MICROWAVE ANTENNA THEORY

MICROWAVE ANTENNA THEORY

AND DESIGN

MA,TSA (7H( “SETTS INSTIT(-TE OF TE~H.VOLOG1’

RADIATION L.ABOR.iTORY SERIES

~oar(l of l<klitors

LorIs X. RI!) EXOIR, IldI/oJ-z’P1-C’lzicf GEORGE 13. COLT.IXS, I)epv(y I?dllor-iw(’hiej

13RITIY)X CF{.4XCE, S. .4. (20[TDSMIT, R. G. HERB, HUBERT XI. J.ANES, JI-LIAN K. Kxlrr, JAMES I,. L.A}VSON,LEON B. LISFORO, CAROL G. l[oxrco~lERy, C. \TEWTON, .41.BER~

hl. STOXE,LOCTISA. TCRNER,GEORGE13.VALLEY, JR., IIERBERT H. JVHE+TON

1, RADAR SYSTEM ~NG1xEERING—I?idenOILT 2. IL.* DAR.41Ds TO NAVIGATION—Hdt 3. RADAR BEAcoNs—Robe?is

4. LOIZAx—Pierce, McKenzie, and lf’ood trar<i 5. ~’~1.sE GE NERA’roRs-G/asOe and ~.i’{mc(lz 6. LIICROWAVE NIAGxETRoxs—COl/l /(,s

7. KLYSTRONS AND MICROIV,+VETRIOIIES Ilm Ilf/[on, Knipp, and Kt[per 8. PRINCIPLES OF MICROWAVE CIII(L lrfi– .Ifo,dqo), tei-y, Ddie, and l’uwell 9. hIICROJVAVETRAXSMISSIOX CIRCI Im -– 12[Lyan

10, \~AVEGUIDE HAsDBOOK—3~arc( (7i/z

11. TECHNIQUE OF iWCROWAVE JIE.iSLmMEWY ,IIOII!{IOUIWY

12. klICRO\VAVEANTEINXA TIIEOFCY.+x I) L)ESIGX --,’iiller 13. PROPAGATION OF SHORT RAI)IO IV.\vEs -Keru 14. IIflCROWAVE ~uPI.ExERs-–S)) L7(/lLrLun<l .lIot<([yo!ltery 15. CRYSTAL RECTIFIERS-T•rMY and 11’k~t))Ler 16. }lICROWAVE hfIxERs—~ounft

17. COMPONENTS HANI)BOOK—~/Uck/)7L~n

18. VACUUM TUBE AMPLIFIERS- T-(i//c!/ aml Tl”a//,rLan

19. \TAvEFOW.ls—(;hanceJ Hfighes, .l/ac.\zcho/, Sayle, and l\’tllia JfLs 20, ~LECTRONIC TIME hIEAScREMENTs-(’/mnce, Hu/sizer, ~[fw.~lcho~,

and tFilliams

21. ~1.ECTROXIC Instruments-Greenlrood, Hofakl))], un~{ .~~uc]iae 22. CATHODE RAY TUBE D1spl,Ays—So//er, Starr, and t’alkg 23, llICROWAVE RECEIYERS-Van I’oorhis

24. THRESHOLI) SIG NALS—La?OSOn a!Ld ( ‘hlenheck

25. THEORY OF SERYOMECIIAXISMS -Ja?,L&!, .I-lchols, and Phillips 26. RADAR SCAXXERS AXD R.41)oA1~s-Cad!/, Kareltlz, and Turner 27. COMPUTIXG hlECH.+XISMS AND I,lxK.iGEs-Swboda

28. INDEX—HelLnQj

\ ,.

MICROWAVE ANTENNA THEORY AND DESIGN

Ediied by

SAMUEL SILVER

ASSOCIATE PROFESSOR OF ELECTRICAL ENGINEERING UNNEB.SITY OF CALIFORNIA, i3EP.KELEY

OFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT NATIONAL DEFENSE RESEARCH COMMITTEE

FIRST EDITION

NEW YORK, TORONTO LONDON

McGRAW-HILL BOOK CO,MPANY, INC.

1949

., ,.,

MICROWAVE .$xTEN\-.$ THEC!R Y .ISD DESIGN

(hPYRIGH,T, 1949, B>- THE

hlC~RA W-HILL BOOK~(IIIP.I.NY, lKC.

P31XTEI) lx THE U>-lTEI) STATES OF AMERICA

.111rights Testwed. This book, or parts thereof, HI(IY not be reproduced in any form (rilho?(l prr)rlission of

/he ,L)(//)/ishers,

THE MAPLE PRESS COMPANY, YORK, PA,

*ienCe

m

,,

/y,, )’” /

,,

‘. \

lf[CRO JV.4 VE A NTE.VNA TfZEOR Y EDITORIAL STAFF

SAMUEL SILVER HUBERT M. JAMES

AND DESIGN

CO.VTRIB L’TI.VG A PTHORS

J. E. llATON R. hf. R IZDHEFFER

L. J. I;YGES J. R. RISSER

T. J. KEARY S. SILVER

H. KRUTTER O. A. TYSON

(2. G. hlAcFARL.4NE L. C. \’AN ATTA

Foreword

T

HE tremendous research and development effort that ~vent into the development of radar and related techniques during }Vorld IJ ar II resulted not only in hundreds of radar sets for military (and some for possible peacetime) use but also in a great body of information and ncm techniques in the electronics and high-frequency fields. 13ecause this basic material may be of great value to science and engineering, it seemed most important to publish it as soon as security permitted.

The Radiation Laboratory of 311T, ~vhich operated under the super- vision of the National Defense Research (’ommittec, undertook the great task of preparing these volumes. The ~vorl{ described berein, ho\\-eyer,is the collective result of ~vork done at many laboratories, Army, Xavy, university, and industrial, both in this country and in JZngland, (<anada, and other Dominions.

The Radiation Laboratory, once its proposals ]vere approved and finances provided by the Office of Scientific Research and l)evelopment, chose Louis N. Ridenour as Fklitor-in-(’bief to led and direct tbe entire -, project. An editorial staff ]vas then selected of those best quulificd for

this type of task. Finally the authors for the various volumes or chapters or sections were chosen from among those experts ~vho ~t-ere intimately familiar with the various fields, and ]vbo \vere able and willing to ]vrite the summaries of them. This entire staff agreed to remain at ~vork at MIT for six months or more after the \\-orkof the Radiation I.aboratory was complete. These volumes stand as a monument to this group.

These volumes serve as a memorial to tbe unnamed hundreds and thousands of other scientists, engineers, and others ]vho actually carried on the research, development, and engineering work tbe results of which are herein described. There ~vere so many involved in this ~vork and they worked so closely together even though often in \\-idelyseparated labora- tories that it is impossible to name or even to know those ]vho contributed to a particular idea or development, (My certain ones ~vho~u-ote reports w- or articles have even been mentioned, But to all those ~vho contributed

~ in any way to this great cooperative development enterprise, both in this

~ country and in England, these volumes are dedicated,

a

L. A. DLTBRIDGE.

z 1,!

Preface

T

^HE need that arose during the ]var for utilizing the microwave region of the radio frequency spectrum for communications and radar stimu- lated the development of nelv types of antennas. ‘l’he problems and design techniques, lying as they do in the domain of both applied electro- magnetic theory and optics, are quite distinct from those of long-wave antennas. It is the aim of the present volume to make available to the antenna engineer a systematic treatment of the basic principles and the fundamental microwave antenna types and techniques. The elements of electromagnetic theory and physical optics that are needed as a basis for design techniques are developed quite fully. Critical attention is paid to the assumptions and approximations that are commonly made in the theoretical developments to emphasize the domain of applicability of the results. The subject of geometrical optics has been treated only to the extent necessary to formulate its basic principles and to sho~v its relation as a short wavelength approximation to the more exact methods of field theory. The brevity of treatment should not be taken as an index of the relative importance of geometrical optics to that of electro- magnetic theory and physical optics. It is in fact true that the former is generally the starting point in the design of the optical elements (reflectors and lenses) of an antenna. However, the use of ray theory for microwave systems presents no new problems over those encountered in optics—on which there are a number of excellent treatises—except that perhaps the law of the optical path appears more prominently in micro~vave applications.

In the original planning of the book it was the intention of the editors to integrate all of the major wQrk done in this country and in Great Britoin and Canada. This proved, however, to be too ambitious an undertaking. Nfany subjects have regrettably been omitted completely, and others have had to be treated in a purely cursory manner. It \vas unfortunately necessary to omit two chapters on rapid scanning antennas prepared by Dr. C. V. Robinson. The time required to revise the material to conform ~vith the requirements of military security and yet to represent an adequate exposition of the subject would have unduly delayed the publication of the hook. Certain sections of Dr. Robinson’s material have been incorporated into Chaps. 6 and 12.

ix

x ^PREFACE

I take pleasure in expressing here my appreciation to Prof. Hubei-t M. James who, as Technical Editor, shared with me much of the editorial work and the attendant responsibilities. The scope of the book, the order of presentation of the material, and the sectional division within chapters were arrived at by us jointly in consultation with the authors.

I am personally indebted to Professor .James for his editorial Ivork on my own chapters.

The responsibility for the final form of the book, the errors of omission and commission, is mine. A word of explanation to the authors of the various chapters is in order. After the close of the Office of I’ublications and the dispersal of the group, I have on occasions made use of my editorial prerogative to revise their presentations. I hope that the results meet ~vith their approval. The policy of assignment of credit also needs explanation. The interpretation of both Professor James and myself of the policy on credit assignment formulated by the Editorial Board for the Technical Series has been to the effect that no piece of work discussed in the text would be associated with an individual or individuals. Radi- ation Laboratory reports are referred to in the sense that they represent source material for the chapter rather than individual acknowledgements.

References to unpublished material of the Radiation Laboratory note- books have been assiduously a~oided, although such material has been dramm upon extensively by all of us. In defense of this policy it may be stated that the ]vorlc at the Radiation Laboratory was truly a cooperative effort, and in only a few instances would it have been possible to assign individual credit unequivocally.

The completion of the book was made possible through the efforis of a number of people; in behalf of the editorial staff and the authors I wish to acknowledge their assistance and contributions. Mrs. Barbara Vogel and Mrs. Ellen Fine of the Radiation Laboratory served as technical assistants; the production of figures and photographs \vas expedited by hlrs. Frances Bourget and Mrs. nary Sheats. It proved impossible to finish the ]t-orl<by the closing date of the Office of l’ublications; the h’aval Research Laboratory accepted the ~vork as one of the projects of the newly formed Antenna Research Section and contributed generously in personnel and facilities. Special thanks are due to A. S. Dunbar, 1, Katz, and Dr. I. Maddaus for their editorial assistance; to Queenie Parigian and Louise Beltramini for preparation of the manuscript;

and to Betty Hodgkins who prepared almost all of the figures.

The editors are indebted to Dr. G. G. Macfarlane of the Tele- communications Research Establishment, Great Britainj for his critical review of several of the theoretical chapters and his contribution on the theory of slot radiators in Chap. 9. John Powell of the Radiation Laboratory prepared material on lenses that was used in

Ch:lp. 11. The S:1( iomd Rcsc:wch (’ouncil of Can:&~ :md the llrit isll (’entnd Radio 13urw~u h~~vc ~rwiously granted us permission to ^ti~li(.

m:ltcrial from ( ‘unudi:m :md I;ritish reports in accord:mcc ~~ith mlrrrnt security U3glllotioms. ‘l>hc I?wII Telephone I.abora,twy supplied the photographs of mct:d lens antennas.

S.4 MUEL khLVlil{.

K:\v\T, lll)sl’.\1i1lI T. WIMWIIY,

‘!f”lslllxlm)x, l). (’.,

:lprd, 1947.

.

Contents

FORE WORD BY L. A. DUBRmGE . . . vii PRE1744CE. . . ix

CHAP.1. SURVEY OF MICROWAVE ANT~~NNADESIGN PROBLEMS 1

1.1. The WavelcngthRegion. . . . . . 1

1.2. .Lntenna Patterns . . . . . . . . . . . . . . . . . . . ..2

1.3. Types of }Iicrowave Beams. 6

1.4. lIicrowave Transmission I,ines . 7

1.5. Radiating llernents . . . . . . . . . ..8

16. .4 Survey of kllcrowavc }.ntenna Types 9

1.7. Impedance Specifications. 13

1.8. Program of the Present Volume 14

CH.4P. 2. CIRCUIT RJ31JATIOIW, Rf3CIPR0CiTY THW3RF~!>fS. 16 21.

22.

23.

2.4.

2.5.

2.6.

2.7.

2.8.

2.9.

Introduction . . . . . . . . . . . . . . . . . . . ...16

The Four-terminal ~etwork. 17

The Rayleigh Reciprocity Theorcnl 19

Th6venin’s Theorem and the Nfzximum-power Theorem 20

The Two-wire Transmission I,ine 21

The Homogeneous Transmission I,ine 23

The LosslessLin e... ..26

Transformation Charts. 29

The Four-terminal N“etwork l’:quivalent of a Sectio]l of Trans-

missiOn Line.... . . . . . 36

TRANSMI~EVG ANn RECEIVING ANTENNAS. . 37

2.10.

2.11.

2.12.

2.13.

2.14.

2.15.

2.16.

2.17.

2.18.

The Antema as a Terminating Impedance 37

The Receiving Antenna System 40

The Transmitter and Receiver as a Coupled System 45 Reciprocity between the Transmitting and Itecei\,ing Patterns of

an Antenna . . . . . . . . . . . . . . . . . . . ...48

The .kverage Cross Section for a Matched System 50

Dependence of the Cross Section on Antenna Mismatch 51

The Four-terminal Network Representation. 53

l)evelopment of the N’etwork Equations 56

The Reciprocity Relation between the Transfer Impedance Coetlicient s, . . . . . . . . . . . . . . . . . . ...59

X111

xiv CO.YYfil.VTS

CHAP. 3. R.\ III.iTIOS FR031 CUIUWXT I) ISTRII)I”T1OSS. (iI

31. Tllc Field Ilquations. 6]

32. The (;onstit,ltive Paramctrrs; I.inc:wity mid SIlperpo sition . 6,5

33. Ilou])dary Contlitions. 66

3 ~. The Field ~q~latio]ls for H:mnonic TIInc ])(, p[,lld(>I1[W 68

3.5. I’aynting’s Thmreln . . . . M)

36. The ll-a\,c k;qll:ltions. 71

3.7. Simple l~avc Sollltions. 73

38. General Sollttion of the Field I}q,,~tiol,s in Tcr],,s of tl)r fk),,rtcs,

for a Ti]llc-pcriodir lri(ld. 8(I

3.9, Field ]),,e to Sollrtt,s in an U]IhoIuI(ltYi Ii(,gion 84 3.10. Field in a licgion Rotmdcd hy S(lrfa((,s of I]lfillltcl}- (’OI)(l\l(tIvr

llc,clia . . . . . . . . . . . . . . . . . . . . . ..8fi

311. Tl](, Far-zone Fields 87

312. I’olarization. !)1

3~13. The I;lcctric l)ipolc !)2

314. Tllc IItignetir lh]mlc 95

3.15. The F:lr-zonr Firl(ls of I,i]l(,-rurr(,nt l)istrilllltif!)ls !)(i

316. The “H:df-~1 IV(, l)ilmlt, ” !)8

317. Sllpcrpm]tion of l~icl{ls !)!1

31S The 1)0111>1(,-(111)01(System 101

319. I{cgldur Space .Irr:iys 104

C][.IP. 4. ll-.l’;l; FI{O>-TS :~~1) RAYS 107

41. TIIC II\lygrns-Crccn Forn~lll:L for thr Ill((,tr(l]]]:Lg]l(ti[, l’itl(l 107 42, Gcol]lctrical ()~]tirs: l~”avefronts and l{:lys 110 43. C1lr~:itllrr of the Ilmys in an Inllo]]Iogc,l](,[~!ls Ilcdiunl 111

4+. Energy FlOIv in (lcometrical Optics 112

45. (;comctrical optics :is :L Zero-~ra~clcngth I,in]it 114 46. The H~lygens-Frrsnrl Principle and Gconlctriral Optics: The Far-

zonc .kpproximation 116

47. The Principle of Stationm-y I’hasc 11{)

48. Ft=rnlat’s I’rincip]e. 122

4.9, The I,a,v of the optiral Path 125

(’]~ \l,, 5, S(’.LTTERISC, .kN-T) DIFFR.ACTIOX. 12!)

51. (;cncral (’onsidcrntions 129

52. Bol]ndary (’o]lditions 130

53. Iieflection hy an Infillite Plane S(lrt’arc; the l’rinril)lv of ItII:igrs 132

APPROXIMATE JIETHODS FOR REFLECTOI+S OF ;lILBITMARY S] J.\PE 54,

55, 56, 57, 58.

59.

510.

511.

512.

The Geometrical-optics IIcthorl Calculation of the Scattrrrd Firl[l

Superposition of the So~lrcc l~icl(l :IIId tl)(, Sc:\ttercd l~icld.

The Current-distril, ~ltion 31cthod Calc(llation of the Scattrrrd Field

Application to Point-source md IJirl{J-sollrre l;ecds.

Reaction of a Reflector on a Point-source Feed The .Aperture-fielci Ifethod

The Fraunhofer Region.

,.. 137 138 139 143 144 146 149 155 . . 158 ,.. 160

.

co’YTA”l’

7’s xv

l) IF1.ll.\(r10N. . .. . . . ...,,162

S.IS, (i,r,crtLI (’~)])si,l,,r:,iit)])s mI tht, .ipproxim:ltc Ilt,tllods 162 514. l{ttlll~,tltJJl to :1 S[alilr l)illr:~(tlf)n I’I’o I)lcIN 164 515. l)~~lli]lct’s l’rl]l{ipl~i for tll(’ l<;lc,~tro]ll:tg])f,ti(, Ir](,ld 167

(’ti~l,. 6. .lI’KI{TURF; ll.LL’llll-ATIOX” AX]) .l>-TI,;X-XA I’ATTERNS 169

61. l’ril]l:~ry and S[,co]ltlxry l’tlttrms 169

62. Tll(, l)iffr:trtion Fieltl 169

(i 3. I’ouri(r Integral li(,l)rc,s(,]ltati{jl~ of the Fraunhofcr lie~ion 174

64, (+CJI(M1 I:caturts of tht, Sccolld:wy l’~ttvm 175

6,5. TIIC l{rctmlg~ll:~r .fporture ]80

6.ti. Tl!o-(lilllt,nsio]lal Prol)lcms 182

67. I’l]:i.w-error kYfects. . 186

08. TIIC (’irc(llm .ipcrturc 192

&9. Th(, Field o]] the Axis in thr Frcsnrl ]tcgion ] 96

(’l[,\],, 7. l[I(:ROIV,.fV}; TRAA-S~f ISSIOA” I,IN-ES 200

71 llicro~j :ivc nnd I,ong-~vave Trimsmission I,illm 200 72. l’rop:l~atio]l in ~f”:~vcgllidcs of l“niform (;ross Swtion 201

73. orthogo]lallty Rcl:ltions and Power Flow. 207

74. Transnlissiun I,inr (’onsidcrations in l~:lvrguidrs 209 75. XctJt ork Kqllivalents of Junrtions and ohstaclcs 214

76. 7’/l.l/-modc Trallsmission I,irlcs 216

77. (’ozxis,l I,incs: ?’~.!f-rnodc 217

7.8. (’oaxial I.ines: T.If - and T]i-nlodcs 219

7.!), (’:Is,.acIc Tmnsformcrs: TJ~.lf-mode 221

71o. I’arallel St~lhs and Series ILeactancm. 223

711. licctang~llar }Vavcguidcs: I’A’- and ?’,lf-modes 226 712. Impcdanrc Transformers for Iiectangular (;uidcs 229

713. Circular ll-aveguide: T~- and TJf-modcw. 233

7.14. Ivindows for LTSCin Circular Guides 235

715. I’arallel-plate i~aveguide. . 235

716.11esignN Totes . . . . . . . . . . . . . .. 238

CHAF. 8. lfICROWAVE DIPOLIl A3JTE~~AS ANI) F13f?DS 239

81. Characteristics of Antenna Feeds 239

8.2, Coaxial I,ine Terminations: The Skirt Dipole 240

83. Asymmetric Dipole Termination. 242

84. Symmetrically 13nergizcri Dipoles: Slot-fed Systems 245

85. Shape and Size of the Dipole . 248

86. lVaveguidc-line-fcd Dipoles. . 250

87. Directive Dipole Feeds, . . . 250

88. Dipole-disk Fords . . . . . . . . . . . . . . . . . . ...251 89, Double-dipole Feces, .,.... . . . . . . . . . . . . .253

8.10. Lfulti-dipole Systems, . . . 256

CHAP. 9. LINI?AR ARRAY AXTEiYNAS AND FF23DS 257

9.1. (kmcral Considerations. . 257

XVI CON TEJVTS

PA~EEN THEORY . . . . . . . . . . . . . . . . . . . . . . ...256

92. General Array Formula. . . 258

93. The Associated Polynomial 261 9.4. U1liformArrays . . . . . ...264

9.5, Broadside 13e:~nls . . . . ...267

9.6. Erl(l-tire I~ean]s . . . . . . . . . ...274

9.7. 13ca1u Synthesis . . . . . . . . . . . . . .. 279

RADIATING EI.EMMNTS . . . . . . . . . . . . . . . . . .. 284

9.8. llipole Radiators . . . . . . . . . . . . . . 284

9.9. Slots in Jvaveguide }Talk. . 286

9.10. Theory of Slot Radiators. . 287

9.11. Slots in Rectangular J$’aveguide; ‘1’~,,-mode 291 912. Experimental Data on Slot l{adi~tors 295 913. Probe-fedS lots . . . . . . . . . . . . . 299

9.14. fVaveguide Radiators 301 9.15. Axially Symmetrical Radiators . 303 9.16. Streamlined Radiators . . . 310

ARRAYS . . . . . . . . . . . . . . . . . . . . .. 312

9.17. Loaded-line Analysis. . 313

9.18. End-fire .4rray . . . . . . . . . . . . . . . . . . . . . . 316

BROADSIDE AREAYS. . . . . . . . . . . . . . . . . . . . . . . .. 318

9.19, Suppression of Extraneous Major I,ohcs . 318 920. ResonantArrays . . . . . . . . . . . . . . . .. 321

921. Beacon Antenna Systems. 327 922. T$onresonant Arrays . . . . . 328

923, Broadband Systems with >Tormal Beams 331 CHAP. 10. WAVEGUIDE AND HORN FE~;~S. . 334

10.1. Radiation from Waveguide of Arhitrmy Cross Scrtion 334 10.2. Radiation from Circular ~~av(’guide 336 103. Radiation from Rectwwlar Guide. 341 10.4. Waveguide Antenna Feeds 347 105. The Double-slot Feed . 348 10.6. Electromagnetic Horns. . . . . . 349

10.7. hrodes in lplane Sectoral Horns 35o 108. Jfodes in If-plane Sectoral Horns 355 109. Vector Diffraction Theory Applied to Srctoral Horns. 357 10.10. Characteristics of Observed Itadiation l’tittmns from Horns of Rectangular Cross Section 358 10.11. Admittance of Waveguidc and Horns . 366 10.12. Transformation of the L’-plaI~c HorII .idulittan cc f mm the Throat tothe Uniform Guide . . . . . . . . . . . . . . . . ...369

10.13, Admittance Characteristics of H-plane Sectoral Horms 374 1014. CompoundHorns. .,.. , . . . . . . . . . . . . ...376

10.15 .The Box Horn... . . . . . . . . ...377

1016. Beam Sllaping hy ~lcans of Obstaclrs in HOHI :md \VaveK{lidv .4pertm’cs. . . . . . . . . . . 380

10.17, Prcssllrizing and hfatch]ng 383

CHAP. 11. DII:I,IcCTILIC i~X1) lIJ:T:lI,-l’I.. fTI<: I. I<:XSES 388 11.1. Uses of l,[>lls(>sin 31icro~v~vc ,~ntcmms. 388

I)ll:l,l:C,rRICIJEXSF;S . . . . . . . . . . . . . . . . . . . . . . .

112. l’rill{ilJlrso fI>rsign, .

113, Sinlplc I,cllses IVltllo(it Zoning

114. Zoned l)lclrctric I,cnscs . .

11,5. Usc of lIatcri:tls ~v]th Hi~ll l{cfmctivc Indcxrs 11.6. I)lclcctric I,osscs mnd Tolcranccs on Irons I’aramctcrs.

11.7. Itcflections from L)iclcctric Surfaccw

389 389 390 395 398 399 401

hfETAL-I,L~TELEXSES . . . . . . . . . . . . . . . . . . . . . ...402

11.8. Parallel-plate I,ensm, . . . . 402

11.!). Other 31eta-lcr,s Structures. 406

11.10. l[cta-plate I.cns Tolrrancrs 407

11.11. Band,vi(lth of l[etal-plztc I,cnscs; Achromatic Doublets 408 11.12. Iteflections from Surfaces of Parallel-plate I,enses 410 CHAP. 12. PENCILBFAhf AND SIhfPLE FANA”l;D-BEAN1 ANTEKA”AS 413

PENCIL-BEAMANTENNAS. . . .,...,...413

12.1. Pencil-beam Requirements and Tcchniqlles 413

12.2. Gcomctriral Parameters 415

123. The Surface-current and Aperture-firldI)istrih(ltions. 417 12.4. The ILadiation Field of the Reflector 420

12.5. The Antenna Gain., . . . . . . . . . . . 423

126. Primary Pattern Designs for hI:mimizing (lain 433

127. Experimental Itcsldts on %condm-y l’attmns 433

128. Impedance Characteristics 439

12.9. The Vertex-plate lf:~tching Trchniquc 443

12.10. Itotation of I’ohu-ization Technique 447

12.11. Structural Design Problems. 448

SIMFLE FANNED-BEAM ANTENNAS. 45o

12.12. Applications of Fanned Beams and Nfcthods of Pmdllrtion 45o

1213. Symmetrically Cut Parahololds 451

12.14. Feed Offset and Contour Cutting of Reflectors 453

1215. The Parabolic Cylinder and Line Source 457

12.16. Parallel-plate Systems 459

12.17. Pdlbox Design Problems 460

CHAP. 13. SHAPED-BEAM ANTENNAS. .

131.

132.

133.

134.

135.

136.

137.

138.

13.9.

Shaped-beam Applications and Requirements Effect of a Directional Target Response Survey of Beam-shaping Techniques.

Design of Extended Feeds. . . . Cylindrical Reflector Antennas .

Reflector Design on the Basis of Ray Theory .

Radiation Pattern Analysis.

Double Curvature Reflector Antennas Variable Beam Shape.

465 465 468 471 487 494 497 500 502 508

,..

XV1ll COA’7’1{.V 7’s

CHAP. 14. ANTk;XNA IXSTALLAT1ON I’ROBI,E31S 510

GE~~It.4L SIKVl~Y OF I~Scr.4LLA’rIO~ I’~OBLEMS. 510

14.1. (:rolm(l .lllt(,llnas 510

14.2.SllilJ.illterlI]as,,, . . . . . . . . ... ..511

143, ~lir(,r:ift<intellnzs 512

14,4. Scanning Antennas on Aircraft 513

14.5. Beacon Antennas on Aircraft 521

522 523 528 537 540 543 543 544 544 545 547 550 552 556 557 557 ,.561 564 570 572 573 574 ,574 578 580 580 581 ,582 ,58!5 58A 587 593 593 5{)4 601 604 60!)

ISl)lI;X . . . . . . . . . . . . . 6 I.5

.

C’11.IPTI;R 1

SURVEY OF MICROWAVE ANTENNA DESIGN PROBLEMS ]]Y s. SII,V1;ll

1.1. The Wavelength Region.—’I’he designation of the boundaries of the micro!mve region of tIw rlcct romagmct ic spectrum is pllrcly arbitrary, Tile Iong-]vavelcngth limit IIas Ixxm set v:~riously at 25 (Jr 40 cm, even at 100 cm. From the point, of vie\v of antenna theory and design techn- iques, the 25-cm val~le is the most appropriate choice, The short-

wa~’elength limit to )ihich it is possible to extend the present terhniq(les ll:~snot ~etl)ec>r~rcaclle(i; it isinthcnciglll)or}loo(lof lmm. Accordingly

\veshall cunsi(lcr the microlvave region to extend in wavelength from 0.1 to 25 cm, in frcqllcncy from 3 X 105to 1200 31c/see,

This is the transition region bet\\-eenthe or(linary radio region, in }vhich the \\-avelengtllis very k~rge comparwl with the dimensions of all the components of the system (cxccpt perhops for theh~rge and cumber- some antennas), and the optical region, in ]t-hich the \vavclengths arc excessil-ely small. I.ong-\vavc concepts rm(l techniques continue to be useful in the micro \vave region, and at the same time certain devices used in the optical regionsllr haslense sandn~irror sarcemployeci. From the point of vie}v of the antenna designer the most important character- istic of this fre(~ucncy region is that the wa~~elengths are of the order of magnitude of the dimcmsilmsof conventional and easily handled mechan- ical devices. This leads to radical modification of earlier antenna techniques and to the appearance of nefv and striking possibilities, especially in the construction and use of complex antenna structures.

It follows from elementary diffraction theory that if D is the maximum dimension of an antenna in a given plane and k the ivavrlength of the radiation, then the minimum angle }vithin which the radiation can be concentrated in that plane is

(1)

With microwaves one can thus produce highly directive antennas such as have no parallel in long-wave practice; if agivendirectivity is desired, it can be obtained \vith a microwave antenna ]vhich is smaller than the equivalent long-!vave antenna. The ease with which these small antennas can be installed and manipulated inarestricted space contributes greatly to the potential uses of microwaves. In addition, the convenient size of

1

2 SURVEY OF MICROIV. t J’E ANTEXAVA DESIG.V PROBLEMS [SEC,1.2 microwave antenna elements and of the complete antenna structure makes it feasible to construct and use antennas of elaborate structure for special purposes; in particular, it is possible to introduce mechanical motions of parts of the antenna with respect to other parts, with consequent rapid motion of the antenna beam.

The microwave region is a transition region also as regards theoretical methods. The techniques required range from lumped-constant circuit theory, on the low-frequency side, through transmission-line theory, field theory, and diffraction theory to geometrical optics, on the high-fre- quency side. There is frequent need for using several of these theories in parallel—combining field theory and transmission-line theory, sup- plementing geometrical optics by diffraction theory, and so on. Optical problems in the microwave antenna field are relatively complex, and some are of quite novel character: For instance, the optics of a curved two-dimensional domain finds practical application in the design of rapid-scanning antennas.

1.2. Antenna Patterns.-Before undertaking a survey of the more important types of microwave antenna, it will be necessary to state precisely the terms in which the performance of an antenna will be described.

The Antenna as a Radiating Device: The Gain Function.—The field set up by any radiating system can be dirided into two components:

the induction field and the radiation field. The induction field is impor- tant only in the immediate vicinity of the radiating system; the energy associated with it pulsates back and forth between the radiator and near-by space. At large distances the radiation field is dominant; it represents a continual flow of energy directly outward from the radiator, with a density that varies inversely with the sq~iarc of the distance and, in general, depends on the direction from the source.

In evaluating the performance of an antenna as a radiating system one considers only the field at a large distance, where the induction field can be neglected. The antenna is then treated as an effective point source, radiating power that, per unit solid angle, is a function of direc- tion only. The directive properties of an antenna are most con~eniently expressed in terms of the “gain function” G(6’,O). I/et 6’and @ be respec- tively the colatitude and azimuth angles in a set of polar coordinates centered at the antenna. Let F’(O,@) be the power radiated per unit solid angle in direction 0, @ and P~ the total power radiated. The gain function is defined as the ratio of the power radiated in a given direction per unit solid angle to the average power radia~ed per unit solid angle:

47r

(2)

SEC. 1.2] ANTENNA PATTERNS 3 Thus G(L9,~) expresses the increase in power radiated in a given direction by the antenna over that from an isotropic radiator emitting the same total power; it is independent of the actual power level. The gain function is conveniently visualized as the surface

r = G(f3,@) (3)

distant from origin in each direction by an amount equal to the gain function for that direction. Typical gain-function surfaces for micro- wave antennas are illustrated in Fig. 1.1.

The maximum value of the gain function is called the “ gain”; it will be denoted by GM. The gain of an antenna is the greatest factor by which the power transmitted in a given direction can be increased by using that antenna instead of an isotropic radiator.

The “transmitting pattern” of an antenna is the surface

(4)

it is thus the gain-function surface normalized to unit maximum radius.

A cross section of this surface in any plane that includes the origin is called the “polar diagram” of the antenna in this plane. The polar diagram is sometimes renormalized to unit maximum radius.

W-hen the pattern of an antenna has a single principal lobe, this is usually referred to as the “antenna beam. ” This beam may have a wide variety of forms, as is shown in Fig. 1.1.

The Antenna as a Receiving Dwice: The Receiving Cross Section .—The performance of an antenna as a receiving device can be described in terms of a receiving cross section or receiring pattern.

A receiving antenna will pick up energy from an incident plane wave and will feed it into a transmission line which terminates in an absorbing load, the detector. The amount of energy absorbed in the load will depend on the orientation of the antenna, the polarization of the wave, and the impedance match in the receiving system. In specifying the performance of the antenna, we shall suppose that the polarization of the wave and the impedance characteristics of the detector are such that maximum power is absorbed. The absorbed power can then be expressed as the power incident on an effecti~-c absorbing area, called the “ receiving cross section, ” or “absorption cross section” A, of the antenna. If S is the power flux density in the incident wave, the absorbed power is

P, = ASA, (5)

The receiving cross section will depend on the direction in which the plane wave is incident on the antenna. We shall write it as A, = A,(d,I$), where o and @ are the spherical angles, already defined, of the direction

4 SL’RJ’E1’ OF JIIC’lK)IV.4 J’E .4.V7’E.\.VA DI<,SIG.I 1’1{01$1.1<.11.V [SW. 12

of incidence of the lvave, This function, like the gain function, is repre- sented conveniently as the surface

?’ = .4, (0,0). (6 J

The “ receiving pattern” of an antenna is drfincd, :malogolls]y t(

the transmitting pattern, as the above surface normalized to unit maxi- mum radius:

(7) It is a consequence of the reciprocity theorem to be discllssed in Chap. 2 that the receiving and transmitting patterns of an antenna are identical:

~(~,o) = ~r(g:y),

G.,, A,.,, (8)

It will also be shown that the ratio .4, u‘0 v is a constant for all matched antennas:

.-lr,f ~ ~,

“G 41r

Thus for any matched receiving system , A,((l, @l) = :; G(e,l+).

(9)

(lo)

Coverage Pattern, One Way.-The characteristics of an antenna may also be described in terms of the performance of a radio or radar system of which it is a part. It is necessary to distinguish between the case of one-way transmission, in which a given antenna serves for transmission or for reception only, and the case of radar or two-way transmission, in which a single antenna performs both functions.

We consider first a transmitting antenna and a receiving antenna separated by a large distance R. Let G, and G, be the respective gain functions of the two antennas for the direction of transmission. If the total power transmitted is P, the power radiated in the direction of the receiver, per unit solid angle, will be (1/4m)PG~. The receiving antenna will present a receiving cross section (1/’47r)G,x2 to the incident wave; it will, in effect, subtend a solid angle G,A2/’47rRzat the transmitter. The power absorbed at the receiver will thus be

(11)

The maximum operating range is determined by the signal-to-noise ratio of the detector system. If P,m is the minimum detectable signal for the receiver, the maximum operating range is

R

(-)

P$i A

.,., =

P ~; (G,G,)’ ~

,m (12:

SEC.12] ANTENNA PATTERNS 5 Thus, if it is possible to ignore the effect of the earth on the propagation of the wave and if G, is constant, it will be possible to operate the receiving system satisfactorily everywhere within the surface

(13)

where the transmitter is taken to be at the origin. This surface will be called the “free-space coverage pattern for one-way transmission. ”

Coverage Pattern, Two Ways. - -In most radar applications the same antenna is used for transmission and reception. One is here interested in detecting a target, which may be characterized by its ‘( scattering cross section” u. This is the actual cross section of a sphere that in the same position as the target would scatter back to the receiver the same amount of energy as is returned by the target. For this fictitious iso- tropic scatterer, the effective angle subtended at the transmitter is U/R2 and the total power intercepted is

(14)

Scattered isotropically, this power would appear back at the transmitter as a power flux, per unit area,

(15)

Actually, the scattering of most targets is not uniform. The scattering cross section of the target will in any case-be defined by Eq. (15), but it will usually be a function of the orientation of the target.

The power absorbed b:- the receiver from the scattered wave will be

P,= A+S=R (16)

since here G, = G,. If the effect of the earth cm transmission of the waves can be neglected, it will be possible to detect the target only when it lies within the surface

(17)

about the transmitter as an origin. This surface will be called the “free- space coverage pattern for t we-way transmissi,m. ”

The extent of the coverage patterns is determined by characteristics of the system and target—output power, receiver sensitivity, target size

—that are not under the control of the antenna designer. The form of the coverage patterns is determined by but is not the same as the form of the antenna transmitting a,nd receiving patterns; in the coverage patterns, r is proportional to [G,(o, r#J)]Jfirather than to G,(o, +). The

6 SURVEY OF MICROWA FE AIV7’EiVA’44 DESIG.V PROBLEWS [SEC.13 desired form of the coverage pattern is largely determined by the use to be made of the system. From it, one can derive the required form of the transmitting or receiving pattern of the antenna; it is usually in terms of this type of pattern that antenna performance is measured and specified.

It is to be emphasized that the discussion of coverage patterns gi~en

(b)

(c) (d)

FIG.I.I.—Typicalgain-functionsurfacesfor microwaveantennas. (a) Toroidal(omni- directional)pattern;(b) pencil-beampattern;(c) flat-topflaredbeam; (d) asymmetrically flaredbeam.

here assumes free-space conditions. In many important applications, coverage is affected by interference and diffraction phenomena due to the earth, by meteorological conditions, and by other factors. A detailed account of these factors, which may be of considerable importance in determining the antenna transmitting pattern required t“ora given appli- cation, will be found in Vol. 13 of the Radiation I,aboratory Series.

103. Types of Microwave Beams.—The most important types of microwave beams are illustrated in Fig. 1.1.

The least directive beam is the “toroidal beam,” 1 which is uniform in 1Such a beam is also referredto as “omnidirectional.” (IRE Standards and Definitions,1946.)

SEC.1.4] MICRO WAVE TRANSMISSION LINES 7 azimuth but directive in elevation. Such a beam is desirable as a marker for an airfield because it can be detected from all directions.

The most directive type of antenna gives a “pencil beam, ” in which the major portion of the energy is confined to a small cone of nearly circular cross section. With the high directivity of this beam goes a very high gain, often as great as 1000. In radar applications such a beam may be used like a searchlight beam in determining the angular position of a target.

Although the pencil beam is useful for precise determination of radar target positions, it is difficult to use in locating random targets. For the latter purpose it is better to use a “fanned beam,” which extends through a greater angle in one plane than it does in a plane perpendicular to that plane. The greater part of the energy is then directed into a cone of roughly elliptical cross section, with the long axis, for example, ver- tical. By sweeping this beam in azimuth, one can scan the sky more rapidly than with a pencil beam, decreasing the time during which a target may go undetected. Such a fanned beam still permits precise location of targets in azimuth, at the expense of loss of information concerning target elevation.

Other applications of microwave beams require the use of beams with carefully shaped polar diagrams. These include one-sided flares, such as is illustrated in Fig. 1Id, in which the polar diagram in the flare plane is roughly an obtuse triangle, whereas in transverse planes the beam remains narrow. In radar use, such a beam at the same time permits precise location of targets in azimuth and assures most effective distribu- tion of radiation within the vertical plane of the beam. Toroidal beams with a one-sided flare in elevation have also been developed.

No theoretical factors limit any of the above beam types to the micro- wave region, but many practical limitations are imposed on long-wave antennas by the necessary relationship between the dimensions of the antenna elements and the wavelengths.

104. Microwave Transmission Lines.-The form of microwave antennas depends upon the nature of the available radiating elements, and this in turn depends upon the nature of the transmission lines that feed energy to these elements. We therefore preface a survey of the main types of microwave antennas with a brief description of microwave transmission lines; a detailed discussion of these lines will be found in Chap. 7.

Unshielded parallel-wire transmission lines are not suitable for micro- wave use; if they are not to radiate excessive y, the spacing of the wires must be so small that the power-carrying capacity of the line is severely limited.

Use of the self-shielding coaxial line is possible in the microwa~ t~

8 S’( “I<i’l{~- 01” .ifl(:l{() WA }’1< .1i<7’liA’.YA DKSIG.V PII’OI{LE.IIS [SE<. 1,5 region but is generally restricted to lfa~-elengths of approximately 10 cm or more. IJor proper action as a transmission line, a coaxial line slLoulcf

7

(b)

(c)

transmit electromagnetic Ir:lves in only a single mode; other\\ise the generator 100!{s into an indetermirmte impedance and tends to be erratic in operation.

on this account it is necessary to keep the at-erage circumference of inner and outer condllctors less than the frce- space wavelength of the transmitted

~ravcs, .\t ~vavelengths shorter than 10 cm this limitation on the dimensions of c~mxial lines begins to limit their polvcr-carrying capacity to a (Ir=gree that m~kes them lmsatisfactory for most purposes.

The most ~lseful transmission line in the miclotvave region is the hollo\\- pipe. Sllrll pipes \vill sllpport the propagatiorr of :lrleiect,rom:~g~lrti(,!j-:~~e only it-hen they are sufficiently large comp:we(l \\ith its free-space \vave- length. As g~lides for long-lrave radi:Ltl(Jn, ]nt,oleral)ly large pipes are reql[ir(,(l, I)llt in the microlrave region it lxw)mes pf)ssit)le to mse pipesof rmn- vcnlcnt, SIZC. I,ike the coaxi:d gllide, there is :Llsfjan llpper limit imp(w(lon the crow-sectional dimension of the pipe if it, is to tr:msmit the \v:ive in only N single mo(le. II()\\-e\-er,in theal)scnce of :ln inner con(lllctor, this size limit:L- tion (l(wnot :Ifl’ect the Ix)li-cr r:llxwily so seril}llsly :Wit does in tllc c(mi:~l line.

1.5. Radiating Elements.—T h e natllre of t hc ra(li:~ting elements trrmin:~ting :L transmission line is to :L (l) USi(l(>I’:Ll)l(’ (’Xt C’llt (1(’t(’l’lllill(’(1 })~

tile n:~tllre of the li]le itwlt’. ‘1’y])ieal l~,ng-lv:~le r:l(li:~tillg clenwnt + :Irr the

“{lil)ole’” :lrl((~]l]l:ls, sll~,ll :1s tllc (,t~lltcr- (Iril.en i]:llf-\\:l\-e (Iil)tlle, nll(l loop

coaxial lines lend themselves to sllch terminations. Many long-wave antenna ideas have lwen rarr-ied uver into the micro\rave region, par- tic~~hwlythose connected with thehalf-]rave dipde; the tramsitiorr, ho\v- ever, is riot rnereiy a mattrr of wovelcmgth scaling. In a microl}ave antenna tl~e cross-sertional dimensions of the transmission line are com- partihlc to the dimensions of the half-~vavc dipole, and consequently, the coupling lmtween the radiator and tile line becomes a more significant prol)lem tlian in a corresp(jnclin~ Iong-ivave system. The cross-sectional dimensions of the dipole element are dso comparable to its length. A typi~al microwave dipole is shown in Fig. 1“2c; the analysis and undt=r- stancling of S1lC}Imicro}vave dipoles is at best still in a qualitative stage.

The ose of hollow ~vaveyuide lines leads to the employment of entirely (Lffc,rent radiating systems. The simplest radiating termination for such a line is j~lst the open end of the g~lirle, through which the energy passes into space. The dimensions of the mouth aperture are then comparable to the wavelength; as a result of diffraction, the energy does not continue in a lwam corresponding to the cross section of the pipe but spreads out considerably about, the direction of propagation defined by the guide.

The degree of spreading depends on the ratio of aperture dimensions to wa~’ekmgth. On flaring or constricting the terminal region of the guide in order to control the directivity of the radiated energy, one arrives at electromagnetic horns based on the same fundamental principles as acoustic horns (Fig. 1.20!).

Another type of element that appears in microwave antennas is the radiating slot (Fig. 1.2r). There is a distribution of current over the inside wall of a waveguide associated with the wave that is propagated in the interior. If a slot is milled in the wall of the guide so as to cut across the lines of current flow, the interior of the guide is coupled to space and energy is radiated through the slot. (If the slot is milled along the line of current flow, the space coupling and radiation are negligible. ) I slot will radiate most effectively if it is resonant at the frequency in question. The long dimension of a resonant slot is nearly a half \\-ave- iength, and the transverse dimension a small fraction of this; the perim- eter rJt”the slot is thus closely a wavelength.

1.6. A Survey of Microwave Antenna Types.—We are now in a posi- tion to mention briefly the principal types of antennas to be considered in this book.

Antennas jo~ Toroidal Beams.—A toroidal beam may be produced by an isolated half-wave antenna. This is a useful antenna over a large frequency range, the iimit being set by the mechanical problems of sup- porting the antenna and achieving the required isolation. The beam thus produced, however, is too broad in elevation for many purposes.

A simple system that maintains azimuthal symmetry but permits control of directivity in elevation is the biconical horn, illustrated in