Book Review

Title: Analysis of Multiconductor Transmission Lines – 2nd Edition
Author: Clayton R. Paul
Publisher: John Wiley, 2008
ISBN: 978-0-470-13154


It is difficult for me to make a fresh review of this Second Edition of the original book. Not only because I learned the majority of the content from the direct voice of the author, but also because its first edition has been used for several years as one of the reference text books in my courses “Basic Electric Principles” and “Signal Integrity” taught to undergraduate and graduate students at the University of L’Aquila (L’Aquila, Italy).
The text, in this new edition, has undergone a significant reorganization with respect to the previous edition. I fully share the strong opinion of the author that organization of subject material into a logical and well thought-out form is perhaps the most important pedagogical technique in a reader’s learning process. The first aspect is the emphasis on a two-conductor line case. Each broad analysis topic (i.e. per-unit-length parameters, frequency or time domain analysis, etc.) now has a chapter concerning two conductor lines followed immediately by a chapter on Multiconductor Transmission Line (MTL) for that topic. This allows the reader and/or the instructor to choose his/her emphasis either on two-conductor lines or MTL or both. In my opinion this new organization also makes it easier for the reader to understand the analysis of MTLs.

In addition to this significant reorganization of the material, the text now contains important developments in analysis methods that have been developed in the intervening 13 years since the first edition was published. Digital technology has virtually taken over the field of electronics. The clock and data speeds in those digital systems have accelerated at an astonishing rate. This has caused most of the signal interconnects in those systems, which were inconsequential from a standpoint of transmission-line effects 13 years ago, to now become critical to the functionality of those systems. Hence, the current emphasis is on the development of macromodels and on “model order reduction” or MOR for the time-domain analysis of these high-density interconnects. Generation of macromodels that compactly describe these interconnects from a port standpoint requires the determination of the transfer functions representing those interconnects. Typical distributed-parameter interconnects have an enormous number of poles such that the transfer functions are ratios of very high order polynomials in the Laplace transform variable. The current analysis methods focus on MOR methods that seek to determine a highly reduced number of dominant poles of those transfer functions, thereby simplifying the analysis. MOR methods such as recursive convolution, complex frequency hopping (CFH), Pade, asymptotic waveform expansion (AWE), and vector fitting (VF) as well as the synthesis of lumped-circuit models are the current methods of choice. Chapters 8 and 9, which cover the time-domain analysis of two-conductor lines and MTLs, respectively, have been considerably expanded to now include those topics among many others that have been developed in the intervening years.
The second edition of this text is now divided into 13 chapters.


Chapter 1 discusses the background and rationale for the use of MTLs. The general properties of the TEM mode of propagation are discussed, and the transmission-line equations are derived for two-conductor lines using several methods. The various classifications of MTLs (uniform, lossless, and homogeneous medium) are discussed along with the restrictions on the use of the TEM mode. An important addition to this chapter has been made in the second edition: the discussion of the time domain versus the frequency domain. This is a crucial aspect for any Electrical Engineer’s (EE) ability to design electronic systems. The chapter presents a very useful method for the time-domain analysis of a linear system such as an MTL having linear terminations by computing the frequency-domain transfer function, decomposing the periodic or non-periodic input signal into its Fourier spectral components, passing those through the system, and recombining in time at the output. This allows a straightforward incorporation of frequency-dependent losses of the conductors and the surrounding medium. These frequency-dependent losses complicate the direct time-domain solution of the transmission-line equations.


Chapter 2 provides a derivation of the two-conductor transmission-line equations along with the general properties of the per-unit-length parameters in those equations, and Chapter 3 discusses these topics for MTLs.


Chapter 4 discusses the derivation of the per-unit-length parameters of inductance, capacitance, resistance, and conductance for two-conductor lines, whereas Chapter 5 repeats this for MTLs. In both chapters, numerical methods for the determination of these important per-unit-length parameters are discussed in detail.


Chapter 6 discusses the frequency-domain solution of the transmission-line equations, and Chapter 7 repeats this for MTLs. The discussion of two-conductor transmission lines in Chapter 6 has been expanded considerably over the first edition coverage and now constitutes a traditional undergraduate coverage.

Chapter 8 discusses and expands (with respect to the first edition) the time-domain analysis of two-conductor lines, and Chapter 9 repeats this for MTLs. In addition, Chapter 8 now includes an extensive discussion of methods for achieving signal integrity (SI) in high-speed digital inter-connects. The finite-difference, time-domain (FDTD) solution method is developed as is the time-domain to frequency-domain transformation (TDFD) method. Both of these allow the inclusion of frequency-dependent losses. Detailed discussions of recursive convolution and MOR techniques such as Pade methods are now included in Chapter 8.


Chapter 9 on the time-domain analysis of MTLs now includes extensive discussion of MOR methods such as the generalized method of characteristics, Pade methods, asymptotic waveform expansion, complex frequency hopping, and vector fitting. In addition, Chapter 9 now includes the development of the FDTD method for dynamic terminations.


Chapter 10 gives the symbolic or literal solution of perhaps the only MTL that admits a closed-form solution in terms of symbols: a three-conductor lossless line in a homogeneous medium. This chapter is virtually the same as in the first edition although it has been revised.


Chapter 11 gives the frequency-domain and time-domain solutions for two-conductor lines with incident field illumination. Chapter 12 repeats that for MTLs. The emphasis is on uniform plane-wave excitation as from a distant antenna or a lightning stroke.
Finally, Chapter 13 discusses the analysis of interconnected transmission-line networks such as branched cables.


Two appendixes enrich the book. Appendix A contains the description of numerous FORTRAN computer codes that implement all the techniques in this text. They can be downloaded from the Wiley ftp site. This is perhaps the only part of this book that can be improved. Although FORTRAN is a solid and portable language, it is not well known to actual students who generally prefer codes such as MATLAB, MATHCAD or similar. Appendix B is new to this edition and contains a brief but thorough tutorial on the PSPICE circuit analysis program.
For those of us that in one way or another work with transmission-lines, this is a valuable book to read and add to your library.


Antonio Orlandi (M’90-SM’97-F’07) received the Laurea degree in Electrical Engineering from the University of Rome “La Sapienza”, Italy, in 1988. He was with the Department of Electrical Engineering, University of Rome “La Sapienza” from 1988 to 1990. Since 1990, he has been with the Department of Electrical Engineering of the University of L’Aquila where he is currently Full Professor and Chair of the UAq EMC Laboratory. Author of more than 170 technical papers, he has published in the field of electromagnetic compatibility in lightning protection systems and power drive systems. Current research interests are in the field of numerical methods and modeling techniques to approach signal/power integrity, and EMC/EMI issues in high speed digital systems. He may be reached at EMC

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