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 .111 rights 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 ~vereso 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 [...]... between electromagnetic ~vaves and obstacles; the general theory of reflectors is here developed as a boundary-condition problem, and a discussion is given of the relation bet~veen this theory and conventional diffraction theory, which also finds application to microwave antenna problems Finally, Chap 6 applies this theory in treating one of the fundamental problems of antenna design the relation between... transmission-line theory, supplementing 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. .. the dimcmsilmsof conventional and easily handled mechanical 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,... of antennas will be considered in parallel with their radiation pat terns 1.8 Program of the Present Volume —This I)(mk falls into f(mu main divisions: basic theory, theory i~nd dcsi~n of fewls, tl~rory and drsign of complete antenna systems, and :~lltenn:L-m(,:~sLlling tc(,llni(llles and equipment The fol]o!ving chapter summarizes certain parts of ct)nventi . 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. 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,. 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.