Transmission Lines in Digital and Analog Electronic Systems

In the last 30 years there have been dramatic changes in electrical technology--yet the length of the undergraduate curriculum has remained four years. Until some ten years ago, the analysis of transmission lines was a standard topic in the EE and CpE undergraduate curricula. Today most of the undergraduate curricula contain a rather brief study of the analysis of transmission lines in a one-semester junior-level course on electromagnetics. In some schools, this study of transmission lines is relegated to a senior technical elective or has disappeared from the curriculum altogether. This raises a serious problem in the preparation of EE and CpE undergraduates to be competent in the modern industrial world. For the reasons mentioned above, today's undergraduates lack the basic skills to design high-speed digital and high-frequency analog systems. It does little good to write sophisticated software if the hardware is unable to process the instructions. This problem will increase as the speeds and frequencies of these systems continue to increase seemingly without bound. This book is meant to repair that basic deficiency.

Preface xi

1 Basic Skills and Concepts Having Application to Transmission Lines 1

1.1 Units and Unit Conversion 3

1.2 Waves, Time Delay, Phase Shift, Wavelength, and Electrical Dimensions 6

1.3 The Time Domain vs. the Frequency Domain 11

1.3.1 Spectra of Digital Signals 12

1.3.2 Bandwidth of Digital Signals 17

1.3.3 Computing the Time-Domain Response of Transmission Lines Having Linear Terminations Using Fourier Methods and Superposition 27

1.4 The Basic Transmission-Line Problem 31

1.4.1 Two-Conductor Transmission Lines and Signal Integrity 32

1.4.2 Multiconductor Transmission Lines and Crosstalk 41

Problems 46

Part I Two-Conductor Lines and Signal Integrity 49

2 Time-Domain Analysis of Two-Conductor Lines 51

2.1 The Transverse Electromagnetic (TEM) Mode of Propagation and the Transmission-Line Equations 52

2.2 The Per-Unit-Length Parameters 56

2.2.1 Wire-Type Lines 57

2.2.2 Lines of Rectangular Cross Section 68

2.3 The General Solutions for the Line Voltage and Current 71

2.4 Wave Tracing and Reflection Coefficients 74

2.5 The SPICE (PSPICE) Exact Transmission-Line Model 84

2.6 Lumped-Circuit Approximate Models of the Line 91

2.7 Effects of Reactive Terminations on Terminal Waveforms 92

2.7.1 Effect of Capacitive Terminations 92

2.7.2 Effect of Inductive Terminations 94

2.8 Matching Schemes for Signal Integrity 96

2.9 Bandwidth and Signal Integrity: When Does the Line Not Matter? 104

2.10 Effect of Line Discontinuities 105

2.11 Driving Multiple Lines 111

Problems 113

3 Frequency-Domain Analysis of Two-Conductor Lines 121

3.1 The Transmission-Line Equations for Sinusoidal Steady-State Excitation of the Line 122

3.2 The General Solution for the Terminal Voltages and Currents 123

3.3 The Voltage Reflection Coefficient and Input Impedance to the Line 123

3.4 The Solution for the Terminal Voltages and Currents 125

3.5 The SPICE Solution 128

3.6 Voltage and Current as a Function of Position on the Line 130

3.7 Matching and VSWR 133

3.8 Power Flow on the Line 134

3.9 Alternative Forms of the Results 137

3.10 The Smith Chart 138

3.11 Effects of Line Losses 147

3.12 Lumped-Circuit Approximations for Electrically Short Lines 161

3.13 Construction of Microwave Circuit Components Using Transmission Lines 167

Problems 170

Part II Three-Conductor Lines and Crosstalk 175

4 The Transmission-Line Equations for Three-Conductor Lines 177

4.1 The Transmission-Line Equations for Three-Conductor Lines 177

4.2 The Per-Unit-Length Parameters 184

4.2.1 Wide-Separation Approximations for Wires 185

4.2.2 Numerical Methods 196

Problems 205

5 Solution of the Transmission-Line Equations for Three-Conductor Lossless Lines 207

5.1 Decoupling the Transmission-Line Equations with Mode Transformations 208

5.2 The SPICE Subcircuit Model 210

5.3 Lumped-Circuit Approximate Models of the Line 227

5.4 The Inductive-Capacitive Coupling Approximate Model 232

Problems 236

6 Solution of the Transmission-Line Equations for Three-Conductor Lossy Lines 239

6.1 The Transmission-Line Equations for Three-Conductor Lossy Lines 240

6.2 Characterization of Conductor and Dielectric Losses 244

6.2.1 Conductor Losses and Skin Effect 244

6.2.2 Dielectric Losses 248

6.3 Solution of the Phasor (Frequency-Domain) Transmission-Line Equations for a Three-Conductor Lossy Line 251

6.4 Common-Impedance Coupling 260

6.5 The Time-Domain to Frequency-Domain Method 261

Problems 270

Appendix A Brief Tutorial on Using PSPICE 273

Index 295

"All mathematical calculations are performed clearly and in a very good manner. From this point of view, the
book is very useful for students and teachers." (Zentralblatt MATH, 2011)

CLAYTON R. PAUL has been the Sam Nunn Eminent Chair in Aerospace Engineering and a professor in the Department of Electrical & Computer Engineering at Mercer University since 1997. He is an emeritus professor in the Department of Electrical Engineering at the University of Kentucky, where he taught for twenty-seven years.

A MUCH-NEEDED PRIMER ON ALL ASPECTS OF TRANSMISSION LINES FOR ELECTRIC AND COMPUTER ENGINEERING GRADUATES

Most of today's electrical engineering and computer engineering graduates lack a critically important skill: the analysis of transmission lines. They need this basic knowledge in order to be able to design high-speed digital and high-frequency analog systems—and this problem will only get worse as the speeds and frequencies of these systems continue to increase. This important text is the remedy. It prepares readers for increasingly difficult design problems in today's ever-changing high-speed digital world, focusing on signal integrity and crosstalk.

Class-tested under the author's expert guidance at Mercer University, the book starts by reviewing the fundamental concepts of waves, wavelength, time delay, and electrical dimensions, as well as the bandwidth of digital signals and its relation to the pulse rise/fall times. It then explains two-conductor transmission lines and designing for signal integrity, addressing the time-domain analysis of those transmission lines and the corresponding analysis in the frequency domain. The terminal voltages and currents of lines with various source waveforms and resistive terminations are computed by hand via wave tracing. This gives considerable insight into the general behavior of transmission lines in terms of forward- and backward-traveling waves and their reflections. The effect of line losses including skin effect in the line conductors and dielectric losses in the surrounding dielectric are increasingly becoming critical, and their detrimental effects are discussed.

Next, the book repeats these topics for three-conductor lines in terms of the important detrimental effects of crosstalk between transmission lines, explaining the transmission-line equations for lossless lines, the important per-unit-length matrices of the inductance and capacitance of the lines, and the solution of three-conductor, lossless lines via mode decoupling. The final chapter concludes by investigating the effects of the line losses on the crosstalk of these three-conductor lines.

Each chapter concludes with numerous problems for the reader to practice his/her understanding of the material. An Appendix contains a brief tutorial on SPICE (PSPICE), an important computational tool that is used extensively throughout the book. A companion website features several computer programs used and described in this book for computing the per-unit-length parameter matrices and a subcircuit model for three-conductor lines, as well as two MATLAB programs for computing the Fourier components of a digital waveform and two versions of PSPICE.

This book is intended as a textbook for a senior/first-year graduate-level course in transmission lines in electrical engineering and computer engineering curricula. It is also essential for industry professionals as a compact review of transmission line fundamentals.