,l(BOHHble CMeCIfTeJIlI (CM. pa3,l(eJI 13.2.2),
BnepBble IfCnOJIb30BaHHhle B [66].
13.2.2. nOcneAHMe AOCTM>KeHMR
KaK IfHorLIa 6bIBaeT B HayqHoH c<t>epe, pa60TbI 1964 rO,l(a CMeHIfJIlICh npon:OJDKlI-
TeJIbHbIM 3aTHllIbeM. B pa60Te [67] npe,L(JIO)l(eHa cxeMa uenoQKo06pa3Horo conpSl-
)l(eHHSI no <t>a3e, r,L(e OLIIfH 3JIeMeHT aHTeHHbI IfCnOJIb3yeTcSI MSI reHeplfpOBaHHSI
<t>a30Boro 3TaJIOHa, KOTOpbIH 3aTeM nepe,L(aeTCSI CJIe,L(yIOlI(eMY 3JIeMeHTY; Ka)l(,[{bIH
3JIeMeHT HMeeT uenh conpIDKeHHSI no <t>a3e, B KOTOpOH HCnOJIb3yIOTCSI CMeCHTeJIH
(CM. TaIOKe [44] ). O,L(HaKO CJIO)I{HOCTb cxeMbI nepeKpbIBaeT JII06bIe npelIMyrn:eCTBa.
B elI(e O,l(HOM BaplfaHTe lICnOJIb3yeTcSI BXO,L(SlII(HH CHrHaJI IIJIIOC BXO,L(SlII(HH nHJIOT-
CHrHaJI C HCnOJIb30BaHlIeM CMeCHTeJIeH [7]. OnlfcaHHbIH paHee cMeCIfTeJIb-<t>a30HH-

 rAa8a 13. Ompa:JICameJ/bHble U nepeU3A)l'IalO14ue aHmeHHble peUlemICU
BepTOp (CM. pHC. 13.8) ,l{aeT OTpIDKeHHR Ha KJIeMMaX aHTeHHbI H3-3a HeCOrJIaCOBaH-
u
HOCTH HMne,l{aHCa H npOCaqHBaHHR OT BXO.LJ:HOrO nopTa CMeCHTeJUI Ha BbIXO,l{HOH
nopT. 3<l><l>eKT npOCaqHBaHHR oueHeH B [68]. 60JIbllIeH qaCTH CHrH8JIa npOCaqHBa-
HHR MOXHO H36exaTb 6JIarO,l{apR HCnOJIb30BaHHIO .LJ:BYX CMeCHTeJIeH [ 17]. Xopo-
maR pa3BR3Ka RF-IF (pq-nq) (panHOqaCTOTa - npOMexyTOqHaR qaCTOTa) o6ec-
neqHBaeTCR nOCpe.LJ:CTBOM ,l{BYXKaH8JIbHOrO cPa30Boro conpRralOIUero YC1pOHCTBa
(CM. pHC. 13.9). JIHHHR 3a.n:ep}Kl(l{ BbI3bIBaeT rallIeHHe pa.n:HOqaCTOTbI Ha nopTe
RF-IF; .LJ:Ba KaHaJIa HMelOT 3a.n:epXKY 180 0 Ha nopTe RF-IF, TeM caMbIM o6eCneqH-
BaR XOpomyIO pa3BR3KY IF (npoMexyTOqHOH qaCToTbI) [49-51].
f
1t/2 ,lVUI pq
1t ,lVUI IT
CMeCHTeJIb
,
CMeCHTeJIb
feTepO.l1HH 2/
feTepO.l1HH 2/
Pac. 13.8. 3JIeMeHTapHbIH cMeCHTeJIb-<pa-
30BbIH HHBepTOp
Pac. 13.9. CMeCHTeJIb-<pa30BbIH HHBepTOp
u
C JIHHHeH 3a,nepXKH
Cy6rapMOHHqeCKOe CMellIHBaHHe n03BOJIReT H36exaTb np06JIeMbI, cBR3aHHoH C
qaCTOTOH reTepO.LJ:HHa, KOTopaR RBJIReTCR CJIHllIKOM BbICOKOH. B TaKoH cxeMe HC-
nOJIb3yK>TCR ,l{BOHHbIe CMeCHTeJIH C qaCTOTOH reTepo,nHHa (IT), COCTaBJIRlOlUeH no-
JIOBHH)' qaCTOTbI CHrH8JIa [42, 41]. KaK BH.LI.HO 11:3 pHC. 13.10, BbIXO,lJ: nepBoro CMe-
CHTeJIR no,ncoe,nHHeH KO BXO,ny BToporo CMeCHTeJIR qepe3 <l>R1Ib1p HH)l{HHX qaCTOT
(<I>Hq), YCTpaHRlOlUHH npOCaqHBaHHe CHrHaJIa reTepO.LJ:HHa H nOCTYJUIeHHe pa.n:HO-
qaCTOTHoro CHrHaJIa.
)];pyrIDI cxeMa, n03BOmIIOIUaR H36exaTb HCnOJIb30BaHHR reTepo,nHHa C qaCTOTOH
CHrH8JIa B ,lJ:Ba pa3a 60JIbIIIe, npe,nYCMa1pHBaeT HCnOJIb30BaHHe ,nBoHHoro C68JIaH-
CHpOBaHHoro rapMOHHqeCKOrO CMeCHTeJIR [6] (CM. pHC. 13.11). CHrHaJI reTepOlIHHa
no.n;aBJIReTCR B rH6pH.LI.HOM KOJIbueBOM coe,nHHeHHH, 06eCneQHBaR XOPOIIIYIO pa3-
--
,
I
l


. ..'" . .
13.2. IIepeU3JlY'talOU4ue aHmeHHble pewemlCu 
. ,
" .
f
«1> HII
I
feTepo,zUfH 2/
feTepO,lU1H 2/
Pac. 13.10. Cy6rapMOHHQeCKOe cMellIHBaHHe-HHBepcHSI <l>a3bI
3/t/4
Bxo,n
reTepo,nHHa
BbIXO,n nIl
CMeCHTeJIb
CMeCHTeJIb
AJ4
Bxo,n PII
Pac. 13.11. Cy6rapMOHHQeCKHH HHBepTOp <}>a3bI C HCnOJIb30BaHHeM rH6pH,.ll;HOrO
KOJIbn;eBOro coe,ZJ;HHeHHSI

 Dlaea 13. OmpaJ/CameJlbHble U nepeU3Ay'talOU{ue aHmeHHble peU1emKU
BR3KY LO-IF (IT-nq) (reTepo,rU1H - npoMe)I()'TOqHaR qaCToTa). npOCaqHBaHHe
pan:MOqaCTOTHoro CHrHaJIa qepe3 JJ:Ba CMeCHTeJIR COBna,aaeT no <}>a3e; 3TO MO)I(HO
McnpaBMTb 6JIaro.n;apR MCnOJIb30BaHMIO JJ:BYX rapMOHMqeCKMX cMeCHTeJIeH B uenH,
QTO n03BOJIReT no.n;aBJIRTb KaK pa,aHOQaCTOTHbIM CHrHaJI, TaK M reTepo.n;MHHbIM (CM.
pHc.13.12).
rr/2
1t
Bxo.n pq
BbIXO,U nq
Bxo.n reTepo.nHHa
PHC. 13.12. <l>a30Ba$I MHBepCM$I C OTMeHOH pa..QMOqaCTOTbI I1 MeCTHoro reHepaTopa
KOJIe6aHHH
B ern:e O.n;HOM cxeMe ,llJIR nOJIyqeHMR MHBepcMM <}>a3bI MCnOJIb3YIOTCR KBa,apaTYP-
HbIe rH6pMLI:HbIe cxeMbI C OKOHeqHbIMH HarpY3KaMH, aHaJIOrHqHbIMH TeM, KOTopble
npHMeHRIOTcR B OTpa)l(alOIll;l1X <J;>a30Bparn:aTeJIRx. IIp" 3TOM cxeMe BXOJJ:HaH H BbI-
XO,UHaR JIHHHM peBepcHp)'lOTCR, n03ToMY MCnOJIb3)'1OTCR nepeKpecTHbIe uenH [30].
Kor.n;a K KOHeqHbIM KJIeMMaM rM6pMJJ:HbIX cxeM nOD:KJIlOqeHbI YCMJIHTeJIH, TO B pe-
3YJIbTaTe nOJIyqaeTcR .n;BYHanpaBJIeHHbIM YCMJIMTeJIb [19].
B03Bparn:aRcb K pemeTKe KaK K pacceMBaTeJIIO, xapaKTepHCTHKH nepeH3JIyqaIO-
meH pemeTKH 6bIJIM npOaHaJIH3HpOBaHbI C TOqKM 3peHHR 3JIeKTpOMarHHTHOfO
nOJIR, pacceRHHoro OT neQaTHbIX 3JIeMeHTOB, OT 3KpaHa H nOJIR nepeH3JIyqeHHR
[18, 70]. PacceRHHbIe nOJIR MHTep<}>epMPYIOT C nOJIeM IIepeM3JIyqeHMR H HeCKOJIbKO
yBeJIHQHBalOT IIHKOB)'IO BeJIHqHHY 06rn:ero nOJI$!.
13.2.3. COBpeMeHHble BMAbl npMMeHeHMSI
I1cnoJIb30BaHHe nepeH3JIyqalOmeH pemeTKH B nOJIHOCTblO ,[(yrrJIeKCHOM CHCTeMe
CBR3H Tpe6yeT CneUMaJIbHOrO cxeMHoro pemeHHR BO H36e)l(aHHe nOBTopHOH ne-
pe,[(aqH rrpMHRToro CMfHaJIa. HanpHMep, IIOCJIe npHeMa <J;>a30MaHMnYJIHpOBaHHoro
-
I

JIumepamypa d
CHrHaJIa YCTpaHSIeTCSI MO,nYJISIU;HSI, 3aTeM Hecyrn;a$l qaCTOTa MOXeT 6bITb HHBepTH-
pOBaHa no <pa3e H MO.aYJIHpOBaHa HOBbIM <pa30MaHHnYJIHpOBaHHbIM CHrHaJIOM
[22]. B ,npyrOM no,nxo,ne HCnOJIb3yroTCSI opTOrOHaJIbHbIe MO,nYJISIU;HH .lL1ISI npHeMa H
nepe,naqH [43]. Erne O.L{HH BapMaHT - C,lI:BMr qaCTOTbI Me)K)J.Y npHeMOM H nepe.n.a-
qeH [20, 37].
Kor.n.a nepeH3JIyqalOm:aSI AP Haxo.n.HTCSI Ha nO,[(BlDKHoH llJIaT<popMe, nepe.n.aBae-
MaSI qaCTOTa CBSI3aHa C U;enblO <pa30BoH HHBepCHH. BbIcoKHe 3HaqeHHSI K03<P<PHUH-
eHTa YCHJIeHIUI, Heo6xo,nHMbIe MSI Heo6xo.n.HMoro nepeH3JIyqeHHSI, MOryT 6bITb He-
COBMeCTHMbI C onpe,neJIeHHbIMH ,nBH)I(eHH$lMH nJIaT<popMbI. [21]. HecTaH,napTHbIM
npHMepOM HCnOJIb30BaHMSI nepeH3JIyqalOmcH perneTKH C <pa30BoH HHBepcHeH SIB-
JI$leTCSI npHMeHeHMe llIYMOBOH KOppeJISIUHH MSI YCKopeHHH npou;ecca 06Hap}')Ke-
HHSI ueJIeH. B 3TOH CHCTeMe qaCTOTa reTepo,nHHa B ,nBa pa3a 60JIbIIIe HeCyn.I;eH qac-
TOTbI [22].
JIHTepaTY))a
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I
S
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PHC. 14.6. lloTepl1 IIpl1 CKaHl1pOBaHI1H ,lI;JUI QI1JII1H,lI;pI1QeCKOrO napa60JII1QeCKOrO
pe<pJIeKTOpa
14. 1.2. BoccTaHoBneHMe nOTepb cKaHMpoBaHMSI,
-
Bbl3BaHHbiX KOMOM
.66JIblIIa51 qaCTb YCHJIeHH5I, YMeHbIIIeHHoro B pe3YJIbTaTe KOMbI, MO)l(eT 6bITb BOC-
CTaHOBJIeHa npH HCnOJIb30BaHHH AP, pa3Mell(eHHOH B <pOKaJIbHOH nJ10CKOCTH.
B TaKOH peIIIeTKe 3JIeMeHTbI ,l{OJDKHbI pacnOJIaraTbC$I B Ka)l(l{OH H3 3JIJII1nTHqeCKI1X
«rop5lqI1X TOqeK», nOKa3aHHbIX Ha pHC. 14.4. AMnJII1Ty,n;bI 3JIeMeHTa B Ka)l(,[(OH «ro-
p$lqeH TOqKe» He O)J;I1HaKOBbI, a <pa3bI He CB$l3aHbI JII1HeHHOH 3aBI1CI1MOCTblO, KaK
B TPMI1Ul10HHOH <pa3HpOBaHHOH peIIIeTKe. ,LLrrH nOJIyqeHI1$1 MaKCI1MaJIbHOrO YCI1J1e-
HI1$1 I1CnOJIb3yeTcH ,l{H<p<pepeHUHaJIbHOe B3BeIIIHBaHI1e CHrHaJIOB Ka)l(,[(OrO KaHaJIa
(maximal ratio combining). MeTo,n; 6bIJI nepBOHaqaJIbHO npe.n.rrO)l(eH B [16] 11 pa3pa-
60TaH M5I MHOr03JIeMeHTHbIX CHCTeM CBH3H B [15], - nepe)J. o6pa6oTKoH Ka)l(,[(bIH
CHrHaJI B3BeIIIHBaeTCH nponOpUHOHaJIbHO ero OTHOIIIeHHIO SIN (cHrHaJI/rnYM).
Kor.l(a perneTKa HCnOJIb3yeTc$I JJ.JI$I KOppeKl(HH KOMbI, CHrHaJI B Ka)l(,[(OM 3J1eMeHTe
B3BeIIIHBaeTC$I KOMTIJIeKCHO conpIDKeHHbIM 3HaqeHHeM nOJIH B Ka)l()].OM 3J1eMeHTe,
Kor)J.a aHTeHHa$l CHCTeMa HaXO)J;HTC$I B pe)l(HMe npHeMa. Me)l(,[(Y aMnJIHTY.l(aMH 11J111
<pa3aMH 3JIeMeHTOB npOCToro COOTHOllIeHH$I He cyw:eCTByeT.
)];JI$I He3Haql1TeJIbHbIX na.n;eHHH YClUleHH$I MOryr HCnOJIb30BaTbC$I rpynnoBbIe
o6nyqaTeJIH (KJIaCTepbI). B 3TOM CJIyqae 3JIeMeHTbI 06JIyqaTeJIeiI pacnOJIaralOTC5I B
v
Bl1,L(e KOJIbua, BKJIlOqalOm;ero HJIH He BKJIlOqalOll(ero ueHTpaJIbHbII1 3JIeMeHT, npl1
3TOM ueHTp KOJIbua HaXO)J;HTC$I B <pOKaJIbHOH TOqKe HJIH CMem;eH [7a]. no Mepe
Toro KaK nyq CMell(aeTC$I H3 oceBoro nOJIO)l(eHHH, )J;OJDKHO ocyw:eCTBJI$lTbC5I ne-
peKJIlOqeHHe KJIaCTepa lIlliI IIO.n;:I:ep)l(aHH$I xoporneH 3<p<peKTI1BHOCTI1. )];JIH 1lII1pOKO-

14.2. 3JlelCmpOMa2HUmHaJl onmUlCa 6JlU;HCHe20 nOM 
nOJIOCHbIX CHCTeM, B qaCTHOCTH, TaKHX KaK perneTKH B cPOKaJIbHOH nJIOCKOCTH
60JIbllIHX napa60JIHqeCKHX aHTeHH ,lLJlfl palIHoaCTpOHOMMH, HCnOJIb3yeTcR cPHKCH-
pOBaHHoe pacnOJIOXeHMe 06JIyqalOI.I.XHX 3JIeMeHTOB H BeCOBbIe K03cPcPHI.J;HeHTbI, qTO
CHIDKaeT 3HaqeHHe SIN [32].
14. 1.3. OrpaHM"IeHMSI no KoppeKu.MM KOMbl
Cym:eCTByeT HeCKOJIbKO cepbe3HbIX TPY,L1;HOCTeH, CBSl3aHHbIX C npMMeHeHHeM pellIe-
TOK B cPOKaJIbHOH nJIOCKOCTH JUISI KoppeKI.J;HM KOMbI. Bo- nepBbIX, no Mepe M3MeHe-
HMSI yrJIa <p BCSI ,L1;MarpaMMa KOMbI (pMC. 14.4) BpaIUaeTCSI BMeCTe C HMM. IIo3ToMY
pellIeTKa J{OJDKHa TaIOKe Bpam:aTbCR. KOHeqHO, 60nbllIaSl pellIeTKa, OXBaTbIBalOIUaR
<p = 2n, 6y,aeT CTaI.J;MOHapHoH, HO TOr,II,a COOTBeTCTBYIOIUHe 3JIeMeHTbI, nopO)I(,.QalO-
m:Me KOMY, ,aOJDKHbI BKJIlOqaTbCR MJIM BbIKJIlOqaTbCSI, M 3aTeHeHMe 6Y,L(eT 60JIbllIMM.
BO-BTOpbIX, no Mepe M3MeHeHHSI yrJIa e M3MeHSleTCSI 3HepreTMqeCKaSl ,II,MarpaMMa
nOJIR B <t>OKaJIbHOH nnOCKOCTH OT elIHHHqHOrO Kpyra (B HanpaBJIeHMM, HOpMaJIb-
HOM K paCKpbIBY, HJIH PMOM C 3TMM HanpaBJIeHMeM) J{O HaqMHalOm:erocSI pacnpe-
,II,eJIeHHR KOMbI C HeCKOJIbKHMH «ropSlqHMH TOqKaMH», ,L1;0 nOJIHOrO pacnpeJ{eJIeHHR
KOMbI, TaKoro, KaK nOKa3aHO Ha pHC. 14.4. B CJIyqae pacnpe,L(eJIeHHR B cPOKaJIbHOH
nJIOCKOCTM npH KOMe no Mepe H3MeHeHMR yrna e Bce «ropSlqMe TOqKM» nepeMeIUa-
IOTCSI Ii C03,II,aIOTCSI HOBbIe «ropRqHe TOqKM». ,[(onOJIHHTeJIbHaR CJIOXHOCTb 3aKJIIO-
qaeTCR B TOM, qTO MHTepBaJIbI Me)I(,.QY «ropRqHMM TOqKaMM» BJ{OJIb JIMHHH + 30° He
RBJIRIOTCR O,II,MHaKOBbIMM M He M3MeHSlIOTCR JII1HeHHO C qaCTOTOH. BpeMeHHaR 3a-
.nepXKa, KOTopaR MCnOJIb3yeTcSI B llIMpOKOnOJIOCHbIX cPa3MpOBaHHbIX pellIeTKax,
3,aeCb HenpMMeHHMa. KOMrrneKCHble K03<pMI1.MeHTbI B3BelliMBaHMSI CMrHaJIOB B
KIDK,llOM 3JIeMeHTe AP H3MeHSllOTCR B 3aBI1CI1MOCTI1 OT yrJIa e, nOJIOXeHI1S1 «ropRqeH
TOqKH» H qaCTOTbI. 3TH cepbe3Hble TPY,II,HOCTI1 orpaHI1QMBalOT MCnOJIb30BaHMe pe-
lIIeTOK B <t>OKaJIbHOH nJIOCKOCTM JUIR KoppeKUMM KOMbI.
14.2. 3neKTpoMarHMTHaR onTMKa 6nM>KHerO nonR
14.2.1. AHTeHHa KaccerpeHa 6nM>KHerO nonSi
B HaCTORm:eM pa3,II,eJIe peQb nOMeT 06 aHTeHHax 6JIIDKHerO nonR KaccerpeHa, fpe-
ropl1 M c<t>OKYCl1pOBaHHbIx aHTeHHax. OHI1I1Hor.ua Ha3bIBalOTCR aHTeHHaMM «orpaHH-
qeHHOrO CKaHl1pOBaHHR». Tpa,n:I1UHoHHaR aHTeHHa KaccerpeHa I1MeeT napa60JIHqe-
CKI1H rJIaBHbIH pecPJIeKTop J{HaMeTpOM D 11 rMnep6oJIMqeCKOe BcnOMOraTeJIbHOe
3epKaJIO ,L(MaMe'TpOM d. OHM, KaK npaBMJIO, 06nyqalOTcSI pyrrOpHOH aHTeHHOH.
B pe<pJIeKTOPHbIX CI1CTeMaX 6JIIDKHerO nOJIR MR OCBemeHHR BcnOMOraTeJIbHOrO
3epKaJIa MCnOJIb3yeTcSI rrnOCKaR BOJIHa; J{JISI aHTeHHbI KaccerpeHa 6JIIDKHerO nOJIR
BcnOMOraTeJIbHOe 3epKaJIO TaIOKe RBlliIeTCR napa60JII1QeCKJ1M. Ha pMC. 14.7 M306pa-
xeHa aHTeHHa KaccerpeHa 6JIlUKHero nOJIR. IIpol1cxo)I(,.QeHMe 3Toro nOHRTHR HeRC-
HO, HO OHO BOCXO,L(HT K ,II,aBHeH pa60Te, r.ue HCnOJIb30BaJIM pyrropHo-napa60JIHQe-
CKJ1H 06.rryqaTeJIb ,L(lliI 06JIyqeHIDI napa60JIHQeCKOrO BcnOMOraTeJIbHOrO 3epKaJIa Ha
paCCTOSlHl111 W216A; pacKpbIB 06JIyqaTeJIR paBHRncR W B pa60Te [13] HcnbITaHa
napa60JIa 16 <PYTOB C pynopHo-napa60nHQeCKMM o6nyqaTeJIeM Ha 6 rrl( C OC06bIM

J Dza80 14. 3epICllJ/bHble OHmeHHbl c pewemICOMU
IIapa6oJlH1.JecIGI:H oTpaxaTeJlb
. I
<l>a3HpoBaHHag
aHTeHHag pemeTKa
BcnOMOraTeJlbHbIH
napa60JlH1.JeCKlfH OTPaxaTeJlb
cI>OKYC
Pac. 14.7. AHTeHHa KaccerpeHa 6JII1JKHerO IIOJIR
ynOpOM Ha mYMoBYIO TeMnepaTYPY aHTeHHbI. 3HaKoBbIe HCCJIe,nOBaHHR BbInOJIHeHbI
B [5, 7], r.zxe HCnOJIb30BaHa <I>AP .n.rrSi 06JIyqeHHSI BcnOMOraTeJIbHOrO 3epKaJIa. Pe-
rneTKa n03BOJIReT o6eCneQHTb orpaHHQeHHOe 3JIeIcrpOHHoe CKaHHpOBaHHe CHCTe-
MOH KaccerpeHa 6JIH)KHerO nOJIR. ,[(onOJIHRIOT HCCJIe.zxOBaHHR pa60TbI [33, 2, 20-
22, 27]. 06pamaeM BHHMaHHe Ha TO, qTO BcnOMOraTeJIbHOe 3epKaJIO Haxo.zxHTCR B
6JIIDKHeM nOJIe <pa3HpOBaHHOH pemeTKH; 6JIH)l{Hee nOJIe npe,nCTaBJISIeT C060H TIJIOC-
K)'IO BOJIHY, r.zxe <pa30BbIH <ppOHT KOTOpOH CO,LI;ep)l(}lT HH<popMaQHIO 0 HanpaBJIeHHI1
JIyqa. ECJIH pemeTKa .nOCTaTOqHO 60JIbmaSi (B WjA, W - ,LI;HaMe1p pemeTKH), TO no
KOHCTpYKTHBHbIM coo6pIDKeHHRM pemeTKa MO)KeT pa3MeIIJ;aTbCSI B BepmHHe fJIaB-
Horo 3epKaJIa (napa60JIbI), npH 3TOM CTpYKTYpa pemeTKH Haxo,nHTCR 3a rJIaBHbIM
napa60JIOH.D:OM, a JIHQeBaR QaCTb pemeTKH pacnOJIaraeTCR B paCKpbIBe B BepmHHe
napa60JIbI. 06paIIJ;aeM BHHMaHHe Ha TO, qTO ,nBYX3epKaJIbHaH CHCTeMa }'MeHbmaeT
yrOJI CKaHHpOBaHHR pemeTKH, KOTOpbIH BbIpIDKaeTCR CJIe,nyroIIJ;HM 06pa30M:
D
tanS arr = - tanS beam.
d
( 14.6)
AMnJIHTY.na nOIDI B <POKaJIbHOH nJIOCKOCTH RBJISleTCSI CHMMe1pHqHOH, a <pa3a -
JIHHeHHOH. KaK 6bIJIO nOKa3aHO B [17], B 3TOM c.rryqae a6eppaQHSI 1peTbero nopSl,L(-
Ka OqeHb MaJIeHbKaSl 11 6oKoBbIe JIeneCTKH He3HaQHTeJIbHbI.
MMelOTcR HeKOTopbIe orpaHHQeHHSI Ha o6JIyqalOIIJ;He <I>AP .n.rrSl 3epKaJIbHbIX CH-
CTeM. ECJIH .zxHaMe1p pe<l>JIeKTOpa H <pOKYCHOe paCCTORHHe D H f, a ,nHaMeTp pemeT-
KH H paCCTORHHe OT pemeTKH .no <l>oKYca paBHSlIOTCSI W H fa", .n.rrSl MaKCHMaJIbHOH
3<p<peKTHBHOCTH conpIDKeHHSI perneTKH C pe<pJIeKTOpOM 1pe6yeTcSI, QTo6bI BbInOJI-
HIDIOCb ycnoBHe flD = fa"jw.

,
14.2. 31leKmpOMa2HUmHllfl onmUKa 6IlUJlCHeO nOI/fl 
3aTeHeHHe, BbI3BaHHoe BcrrOMOraTeJIbHbIM 3epKaJIOM 11 pellIeTKoH, rrOBblIIIaeT
60KoBble JIerreCTKH If CHl'DKaeT YCRJIeHHe. bbIJIH rrpoBe.n;eHbI paCqeTbI CI1CTeMbI C
HCnOJIb30BaHHeM O,L(HOrrapaMeTpl1qeCKOrO KpyroBoro anepTypHoro pacnpe,L(eJIeHI1
[8], KOTopoe M 3HaqeHHH 60KOBbIX JIerreCTKOB B 25 ,L(D OqeHb XOpOIIIO nO,L(XO,L(HT
MR 60JIbllIHHCTBa OTpIDKaTeJIbHbIX aHTeHH. Ha pl1C. 14.8 nOKa3aHa 3aBI1CI1MOCTb
YEJI OT diD LLJllI HeCKOJIbKI1X YPoBHeH 60KOBbIX JIeneCTKOB. ,L(JI 25 .n.D COOTHOllIe-
HHe .D:HaMeTpa BcnOMOraTeJIbHOrO 11 OCHOBHoro 3epKaJI, paBHoe 0,25, 06eCneql1BaeT
ypOBeHb 60KOBoro JIeneCTKa -16 .n.b. ,lI.aHHble no H3MeHeHI1M YCHJIeHI1 OTCyrCT-
ByroT. PeaJIH3al(HR y6bIBaHH aMIIJIHT)',n;bI Ha pellIeTKe npl1Be.n.eT K y6bIBaHMIO aMn-
JIHTy,n;bI Ha BcnOMOraTeJIbHOM 3epKaJIe, HO 3TO CHI13HT ypOBeHb 60KOBbIX JIeneCTKOB
Ha 0,5 ,n;b M BbI6paHHoro KpyroBoro O.ll.HOnapaMeTpHqeCKOrO 25 ,n;b pacnpe,L(eJIe-
HHR 3a CqeT nOTepb YCRJIeHHR. YEll CHCTeMbI KOHTpOJIMpyeTcR nOCpe,L(CTBOM COOT-
HOllIeHHR 3aTeHeHHR diD. BblnOJIHeHHbIe paCqeTbI 11 113MepeHHR nOKa3bIBaIOT, qTO
YEJI COCTaBJIReT npl16JII13HTeJIbHO -12 .lI.E KaK M paBHOMepHoro, TaK 11 .lLTI y6bI-
BalOrn;ero B036}')KJIeHl1it
-10
-15
--

 -20
-
::s:
::s:
x
Cd

0 -25
0.
::s:
x
Cd

(.)
::s: -30
0.
t=
::s:
0.
(1)
E-< -35
0
t::
-40
o
0.05
0.1
0.15
0.2 0.25
diD
0.3
0.35
0.4
PRC. 14.8. 3aBHcHMoCTb ypOBHH 60KOBbIX JIeneCTKOB OT OTHOCHTeJIbHOrO ,nHaMeTpa
3aTeHeHHH ,nJUI o,nHonapaMeTpHQeCKOrO KpyroBoro pacrrpe,aeJIeHHH
Pa3Mern;eHHe 3JIeMeHTOB peIIIeTKH C rnarOM > A/2 MO)l(eT C03,n;aBaTb .n;H<l>paK-
l(HOHHbIe JIeneCTKH, HO OHH HaXO,L(HTCR 3a npe.n;eJIaMH KOHyca BcnOMOraTeJIbHOrO
3epKaJIa H, TaKHM 06pa30M, He YBeJIl1qI1BaIOTC.H 3a CQeT YCRJIeHM OCHOBHoro pe<l>-
JIeKTopa. B 3TOH CBR3H peaJIbHbIMH 5IBJI5IIOTCR HHTepBaJIbI Me)l(,[(y 3JIeMeHTaMH, paB-
HbIe A RJIH 60JIee. O.ll.HaKO TeopeMa llIeHHOHa rJIaCHT, QTO 1'pe6yroTcR ,L(Ba TOQeQ-
HbIX 3JIeMeHTa Ha O,l(HY ,lUIHHY BOJIHbI LVIR rrpaBRJIbHOrO OTpa)l(eHH5I 6JIIDKHerO

 F/1080 14. 3eplCO/lbHble OHmeHHbI c pewemlCOMU
nOllS!. 3JIeMeHTbI pemeTKH, KaK npaBIUIO, ,1IJlnOJIH H neqaTHbIe H3nyqaTeJIH, He RB-
JIRIOTCH TOQeqHbIMH H3nyqaTeIDIMH. BepORTHO, qTO B03MO)l(eH mar ,lI0 A.
B JII060H 3epKaJIbHOH CHCTeMe no Mepe CKaHHpOBaHHH nyqoM ,lIHarpaMMa 06-
JIyqaTeJIR B036y)1(}.(aeT He BeCb pe<pJIeKTOp (3HeprHR nepeJIHBaeTCH 3a KpaH). 3TO
BHHbeTHpoBaHHe YMeHbmaeT YCHJIeHHe. TIo Mepe Toro KaK 06nacTb 06JIyqeHHR, CO-
3,lIaHHaR 06nyqaTeneM, pacnpocTpaHReTcR MHMO napa60nHQeCKOrO pe<}>neKTopa,
3<t><}>eKTHBHaR ITJIOIll.arI:b pe<}>JIeKTopa npe,lICTaBnReT C060H ,lIBa KpyrOBbIX cerMeHTa
(CM. pHC. 14.9). C nOMOIll.blO <}>opMynbI nnOI.IJ;a,zJ;H ceKTopa [1] 3aBHCHMOCTb 3<p<peK-
THBHOCTH OT CKaHHpOBaHHR BbIpa)l(aeTCR npH6JIH3HTenbHo Cne,lIYIOrn:HM o6pa30M:
eff=  [arccO{l-  )-(l-  )  (2-  )1
(14.7)
r,lIe h - 3TO QeHTpaJIbHaR TOJIrn:HHa cerMeHTa, a a = Dj2. TIpH nOBopoTe rnaBHoro
nyqa BOKpyr <}>oKyca I Ha yrOJI 8 (a - h)11 = tan 8j2. llpHBO,lIR K liD, nonyqaeM
YHHBepCaJIbHOe ypaBHeHHe
! ( 1 - h ) = I tan 8 .
2 a D 2
h h
PHC. 14.9. BI1HbeTl1pOBaHl1e 113-38 CKaHl1pOBaHI1H
( 14.8)
Ha pHC. 14.10 npHBO,lIHTCH 3aBHCHMOCTb 3<p<peKTHBHoCTH BHHbeTHpOBaHHR
(naneHHe YCHJIeHHR) OT Ij D. tan8j2. HanpHMep, nOJIaraR nOTepH B 3 ,lIE, HaXO,lIHM:
f tan 8 = 0,20147,
D 2
( 14.9)
qTO lJ)IJIIID = 0,40 n03BOJIReT CKaHHpOBaTb B ceKTope + 53,47°, a lJ)IJIIID = 0,5 - B
ceKTope + 43,89°.
TIpoBe,lIeHHOe paCCMOTpeHHe Tpe6yeT OTBeTa Ha Borrpoc: HaCKOJIbKO 6nH3KO
,lIOJDKHa HaxO,lIHTbCR pemeTKa K BcrrOMOraTeJIbHOMY 3epKaJIy, QT06bI 6bITb B 6JIIDKHeM
none? HanHcaHo MHoro pa60T 0 6JIIDKHHX nonRX paCKpbIBa HAP, HanpHMep, pa60Ta
[12]. XopomeH 3MnHpHQeCKOH 3aKOHOMepHOCTblO RBJIReTCR CJIeL{)'.lOrn:ee: paCCTORHHe
OT BcnOMOraTeJIbHOrO 3epKaJIa ,lIO pemeTKH ,lIOmKHO 6bITb He 60JIbme 0,05 x 2W2jA,

14.2. 3JleKmpOMa2HUmHaJl onmUKa 6flUJlCHecO nOJlJl 
r,ne W - 3TO ,nMaMeTp perneTKlI [10].
HanpMMep, eCJlM WjA = 100, paCCTOH-
HMe ,nOJDKHO 6bITb He 60Jlee lOW
I1Hor,na YTBep)l(,[{alOT, qTO CMCTeMa
6J1HXHerO 110JlH KaccerpeHa HMeeT
Q;>MKCHpOBaHHyIO 30HY 0630pa, 110-
CKOJlbKY npH yqeTe Q;>a30BbIX MCKaxe-
 
HHH qHCJlO nOJlOXeHMH Jlyqa npH CKa-
HHpOBaHHH OrpaHHqeHO. 3TOT BbIBO,n
He HBJlHeTCH Y.IJJ'IBHTeJlbHbIM, - 60JIb-
IIIHHCTBO CHCTeM TaK xe OrpaHHQeHbI.
B pa60Te [5] I1peJUIaraeTCH 3MnHpHQe-

CKaH oueHKa CKaHHpYlOlUHX CBOHCTB:
qHCJlO nOJlOXeHHM JIyqa (IllHpHHa JIyqa
110 110JlOBHHHOH MomHocTH) npH CKa-
HHpOBaHHH OT oceBoro Hal1paBJIeHHH
paBHO OTHOIlleHHIO 0,5djA. 3Ta Ol.{eH-
Ka CnpaBeJUIHBa JUI$I 60JIbIlIHX D jA
H paBHOMepHoro B036y)1()1eHH5I pe-
IlleTKH.
KaK )')Ke ynOMHHaJIOCb, y6bIBalO-
lUee pacnpe,neJleHHe He $IBJlReTCR I1pe,n-
nOqTHTeJlbHbIM. 3Ta Q;>opMYJla ou;eHKH

CKaHHpyIOlI(HX CBOHCTB He3HaqMTeJIbHO
H3MeH5IeTC5I .lU1JI liD OT 0,3 no 0,5. Ha-
npHMep, JUI5I rJIaBHOrO napa60JIHQeCKOrO 3epKaJIa C DjA = 600, HMeeM 8 3 - 0,1 0. TIpH
diD = 0,2 BcnOMOraTeJIbHOe 3epKaJIO HMeeT djA = 120. CJle,noBaTeJIbHO, ,aHana30H
CKaHHpOBaHHR no ypOBHIO 3 .lI.E 6Y.lI.eT COCTaBJUITb 60 JlyqeH C KIDK.[(OH CTOpOHbI
OT HOpMaJIH K paCKpbIBY, HJIH 6° CKaHHpOBaHHH C KIDK.[(OH CTOpOHbI. npH Illare Mex-
J1,Y 3J1eMeHTaMM lA peIlleTKa 06JIyqaTeJI5I 6Y.lI.eT HMeTb npH6JIH3HTeJlbHO 11310 3JIe-
MeHTOB )J)UI CJIyqaH pa3MemeHHH peIlleTKH B BepillMHe pe<pJIeKTopa.
CKa3aHHoe KacaeTCH Y3KOnOJIOCHbIX CHCTeM. ,[(.rrH nOJIOCbI B HeCKOJIbKO OKTaB
HHTepBaJI Me)l(,[{Y 3JIeMeHTaMM npoeKTHpyeTcH MCXO.lI.H H3 BeJlHqHHbI lA Ha caMOH
BbICOKOH QaCTOTe. Pacnpe,neJIMTeJIbHaH CHCTeMa 06JIyqaTeJIH perneTKM nOTpe6yeT
BKJIlOqeHMR Q;>a30BpamaTeJIeH Ha Ka)l(,[{OM 3JIeMeHTe M COOTBeTCTByIOlI(yIO BpeMeH-
HyIO 3a;::(epXKY. 06pawaeM BHHMaHMe Ha TO, qTO 06mee B036y)1()1eHHe C y,nBoeHHoH
3a;::(ep)I(KOH Ha KIDK.[(OM nOCJIe.lI.yK>lI(eM ypOBHe nHTaHHH MoxeT 06eCI1eQHTb npaBH-
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JIHTepaTypa
1. Burington, R. S., Handbook of Mathematical Tables and Formulas, McGraw-Hill, 1973.
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b Tlla6a 14. 3eplCaJ/bHble aHmeHHbl c peUlemlCOMU
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rl1ABA IS
H3MEPEHHJI H AOnYCKH
CymeCTByIDT npeBOCXO,[(Hble KHJ1TI1 no M3MepeHJ1JIM, cnMCOK KOTOpbIX npMBe,[(eH
HI1JKe. TaKMM 06pa30M, B HaCT05llI..(eM rJIaBe 6y,[(YT paCCMaTpMBaTbC5I TOJIbKO cneUI1-
aJIbHble TeMhI, KaCaIOIUl1eC5I perneTOK. OHI1 BKJIlOqalOT B ce651 M3MepeHI1e xapaKTe-
pMCTMK aHTeHH C HM3KMM YPOBHeM 60KOBblX JIerreCTKOB, ,L(MarHOCTMKY perneTOK M
MMMTaTopbI MMrre,[(aHca CKaHMpOBaHM.H. TIOCKOJIbKY Ha pa60Tocnoc06HOCTb aHTeH-
HbI BJIM5IIOT CJIyqaMHbIe 01IIM6KI1, BonpOCbI TOQHOCTI1 M3MepeHMH (,[(orrYCKM -
tolerances) TaIOKe paCCMaTpMBaIOTC5I B HaCTO.HIUeM rJIaBe.
A.E. Bailey, Microwave Measurement, IEEjPeregrinus, 1985.
G.H. Bryant, Principles of Microwave Measurement, IEEjPeregrinus, 1988.
G.E. Evans, Antenna Measurement Techniques, Artech House, 1990.
J.E. Hansen, Spherical Near-field Antenna .Measurements, IEEjPeregrinus, 1988.
J.S. Hollis, T.J. Lyon, and L. Clayton, Microwave Antenna Measurements,
Scientific Atlanta, 1970.
IEEE Standard Test Procedures of Antennas, Std. 149, 1979.
15. 1. M3MepeHMe AMarpaMM HanpaBneHHOCTM aHTeHH
C HM3KMM YPOBHeM 60KOBbiX neneCTKOB
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8 pacnpe.n:eJIeHHe
6
KpKaMH OTMeqeHbI TOqKH
COBMeIJJ;eHHR 6oKoBoro JIeneCTKa
C fJIaBHbIM
(YEJI)-l = 20 .n:E
4
3
2
0

1 0
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0.8 0

0_
0.6 '-O
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cu
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0.3 ::s::
0.2
0.1
0.1
0.2 0.3 0.4 0.6 0.8 1
2
3 4
6 8 10
R
y = 2D 2 0.
PHC. 15.4. 3aBI1CI1MOCTh 113MeHeHI1R 6oKoBoro JIeneCTKa OT HOpMl1pOBaHHoro
paCCTORHI1R lI,JIR JII1HeHHOro I1CTOQHI1Ka EeHJII1CCa

 Dla6a 15. H3MepeHUR U aonyC1<;u
neCTKa. nporpeccMPYIOIllee YBeJIMQeHl1e ypOBHH 60KOBbIX JIeneCTKOB 11 CJII1HHMe
nepBoro C rJIaBHbIM npo,lJ,OJI)I(aeTC5I C YMeHbllleHl1eM 3HaqeHM5I R. Ha pMC. 15.3
nOKa3aH cJIyqait, r,lI,e rrepBbIM 60KOBOM JIeneCTOK yxe nOrJIOmeH rJIaBHbIM JIY-
qOM, a BTOpOit 60KOBOit JIeneCTOK M HOJIb YBeJII1QeHbi. Ha YHMBepCaJIbHOM rpaqn1-
Ke [28], pl1C. 15.4, npMBO,lJ,MTCH 3aBI1CMMOCTb YBeJIl1qeHI1H nepBoro 60KoBoro JIe-
neCTKa M 3HaqeHI1H «nJIeqa» OT HOpMMpOBaHHoro paCCTOHHMH .aJIH (YEJI)-l OT
13 (paBHoMepHoe pacrrpe.aeJIeHlfe) ,lI,0 50 ,lI,E. 06paTMM BHMMaHMe Ha TO, qTO pa3-
HOCTHbIe ,lI,MarpaMMbI HarrpaBJIeHHOCTM Tpe6YIOT HeCKOJIbKO 60JIbllIerO paCCTO-
HHMH H3MepeHMH, qeM COOTBeTCTBYIOll.J,Me CYMMapHbIe LIMarpaMMbI HanpaBJIeH-
HOCTH.
15.2. AMarHOCTMKa aHTeHHOM peweTKM
OllIM6KI1 B 3JIeMeHTax AP pe,lI,KO CBH3aHbI C MeXaHMQeCKI1MI1 ,lI,OnYCKaMM. OHM BbI-
3BaHbI MeHee 3aMeTHbIMM <paKTopaMM, B qaCTHOCTM, TaKMMM KaK B3aMMHaH CB5I3b,
OKa3bIBalOll.J,aH BJII1HHMe KaK Ha <Pa3Y, TaK M Ha aMnJIMTYLIY B036Y)l(UeHMH, nOTepM B
<pa30Bpall.J,aTeJI5IX 11 pacrrpe,lJ,eJIMTeJIbHOM CMCTeMe, a TaIOKe <pa30Bble 01lIM6KM B <pa-
30 BpamaTeJIHX.
HaM60JIee HarJIH,lI,HbIM cnoc060M onpe,lJ,eJIeHI1H 3TMX <paKTOPOB HBJIHeTCH 30H-
u
,lJ,MpOBaHMe, npM KOTOpOM nO,l1Bl1)1(HbII1 30H,lJ, elll1HOBpeMeHHO COelll1HHeTCH C OLIHMM
3JIeMeHTOM. OQeBI1,lJ,Hoit np06JIeMOH 51BJI5IeTCH B3aI1MO,lJ,eMCTBMe Me)l()].Y 3JIeMeHTOM
peilleTKI1 11 30H,lI,OM. ,[{JIH YCTpaHeHM5I 3TOM np06JIeMbI BMeCTO 30H,lI,a MCnOJIb30Ba-
JIMCb He60JIbiliMe MOn:YJIMpOBaHHbIe pacceMBaTeJII1. 0630p 113MepeHI1M 6JII1)1(HerO
nOJI5I C 06111MpHOM 6M6JIl1orpa<pMeM npMBO,lJ,MTCfI B [14], a TaIOKe B pa60Tax [4, 18].
Bo Bcex 3TMX npoue,lI,ypax M3MepeHHoe 6JIM)I(Hee nOJ1e npe06pa3yeTcH B KOMnJ1eKC-
HYIO LIMarpaMMY HanpaBJIeHHOCTM B ,lJ,aJIbHeM 30He. 3aTeM npOBO,l1MTC5I 06paTHoe
npe06pa30BaHMe 3TOM LIMarpaMMbI HanpaBJIeHHOCTM K nJ10CKOCTM paCKpbIBa. Kor,lI,a
M3MepeHM 6J1M)I(HerO nOJ1H npOBO,lI,51TCH Ha nJ10CKOM nOBepXHOCTM, llJ1H 060l1x npe-
06pa30BaHMM MO)l(eT IfCrrOJIb30BaTbC5I 6bIcTpoe npe06pa30BaHMe <l>YPbe. Ba)l(HO
yqMTbIBaTb KoppeKUMIO ,lJ,B)'MepHOM ,lJ,l1arpaMMbI 30H,lI,a. B 3TOM CJIyqae ,lI,JIH yqeTa
BJ1M5IHM5I 30H,l1a nOJ1e 30Hlla npe,lI,CTaBJ1f1eTC5I B BM,l1e pa3JIO)l(eHMfI no rrJIOCKHM BOJI-
HaM [40, 32]. n0J1e3HbIMM I1CT01.JHMKaMM no M3MepeHMflM 6JIM)I(HerO nOJIH ,l1J1R npH-
MeHeHHR B KaQeCTBe ,l1lfarHOCTHQeCKOrO I1HCTPYMeHTa HBJI5IIOTCfI pa60TbJ [34, 17,
42, 35, 16, 20 ].
AHaJIOrMQHbIe npe06pa30BaHHH Mor)'T npl1MeHHTbCH K UMJ1MH,lI,pM1.JeCKMM [33] M
K 6MnOJIflpHbIM M3MepeHM5IM 6JIM)I(HerO rrOJIH [51, 52]. KoppeKUMH 30H,lI,a 11 npe06-
pa30BaHM5I 51BJI5IIOTC5I 60JIee CJIO)l(HbIMI1 rrpoueccaMM B CJIyqae c<pepMQeCKI1X 113Me-
peHMit 6JIM)I(HerO nOJI5I, HO 3TH 3a,lJ,aQI1 JIerKO pellialOTC5I C nOMOlUblO COBpeMeHHbIX
BbIQMCJIMTeJIbHbIX cpeLICTB [26, 41]. KOHeQHO, 113MepeHMfI B ,lI,aJIbHeit 30He MOryr
3aMeH5ITb 113MepeHI1f1 6JIM)I(HerO nOJIfi [15, 21, 31], o,aHaKO He06xo,llI1MO BbInOJIH5ITb
M3MepeHMe Ha IIJIOCKOCTIf, npoCTlfpalOll.J,eitC5I ,lI,aJIeKO 3a rrpe,l1eJIbI perneTKM, IUIM
npOBO,lJ,MTb M3MepeHMH B ceKTope yrJIOB, 6JIM3KOM K nOJIyc<pepe. KpoMe Toro, He-
06XO,lJ,IfMO 3HaTb <pa3Y If aMnJII1TY,ay, a MHorlfe nOJIMrOHbI ,aaJIbHeit 30HbI IUIIf KaMe-
pbI I1MelOT He,lJ,OCTaTOQHYIO ,lI,JIfi 3Toro 30HY OXBaTa.
IIpMMepbI ,lJ,HarHOCTIfKJ1 Ha rrJIOCKOCTH B 6J1IDKHeM 30He rrplfBe,lI,eHbI Ha
pHC. 15.5 H 15.6 ,lJ,JI5I rrO,lI,perneTKIf 1f3 MHKpOrrOJlOCKOBbIX M3JIyqaTeJIeit, CocToHIUeif
.. I

15.2. jl,ua2HOCmUlCG aHmeHHOU pewemKU 
eo
3JIeMeHTbI
rro,n:pe-
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Poc. 15.5. AMnJII1TY,L{HOe pacnpe,L{eJ1eHJ1e B aHTeHHOM perneTKe (BH,L{ Ha perneTKY)
[42]
113 8 x 16 3JIeMeHTOB. Ha pMC. 15.5 nOKa3aHa aMnJIMTy,aa B036y)1():(eHMR 3JIeMeH-
TOB, M 06Hap}T)KMBaIOTcR ,aBa JIe<peKTHbIx 3JIeMeHTa. <l>a3a B036y)1():(eHMH rrpMBO-
,aI1TCR Ha pl1C. 15.6, r,ae O,aMH 3JIeMeHT nOKa3bIBaeT HeCOOTBeTCTBYIOlIJ;YIO aMTIJIM-
TY,ay 11 <pa3Y [42].
,L(l1arHOCTI1Ka 6JIIDKHerO nOJIR CTaJIa MOlIJ;HbIM I1HCTpyMeHTOM ,lL1IR rrpOBepKM
peaJII13aUl111 HyxHoro paCTIpen.eJIeHMR rrOJIR B paCKpbIBe. ,LI.pyroH crroco6 rrpOBepKM
(a B 3TOM CJIyqae TaIOKe KOHTpOJIR) pacnpe,aeJIeHMR rrOJIR B paCKpbIBe rrpe,aYCMaT-
pl1BaeT I1CrrOJIb30BaHMe BTOpOH perneTKI1, pacnOJIO)KeHHOH pR,aOl\I, HO cJIa60 CBR-
3aHHOH C OCHOBHOH AP [3]. 3aMepeHHble MJIM paCCqMTaHHble B3aMMHble CBH3M 3a-
TeM MCrrOJIb3YlOTCH B aJIrOpMTMe ,aJIH onpe,aeJIeHMH pacnpe,aeJIeHMH OCHOBHOH AP.
HaKoHeu, B CJIyqae npl1eMHOH AP C QM<PPOBbIM <pOpMMpoBaHMeM JIyqa OTKa3 3JIe-
MeHTa MO)KeT 6bITb qaCTMQHO CKoppeKTMpOBaH nyreM paCqeTa nOJIeH CMe)I(HbIX
3JIeMeHTOB M rrOCJIe,aYIDlIJ;eH MHTepnOJIHQMeH ,aJIH <pOpMMpOBaHMH CMrHaJIa OT Hepa-
60TalOlIJ;erO 3JIeMeHTa [37].


Ffla6a 15. H3MepeHUJl U iJonycKu
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PUC. 15.6. <l>a30Boe pacnpe,aeJIeHMe B aHTeHHOH perneTKe (BI1.D: Ha pellieTKY) [42]
-60
-40
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40
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15.3. BonHOBOAHble MMMTaTopbl
IIpOCTbIM MHKpOBOJIHOBbIM HHCTpYMeHTOM, II03BOJI5IIOIl(HM H3MepHTb HMIIe.n:aHC
CKaHHpOBaHH5I (<pYHKllHOHaJIbHyro. 3aBHCHMOCTb MMrre.n:aHca 3JIeMeHTa OT yrJIOB
CKaHHpOBaHM5I) rrOClIe,[(OBaTeJIbHO ,[(JI5I O,[(Horo HarrpaBJIeHH5I CKaHHpOBaHH5I H <pHK-
CHpOBaHHOH qaCTOTbI, 51BJI5IeTC5I BOJIHOBO,[(HbIH HMHTaTOp (BOJIHOBo.n:Hoe Mo,[(eJIHpy-
lOIl(ee YCTPOHCTBO), pa3pa6oTaHHbIH B [9, 25]. XOT5I BHPTYaJIbHbIe CTeHKH e.n:HHHq-
OJ OJ
HOH 51qeHKH perneTKH, B lleJIOM, 51BJI5IIOTCR I1Mrre.n:aHCHbIMM CTeHKaMH, HMeeTCR
OJ
HeCKOJIbKO CHMMeTpHqHbIX IIJIOCKOCTeH 11 yrJIOB CKaHHpOBaHHR, rrpH KOTOpbIX
CTeHKH MOryT 3aMeIDITbCR l-I.neaJIbHbIM rrpOBO.n:HHKOM. 3TH CTeHKH MOryT TOr.n:a
6bITb MeTaJIJIHqeCKMM BOJIHOBO,[(OM, Ha-
. rpyxeHHbIM Ha ceKllMIO pellIeTKH C He-
60JIbllIHM QMCJIOM 3JIeMeHTOB. ,[(pyrOH
CIIoco6 BM3YaJIH3allMI1 rrpouecca IIpe,[(-
YCMaTpMBaeT pa3JIO)l(eHHe BOJIHbI, Harrpl1-
Mep, THIIa TE 10 , Ha .n:Be TIJIOCKHe BOJIHbI,
OTpa)l(alOIl(l1eC5I OT 60KOBbIX CTeHOK, KaK
M306pa)l(eHO Ha pMC. 15.7.
PUC. 15.7. ITJIOCKMe BOJIHbI, COCTaBJHIIO-
lURe MO,ay TE 10

Yron rrnOCKOH BOnHbI C OCblO BOnHO-
BO,l(a COOTBeTcTByeT yrJIY CKaHHpOBaHHH
8 0 . Kor,l(a HH O,l(HH H3 HH,l(eKCOB MO,l( He
paBeH HynlO, OT llIHpOKHX CTeHOK OTpIDKa-
eTCH ,l(OnOJIHHTeJIbHaH napa IIJIOCKHX BOJIH
[12]. ,LI;nH MeHee qaCTO Hcnonb3yeMoro
TpeyronbHoro BOJIHOBO,l(HOrO HMHTaTopa
HMeeTCH TPH Ha60pa rrnOCKHX BOJIH. ,LI;o-
IIYCTHMble IIJIOCKOCTH CKaHHpOBaHHH
H306pIDKeHbI Ha pHC. 15.8. B npHMoyrOJIb-
HOM BOJIHOBO,l(HOM HMHTaTope IIpeo6JIMa-
IOIII:He MO,l(bI 06eCIIeqHBalOT CKaHHpOBa-
HHe B OCHOBHbIX rrnOCKOCTHX, B TO BpeMH
KaK AnH CKaHHpOBaHHH B ,l(HarOHaJIbHMX
IIJIOCKOCTHX Tpe6YlOTCH 60JIee BbICOKHe
MO,l(bI. ,LI;JIH TpeyrOJIbHOrO BOJIHOBO,l(HOrO
HMHTaTopa HH311IHH THII MO,l(bI TE o6ec-
IIeqHBaeT IIJIOCKOCTH CKaHHpOBaHHH B,l(OJIb
IIJIOCKOCTeH CHMMeTpHH, a 60JIee BblCOKHe
MO,l(bI 06eCIIeqHBalOT IIJIOCKOCTH CKaHHpo-
BaHHH C ,l(pyrHM yrJIOM HaKJIOHa. Ha pHC. 15.9 nOKa3aHa AP C KBMpaTHoH ceTKOH
paCIIOJIO)l{eHHH 3JIeMeHTOB H ,UBYMH H3 MHorHX B03MO)l{HbIX THnOB HMHTaTopOB, B
v
KOTOpbIX HCIIOJIb3yeTcH IIpHMoyrOJIbHbIH BOJIHOBO,l(.
0 0 0
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15.3. BOJlHoooOHble UMumamopbl 
TEmo
TErnn
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TaTOpa
o
a
b
Pac. 15.9. PerneTKa C KBa,n;paTHoH ceTKOH C HMHTaTopaMH
06paTHM BHHMaHHe Ha HCnOJIb30BaHHe IIOJIOBHHHbIX H qeTBepTHbIx 3JIeMeH-
TOB. CHMMeTpHqHaH AP C reKCarOHaJIbHOH ceTKoH H306pIDKeHa Ha pHC. 15.10 BMe-
CTe C B03MO)l{}{bIMH BOJIHOBO.l(HbIMH HMHTaTopaMH. 06paTHM BHHMaHHe, qTO npH-
MoyrOJIbHbIe BOJIHOBO.l(HbIe HMHTaTopbI MOryT HCnOJIb30BaTbCR AnR AP C
v v
TpeyrOJIbHOH ceTKOH, a TaIOKe Ha TO, qTO HMHTaTopbI MOryT BKJIlOqaTb TonbKO
qaCTb 3JIeMeHTa.
THIIHqHbIH HMHTaTOp COCTOHT H3 nepeXO,UHOH CeKl(HH OT CTaH,l(apTHoro BOJIHO-
BO.l(a K BOJIHOBO.uy-HMHTaTOpy, caMoro BOJIHOBo.na-HMHTaTopa H nopTa 3JIeMeHTa. Ha
v v
Topue BOJIHOBo.na-HMHTaTopa nOMeIII:aeTCR TOHKHH MeTaJIJIHqeCKHH nHCT C III:eJIeBbI-

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t
28
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a
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a
b
b

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a
Pac. 15.10. PellIeTKa C llIecTHyrOJIbHOH ceTKOH C HMHTaTopaMH
MI1 3JIeMeHTaMI1 B Bl1,l:(e oTBepcTHit 3a 3THM nHCTOM HaxO,rU1TC BonHoBo,n;, BKJIIOqa-
IOIUHH HarpyxeHHbIH Ha cornacoBaH'HyID HarpY3KY IIOpT. B cnyqae ,n;pyrl1X 3neMeH-
 
TOB, KpoMe IUeneH, HJIH B cnyqae CnO)KHOH CTPYKTYPbI 3neMeHTOB Ha MeCTe
nnaCTI1HbI paCIIOnO)l(eHbI 3neMeHTbI AP. BonHoBo,n; ,n;OJDKeH 6bITb ,n;OCTaTOqHO JUIHH-
HbIM JUI Toro, qT06bI 3aT}'XalOIUHe MO,n;bI OT nepexo,n;HoH CeKUI1H OCna6JIH. Bce I1MI1-

TaTopbI ,lU1arOHaJIbHbIX IIJIOCKOCTeH co,n;ep)KaT HeIIonHbIe 3neMeHTbI, nocKonbKY Bon-
HOBO,n;-HMHTaTop Bcer,n;a 60nbIlle e,n;HHHQHOH QeHKH peIlleTKH. TpeyrOJIbHbIe
BOJIHOBO,l1HbIe HMHTaTopbI TaIOKe co.nep)KaT HenonHbIe 3neMeHTbI JUI nlO60H nnoc-
KOCTH cKaHHpOBaHI1. llOCKOnbKY 3KBH,lIMCTaHTHbIe peIIIeTKM MMelOT npMoyronb-
HbIe IDIM TpeyronbHbIe ceTKH, BonHOBO,n; MMMTaTopa OpraHMQeH MHoroyronbHbIMI1
CeQeHMMM C TPeM HJIM qeTbIpbM cTopoHaMM H BHYTpeHHMMM yrnaMI1 30, 45, 60
IDII1 90°. KOHeqHO, B 60nbIIIHHCTBe MMHTaTopOB I1cnonb3yeTc npMoyronbHbIH MnM

KBa.n.paTHbIH BonHOBO,n;, nOCKonbKY MO,n;bI BnIOTC IIpOCTbIMI1, a coe,n;MHeHl1e co
CTaH.napTHbIM BonHOBo.nOM BJUleTC HeCnO)KHbIM. llOCKOnbKY IIJIOCKHe BonHbI, co-
CTaBnIOIUMe BonHoBo,n;HbIH THII MO,n;bI, OTpIDKaIOTC B H-nnocKocTM, HMMTaUM CKa-
Hl1pOBaHH B H-IIJIOCKOCTH JII160 B paMKax rJIaBHOH, JIH60 B .nMarOHaJIbHOH nnOCKO-
CTI1 Mo,n;eJIHpyeTc BHO. 11 Hao6opoT, nOCKOJIbKY He Cyu.I;eCTByeT CHTYaUMI1, Kor,n:a
HMeeTC TOJIbKO ,n;Be COCTaBJIIOIUMe IIJIOCKOH BOJIHbI, OTPIDKaIOIUHec B E-IIJIOCKO-
CTM, JIMHeHHO IIonpM30BaHHbIe MMHTaTopbI E-nrrOCKOCTH OTCYTCTByIDT. llpl16nH-
)l(eHHa MMMTaUH B E-IIJIOCKOCTH 6y,n;eT paCCMaTPMBaTbC HIDKe.
113 npe,n;bI,l(yu.I;ero paCCMOTpeHH CHO, qTO KaJK,[(bIH MMMTaTOp n03BoneT no-
JIyqMTb orpaHHqeHHbIe ,n;aHHbIe 06 HMne,n;aHce CKaHHpOBaHIDI, XOT M3MeHeHHe qa-
CTOTbI MO)l(eT npe.nOCTaBHTb orpaHMqeHHbIH 06'beM ,n;oIIonHMTeJIbHOH HH<popMaUHM.
TaKHM o6pa30M, npouecc BbI60pa HaMMeHbIIIero KOJIHqeCTBa M HaM60JIee 3KOHO-
MMQHbIX I1MHTaTOpOB JUI ,n;aHHoro Bl1,l:(a npHMeHeHM no,n;06eH, KaK 3aMeQeHO B
[ 50], Mrpe B IllaXMaTbI.
PaccMoTpHM BOJIHOBO,n; npMoyrOJIbHOrO MMHTaTopa C pa3MepaMM a M b H 060-
3Haql1M I1HTepBaJI MeXlIY CHMMeTpMqHbIMM nnOCKOCTMM B perneTKe g 11 h
(CM. pMC. 15.9, r,n;e ceTKa perneTKH BJIeTC KBa.n.paTHoH, a e,n;MHHqHa qeHKa
HMeeT pa3Mep 2g x 2h. KpHTHqeCKa ,l1JIHHa BonHbI B BonHOBo,n;e-HMHTaTope paBHa
2
A.c .J<rn / 0)2 + (n / b)2 ,
(15.1)

15.3. BOIIHo6odHble UMumamopbl 
a yrJIbI CKaHl1pOBaHI1H COCTaBJIHIOT
. 8 A na (15.2)
SIn =- tan<p =-.
Ac mb
T or,lI,a
m 2. 8 n 2. 8 . ( 15.3)
- = - SIn COS<P - = - SIn SIn<p.
a A b A
Pa3MepbI BOJIHOBO,lI,a-I1MI1TaTOpa BbI6MpalOTcR KaK u;eJIbIe QI1CJIa, KpaTHbIe I1H-
TepBaJIaM I1JIOCKOCTI1 CI1MMeTpMM:
a =pg
b = qh,
(15.4)
r,lI,e p 11 q HBJIHIOTCH u;eJIbIMI1 QI1CJIaMI1. HaKOHell"
m = 2g sin8cos8
p h
n 2h. 8 .
- = - SIn SIn<p.
q A
( 15.5)
r
Ha pl1C. 15.11 nOKa3aHbI I1MI1TaTOpbI ,lI,JIH AP C KBa,apaTHoi1: CeTKO:H [25]. ,lLrrH MO-
,lI,eJIl1pOBaHI151 CKaHl1pOBaHI1R B H-rrJIOCKOCTI1, rJIaBHoti (C) I1JII1 ,lI,l1arOHaJIbHoi1: I1JIOC-
KOCTHX (IC) MCnOJIb3yeTcH TE IO MOn;a. Mo,Ua TEll MCrrOJIb3yeTcH npM MO,lI,eJIl1pOBa-
HI1I1 B E-nJ10CKocTM. Bce 3TO ,lI,JIH AP C rnarOM 3J1eMeHTOB, paBHbIM 0,575"-.
PaCqeT yrJIa CKaHMpOBaHI1H JIyqa npocToi1:. ,[(JI5I MMMTaU;MM CKaHMpOBaHI1H, 6JIM3KOrO
K HanpaBJIeHMIO HOpMaJIM K paCKpbIBY, K03<1><PMU;l1eHT p = 8 11 1/8 = 0,575 sin 12.56.
,[(JI5I OCHOBHoro MMI1TaTOpa B E-nJ10CKOCTI1 p = 3 M 1/3 = 0,575 sin 35.43. HaKOHeu.,
M5I ,al1arOHaJIbHOrO MMMTaTopa B E-nJIOCKOCTM p = 4 11 1/4 = (0.5751.fi) sin 37,94.
I1MMTaTopbI pellleTKH C paBHocTopoHHei1: TpeyrOJIbHOM ceTKoti rrOKa3aHbI Ha
pMC. 15.12 [5].
Mo,aa TE IO MCnOJIb3yeTcH B MMI1TaTOpax CKaHl1pOBaHMH B H-nJIOCKOCTI1 Ha ]4,
34 M 57°, B TO BpeMR KaK TE 20 Mo,aa MCnOJIb3yeTcH B Mo,aeJIM 40° CKaHMpOBaHI1H B
.: ...-: '-. -".' :.'
.--...... .." ."."
..-:. . ".
/"'.,:
'.lr.'
"'I;'
'.::;,  \i. " . .:.
.,,1,. \. 'ii,
.:3\\\. \\ ". \ .\\\ ."._
'\\;':';1
""::ti\,i;f::,f;\;{ \,.-- 'tel' -- " "'..('/:\:?\ .
.\.<:.....;\
Iiff,:;;, ,.'
} ..
::.:::.:::::"
.,,::::::,::
it:::-:
: \.-
...-:.
. ..:":,"
....... - '. . \ I
."
.,.- ...
:........... .If.".
-.
. .." :"
.' .:....:.":.:..."-:
':,i :i\I;
:.-
... . .'
; t;, .':, :,
}li... __,.' ':.
:':. .- ..'S:._:.' ....
;,",
.':
1:
-
.::.::':,::
-.:::.:'
,
;".."Iot1\'\.ot\Io"
.   , \,. . 
.... .' ',".
. - . -.. .'. :;.; -;':::::".::'.' -\:. .
'iltf!' ,':,.>\'jSiACJ
.\..... .
. ".."-"'."..,......,,.,.
,.
.' . :S. ...::.
. ::::
-.::,:'
1"
'. .<;..
.- .::':\:::
:;jD':'"
'. ...,.::,' ',;i;
3S.E.C _{C \ ' .' \C \
ll",)W";::\t;:i\';'1'-;"
'-:.-.-:
::-
:::':::'.":;
t
-:::
:::..-
- - . .
--::: ..'--.
.::
-- -
--'
...:'.
...:-.
.;.'
"':""::.':
,
12° H. C
35° H.. C
':7;.....':-. ::.:.::.__
;.-:.:::}
. -:...:-..--:...-
",\$\l\
j
:. _:: :..:'
.. - .
- -' -. -
.' -. --. -
. . ...... -..-..----.---...--.
PHC. 15.11. BOJIHOBO,L:(HbIe HMHTaTopbI KBa.rrpaTHOH ceTKH

 Dla6a 15. lf3MepeHUJl U iJonyC1cu
PHC. 15.12. BOJIHOBO,lIHbIe HMHTaTopbI TpeyrOJIbHOM ceTKH
H-nJIOCKOCTM. B npRMoyrOJIbHbIX MMHTaTopax cKaHHpoBaHHR B E-nJIOCKOCTI1 HC-
nOJIb3yeTcR TEll Mo,aa; B TpeyrOJIbHbIX HMHTaTopax CKaHHpOBaHMR B E-nJIOCKOCTM
MCnOJIb3yeTcR caMbIH HH3KHH THn MO,abI TM [46]. PaCqeT yrJIa CKaHHpOBaHMR npo-
CTOH. War Me)l()];y 3JIeMeHTaMH AP COCTaBJIReT 0,6A, a MR Mo,aeJIHpOBaHHR, 6JIH3-
Koro K HanpaBJIeHHIO, HOpMaJIbHOMY K paCKpbIBY, K03<P<PHIJ;HeHT p = 4 H 1/4 =
= 0,6.J3 sin 13.92. llpl1 ,apyrOM yrJIe CKaHHpOBaHHR HCnOJIb3yeTcR p = 3 H 1/3 =
= 0.6.J3 sin 18,71. )];JIR HMHTaTopa THna MO,abI TE 20 3HaqeHHR p = 3 H 2/3 = 0,6 x
x sin 39,90. 06paTHM BHHMaHHe, qto Ha <poTorpa<pMRx HeKOTopbIe H3 QaCTl1qHbIX
3JIeMeHTOB He Harp)')KeHbI.
)];JIR HCnOJIb30BaHHR HMHTaTo.pa H)')KHbIH THn MO,abI (MO,a) B036y)1(,[(aeTCR B BOJI-
HOBo,ae-HMHTaTope COrJIaCOBaHHbIM nopTOM (nopTaMH). HenOJIHbIe 3JIeMeHTbI He
Tpe6yIOT no,acoe,aHHeHHR K nopTY HJII1 HarpY3Ke, eCJIH OHH He B3aHMo,aeHCTBYIOT C
BOJIHOBO,aHOH Mo,noit O,nHaKO Bce 3JIeMeHTbI AP ,aOJI)I(HbI BKJIlOqaTb Bce Y3JIbI, B03-
,aeHCTByIDIIU1e Ha HaKallJIHBaeMyIO 3HeprHIO (,nH3JIeKTpHKH, ,nHa<pparMa H T .,lI,.). Ko-
3<P<PHI.{MeHT OTpa)l(eHI1R 113MepReTCR B BOJIHOBo,ae-HMHTaTope, qTO n03BOJIReT HaH-
TH HMne,aaHC, nOPo.)I()];eHHbIH na,nalOIl(eH nJIo.CKOH Bo.JIHo.it ArrR MHOr03JIeMeHTHbIX
HMI1TaTo.Po.B Heo6xo,nHMo. ,no.nOJIHHTeJIbHo.e npe06pa3o.BaHI1e ,IUUI nOJIyqeHHR UMne-
iJallca CKa1lUp08a1lUJl H3 I1Mne,naHca Bo.JIHbI. 3TO OCHOBbIBaeTCR Ha coe,nHHeHHH ,aBYX
BOJIHOBO,aOB H BKJIIOQaeT MI1HbI JIHHHH H TpaHc<popMaTop [24]. )];aJIee 6y,ayr pac-
CMOTpeHbI o,nHonopTOBbIe HMHTTOpbI, n03BOJIRIOIl(He IIOJIyqHTb 3HaQeHHe HMne-
,aaHca CKaHl1pOBaHI1R HanpRMyIO. B HMHTaTopax ,nH3JIeKTpI1QeCKH Harp)')KeHHbIX
3JIeMeHTOB 6bIJII1 paCCMOTpeHbI nOBepXHOCTHbIe Bo.JIHbI B [23].
BOJIHOBo,nHoe Mo,neJIl1pOBaHHe JIyqa no. Ho.PMaJIH K paCKpbIBY HeB03MO}I(HO, -
MaJIbIe yrJIbI Tpe6yIOT 60JIbIlll1X HMHTaTo.Po.B. TaK)I(e E-no.JIRpI13aIJ;HR, C03,aaBaeMaR
JII1HeHHbIM 3JIeMeHTOM, TOqHO Mo,neJIHPo.BaTbCR He Mo.)I(eT. B paHee paCCMo.TpeH-
HbIX I1MI1TaTOpax CKaHI1Po.BaHI1R B E-IIJIOCKOCTH HCnOJIb3yIOTCR 3JIeMeHTbI C KpyrO-
Bo.H nOJIRp113aIJ;l1eH IDII1 KpOCC-JIHHeHHO no.JIRpH30BaHHbIe 3JIeMeHTbI. npH BOJIHO-

15.3. BOJlHoeoOHble UMumamopbl 
v
BOLI:HOM MOLI:eJIHpOBaHHH cKaHHpoBaHHH B LI:HarOHaJIbHOH IIJIOCKOCTH )JJIH
E-nOJIHpH3aU;HH llCnOJIb3yeTcH napa MOLI: - TE H TM C If,[(eHTHqHbIMH HeH)'JIeBbI-
MH HH,L(eKCaMH. IIo,L(p06HbIH 0630p pa3pa60TKH H npaKTHqeCKOrO npHMeHeHHH
BOJIHOBOLI:HbIX HMHTaTopoB ,L(aH B [50], a TaIOKe B pa60Tax [24, 19, 10].
«O,L(HOnOpToBbIe» HMHTaTopbI HMelOT TOJIbKO O,aHH u;eJIbIH nopT 3JIeMeHTa Ha-
PMY C qaCTHqHbIMH nopTaMH. TaKHM 06pa30M, Tpe6yeTcH HarpY3Ka JIl1llIb o,aHoro
nopTa. 3TH npOCTbIe HMHTaTopbI XopOWO no,aXO,lJ;HT MH H-nJlOCKOCTH, 60JIbllIOrO
yrJla OTKJIOHeHHH JIyqa, pa60TbI B rJIaBHOH nJIOCKOCTH, r,L(e He nOHBJlHIOTCH ,L(HQ>-
paKl.{HOHHbIe JleneCTKH [6].
Ha pHC. 15.13 nOKa3aHbI TpH HMHTaTopa ,lLJIH pellIeTKH C KBMpaTHoH CeTKO:H.
80 Bcex I1CnOJIb3yeTcH TEol Mo,aa. Ha pRC. 15.13,a HcnOJlb3YlOTCH 3HaqeHHH p = 4,
q = 2 C JIyqOM B rJIaBHOH llJIOCKOCTH, OTKJIOHeHHbIM Ha yrOJI 30°. Ha pHC. 15.13,b
HCrrOJIb3yIOTCH 3HaqeHHH p = 3, q = 2, C JIyqOM B rJIaBHOH IIJIOCKOCTH, OTKJIOHeH-
HbIM Ha yrOJI 41.8°. Ha pHC. 15.13,c HCrrOJIb3YlOTCH 3HaqeHHH p = q = 2 npH yrJIe
45°. War perneTKH COCTaBJIHeT A/2. MMHT,arOpbI paBHocTopoHHeH TpeyrOJIbHOH
(cHMMeTpHqHOH rnecTHyrOJIbHOH) perneTKH nOKa3aHbI Ha pHC. 15.14. PHC. 15.14,b
oT06pa)l(aeT.rryq B rJIaBHOH H-llJIOCKOCTH C yrJIOM CKaHHpOBaHHH 60° H 3HaqeHHH-
MH p = q = 2. Ha pHC. 15.14,a nOKa3aH HMHTaTOp CKaHHpOBaHHH B ,aHarOHaJIbHO:H
rrJIOCKOCTH, p = q = 2 H C yrJIOM JIyqa 30°. TpeyrOJIbHbIM HMHTaTOp nOKa3aH Ha
pHC. 15.14,c; 3,aeCb rrOKa3aTeJIb paBeH 3, a JIyq B ,aHarOHaJIbHOH IIJIOCKOCTH pacrro-
JIO)l(eH rro,a yrJIOM 14,81 0.
TaIOKe HMHTHpOBaJIHCb AP C MHKpOnOJIOCKOBbIMH 113JIyqaTeJIHMH. B [48] HC-
rrOJIb30BaHbI LI:Ba BOJIHOBO,L(HbIX HMHTaTopa CKaHHpOBaHHSI B H-nJIOCKOCTH, COOT-
(a)
(c)
(b)
8
8
PHC. 15.13. O.aHorropToBbIe HMHTaTopbI .aJUI pemeTKH C KBa.apaTHoH ceTKOH
(a)
(c)
o
o
(b)
o
PHC. 15.14. O.aHonopToBbIe HMHTaTopbI ,L(JUI pemeTKH C reKCarOHaJIbHOH ceTKOH

b Dla6a 15. Jf3MepeHUfl U iJonyC1w
BeTCTBYIOrn:l1e pl1c. 15.13,a 11 b. AKKypaTHo BOCnp0I13Be.n:eHbI 3anl1TKa 113nyqaTeneH
11 COnpOTI1BneHI1R HarpY30K. TaKl1e I1MI1TaTOpbI o6eCneqIIBalOT yrnbI 11,92° 11
43,53°. 3TI1 I1ccne.n:OBaHI1R HallInl1 CBoe npo,n:OJDKeHl1e B pa60Tax [1, 2]. EbInl1 npo-
Be.n:eHO BonHOBo.n:Hoe Mo,aenl1pOBaHl1e C MO,aOM TE 10 AP, COCTORll(eH II3 MI1KpOnO-
u
nOCKOBbIX 113nyqaTenel1, 3anl1TbIBaeMbIX npl1 nOMOml1 30H,L1;a, II MIIKpononOCKOBbIX
113nyqaTeneH C .n:onOnHI1TenbHbIMI1 3neMeHTaMI1. Mcnonb30BaH O.n:IIHOqHbIM n;eHTpa-
nbHbIM 113nyqaTenb C qeTbIpbMR TaKlfMI1 )l(e, HO o6pe3aHHbIMI1 Ha qeTBepTb no yr-
naM (CM. pl1C. 15.14). CeTKa pellIeTKIf 6bIna cl1MMeTpl1qHOM reKCarOHaJIbHOM, a llIar
pellIeTKM o6eCneQl1BaJJ yron YCTaHOBKI1 nyqa 22,48°.
I1MI1TaTop 60nee o6rn:ero Ha3HaqeHI1R pa3pa6oTaH B [22, 13]. TaKoM I1MMTaTOp
n03BonReT onpe,aenl1Tb npo6oiJuMocmb npl1 pa3nl1QHbIX yrnax OTKJIOHeHI1R nyqa, a
TaIOKe MO,LJ;enl1pOBaTb ,LJ;11<ppaKl(IIOHHbIe neneCTKIf. B BOJIHOBO,aHOM I1MI1TaTOpe MC-
nOJIb3yeTcR MHoro 3neMeHTOB pemeTKIf, BKJIlOqaR uenbIe 11 QaCTI1QHbIe 3neMeHTbI,
HO .n:Ba Harp}')KeHHbIX. ,L(aJIee npOBo,aRTCR 113MepeHI1S1 K03<P<PI1UMeHTa nepe.n:aql1
Me)l(,L{y 3TI1MM .n:BYMSI 3neMeHTaMI1. B CBOJO Oqepe,ab, .n:Ba aKTI1BHbIX 3neMeHTa 3aHM-
MalOT nocne.n:OBaTenbHO Bce n0311Ul111 B MMI1TaTOpe, KOTopbIe n03BOJIRIOT paCCQI1-
TaTb 3aBI1CIIMOCTb npo8oiJuMocmu npl1 CKaHl1pOBaHl111 MSI N yrJIOB CKaHl1pOBaHI1S1,
eCJII1 I1MeeTCSI N 3JIeMeHTOB I1MI1TaTopa.
BOJIHOBo,UHoe Mo,UenIIpOBaHl1e MO)l(HO TaIOKe peaJIM30BaTb Ha KOMnblOTepe, r.n:e
CTeHKlI BonHOBo.n:a 11 3neMeHTbI pemeTKI1 Mo.n:enl1pYIOTCR MeTo.n:OM MOMeHTOB I1nl1
CeTOQHbIMI1 npoue.n:ypaMII, I1cnonb3yeMbIMI1 B MeTo.n:ax KOHeQHbIX 3JIeMeHTOB II Me-
To,ae KOHeqHbIX pa3HocTeM BO BpeMeHH6M o6nacTI1
15.4. AonYCKM B aHTeHHblX peweTKax
OlllM6KM (norpelllHocTM, OTKJIOHeHI1S1) B AP BKJIlOqalOT OlllM6KM B pa3MemeHMM M
Opl1eHTaUMM 3neMeHTOB, a TaIOKe Oml16KI1 <pa3bI M aMnnl1T)',LlbI B036Y)l(,L{eHMR 3JIe-
MeHTOB. Bce 01ll116KII OTHOCSlTCSI K ,LlBYM Tl1naM: CHCTeMaTlf1leCKHe 11 cnyqaMHbIe.
EOJIbllIaSl qaCTb OlllM6oK npe,aCTaBnSleT C060M COQeTaHl1e 060MX Tl1nOB. npM CI1CTe-
MaTMqeCKMX OllIM6Kax (KoppenMpoBaHHbIe OllII16K1f Ii OllIH6KM OTKJIOHeHMR) 06bIq-
HO Tpe6yeTc5I paCqeT AP, BKJIlOqalOll(MM KOHKpeTHbIe OIlIM6KM; He cymecTByeT 06-
Il{MX npaBI1JI .LIJIR TaKI1X 3<t>cpeKToB, nOTOMY QTO HMeeTCSI MHoro Tl1nOB H COqeTaHI1M
3TI1X 01llM6oK. O,aHaKo cnyqaMHbIe ollII16KM MOryT 6bITb CTaTMCTMqeCKH 06pa60Ta-
HbI, H 3TO n03BOn5leT nonyqMTb o6ml1e 11 qaCTO npOCTbIe pe3ynbTaTbI.
B XOpOlllO CKOHCTpYl1pOBaHHbIX 11 113rOTOBJIeHHbIX AP 01ll116KM pa3MemeHM5I 11
opMeHTaUI1II 3neMeHTOB MaJIbI II MOryT 3aMeHRTbCR 3KBI1BaJIeHTHbIMM <t>a30BbIMI1
01lI116KaMI1 (11, eCJII1 He06xo.n:MMO, aMnnI1TY,LJ;HbIMI1). TaKlfM 06pa30M, B .n:aHHOM
pa3,UeJIe peqb l1,UeT TonbKO 06 3cpcpeKTax ollII16oK <t>a3bI 11 aMnnMT)'llbI. KBaHToBa-
HMe <pa3bI M CBSl3aHHbIe C 3TI1M 5IBneHI1S1 paCCMaTpl1BalOTCR no.n:po6HO B rnaBe 2.
OnTI1MI13aQI1R pellIeTOK C yqeToM OrpaHI1QeHI1H no .n:onYCKaM 06Cy)I(!{aeTC5I B rna-
Be 4. OllII16KI1 B AP OueHI1BaJOTCR no TpeM HanpaBJIeHI1RM: CHII)I(eHMe HanpaBJIeH-
HOCTM (ycl1neHI1S1); B03paCTaHI1e Cpe,LlHerO YEJI neneCTKOB M HeKOTopbIX OT.n:eJIb-
HbIX 60KOBbIX neneCTKOB; 113MeHeHI1e TOQHOCTM YCTaHOBKIf 11, B03MO)l(HO, <POpMbI
OCHOBHoro nyqa. Ka)l(,[(aSl 113 OllII160K aHaJII1311pyeTcR OT.n:eJIbHO. llpl1 3TOM ,aena-
eTCSI .n:onyIIleHl1e 0 TOM, QTO Bce cnyqaMHbIe OllIM6K1f HOpMaJIbHO pacnpe.n:eneHbI
(raYCCOBO pacnpe.n:eneHl1e) 11 I1MelOT HyneBoe cpe.n:Hee 3HaqeHI1e 11 .n:McnepCI1IO 0 2 .

15.4. J!onycKu 8 aHmeHHblX peUlemKax 
PemeTKH npHHMMalOTCR ,nOCTaTOqHO 60JlbllIMMH, TaK qTO HCnOJIb3yeTcR ueHTparrb-
HaR npe,neJIbHa TeopeMa. 3TO npe,nnOJIaraeT npHMeHeHHe .LJ:JIR JIHHeHHOH peilleTKH
N > 10 If XeJIaTeJIbHO N > 20. AHaJIH3H'pyroTCB JIHHeHHbIe AP; pacnpOCTpaHeHHe
nOJIyqeHHbIx pe3YJIbTaTOB Ha nJIOCKHe ,nBYMepHbIe pemeTKH npHBo,nHTCR n03.nHee.
15.4. 1. CHM>KeHMe HanpaBneHHocTM M YBenMlLleHMe
cpeAHero YPOBHR 60KOBbiX neneCTKOB
PaCCMOTpHM JIHHeHHyro AP H3 H30TponHbIX 3JIeMeHTOB C MHOXHTeJIeM pemeTKH
fo (u) = L An exp jnnu.
C yqeToM 01lIH60K K03<P<PHUHeHT CTaHOBHTCR
An (1 + 8 a) exp j8 <p ,
( 15.6)
(15.7)
r,ne omH6Ka aMnJIHT)',nbI COCTaBJIReT l)a, a oillH6Ka cl>a3bI 8 <p B pa,aHaHax. ,lJ;HarpaM-
Ma HanpaBJIeHHOCTH no MOI.l.{HOCTH npHHHMaeT BH,n
f2 = LLAnA;' (1 + 8 an)(1 + 8 am) exp{J18 <pn - 8 <pm + (n - m)nu]}.
( 15.8)
B COOTBeTCTBMH C BbImeYKa3aHHbIMH ,nonym;eHHRMH cpe,nHee 3HaqeHHe CYMMbI
OJ
He3aBHCHMbIX nepeMeHHbIX paBHReTCR CYMMe cpe,nHHX 3HaqeHHH H ,naeT cpe,nHIOIO
,LU1arpaMMY HanpaBJIeHHOCTH
0'2
1 2 = 1"2 +-
J 0 GO '
( 15.9)
r,ae Go - 3TO HarrpaBJIeHHOCTb (K03<l><l>HUlfeH HanpaBJIeHHOrO ,aeHCTBHR - KH,D;)
6e3 yqeTa omH60K, 0 2 = 0 2 a + 0 2 q>' r,ne 0 a - 3TO CTaH.LJ:apTHOe OTKJIOHeHMe aMTIJIH-
Ty,n;bI, a Oq> - CTaH.LJ:apTHOe OTKJIOHeHHe <l>a3bI B pa,aHaHax. 3HaqeHHe KH)];, HOp-
MHpOBaHHoe OTHOCHTeJIbHO Go, paBHReTCR
,

G 1
-  exp(--a 2 ) 
Go 1 +0'2
(15.10)
HarrpHMep, OIIIH6KH 10, paBHbIe <pa3e 10° H aMnJIHT)',ne 1 -,n;E, CHlUKalOT Ha-
npaBJIeHHOCTb Ha 0,193 ,nE. 3Ta TeopHR pa3pa60TaHa B [44, 45], r,n;e .nOKa3bIBaeTCH,
qTO ypOBeHb ,aHarpaMMbI RBHO nOBbIlliaeTCR TOJIbKO B 06JIaCTH 60KOBbIX JIerreCTKOB.
3TO YBeJIHqeHHe 6bIBaeT MeHbille .LJ:JIR pemeTOK C 60JIee BbICOKOH HanpaBJIeHHO-
CTblO. OqeBIi,nHo, qTO YBeJIHqeHHe YEJI (SLL) BJIHHeT Ha aHTeHHbI C HH3KHM YEJI
B 60JIbIIIeH CTeneHH, qeM Ha aHTeHHbI C paBHOMepHbIM aMTIJIHT)',nHbIM pacnpe,neJIe-
HHeM H YEJI, paBHbIM MHHYC 13 ,nE. 113 ypaBHeHHR (15.10) CJIe,nyeT, qTO cpe.nHee
3HaqeHHe YEJI COOTHOCHTCR C rrpOeKTHbIM ypOBHeM 60KoBoro JIeneCTKa YEJI o
(SLL o ) CJIe.nyroI.l.{HM 06pa30M:
SLL = SLL o  1 + 0'2 / (Go' SLL2 0 ). (15.11)
3TO OTpaxeHO Ha pHC. 15.15 B 3aBHCHMOCTH OT YHHBepCaJIbHOrO napaMeTpa o.
OTMeTHM, QTO B 3TOM BbIpaxeHHH ypOBHH 60KoBoro JIeneCTKa BbIpaxeHbI B
BOJIbTax. OqeBH,LJ:HO, qTO 60JIee KpynHbIe AP (c 60JIee BbICOKOH HanpaBJIeHHOcTblO)
RBJIRIOTCR MeHee qYBCTBHTeJIbHbIMH. IIpH6JIH3HTeJIbHbIH pe3YJIbTaT .LJ:JIR cpe,nHero

b flla8a 15. H3MepeHUJI U iJonyclCu
-10 -13.26
dB
-20 -20
npOeKTHpyeMbIH
YEJI -30
,,-..., -30
LQ
I::!
--
,..J -40
,..J
CI.) -40
-50
-50
-60
0.001
0.01
0.1
allG
PHC. 15.15. 3aBHcHMoCTb cpe.n;Hero 3HaqeHHH ypOBHR 60KOBoro JIeneCTKa OT YHH-
BepCaJIbHOrO K03<P<PHlU1eHTa
YBJI OTHOCHTeJIbHO H30TponHoH aHTeHHbI OCHOBaH Ha anepType TIJIOI.Qa,Il.blO A
C HanpaBJIeHHOCTIO 43tA/A 2 [36]:
SLL  n(02 a + o2cp). (15.12)
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IIIar pellIeTKM, Kpl1Tepl1eM OIIII16KI1 OTKJIOHeHI1S1 YCTaHOBKI1 JIyqa, HOpMl1pOBaHHOM
no OTHOllIeHl11O K llIl1pMHe JIyqa no ypOBHIO 3-,[(E, RBJIReTCR
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SLL. SLL o [ SLL2 + SLL ) SLL. SLL o
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L.

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llOCKOJIbKY cymecTByeT 60JIbllIaH B03MO)l(HOCTb Toro, QTO BepoHTHoCTb 6y.n:eT 3a,aa-
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3Toro, /YEno = I/A = 0,2935 3HaqeHl1e, KOTopoe MO)KeT 6bITb nOJIyqeHo Hanp5l-
MYIO 113 pJ1c. 15. 18. )];aJIee .n;eJIaeM JJ:onymeHMe 0 TOM, qTO YCHJIeHMe AP paBHo
20 J(E 11 YEll pacccMaTpMBaeMoti perneTKM paBeH - 30 ,n:E. TOf,n:a  = 0,009281, H
rrOCKOJIbKY 0 2 = 0 2 0 + 0 2 q> = 2/2Go, 06maH .n;HcnepCHH 01lIH6KH 0 2 = 0,01723. ECJIH
Terrepb JJ:HcnepCHM aMnJIMTYJJ:bI M <pa3bI paBHbI, 0 0 = 0,0928 Ii oq> = 5,32°. TaKMM 06-
pa30M, KpHTepMH OTKJIOHeHHH 01lIH60K, paBHbIe 9% no aMnJIMTYlI.e M 5° no <pa3e,
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yrroMMHaeTCH BbIllIe, 60JIee JJ:JIMHHbIe AP MMelOT 66JIbllIMe JJ:onYCKM, paBHO KaK M
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JIHTepaTYpa
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.
,

cnMCOK nOHSlTM'1 M COKPAUJ.EHMM
AMC (Artificial Magnetic Conductor)
ARPA (Advanced Research Project
Agency)
BDF (Beam Deviation Factor)
BW (Bandwidth)
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Factor)
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- I1CKYCCTBeHHbIH MarHI1THbII1 npOBo.n:HI1K
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Antennas) pacceSlHMeM
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Domain) HOM 06JIaCTM
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Ceramic) paMI1KIl
MSA (Microwave Scanning Antennas) - CKaHMpYIOW;l1e aHTeHHbI CBq
MSA (Minimum Scattering Antennas) - aHTeHHbI C MIlHHMaJIbHbIM paCCe5lHlleM
PD F (Probability Density Function) - <PYHKlJ;Il51 nJIOTHOCTIl Bep05ITHOCTM
QL (Quantization Lobes) - JIeneCTKIl KBaHTOBaHI15I
RCS (Radar Cross Section) - 3<p<peKTIlBHa5I OTpa)l(alOll.{a5I nOBepXHOCTb
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SLM (Spatial Light Modulator) - npocTpaHcTBeHHbIM MOLlYJI5ITOP CBeTa
SLR (Sidelobe Ratio) - BeJII1QIlHa, o6paTHa5I YEJI
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Waveguides)
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CnucOic COKpaU{eHUii d
- aHTeHHaH pemeTKa
- aHaJIOrO-U;H«PPOBOH npe06pa30BaTeJIb
- 6bICTpOe npe06pa30BaHHe <l>YPbe
- ,JJ;HarpaMMa HanpaBJIeHHOCTH
- ,l(HarpaMMa HanpaBJIeHHOCTH aHTeHHbI
- ,l(H«ppaKI.J:HOHHbIH JIeneCTOK
- ,l(HarpaMM006pa3yJOIUee YCTPOHCTBO
- K03<P<PHU;HeHT HCnOJIb30BaHHH nOBepXHOCTH
- K03<P<PHU;HeHT HanpaBJIeHHOrO ,neHCTBHH
- K03<P<PHU;HeHT nOJIe3HOrO ,neHCTBHJI
- K03<P<PHU;HeHT CTOJlqeH BOJIHbI no HanpIDKeHHIO
- K03<P«PHU;HeHT YCR1IeHHJI
u
- npOC1paHCTBeHHbIH MO,n;YJIHTOp CBeTa
- npe06pa30BaHHe <l>ypbe
- ypOBeHb 60KOBoro JIeneCTKa (ypOBeHb JIeneCTKa OTHOCHTeJIbHO ypOBHH
JIyqa)
- YJIbTpaKOpOTKHe BOJIHbI
- <pa3HpOBaHHaH aHTeHHaH peIIIeTKa
- <pHJIb1'p HIDKHHX qaCTOT
- qHCJIOBOe nporpaMMHoe ynpaBJIeHHe
- 3<p<peKTHBHaH nOBepXHOCTb pacceHHHH

nPEAMETHblA YKA3ATEnb
AKTMBHoe COnpOTMBneHMe CKaHMpOBa-
HMH 246, 273
AKTMBHbI:H MMne,n:aHC 18
AHTeHHa fperopM 6nM)l(Hero nonH 522
C perneTKoH B036y)1{,lJ;eHMH 523
C perneTKoH M nMH30H 524
co C<POKycMpoBaHHoH perneTKoH 524
AHTeHHa KaccerpeHa 6nIDKHero nonH
517
AHTeHHaH perneTKa 6erymeH BonHbI
198
AHTeHHaH perneTKa BaH ATIa 502
l(MJIMH,n:pMqeCKaH pellIeTKa 432
B3aMMHaSl npOBo,n:MMOCTb menH 442
,n:H<ppaKUMoHHble neneCTKM 434
ceKTopHbIH 452
cMH<pa3Hoe B036y)1{,lJ;eHMe nyqa 425
cpaBHeHHe C nJIaHapHOH (nJIOCKoH)
perneTKoH 454
meJIeBO:H 3JIeMeHT 533
AHTeHHaSl perneTKa C MMHMMaJIbHOH
M36bITOqHOCTblO 124
AHTeHHaSl perneTKa C He3KBH,n:MCTaHT-
HbIM pacnOJIO)KeHMeM 123
AHTeHHaH perneTKa C llIYMOBOH Koppe-
JISlUMeH 507
AHTeHHaSl perneTKa, COCTOHI.UaH M3
1130TponHbIX 3neMeHTOB 55
AHTeHHbI C MMHMMaJIbHbIM pacceHHMeM
257, 295
AnepTYPHOe pacnpe,n:eneHHe, CM. CHH-
Te3 ,n:HarpaMMbI HanpaBneHHOCTH
BOKOBble neneCTKH 47, 91, 398, 484,
519, 527, 538, 541
B3aHMHaSl npOBo,n:MMOCTb 443
B3aHMHaH CBH3b, CM. B3aHMHbIH MMne-
,n:aHC
B3aHMHbIH MMne,n:aHC KapTepa 260, 280
B3aMMHbIH MMne,n:aHC 245, 247, 259
BI1BaJIb,n:l1, CM. pynOpHbIH TEM H3JIY-
qaTenb
BHHbeTl1pOBaHHe 520
BHellIHHH BOJIHOBOH <pMnbTp 299
BonHoBo,n: C OTKpbITbIM KOHUOM 168
BOJIHOBO,n:, BCTpoeHHbIH B nO)J)loXKy
168
JIeneCTKH KBaHTOBaHMSI 42, 53
nepeKpbIBalOI.UHHCH 53
BOJIHOBo,n:HaH JIHH3a 396
BOJIHOBO,n:HbIH HMI1TaTOp 289
BocCTaHOBJIeHHe nOTepb CKaHMpOBaHMH
516
BbIHy)I{,lJ;eHHOe B036y)1{,lJ;eHMe 246
BblcoKoTeMnepaTYPHble CBepxnpOBO,n:-
HMKH, CM. CBepxnpOBo,n:HHKM
BbITeKalOI.UaSl BOJIHa 290
BaH ATI 502
,LJ;yroBaH 428, 452
KOJIbueBaSl 419
KOHeQHO-6eCKOHeQHaSl 312, 320
KOHHQeCKaH 461
KOH<popMHaSl 418
JIHHeHHaH 24, 67
MaJIaSl 315
MMHMMaJIbHaH M36bITOQHOCTb 124
He3KBH,n:MCTaHTHbIe 118
nepeM3JIyqalOll(aSl 502
nJIOCKaSl/ ,n:BYMepHaSl/nJIaHapHaSl 61,
122
nOJIy6ecKOHeQHaH 307
pacnpe,n:eneHHaSl 217
CBH3aHHaH 482
c<pepHQeCKaH 474

,IJ;BYMepHaH MaTpHua MaK<I>apJIeHL(a
371
,lI;BYMepHaH <pM,n:epHaH nMH3a 388
L(enOJIHpH3aUHH 442, 466
,lJ.HafHocTMKa aHTeHHOH perneTKJ1 530
,lJ.MarpaMMa DHKMopa-CnenMaHpa 84
,lJ.MarpaMMa HanpaBneHHOCTM aKTHBHO-
fO 3JIeMeHTa 18
,lJ.HarpaMMa HanpaBJIeHHOCTM BYllBOP-
,n:a-JIoycoHa 112
j

..
-'.
,[(HarpaMMa HanpaBneHHOCTH ,[(OJIbcpa-
qe6bIllieBa 71, 77, 350, 438
,[{HarpaMMa HanpaBJIeHHOCTH XeMMHH-
ra 92
,[(HarpaMMa CKaHHpOBaHHR 3JIeMeHTa
18, 248, 273, 450
)J;l1arpaMMa CKaHl1pOBaHHR 3neMeHTa
npH pacceRHMM 18
)J;l1arpaMMa HanpaBJIeHHOCTM XaHceHa
129
)J;l1arpaMMoo6pa3yJOrn;ee YCTPOMCTBO
364
)J;I1HaMH1JeCKMH ,n:Hana30H, CM. [CBO-
60,n:HbIH OT BbI6poCOB] ,n:I1HaMH1JeCKHH
,n:l1ana30H
)J;HnOJIb 149, 259, 270, 285
)J;l1nOJIbHbIe aHTeHHbIe pemeTKM 59
KOJIJII1HeapHbIM 60, 412
napaJIJIeJIbHbIH 60, 347, 412
;:I;l1cneprI1PYIOrn;ee OnTOBOJIOKHO 234
)J;McnepcHR 19
)J;McppaKl.(110HHbIe neneCTKH 28, 37, 39,
329, 434, 437
,[(HcppaKUHoHHbIH JIeneCTOK KOJIbueBoi1
aHTeHHOH pemeTKM 425
)J;orrycK, CM. IIorpemHocTI1
"'
1
E,n:HHI1QHaR OKp}')KHOCTb 68, 111, 116
)
3epKaJIbHbIe aHTeHHbI C pemeTKaMM
511
3MeeBH,n:HaR JIHHMR nHTaHHR, CM. qac-
TOTHoe CKaHHpOBaHHe
3MeeBHaR cxeMa nHTaHI1H, CM. qac-
TOTHoe CKaHHpOBaHMe
1
I
I

J
HneaJIbHaR ,n:HarpaMMa HanpaBJIeHHO-
CTH 3JIeMeHTa 246
113MepeHM$I 527, 530
HMHTaTop, CM. BonHOBo.n:HbIH HMI1Ta-
TOp
HMne,n:aHC CKaHMpOBaHIDI 18, 246, 248,
267, 273, 308
I1Mne.n:aHc, CM. B3aHMHbIH I1Mne.n:aHC
I1HTepnoJI$IU;HR nyqa 403
I1TepaU;MoHHbIH MeTO,n: HbIOToHa-Pa<p-
COHa 110, 115, 197, 207
J
}
IIpeaMemublu YK03ameJ/b 
KrracCMQeCKI1e aHTeHHbI C MHHMMaJIb-
HbIM paCCeRHl1eM 257
KOJIbu;eBaR aHTeHHaR pemeTKa 419
KOMa 511
KOMneHcalU1$I 3<p<peKToB CKaHHpOBa-
HMH 289
BHellIHMe <pI1JIb'TpbI 299
MHoroMo.n:oBbIM 295
rreperopo,n:KH 292
I.J;enM 292
IlIHpoKoyrOJIbHOe COrJIaCOBaHl1e I1M-
neL(aHCOB 299
rn;eJIb C MOHOnOJIHMM 298
KOHe1JHa$I aHTeHHaH pellIeTKa 307
KOHe1JHO-6eCKOHe1JHaR aHTeHHa$I pe-
rneTKa 312
KOHM1.JecKaR aHTeHHaR perneTKa 461
KOHycHaR ll.(eJIeBaR, CM. PynopHbIH
TEM 113JIyqaTeJIb
KOH<popMHaR aHTeHHaR pellIeTKa 418
K03<P<PMI.J;HeHT HCrrOJIb30BaHMR nOBepx-
HOCTI1 (KI1II) aHTeHHOM pellIeTKM,
CM. KH,[(
K03<P<PMQHeHT HCrrOJIb30BaHMR nOBepx-
HOCTH KHTI 76, 77, 82, 83, 89, 90,
91, 92, 97, 98, 99, 104, 131, 132, 133,
135, 137, 142
CM. K03<P<PMUMeHT HanpaBJIeHHOrO
,n;ei1cTBHR (KH)J;)
K03<P<PMIJ;HeHT OTKJIOHeHI1H nyqa 512
K03<P<PHU;HeHT OTKJIOHeHM$I 512
K03<P<PHIJ;MeHT OTpa)l(eHI1H npM CKaHH-
pOBaHMM 247
K03<P<PMQl1eHT rrOJIe3HOrO ,n:eMcTBM$I,
CM. KilL( aHTeHHOM pemeTKH
K03<P<PHIJ;MeHT YMHHeHI1H 86, 96, 102,
109, 133, 134, 141
KpyroBoe pacnpe.n:eJIeHMe XaHceHa
511
KCBH 179
KynOJIbHaR JII1H3a 393
JIarpaH)l(a 338
J1enecTKH KBaHTOBaHMR 42
no.n:pellIeTKa 51
pac<pa3MpoBaHHe 53
<pa30BpamaTeJIb 42

 IlpeaMemHlJlu YKtl3ameJIb
JIHHeMHaR aHTeHHaR pemeTKa 23
60KOBbIe JIeneCTKH 27, 79, 84, 85
.aHarpaMMbI HanpaBJIeHHOCTH 23, 67,
72, 79, 86, 100, 102, 105
,ltH<ppaKllHoHHbIe JIeneCTKH 28
JIeneCTKH KBaHTOBaHH5I 46, 49
HanpaBJIeHHOCTb 55, 76, 80, 89, 338,
341
nOJIoca nponYCKaHHR 31, 42, 192, 343
YCTaHOBKa JIyqa 33, 198, 210, 541
llIHpHHa JIyqa 26, 74, 80, 86
3<p<peKTHBHoCTb JIyqa 81, 90
JIHH3a POTMaHa 374, 375
JIHH3a 374, 387, 391
JIHHH5I 3a,aep)l(}(H 44
JIHCT TOKa 244
JIyq CneUHaJIbHOH <pOpMbI 112
MaTpHua 266
MaTpHl.(a DaTJIepa 365, 427
MaTpHua EJIacca 369
MaTpHua HOJIeHa 369
MeTo.a 60JIbllIHX perneTOK 308
MHKpOnOJIOCKOBaR ne'IaTHaR aHTeHHa
(MHKpOnOJIOCKOBbIH H3JIyqaTeJIb) 175,
263, 282, 499
MHOrOJIyqeBaR aHTeHHaR perneTKa 364
lIBYMepHa51 <pHlIepHaH JIHH3a 388
,lteJIHTeJIb MOIUHOCTH 364
HHTeprrOJIHI.(HH JIyqa 403
JIHH3a POTMaHa 374, 375
MaTpHua DaTJIepa 365, 427
MaTpHua DJIaCCa 369
MaTpHl.(a MaK<I>apJIeH.aa 371
MaTpHl.(a HOJIeHa 369
opTOrOHaJIbHOCTb 405
MHOrOMO,ltOBbIe 3JIeMeHTbI 295
MO.aaJIbHbIe PH.abI 444, 476
Mo.aeJIb fH66ca 320
MO.aYJIb 215,217,222,228
HarrpaBJIeHHOCTb aHTeHHOM pellIeTKH,
CM. CHHTe3 .aHarpaMMbI HarrpaBJIeH-
HOCTH
HarrpaBJIeHHOCTb
aHTeHHa KaccerpeHa 6JIIDKHerO nOJIR
521
aHTeHHaR perneTKa, COCTOSImaR H3
H30TPonHbIX 3JIeMeHTOB 55
BeitrrHcc 104
BHJIbHeB 98
.aHarpaMMa HanpaBJIeHHOCTH fieMJIHCa
,lLTIH KpyrJIOM arrepTYpbI 140
JIHHeMHaH aHTeHHa perneTKa 55, 337
o.aHorrapaMeTpH'IeCKaH lIHarpaMMa
HanpaBJIeHHOCTH XaHceHa 129
o,nHonapaMeTpH'IeCKOe pacnpe.aeJIe-
HHe TeMJIOpa 79
oceBOM OCH 64, 341
nJIaHapHaH (IIJIOCKaH)/.aBYMepHaSi aH-
TeHHaH perneTKa 61, 63
pacrrpe.aeJIeHHe XaHceHa- By.a'bHPlIa
342
perneTKH ,L(oJIb<pa-Qe6bIrneBa 74, 79,
340
CBepXHarrpaBJIeH 338, 343, 350
ceKTopHaSi IDIH .ayroBaH aHTeHHaR pe-
rneTKa 428, 452
n - rrapaMeTpH'IeCKOe pacrrpe.aeJIeHHe
Teitrropa ,lLTIH KpyrJIbIX anepTYP 133
n-napaMeTJ)H'IeCKOe pacrrpe.aeJIeHHe
TeMJIOpa 88
HarrpaBJIHIOIUHH KOCHHYC 34
He3KBH,ltHCTaHTHaH aHTeHHaSi perneTKa
118, 122
HH3KHM ypOBeHb 60KOBbIX JIeneCTKOB
91, 208, 398, 542
06JIaCTb BH.aHMOCTH 29
06JIaCTb HMrre,l1aHCa 268
0606IUeHHaH .aHarpaMMa HanpaBJIeHHO-
CTH 281
O,nHonapaMeTpH'IeCKOe pacnpe.aeJIeHHe
Teitrropa 79
OnTHMH3al.(HH 350
rpa,aHeHT 113, 119, 144
HanpaBJIeHHOCTb 354
CYMMapHaSi H pa3HOCTHaSi .aHarpaMMbI
HanpaBJIeHHOCTH 105, 142
OrrTHMH3al.(IDI MeTo.aOM MHHHMH3al.(1I1I
p-ro nOpH.lIKa 114, 145
OnTHMH3al.(HH C orpaHH'IeHHSlMI1 350
OrrTH'IeCKaH (<}>oToHHaH) ClICTeMa nlI-
TaHHH 230

aKYCTO-OnTHqeCKaH nepeKJIlOqaeMaH
232
,LI;BO.l1qHaH nepeKJIIOQaeMaR JI.I1H.I1H 3a-
,LI;ep)l(K.I1 230
,LI;.I1CnepCHOHHoe OnTOBOJIOKHO 234
OnTl1qeCKOe npeo6pa30BaH.I1e <DYPbe
237
OnTOBOJIOKHO, CM. OnTI1QeCKlie (<pOTO-
HHbIe) C.I1CTeMbI nl1TaH.I1H
OpTOrOHaJIbHbIe JIyql1 399, 405
OTHOIlleH.I1e 60KOBoro JIeneCTKa (SLR)
70
OTpa)l(aTeJIbHaH aHTeHHaH peIlleTKa
495
neQaTHbIe aHTeHHbI (3JIeMeHTbI) 499
nOJIoca nponYCKaH.I1H 500
<l>a3.11pOBaH.I1e 497
3JIeMeHTbI 497
3<p<peKTI1BHOCTb 496
OIIIH6Ka YCTaHOBKH JIyqa 541
napaJIJIeJIbHaH JIHHHH nl1TaHHH 216
ITaCC.I1BHbIH neQaTHbIH 3JIeMeHT 181,
284
ITeperOpO,LI;KlI 292
TIepeH3JIyqalOIUHe aHTeHHbIe peIlleTKH
502
conpIDKeHHe no <pa3e 503
<pa30BaH HHBepCHH 504, 506
Ill}'MOBaH KOppeJIHl.{HH 507
ITepeKpbIBalOIUlieCH nOlIpeIlleTKH 53,
396
ITepI10,LI;I1QeCKaH HQeHKa, CM. E,n;HHHQ-
'-'
HaH HQel1Ka
ITeQaTHaH aHTeHHa (3JIeMeHT), CM.
HKpOnOJIOCKOBaH neqaTHaH aHTeH-
Ha
TIeqaTHbIe aHTeHHbI, CM. M.I1KpOnOJIO-
CKOBaH neQaTHaH aHTeHHa
ITeqaTHbIH pynop, CM. PynopHbIM TEM
H3JIyqaTeJIb
IlJIaHapHaH (nJIOCKaH) aHTeHHaH pe-
IlleTKa 33
reKCarOHaJIbHaR ceTKa 40
,n;l1arpaMMbI HanpaBJIeHHOCTH 34
,LI;11<ppaKl.{110HHbIe JIeneCTKH 37, 39,
329
llpeiJMemHblu YK03ameJlb d
JIeneCTKH KBaHTOBaHIiH 48
HarrpaBJIeHHOCTb 61, 63, 142
npoeKTHpOBaH.I1e 215
CI1HTe3 ,n;.I1arpaMMbI HarrpaBJIeHHOCTH
128, 134, 139, 146
'-' '-'
cpaBHeH.I1e C ceKTOpHO.l1 aHTeHHOH
perneTKoH 454
ynpaBJIeH.I1e JIyqOM 42, 541
IIIHpliHa JIyqa 34, 131, 134
3tP<peKT.I1BHOCTb JIyqa 132
ITJIOCKa5I IIleJIeBaH aHTeHHa5I perneTKa
128, 219
TIoBepxHocTHaH aHTeHHaH perneTKa
418
TIoBepxHocTHaH BOJIHa 288
TIoBepxHocTb neTl.{BaJIH 513
TIorpelliHocTH 237, 349, 382, 389
TIopeIIIeTKa 219
pa3HOCTHaH lI.I1arpaMMa HanpaBJIeH-
HOCTH 104
TIOJIHHOM qe6bIrneBa 71, 78
TIOJIHa5I rrpOBOHMOCTb IUeJIH 161, 166,
442, 444
TIoJIoca nponYCKaHMH 31, 42, 177, 192,
500
TIOJIy6ecKOHeQHaH perneTKa 307
TIoH5ITlie ,n;11<ppaKl.(MOHHbIX JIeneCTKOB
267
IlopT JIyqa 375
TIOpT 3JIeMeHTa 375
TIoCJIe,n;oBaTeJIbHaH JI.I1H.I1H n.l1TaHHH
191, 223
IIocJIe,n;oBaTeJIbHoe B036}')K,IJ;eH.I1e 221
TIoCJIe,n;oBaTeJIbHOe nl1TaHHe 105
IIOCJIelIOBaTeJIbHO-o6'belI.I1HeHHa51 cxeMa
nl1TaHI1H 216, 227
IIoTepH rrp.l1 CKaHl1pOBaHI1H 514
TIpHHl.{HnbI TeHJIOpa 70
IlpOBO,n;I1MOCTb aHTeHHOM peIlleTKI1 6e-
ryIl(ei1 BOJIHbI 202
IIpoBo,n;HMocTb, CM. B3aHMHaH npOBO-
,n;HMOCTb
TIpo,n;OJIbHaR IlleJIb 161
TIpocTpaHcTBeHHa51 06JIaCTb 259, 313
IlpocTpaHcTBeHHbIi1 MHO)l(lfTeJIb Ha-
npaBJIeHHOCT.I1 24; CM. TaIOKe CI1HTe3
,lI;l1arpaMMbI HarrpaBJIeHHOCTIi

 IIpeoMemHblu YKa3ameAb
Pa3HOCTHaR ,lU1arpaMMa HarrpaBJIeHHO-
CTH 30JIOTapeBa 107
Pa3HocTHaR ,aHarpaMMa HarrpaBneHHO-
CTH C pacrrpe,aeJIeHHeM fieitrrHcca 103,
138, 529
Pa3HOCTHaR ,aHarpaMMa HarrpaBneHHO-
CTH 98, 101, 107, 138
Pa3HocTHaR ,UHarpaMMa C KPYTH3HOM
99, 108
Pacnpe,aeJIeHHe aHTeHHOM perneTKH,
CM. CHHTe3 ,[J;HarpaMMbI HanpaBJIeH-
HOCTH
Pac<pa3HpoBaHHe 53
PeaKTHBHoe conpOTHBJIeHHe CKaHHpo-
BaHHR 273
Pe3HcTHBHoe cnauaHHe 399
Pe30HaHCHaH aHTeHHaH perneTKa 192,
196
PerneTKH B <pOKaJIbHOM nJIOCKOCTM 511
Pynop, CM. PynopHbIM TEM H3JIyqa-
TeJIb
PynopHbIM TEM H3nyqaTeJIb 169, 287
CBepHYTaR MaTpHua 287
CBepxHanpaBJIeHHaR aHTeHHaR perneTKa
343,.350
CBepxnpoBo,aHHKH 349, 361
CBo6o,aHoe B036}')KL{eHHe 246
[CBo6o,aHbIM OT BbI6poCOB] ,l(HHaMHqe-
CKHM ,l(Harra30H 231
CBR3aHHbIe aHTeHHbIe perneTKH 482
HMne,aaHC 482
coe,aHHeHHe nocpe,aCTBOM peaKTHBHO-
ro corrpOTHBJIeHHR 491
TOKH 484
<t>a3a 483
CerHeT03JIeKTpHqeCKaH JIHH3a 395
CHMMeTpHpYIOIl(HM TpaHc<popMaTop
152, 172
CHHTe3,UHarpaMM HanpaBJIeHHOCTH 67
fieMJIHCC 103, 138
fiHKMopa-CneJIMaHpa 84
By,aBOp,l(a-JloycoHa 112
,[J;oJIb<pa-Qe6bIrneBa 71, 350
e,aHHHQHaH OKpyxHOCTb 68
30JIOTapeB 107
KonbueBOM 60KOBOH JIerreCTOK 145
nyqH CneU;HaJIbHotf <pOpMbI 112
HH3KHH YPOBeHb 60KOBMX JIeneCTKOB
91
o,aHorrapaMeTpHQeCKaR ,l(HarpaMMa
HanpaBJIeHHOCTH XaHceHa 129
o,aHonapaMeTpHQeCKOe pacnpe,aeJIe-
HHe TetfJIopa 79
npHHUHnbI Teitrropa 70
pa3HocTHbIM 98, 104
pacnpe.LIeJIeHHe EetfJIHCa ,l(JIH KpyrJIbIX
anepTYP 138
<popMa orH6alOmeM 60KOBbIX JIeneCT-
KOB 109
XaHceH- By,a'bRp,a 342
XeMMHHf 92
3IDIHOIT 115
n - napaMeTpHQeCKOe pacnpe,aeJIeHHe
BHJIbHeBa 95
n-rrapaMeTpl1QeCKOe pacnpe,aeJIeHHe
TeluIopa ,l(JIH KpyrJIbIX anepTYP 133
n-napaMeTpHQeCKOe pacnpelI.eJIeHHe
TeMJIOpa 85
CHHTe3 3JIJIMOTIa 115
CI1H<pa3Hoe B036}')KL{eHHe JIyqa 425
CHcTeMaTHQeCKHe norpernHOCTH 237
CHcTeMHbIe <paKTopbI 17
CHcTeMbI fIMTaHHR aHTeHHbIX perneTOK
191
6erYIl(aR BOJIHa 198, 202
,aBYMepHbIH 219
3epKaJIbHaR aHTeHHa 511
06'be,aMHeHHbIM 216
OnTHQeCKHM 230
napaJIJIeJIbHbIM 216
nOCJIe,aoBaTeJIbHbIM 191
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Q (06pOTHOCTb) 290, 343, 352

WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING
KAI CHANG, Editor
Texas A&M University
FIBER-OPTIC COMMUNICATION SYSTEMS, Third Edition. Covind P. Agra-
wal
ASYMMETRIC PASSIVE COMPONENTS IN MICROWAVE INTEGRATED
CIRCUITS. Hee-Ran Ahn
COHERENT OPTICAL COMMUNICATIONS
o Betti, Giancario De Marchis, and Eugenio Iannone
PHASED ARRAY ANTENNAS: FLOQUET ANALYSIS, SYNTHESIS, BFNs,
AND ACTIVE ARRAY SYSTEMS. Arun K Bhattacharyya
HIGH-FREQUENCY ELECTROMAGNETIC TECHNIQUES: RECENT AD-
VANCES AND APPLICATIONS. Asoke K. Bhattacharyya
RADIO PROPAGATION AND ADAPTIVE ANTENNAS FOR WIRELESS COM-
MUNICATION LINKS: TERRESTRIAL, ATMOSPHERIC, AND IONOSPHE-
RIC. Nathan Blaunstein and Christos G. Christodoulou
SYSTEMS · Silvell
COMPUTATIONAL METHODS FOR ELECTROMAGNETICS AND MICRO-
WAVES · Richard C. Booton, jr.
ELECTROMAGNETIC SHIELDING. Salvatore Celozzi, Rodolfo Araneo, and Gi-
ampiero Lovat
MICROWAVE RING CIRCUITS AND ANTENNAS. Kai Chang
MICROWAVE SOLID-STATE CIRCUITS AND APPLICATIONS · Kai Chang
RF AND MICROWAVE WIRELESS SYSTEMS. Kai Chang
RF AND MICROWAVE CIRCUIT AND COMPONENT DESIGN FOR WIRE-
LESS SYSTEMS . Kai Chang, lnder Bahl, and Vijay Nair
MICROWAVE RING CIRCUITS AND RELATED STRUCTURES, Second Editi-
on . Kai Chang and Lung- Hwa Hsieh
MULTIRESOLUTION TIME DOMAIN SCHEME FOR ELECTROMAGNETIC
ENGINEERING. Yinchao Chen, Qunsheng Cao, and Raj Mittra
DIODE LASERS AND PHOTONIC INTEGRATED CIRCUITS. Larry Coldren
and Scott Corzine
EM DETECTION OF CONCEALED TARGETS. David J. Daniels
RADIO FREQUENCY CIRCUIT DESIGN. w: Alan Davis and Krishna AgaIWal
MULTICONDUCTOR TRANSMISSION-LINE STRUCTURES: MODAL ANA-
LYSIS TECHNIQUES. A. Brandao Faria

Wiley series in microwave and optical engineering 
PHASED ARRAY-BASED SYSTEMS AND APPLICATIONS. Nick Fourikis
FUNDAMENTALS OF MICROWAVE TRANSMISSION LINES. Jon C. Free-
man
OPTICAL SEMICONDUCTOR DEVICES. Mitsuo Fukuda MICROSTRIP CIR-
CUITS . Fred Cardiol
HIGH-SPEED VLSI INTERCONNECTIONS, Second Edition. Ashok K. Goel
FUNDAMENTALS OF WAVELETS: THEORY, ALGORITHMS, AND APPLI-
CATIONS. jaideva C. Coswami and Andrew K. Chan
HIGH-FREQUENCY ANALOG INTEGRATED CIRCUIT DESIGN · Ravender
Go/a/ (ed.)
ANALYSIS AND DESIGN OF INTEGRATED CIRCUIT ANTENNA MODU-
LES . K C. Gupta and Peter S. Hall
PHASED ARRAY ANTENNAS, Second Edition. R. C Hansen
STRIPUNE CIRCULATORS. Joseph Helszajn
THE STRIPLINE CIRCULATOR: THEORY AND PRACTICE · Joseph Helszajn
LOCALIZED WAVES. Hugo E. Hernandez-Figueroa, Michel Zamboni-Rached, and
Erasmo Recami (eds.)
MICROSTRIP FILTERS FOR RF/MICROWAVE APPLICATIONS. Jia-Sheng
Hong and M. J. Lancaster
MICROWAVE APPROACH TO HIGHLY IRREGULAR FIBER OPTICS. Huang
Hung-Chia
NONLINEAR OPTICAL COMMUNICATION NETWORKS. Eugenio Iannone,
Francesco Matera, Antonio Mecozzi, and Marina Settembre
FINITE ELEMENT SOFTWARE FOR MICROWAVE ENGINEERING. Tatsuo
Itoh, Giuseppe Pelosi, and Peter P. Silvester (eds.)
INFRARED TECHNOLOGY: APPLICATIONS TO ELECTROOPTICS, PHO-
TONIC DEVICES, AND SENSORS. A. R. Jha
SUPERCONDUCTOR TECHNOLOGY: APPLICATIONS TO MICROWAVE,
ELECTRO-OPTICS, ELECTRICAL MACHINES, AND PROPULSION SYS-
TEMS . A. R. Jha
OPTICAL COMPUTING: AN INTRODUCTION. M. A. Karim and A. S. S. Aw-
wal
INTRODUCTION TO ELECTROMAGNETIC AND MICROWAVE ENGINEE-
RING. Paul R. Karmel, Gabriel D. Cole/, and Raymond L. Camisa
MILLIMETER WAVE OPTICAL DIELECTRIC INTEGRATED GUIDES AND
CIRCUITS. Shiban K Koul
ADVANCED INTEGRATED COMMUNICATION MICROSYSTEMS · Joy Las-
kar, Sudipto Chakraborty, Manos Tentzeris, Franklin Bien, and Anh- Vu Ph am

 Wiley series in microwave and optical engineering
MICROWAVE DEVICES, CIRCUITS AND THEIR INTERACTION. Charles A.
Lee and G. Conrad Dalman
ADVANCES IN MICROSTRIP AND PRINTED ANTENNAS. Kai-Fong Lee and
Wei Chen (eds.)
SPHEROIDAL WAVE FUNCTIONS IN ELECTROMAGNETIC THEO-
RY. Le-Wei Li, Xiao-Kang Kang, and Mook-Seng Leong
ARITHMETIC AND LOGIC IN COMPUTER SYSTEMS. Mi Lu
OPTICAL FILTER DESIGN AND ANALYSIS: A SIGNAL PROCESSING AP-
PROACH · Christi K Madsen and Jian H. Zhao
THEORY AND PRACTICE OF INFRARED TECHNOLOGY FOR NONDEST-
RUCTIVE TESTING. Xavier P.  Maldague
METAMATERIALS WITH NEGATIVE PARAMETERS: THEORY, DESIGN,
AND MICROWAVE APPLICATIONS. Ricardo Marques, Ferran Martin, and Ma-
rio Sorolla
OPTOELECTRONIC PACKAGING. A. R. Mickelson, N. R. Basavanha lly, and
 C. Lee (eds.)
OPTICAL CHARACTER RECOGNITION. Shunji Mori, Hirobumi Nishida, and
Hiromitsu Yam ada
ANTENNAS FOR RADAR AND COMMUNICATIONS: A POLARIMETRIC
APPROACH. Harold Mott
INTEGRATED ACTIVE ANTENNAS AND SPATIAL POWER COMBI-
NING . Julio A. Navarro and Kai Chang
ANALYSIS METHODS FOR RF, MICROWAVE, AND MILLIMETER-WAVE
PLANAR TRANSMISSION LINE STRUCTURES. Carn Nguyen
FREQUENCY CONTROL OF SEMICONDUCTOR LASERS. Motoichi Ohtsu
( ed.)
WAVELETS IN ELECTROMAGNETICS AND DEVICE MODELING. George
W. Pan
OPTICAL SWITCHING. Georgios Papadimitriou, Chrisoula Papazoglou, and An-
dreas S. Pornportsis
SOLAR CELLS AND THEIR APPLICATIONS. Larry D. Partain (ed.)
ANALYSIS OF MULTICONDUCTOR TRANSMISSION LINES. Clayton R.
Paul
INTRODUCTION TO ELECTROMAGNETIC COMPATIBILITY, Second Editi-
on · Clayton R. Paul
ADAPTIVE OPTICS FOR VISION SCIENCE: PRINCIPLES, PRACTICES, DE-
SIGN AND APPLICATIONS. Jason Porter, Hope Queener, Julianna Lin, Karen
Thorn, and Abdul Awwal (eds.)

Wiley series in microwave and optical engineering 
ELECTROMAGNETIC OPTIMIZATION BY GENETIC ALGORITH1S · Yahya
Rahmat-Samii and Eric Michielssen (eds.)
[NTRODUCTION TO HIGH-SPEED ELECTRONICS AND OPTOELECTRO-
NICS · Leonard M. Riaziat
NEW FRONTIERS IN MEDICAL DEVICE TECHNOLOGY. Arye Rosen and
Hare! Rosen (eds.)
ELECTROMAGNETIC PROPAGATION IN MULTI-MODE RANDOM ME-
DIA. Harrison E. Rowe
ELECTROMAGNETIC PROPAGATION IN ONE-DIMENSIONAL RANDOM
MEDIA. Harrison E. Rowe
HISTORY OF WIRELESS. Tapan K. Sarkar, Robert J. Mailloux, Arthur A. Oliner,
Magdalena Salazar-Palma, and Dipak L Sengupta
PHYSICS OF MULTIANTENNA SYSTEMS AND BROADBAND PROCES-
SING. Tapan K. Sarkar, Magdalena Salazar-Palma, and Eric L Mokole
SMART ANTENNAS. Tapan K Sarkar, Michael C. Wicks, Magdalena Sala-
zar-Palma, and Robert J. Bonneau
NONLINEAR OPTICS. J C. Sauter
APPLIED ELECTROMAGNETICS AND ELECTROMAGNETIC COMPATIBI-
LITY . Dipak L. Sengupta and Valdis  Liepa
COPLANAR WAVEGUIDE CIRCUITS, COMPONENTS, AND SYSTEMS. Ra-
inee N. Simons
ELECTROMAGNETIC FIELDS IN UNCONVENTIONAL MATERIALS AND
STRUCTURES. Onkar N. Singh and Akhlesh Lakhtakia (eds.)
ANALYSIS AND DESIGN OF AUTONOMOUS MICROWAVE CIRCUITS · Al-
mudena Suarez
ELECTRON BEAMS AND MICROWAVE VACUUM ELECTRONICS. Shulim
E. Tsimring
FUNDAMENTALS OF GLOBAL POSITIONING SYSTEM RECEIVERS:
A SOFTWARE APPROACH, Second Edition. James Bao-yen Tsui
RF/MICROWAVE INTERACTION WITH BIOLOGICAL TISSUES. Andre Van-
der Vorst, Arye Rosen, and Youji Kotsuka
InP-BASED MATERIALS AND DEVICES: PHYSICS AND TECHNOLO-
GY. Osamu Wada and Hideki Hasegawa (eds.)
COMPACT AND BROADBAND MICROSTRIP ANTENNAS. Kin-Lu Wong
DESIGN OF NONPLANAR MICROSTRIP ANTENNAS AND TRANSMISSI-
ON LINES. Kin-Lu Wong
PLANAR ANTENNAS FOR WIRELESS COMMUNICATIONS. Kin-Lu Wong
FREQUENCY SELECTIVE SURFACE AND GRID ARRAY. T. K. Wu (ed.)

b Wiley series in microwave and optical engineering
ACTIVE AND QUASI-OPTICAL ARRAYS FOR SOLID-STATE -POWER COM-
BINING . Robert A. York and Zoya B. Popovic (eds.) .
OPTICAL SIGNAL PROCESSING, COMPUTING AND NEURAL NET-
WORKS. Francis T. S. Yu and Suganda Jutamulia
ELECTROMAGNETIC SIMULATION TECHNIQUES BASED ON THE FDTD
METHOD. Wenhua Yu, Xiaoling Yang, Yongjun Liu, and Raj Mittra
SiGe, GaAs, AND InP HETEROJUNCTION BIPOLAR TRANSISTORS. Jiann
Yuan
PARALLEL SOLUTION OF INTEGRAL EQUATION-BASED EM PROB-
LEMS . Yu Zhang and Tapan K. Sarkar
ELECTRODYNAMICS OF SOLIDS AND MICROWAVE SUPERCONDUCTI-
VITY. Shu-Ang Zhou

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AHTEHHblM PEWETKAM
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ISBN 978-5-94836-323-3
9 785948 363233
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