Microwave Filters, Impedance-Matching Networks, and Coupling Structures

1115 Pages·1965·18.625 MB·English

by  G. Matthaei, L. Young

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. М. T. JONES
Technology for Communications
International
Mountain View, CA
ARTECH HOUSE
Copyright © 1980
ARTECH HOUSE, INC.
685 Canton Street
Norwood, MA 02062
Reprint of the edition published by McGraw-Hill
Book Company, Inc., 1964
Printed and bound in the United States of America
All rights reserved. No part of this book may be repro­
duced or utilized in any form or by any means, elec­
tronic or mechanical, including photocopying, recording,
or by any information storage and retrieval system,
without permission in writing from the publisher.
Library of Congress Catalog Card Number: 80-68976
Standard Book Number 0-89006-099-1
Printed and bound by BookMart Press, North Bergen,
NJ, USA, November, 1985.
10
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 is 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
is 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
of the microwave filter techniques described in this book are potentially
useful for the design of microwave devices not ordinarily thought of as
having anything to do with filters. Some examples are tubes, parametric
devices, and antennas, where filter structures can serve as efficient
impedance-matching networks for achieving broad-band operation. Filter
structures are also useful as slow-wave structures or time-delay struc­
tures. In addition, microwave filter techniques can be applied to other
devices not operating in the microwave band of frequencies, as for
instance to infrared and optical filters.
The three objectives above are not listed in any order of importance, nor
is this book entirely separated into parts according to these objectives.
However, in certain chapters where the material lends itself to such
organization, the first section or the first few sections discuss general
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
the derivations of the various design equations. Also, at numerous places
cross references are made to other portions of the book where information
useful for the design of the particular structure under consideration can
be found. For example, Chapter 11 describes procedures for measuring the
unloaded Q and external Q of resonators, and for measuring the coupling
coefficients between resonators. Such procedures have wide application
in the practical development of many types of band-pass filters and
impedance-matching networks.
Chapter 1 of this book describes the broad range of applications for
which microwave filter structures are potentially useful. Chapters 2
through 6 contain reference data and background information for the rest
of the book. Chapter 2 summarizes various concepts and equations that
are particularly useful in the analysis of filter structures. Although
the image point of view for filter design is made use of only at certain
points in this book, some knowledge of image design methods is desirable.
Chapter 3 gives a brief summary of the image design concepts which are
particularly useful for the purposes of this book. Chapters 1 to 3 should
be especially helpful to readers whose background for the material of this
book may have some gaps.
Most of the filter and impedance-matching network design techniques
described later in the book make use of a low-pass prototype filter as a
basis for design. Chapter 4 discusses various types of lumped-element,
low-pass, prototype filters, presents tables of element values for such
filters, discusses their time-delay properties, their impedance-matching
properties, and the effects of dissipation loss upon their responses. In
later chapters these low-pass prototype filters and their various proper­
ties are employed in the design of low-pass, high-pass, band-pass, and
band-stop microwave filters, and also in the design of microwave impedance-
matching networks, and time-delay networks.
Various equations, graphs, and tables relevant to the design of
coaxial line, strip-line, waveguide, and a variety of resonators, coupling
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 impedance-transformer
applications, but also for use as prototypes for certain types of band­
pass or pseudo high-pass filters discussed in Chapter 9.
Design of low-pass filters and high-pass filters from the semi­
lumped- element point of view are treated in Chapter 7. Chapters 8, 9,
and 10 discuss band-pass or pseudo-high-pass filter design using three
different design approaches. Which approach is best depends on the type
of filter structure to be used and the bandwidth required. A tabulation
of the various filter structures discussed in all three chapters, a
summary of the properties of the various filter structures, and the
section number where design data for the various structures can be found,
are presented at the beginning of Chapter 8.
Chapter 11 describes various additional techniques which are useful
to the practical development of microwave band-pass filters, impedance-
matching networks, and time-delay networks. These techniques are quite
general in their application and can be used in conjunction with the
filter structures and techniques discussed in Chapters 8, 9, and 10, and
elsewhere in the book.
Chapter 12 discusses band-stop filters, while Chapter 13 treats
certain types of directional couplers. The TEM-mode, coupled-transmission-
line, directional couplers discussed in Chapter 13 are related to certain
types of directional filters discussed in Chapter 14, while the branch-
guide directional couplers can be designed using the step-transformer
prototypes in Chapter 6. Both waveguide and strip-line directional filters
are discussed in Chapter 14, while high-power filters are treated in Chapter 15.
Chapter 16 treats multiplexers and diplexers, and Chapter 17 deals with
filters that can be tuned either mechanically or by varying a biasing
magnetic field.
It is hoped that this book will fill a need (which has become in­
creasingly apparent in the last few years) for a reference book on design
data, practical development techniques, and design theory, in a field of
engineering which has been evolving rapidly.
v

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, DA 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 Research Institute and presently
of the Rantec Corporation, led the microwave filter and coupling structure
research at Stanford Research Institute during the earlier Signal Corps
filter programs at SRI. In many places this book presents research results
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.
And finally, the authors thank the many people at SRI who took a special
interest in the huge job of preparing this book. Mrs. Edith Chambers
spent countless painstaking hours supervising the preparation of the
staggering number of illustrations in this book, and helped greatly in
insuring illustrations of high quality and clarity. 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
were very cooperative in the production of this book.
CONTENTS
PREFACE............................................................................. iii
ACKNOWLEDGMENTS .................................................................. vii
CHAPTER 1 SOME GENERAL APPLICATIONS OF FILTER STRUCTURES
IN MICROWAVE ENGINEERING............................................... 1
Sec. 1.01, Introduction .............................................. 1
Sec. 1.02, Use of Filters for the Separation or Summing
of Signals................................................. 1
Sec. 1.03, Impedance-Matching Networks............................... 3
Sec. 1.04, Coupling Networks for Tubes and Negative-
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 Relation
to Input-Impedance Poles and Zeros ....................... 18
Sec. 2.04, Fundamental Properties of Transfer Functions ............ 20
Sec. 2.05, General Circuit Parameters ............................... 26
Sec. 2.06, Open-Circuit Impedances and Short-Circuit
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 Coefficienta,
and One Kind of Transmission Coefficient................. 34
Sec. 2.09, Calculation of the Input Impedance of a Terminated,
Two-Port Network ........................................... 35
Sec. 2.10, Calculation of Voltage Transfer Functions................ 36
Sec. 2.11, Calculation of Power Transfer Functions and
"Attenuation”. ........................................... 38
Sec. 2.12, Scattering Coefficients.................................... 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 .............................................. 49
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-Circuit Impedances, and
Short-Circuit Admittances.................................. 52
CONTENTS
Sec. 3.04, Image Parameters for Some Common Structures.............. 54
Sec. 3.05, The Special Image Properties of Dissipationless
Networks................................................... 56
Sec. 3.06, Conatant-fc and л-Derived Filter Sections ................ 60
Sec. 3.07, The Effects of Terminations Which Mismatch the
Image Impedances........................................... 58
Sec. 3.08, Design of Matching End Sections to Improve the
Response of Filters Designed on the Image Basis........... 72
Sec. 3.09, Measurement of Image Parameters........................... 78
References.............................................................. 81
CHAPTER k LOW-PASS PROTOTYPE FILTERS OBTAINED BY NETWORK
SYNTHESIS METHODS ..................................................... 83
Sec. 4.01, Introduction .............................................. 83
Sec. 4.02, Comparison of Image and Network Synthesis
Methods for Filter Design.................................. 83
Sec. 4.03, Maximally Flat and Tchebyscheff Filter
Attenuation Characteristics................................ 85
Sec. 4.04, Definition of Circuit Parameters for Low-
Pass Prototype Filters .................................... 95
Sec. 4.05, Doubly Terminated, Maximally Flat and
Tchebyscheff Prototype Filters ............................ 97
Sec. 4.06, Singly Terminated Maximally Flat and
Tchebyscheff Filters ...................................... 104
Sec. 4.07, Maximally Flat Time-Delay Prototype Filters................ 108
Sec. 4.08, Comparison of the Time-Delay Characteristics
of Various Prototype Filters .............................. 113
Sec. 4.09, Prototype, Tchebyscheff Impedance-Matching
Networks Giving Minimum Reflection ....................... 120
Sec. 4.10, Computation of Prototype Impedance-Matching
Networks for Specified Ripple or Minimum
Reflection....................................................130
Sec. 4.11, Prototypes for Negative-Resistance Amplifiers.............. 135
Sec, 4.12, Conversion of Filter Prototypes to Use Impedance-
or Admittance-Inverters and Only One Kind of
Reactive Element ........................................... 144
Sec. 4.13, Effects of Dissipative Elements in Prototypes
for Low-Pass, Band-Pass, or High-Pass Filters ........... 149
Sec. 4.14, Approximate Calculation of Prototype Stop-Band
Attenuation....................................................I33
Sec. 4.15, Prototype Representation of Dissipation Loss in
Band-Stop Filters.............................................1^°
References................................................................162
CHAPTER PROPERTIES OF SOME COMMON MICROWAVE FILTER ELEMENTS .................. 163
Sec. 5.01, Introduction .............................................. 163
Sec. 5.02, General Properties of Transmission Lines ................ 163
Sec. 5.03, Special Properties of Coaxial Lines......... 165
Sec. 5.04, Special Properties of Strip Lines............................16®
Sec. 5.05, Parallel-Coupled Lines and Arrays of
Lines Between Ground Planes...................................1'4
Sec. 5.06, Special Properties of Waveguides ......................... 1^
Sec. 5.07, Common Transmission Line Discontinuities ................ 203
Sec. 5.08, Transmission Lines as Resonators ......................... 214
Sec. 5.09, Coupled-Strip-Transmission-Line Filter Sections............ 217
X