Applied Electromagnetics: Early Transmission Lines Approach

Chapter 1 Introduction 1

1.1 Electromagnetic Fields 2

Electric Fields 3

Magnetic Fields 4

Field Linkage 4

1.2 The Electromagnetic Spectrum 5

1.3 Wireless Communications 6

1.4 Dealing with Units 8

1.5 Working with MATLAB 10

MATLAB Programs 15

1.6 Wave Fundamentals 19

1.7 Phasors 26

Summary 29

Problems 29

Chapter 2 Transmission Lines 31

2.1 Distributed-Parameter Model 32

Coaxial Cable 34

Telegraphist’s Equations 37

2.2 Time-Harmonic Waves on Transmission Lines 39

Characteristic Impedance 42

Lossless Line 43

2.3 Power Transmission 45

2.4 Terminated T-Lines 48

Voltage Standing Wave Ratio 50

Input Impedance 51

Complex Loads 53

Special Terminations 54

2.5 The Complete Circuit 55

2.6 The Smith Chart 62

Smith Chart Derivation 62

Using the Smith Chart 69

Impedance Measurement 73

2.7 Impedance Matching 76

Quarter-Wave Transformer 78

Matching with the Smith Chart 79

Admittance of Shunt Stubs 81

Shunt Stub Matching 84

2.8 Transients 87

Pulse Response 91

Practical Application: Schottky-Diode Terminations 95

Reactive Loads 96

Time-Domain Reflectometry 99

2.9 Dispersion 101

Summary 107

Problems 108

Chapter 3 Electrostatics 114

3.1 Vectors in the Cartesian Coordinate System 115

3.2 Coulomb’s Law 122

Electric Field Intensity 124

Field Lines 125

3.3 The Spherical Coordinate System 126

3.4 Line Charges and the Cylindrical Coordinate System 129

Infinite Length Line of Charge 133

Ring of Charge 138

3.5 Surface and Volume Charge 139

Volume Charge 145

Practical Application: Laser Printer 148

3.6 Electric Flux Density 149

3.7 Gauss’s Law and Applications 153

Coaxial Cable 157

3.8 Divergence and the Point Form of Gauss’s Law 161

3.9 Electric Potential 166

Gradient 171

3.10 Conductors and Ohm’s Law 176

Current and Current Density 178

Joule’s Law 181

3.11 Dielectrics 182

Practical Application: Electret Microphone 185

3.12 Boundary Conditions 186

3.13 Boundary Value Problems 190

3.14 Capacitance 194

Electrostatic Potential Energy 198

Practical Application: Electrolytic Capacitors 199

Summary 200

Problems 202

Chapter 4 Magnetostatics 208

4.1. Magnetic Fields and Cross Product 209

Oersted’s Experiment 214

4.2 Biot-Savart’s Law 214

Solenoid 221

Surface and Volume Current Densities 222

4.3 Ampe`re’s Circuital Law 224

4.4 Curl and the Point Form of Ampere’s Circuital Law 234

Stoke’s Theorem 236

4.5 Magnetic Flux Density 237

4.6 Magnetic Forces 240

Force on a Current Element 241

Magnetic Torque and Moment 246

Practical Application: Loudspeakers 250

4.7 Magnetic Materials 251

4.8 Boundary Conditions 251

4.9 Inductance and Magnetic Energy 261

Mutual Inductance 264

Magnetic Energy 266

4.10 Magnetic Circuits 269

Electromagnets 273

Practical Application: Maglev 276

Summary 278

Problems 280

Chapter 5 Dynamic Fields 286

5.1 Current Continuity and Relaxation Time 286

5.2 Faraday’s Law and Transformer EMF 288

Transformer EMF 290

Transformers 293

Point Form of Faraday’s Law 295

5.3 Faraday’s Law and Motional EMF 296

Generators 299

5.4 Displacement Current 301

5.5 Maxwell’s Equations 305

5.6 Lossless TEM Waves 306

5.7 Time-Harmonic Fields and Phasors 312

Summary 315

Problems 316

Chapter 6 Plane Waves 320

6.1 General Wave Equations 321

Time-Harmonic Wave

Equations 322

Propagating Fields Relation 327

6.2 Propagation in Lossless, Charge-Free Media 328

6.3 Propagation in Dielectrics 330

Low-Loss Dielectrics 332

Loss Tangent 333

6.4 Propagation in Conductors 335

Current in Conductors 337

6.5 The Poynting Theorem and Power Transmission 342

UPW Power Transmission 344

6.6 Polarization 347

Practical Application: Liquid Crystal Displays 352

6.7 Reflection and Transmission at Normal Incidence 353

General Case 353

Standing Waves 358

6.8 Reflection and Transmission at Oblique Incidence 359

TE Polarization 360

TM Polarization 366

Summary 368

Problems 370

Chapter 7 Waveguides 373

7.1 Rectangular Waveguide Fundamentals 374

Wave Propagation 377

Waveguide Impedance 381

Practical Application: Microwave Ovens 384

7.2 Waveguide Field Equations 385

TM Mode 388

TE Mode 394

7.3 Dielectric Waveguide 398

TE Mode 401

TM Mode 403

Field Equations 404

7.4 Optical Fiber 407

Numerical Aperture 410

Signal Degradation 411

Attenuation 412

Graded-Index Fiber 413

7.5 Fiber-Optic Communication Systems 413

Optical Sources 414

Optical Detectors 416

Repeaters and Optical Amplifiers 417

Connections 418

7.6 Optical Link Design 419

Power Budget 419

Rise-Time Budget 420

Summary 423

Suggested References 424

Problems 424

Chapter 8 Antennas 426

8.1 General Properties 428

Radiated Power 428

Radiation Patterns 429

Directivity 431

Impedance and Efficiency 436

A Commercial Antenna 445

8.2 Electrically Short Antennas 438

Vector Magnetic Potential 438

The Hertzian Dipole 441

The Small Loop Antenna 445

8.3 Dipole Antennas 447

Derivation of Fields 448

Antenna Properties 451

Half-Wave Dipole 458

8.4 Monopole Antennas 462

Image Theory 462

Antenna Properties 463

Practical Considerations 465

8.5 Antenna Arrays 467

Pair of Hertzian Dipoles 469

N-Element Linear Array 473

Parasitic Arrays 475

8.6 The Friis Transmission Equation 476

Polarization Efficiency 476

Receiver Matching 483

8.7 Radar 484

Doppler Frequency Shift 486

8.8 Antennas for Wireless Communications 487

Parabolic Reflectors 488

Patch Antennas 489

Slot Antennas 490

Folded Dipole Antennas 491

Summary 492

Suggested References 494

Problems 494

Chapter 9 Electromagnetic Interference 499

9.1 Interference Sources 500

Lightning 500

Electrostatic Discharge 500

Power Disturbance Sources 501

Radio Transmitters 502

9.2 Passive Circuit Elements 503

Conductors 503

Resistors 506

Inductors 510

Capacitors 513

9.3 Digital Signals 517

9.4 Grounds 519

Bond Wires 521

Signal Grounds 521

Loop Area 524

9.5 Shields 524

Shielded Cable 531

9.6 Filters 531

Reflective Filters 531

Ferrite Chokes 537

Summary 538

Suggested References 539

Problems 540

Chapter 10 Microwave Engineering 541

10.1 Microstrip 543

Attenuation 549

Other Planar T-Lines 550

10.2 Lumped-Element Matching Networks 551

10.3 Scattering Parameters 557

Reciprocal Networks 562

Lossless Networks 563

Return Loss and Insertion Loss 564

Shift in Reference Plane 565

The Vector Network Analyzer 567

10.4 Couplers and Dividers 568

Circulators 568

Three-Port Dividers 570

Couplers 571

10.5 Filters 576

Simple Filters 579

Multisection Filters 581

High-Pass Filters 586

Bandpass Filters 588

10.6 Amplifiers 592

Designing Matching Networks 596

Balanced Amplifiers 600

10.7 Receiver Design 602

Oscillators 602

Mixers 603

Microwave CAD 605

Practical Application: Radio Frequency Identification 606

Summary 607

Suggested References 608

Problems 609

Appendix A Vector Relations 614

Appendix B Coordinate System Transformations 617

Appendix C Complex Numbers 621

Appendix D Integrals, Conversions, and Constants 623

Appendix E Material Properties 625

Appendix F Common MATLAB Math Functions 627

Appendix G Answers to Selected Problems 628

Index 650