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 a 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 I is a refresher course in the underlying mathematics; Part II provides the foundational concepts of electrical circuit theory; Part III 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.

This book:

is unique in packaging the three key topics of mathematics, circuits, and electromagnetics foundations into one comprehensive reference is supported by each chapter′s practical EMC applications, which illustrate the applicability of the topics has an appendix reviewing the fundamentals of EMC testing and measurements refreshes the mathematical and circuits skills of the EMC engineer has useful support texts for those undertaking self–study or attempting to follow more advanced EMC texts.

1.0 MATRIX AND VECTOR ALGEBRA 9

1.1 BASIC CONCEPTS AND OPERATIONS 9

1.2 MATRIX MULTIPLICATION 11

1.3 SPECIAL MATRICES 13

1.4 MATRICES AND DETERMINANTS 14

1.5 INVERSE OF A MATRIX 17

1.6 MATRICES AND SYSTEMS OF EQUATIONS 18

1.7 SOLUTION OF SYSTEMS OF EQUATIONS 19

1.8 CRAMER S RULE 21

1.9 VECTOR OPERATIONS 22

1.9.1 Scalar Product 22

1.9.2 Vector Product 23

1.10 EMC APPLICATIONS 23

1.10.1 Crosstalk Model of Transmission Lines 23

1.10.2 Radiated Susceptibility Test 27

1.10.3 S Parameters 31

2.0 COORDINATE SYSTEMS 33

2.1 CARTESIAN COORDINATE SYSTEM 33

2.2 CYLINDRICAL COORDINATE SYSTEM 36

2.3 SPHERICAL COORDINATE SYSTEM 39

2.4 TRANSFORMATIONS BETWEEN COORDINATE SYSTEMS 41

2.4.1 Transformation between Cartesian and Cylindrical Systems 41

2.4.2 Transformation between Cartesian and Spherical Systems 45

2.5 EMC APPLICATIONS 46

2.5.1 Radiation Fields of an Electric Dipole Antenna 46

3.0 VECTOR DIFFERENTIAL CALCULUS 50

3.1 DERIVATIVES 50

3.1.1 Basic Definition and Formulas 50

3.1.2 Composite Function and Chain Rule 53

3.1.3 Partial Derivative 54

3.2 DIFFERENTIAL ELEMENTS 54

3.2.1 Differential Length Element 54

3.2.2 Differential Surface Element 58

3.2.3 Differential Volume Element 61

3.3 CONSTANT–COORDINATE SURFACES 62

3.3.1 Cartesian Coordinate System 62

3.3.2 Cylindrical Coordinate System 63

3.3.3 Spherical Coordinate System 64

3.3.4 Differential Elements on Constant Coordinate Surfaces 65

3.4 DIFFERENTIAL OPERATORS 67

3.4.1 Gradient 67

3.4.2 Divergence 69

3.4.3 Curl 71

3.4.4 Laplacian 75

3.5 EMC APPLICATIONS 76

3.5.1 Transmission–Line Equations 76

3.5.2 Maxwell s Equations in a Differential Form 78

3.5.3 Electromagnetic Wave Equation 78

4.0 VECTOR INTEGRAL CALCULUS 80

4.1 LINE INTEGRALS 80

4.1.1 Indefinite Integral and Definite Integral 80

4.1.2 Line Integral 82

4.1.3 Properties of Line Integrals 85

4.2 SURFACE INTEGRALS 89

4.2.1 Double Integrals 89

4.2.2 Surface Integrals 92

4.3 VOLUME INTEGRALS 96

4.4 DIVERGENCE THEOREM OF GAUSS 97

4.5 STOKES THEOREM 97

4.6 EMC APPLICATIONS 98

4.6.1 Maxwell s Equations in an Integral Form 98

4.6.2 Loop and Partial Inductance 99

4.6.3 Ground Bounce and Power Rail Collapse 101

5.0 DIFFERENTIAL EQUATIONS 109

5.1 FIRST ORDER DIFFERENTIAL EQUATIONS RC AND RL CIRCUITS 109

5.1.1 RC Circuit 109

5.1.2 RL Circuit 111

5.2 SECOND–ORDER DIFFERENTIAL EQUATIONS SERIES AND PARALLEL RLC CIRCUITS 114

5.2.1 Series RLC Circuit 114

5.2.2 Parallel RLC Circuit 126

5.3 HELMHOLTZ WAVE EQUATIONS 127

5.4 EMC APPLICATIONS 133

5.4.1 Inductive Termination of a Transmission Line 133

5.4.2 Ringing on a Transmission Line 136

6.0 COMPLEX NUMBERS AND PHASORS 144

6.1 DEFINITIONS AND FORMS 144

6.2 COMPLEX CONJUGATE 147

6.3 OPERATIONS ON COMPLEX NUMBERS 149

6.4 PROPERTIES OF COMPLEX NUMBERS 156

6.5 COMPLEX EXPONENTIAL FUNCTION 157

6.6 SINUSOIDS AND PHASORS 159

6.6.1 Sinusoids 159

6.6.2 Phasors 161

6.7 EMC APPLICATIONS 164

6.7.1 Maxwell s Equations in a Phasor Form 164

6.7.2 Transmission Line Equations in a Phasor Form 166

6.7.3 Magnetic Vector Potential 166

6.7.4 Radiated Fields of Electric Dipole 170

6.7.5 Electric Dipole Antenna Radiated Power 182

7.0 BASIC LAWS AND METHODS OF CIRCUIT ANALYSIS 187

7.1 FUNDAMENTAL CONCEPTS 187

7.1.1 Current 187

7.1.2 Voltage 187

7.1.3 Power 189

7.1.4 Average Power in Sinusoidal Steady–State 189

7.2 LAPLACE TRANSFORM BASICS 193

7.2.1 Definition of Laplace Transform 193

7.2.2 Properties of Laplace Transform 194

7.2.3 Inverse Laplace Transform 196

7.3 FUNDAMENTAL LAWS 198

7.3.1 Resistors and Ohm s Law 199

7.3.2 Inductors and Capacitors 203

7.3.3 Phasor Relationships for Circuit Elements 206

7.3.4 s–Domain Relationships for Circuit Elements 209

7.3.5 Impedance in Phasor Domain 212

7.3.6 Impedance in s–Domain 215

7.3.7 Kirchhoff s Laws in the Time Domain 217

7.3.8 Kirchhoff s Laws in the Phasor Domain 222

7.3.9 Kirchhoff s Laws in s Domain 223

7.3.10 Resistors in Series and Voltage Divider 224

7.3.11 Resistors in Parallel and Current Divider 229

7.3.12 Impedance Combinations and Divider Rules in Phasor Domain 237

7.4 EMC APPLICATIONS 246

7.4.1 Crosstalk between PCB Traces 246

7.4.2 Capacitive Termination of a Transmission Line 248

8.0 SYSTEMATIC METHODS OF CIRCUIT ANALYSIS 253

8.1 NODE VOLTAGE ANALYSIS 253

8.1.1 Node Analysis for the Resistive Circuits 253

8.2 MESH CURRENT ANALYSIS 257

8.2.1 Mesh Analysis for the Resistive Circuits 257

8.3 EMC APPLICATIONS 261

8.3.1 Power Supply Filters Common– and Differential–Mode Currents Circuit Model 261

9.0 CIRCUIT THEOREMS AND TECHNIQUES 271

9.1 SUPERPOSITION 271

9.2 SOURCE TRANSFORMATION 276

9.3 THEVENIN EQUIVALENT CIRCUIT 283

9.4 NORTON EQUIVALENT CIRCUIT 292

9.5 MAXIMUM POWER TRANSFER 297

9.5.1 Maximum Power Transfer – Resistive Circuits 297

9.5.2 Maximum Power Transfer – Sinusoidal Steady–State 300

9.6 TWO–PORT NETWORKS 302

9.7 EMC APPLICATIONS 318

9.7.1 Fourier Series Representation of Signals 318

9.7.2 Maximum Power Radiated by an Antenna 321

9.7.3 S Parameters 324

10.0 MAGNETICALLY–COUPLED CIRCUITS 327

10.1 SELF AND MUTUAL INDUCTANCE 327

10.2 ENERGY IN A COUPLED CIRCUIT 334

10.3 LINEAR (AIR–CORE) TRANSFORMERS 336

10.4 IDEAL (IRON–CORE) TRANSFORMERS 338

10.5 EMC APPLICATIONS 343

10.5.1 Common–Mode Choke 343

11.0 FREQUENCY–DOMAIN ANALYSIS 348

11.1 TRANSFER FUNCTION 348

11.2 FREQUENCY–TRANSFER FUNCTION 359

11.2.1 Sinusoidal Steady–State Output 360

11.3 BODE PLOTS 366

11.4 PASSIVE FILTERS 373

11.4.1 RL and RC Low–Pass Filters 374

11.4.2 RL and RC High–Pass Filters 379

11.4.3 Series and Parallel RLC Band–Pass Filters 383

11.4.4 Series and Parallel RLC Band–Reject Filters 390

11.5 RESONANCE IN RLC CIRCUITS 396

11.5.1 Resonance in Series RLC Bandpass Filter 396

11.5.2 Resonance in Parallel RLC Bandpass Filter 406

11.5.3 Resonance in other RLC Circuits 412

11.6 EMC APPLICATIONS 417

11.6.1 Non–Ideal Behavior of Capacitors and Inductors 417

11.6.2 Decoupling Capacitors 421

11.6.3 EMC Filters 431

12.0 FREQUENCY CONTENT OF DIGITAL SIGNALS 444

12.1 FOURIER SERIES AND FREQUENCY CONTENT OF SIGNALS 444

12.1.1 Trigonometric Fourier Series 444

12.1.2 Exponential Fourier Series 452

12.1.3 Spectrum of the Digital Clock Signals 455

12.1.4 Spectral Bounds on Digital Clock Signals 463

12.2 EMC APPLICATIONS 466

12.2.1 Effect of the Signal Amplitude, Fundamental Frequency, and Duty Cycle on the Frequency Content of Trapezoidal Signals 466

PART III ELECTROMAGNETICS FOUNDATIONS OF EMC 471

13.0 STATIC AND QUASI–STATIC ELECTRIC FIELDS 472

13.1 CHARGE DISTRIBUTIONS 472

13.2 COULOMB S LAW 473

13.3 ELECTRIC FIELD INTENSITY 475

13.4 ELECTRIC FIELD DUE TO CHARGE DISTRIBUTIONS 476

13.5 ELECTRIC FLUX DENSITY 477

13.6 GAUSS LAW FOR THE ELECTRIC FIELD 478

13.7 APPLICATIONS OF GAUSS LAW 479

13.8 ELECTRIC SCALAR POTENTIAL AND VOLTAGE 489

13.9 VOLTAGE CALCULATIONS DUE TO CHARGE DISTRIBUTIONS 492

13.10 ELECTRIC FLUX LINES AND EQUIPOTENTIAL SURFACES 496

13.11 MAXWELL S EQUATIONS FOR STATIC ELECTRIC FIELD 497

13.12 CAPACITANCE CALCULATIONS OF STRUCTURES 498

13.12.1 Definition of Capacitance 498

13.12.2 Calculations of Capacitance 501

13.13 ELECTRIC BOUNDARY CONDITIONS 506

13.14 EMC APPLICATIONS 514

13.14.1 Electrostatic Discharge (ESD) 514

13.14.2 Human–Body Model 524

13.14.3 Capacitive Coupling and Shielding 527

14.0 STATIC AND QUASI–STATIC MAGNETIC FIELDS 539

14.1 MAGNETIC FLUX DENSITY 539

14.2 MAGNETIC FIELD INTENSITY 540

14.3 BIOT–SAVART LAW 540

14.4 CURRENT DISTRIBUTIONS 542

14.5 AMPERE S LAW 543

14.6 APPLICATIONS OF AMPERE S LAW 544

14.7 MAGNETIC FLUX 547

14.8 GAUSS LAW FOR MAGNETIC FIELD 547

14.9 MAXWELL S EQUATIONS FOR STATIC FIELDS 548

14.10 VECTOR MAGNETIC POTENTIAL 549

14.11 FARADAYS LAW 550

14.12 INDUCTANCE CALCULATIONS OF STRUCTURES 556

14.13 MAGNETIC BOUNDARY CONDITIONS 559

14.14 EMC APPLICATIONS 565

14.14.1 Current Probes 565

14.14.2 Magnetic Flux and Decoupling Capacitors 570

14.14.3 Magnetic Coupling and Shielding 574

15.0 RAPIDLY VARYING ELECTROMAGNETIC FIELDS 583

15.1.1 Eddy Currents 583

15.2 CHARGE–CURRENT CONTINUITY EQUATION 585

15.3 DISPLACEMENT CURRENT 586

15.4 EMC APPLICATIONS 589

15.4.1 Grounding and Current Return Path 589

15.4.2 Common–Impedance Coupling 598

16.0 ELECTROMAGNETIC WAVES 602

16.1 UNIFORM WAVES TIME DOMAIN ANALYSIS 602

16.2 UNIFORM WAVES SINUSOIDAL STEADY–STATE ANALYSIS 611

16.3 REFLECTION AND TRANSMISSION OF UNIFORM WAVES AT BOUNDARIES 617

16.4 EMC APPLICATIONS 621

16.4.1 Electromagnetic Wave Shielding 622

17.0 TRANSMISSION LINES 631

17.1 TRANSIENT ANALYSIS 631

17.1.1 Reflections on Transmission Lines 635

17.1.2 Bounce Diagram 654

17.1.3 Reflections at the Inductive Load 660

17.1.4 Reflections at the Capacitive Load 663

17.1.5 Transmission Line Discontinuity 666

17.2 STEADY–STATE ANALYSIS 675

17.2.1 Lossy Transmission Lines 675

17.2.2 Standing Waves 680

17.3 S PARAMETERS 691

17.4 EMC APPLICATIONS 701

17.4.1 Crosstalk between PCB traces 701

17.4.2 LISN Impedance Measurement 711

17.4.3 Preamp Gain and Attenuator Loss Measurement 717

18.0 ANTENNAS AND RADIATION 721

18.1 BRIDGE BETWEEN THE TRANSMISSION LINE AND ANTENNA THEORY 721

18.2 HERTZIAN DIPOLE ANTENNA 724

18.3 FAR FIELD CRITERIA 727

18.3.1 Wire–Type Antennas 728

18.3.2 Surface–Type Antennas 730

18.4 HALF–WAVE DIPOLE ANTENNA 732

18.5 QUARTER–WAVE MONOPOLE ANTENNA 735

18.6 IMAGE THEORY 736

18.7 DIFFERENTIAL– AND COMMON–MODE CURRENTS AND RADIATION 740

18.7.1 Differential– and Common–Mode Currents 740

18.7.2 Radiation from Differential– and Common–Mode Currents 743

18.8 COMMON MODE CURRENT CREATION 750

18.8.1 Circuits with a Shared Return Path 751

18.8.2 Differential Signaling 755

18.8.3 Common–Mode Current Creation 758

18.9 ANTENNA CIRCUIT MODEL 760

18.9.1 Transmitting–Mode Model 760

18.9.2 Receiving–Mode Model 762

18.10 EMC APPLICATIONS 764

18.10.1 EMC Antenna Measurements 764

18.10.2 Antenna VSWR and Impedance Measurements 767

18.10.3 Comb Transmitter Measurements 771

APPENDIX A EMC TESTS AND MEASUREMENTS 773

A.1 INTRODUCTION FCC PART 15 AND CISPR 22 STANDARDS 773

A.1.1 Peak vs. Quasi–Peak vs. Average Measurements 773

A1.2 FCC and CISPR 22 Limits 776

A.2 CONDUCTED EMISSIONS 782

A.2.1 FCC and CISPR 22 Voltage Method 785

A.2.2 CISPR 25 Voltage Method 787

A.2.3 CISPR 25 Current Probe Method 791

A.3 RADIATED EMISSIONS 794

A.3.1 Open–Area Test Site (OATS) Measurements 795

A.3.2 Semi–Anechoic Chamber Measurements 797

A.4 CONDUCTED IMMUNITY ISO 11452–4 805

A.4.1 Substitution Method 808

A.4.2 Closed–Loop Method with Power Limitation 810

A.5 RADIATED IMMUNITY 812

A.5.1 Radiated Immunity ISO 11452–11 812

A.5.2 Radiated Immunity ISO 11452–2 816

A.6 ELECTROSTATIC DISCHARGE (ESD) 819

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.