CARL T. A. JOHNK

Professor of Electrical Engineering University of Colorado, Boulder

Engineering Electromagnetic

Fields and Waves

JOHN WILEY & SONS

New York Chichester Brisbane Toronto Singapore

CONTENTS

CHAPTER 1

Vector Analysis and Electromagnetic Fields in Free Space 1

1-1 Scalar and Vector Fields 1

1-2 Vector Sums 3

1-3 Product of a Vector and a Scalar 4

1-4 Coordinate Systems 4

1-5 Differential Elements of Space 9

1-6 Position Vector 11 1-7 Scalar and Vector Products of Vectors 14

1-8 Vector Integration 20

1-9 Electric Charges, Currents, and Their Densities 23

1-10 Electric and Magnetic Fields in Terms of Their Forces 28

1-11 Maxwell's Integral Relations for Free Space 29

1-12 Coordinate Transformations 45

1-13 Units and Dimensions 49

CHAPTER 2

Vector Differential Relations and Maxwell's Differential Relations in Free Space 61

2-1 Differentiation of Vector Fields 61

2-2 Gradient of a Scalar Function 63

2-3 The Operator V (Del) 66 2-4 Divergence of a Vector Function 67

2-5 Curl of a Vector Field 76

2-6 Summary of Maxwell's Equations: Complex, Time-Harmonic Forms 85

2-7 Laplacian and Curl Curl Operators 88

2-8 Green's Integral Theorems: Uniqueness 92

2-9 Wave Equations for Electric and Magnetic Fields in Free Space 93

2-10 Uniform Plane Waves in Empty Space 96 2-11 Wave Polarization 103

CHAPTER 3

Maxwell's Equations and Boundary Conditions for Material Regions at Rest 111

3-1 Electrical Conductivity of Metals 111 3-2 Electric Polarization and Div D for Materials 116

CONTENTS XI

3-3 Div В for Materials: Its Integral Form and a Boundary Condition for Normal В 126

3-4 Magnetic Polarization and Curl H for Materials 127 3-5 Maxwell's Curl E Relation: Its Integral Form and Boundary Condition

for Tangential E 146 3-6 Conservation of Electric Charge 150 3-7 Uniform Plane Waves in an Unbounded Conductive Region 152 3-8 Classification of Conductive Media 160 3-9 Linearity, Homogeneity, and Isotropy in Materials 163 3-10 Electromagnetic Parameters of Typical Materials 167 3-11 General Boundary Conditions for Normal D and J 169

CHAPTER 4

Static and Quasi-Static Electric Fields 180

4-1 Maxwell's Equations for Static Electric Fields 180 4-2 Static Electric Fields of Fixed-Charge Ensembles in Free Space 181 4-3 Gauss's Law Revisited 187 4-4 Electrostatic Scalar Potential 188 4-5 Capacitance 196 4-6 Energy of the Electrostatic Field 199 4-7 Poisson's and Laplace's Equations 204 4-8 Uniqueness of Electrostatic Field Solutions 206 4-9 Laplace's Equation and Boundary-Value Problems 209 4-10 Finite-Difference Solution Methods 215 4-11 Image Methods 219 4-12 An Approximation Method for Statically Charged Conductors 225 4-13 Capacitance of Two-Dimensional Systems by Field Mapping 228 4-14 Conductance Analog of Capacitance 232 4-15 Electrostatic Forces and Torques 241

CHAPTER 5

Static and Quasi-Static Magnetic Fields 258

5-1 Maxwell's Equations and Boundary Conditions for Static Magnetic Fields 258 5-2 Ampere's Circuital Law 259 5-3 Magnetic Circuits 262 5-4 Vector Magnetic Potential 269 5-5 An Integral Solution for A in Free Space: Biot-Savart Law 270

XU CONTENTS

5-6 Quasi-Static Electromagnetic Fields 276 5-7 Open-Circuit Induced Voltage 277 5-8 Motional Electromotive Force and Voltage 280 5-9 Induced Emf from Time-Varying Vector Magnetic Potential 286 5-10 Voltage Generators and KirchhofF's Laws 290 5-11 Magnetic Energy and Self-Inductance 296 5-12 Coupled Circuits and Mutual Inductance 318 5-13 Magnetic Forces and Torques 328

CHAPTER 6

Wave Reflection and Transmission at Plane Boundaries 342 6-1 Boundary-Value Problems 342 6-2 Reflection from a Plane Conductor at Normal Incidence 344 6-3 Two-Region Reflection and Transmission 347 6-4 Normal Incidence for More Than Two Regions 350 6-5 Solution Using Reflection Coefficient and Wave Impedance 352 6-6 Graphical Solutions Using the Smith Chart 358 6-7 Standing Waves 361 6-8 Reflection and Transmission at Oblique Incidence 365

CHAPTER 7

The Poynting Theorem and Electromagnetic Power 385 7-1 The Theorem of Poynting 385 7-2 Time-Average Poynting Vector and Power 394

CHAPTER 8

Mode Theory of Waveguides 409 8-1 Maxwell's Relations When Fields Have е>шЧуг Dependence 410 8-2 ТЕ, ТМ, and ТЕМ Mode Relationships 414 8-3 TM Mode Solutions of Rectangular Waveguides 418 8-4 ТЕ Mode Solutions of Rectangular Waveguides 428 8-5 Dispersion in Hollow Waveguides: Group Velocity 440 8-6 Wall-Loss Attenuation in Hollow Waveguides 447

CONTENTS x i i i

CHAPTER 9

ТЕМ Waves on Two-Conductor Transmission Lines 457

9-1 ТЕМ Mode Fields Based on Static Fields 459 9-2 Characteristic Impedance 469 9-3 Transmission-Line Parameters, Perfect Conductors Assumed 471 9-4 Circuit Model of a Line with Perfect Conductors 479 9-5 Wave Equations for a Line with Perfect Conductors 481 9-6 Transmission-Line Parameters, Conductor Impedance Included 482 9-7 Waves of Arbitrary Shape on Lossless Lines 488

CHAPTER 10

Phasor Analysis of Reflective Transmission Lines 511

10-1 Voltage and Current Calculation on Lines with Reflection 512 10-2 Graphical Solutions Using the Smith Chart 520 10-3 Standing Waves on Transmission Lines 526 10-4 Analytical Expressions for Line Impedance 531 10-5 Impedance-Matching: Stub-Matching of Lossless Lines 536

CHAPTER 11

Radiation from Antennas in Free Space 545

11-1 Wave Equations in Terms of Electromagnetic Potentials 546 11-2 Integration of the Inhomogeneous Wave Equation in Free Space 548 11-3 Radiation from the Infinitesimal Current Element 550 11-4 Radiation Fields of a Linear Center-Fed Thin-Wire Antenna 555 11-5 Symmetric Maxwell's Equations and Their Vector Potentials: The Field

Equivalence Theorem 563 11-6 Antenna Directive Gain 575 11-7 Transmit-Receive Systems: Receiving Antenna 579

Appendixes 595

A Oblique Incidence: Region 2 Conductive 595 В Transmission Line Parameters 602 С Integration of the Inhomogeneous Wave Equation 616 D Development of the Smith Chart 621

INDEX 627