Fundamentals of Applied Electromagnetics, 5th Edition

Contents

Timeline and Technology Briefs iv

Preface to the 2006 Edition xiii

1 Introduction: Waves and Phasors 2

1-1 Dimensions, Units, and Notation 5

1-2 The Nature of Electromagnetism 12

1-2.1 The Gravitational Force: A Useful Analogue 13

1-2.2 Electric Fields 14

1-2.3 Magnetic Fields 16

1-2.4 Static and Dynamic Fields 18

1-3 Traveling Waves 18

1-3.1 Sinusoidal Wave in a Lossless Medium 21

1-3.2 Sinusoidal Wave in a Lossy Medium 23

1-4 The Electromagnetic Spectrum 26

1-5 Review of Complex Numbers 28

1-6 Review of Phasors 31

2 Transmission Lines 40

2-1 General Considerations 41

2-1.1 The Role of Wavelength 42

2-1.2 Propagation Modes 43

2-2 Lumped-Element Model 45

2-3 Transmission-Line Equations 49

2-4 Wave Propagation on a Transmission Line 50

2-5 The Lossless Transmission Line 53

2-5.1 Voltage Reflection Coefficient 54

2-5.2 Standing Waves 57

2-6 Input Impedance of the Lossless Line 61

2-7 Special Cases of the Lossless Line 64

2-7.1 Short-Circuited Line 64

2-7.2 Open-Circuited Line 66

2-7.3 Application of Short-Circuit and Open-Circuit Measurements 66

2-7.4 Lines of Length l = nλ/2 68

2-7.5 Quarter-Wave Transformer 68

2-7.6 Matched Transmission Line: ZL = Z0 68

2-8 Power Flow on a Lossless Transmission Line 70

2-8.1 Instantaneous Power 70

2-8.2 Time-Average Power 71

2-9 The Smith Chart 72

2-9.1 Parametric Equations 72

2-9.2 Input Impedance 77

2-9.3 SWR, Voltage Maxima and Minima 79

2-9.4 Impedance to Admittance Transformations 80

2-10 Impedance Matching 88

2-11 Transients on Transmission Lines 92

2-11.1 Transient Response 92

2-11.2 Bounce Diagrams 96

3 Vector Analysis 108

3-1 Basic Laws of Vector Algebra 109

3-1.1 Equality of Two Vectors 110

3-1.2 Vector Addition and Subtraction 111

3-1.3 Position and Distance Vectors 111

3-1.4 Vector Multiplication 112

3-1.5 Scalar and Vector Triple Products 115

3-2 Orthogonal Coordinate Systems 116

3-2.1 Cartesian Coordinates 117

3-2.2 Cylindrical Coordinates 117

3-2.3 Spherical Coordinates 121

3-3 Transformations between Coordinate Systems 123

3-3.1 Cartesian to Cylindrical Transformations 123

3-3.2 Cartesian to Spherical Transformations 125

3-3.3 Cylindrical to Spherical Transformations 127

3-3.4 Distance between Two Points 127

3-4 Gradient of a Scalar Field 130

3-4.1 Gradient Operator in Cylindrical and Spherical Coordinates 131

3-4.2 Properties of the Gradient Operator 132

3-5 Divergence of a Vector Field 133

3-5.1 Divergence Theorem 135

3-5.2 Remarks on Notation 135

3-6 Curl of a Vector Field 139

3-6.1 Vector Identities Involving the Curl 140

3-6.2 Stokes’s Theorem 141

3-7 Laplacian Operator 142

Problems 144

4 Electrostatics 150

4-1 Maxwell’s Equations 151

4-2 Charge and Current Distributions 152

4-2.1 Charge Densities 152

4-2.2 Current Density 154

4-3 Coulomb’s Law 155

4-3.1 Electric Field due to Multiple Point Charges 156

4-3.2 Electric Field due to a Charge Distribution 157

4-4 Gauss’s Law 160

4-5 Electric Scalar Potential 163

4-5.1 Electric Potential as a Function of Electric Field 163

4-5.2 Electric Potential due to Point Charges 165

4-5.3 Electric Potential due to Continuous Distributions 165

4-5.4 Electric Field as a Function of Electric Potential 165

4-5.5 Poisson’s Equation 167

4-6 Electrical Properties of Materials 168

4-7 Conductors 169

4-7.1 Resistance 170

4-7.2 Joule’s Law 172

4-8 Dielectrics 173

4-9 Electric Boundary Conditions 177

4-9.1 Dielectric–Conductor Boundary 180

4-9.2 Conductor–Conductor Boundary 181

4-10 Capacitance 182

4-11 Electrostatic Potential Energy 190

4-12 Image Method 191

Problems 194

5 Magnetostatics 204

5-1 Magnetic Forces and Torques 205

5-1.1 Magnetic Force on a Current-Carrying Conductor 207

5-1.2 Magnetic Torque on a Current-Carrying Loop 210

5-2 The Biot–Savart Law 213

5-2.1 Magnetic Field due to Surface and Volume Current Distributions 214

5-2.2 Magnetic Field of a Magnetic Dipole 217

5-3 Magnetic Force between Two Parallel Conductors 218

5-4 Maxwell’s Magnetostatic Equations 219

5-4.1 Gauss’s Law for Magnetism 219

5-4.2 Amp`ere’s Law 220

5-5 Vector Magnetic Potential 226

5-6 Magnetic Properties of Materials 228

5-6.1 Orbital and Spin Magnetic Moments 228

5-6.2 Magnetic Permeability 229

5-6.3 Magnetic Hysteresis of Ferromagnetic Materials 230

5-7 Magnetic Boundary Conditions 233

5-8 Inductance 234

5-8.1 Magnetic Field in a Solenoid 235

5-8.2 Self-inductance 238

5-8.3 Mutual Inductance 240

5-9 Magnetic Energy 241

Problems 245

6 Maxwell’s Equations for Time-Varying Fields 254

6-1 Faraday’s Law 255

6-2 Stationary Loop in a Time-Varying Magnetic Field 257

6-3 The Ideal Transformer 261

6-4 Moving Conductor in a Static Magnetic Field 262

6-5 The Electromagnetic Generator 265

6-6 Moving Conductor in a Time-Varying Magnetic Field 267

6-7 Displacement Current 268

6-8 Boundary Conditions for Electromagnetics 270

6-9 Charge–Current Continuity Relation 271

6-10 Free-Charge Dissipation in a Conductor 273

6-11 Electromagnetic Potentials 276

6-11.1 Retarded Potentials 276

6-11.2 Time-Harmonic Potentials 277

Problems 281

7 Plane-Wave Propagation 286

7-1 Time-Harmonic Fields 288

7-1.1 Complex Permittivity 289

7-1.2 Wave Equations for a Charge-Free Medium 289

7-2 Plane-Wave Propagation in Lossless Media 290

7-2.1 Uniform Plane Waves 290

7-2.2 General Relation between E and H 294

7-3 Wave Polarization 295

7-3.1 Linear Polarization 296

7-3.2 Circular Polarization 297

7-3.3 Elliptical Polarization 299

7-4 Plane-Wave Propagation in Lossy Media 304

7-4.1 Low-Loss Dielectric 306

7-4.2 Good Conductor 306

7-5 Current Flow in a Good Conductor 308

7-6 Electromagnetic Power Density 311

7-6.1 Plane Wave in a Lossless Medium 312

7-6.2 Plane Wave in a Lossy Medium 313

7-6.3 Decibel Scale for Power Ratios 314

Problems 316

8 Reflection, Transmission, and Waveguides 320

8-1 Wave Reflection and Transmission at Normal Incidence 322

8-1.1 Boundary between Lossless Media 322

8-1.2 Transmission-Line Analogue 325

8-1.3 Power Flow in Lossless Media 326

8-1.4 Boundary between Lossy Media 329

8-2 Snell’s Laws 331

8-3 Fiber Optics 334

8-4 Wave Reflection and Transmission at Oblique Incidence 336

8-4.1 Perpendicular Polarization 337

8-4.2 Parallel Polarization 341

8-4.3 Brewster Angle 343

8-5 Reflectivity and Transmissivity 346

8-6 Waveguides 349

8-7 General Relations for E and H 351

8-8 TM Modes in Rectangular Waveguide 352

8-9 TE Modes in Rectangular Waveguide 357

8-10 Propagation Velocities 358

8-11 Cavity Resonators 363

8-11.1 Resonant Frequency 364

8-11.2 Quality Factor 364

Problems 366

9 Radiation and Antennas 372

9-1 The Short Dipole 375

9-1.1 Far-Field Approximation 377

9-1.2 Power Density 378

9-2 Antenna Radiation Characteristics 380

9-2.1 Antenna Pattern 381

9-2.2 Beam Dimensions 383

9-2.3 Antenna Directivity 383

9-2.4 Antenna Gain 386

9-2.5 Radiation Resistance 386

9-3 Half-Wave Dipole Antenna 387

9-3.1 Directivity of λ/2 Dipole 389

9-3.2 Radiation Resistance of λ/2 Dipole 389

9-3.3 Quarter-Wave Monopole Antenna 390

9-4 Dipole of Arbitrary Length 391

9-5 Effective Area of a Receiving Antenna 392

9-6 Friis Transmission Formula 395

9-7 Radiation by Large-Aperture Antennas 397

9-8 Rectangular Aperture with Uniform Aperture Distribution 400

9-8.1 Beamwidth 401

9-8.2 Directivity and Effective Area 402

9-9 Antenna Arrays 403

9-10 N-Element Array with Uniform Phase Distribution 410

9-11 Electronic Scanning of Arrays 412

9-11.1 Uniform-Amplitude Excitation 414

9-11.2 Array Feeding 415

Problems 418

10 Satellite Communication Systems and Radar Sensors 424

10-1 Satellite Communication Systems 425

10-2 Satellite Transponders 427

10-3 Communication-Link Power Budget 430

10-4 Antenna Beams 432

10-5 Radar Sensors 433

10-5.1 Basic Operation of a Radar System 433

10-5.2 Unambiguous Range 434

10-5.3 Range and Angular Resolutions 435

10-6 Target Detection 436

10-7 Doppler Radar 439

10-8 Monopulse Radar 440

Problems 444

A Symbols, Quantities, and Units 445

B Material Constants of Some Common Materials 447

C Mathematical Formulas 449

D Answers to Odd-Numbered Problems 451

Bibliography 457

Index 459