Electromagnetic Theory for Electromagnetic Compatibility Engineers

386 Pages·2013·7.2 MB·English

Electromagnetic Theory
for Electromagnetic
Compatibility Engineers
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Electromagnetic Theory
for Electromagnetic
Compatibility Engineers

Tze-Chuen Toh
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CRC Press
Taylor & Francis Group
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Version Date: 20131009
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To my wise and inspirational parents Nancy and Swee-Hock, my endearing
wife and muse Linnie, my cherished children by marriage, Courtney,

Allison, and Paul . . . and in memory of our cheeky dog Lucky.
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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
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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
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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
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