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发表于 2012-4-25 12:26:54
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Book Review
Al Ruehli, Guest Reviewer
Title: INDUCTANCE Loop and Partial
Author: Clayton R. Paul
Publisher: John Wiley, 2010
ISBN: 978-0-470-46188-4
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 self-education.
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 quasi-static aspects of inductance such as Faraday’s Law are considered. Time delay must be small for quasi-static 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 two-dimensional 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 non-parallel 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 cross-sections. 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 cross-sections. 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 cross-section is represented by an equivalent filament. The volume filament model where the skin-effect can be considered for arbitrary cross-sections 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. |
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