RF and Microwave Coupled-Line Circuits, Second Edition

574 Pages·2007·4.9 MB·English

RF and Microwave Coupled-Line Circuits

Second Edition

For a listing of recent titles in the Artech House
Microwave Library, turn to the back of this book.

RF and Microwave Coupled-Line Circuits

Second Edition

R. K. Mongia
I. J. Bahl
P. Bhartia
J. Hong

Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the U.S. Library of Congress.

British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library.

ISBN-13: 978-1-59693-156-5

Cover design by Yekaterina Ratner

� 2007 ARTECH HOUSE, INC.
685 Canton Street
Norwood, MA 02062

Sonnet Lite� and Sonnet� are trademarks of Sonnet Software, Inc., Syracuse, New York.
Mathcad� is a trademark of Mathsoft, Inc., Needham, Massachusetts.
MATLAB� is a trademark of The MathWorks, Inc., Natick, Massachusetts.

All rights reserved. Printed and bound in the United States of America. No part of this
book may be reproduced or utilized in any form or by any means, electronic or mechanical,
including photocopying, recording, or by any information storage and retrieval system,
without permission in writing from the publisher.
All terms mentioned in this book that are known to be trademarks or service marks
have been appropriately capitalized. Artech House cannot attest to the accuracy of this
information. Use of a term in this book should not be regarded as affecting the validity of
any trademark or service mark.

10 9 8 7 6 5 4 3 2 1

In memory of Dr. K. C. Gupta—a friend, colleague, and mentor

Contents

Foreword to the First Edition
xv

Preface to the Second Edition
xvii

Preface to the First Edition
xxi

CHAPTER 1
Introduction
1

1.1
Coupled Structures
1
1.1.1
Types of Coupled Structures
3
1.1.2
Coupling Mechanism
4
1.2
Components Based on Coupled Structures
6
1.2.1
Directional Couplers
6
1.2.2
Filters
8
1.3
Applications
11
1.4
Scope of the Book
13
References
13

CHAPTER 2
Microwave Network Theory
17

2.1
Actual and Equivalent Voltages and Currents
17
2.1.1
Normalized Voltages and Currents
18
2.1.2
Unnormalized Voltages and Currents
21
2.1.3
Reflection Coefficient, VSWR, and Input Impedance
22
2.1.4
Quantities Required to Describe the State of a Transmission
Line
24
2.2
Impedance and Admittance Matrix Representation of a Network
26
2.2.1
Impedance Matrix
26
2.2.2
Admittance Matrix
27
2.2.3
Properties of Impedance and Admittance Parameters of a
Passive Network
27
2.3
Scattering Matrix
28
2.3.1
Unitary Property
30
2.3.2
Transformation with Change in Position of Terminal Planes
31

vii

viii
Contents

2.3.3
Reciprocal Networks
32
2.3.4
Relationship Between Normalized and Unnormalized Matrices
32
2.4
Special Properties of Two-, Three-, and Four-Port Passive, Lossless
Networks
32
2.4.1
Two-Port Networks
33
2.4.2
Three-Port Reciprocal Networks
34
2.4.3
Three-Port Nonreciprocal Networks
35
2.4.4
Four-Port Reciprocal Networks
36
2.5
Special Representation of Two-Port Networks
38
2.5.1
ABCD Parameters
38
2.5.2
Reflection and Transmission Coefficients in Terms of ABCD
Parameters
40
2.5.3
Equivalent T and � Networks of Two-Port Circuits
41
2.6
Conversion Relations
43
2.7
Scattering Matrix of Interconnected Networks
45
2.7.1
Scattering Parameters of Reduced Networks
47
2.7.2
Reduction of a Three-Port Network into a Two-Port Network
48
2.7.3
Reduction of a Two-Port Network into a One-Port Network
49
2.7.4
Reduction of a Four-Port Network into a Two-Port Network
50
References
51

CHAPTER 3
Characteristics of Planar Transmission Lines
53

3.1
General Characteristics of TEM and Quasi-TEM Modes
53
3.1.1
TEM Modes
57
3.1.2
Quasi-TEM Modes
58
3.1.3
Skin Depth and Surface Impedance of Imperfect Conductors
59
3.1.4
Conductor Loss of TEM and Quasi-TEM Modes
60
3.2
Representation of Capacitances of Coupled Lines
61
3.2.1
Even- and Odd-Mode Capacitances of Symmetrical Coupled
Lines
62
3.2.2
Parallel-Plate and Fringing Capacitances of Single and Coupled
Planar Transmission Lines
66
3.3
Characteristics of Single and Coupled Striplines
68
3.3.1
Single Stripline
69
3.3.2
Edge-Coupled Striplines
73
3.4
Characteristics of Single and Coupled Microstrip Lines
74
3.4.1
Single Microstrip
75
3.4.2
Coupled Microstrip Lines
81
3.5
Single and Coupled Coplanar Waveguides
83
3.5.1
Coplanar Waveguide
84
3.5.2
Coplanar Waveguide with Upper Shielding
86
3.5.3
Conductor-Backed Coplanar Waveguide with Upper Shielding
87
3.5.4
Coupled Coplanar Waveguides
88
3.6
Suspended and Inverted Microstrip Lines
88

Contents
ix

3.7
Broadside-Coupled Lines
93
3.7.1
Broadside-Coupled Striplines
94
3.7.2
Broadside-Coupled Suspended Microstrip Lines
95
3.7.3
Broadside-Coupled Offset Striplines
96
3.8
Slot-Coupled Microstrip Lines
99
References
102

CHAPTER 4
Analysis of Uniformly Coupled Lines
105

4.1
Even- and Odd-Mode Analysis of Symmetrical Networks
106
4.1.1
Even-Mode Excitation
108
4.1.2
Odd-Mode Excitation
109
4.2
Directional Couplers Using Uniform Coupled Lines
111
4.2.1
Forward-Wave (or Codirectional) Directional Couplers
114
4.2.2
Backward-Wave Directional Couplers
116
4.3
Uniformly Coupled Asymmetrical Lines
120
4.3.1
Parameters of Asymmetrical Coupled Lines
121
4.3.2
Distributed Equivalent Circuit of Coupled Lines
126
4.3.3
Relation Between Normal Mode (c and �) and Distributed
Line Parameters
130
4.3.4
Approximate Distributed Line or Normal-Mode Parameters of
Asymmetrical Coupled Lines
132
4.4
Directional Couplers Using Asymmetrical Coupled Lines
133
4.4.1
Forward-Wave Directional Couplers
133
4.4.2
Backward-Wave Directional Couplers
136
4.5
Design of Multilayer Couplers
138
4.5.1
Determination of Capacitance and Inductance Parameters
Using Sonnet Lite
139
4.5.2
Coupler Design
140
References
147

CHAPTER 5
Broadband Forward-Wave Directional Couplers
149

5.1
Forward-Wave Directional Couplers
150
5.1.1
3-dB Coupler Using Symmetrical Microstrip Lines
151
5.1.2
Design and Performance of 3-dB Asymmetrical Couplers
153
5.1.3
Ultra-Broadband Forward-Wave Directional Couplers
155
5.2
Coupled-Mode Theory
156
5.2.1
Nature of Coupling Coefficient K12 and K21
158
5.2.2
Waves on Lines 1 and 2 in the Presence of Coupling
158
5.2.3
Coupled-Mode Theory and Even- and Odd-Mode Analysis
160
5.2.4
Coupling Between Asymmetrical Lines
161
5.3
Coupled-Mode Theory for Weakly Coupled Resonators
163
References
165

x
Contents

CHAPTER 6
Parallel-Coupled TEM Directional Couplers
167

6.1
Coupler Parameters
167
6.2
Single-Section Directional Coupler
169
6.2.1
Frequency Response
169
6.2.2
Design
171
6.2.3
Compact Couplers
176
6.2.4
Equivalent Circuit of a Quarter-Wave Coupler
176
6.3
Multisection Directional Couplers
177
6.3.1
Theory and Synthesis
177
6.3.2
Limitations of Multisection Couplers
184
6.4
Techniques to Improve Directivity of Microstrip Couplers
186
6.4.1
Lumped Compensation
186
6.4.2
Use of Dielectric Overlays
189
6.4.3
Use of Wiggly Lines
189
6.4.4
Other Techniques
192
References
194

CHAPTER 7
Nonuniform Broadband TEM Directional Couplers
197

7.1
Symmetrical Couplers
197
7.1.1
Coupling in Terms of Even-Mode Characteristic Impedance
199
7.1.2
Synthesis
201
7.1.3
Technique for Determining Weighting Functions
206
7.1.4
Electrical and Physical Length of a Coupler
209
7.1.5
Design Procedure
210
7.2
Asymmetrical Couplers
214
References
217

CHAPTER 8
Tight Couplers
219

8.1
Introduction
219
8.2
Branch-Line Couplers
220
8.2.1
Modified Branch-Line Coupler
223
8.2.2
Reduced-Size Branch-Line Coupler
225
8.2.3
Lumped-Element Branch-Line Coupler
230
8.2.4
Broadband Branch-Line Coupler
233
8.3
Rat-Race Coupler
233
8.3.1
Modified Rat-Race Coupler
237
8.3.2
Reduced-Size Rat-Race Coupler
239
8.3.3
Lumped-Element Rat-Race Coupler
240
8.4
Multiconductor Directional Couplers
242
8.4.1
Theory of Interdigital Couplers
243
8.4.2
Design of Interdigital Couplers
245
8.5
Tandem Couplers
252

Contents
xi

8.6
Multilayer Tight Couplers
255
8.6.1
Broadside Couplers
255
8.6.2
Re-Entrant Mode Couplers
258
8.7
Compact Couplers
261
8.7.1
Lumped-Element Couplers
262
8.7.2
Spiral Directional Couplers
262
8.7.3
Meander Line Directional Coupler
263
8.8
Other Tight Couplers
264
References
265

CHAPTER 9
Coupled-Line Filter Fundamentals
269

9.1
Introduction
269
9.1.1
Types of Filters
270
9.1.2
Applications
270
9.2
Theory and Design of Filters
271
9.2.1
Maximally Flat or Butterworth Prototype
272
9.2.2
Chebyshev Response
272
9.2.3
Other Response-Type Filters
275
9.2.4
LC Filter Transformation
275
9.2.5
Filter Analysis and CAD Methods
279
9.2.6
Some Practical Considerations
280
9.3
Parallel-Coupled Line Filters
283
9.3.1
Design Example
285
9.4
Interdigital Filters
287
9.4.1
Design Examples
287
9.5
Combline Filters
290
9.5.1
Design Example
291
9.6
The Hairpin-Line Filter
295
9.6.1
Design Example
297
9.7
Parallel-Coupled Bandstop Filter
300
9.7.1
Design Example
301
References
304

CHAPTER 10
Advanced Coupled-Line Filters
307

10.1 Introduction
307
10.2 Coupled-Line Filters with Enhanced Stopband Performance
307
10.2.1
Design Using Unevenly-Coupled Stages
307
10.2.2
Design Using Periodically Nonuniform Coupled Lines
314
10.2.3
Design Using Meandered Parallel-Coupled Lines
320
10.2.4
Design Using Defected Ground Structures
324
10.3 Coupled-Line Filters Exhibiting Advanced Filtering Characteristics
327
10.3.1
Filters with Cross-Coupled Resonators
327
10.3.2
Filters with Source-Load Coupling
335
10.3.3
Filters with Asymmetric Port Excitations
347

xii
Contents

10.4 Interdigital Filters Using Stepped Impedance Resonators
352
10.4.1
Narrowband Design
354
10.4.2
Wideband Design
356
10.5 Dual-Band Filters
359
References
367

CHAPTER 11
Filters Using Advanced Materials and Technologies
371

11.1 Introduction
371
11.2 Superconductor Coupled-Line Filters
371
11.2.1
Cascaded Quadruplet and Triplet Filters
371
11.2.2
High-Order Selective Filters with Group-Delay Equalization
377
11.3 Micromachined Filters
385
11.3.1
Miniature Interdigital Filters on Silicon
387
11.3.2
Overlay Coupled CPW Filters
390
11.4 Filters Using Advanced Dielectric Materials
391
11.4.1
Low-Temperature Cofired Ceramic Filters
392
11.4.2
Liquid Crystal Polymer Filters
396
11.5 Filters for Ultra-Wideband (UWB) Technology
400
11.5.1
Optimum Stub Line Filters
401
11.5.2
Multimode Coupled-Line Filters
406
11.5.3
Microstrip-Coplanar Waveguide Coupled-Line Filters
410
11.5.4
UWB Filters with Notch Band
421
11.6 Metamaterial Filters
428
References
438

CHAPTER 12
Coupled-Line Circuit Components
443

12.1 DC Blocks
443
12.1.1
Analysis
443
12.1.2
Broadband DC Block
446
12.1.3
Biasing Circuits
446
12.1.4
Millimeter-Wave DC Block
449
12.1.5
High-Voltage DC Block
451
12.2 Coupled-Line Transformers
452
12.2.1
Open-Circuit Coupled-Line Transformers
452
12.2.2
Transmission Line Transformers
456
12.3 Interdigital Capacitor
461
12.3.1
Approximate Analysis
462
12.3.2
Full-Wave Analysis
464
12.4 Spiral Inductors
465
12.5 Spiral Transformers
472
12.6 Other Coupled-Line Components
475
References
476

Contents
xiii

CHAPTER 13
Baluns
481

13.1 Introduction
481
13.2 Microstrip-to-Balanced Stripline Balun
482
13.3 Analysis of a Coupled-Line Balun
486
13.4 Planar Transmission Line Baluns
490
13.4.1
Analysis
493
13.4.2
Examples
496
13.5 Marchand Balun
498
13.5.1
Coaxial Marchand Balun
501
13.5.2
Synthesis of Marchand Balun
505
13.5.3
Examples of Marchand Baluns
509
13.6 Other Baluns
518
13.6.1
Coplanar Waveguide Baluns
518
13.6.2
Triformer Balun
518
13.6.3
Planar-Transformer Balun
519
References
524

About the Authors
529

Index
531

Foreword to the First Edition

It has been a privilege for me to go through the manuscript of the RF and Microwave
Coupled-Line Circuits.
Sections of coupled transmission structures are critical components in distrib-
uted RF and microwave passive circuits. Significance of their role as basic building
blocks is second only to the sections of single transmission structures. Their applica-
tions in design of directional couplers and filters are well known, but equally
important is the role played by coupled-line sections in the design of baluns,
capacitors, inductors, transformers and dc blocks. Availability of high dielectric
constant materials has extended the usage of coupled-line sections to lower micro-
wave and RF frequencies. Traditionally, coupled sections consisting of two single
lines have been used extensively. However, as the circuit designers understand
modeling and characterization of multiple coupled lines, we can look forward to
significantly larger applications of multiple coupled transmission line structures.
Three-line balun structures reported recently are a step in this direction. Also, as
the multilayer RF and microwave circuits become more popular, couplings among
the transmission lines at different levels of a multilayer structure become a critical
design consideration. In some cases this multilayer-multiconductor coupling can
be advantageous as a useful circuit component, while in other cases this coupling
can become an undesirable effect that should be mitigated. Both of these situations
need the modeling and characterization of multiconductor transmission line struc-
tures.
Recognizing the role of coupled lines, it is hard to comprehend why a compre-
hensive book on this topic has not been available so far. But then, someone has
to be the leader. Bahl and Bhartia have a history of providing to the microwave
design community several well-needed ‘‘firsts,’’ and this book is their most recent
contribution. Congratulations Rajesh, Inder, and Prakash on a book which I am
confident will be very well received in the RF/microwave community.

K. C. Gupta
University of Colorado at Boulder
November 1998

xv