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1The Electromagnetic Model 1

1-1 Introduction 1

1-2 The Electromagnetic Model 3

1-3 SI Units and Universal Constants 8

Review Questions 10

2Vector Analysis 11

2-1 Introduction 11

2-2 Vector Addition and Subtraction 12

2-3 Products of Vectors 14

2-3.1 Scalar or Dot Product 14

2-3.2 Vector or Cross Product 16

2-3.3 Product of Three Vectors 18

2-4 Orthogonal Coordinate Systems 20

2-4.1 Cartesian Coordinates 23

2-4.2 Cylindrical Coordinates 27

2-4.3 Spherical Coordinates 31

2-5 Integrals Containing Vector Functions 37

2-6 Gradient of a Scalar Field 42

2-7 Divergence of a Vector Field 46

2-8 Divergence Theorem 50

2-9 Curl of a Vector Field 54

2-10 Stokes’s Theorem 58

2-11 Two Null Identities 61

2-11.1 Identity Ⅰ 61

2-11.2 Identity Ⅱ 62

2-12 Helmholtz’s Theorem 63

Review Questions 66

3Static Electric Fields 72

3-1 Introduction 72

3-2 Fundamental Postulates of Electrostatics in Free Space 74

3-3 Coulomb’s Law 77

3-3.1 Electric Field Due to a System of Discrete Charges 82

3-3.2 Electric Field Due to a Continuous Distributionof Charge 84

3-4 Gauss’s Law and Applications 87

3-5 Electric Potential 92

3-5.1 Electric Potential Due to a Charge Distribution 94

3-6 Conductors in Static Electric Field 100

3-7 Dielectrics in Static Electric Field 105

3-7.1 Equivalent Charge Distributions ofPolarized Dielectrics 106

3-8 Electric Flux Density and Dielectric Constant 109

3-8.1 Dielectric Strength 114

3-9 Boundary Conditions for Electrostatic Fields 116

3-10 Capacitance and Capacitors 121

3-10.1 Series and Parallel Connections of Capacitors 126

3-10.2 Capacitances in Multiconductor Systems 129

3-10.3 Electrostatic Shielding 132

3-11 Electrostatic Energy and Forces 133

3-11.1 Electrostatic Energy in Terms of Field Quantities 137

3-11.2 Electrostatic Forces 140

Review Questions 143

Problems 145

4Solution of Electrostatic Problems 152

4-1 Introduction 152

4-2 Poisson’s and Laplace’s Equations 152

4-3 Uniqueness of Electrostatic Solutions 157

4-4 Method of Images 159

4-4.1 Point Charge and Conducting Planes 161

4-4.2 Line Charge and Parallel Conducting Cylinder 162

4-4.3 Point Charge and Conducting Sphere 170

4-4.4 Charged Sphere and Grounded Plane 172

4-5 Boundary-Value Problems in Cartesian Coordinates 174

4-6 Boundary-Value Problems in Cylindrical Coordinates 183

4-7 Boundary-Value Problems in Spherical Coordinates 188

Review Questions 192

Problems 193

5Steady Electric Currents 198

5-1 Introduction 198

5-2 Current Density and Ohm’s Law 199

5-3 Electromotive Force and Kirchhoff’s Voltage Law 205

5-4 Equation of Continuity and Kirchhoff’s Current Law 208

5-5 Power Dissipation and Joule’s Law 210

5-6 Boundary Conditions for Current Density 211

5-7 Resistance Calculations 215

Review Questions 219

Problems 220

6Static Magnetic Fields 225

6-1 Introduction 225

6-2 Fundamental Postulates of Magnetostatics in Free Space 226

6-3 Vector Magnetic Potential 232

6-4 The Biot-Savart Law and Applications 234

6-5 The Magnetic Dipole 239

6-5.1 Scalar Magnetic Potential 242

6-6 Magnetization and Equivalent Current Densities 243

6-6.1 Equivalent Magnetization Charge Densities 247

6-7 Magnetic Field Intensity and Relative Permeability 249

6-8 Magnetic Circuits 251

6-9 Behavior of Magnetic Materials 257

6-10 Boundary Conditions for Magnetostatic Fields 262

6-11 Inductances and Inductors 266

6-12 Magnetic Energy 277

6-12.1 Magnetic Energy in Terms of Field Quantities 279

6-13 Magnetic Forces and Torques 281

6-13.1 Hall Effect 282

6-13.2 Forces and Torques on Current-Carrying Conductors 283

6-13.3 Forces and Torques in Terms of StoredMagnetic Energy 289

6-13.4 Forces and Torques in Terms of Mutual Inductance 292

Review Questions 294

Problems 296

7Time-Varying Fields and Maxwell’s Equations 307

7-1 Introduction 307

7-2 Faraday’s Law of Electromagnetic Induction 308

7-2.1 A Stationary Circuit in a Time-VaryingMagnetic Field 309

7-2.2 Transformers 310

7-2.3 A Moving Conductor in a Static Magnetic Field 314

7-2.4 A Moving Circuit in a Time-Varying Magnetic Field 317

7-3 Maxwell’s Equations 321

7-3.1 Integral Form of Maxwell’s Equations 323

7-4 Potential Functions 326

7-5 Electromagnetic Boundary Conditions 329

7-5.1 Interface between Two Lossless Linear Media 330

7-5.2 Interface between a Dielectric and aPerfect Conductor 331

7-6 Wave Equations and Their Solutions 332

7-6.1 Solution of Wave Equations for Potentials 333

7-6.2 Source-Free Wave Equations 334

7-7 Time-Harmonic Fields 335

7-7.1 The Use of Phasors—A Review 336

7-7.2 Time-Harmonic Electromagnetics 338

7-7.3 Source-Free Fields in Simple Media 340

7-7.4 The Electromagnetic Spectrum 343

Review Questions 346

Problems 347

8Plane Electromagnetic Waves 354

8-1 Introduction 354

8-2 Plane Waves in Lossless Media 355

8-2.1 Doppler Effect 360

8-2.2 Transverse Electromagnetic Waves 361

8-2.3 Polarization of Plane Waves 364

8-3 Plane Waves in Lossy Media 367

8-3.1 Low-Loss Dielectrics 368

8-3.2 Good Conductors 369

8-3.3 Ionized Gases 373

8-4 Group Velocity 375

8-5 Flow of Electromagnetic Power and the Poynting Vector 379

8-5.1 Instantaneous and Average Power Densities 382

8-6 Normal Incidence at a Plane Conducting Boundary 386

8-7 Oblique Incidence at a Plane Conducting Boundary 390

8-7.1 Perpendicular Polarization 390

8-7.2 Parallel Polarization 395

8-8 Normal Incidence at a Plane Dielectric Boundary 397

8-9 Normal Incidence at Multiple Dielectric Interfaces 401

8-9.1 Wave Impedance of the Total Field 403

8-9.2 Impedance Transformation with Multiple Dielectrics 404

8-10 Oblique Incidence at a Plane Dielectric Boundary 406

8-10.1 Total Reflection 408

8-10.2 Perpendicular Polarization 411

8-10.3 Parallel Polarization 414

Review Questions 417

Problems 419

9Theory and Applications of Transmission Lines 427

9-1 Introduction 427

9-2 Transverse Electromagnetic Wave along a Parallel-Plate Transmission Line 429

9-2.1 Lossy Parallel-Plate Transmission Lines 433

9-2.2 Microstrip Lines 435

9-3 General Transmission-Line Equations 437

9-3.1 Wave Characteristics on an InfiniteTransmission Line 439

9-3.2 Transmission-Line Parameters 444

9-3.3 Attenuation Constant from Power Relations 447

9-4 Wave Characteristics on Finite Transmission Lines 449

9-4.1 Transmission Lines as Circuit Elements 454

9-4.2 Lines with Resistive Termination 460

9-4.3 Lines with Arbitrary Termination 465

9-4.4 Transmission-Line Circuits 467

9-5 Transients on Transmission Lines 471

9-5.1 Reflection Diagrams 474

9-5.2 Pulse Excitation 478

9-5.3 Initially Charged Line 480

9-5.4 Line with Reactive Load 482

9-6 The Smith Chart 485

9-6.1 Smith-Chart Calculations for Lossy Lines 495

9-7 Transmission-Line Impedance Matching 497

9-7.1 Impedance Matching by Quarter-Wave Transformer 497

9-7.2 Single-Stub Matching 501

9-7.3 Double-Stub Matching 505

Review Questions 509

Problems 512

10Waveguides and Cavity Resonators 520

10-1 Introduction 520

10-2 General Wave Behaviors along Uniform Guiding Structures 521

10-2.1 Transverse Electromagnetic Waves 524

10-2.2 Transverse Magnetic Waves 525

10-2.3 Transverse Electric Waves 529

10-3 Parallel-Plate Waveguide 534

10-3.1 TM Waves between Parallel Plates 534

10-3.2 TE Waves between Parallel Plates 539

10-3.3 Energy-Transport Velocity 541

10-3.4 Attenuation in Parallel-Plate Waveguides 543

10-4 Rectangular Waveguides 547

10-4.1 TM Waves in Rectangular Waveguides 547

10-4.2 TE Waves in Rectangular Waveguides 551

10-4.3 Attenuation in Rectangular Waveguides 555

10-4.4 Discontinuities in Rectangular Waveguides 559

10-5 Circular Waveguides 562

10-5.1 Bessel’s Differential Equation andBessel Functions 563

10-5.2 TM Waves in Circular Waveguides 567

10-5.3 TE Waves in Circular Waveguides 569

10-6 Dielectric Waveguides 572

10-6.1 TM Waves along a Dielectric Slab 572

10-6.2 TE Waves along a Dielectric Slab 576

10-6.3 Additional Comments onDielectric Waveguides 579

10-7 Cavity Resonators 582

10-7.1 Rectangular Cavity Resonators 582

10-7.2 Quality Factor of Cavity Resonator 586

10-7.3 Circular Cavity Resonator 589

Review Questions 592

Problems 594

11Antennas and Radiating Systems 600

11-1 Introduction 600

11-2 Radiation Fields of Elemental Dipoles 602

11-2.1 The Elemental Electric Dipole 602

11-2.2 The Elemental Magnetic Dipole 605

11-3 Antenna Patterns and Antenna Parameters 607

11-4 Thin Linear Antennas 614

11-4.1 The Half-Wave Dipole 617

11-4.2 Effective Antenna Length 619

11-5 Antenna Arrays 621

11-5.1 Two-Element Arrays 622

11-5.2 General Uniform Linear Arrays 625

11-6 Receiving Antennas 631

11-6.1 Internal Impedance and Directional Pattern 632

11-6.2 Effective Area 634

11-6.3 Backscatter Cross Section 637

11-7 Transmit-Receive Systems 639

11-7.1 Friis Transmission Formula and Radar Equation 639

11-7.2 Wave Propagation near Earth’s Surface 642

11-8 Some Other Antenna Types 643

11-8.1 Traveling-Wave Antennas 643

11-8.2 Helical Antennas 645

11-8.3 Yagi-Uda Antenna 648

11-8.4 Broadband Antennas 650

11-9 Aperture Radiators 655

References 661

Review Questions 662

Problems 664

Appendixes 671

A Symbols and Units 671

A-1 Fundamental SI （Rationalized MKSA） Units 671

A-2 Derived Quantities 671

A-3 Multiples and Submultiples of Units 673

B Some Useful Material Constants 674

B-1 Constants of Free Space 674

B-2 Physical Constants of Electron and Proton 674

B-3 Relative Permittivities （Dielectric Constants） 675

B-4 Conductivities 675

B-5 Relative Permeabilities 676

C Index of Tables 677

General Bibliography 679

Answers to Selected Problems 681

Index 693