Title: Electromagnetic Field Interaction with Transmission Lines
Authors: F. Rachidi and S. V. Tkachenko
Publisher: WIT Press, June 2008
ISBN: 9781845640637
The evaluation of electromagnetic field coupling to transmission lines is an important problem in electromagnetic compatibility. Very often use is made of the transmission line (TL) approximation which applies to uniform transmission lines with electrically small crosssectional dimensions, where the dominant mode of propagation is transverse electromagnetic (TEM). Antennamode currents and higherorder modes appearing at higher frequencies are neglected in the classical TL theory.
Since the development of the TL theory and the derivation of the socalled telegrapher’s equations, significant progress has been achieved in the understanding of wave propagation along transmission lines. In 1965, Taylor, Satterwhite and Harrison extended the classical TL equations to include the presence of an external electromagnetic field. Their fieldtotransmission coupling equations – as well as their equivalent formulations derived later – have been successfully applied to solve a large range of problems dealing with EMP and lightning interaction with power and telecommunication lines.
The unabated increase in the operating frequency of electronic products and the emergence of sources of disturbances with higher frequency content (such as High Power Microwave and UltraWide Band systems) have led to a breakdown of the TL approximation’s basic assumptions for a number of applications. In the last decade or so, the generalization of the TL theory to take into account high frequency effects has emerged as an important topic of study in electromagnetic compatibility. This effort resulted in the elaboration of the socalled ‘generalized’ or ‘fullwave’ TL theory, which incorporates high frequency radiation effects, while keeping the relative simplicity of TL equations.
This book has two main intentions, in my opinion perfectly achieved: to cover the classical Transmission Line (TL) theory and to provide a reference source for its recent enhancements. This is offered by using examples spanning from the high voltage lines to the nanointerconnections.
Another characteristic of this book that I appreciate is the large quantity of application results. They are used as conceptual tools to guide the reader towards the technical conclusions or show how the solutions proposed have an impact on the overall system. At the same time, the black and white edition does not help the full readability of the graphs.
The book is composed into two parts and seven chapters totalling about 254 pages. All chapters contain several examples to illustrate the concepts and some of them can be used as a benchmark to evaluate the accuracy and speed of TL commercial tools that are available today. A well done index at the end of the book helps the reader in finding specific topics.
Chapter 1 discusses the assumptions of the TL theory and presents the derivation of the fieldtotransmission line coupling equations. Three different but completely equivalent approaches that have been proposed to describe electromagnetic field coupling to transmission lines are also presented and discussed; including the “Taylor, Satterwhite, Harrison” model, the “Agrawal, Price, Gurbaxani” model and the “Rachidi” model. This comparison is very instructive and is one of the precious contents of the book. This chapter also presents the extension to a Multiconductor Line (MTL) in time and frequency domain.
Chapters 2 and 3 deal, respectively, with the specific cases of overhead multiconductor lines and buried cables. Various factors influencing the pulse propagation and crosstalk along multiconductor systems are discussed, and methods for the calculation of the line longitudinal and transverse line parameters are presented.
Part II presents different approaches developed to generalize the TL theory in order to include high frequency effects.
In Chapter 4, a TLlike pair of equations is derived under the thinwire approximation for evaluating currents and potentials induced by external electromagnetic fields on a wire of a given geometric form above a perfect conducting ground. Based on perturbation theory, an iterative procedure is proposed to solve the derived coupling equations, where the zeroiteration term is determined by using the classical TL approximation.
Chapter 5 presents an efficient hybrid method to compute high frequency electromagnetic field coupling to long, loaded lines including lumped discontinuities.
Chapter 6 shows that the classical TL theory may be included in a more general model based on an integral formulation of the general fullwave problem. The derived general model is applied to conventional highspeed microelectronics, as well as to nanoelectronics applications.
Chapter 7 deals specifically with high frequency electromagnetic field coupling to buried wires. Two approaches, one in the frequency domain based on the Pocklington’s integral equation, and the other in the time domain using the Hallen integral equation, are proposed and discussed.
This book it is very useful for graduate students and professionals concerned about transmission line theory and electromagnetic field interaction with transmission lines, with special emphasis on high frequency effects. EMC
Book Review
Al Ruehli, Guest Reviewer
Title: INDUCTANCE Loop and Partial
Author: Clayton R. Paul
Publisher: John Wiley, 2010
ISBN: 9780470461884
In 1970, I was privileged to meet Professor Frederick Grover, the author of the book Inductance Calculations: Working Formulas and Tables, Dover, 1962. He was then 81 and had just returned from a trip to Spain. His book had a special value to me because he had autographed it for me. The world of integrated circuits was quite foreign to him because he had spent his career working on large structures as they appear in power engineering. Most of Grover’s book is dedicated to inductance computations using a slide rule; the advantages of an electronic computer were not then available to him. This contrasts with current technology. We can now compute problems with thousands of partial inductances.
So why do we all occasionally use this old book – first issued in 1945? The answer is simple. No other book as comprehensive has been written since then on inductance computations that would or could replace Grover’s book with a 21st century edition. Fortunately, Dr. Clayton Paul’s book, INDUCTANCE: Loop and Partial, closes this gap. His book, however, is more than a simple replacement of Grover’s book. Personally, I prefer self contained books such as this because I don’t have to research other books in order to look up derivations. Dr. Paul’s book gives some quite difficult derivations of interest for computing partial inductances. The book is carefully written and can be used easily for selfeducation.
Chapter 1 starts with a short history on inductance and on the basics of lumped circuits. This short chapter ends with two excellent examples demonstrating why partial inductances are important.
The reader is first given a review of the fundamentals relevant for inductance computations in Chapter 2. Magnetic field calculations which, of course, are closely related to inductances are considered for typical geometries such as wires and loops. The current distribution and magnetic fields for a coaxial structure are analyzed in detail. Fortunately, the vector magnetic potential is carefully considered as it represents a powerful tool for inductance computations. Again, several relevant geometries are considered in view of the applications at hand. An important aspect for inductance computations is the solution of the complex integrals which must be evaluated in the process. The author consistently solves some of the difficult integrals required. The chapter ends with the energy stored in the magnetic field, which in some cases produces a convenient formula for inductance computations. Images for currents and the current continuity follow as relevant topics.
Chapter 3 is again dedicated to fundamentals. The derivations of the quasistatic aspects of inductance such as Faraday’s Law are considered. Time delay must be small for quasistatic models.
For this reason, a small section is dedicated to this aspect. Another introduction to the dynamic solution of Maxwell’s equation using vector potentials is given leading to an excellent explanation of the Poynting Theorem based on the energy stored in the electrical and magnetic fields. These sections are again easy to read as are all the derivations in this book. The last section in this chapter considers a loop where the induced voltage is derived in terms of the time derivative of the magnetic field and the vector potential.
Dr. Paul dedicates Chapter 4 to loop inductance. Loop inductance is restricted to a small class of fixed geometries. Circular loops are structures for which this concept seems to be more relevant. This case is treated well in this chapter. I personally do not have much use for loop inductance since I believe that partial inductances are much more general. I think that this opinion is also clearly expressed in this book. The case for multiple loop as well as twodimensional coaxial structures is considered here. Fortunately, there are a few geometries which have exact closed form solutions. An interesting case of this is represented by coaxial loops which again are treated well in this book.
One of the most important parts of this book is Chapter 5. First, the concept of partial element circuits is introduced with a rectangular loop example in terms of partial inductances. This example is quite suitable for showing how partial inductances work. The physical meaning of the partial inductance is given next. We all should be interested in how some of the approximate formulae such as those in Grover’s book are derived. The author shows examples for several of them. An interesting aspect is how the Weber approximation in Reference [11] is applied to avoid the singularity in the computation for partial self inductances. Mutuals are computed for wire configurations which occur in practical geometries. An interesting case is the computation of the partial inductance for nonparallel wires. Dr. Paul gives the detailed derivation for the difficult case where segments of wires are not parallel, a result that can also be found in Grover. However, here the author gives an intricate and detailed derivation of the computation which is exact for zero diameter wires.
Chapter 6 is mostly devoted to rectangular crosssections. Partial inductances can be computed from energy concepts as is shown in the first section of this chapter. The results are the same as the conventional formulation, with averaging over the crosssections. The exact partial inductance evaluation for rectangular structures is very complicated. This becomes apparent from the formulas given. Unfortunately, the accurate implementation of the formulas is difficult for large aspect ratio conductor geometries. A section in this chapter covers the concept of geometric mean distance where the conductor crosssection is represented by an equivalent filament. The volume filament model where the skineffect can be considered for arbitrary crosssections is discussed in the last section of this chapter.
The last chapter in the book discusses applications of loops and partial inductances. It describes the limitations of loop inductances. Examples are shown where loop inductances cannot be applied to model problems like ground bounce. Other practical geometries such as via conductors and series and parallel partial inductances are considered. The chapter ends with a small example which shows how partial inductances in a circuit solver like PSPICE are used to solve circuits.
In an Appendix, the basic concepts of vector analysis and coordinate systems are presented which completes this book. Again, the comprehensiveness of this book means one doesn’t require other texts to refresh one’s self on these subjects.
In summary, I am delighted that at last a modern book exists which connects the early work to the current work on inductance computations. Exactly forty years after Professor Grover signed my copy of his book, it would be a privilege to have a similar autograph for my copy of Dr. Paul’s excellent work, INDUCTANCE: Loop and Partial.
Albert E. Ruehli received his Ph.D. degree in Electrical Engineering in 1972 from the University of Vermont, Burlington, and an honorary doctorate in 2007 from the Lulea University in Sweden. He is an Emeritus of IBM Research and an adjunct professor in the EMC area at the Missouri University of Science & Technology. He has received numerous awards for his outstanding technical contributions from the IEEE Circuits and Systems Society and Electromagnetic Compatibility Society. He is a life fellow of the IEEE and a member of SIAM. EMC
Meeting Announced for EMC Aviators Club
New Members Welcome!
The EMC Aviators Club will meet during the 2010 IEEE International Symposium on EMC in Fort Lauderdale, Florida the week of July 26. Club CoFounders, Professors Antonio Orlandi and Andy Marvin, will chair the meeting. Founded in 2007, this club is open to all IEEE EMC Society members who have an interest in aviation. The club meets at the annual IEEE EMC Symposia and on other professional visits. Members are encouraged to arrange to fly together whenever possible. For more information, please visit the club website at http://orlandi.ing.univaq.it/EMCfly/index.htm or contact Professor Marvin at acm@ohm.york.ac.uk and Professor Orlandi at antonio.orlandi@univaq.it.
PHOTOS BY ANDY MARVIN 


The view of Professor Marvin’s University of York area
in the United Kingdom. Do you have any photos to share
with your fellow EMC Aviators? If so, please contact
Professor Marvin! 
Andy Marvin’s “home away from home” is a magical
place. What does your “home away from home” look like?
Share the details in the EMC Aviators Club. 
