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
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
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
xiii 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