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A C LA S S l C R E I S S U E

Foundations for Microwave

Engineering

SECOND EDITION

Robert E. Collin

Foundations for Microwave Engineering

SECOND EDITION

D o n a l d G. Dudley, Series Editor

muiaUomjor Microwatt Engineering. Second Edition, covers the major topics of microwave engineering- Its presentation defines the accepted standard for both advanced undergraduate and graduate level courses on microwave engineering. An essential reference book lor the practicing microwave engineer, it features.-

• Planar transmission lines, as well as an appendix that describes in detail conformal mapping methods for their analysis and attenuation characteristics.

• Small aperture coupling and its application in practical components such as directional couplers and cavity coupling

• Printed circuit components with an emphasis on techniques such as even and odd mode analysis and the use of symmetry properties

• Microwave linear amplifier and oscillator design using solid-state circuits such as varactor devices and transistors. Foimdationi for Microwave Engineering, Second Edition, has extensive coverage of transmission lines, waveguides, microwave circuit theory, impedance matching, and cavity resonators. It devotes an entire chapter to fundamental microwave tubes, as well as other chapters on periodic structures, microwave filters, small signal solid-state microwave mplifier and oscillator design, and negative resistance devices and circuits. Completely updated in 1992, it is being eissued by the IEEE Press in response to requests from our many members, who found u an invaluable textbook and an enduring reference for practicing microwave engineers.

Robert E. Collin is the author or coauthor ol more than 150 technical papers and five books on electromagnetic nSeory and applications. His classic text, Field Theory of Guided Waves, is also a volume in the series. Professor Collin has had a long and distinguished academic career at Case Western Reserve University. In addition to his professorial duties, he has served as chairman of the Department of Electrical Engineering and as interim dean of engineering.

Professor Collin is a life fellow of the IEEE and a member of the Microwave Theory and Techniques Society and the Antennas and Propagation Society (APSI He is a member of the U.S. Commission B of URSI and a member of the Geophysical Society. Other honors include the Diekman Award from Case Western Reserve University for distinguished graduate teaching, the IEEE APS Distinguished Career Award (1992), the IEEE Schelkunoff Prize Paper Award (1992). the IEEE Electromagnetics Award (1998), and an IEEE Third Millennium Medal in 2000. In 1990 Professor Collin was elected to the National Academy of Engineering.

The IEEE Press Series on Electromagnetic Wave Theory offers outstanding coverage of the field. It consists of new titles of contemporary interest, as well as reissues and revisions of recognized classics by established authors and researchers. The series emphasizes works of long-term archival significance in electromagnetic waves and applications. Designed specifically for graduate students, researchers and practicing engineers, the series provides affordable volumes that explore and explain electromagnetic waves beyond the undergraduate level.

Visit wftww.wiley.com/ieee

>W1LEY'INTERSCIEN'

ISBN

••

D-7flD3-bD31-l

780780"36rmr)"

An IEEE Press Classic Reissue

FOUNDATIONS FOR MICROWAVE ENGINEERING

SECOND EDITION

IEEE PRESS SERIES ON ELECTROMAGNETIC WAVE THEORY

The IEEE Press Series on Electromagnetic Wave Theory consists of new titles as well as reprintings and revisions of recognized classics that maintain long-term archival significance in electromagnetic waves and applications.

Scries Editor Donald G. Dudley University of Arizona

Advisory Board Robert E. Collin Case Western Reserve University

Akira Ishimaru University of Washington

D. S. Jones University of Dundee

Associate Editors

ELECTROMAGNETIC THEORY, SCATTERING, AND DIFFRACTION

Ehud Heyman Tel-Aviv University

INTEGRAL EQUATION METHODS

Donald R. Wilson University of Houston

DIFFERENTIAL EQUATION METHODS

Andreas C. Cangellans

University

of

A

rizona

ANTENNAS. PROPAGATION, AND MICROWAVES

David R. Jackson University of Houston

BOOKS IN THE IEEE PRESS SERIES ON ELECTROMAGNETIC WAVE THEORY

Christopoulos. C, The Transmission-Line Modeling Methods: TLM Clemmow, R C. The Plane Wave Spectrum Representation of Electromagnetic Fields Collin. R. E.. Field Theory of Guided Waves, Second Edition Collin, R. E.. Foundations for Microwave Engineering, Second Edition Dudley. D. G., Mathematical Foundations for Electromagnetic Theory Elliot. R. S., Electromagnetics: History, Theory, and Applications Felsen. L. B.. and Marcuvitz. N.. Radiation and Scattering qf Waves Harrington. R. F, Field Computation by Moment Methods Hansen et aL, Plane-Wave Theory of Time-Domain Fields: Near-Field Scanning Applications Ishimaru. A., Wave Propagation and Scattering in Random Media Jones, D. S.. Methods in Electromagnetic Wave Propagation. Second Edition Lindell. 1. V., Methods for Electromagnetic Field Analysis Peterson el al.. Computational Methods for Electromagnetics Tai. C. T, Generalized Vector and Dyadic Analysis: Applied Mathematics in Field Theory Tai. C. T. Dyadic Green Functions in Electromagnetic Theory. Second Edition Van Bladel, J., Singular Electromagnetic Fields and Sources Volakis et al., Finite Element Method for Electromagnetics: Antennas, Micmwave Circuits, and Scattering Applications Wail. J.. Electromagnetic Waves in Stratified Media

An IEEE Press Classic Reissue

FOUNDATIONS FOR MICROWAVE ENGINEERING

SECOND EDITION

IEEE Press Series on Electromagnetic Wave Theory

Robert E. Collin

Professor of Electrical Engineering Case Western Reserve University

Cleveland, OH

IEEE Antennas & Propagation Society, Sponsor IEEE Microwave Theory and Techniques Society, Sponsor

The Institute of Electrical and Electronics Engineers. Inc., New York

WlLEY'INTERSCIENCE

A JOHN WILEY & SONS, INC.. PUBLICATION

© 2001 THE INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS, INC. 3 Park Avenue, 17th Floor, New York, NY 10016-5997

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 97S-750-8400, fax 978-750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken. NJ 07030, (201) 748-6011, fax (201) 748-6008, e-mail: [email protected]

For general information on our other products and services please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993 or fax 317-572-4002.

Printed in the United States of America 1098765432

ISBN 0-7803-6031-1

Library of Congress Cataloging-in-Publication Data

Collin. Robert E. Foundations lor microwave engineering / Robert E. Collin.- 2nd ed. p. cm. - (IEEE Press series on electromagnetic wave theory) Originally published : New York : McGraw Hill, cl992. "An IEEE Press classic reissue." Includes bibliographical references and index. ISBN 0-7803-6031-1 I. Microwave devices. I. Title. II. Series.

TK7876 .C645 2000 621.381'3--dc21

00-053874

FOREWORD TO THE REISSUED EDITION

The purpose of the IEEE Press Series on Electromagnetic Wave Theory is to publish books of long-term archival significance in electromagnetics. Included are new titles as well as reprints and revisions of recognized classics. The book Foundations for Microwave Engineering, by Robert E. Collin, is by any measure such a classic. The original edition of the book appeared in 1966 and remained in print until the appearance of the second edition in 1992, a span of 26 years.

In the second edition. Professor Collin completely updated and modernized his book to include the many advances that had occurred in microwave engineering since the appearance of the original edition. That the second edition has gone out of print has caused concern among many of my colleagues in the IEEE Antennas and Propagation Society (APS) and the IEEE Microwave Theory and Techniques Society (MTT). We at the IEEE Press are delighted to be able lo overcome this difficulty by introducing a reprint of the second edition into our Series on Electromagnetic Wave Theory. The book is a thorough and in-depth exposition on microwave engineering. Furthermore, it will make an excellent companion to Professor Collin's book, Field Theory- of Guided Waves, also included in the series.

Professor Collin has been a valued colleague for many years. He is the author or coauthor of five books and more than 150 technical papers. His contributions to electromagnetics span a wide range of subjects and have brought him international respect and many awards. Among these are election to the National Academy of Engineering, the IEEE Electromagnetics Field Award, the IEEE/APS Distinguished Career Award, an IEEE/APS Schelkunoff Prize Paper Award, and the IEEE Third Millennium Medal.

It is with pleasure that I welcome this book into the series.

Donald G. Dudley University of Arizona

Series Editor IEEE Press Series on Electromagnetic Wave Theory

IEEE Press 445 Hoes Lane, P.O. Box 1331

Piscataway, NJ 08855-1331

IEEE Press Editorial Board Robert J. Herrick, Editor in Chief

M.Akay J. B. Anderson P. M. Anderson J. E. Brewer

M.Eden M. E. El-Hawary R. F. Hoyt S. V. Kartalopoulos D. Kirk

M.S.Newman M. Padgett W.D. Reeve G. Zobrist

Kenneth Moore, Director of IEEE Press Catherine Faduska. Senior Acquisitions Editor Linda Matarazzo. Associate Acquisitions Editor

Marilyn G. Catis, Marketing Manager Mark Morrell, Associate Production Editor

IEEE Antennas & Propagation Society. Sponsor AP-S Liaison to IEEE Press, Robert Mailloux

IEEE Microwave Theory and Techniques Society, Sponsor MTT-S Liaison to IEEE Press, Karl Varian

Cover design: William T. Donnelly, WT Design

CONTENTS

Preface

XV

1 Introduction

1

1.1 Microwave Frequencies

1

1.2 Microwave Applications

3

1.3 Microwave Circuit Elements and Analysis

6

References

16

2 Electromagnetic Theory

17

2.1 Maxwell's Equations

17

2.2 Constitutive Relations

23

2.3 Static Fields

28

2.4 Wave Equation

31

2.5 Energy and Power

33

2.6 Boundary Conditions

39

2.7 Plane Waves

44

Plane Waves in Free Space

44

2.8 Reflection from a Dielectric Interface

49

1. Parallel Polarization

49

2. Perpendicular Polarization

52

2.9 Reflection from a Conducting Plane

53

2.10 Potential Theory

56

•2.11 Derivation of Solution for Vector Potential

59

62

2.12 Lorentz Reciprocity Theorem

65

Problems

70

References

3 Transmission Lines and Waveguides

71

Part 1 Waves on Transmission Lines

72

3.1 Waves on An Ideal Transmission Line

72

3.2 Terminated Transmission Line: Resistive Load

78

vii

ViU COOTENTS

3.3 Capacitive Termination 3.4 Steady-State Sinusoidal Waves 3.5 Waves on a Lossy Transmission Line

Loss-Free Transmission Line Low-Loss Transmission Line

3.6 Terminated Transmission Line: Sinusoidal Waves Terminated Lossy Line Part 2 Field Analysis of Transmission Lines

3.7 Classification of Wave Solutions TEM Waves TE Waves TM Waves

82

85

86

88

.

89

89

94

96

96

99

100

102

3.8 Transmission Lines (Field Analysis)

104

Lossless Transmission Line

104

Transmission Line with Small Losses

108

3.9 Transmission-Line Parameters

112

3.10 In homogeneously Filled Parallel-Plate Transmission Line 117

Low-Frequency Solution

121

High-Frequency Solution

123

3.11 Planar Transmission Lines

125

3.12 Microstrip Transmission Line

130

Low-Frequency Solutions

136

Microstrip Attenuation

153

High-Frequency Properties of Microstrip Lines

158

Attenuation

163

3.13 Coupled Microstrip Lines

164

3.14 Strip Transmission Lines

170

Attenuation

171

3.15 Coupled Strip Lines

173

3.16 Coplanar Transmission Lines

175

Attenuation

178

High-Frequency Dispersion

180

Part 3 Rectangular and Circular Waveguides

180

3.17 Rectangular Waveguide

181

TE Waves

182

Power

186

Attenuation

187

Dominant TE10 Mode

190

TM Modes

193

3.18 Circular Waveguides

194

TM Modes

194

TE Modes

196

3.19 Wave Velocities

198

Phase Velocity

199

Group Velocity

200

Energy-Flow Velocity

204

3.20 Ridge Waveguide

205

3.21 Fin Line

208

Problems

210

References

219

Foundations for Microwave

Engineering

SECOND EDITION

Robert E. Collin

Foundations for Microwave Engineering

SECOND EDITION

D o n a l d G. Dudley, Series Editor

muiaUomjor Microwatt Engineering. Second Edition, covers the major topics of microwave engineering- Its presentation defines the accepted standard for both advanced undergraduate and graduate level courses on microwave engineering. An essential reference book lor the practicing microwave engineer, it features.-

• Planar transmission lines, as well as an appendix that describes in detail conformal mapping methods for their analysis and attenuation characteristics.

• Small aperture coupling and its application in practical components such as directional couplers and cavity coupling

• Printed circuit components with an emphasis on techniques such as even and odd mode analysis and the use of symmetry properties

• Microwave linear amplifier and oscillator design using solid-state circuits such as varactor devices and transistors. Foimdationi for Microwave Engineering, Second Edition, has extensive coverage of transmission lines, waveguides, microwave circuit theory, impedance matching, and cavity resonators. It devotes an entire chapter to fundamental microwave tubes, as well as other chapters on periodic structures, microwave filters, small signal solid-state microwave mplifier and oscillator design, and negative resistance devices and circuits. Completely updated in 1992, it is being eissued by the IEEE Press in response to requests from our many members, who found u an invaluable textbook and an enduring reference for practicing microwave engineers.

Professor Collin is a life fellow of the IEEE and a member of the Microwave Theory and Techniques Society and the Antennas and Propagation Society (APSI He is a member of the U.S. Commission B of URSI and a member of the Geophysical Society. Other honors include the Diekman Award from Case Western Reserve University for distinguished graduate teaching, the IEEE APS Distinguished Career Award (1992), the IEEE Schelkunoff Prize Paper Award (1992). the IEEE Electromagnetics Award (1998), and an IEEE Third Millennium Medal in 2000. In 1990 Professor Collin was elected to the National Academy of Engineering.

The IEEE Press Series on Electromagnetic Wave Theory offers outstanding coverage of the field. It consists of new titles of contemporary interest, as well as reissues and revisions of recognized classics by established authors and researchers. The series emphasizes works of long-term archival significance in electromagnetic waves and applications. Designed specifically for graduate students, researchers and practicing engineers, the series provides affordable volumes that explore and explain electromagnetic waves beyond the undergraduate level.

Visit wftww.wiley.com/ieee

>W1LEY'INTERSCIEN'

ISBN

••

D-7flD3-bD31-l

780780"36rmr)"

An IEEE Press Classic Reissue

FOUNDATIONS FOR MICROWAVE ENGINEERING

SECOND EDITION

IEEE PRESS SERIES ON ELECTROMAGNETIC WAVE THEORY

The IEEE Press Series on Electromagnetic Wave Theory consists of new titles as well as reprintings and revisions of recognized classics that maintain long-term archival significance in electromagnetic waves and applications.

Scries Editor Donald G. Dudley University of Arizona

Advisory Board Robert E. Collin Case Western Reserve University

Akira Ishimaru University of Washington

D. S. Jones University of Dundee

Associate Editors

ELECTROMAGNETIC THEORY, SCATTERING, AND DIFFRACTION

Ehud Heyman Tel-Aviv University

INTEGRAL EQUATION METHODS

Donald R. Wilson University of Houston

DIFFERENTIAL EQUATION METHODS

Andreas C. Cangellans

University

of

A

rizona

ANTENNAS. PROPAGATION, AND MICROWAVES

David R. Jackson University of Houston

BOOKS IN THE IEEE PRESS SERIES ON ELECTROMAGNETIC WAVE THEORY

Christopoulos. C, The Transmission-Line Modeling Methods: TLM Clemmow, R C. The Plane Wave Spectrum Representation of Electromagnetic Fields Collin. R. E.. Field Theory of Guided Waves, Second Edition Collin, R. E.. Foundations for Microwave Engineering, Second Edition Dudley. D. G., Mathematical Foundations for Electromagnetic Theory Elliot. R. S., Electromagnetics: History, Theory, and Applications Felsen. L. B.. and Marcuvitz. N.. Radiation and Scattering qf Waves Harrington. R. F, Field Computation by Moment Methods Hansen et aL, Plane-Wave Theory of Time-Domain Fields: Near-Field Scanning Applications Ishimaru. A., Wave Propagation and Scattering in Random Media Jones, D. S.. Methods in Electromagnetic Wave Propagation. Second Edition Lindell. 1. V., Methods for Electromagnetic Field Analysis Peterson el al.. Computational Methods for Electromagnetics Tai. C. T, Generalized Vector and Dyadic Analysis: Applied Mathematics in Field Theory Tai. C. T. Dyadic Green Functions in Electromagnetic Theory. Second Edition Van Bladel, J., Singular Electromagnetic Fields and Sources Volakis et al., Finite Element Method for Electromagnetics: Antennas, Micmwave Circuits, and Scattering Applications Wail. J.. Electromagnetic Waves in Stratified Media

An IEEE Press Classic Reissue

FOUNDATIONS FOR MICROWAVE ENGINEERING

SECOND EDITION

IEEE Press Series on Electromagnetic Wave Theory

Robert E. Collin

Professor of Electrical Engineering Case Western Reserve University

Cleveland, OH

IEEE Antennas & Propagation Society, Sponsor IEEE Microwave Theory and Techniques Society, Sponsor

The Institute of Electrical and Electronics Engineers. Inc., New York

WlLEY'INTERSCIENCE

A JOHN WILEY & SONS, INC.. PUBLICATION

© 2001 THE INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS, INC. 3 Park Avenue, 17th Floor, New York, NY 10016-5997

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 97S-750-8400, fax 978-750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken. NJ 07030, (201) 748-6011, fax (201) 748-6008, e-mail: [email protected]

For general information on our other products and services please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993 or fax 317-572-4002.

Printed in the United States of America 1098765432

ISBN 0-7803-6031-1

Library of Congress Cataloging-in-Publication Data

Collin. Robert E. Foundations lor microwave engineering / Robert E. Collin.- 2nd ed. p. cm. - (IEEE Press series on electromagnetic wave theory) Originally published : New York : McGraw Hill, cl992. "An IEEE Press classic reissue." Includes bibliographical references and index. ISBN 0-7803-6031-1 I. Microwave devices. I. Title. II. Series.

TK7876 .C645 2000 621.381'3--dc21

00-053874

FOREWORD TO THE REISSUED EDITION

The purpose of the IEEE Press Series on Electromagnetic Wave Theory is to publish books of long-term archival significance in electromagnetics. Included are new titles as well as reprints and revisions of recognized classics. The book Foundations for Microwave Engineering, by Robert E. Collin, is by any measure such a classic. The original edition of the book appeared in 1966 and remained in print until the appearance of the second edition in 1992, a span of 26 years.

In the second edition. Professor Collin completely updated and modernized his book to include the many advances that had occurred in microwave engineering since the appearance of the original edition. That the second edition has gone out of print has caused concern among many of my colleagues in the IEEE Antennas and Propagation Society (APS) and the IEEE Microwave Theory and Techniques Society (MTT). We at the IEEE Press are delighted to be able lo overcome this difficulty by introducing a reprint of the second edition into our Series on Electromagnetic Wave Theory. The book is a thorough and in-depth exposition on microwave engineering. Furthermore, it will make an excellent companion to Professor Collin's book, Field Theory- of Guided Waves, also included in the series.

Professor Collin has been a valued colleague for many years. He is the author or coauthor of five books and more than 150 technical papers. His contributions to electromagnetics span a wide range of subjects and have brought him international respect and many awards. Among these are election to the National Academy of Engineering, the IEEE Electromagnetics Field Award, the IEEE/APS Distinguished Career Award, an IEEE/APS Schelkunoff Prize Paper Award, and the IEEE Third Millennium Medal.

It is with pleasure that I welcome this book into the series.

Donald G. Dudley University of Arizona

Series Editor IEEE Press Series on Electromagnetic Wave Theory

IEEE Press 445 Hoes Lane, P.O. Box 1331

Piscataway, NJ 08855-1331

IEEE Press Editorial Board Robert J. Herrick, Editor in Chief

M.Akay J. B. Anderson P. M. Anderson J. E. Brewer

M.Eden M. E. El-Hawary R. F. Hoyt S. V. Kartalopoulos D. Kirk

M.S.Newman M. Padgett W.D. Reeve G. Zobrist

Kenneth Moore, Director of IEEE Press Catherine Faduska. Senior Acquisitions Editor Linda Matarazzo. Associate Acquisitions Editor

Marilyn G. Catis, Marketing Manager Mark Morrell, Associate Production Editor

IEEE Antennas & Propagation Society. Sponsor AP-S Liaison to IEEE Press, Robert Mailloux

IEEE Microwave Theory and Techniques Society, Sponsor MTT-S Liaison to IEEE Press, Karl Varian

Cover design: William T. Donnelly, WT Design

CONTENTS

Preface

XV

1 Introduction

1

1.1 Microwave Frequencies

1

1.2 Microwave Applications

3

1.3 Microwave Circuit Elements and Analysis

6

References

16

2 Electromagnetic Theory

17

2.1 Maxwell's Equations

17

2.2 Constitutive Relations

23

2.3 Static Fields

28

2.4 Wave Equation

31

2.5 Energy and Power

33

2.6 Boundary Conditions

39

2.7 Plane Waves

44

Plane Waves in Free Space

44

2.8 Reflection from a Dielectric Interface

49

1. Parallel Polarization

49

2. Perpendicular Polarization

52

2.9 Reflection from a Conducting Plane

53

2.10 Potential Theory

56

•2.11 Derivation of Solution for Vector Potential

59

62

2.12 Lorentz Reciprocity Theorem

65

Problems

70

References

3 Transmission Lines and Waveguides

71

Part 1 Waves on Transmission Lines

72

3.1 Waves on An Ideal Transmission Line

72

3.2 Terminated Transmission Line: Resistive Load

78

vii

ViU COOTENTS

3.3 Capacitive Termination 3.4 Steady-State Sinusoidal Waves 3.5 Waves on a Lossy Transmission Line

Loss-Free Transmission Line Low-Loss Transmission Line

3.6 Terminated Transmission Line: Sinusoidal Waves Terminated Lossy Line Part 2 Field Analysis of Transmission Lines

3.7 Classification of Wave Solutions TEM Waves TE Waves TM Waves

82

85

86

88

.

89

89

94

96

96

99

100

102

3.8 Transmission Lines (Field Analysis)

104

Lossless Transmission Line

104

Transmission Line with Small Losses

108

3.9 Transmission-Line Parameters

112

3.10 In homogeneously Filled Parallel-Plate Transmission Line 117

Low-Frequency Solution

121

High-Frequency Solution

123

3.11 Planar Transmission Lines

125

3.12 Microstrip Transmission Line

130

Low-Frequency Solutions

136

Microstrip Attenuation

153

High-Frequency Properties of Microstrip Lines

158

Attenuation

163

3.13 Coupled Microstrip Lines

164

3.14 Strip Transmission Lines

170

Attenuation

171

3.15 Coupled Strip Lines

173

3.16 Coplanar Transmission Lines

175

Attenuation

178

High-Frequency Dispersion

180

Part 3 Rectangular and Circular Waveguides

180

3.17 Rectangular Waveguide

181

TE Waves

182

Power

186

Attenuation

187

Dominant TE10 Mode

190

TM Modes

193

3.18 Circular Waveguides

194

TM Modes

194

TE Modes

196

3.19 Wave Velocities

198

Phase Velocity

199

Group Velocity

200

Energy-Flow Velocity

204

3.20 Ridge Waveguide

205

3.21 Fin Line

208

Problems

210

References

219

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