Fundamentals of Electromagnetics with MATLAB.pdf

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Contents

Preface

ix

Chapter 1

MATLAB and Vectors

2

1.1 MATLAB and a Review of Vectors 3

1.2 Coordinate Systems 16

1.3 Integral Relations for Vectors 29

1.4 Differential Relations for Vectors 39

1.5 Phasors 56

1.6 Conclusion 60

1.7 Problems 60

Chapter 2

Static Electric and Magnetic Fields

70

2.1 Coulomb’s Law 71

2.2 Electric Field 76

2.3 Superposition Principles 78

2.4 Gauss’s Law 87

2.5 Potential Energy and Electric Potential 95

2.6 Numerical Integration 111

2.7 Dielectric Materials 121

2.8 Capacitance 126

2.9 Electrical Currents 130

2.10 Fundamentals of Magnetic Fields 135

2.11 Magnetic Vector Potential and the Biot-Savart Law 146

2.12 Magnetic Forces 155

2.13 Magnetic Materials 166

2.14 Magnetic Circuits 172

2.15 Inductance 175

2.16 Boundary Conditions 181

2.17 Conclusion 189

2.18 Problems 190

v

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Contents

Chapter 3

Boundary Value Problems Using MATLAB

204

3.1 Poisson’s and Laplace’s Equations 205

3.2 Analytical Solution in One Dimension—Direct Integration

Method 211

3.3 Numerical Solution of a One-Dimensional Equation—

Finite Difference Method 222

3.4 Analytical Solution of a Two-Dimensional Equation—

Fourier Series Expansion 233

3.5 Finite Difference Method Using MATLAB 243

3.6 Finite Element Method Using MATLAB 249

3.7 Method of Moments Using MATLAB 263

3.8 Conclusion 273

3.9 Problems 274

Chapter 4

Time-Varying Electromagnetic Fields

282

4.1 Faraday’s Law of Induction 283

4.2 Equation of Continuity 296

4.3 Displacement Current 301

4.4 Maxwell’s Equations 307

4.5 Poynting’s Theorem 312

4.6 Time-Harmonic Electromagnetic Fields 318

4.7 Conclusion 322

4.8 Problems 322

Chapter 5

Electromagnetic Wave Propagation

330

5.1 Wave Equation 331

5.2 One-Dimensional Wave Equation 336

5.3 Time-Harmonic Plane Waves 352

5.4 Plane Wave Propagation in a Dielectric Medium 361

5.5 Reflection and Transmission of an Electromagnetic

Wave 373

5.6 Waveguide—Propagation with Dispersion 388

5.7 Conclusion 398

5.8 Problems 398

Chapter 6

Transmission Lines

408

6.1 Equivalent Electrical Circuits 409

6.2 Transmission Line Equations 412

6.3 Sinusoidal Waves 418

6.4 Terminations 423

6.5 Impedance on the Transmission Line and Matching 431

6.6 Smith Chart 438

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vii

6.7 Transient Effects and the Bounce Diagram 449

6.8 Pulse Propagation 457

6.9 Lossy Transmission Lines 462

6.10 Dispersion and Group Velocity 468

6.11 Conclusion 476

6.12 Problems 477

Chapter 7

Radiation of Electromagnetic Waves

484

7.1 Radiation Fundamentals 485

7.2 Short Electric Dipole Antenna 493

7.3 Long Dipole Antenna 501

7.4 Antenna Parameters 506

7.5 Magnetic Dipole Antenna 517

7.6 Aperture Antennas, Diffraction of Waves 522

7.7 Antenna Arrays 535

7.8 Conclusion 546

7.9 Problems 547

Appendix A Mathematical Formulas

552

A.1 Vector Identities 553

A.2 Vector Operations in the Three Coordinate Systems 554

A.3 Summary of the Transformations Between Coordinate

Systems 555

A.4 Integral Relations 557

Appendix B Mathematical Foundation of the Finite Element Method 558

B.1 Minimum Energy Condition 559

B.2 Linear Interpolation Coefficients 560

B.3 S-matrix Elements 560

B.4 Decoupled and Coupled Node Potentials 561

B.5 The Matrix Equation for the Unknown Potentials 563

Appendix C Material Parameters

564

Appendix D Transmission Line Parameters of Two Parallel Wires 568

Appendix E Plasma Evolution Adjacent to a Metallic Surface

574

Appendix F References

578

Appendix G Answers

582

Index

635

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