Electromagnetic Theory for Electromagnetic Compatibility Engineers K15149_Book.indb 1 10/18/13 10:43 AM Electromagnetic Theory for Electromagnetic Compatibility Engineers Tze-Chuen Toh K15149_Book.indb 3 10/18/13 10:43 AM CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20131009 International Standard Book Number-13: 978-1-4665-1816-2 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. 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K15149_Book.indb 5 10/18/13 10:43 AM Contents Preface ......................................................................................................................ix About the Author ...................................................................................................xi Notations ..............................................................................................................xiii 1 Brief Review of Maxwell’s Theory .............................................................1 1.1 Electrostatics ..........................................................................................1 1.2 Magnetostatics .....................................................................................12 1.3 Maxwell’s Equations ...........................................................................16 1.4 Electromagnetic Waves ......................................................................21 1.5 Worked Problems ................................................................................32 References .......................................................................................................34 2 Fourier Transform and Roll-Off Frequency ............................................35 2.1 Fourier Series .......................................................................................35 2.2 Fourier Transform ...............................................................................40 2.3 Roll-Off Frequency .............................................................................46 2.4 Frequency Response and Filter Theory: A Primer .........................50 2.5 Worked Problems ................................................................................60 References .......................................................................................................65 3 Boundary Value Problems in Electrostatics ............................................67 3.1 Electromagnetic Boundary Conditions ...........................................67 3.2 Image Theory Revisited .....................................................................71 3.3 Multipole Expansion ...........................................................................80 3.4 Steady-State Currents .........................................................................84 3.5 Duality ..................................................................................................88 3.6 Worked Problems ................................................................................91 References .......................................................................................................98 4 Transmission Line Theory ........................................................................101 4.1 Introduction .......................................................................................101 4.2 Transmission Line Equations ..........................................................102 4.3 Characteristic Impedance and the Smith Chart ...........................108 4.4 Impedance Matching and Standing Waves ..................................122 4.5 Worked Problems ..............................................................................135 References .....................................................................................................141 5 Differential Transmission Lines .............................................................143 5.1 Differential Pair: Odd and Even Modes ........................................143 5.2 Impedance Matching Along a Differential Pair ...........................157 vii K15149_Book.indb 7 10/18/13 10:43 AM viii Contents 5.3 Field Propagation Along a Differential Pair .................................160 5.4 Worked Problems ..............................................................................167 References .....................................................................................................182 6 Cross-Talk in Multiconductor Transmission Lines .............................183 6.1 Reciprocity Theorem and Mutual Capacitance ............................183 6.2 Mutual Inductance and Mutual Impedance .................................192 6.3 Multiconductor Transmission Lines and Cross-Talk ...................199 6.4 S-Parameters: Scattering Parameters .............................................210 6.5 Worked Problems ..............................................................................218 References .....................................................................................................221 7 Waveguides and Cavity Resonance ........................................................223 7.1 Parallel Plate Guides .........................................................................223 7.2 Rectangular Waveguides .................................................................236 7.3 Cavity Resonance ..............................................................................243 7.4 Worked Problems ..............................................................................251 References .....................................................................................................259 8 Basic Antenna Theory ...............................................................................261 8.1 Radiation from a Charged Particle .................................................261 8.2 Hertzian Dipole Antenna ................................................................263 8.3 Magnetic Dipole Antenna ................................................................270 8.4 Microstrip Antenna: A Qualitative Overview ..............................276 8.5 Array Antenna and Aperture Antenna .........................................280 8.6 Worked Problems ..............................................................................295 References .....................................................................................................302 9 Elements of Electrostatic Discharge .......................................................303 9.1 Electrostatic Shielding ......................................................................303 9.2 Dielectric Properties: the Kramers–Kronig Relations .................305 9.3 Beyond Classical Theory ..................................................................311 9.4 Dielectric Breakdown .......................................................................319 9.5 Worked Problems ..............................................................................324 References .....................................................................................................328 Appendix A .........................................................................................................331 Index .....................................................................................................................365 K15149_Book.indb 8 10/18/13 10:43 AM Preface The irony of a preface is that it is often ignored by the reader; notwithstand- ing, it is occasionally employed by authors to justify formally the existence of their work. This primer is an outgrowth, and indeed a much expanded ver- sion, of a course I gave at Gateway Inc. to help electromagnetic compatibility (EMC) engineers be less dependent upon empirical data when solving puz- zling electromagnetic interference (EMI) problems. In short, it is a vehicle to transform practical engineers into theoretical engineers, and in particular, to cultivate academic skills left by the wayside after they have completed their tertiary education. Furthermore, as this course is designed for practical applications, historical developments are bypassed altogether. This set of lecture notes is written at a level equivalent to that of third- or fourth-year Honors undergraduate study. It is, in essence, a refresher for professional engineers who already have their Bachelor’s degree and to reacquaint them with the power of mathematical rigor in solving real- world problems. Conversely, it also serves to introduce undergraduates to the basics of EMC encountered in the technology industry. It is completely self-contained and designed with self-study in mind. For a condensed course, the recommended topics to cover are Chapters 1, 4, 5, and 6. Having pointed this out, I must nevertheless emphasize that each topic presented herein is essential for EMC engineers to be competent EMC theoreticians. Clearly, in a brief course such as this, it is impossible to cover every aspect of electromagnetic theory. A list of references upon which parts of this course are based is provided for the reader who wishes to delve deeper into topics glossed over for want of space. More importantly, it was written specifically for theoretical physicists and mathematicians new to the field of EMC, signal integrity and RF design. Electromagnetic theory is the simplest theory among the four known forces of the universe. Indeed, it is the first step toward finding the holy grail of the- oretical physics: the grand unification of the four known forces. Maxwell’s theory achieved the unification of the electric field and the magnetic field into a single entity called the electromagnetic field. Notwithstanding, its underlying mathematical structure is similar to the other three forces—the weak nuclear force, strong nuclear force, and gravitational force—to wit, gauge theory. Gauge theory provides a common arena for the foundational description of these forces. However, studying gauge theory, fascinating as it is, will take the reader too far afield from the original intent of these notes. Engineers, after all, are practical and down to earth, and hold little interest in the more abstruse mathematical guise of nature. The primary purpose of this monograph is to integrate theory with prac- ticable engineering applications. As a case in point, it is often difficult to ix K15149_Book.indb 9 10/18/13 10:43 AM