Engineering Electromagnetics and Waves, 2nd edition

1 Introduction 1

1.1 Lumped versus Distributed Electrical Circuits 5

1.2 Electromagnetic Components 14

1.3 Maxwell’s Equations and Electromagnetic Waves 15

1.4 Summary 17

 

 

2 Transient Response of Transmission Lines 23

2.1 Heuristic Discussion of Transmission Line Behavior and Circuit

Models 25

2.2 Transmission Line Equations and Wave Solutions 29

2.3 Reflection at Discontinuities 36

2.4 Transient Response of Transmission Lines with Resistive

Terminations 47

2.5 Transient Response of Transmission Lines with Reactive

Terminations 60

vi Contents

2.6 Time-Domain Reflectometry 70

2.7 Transmission Line Parameters 75

2.8 Summary 78

 

3 Steady-State Waves on Transmission Lines 99

3.1 Wave Solutions Using Phasors 101

3.2 Voltage and Current on Lines with Short- or Open-Circuit

Terminations 105

3.3 Lines Terminated in an Arbitrary Impedance 117

3.4 Power Flow on a Transmission Line 138

3.5 Impedance Matching 147

3.6 The Smith Chart 164

3.7 Sinusoidal Steady-State Behavior of Lossy Lines 176

3.8 Summary 193

 

4 The Static Electric Field 211

4.1 Electric Charge 213

4.2 Coulomb’s Law 218

4.3 The Electric Field 226

4.4 The Electric Potential 239

4.5 Electric Flux and Gauss’s Law 257

4.6 Divergence: Differential Form of Gauss’s Law 268

4.7 Metallic Conductors 276

4.8 Poisson’s and Laplace’s Equations 291

4.9 Capacitance 297

4.10 Dielectric Materials 305

4.11 Electrostatic Boundary Conditions 321

4.12 Electrostatic Energy 328

4.13 Electrostatic Forces 337

4.14 Microelectromechanical Systems (MEMS) 343

4.15 Summary 354

Contents vii

 

5 Steady Electric Currents 367

5.1 Current Density and the Microscopic View of Conduction 368

5.2 Current Flow, Ohm’s Law, and Resistance 374

5.3 Electromotive Force and Kirchhoff’s Voltage Law 381

5.4 The Continuity Equation and Kirchhoff’s Current Law 385

5.5 Redistribution of Free Charge 387

5.6 Boundary Conditions for Steady Current Flow 389

5.7 Duality of J and D: The Resistance—Capacitance Analogy 395

5.8 Joule’s Law 400

5.9 Surface and Line Currents 402

5.10 Summary 404

 

6 The Static Magnetic Field 415

6.1 Amp`ere’s Law of Force 417

6.2 The Biot—Savart Law and Its Applications 424

6.3 Amp`ere’s Circuital Law 438

6.4 Curl of the Magnetic Field: Differential Form of Amp`ere’s Law 446

6.5 Vector Magnetic Potential 459

6.6 The Magnetic Dipole 467

6.7 Divergence of B, Magnetic Flux, and Inductance 473

6.8 Magnetic Fields in Material Media 491

6.9 Boundary Conditions for Magnetostatic Fields 504

6.10 Magnetic Forces and Torques 508

6.11 Summary 517

 

7 Time-Varying Fields and Maxwell’s Equations
7.1 Faraday’s Law 534

7.2 Induction Due to Motion 546

7.3 Energy in a Magnetic Field 556

7.4 Displacement Current and Maxwell’s Equations 568

viii Contents

7.5 Review of Maxwell’s Equations 579

7.6 Summary 584

 

8 Waves in an Unbounded Medium 595

8.1 Plane Waves in a Simple, Source-Free, and Lossless Medium 596

8.2 Time-Harmonic Uniform Plane Waves in a Lossless Medium 604

8.3 Plane Waves in Lossy Media 615

8.4 Electromagnetic Energy Flow and the Poynting Vector 635

8.5 Polarization of Electromagnetic Waves 653

8.6 Arbitrarily Directed Uniform Plane Waves 667

8.7 Nonplanar Electromagnetic Waves 673

8.8 Summary 674

 

9 Reflection, Transmission, and Refraction of Waves

at Planar Interfaces 689

9.1 Normal Incidence on a Perfect Conductor 690

9.2 Normal Incidence on a Lossless Dielectric 700

9.3 Multiple Dielectric Interfaces 708

9.4 Normal Incidence on a Lossy Medium 721

9.5 Oblique Incidence upon a Perfect Conductor 734

9.6 Oblique Incidence at a Dielectric Boundary 747

9.7 Total Internal Reflection 765

9.8 Oblique Incidence on a Lossy Medium 777

9.9 Summary 787

 

10 Parallel-Plate and Dielectric Slab Waveguides 811

10.1 Waves between Parallel Metal Plates 814

10.2 Dielectric Waveguides 844

10.3 Wave Velocities and Waveguide Dispersion 864

10.4 Summary 876

Contents ix

 

11 Field—Matter Interactions and Metamaterials 885

11.1 Wave Propagation in Ionized Gases (Plasmas) 887

11.2 Frequency Response of Dielectrics and Conductors 899

11.3 Metamaterials 906

11.4 Summary 924

A Vector Analysis 929

A.1 Vector Components, Unit Vectors, and Vector Addition 930

A.2 Vector Multiplication 932

A.3 Cylindrical and Spherical Coordinate Systems 935

A.4 Vector Identities 943

B Uniqueness Theorem 947

C Derivation of Ampe` re’s Circuital Law from the Biot—Savart Law 951

Symbols and Units for Basic Quantities 955

General Bibliography 961

Answers to Odd-Numbered Problems 963

Index 975