Foundations of Electromagnetic Compatibility With Practical Applications

There is currently no single book that covers the mathematics, circuits, and electromagnetics backgrounds needed for the study of electromagnetic compatibility (EMC). This book aims to redress the balance by focusing on EMC and providing the background in all three disciplines. This background is necessary for many EMC practitioners who have been out of study for some time and who are attempting to follow and confidently utilize more advanced EMC texts.

The book is split into three parts: Part 1 is the refresher course in the underlying mathematics; Part 2 is the foundational chapters in electrical circuit theory; Part 3 is the heart of the book: electric and magnetic fields, waves, transmission lines and antennas. Each part of the book provides an independent area of study, yet each is the logical step to the next area, providing a comprehensive course through each topic. Practical EMC applications at the end of each chapter illustrate the applicability of the chapter topics. The Appendix reviews the fundamentals of EMC testing and measurements.

About the Author
Bogdan Adamczyk is Professor of Engineering and the founder and director of the EMC Center at Grand Valley State University, Grand Rapids, USA. He is also the founder and principal educator of EMC Educational Services LLC, which specializes in EMC courses for industry. Professor Adamczyk's area of expertise is EMC education and EMC pre-compliance testing.

He is an iNARTE-certified EMC Master Design Engineer, a founding member and the chair of the IEEE EMC Chapter of West Michigan, and a member of the IEEE EMC Society Education Committee. He was a 2016 IEEE EMC Symposium Global University and Fundamentals of EMC instructor. This book has evolved from his participation at several IEEE EMC Symposia, EMC pre-compliance testing at the EMC Center, and his teaching of the Foundations of Electromagnetic Compatibility certificate courses for industry.

Preface xiii

Part I Math Foundations of EMC 1

1 Matrix and Vector Algebra 3

1.1 Basic Concepts and Operations 3

1.2 Matrix Multiplication 5

1.3 Special Matrices 6

1.4 Matrices and Determinants 7

1.5 Inverse of a Matrix 9

1.6 Matrices and Systems of Equations 10

1.7 Solution of Systems of Equations 11

1.8 Cramer’s Rule 12

1.9 Vector Operations 13

1.10 EMC Applications 14

References 21

2 Coordinate Systems 23

2.1 Cartesian Coordinate System 23

2.2 Cylindrical Coordinate System 25

2.3 Spherical Coordinate System 27

2.4 Transformations between Coordinate Systems 29

2.5 EMC Applications 33

References 35

3 Vector Differential Calculus 37

3.1 Derivatives 37

3.2 Differential Elements 40

3.3 Constant�]Coordinate Surfaces 45

3.4 Differential Operators 50

3.5 EMC Applications 55

References 57

4 Vector Integral Calculus 59

4.1 Line Integrals 59

4.2 Surface Integrals 66

4.3 Volume Integrals 71

4.4 Divergence Theorem of Gauss 71

4.5 Stokes’s Theorem 71

4.6 EMC Applications 72

References 79

5 Differential Equations 81

5.1 First Order Differential Equations – RC and RL Circuits 81

5.2 Second�]Order Differential Equations – Series and Parallel RLC Circuits 85

5.3 Helmholtz Wave Equations 95

5.4 EMC Applications 99

References 108

6 Complex Numbers and Phasors 109

6.1 Definitions and Forms 109

6.2 Complex Conjugate 111

6.3 Operations on Complex Numbers 113

6.4 Properties of Complex Numbers 118

6.5 Complex Exponential Function 118

6.6 Sinusoids and Phasors 119

6.7 EMC Applications 123

References 140

Part II Circuits Foundations of EMC 141

7 Basic Laws and Methods of Circuit Analysis 143

7.1 Fundamental Concepts 143

7.2 Laplace Transform Basics 147

7.3 Fundamental Laws 152

7.4 EMC Applications 183

References 187

8 Systematic Methods of Circuit Analysis 189

8.1 Node Voltage Analysis 189

8.2 Mesh Current Analysis 192

8.3 EMC Applications 195

References 202

9 Circuit Theorems and Techniques 203

9.1 Superposition 203

9.2 Source Transformation 207

9.3 Thévenin Equivalent Circuit 211

9.4 Norton Equivalent Circuit 217

9.5 Maximum Power Transfer 220

9.6 Two�]Port Networks 224

9.7 EMC Applications 236

References 241

10 Magnetically Coupled Circuits 243

10.1 Self and Mutual Inductance 243

10.2 Energy in a Coupled Circuit 248

10.3 Linear (Air�]Core) Transformers 250

10.4 Ideal (Iron�]Core) Transformers 251

10.5 EMC Applications 255

References 258

11 Frequency�]Domain Analysis 259

11.1 Transfer Function 259

11.2 Frequency�]Transfer Function 267

11.3 Bode Plots 272

11.4 Passive Filters 277

11.5 Resonance in RLC Circuits 294

11.6 EMC Applications 308

References 327

12 Frequency Content of Digital Signals 329

12.1 Fourier Series and Frequency Content of Signals 329

12.2 EMC Applications 347

References 351

Part III Electromagnetics Foundations of EMC 353

13 Static and Quasi�]Static Electric Fields 355

13.1 Charge Distributions 355

13.2 Coulomb’s Law 356

13.3 Electric Field Intensity 357

13.4 Electric Field Due to Charge Distributions 358

13.5 Electric Flux Density 359

13.6 Gauss’s Law for the Electric Field 360

13.7 Applications of Gauss’s Law 360

13.8 Electric Scalar Potential and Voltage 367

13.9 Voltage Calculations due to Charge Distributions 369

13.10 Electric Flux Lines and Equipotential Surfaces 373

13.11 Maxwell’s Equations for Static Electric Field 374

13.12 Capacitance Calculations of Structures 374

13.13 Electric Boundary Conditions 380

13.14 EMC Applications 385

References 402

14 Static and Quasi�]Static Magnetic Fields 403

14.1 Magnetic Flux Density 403

14.2 Magnetic Field Intensity 404

14.3 Biot–Savart Law 404

14.4 Current Distributions 405

14.5 Ampere’s Law 406

14.6 Applications of Ampere’s Law 407

14.7 Magnetic Flux 409

14.8 Gauss’s Law for Magnetic Field 410

14.9 Maxwell’s Equations for Static Fields 410

14.10 Vector Magnetic Potential 411

14.11 Faraday’s Law 412

14.12 Inductance Calculations of Structures 416

14.13 Magnetic Boundary Conditions 418

References 437

15 Rapidly Varying Electromagnetic Fields 439

15.1 Eddy Currents 439

15.2 Charge�]Current Continuity Equation 440

15.3 Displacement Current 441

15.4 EMC Applications 444

References 452

16 Electromagnetic Waves 453

16.1 Uniform Waves – Time Domain Analysis 453

16.2 Uniform Waves – Sinusoidal Steady�]State Analysis 460

16.3 Reflection and Transmission of Uniform Waves at Boundaries 464

16.4 EMC Applications 467

References 474

17 Transmission Lines 475

17.1 Transient Analysis 475

17.2 Steady�]State Analysis 509

17.3 s Parameters 520

17.4 EMC Applications 527

References 542

18 Antennas and Radiation 543

18.1 Bridge between the Transmission Line and Antenna Theory 543

18.2 Hertzian Dipole Antenna 544

18.3 Far Field Criteria 548

18.4 Half�]Wave Dipole Antenna 551

18.5 Quarter�]Wave Monopole Antenna 554

18.6 Image Theory 554

18.7 Differential�] and Common�]Mode Currents and Radiation 557

18.8 Common Mode Current Creation 565

18.9 Antenna Circuit Model 571

18.10 EMC Applications 575

References 582

Appendix A EMC Tests and Measurements 583

A.1 Introduction – FCC Part 15 and CISPR 22 Standards 583

A.2 Conducted Emissions 588

A.3 Radiated Emissions 600

A.4 Conducted Immunity – ISO 11452�]4 608

A.5 Radiated Immunity 615

A.6 Electrostatic Discharge (ESD) 620

References 627

Index 629

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