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.

Table of Contents:
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