MICROWAVE FILTERS, IMPEDANCE-MATCHING NETWORKS, AND COUPLING STRUCTURES GEORGE L. MATTHAEI Department of Electrical & Computer Engineering University of California Santa Barbara, CA LEO YOUNG Naval Research Laboratory Washington, DC E. M. T. JONES Technology for Communications International Mountain View, CA For a complete listing of the Artech House Microwave Lihaty, turn to the back of this book. ARTECH HOUSE PREFACE The organization of this book has three general objectives. The first objective is to present fundamental concepts, techniques, and data that are of general use in the design of the wide range of microwave structures discussed in this book. The second objective i s to present specialized data in more or less handbook form so that a designer can work out practical designs for structures having certain specific con- figurations, without having to recreate the design theory or the deriva- tion of the equations. (However, the operation of most of the devices discussed herein is sufficiently complex that knowledge of some of the basic concepts and techniques is usually important.) The third objective i s to present the theory upon which the various design procedures are based, so that the designer can adapt the various design techniques to new and unusual situations, and so that researchers in the field of microwave devices may use some of this information as a basis for deriv- ing additional techniques. The presentation of the material so that it can be adapted to new and unusual situations is important because many Copyright O 1980 of the microwave filter techniques described in this book are potentially ARTECH HOUSE, INC. useful for the design of microwave devices not ordinarily thought of as 685 Canton Street having anything to do with filters. Some examples are tubes, parametric Norwood, MA 02062 devices, and antennas, where filter structures can serve as efficient Reprint of the edition publiied by McGraw-Hill Book Company, Inc., 1964 impedance-matching netwbrks for achieving broad-band operation. Filter Printed and bound in the United States of America structures are also useful as slow-wave structures or time- delay struc- All rights reserved. No part of this book may be repro- tures. In addition, microwave filter techniques can be app lied to other duced or utilized in any fonn or by any means, elec- devices not operating in the microwave band of frequencies, as for tronic or mechanical, including photocopying, recording, instance to infrared and optical filters. or by any information rtorage,and retrieval system, without permission in writing from the publieher. The three objectives aboveare notlistedin any order of mportance, nor Library of Congress Catalog Card Number: 80.68976 is this book entirely separated into parts according to these objectives. Standard Book Number 049006-099-1 However, in certain chapters where the material lends itself to such Printed and bound by BookMart Press, North Bergen, organization, the first section or the first few sections discuss general NJ, USA, November, 1985. principles which a designer should understand in order to make best use of the design data in the chapter, then come sections giving design data iii for specific types of structures, and the end of the chapter discusses applications, but also for use as prototypes for certain types of band- the derivations of the various design equations. Also, at numerous places pass or pseudo high-pass filters discussed in Chapter 9. cross references are made to other portions of the book where information useful for the design of the particular structure under consideration can Design of low-pass filters and high-pass filters from the semi- be found. For example, Chapter 11 describes procedures for measuring the lumped-element point of view are treated in Chapter 7. Chapters 8, 9, unloaded Q and external Q of resonators, and for measuring the coupling and 10 discuss band-pass or pseudo-high-pass filter design using three coefficients between resonators. Such procedures have wide application different design approaches. Which approach is best depends on the type in the practical development of many types of band-pass filters and of filter structure to be used and the bandwidth required. A tabulation impedance-matching networks. of the various filter structures discussed in all three chapters, a summary of the properties of the various filter structures, and the Chapter 1 of this book describes the broad range of applications for section number where design data for the various structures can be found, which microwave filter structures are potentially useful. Chapters 2 are presented at the beginning of Chapter 8. through 6 contain reference data and background information for the rest of the book. Chapter 2 summarizes various concepts and equations that Chapter 11 describes various additional techniques which are useful are particularly useful in the analysis of filter structures. Although to the practical development of microwave band-pass filters, impedance- the image point of view for filter design is made use of only a t certain matching networks, and time-delay networks. These techniques are quite points in this book, some knowledge of image design methods is desirable. general in their application and can be used in conjunction with the Chapter 3 gives a brief summary of the image design concepts which are filter structures and techniques discussed in Chapters 8, 9, and 10, and particularly useful for the purposes of this book. Chapters 1 to 3 should elsewhere in the book. be especially helpful to readers whose background for the material of this Chapter 12 discusses band-stop filters, while Chapter 13 treats book may have some gaps. certain types of directional couplers. The TEM-mode, coupled-transmission- Most of the filter and impedance-matching network design techniques line, directional couplers discussed in Chapter 13 are related to certain described later in the book make use of a low-pass prototype filter as a types of directional filters discussed in Chapter 14, while the branch- basis for design. Chapter 4 discusses various types of lumped-element, guide directional couplers can be designed using the step-transformer low-pass, prototype filters, presents tables of element values for such prototypes in Chapter 6. Both waveguide and strip-line directional filters filters, discusses their time-delay properties, their impedance-matching are discussed in Chapter 14, while high-power filters are treated in Chapter 15. properties, and the effects of dissipation loss upon their responses. In Chapter 16 treats multiplexers and diplexers, and Chapter 17 deals with later chapters these low-pass prototype filters and their various proper- filters that can be tuned either mechanically or by varying a biasing ties are employed in the design of l~w-~assh,ig h-pass, band-pass, and magnetic field. band-stop microwave filters, and also in the design of microwave impedance- It is hoped that this book will fill a need (which has become in- matching networks, and time-delay networks. creasingly apparent in the last few years) for a reference book on design Various equations, graphs, and tables relevant to the design of data, practical development techniques, and design theory, in a field of coaxial line, strip-line, waveguide, and a variety of resonators, coupling engineering which has been evolving rapidly. structures, and discontinuities, are summarized for easy reference in Chapter 5. Chapter 6 discusses the design of step transformers and pre- sents tables of designs for certain cases. The step transformers in Chapter 6 are not only for use in conventional im~edance-transformer ACKNOWLEDGMENTS The preparation of this book was largely supported by the Signal Corps, under Contract DA 36-039 SC-87398; its preparation was also partially sup- ported by Stanford Research Institute, and by off-work time contributed by the authors. Many of the design techniques described in this book are the result of research programs sponsored by the Signal Corps under Contracts DA 36-039 SC-63232, DA 36-039 SC-64625, UA 36-039 SC-74862, and DA 36-039 SC-87398. Mr. Nathan Lipetz of the U.S. Army Electronics Research Laboratory, Ft. Monmouth, N. J., because of his belief in the importance of research work in the area of microwave filters and coupling structures, and in the potential value of a book such as this, did much to-make this book possible Mr. John P. Agrios and Mr. William P. Dattilo, both of the U.S. Army Electronics Research Laboratory also were of great help. Mr. Agrios main- tained a close interest in this project throughout the preparation of this book, as did Mr. Dattilo, who reviewed all of the chapters as they were prepared. He made numerous suggestions which have resulted in valuable improvement in the clarity and usefulness of this book. Dr. S. B. Cohn, formerly of Stanford Hesearch Institute and presently of the Rantec Corporation, led the microwave filter and coupling structu research at Stanford Research Institute during the earlier Signal Corps filter programs at SRI. In many places this book presents research resu or reflects points of view, which are due to him. The authors' colleagues at SRI, and numerous researchers elsewhere have made many valuable contributions to the subject area of this book, and many results of their work have been incorporated into this book. The authors thank the various journals, book publishers, and elec- tronics firms who have given permission for the use of numerous figures and tables. vii And finally, the authors thank themany people at SRI who took a special interest in the huge job of preparing this book. Mrs. Edith Chambers CONTENTS spent countless painstaking hours supervising the preparation of the staggering number of illustrations in this book, and helped greatly in insuring illustrationsofhigh quality andclarity. Mrs. Mary F. Armstrong supervised the Varityping of the text. The authors' thanks also go to the editors, secretaries, and report production staff at SRI who all PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii were very cooperative in the production of this book. ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v ii CHAPTER 1 SOME GENERAL APPLICATIONS OF FILTER STRUCTURES . . . . . . . . . . . . . . . . . . . . . . IN MICROWAVE ENGINEERING. 1 . . . . . . . . . . . . . . . . . . . . . . . Sec. 1.01, Introduction 1 Sec. 1.02, Use of Filter.s .for. t.he. S.ep.ar.at.io.n .or. S.um.mi.ng. . . . . . . . of Signals. 1 . . . . . . . . . . . . . . . Sec. 1.03, Impedance-Matching Networks. 3 Sec. 1.04, Coupling Networks for Tu.be.s .an.d .Ne.ga.ti.ve.- . . . . . . . . . Resistance Amplifiers. 6 . . . . . . . Sec. 1.05, Time-Delay Networks and Slow-Wave Structures 9 Sec. 1.06, General Use of Filter Principles in the . . . . . . . . . . . . . . Design of Microwave Components 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. 14 . . . . . . . . . . . . . CHAPTER 2 SOME USEFUL CIRCUIT CONCEPTS AND EQUATIONS. 15 . . . . . . . . . . . . . . . . . . . . . . . Sec. 2.01, Introduction 15 . . . . . . . . . . Sec. 2.02, Complex Frequency and Poles and Zeros. 15 Sec. 2.03, Natural Modes of Vibration and Their. R.el.at.io.n . . . . . . . to Input-Impedance Poles and Zeros 18 . . . . . . . Sec. 2.04, Fundamental Properties of Transfer Functions 2 0 . . . . . . . . . . . . . . . . Sec. 2.05, General Circuit Parameters 26 Sec. 2.06, Open-Circuit I.mp.ed.an.ce.s .an.d .Sh.or.t-.ci.rc.ui.t . . Admittances. 29 Sec. 2.07, Relations Between General Circuit Parameters . . . . . . . . . . and Open- and Short-circuit Parameters 29 Sec. 2.08, Incident and Reflected Waves, Reflection C.o e. ff.ic.ie.nt.s,. . . and One Kind of Transmission Coefficient 34 Sec. 2.09, Calculation of the. I.np.ut. I.mp.ed.an.ce. o.f .a .Te.rm.i n. at.ed., . . . . Two-Port Network 3 5 . Sec. 2.10, Calculation of Voltage Transfer Functions. 3 6 Sec. 2.11, ,plculation of P.ow.er. T.ra.ns.fe.r .Fu.nc.ti.on.s .an.d . Attenuation". 38 . . . . . . . . . . Sec. 2.12, Scattering Coefficienta. 42 . . . . . . . . Sec. 2.13, Analysis of Ladder Circuits. 45 . . . . . . . . . . . . . . . . . . . . . . - References. 48 . . . CHAPTER 3 PRINCIPLES OF THE IMAGE METHOD FOR FILTER DESIGN. 49 . . . . . . . . . . . . . . . . . . . . . . . Sec. 3.01, Introduction 4 9 Sec. 3.02, Physical and Mathematical Definition of Image . . . . . . . . . Impedance and Image Propagation Function 49 Sec. 3.03, Relation Between the Image Parameters and General Circuit Parameters, Open-Cir.cu.it. I.mp.ed.an.ce.a,. a.nd. . . . . . Short-circuit Admittances. 5 2 viii CONTENTS CONTENTS . . . . . . . . . . . . . . . . . . . . . . . Sec 5.10. Iris-Coupled Waveguide Junctions SSeecc . 33..0045., TIhmea gSep ePcairaa.lm e.Itme.args.e f.Porr.o pS.eorm.tei .Ceos.m om.ofn .D iS.stsr.iupc.attu.iroe.nsl .es.s . . . . . . Sec . 5.11, RWeasvoengaunitd e FRreesqouneantcoiress a.nd. U.nl.oa.de.d .Q .of. . . . . . . . . . . Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References Sec 3.06. Constant-k and a-Derived Filter Sections Sec . 3.07, The Effects of Ter.mi.na.ti.on.s .Wh.ic.h .Mi.sm.at.ch. t.he. . . . . . . CHAPTER 6 STEPPED-IMPEDANCE TRANSFORMERS AND FILTER PROTOTYPES. . . . . . . . . Image Impedances . . . . . . . . . . . . . . . . . . . . . . . . . Sec 6.01. Introduction Sec 3.08, Design of Matching End Sections to Improve the . Response of Filters Designed on the Image Basis . . . . . . Sec 6.02, The Performanc.e. o.f H.o.mo.ge.ne.ou.s .Qu.ar.te.r-.Wa.ve. . . . . . . . . . . . . . . . . . . . . . . . Transformers Sec 3.09. .Me.as.ur.em.en.t .of. I.ma.ge. P.ar.am.et.er.s . . . . . . . . . . . . . . Sec . 6.03. The Performance of Homogeneous Half-Wave Filters . . . . . References . Sec 6.04, Exact Tchebyscheff and M.ax.im.al.ly. F.la.t .So.lu.ti.on.s . . . . . . for Up to Four Sections CHAPTER 4 LSOYWNT-HPEASSISS P MREOTTHOOTDYSP E .FI.LT.ER.S .OB.TA.IN.ED. B.Y .NE.TW.OR.K . . . . . . . . . . . Sec . 6.05, Exact Maxi.ma.ll.y .F.la.t .So.lu.ti.on.s .fo.r .Up. t.o .Ei.gh.t . . . . . . Sec . 4.01. Introduction . . . . . . . . . . . . . . . . . . . . . . . . Sections . . . . . . . . . . . . Sec . 4.02, CMoemtphaordiss ofno ro fF iIlmtearg eD aensdi gNne .tw.or.k .Sy.nt.he.si.s . . . . . . . . . SSeecc . 66..0067.. AApppprrooxxiimmaattee DDeessiiggnn wfhoern U Rp Itos MSomdaelrla tely Large R . . . . . . Sec . 4.03, Maximally Flat and Tchebysch.ef.f .Fi.lt.er. . . . . . . . . . . Sec . 6.08, Correction for. S.ma.ll. S.te.p-.Di.sc.on.ti.nu.it.y . . . . . . . . . . Attenuation Characteristics Capacitances Sec . 4.04, Definition of Circuit Parameters for Low- Sec . 6.09. Approximate Design when R Is Large . . . . . . . . . . . . . Pass Prototype Filters . . . . . . . . . . . . . . . . . . Sec . 6.10. Asymptotic Behavior as R Tends to Infinity . . . . . . . . . SSSeeeccc .. 444...000576.,, TTDMSoccaiuhhxnbieeglmlbbyayyy l sslTTccyeehh rreemmffFiifflnn aaPaFttrti eoelTdtdti.o em tMreMays-axp Dxie.eim lmaFa.aliylll .lyPty er. FroFlst.la oat.t.t y a.p.anend. . dF i..l.t.e.r.s. .. ... .................. SSSeeeccc ... 666...111321.,, oAoII nnffNhh OooTonnmwmesoooySg gneoeecnrnchee trMooioouuonrsson e uWW saaS. vveeTec.grgtuau.iiniodsd.nefes o .. QrQumu..aearrr..t tee...rr-.-..WWa..a.vve..e. ..TT.rr.a.a.nn.s.s.ffo..o.rrm..m.eer...rss ... ... ... ... ... Sec . 4.08, Comparison of the Time-Delay C.ha.ra.ct.er.is.ti.cs. . . . . . . . Sac . 6.14. Internal Dissipation Losses . . . . . . . . . . . . . . . . of Various Prototype Filters . . . . . . . . . . . . . . . . . . . . . . . . . . Sec 6.15. Group Delay Sec 4.09, Prototype. Tchebyscheff Impedance-Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Networks Giving Minimum Reflection . . . . . . . . . . . . References . Sec 4.10, Computation of Prototype Impedance-Matching NReeftlweocrtkiso nf or. S.pe.ci.fi.ed. R.ip.pl.e .or. M.in.im.um. . . . . . . . . . CHAPTER 7 OLORW W-APVAESGSU IADNED HCIOGRHRU-GPAATSISO NFSI LT.ER.S. US.IN.G .SE.MI.-.LU.MP.ED. EL.EM.EN.TS. . . . . . . Sec . 4.11. Prototypes for Negative-Resistance Amplifiers . . . . . . . Sec . 7.01, Properti.es. o.f. t.he. F.il.te.rs. D.is.cu.ss.ed. i.n .Th.is. . . . . . . . . Chapter Sec 4.12, Conversion of Filter Prototypes to Use Impedance- . . Rore aAcdtmiivtet aEnlceem-eInntv e.rt.er.s .an.d .On.ly. O.ne. K.in.d .of. . . . . . . . Sec . 7.02, AEplpermoexnitmsa t.e .Mi.cr.ow.av.e .Re.al.iz.at.io.n .of. L.um.pe.d .. .. .. .. .. .. .. .. Sec 4.13, Effects of Dissipative Elements in Prototypes . . . . . . Sec . 7.03. Low-Pass Filters Using Semi-Lumped Ele.me.nt.s . . . . . . . . for Low-Pass. Band-Pass. or' High-Pass Filters Sec 7.04. Low-Pass Corrugated-Waveguide Filter . . Sec 4.14, Approximate .Ca.lc.ul.at.io.n .of. P.ro.to.ty.pe. S.to.p-.Ba.nd. . . . . . . Sec 7.05, Low-Pass Waf.fl.e-.lr.o.n F.il.te.ra. H.av.in.g .Ve.ry. W.id.e . . . . . . . . Attenuation . Stop Bands Sec 4.15, Prototype Represen.ta.ti.on. o.f .Di.ss.ip.at.io.n .Lo.ss. i.n . . . . . . Sec 7.06, Low-Pasa Fil.t.er.s .fr.om .Qu.ar.te.r-.Wa.ve. T.ra.ns.fo.rm.er. . . . . . . Band-Stop Filters Prototypes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References Sec 7.07. High-Pass Filters Using Semi-Lumped Element6 . CHAPTER 5 PSReOcP . ER5T.I01E.S OIFnt SrOoMdEu cCtOiMoMnO N. M.IC.RO.WA.VE. F.IL.TE.R .EL.EM.EN.TS. .. .. .. .. .. .. .. .. .. SSeecc . 77..0098., LNLeootwww--oPPraaksssss Ta.indm. eH-.iDge.hl-a.Pya .Nses.t wI.omrp.kesd. a.n.c.e.-.M.a.t.ch..in..g .. .. .. .. .. .. .. .. .. Sec .. 5.02. General Properties of Transmienion L.in.es. .. .. .. .. .. .. .. .. .. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sec 5.03. Special Properties of Coaxial Lines . . . . . . . . . . . . . . Sec 5.04. Special Properties of Strip Lines CHAPmR 8 BANI)-PASS FILTERS (A GENERAL SUMMARY OF BAND-PASS FILTERS. Sec . 5.05, Parallel-Coupled Lines and Arrays of AND A VERSATILE DESIGN TE.CH.N.IQ.UE. F.OR. FI.L.TE.RS. WI.T.H N.AR.RO.W . . . . . . . . . . . . . . . . . . . . . . . OR MODERATE BANDWIDTHS) Sec . 5.06. LSipneecsi aBle tPwreoepne rGtrioeusn do fP lWaavneegsu idea . . . . . . . . . . . . . Sec . 8.01, A Summary of the Propertiea of the Band-Pass or SSeecc .. 55..0078.. CTormamnosnm iTsrsainosnm iLsisnieosn aLsi nRee sDoinsactoonrtsi n.ui.ti.es. .. .. .. .. .. .. .. .. .. Sec . 8.02. GPaesnnedeu1rdao0l H.iPrg.ihn-.cPie.pals.e sF. iol.tfe. Cros.u pT.rlee.adt-.eRde. noi.nna .Ctho.arp .tFei.rlst. e8r..s ..9... .. .. .. .. . . . . . . . Sec 5.09. Coupled-Strip-Transmiasion-Line Filter Sections CONTENTS CONTENTS . . . . . . SSeecc.. 88..0043,, PUrsea cotfi cLaol wR-Peaaslsi zatoti oBna nodf- PKa-s s anMda pJp-iInngvse. rt.er.s.. . . . . . . Sec. 10.07, BInatnedrwdiidgthitsa l.-L.in.e .F.il.te.rs. H.av.ing. W. i.de . . . . . . . . . . Sec. 8.05, Capacitive.-G.ap.-C.ou.pl.ed. T.ra.ns.m.iss.io.n .Li.ne. . . . . . . . . Sec. 10.08, Derivation of the Design Equations .fo.r . . . . . . . . . Filters. Parallel-Coupled and Stub Filters. . . . . . . Sec. 10.09, Derivation of the Design Equations for Sec. 8.06, Shunt-Inductance-Coupled, Waveguide Filters. . . . . . . . . . . . . . . . Interdigital-Line Filters. Sec. 8.07, Nbya rrSomwa-Blla nIdr isCeasv.i ty. R.e.son.at.or. F.il.te.rs. C.ou.pl.ed. . . . . . . Sec. 10.10, S.ele.ct.io.n .of. M.ap.pi.ng. F.un.ct.ion.s ............ .. .. .. .. .. .. . References Sec. 8.08, Filters Usin.g .T.wo.-P.or.t, .Qu.ar.te.r-W. a.ve.le.ng.th . . . . . . . . Resonators Sec. 8.09, Filters with. P.ar.al.le.l-C.o.up.le.d .St.rip.-L.in.e. . . . . . . . . CHAPTER li SPECIAL PROCEDURES TO AID IN THE PRACTICAL DEVELOPMENT Resonators . . . . . . . OF COUPLED-RESONATOR BAND-PASS FILTERS, IMPE.DA.N.CE.- . . . Sec. 8.10, Filters with Quarter-Wavelength Couplings. MATCHING NETWORKS, AND TIME-DELAY NETWORKS . . . . . . . . . . . . . . . . . . . . . . . Sec. 8.11, Lumped-Element, Coupled-Resonator Filters. Sec. 11.01, Introduction . . . . . . . . . Sec. 8.12, Band-Pass Filters with Wide Stop Bands Sec. 11.02, Measurement of V , and QL of a Singly Sec. 8.13, Comb-Line, Band-Pass Filters . . . . . . . . . . . . . . Loaded ~esonator~Q..e ., . . . . . . . . . . . RSeecf.e re8n.1c4e,s .PCr.oenc.ceed.rinni.gn g.E tq.huea. tDi.oenr.si.v. a.t.io..n ..of.. S..om..e ..of.. t..he.. .. .. .. .. .. .. .. .. SSeecc.. 1111..0043,, TTaeet ssBttsso thoon n ESSnyidnsm gm.lee .trRi.ecsa.ol nP.aato.irrss. wo.fi t.hR .eLsoo.and.aitno.gr s. .. .. Sec. 11.05, Tuning of .M.ul.tip.le.-R.es.on.at.or. B.a.nd.-P.ass. . . . Filters. CHAPTER 9 BAND-PASS FILTERS, CONTINUED (WIDE-BAND AND NARROW-BAND BAND-PASS FILTERS CONSISTING OF TRANSMISSION LINES WITH Sec. 11.06, Calculation of the Midband D.i.ss.ipa.ti.on. . . . REACTIVE DISCONTINUITIES). . . . . . . . . . . . . . . . Loss of Band-Pass Filters. Sec. 9.01, Introduction . . . . . . . . . . . . . . . . Sec. 11.07, Design of Narrow-Band Filters for Minimum Midband Loss and Specified High Attenuation Sec. 9.02, Filters with. I.m.ped.an.ce. S.te.ps. a.nd. I.m.pe.da.nce. . at some Nearby Frequency . . . . . . . . . . Inverters. Sec. 11.08, Design of Band-Pass Impedance-Matching Net- Sec. 9.03, Synchronously .Tu.ne.d .R.ea.cta.nc.e-.Co.up.le.d .H.alf.- . works Using the Methods of Chapter 8 . . . . Wave Filters Sec. 9.04, Narrow-Band Half-Wave Filters. . . . . . . . Sec. 11.09, NDeetswigonr kso f byB atnhde-P Masest hIomdsp eodfa nCceh-aMptaetrc h1in0g. . . . . . . . . . Sec. 9.05, Practical Realization of Reactive Couplings. Sec. 11.10, Design of Wide-Band Coupling Str.u.ctu.r.es. fo.r . . . . . . . Sec. 9.06, Some Standardized Pseudo-High-Pass Filter Negative-Resistance Amplifiers Designs. . . . . . . . . . . . . . . . . . . Sec. 11.11, Band-Pass Time-Delay Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sec. 9.07, An Experimental Wide-Band Waveguide Filter References Sec. 9.08, Design for Specifi.ed. B.an.d-.Ed.ge.s .an.d .St.op.- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Band Attenuation 547 CHAPTER 12 BAND-STOP FILTERS. . . . . . . . . . . . . . . . . . . . . . . Sec. 9.09, Examples of .F.ilt.er.s .H.avi.ng. M.ed.ium. .an.d .La.rg.e . . . . . . . Sec. 12.01, Introduction Bandwidths 557 Sec. 12.02, Lumped-Element Ban.d.-St.op. F.i.lte.rs. f.ro.m .Lo.w-. . . . . . . . Sec. 9.10, Derivation of the Data fo.r B.a.nd.wi.dth. C.o.nt.rac.ti.on. . . . . Pass Prototypes. and Pass-Band Distortion 564 . . . . . . . . . . . . . Sec. 12.03, The Effects of Dissipation. L.o.ss .on. B.an.d-. . . . . . . . . Sec. 9.11, Optimizing the Line Impedances 569 Stop Filter Performance. . . . . . . . . . Sec. 9.12, R.ea.cta.nc.e-.Co.up.le.d .Qu.ar.te.r-W.a.ve. F.il.te.rs. . . . . . . . . . 571 Sec. 12.04. An Approximate Deaign Procedure for M.icr.ow.av.e . . . . . . References 582 Filters with Very Narrow Stop Bands. Sec. 12.05, Practical Realization of Band.-S.top. R.e.so.na.to.rs . . . . . . CHAPTER 10 BAND-PASS FILTERS, CONTINUED (BAND-PASS AND PSEUW HIGH- for Narrow-Stop-Band Filters CPAOSUSP LEFDIL TAERRRSA YCS OONFS ILSTININEGS) OF. L.IN.ES. A.ND. S.TU.BS., .OR. P.AR.AL.LE.L- . . . . . . . Sec. 12.06, ETuxnpienrgim oefn tBala nAd-dSjtuospt mRenets oonfa ttohres C.o.up.lin.gs. a.nd. . . . . . . Sec. 10.01, Concerning the Fi.lte.rs. a.nd. D.es.ig.n .Pr.oc.ed.ur.es. . . . . . . Sec. 12.07, Example of a Str.ip.-L.in.e,. N.ar.ro.w-.St.op.-B.an.d . . . . . . . . in this Chapter. 583 Filter Design. . . . . . SSeecc.. 1100..0023,, FPailrtaellresl -wCiotuh pSlehdu nFt ioltre Srse rwieisth A A00/4/2 SRtuebsso.n a.to.rs.. . . . . . 558955 Sec. 12.08, NCaornrosiwd-eSrtaotpi-oBnasn,d anWda vaeng uEidxea mFpilel te.r .D.es.ign. . . . . . . . . Sec. 10.04, Filters w.ith. A.0/.2 .St.ub.s .an.d .A0./4. C.on.ne.ct.in.g . . . . . . . Set. 12.09, A Design Procedure Which Is Accurate for F.i.lte.rs. . . . . Lines.. 605 with Wide (and Narrow) Stop-Band Widths. Sec. 10.05, Filters Using both Series and Shunt Stubs. . . . . . . . 609 Sec. 12.10, Some Examples Illustrating the Performance . . . . . . Obtainable Using the Equations in Sec. 12.09 Sec. 10.06, MInotdeerrdaitge itBaaln-dLwiindeth F.il.ter.s .of. N.ar.ro.w .or. . . . . . . . . . 614 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii xiii CONTENTS CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER 13 ATENMD .MBORDAEN. CHC-OLUINPEL EDDI-RTERCATNIOSMNAISLS IOCNO-ULPILNEER S DI.RE.CT.IO.NA.L .CO.UP.LE.RS.. . . . . . . 7 75 CHAPTER 15 HIGH. - POWER FILTERS . . . . . . . . 889 . . . . . . . . . . . . . . . . . . . . . . . Sec 15.01. Introduction and General Considerations 889 Sec 13.01, Introduction . Sec . 13.02, Design Relations for TEM.Mode. Coupled- Sec 15.02, PTorawnesrm-Hiassnidolnin-gL iCneasp a.cit.y .of. V.a.rio.us. . . . . . . . . . . 895 Transmission-Line Directional Couplers . ofonesection . . . . . . . . . . . . . . . . . . . . . Sec 15.03, Theoretical Pulse-Power C.ap.ac.ity. o.f .D.ire.c.t- . . . . . . Sec . 13.03 Design Relations for TEM.Mode. Coupled- . Coupled-Resonator Filters . . 910 Sec 15.04 A High-Power Tunable Narrow-Band TEOl1-Mode Filter 921 oTfr aTnshmreies sSioenc-tLioinnes . D.ire.c.tio.na.l .C.ou.ple.rs. . . . . . . . . . Sec . 15.05. High-Power Waffle-Iron Filters . . . . . . . . . . . . 937 . . . . . . . . . . . . . . . Sec 15.06. Dissipative Waveguide Filters 952 Sec 13.04, Relations for TEM-Mode Coupled-Transmission- . . . . . . . . . . . . Line Directional Couplers of Five and More Sec 15.07. Dissipative Coaxial-Line Filters 957 Sections . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . 961 . Sec 13.05, Typical Designs for TEM.Mode. Coupled- . . . . . . . . . . . . . . . . . . . . . . . . Transmission-Line Directional Couplers of CHAPTER 16 MULTIPLEXER DESIGN 965 One Section with Approximately 3 db Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sec 16.01. Introduction 965 Coupling . . . . . . . . . . Sec 16.02. Multiplexers Using Directional Filters 966 Sec 13.06, Typical Designs for TEM Mode. Coupled- . Transmission-Line Directional Couplers of Sec 16.03, Mu1 tiplexers Using Reflecting Narrow-Band . . . . . . Sec . 13.07, ODneer iSvaetcitoino no afn dD ewsiigtnh FWoeramk uClaosu pfloinrg T E.M..Mo.de.. . . . . . . . Sec . 16.04. MFiulltteirpsle. xweristh wGituha rCd oBnatingduso Buse twPeaesns CBahnadnsn .els. . . . . . . 996783 Coupled-Tran.sm.is.si.on.-L.in.e .Co.u.ple.rs. o.f . . . . . . . . . . Sec . 16.05. Diplexers with Contiguous Pass Bands . . . . . . . . . 991 Onesection . . . . . . . . . . . . . . . . . . . . . . . . . . . . References 1000 Sec 13.08, Quarter-Wave Filter Prototype Circuits for TEM.Mode. Coupled-Transmission-Line . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER 17 MECHANICALLY AND MAGNETICALLY TUNABLE MICROWAVE FILTERS 1001 Directional Couplers . . . . . . . . . . . . . . . . . . . . . . SSeecc .. 1133..0190,, CBPeroarnnisocihdd-ieLcr ianBteiro anCnsco hua-pLnldie nrGes eC.noe.ruapl.l eF.ros .r.m..ul.a.s ..fo..r .. .. .. .. .. .. .. .. .. SSSeeeccc . . 111777...000213... MTInhetecrohoradyn uiocctfai loIlnyd eTaul.n aTbulen aCbolea xBiaaln dB-Paansds- PFasisl teFrisl te.rs. .. .. .. .. 111000001613 . . . . . Sec 13.11, The Characteristics and Performan.ce. of. . . . . . . . . . Sec . 17.04. Waveguide Mechanically Tunable Band-Pass. F.il.te.rs. . . . 1020 Synchronous Branch-Line Couplers Sec 17.05. Properties of Ferrimagnetic Resonators 1027 Sec . 13.12 Tables of Imm.it.tan.ce.s .of. S.yn.ch.ro.no.us. B.ra.nc.h-. . . . . . . Sec . 17.06, Determination of the Crys.ta.l A.x.es .of. S.ph.e.ric.al. . . . . Line Couplers Ferrimagnetic Resonators 1040 . . Sec 13.13, Examples Illustrating the Design and Perfo.rm.- . . . . . . Sec 17.07, Design of Magnetically Tunable Band-Pass Filters . ance of Synchronous Branch-Line Couplers with 'EM-Mode Inputs and Outputs. and a. . . . . . . . Sec 13.14, Design of an Experimental Branch-Line Coupler Discussion of General Design Principles 1043 inwaveguide . . . . . . . . . . . . . . . . . . . . . . Sec . 17.08, nesults of Some Trial Magnetically Tunable Band- References Pass Filter. I).es.ign.s .H.av.ing. S.tr.ip.-L.in.e .In.p.uts. . . . . . and Outputs 1056 . CHAPTER 14 DIRECTIONAL. CHANNEL-.SEP.AR.A.TIO.N .FI.LT.ER.S .AN.D .TR.AV.EL.IN.G-. . . Sec 17.09, Magnetically Tunable Rand-Pass. F.i.lt.er.s w.i.th . . . . . . WAVE RING.RESONATORS Waveguide Inputs and Outputs 1068 Sec .. 14.01. Introduction . . . . . . . . .. .. .. .. .. .. .. .. .. Sec . 17.10, Magnetically Tunable Dire.ct.io.na.l .Fi.lt.er.s . . . . . . . . Sec 14.02. Waveguide Directional Filters Having Circulator Action 1072 . . . . . . . . . . Sec . 14.03, UStsrinigp HTraalnf-s moirs sFiounll -LWinaev eDleinrgetcht ioSntaril pFs. ilt..e.r.s. . .. SReecf ere1n7c.1e1s. M.ag.ne.ti.ca.lly. T.un.ab.le. B.an.d-.St.op. F.il.te.rs. . . . . . . . . 11008768 Sec 14.04. Traveling-Wave-Loop Directional Filter . . . . . . . . . . Sec . 14.05. Traveling-Wave Ring Resonator INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1089 Sec 14.06, Derivation of Formulas for Waveguide . . . . . . . . . . . . . . Directional Filters . Sec 14.07, Derivation of Formulas for Traveling-Wave Loop Directional Filters and the Traveling- . . . . . . . . . . . . Wave Ring Resonator . Sec 14.08, Derivation of Formulas for Strip-Transmission- Line Directional Filters Using Half-Wavelength . . . . . . . . . . . and One-Wavelength Strips . . . . . . . . . . . . . . . . . . . . . . . References xiv MICROWAVE FILTERS, IMPEDANCE-MATCHING NETWORKS, AND COUPLING STRUCTURES CHAPTER I SOME GENERAL APPLICATIONS OF FILTER STRUCTURES IN MICROWAVE ENGINEERING SEC. 1.01. INTRODUCTION Most readers will be familiar with the use of filters as discussed in Sec. 1.02 below. However, the potential applications of the material in this book goes much beyond these classical filter applications to cover many other microwave engineering problems which involve filter-type structures but are not always thought of as being filter problems. Thus, the purpose of this chapter is to make clear to the reader that this book is not addressed only to filter design specialists, but also to antenna engineers who may need a broadband antenna feed, to microwave tube engineers who may need to obtain broadband impedance matches in and out of microwave tubes, to system engineers who may need a microwave time-delay network, and to numerous others having other special microwave circuit design problems. SEC. 1.02, USE OF FILTERS FOR THE SEPARATION OR SUMMING OF SIGNALS The most obvious application of filter structures, of course, i s for the rejection of unwanted signal frequencies while permitting good transmission of wanted frequencies. The most common filters of this sort are designed for either low-pass, high-pass, band-pass or band-stop attenuation characteristics such as those shown in Fig. 1.02-1. Of course, in the case of practical filters for the microwave or any other frequency range, these characteristics areonly achieved approximately, since there is a high-frequency limit for any given practical filter structure above - which its characteristics will deteriorate due tojunction effects, reso- nances within the elements, etc. Filters are also commonly used for separating frequencies in diplexers or multiplexers. Figure 1.02-2 shows a multiplexer which segregates signals within the 2.0 to 4.0 Gc band into three separate