Table Of ContentELECTRICAL SCIENCE
A Series of Monographs and Texts
Edited by
Henry G. Booker Nicholas DeClaris
t:NIVERSITY OF CM,IFORNIA AT SA:,/ U!F.GO UNIVERSITY OF MARYLAND
LA JOLLA, CALIFORNIA COLLEGE PARK, MARYLAND
JOSEPH E. RowE. Nonlinear Electron-Wave Interaction Phenomena. 1965
MAX J. 0. STRUTT. Semiconductor Devices: Volume l.
Semiconductors and Semiconductor Diodes. 1966
AUSTIN BLAQUIERE. Nonlinear System Analysis. 1966
VICTOR RUMSEY. Frequency Independent Antennas. 1966
CHARLES K. BIRDSALL AND WILLIAM B. BRIDGES. Electron Dynamics of
Diode Regions. 1966
A. D. Kuz'MIN AND A. E. SALOMONOVICH. Radioastronomical Methods of Antenna
Measurements. 1966
CHARLES COOK AND MA:A.VIN BERNFELD. Radar Signals: An Introduction to Theory
and Application. 1967
}. W. CRISPIN, JR., AND K. M. SIEGEL (eds.). Methods of Radar Cross Section
Analysis. 1968
GIUSEPPE BIORCI (ed.). Network and Switching Theory. 1968
ERNEST C. OKRESS (ed.). Microwave Power :Engineering:
Volume 1. Generation, Transmission, Rectification. 1968
Volume 2. Applicarions. 1968
T. R. BASHKOW (ed.). Engineering Applications of Digital Computers. 1968
Juuus T. Tou (ed). Applied Automata Theory. 1968
ROBERT LYON-CAEN. Diodes, Transistors, and lntegrated Circuits
for Switching Systems. 1969
M. RONALD WOHLERS- Lumped and Distributed Passive Networks. 1969
MICHEL CUENOD AND ALLEN E. DURLING. A Discrete-Time Approach for System
Analysis. 1969
K. KUROKAWA. An Introduction to the Theory of Microwave Circuits. 1969
In Preparation
GEORGE TYRAS. Radiation and Propagation of Electromagnetic Waves.
GEORGE METZGER AND JEAN PA.UL VABRE. Transmission Lines with Pulse Excitation.
C. L. SHENG. Threshold Logic.
Huoo MESSERLE. Energy Conversion Statics.
ANI NTRODUCTION
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YI Preface
large cross-sectional dimensions required. At infrared or optical frequencies,
they again become impractical since the cross-sectional dimensions become
too small. As a result, the microwave portion of the spectrum is the only
region in which ordinary waveguides can be used in practice.
In ordinary waveguides, there are no separate conductors between which
the voltage can be defined and the concept of power expressed by the product
of voltage and current is no longer directly applicable. Consequently, the
electromagnetic field itself has to be investigated first rather than the voltage
and current which, in a sense, represent the field. In general, it is hopelessly
difficult to solve Maxwell's equations under appropriate boundary conditions
and to analyze the electromagnetic field of complex waveguide systems en
countered in practice or in laboratories. Even if a formal solution is easily
obtainable, the interpretation of the result may become so complicated that
no usefull information can be extracted from it. In conventional circuit
theory, the resistance, capacitance, and inductance are defined without
specifying their physical structures or materials used. The relations between
the voltage and current at the terminals of such elements are first clarified.
Then, the properties of a complex network are studied as a combination
of the effects of each element making up the network. There is no need to
solve Maxwell's equations explicitly and yet much useful information is
obtainable. In a similar fashion, it is possible to study each discontinuity or
junction of waveguides separately and to clarify its effect on the propagating
modes of the electromagnetic fields either by experiments or by solving
Maxwell's equations. The behavior of a complex waveguide system can then
be discussed as a combination of the effects of such elements. By this ap
proach, a better understanding can be obtained with less difficulty than
trying to solve Maxwell's equations directly for the whole system. The
theory of microwave circuits is the study of this approach. The word circuit
comes from the similarity existing between this approach and that of con
ventional circuit theory. The concept of voltage and current can be esta
blished by observing the fact that the transverse electric and magnetic fields
in a waveguide vary with distance in the same manner as the voltage and
current do along a conventional transmission line. Using this concept,
impedance can be defined and power appears as the product of voltage and
current. Many other useful theorems in conventional ac circuits also become
applicable to waveguide systems.
In our category of microwave circuits, we shall include any electromagnetic
phenomena in the inside of a hollow region enclosed by conducting walls.
We are especially interested in the study of their effect on the propagating
Preface vii
modes of electromagnetic fields in waveguides connected to the hollow region.
The actual wavelength is not important; it can be longer or shorter than the
centimeter or millimeter ranges as long as the electromagnetic field is
confined in a finite region. On the other hand, we shall not discuss waves in
free space as in radio and in optics nor those along a dielectric rod or coated
wires in open space.
In Chapter l, some of the topics in the conventional circuit theory are
reviewed, which have particular importance in the theory of microwave
circuits. These include the theory of transmission lines, bilinear transforma
tions, and power waves. Chapter 2 gives a review of vector analysis and the
fundamental properties of electromagnetic fields to facilitate our later study.
In Chapter 3, waveguides are discussed for the first time. Here, the eigenvalue
problem is studied in detail including the completeness of eigenfunctions.
Without the discussion of the completeness, the theory is only partially
correct since no answer is given to certain fundamental questions such as
why an exponential variation with distance is assumed for each mode and
no other possible functional form is considered. Chapter 4 discusses resonant
cavities using a similar eigenfunction approach. In Chapter 5, various
properties of waveguide junctions are discussed using matrices.
Matrices are introduced since the multitude of symbols and lengthy
expressions, which would otherwise be necessary, could interfere with our
concentration on the heart of a problem. Just as vectors do, matrices help
in studying relatively complex problems, systematically. Chapter 6 discusses
two phenomena: One is the coupling between traveling waves and the other
is that between electromagnetic fields in cavities. Each illustrates an in
teresting application of eigenvalue problems. Chapter 7 is a study of linear
amplifiers. The central topic is their noise performance. In Chapter 8, we
discuss a circuit-theoretical analysis of electron beams which clarifies a
number of properties of practical interest. Finally, Chapter 9 contains a
discussion of oscillators. Although oscillators are inherently nonlinear, some
of their important properties are studied here without specifying the details
of the nonlinearity.
Each chapter is followed by a set containing two types of problems: one
helps to give deeper understanding of the discussion in the text while the
other covers topics which could not be included in the text. The reader is
advised to at least read each problem even when he has no time to solve it.
Obviously, this book is not intended to supply microwave circuit design
data. Those who want such information should refer to a large collection
of books already available on the market (for example, MIT Radiation
viii Preface
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CONTENTS
Preface . V
1. Elements of Conventional Circuit Theory
1.1 Transmission Line Theory. I
1. 2 Smith Chart. 12
1.3 Bilinear Transformations 23
1.4 Power Waves 33
Problems 38
2. Electromagnetic Field Vectors
2.1 Vectors . 40
2.2 Maxwell's Equations 63
2.3 Plane Waves 73
Problems 83
3. Waveguides
3.1 Perfect Conductors. 85
3.2 TEio Mode in Rectangular Waveguides . 87
3.3 Introductory Eigenvalue Problem 99
3.4 Eigenfunctions for Waveguides 113
3.5 General Theory of Waveguides 130
3.6 Examples of Waveguides . 138
ix
Contents
X
3.7 Waveguide Discontinuities 149
3.8 Effect of Wall Losses . 1S6
3.9 Waveguides with Inhomogeneous Media 164
Problems 167
4. Resonant Cavities
4.1 Introduction. 170
4.2 Expansions of Electrornagnetic Fields 173
4.3 Equivalent Circuits. 18S
4.4 Perturbation of Boundaries . 193
4.5 Cavities with Imhomogeneous Media 196
Problems 198
5. Matrices and Waveguide Junctions
5.1 Matrices. 200
5.2 Reciprocal Conditions . 217
5.3 Lossless Conditions 224
5.4 Frequency Characteristic of Lossless Reciprocal ]unctions 226
5.5 Lossless Reciprocal Three-port Networks 232
5.6 Symmetrical Y Junctions . 234
5.7 Tensor Permeability of Ferrites 240
5.8 Three-port Circulators . 247
Problems 253
6. Coupled Modes and Periodic Structures
6.1 Distributed Couplings . 2S7
6.2 Perturbation Method for the Eigenvalue Problem . 264
6.3 Interactions between Two Waves. 269
6.4 Periodic Structures . 274
6.5 wMP Diagram 282
Problems 288
7. Linear Amplifiers
7.1 Canonical Forms 290
7.2 Noise Measure . 299
7.3 Unconditional Stability 308
7.4 Unilateral Gain. 31S
7.5 Tunnel Diode Amplifiers 318
Contents xi
7.6 Manley-Rowe Relations . 333
7.7 Negative Resistance Parametric Amplifiers . 337
Problems 343
8. Electron Beams
8.1 An Electron Beam Model. 346
8.2 Space Charge Waves . 351
8.3 Gap Interactions 359
8.4 Continuous Interaction with a Slow Wave Structure 367
8.5 Electron Beam Noise 372
Problems 378
9. Oscillators
9.1 A Simplified Oscillator Model 380
9.2 Synchronization by Injection Locking 386
9.3 Noise in Oscillators 389
Problems 397
Appendix I Proof of limk; = oo
a➔oo
1. One-Dimensional Case. 399
2. Two-Dimensional Case 404
3. Three-Dimensional Case 409
4. Resonant Cavities with Inhomogeneous Media. 410
Appendix II Generalized Functions and Fourier Analysis
References
Subject Index . 431
