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Library of Congress Cataloging-in-Publication Data:

Paul, Clayton R.

Transmission lines in digital systems for EMC practitioners / Clayton R. Paul.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-118-14399-5 (hardback)

1. Electromagnetic compatibility. 2. Telecommunication lines. I. Title.

TK7867.2.P383. 2012

621.382'24–dc23

2011021000

oBook ISBN: 9781118145579

ePDF ISBN: 9781118145548

ePub ISBN: 9781118145562

MOBI ISBN: 9781118145555

This book is dedicated to the humane and compassionate treatment of animals

and my beloved pets:

Patsy, Dusty, Megan, Tinker, Bunny, Winston, Sweetheart, Lady, Tigger,
Beaver, Ditso, Buru, Old Dog, Zip, Tara, Timothy, Kiko, Valerie, Red, Sunny,
Johnny, Millie, Molly, Angel, Autumn, and Shabby.

Those readers who are interested in the humane and compassionate
treatment of animals are encouraged to donate to

The Clayton and Carol Paul Fund for Animal Welfare
c/o the Community Foundation of Central Georgia
277 MLK, Jr. Blvd.

Suite 303

Macon, GA 31202

Preface

Most of the numerous textbooks I have published were intended for class instructional books for electrical engineering (EE) and computer engineering (CpE) courses in a university environment. I decided to write this book for the industrial professional. My work has been in the field of electromagnetic compatibility (EMC), known more commonly as interference in electronic systems. In the course of my teaching, I have also had the pleasure of working with many EMC professionals. It is to this group of professionals that I have focused the book.

I have written a brief but comprehensive book covering the set of transmission-line skills that EMC practitioners today require in order to be successful in high-speed digital electronics. The basic skills in the book weren't studied in most curricula some ten years ago. The rapidly changing digital technology has created this demand for a discussion of new analysis skills, particularly for the analysis of transmission lines where the conductors that interconnect the electronic modules have become “electrically large,” longer than a tenth of a wavelength, which are becoming increasingly important. Crosstalk between the lines is also rapidly becoming a significant problem in getting modern electronic systems to work satisfactorily. Hence this small volume is concentrated on modeling “electrically long” connection conductors where previously used Kirchhoff's voltage and current laws and lumped-circuit modeling have become obsolete because of the increasing speeds of modern digital systems. One important exception is Chapter 5, where electrically short lines are considered exclusively when we consider the use of shielded lines and twisted pairs of wires to eliminate or reduce crosstalk for electrically short lines.

Until as recently as some ten years ago, digital system clock speeds and data rates were in the low megahertz range. The “lands” on printed circuit boards (PCBs) that interconnect the electronic modules had little or no impact on the proper functioning of those electronic circuits. Today, the clock and data speeds have moved into the low gigahertz range. As the demand for faster data processing continues to escalate, these speeds will no doubt continue to increase into the gigahertz frequency range. In addition, analog communication frequencies have also moved steadily into the gigahertz range and will no doubt continue to increase. Although the “physical dimensions” of these lands and the PCBs supporting them have not changed significantly over the intervening years, the spectral content of the signals they carry has increased significantly. Because of this, the “electrical dimensions” (in wavelengths) of the lands have increased to the point where these “interconnects” have a significant effect on the signals they are carrying, so that just getting the systems to work properly has become a major design problem. Prior to some ten years ago, these interconnects could be reliably modeled with lumped-circuit models that are easily analyzed using Kirchhoff's voltage and current laws and other lumped-circuit analysis methods. Because these interconnects are becoming “electrically long,” lumped-circuit modeling of them is becoming inadequate and gives erroneous answers. Most of the interconnect conductors must now be treated as distributed-circuit transmission lines.

In Chapter 1, the increasingly important fundamental concepts of waves, wavelength, time delay, and electrical dimensions are discussed. In addition, the bandwidth of digital signals and its relation to pulse rise and fall times are discussed. The effect of electrically long conductors on signal integrity is discussed.

Chapter 2 covers the time-domain analysis of two-conductor transmission lines. The transmission-line equations are derived and solved, and the important concept of characteristic impedance is covered. The important per-unit-length parameters of inductance and capacitance that distinguish one line from another are obtained for typical lines. 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 reflection. The SPICE computer program and its personal computer version, PSPICE, contains an exact model for a two-conductor lossless line and is discussed as a computational aid in solving for the transmission-line terminal voltages and currents. SPICE is an important computational tool, since it provides a determination of the terminal voltages and currents for practical linear and nonlinear terminations such as CMOS and bipolar devices, for which hand analysis is very formidable. Matching schemes for achieving signal integrity are covered, as are the effects of line discontinuities. Chapter 3 covers the corresponding analysis in the frequency domain. The important analog concepts of input impedance to the line and high-frequency modeling of electronic circuits are also discussed.

The remaining chapters, Chapters 4, 5, and 6, cover crosstalk between adjacent transmission lines. Chapter 4 covers the derivation of the multiconductor transmission line (MTL) equations, consisting of lines having three conductors and the crosstalk between these lines. The derivation of the per-unit-length parameters in the 2×2 inductance and capacitance matrices, L and C, for three-conductor lines are discussed either in an approximation fashion for widely spaced lines or in terms of computer programs for handling these difficult calculations. These computer programs can be downloaded from the John Wiley ftp site:

ftp://ftp.wiley.com/public/sci_tech_med/multiconductor_transmission/

Their use is discussed for various cross-sectional geometries.

Chapter 5 discusses an approximate solution of the MTL equations for electrically short lines. This model is not only easy to use to compute the crosstalk in an approximate fashion but also illustrates the use of (1) shielded wires and (2) twisted pairs of wires for eliminating crosstalk. Numerous experimental results are shown that verify the model. The effect of pigtails in degrading the effect of shielded wires is shown along with experimental results.

Finally, Chapter 6 discusses an exact PSPICE subcircuit for the solution of any lossless MTL. Several experimental results that verify the accuracy of this model are shown. A computer program, SPICEMTL, that generates a PSPICE subcircuit model that can readily be embedded in a SPICE program to provide the exact solution can be downloaded from the ftp site.

Several important features of this textbook are (1) the basics of transmission-line fundamentals, (2) the numerous experimental results that illustrate and verify the mathematical results, and (3) the availability of computer programs that facilitate the solution of transmission lines for determining signal integrity as well as crosstalk.

The appendix gives a brief tutorial of SPICE (PSPICE), which is used extensively throughout the book.

Clayton R. Paul

Macon, Georgia