DAVID K. CHENG SYRACUSE UNIVERSITY

A vv ADDISON-WESLEY PUBLISHING COMPANY

Reading, Massachusetts Menlo Park, California

London Amsterdam Don Mills, Ontario Sydney

DAVID K. CHENG SYRACUSE UNIVERSITY

A , vv

ADDISON-WESLEY PUBLISHING COMPANY

I 1 Reading, Massachusetts Menlo Park, California

m on don' Amsterdam Don Mills, Ontario' Sydney

I

This book is in the API)ISON7WESLEY SERIES IN ELERRICAL ENGINEERING

, . SPONSORING EDIT& Tom Robbins

PRODUCTION EDITOR: Marilee Sorotskin

TEXT DESIGNER: Mednda Grbsser

ILLUSTRATOR: Dick Morton , -

COVER DESIGNER AND ILLUSTRATOR: Richard H a n y s

ART COORDINATOR: Dick Morton i.:

PRODUCTION MANAGER: Herbert Nolan

The text of this book was composed in Times Roman by Syntax International.

Library of Congress Cataloging in Publication Data

Cheng, David K. avid-~(euni dqte- Field and wave e ~ e c t r o ~ ~ e t i ~ s .

Bibliography: p. I

1. Electromagnetism. 2. Fiqld th :ory (Physics) I. Title. I -

QC760. C48 < 530.1'41 . 81-12749 ISBN 0-201-01239-1 AACR2 .

3 I I

I

COPY%^^ O 1983 by Addison-W+ey Publishing Company, Inc. rights reserved. NO part of @is publication may be reproduqd, btored in a retrieval system, or tnns-

m,ltted. in any, form or by any means. electmnic, mechanica~. photocopying, recordmg, or othenu~se, without the prior written permission df the publisher. Prmted m the Uolted States of Amenca. Published simultaneously in Canada. ,

ISBN 0-201-01239-1 ABCDEFGHIJ-AL-89876543

I

1-1 Introduction

1-2 The electromagnetic model

1-3 SI units and universal constants

Review questions

Introduction

Vector addition and subtraction

Products of vectors

2-3.1 Scalar or dot product

2-3.2 Vector or cross product 2-3.3 Product of three vectors

Orthogonal coordinate systems

2-4.1 Cartesian coordinates

2-4.2 Cylindrical coordinates

2-4.3 Spherical coordinates

Gradient of a scalar field

Divergence of a vector field

Divergence theorein

Curl of a vector field

Stokes's theorem

2-10 Two null identities

2-10.1 Identity I

2-10.1 Identity I1

2-1 1 Helmholtz's theorem

Review questions . Problems

3-1 Introduction

3-2 Fundamental postulates of electrostatics in free space - I

J-2 Coulonb's law 3 ?.: Electric fitla ciue LO a system of discrete charges

3-3.2 Electric field due to a contipuous distribution of charge

3-4 Gauss's law and applications

3-5 Electric potential I

3-5.1 Electric potential due to a charge distribution

3-6 Condugtors in static electric field

3-7 Dielectrics in static electric field 3-7.1 Equivalent charge distributions of polarized dielectrics

3-8 Electric flux density and dielectric constant 3-8.1 ~ielectric'strength

3-9 Boundary conditions for electrostatic fields

3-10 Capacitance and ~apacitors

3 - 10.1 Series aqd parallel connections of capacitors

3-1 1 Electrostatic enerpy and forces . , 3- 11.1 ~lectrost'atic energy in terms of field quantities

3- 11.2 Electrostatic forces

Review. questions Problems 6 , I

\- :

2 .

Solution of Electrostati~ Problems . . 4-1 Introduction i

4-2 Poisson's and La~lace's equations

4-3 Uniqueness of eleptrgstatic solutions i 4-4 Method of imageg' : : I

4-4.1 Point charge and conducting planes

4-4.2 Line charge and parallel . I

conducting cylindpr . 4-4.3 Point charge aqd conducting sbhera,

1

4-5 Boundary-value problems in Cartesian coordinates

, 4-6 Boundary-value problems in cylindrical coordinates

4-7 Boundary-value problems in spherical coordinates

Review questions

~roblems . Steady Electric Currents

5-1 Introduction

5-2 Current density and Ohm's law

5-3 Electromotive force and Kirchhoff's voltage law

5-4 Equation of continuity and Kirchhoff's current law

5-5 Power dissipation and Joulc's law

5-6 Boundary conditions for current density,

5-7 Resistance calculations

Review questions

Problems

1

Static Magnetic Fields ,

6-1 Introduction

6-2 Fundamental postulates of magnetostatics in free space

6-3 Vector magnetic potential

6-4 Biot-Savart's law and applications

6-5 The magnetic dipole

6-5.1 Scalar magnetic potential

6-6 - Magnetization ;~ntl cquivalcnt currcnt dcnsiiics

6-7 Magnetic field intensity and relative permeability I

6-8 Magnetic circuits

6-9 Behavior of magnetic materials I

6-10 Boundary conditions for magnetostatic fields 1 6-1 1 Inductances and Inductors

1

. 6-12 Magnetic energy . 6-12.1 Magnetic energy in terms of field quantities

/

I CONTENTS xiii 1

1 . I

8-2.1 Transverse electromagnetic waves 312

8-2.2 Polarization of plane waves I 314

Plane waves in conducting media 1 317 8-3.1 Low-loss dielectirc I 318

8-3.2 Good conductor

8-3.3 Group velocity

Flow of electromagnetic power and the Poynting vector

8-4.1 Instantaneous ana average power densities

Normal incidence at a plane conducting boundary

Oblique incidence at a plane conducting boundary

8-6.1 Perpendicular polarization

8-6.2 Parallel polarization

Normal incidence at a plane dielectric boundary

Normal incidence at multiple dielectric interfaces

8-8.1 Wave impedance of total field

8-8.2 Impedance transformation wish- multiple dielectrics

Oblique incidence at a plane dielectric boundary

8-9.1 Total reflection 8-9.2 Perpendicular polarization

8-9.3 Parallel polarization

Review questions

Problems

9 Theay and Applications of Mnsmission Lines

Introduction

Transverse electromagnetic wave along a parallel-plate transmission line

9-2.1 Lossy parallel-plate transmission lines

General transmission-line equations

9-3.1 Wave characteristics on an infinite transmission line

9-3.2 Tr:lnsrnission-li11c uurumctcl.~

9-3.3 Attenuation constant from power relations

Wave characteristics on finite transmission'lines

9-4.1 Transmission lines as circuit elements

9-4.2 Lines with resistive termination

. I 1 I '! I

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xiv CONTENTS 1

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* ' . t + . - i . . i I i

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9-4.3 Lines with Gbj t iaq terminafian . ,

404 9-4.4 ~ransmissioa-link circuits . 407

11 An

: 9-5 The Smith chart 41 1 11 1

9-5.1, Smith-chart ca1culations for losiy lines I 420

11

9 -6 Transmission-line im&d&ce matching 1 - . , . 422 9 4 . 1 Impedance rnatc$ng by quarter:

wave transformer , 423 ! 1 9-6.2 Single-stub matching 426 11 9-6.3 Double-stub matching 43 1 Review questions 1 . 435 11 Problems , , 437

F

(

1 0 Waveguides and Cavity R8so"ators ,

Introduction

General wave behaviors along uniform '

guiding structures , -

10-2.1 Transverse electromagnetic waves

10-2.2 Transverse magnetic waves

10-2.3 Transverse e1ecp;ic waves ,

Parallel-plate waveg$de* t

10-3.1 TM waves petween yarahlel plates

10-3.2 TE waves between parallel plates 10-3.3 Attenuatioq in.~~rallel-plate ' waveguides . t

Rectangular waveguides

10-4.1 TM waves in rectangular wqvebides 10-4.2 TE waves in recrangular waveguides

10-4.3 ~ t tenui i t i$n)rk tan~ular waveguides

Dielectric waveguide6 : ! 10-5.1 TM wayes lo^& a dielectric slab 10-5.2 TE waves ;)ong ii dielectric slab '

> , Cavity resonators \

10-6. ! TM,,,, moqes I I , I

10-6.2 TE,,, modts

10-6.3 Quality factor &(cavity resonatbr

Review questions

Problems

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Antekms and Radiating Systems. " , . , ,. . . .

, . I S

Introduction ~ ' ~ 1 . , { 500

Radiation fields of elemental dipoles 502 11 -2.1 The elemental electric dipole

11 -2.2 The elemental magnetic dipole

Antenna patiefh5 and at. tenna parameters * . Thi;. linear antennas

11 -4.1 The halt-wave aipde

Antenna arrays

11 -5.1 Two-element arrays

1 1-5.2 General uniform linear arrays

Receiving antennas

11 -6.1 Internal impedance and directional pattern

11 -6.2 Effective area

Some other antenna types

11 -7.1 Traveling-wave antenna '-\

11-7.2 Yagi-Uda antenna

11 -7.3 Broadband antennas

Apeiture Radiators

References

Review questions

ProbIems

Amendix A Symbols and Units

A-1 Fundamental SI (rationalized MKSA) units

A-2 Derived quantities

A-3 Multiples and s~bmultiples of units

Appendix B Some Useful Material Constants

B-1 Constants of free space

B-2 Physical constants.of electron and proton