Electromagnetics 1


Ivor Catt.










Westfields Press,

121 Westfields, St. Albans AL3 4JR,

England 1995


First published in 1995

First impression

This book is a repeat of the 1994

book Electromagnetism 1,

ISBN 0 906340 07 1. This version

has smaller pages, A5 instead

of the previous A4.

Computer files nos.

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Copyright Ivor Catt 1995


British Library Cataloguing in Publication Data

Catt, Ivor

Electromagnetics 1

I. Title


ISBN: 0 906340 10 1





Battery and resistor

1 Steady state

2 Initial state

3 Unterminated transmission line

Battery and resistor. Numerical values

3 Steady state

5 Initial state

6 Unterminated transmission line

7 The Pulse

8 The Capacitor

9 The spherical capacitor, the square capacitor

10 The isolated, charged sphere

10 The electron

11 Interacting TEM waves

11 Partial reflection in a transmission line

13 Interaction between TEM pulses

13 Dissimilar pulses, Similar pulses

15 The car headlight

15 The Crystal

16 Difficulties with the Crystal model

17 The perforated capacitor

17 Summary of interactions

18 Future developments

18 The analogy between L, C and R

20 Impedance of a co-axial line

20 The L-C Model for the transmission line

21 The Transmission Line Reconsidered

21 Historical background

22 The Transmission Line

22 The Transmission line Transmission Line

23 The Dielectric Constant of Copper

The transmission line with:

24 resistive conductors

24 transmission line conductors








25 Copper as a dielectric

25 Implications

27 Theory C

27 The Battery

28 The Reed Relay Pulse Generator

30 Properties of a Transmission Line,

or, Proof that only one type of wave-front pattern

can be propagated down a two-wire system

31 Crosstalk in digital systems

32 EM wave

33 OM wave

Description of crosstalk

34 between parallel buried conductors (Stripline)

36 between parallel surface conductors (Microstrip)

40 Printed circuit boards for high speed logic

41 Calculation

41 Decoupling by Voltage Planes

42 Calculation

43 The L-C Oscillator Circuit

45 The Inductor as a Transmission Line

47 Calculation of Formulae

47 Magnetic field surrounding current in a long conductor

48 Self Inductance of a Pair of Parallel Conductors

49 Mutual Inductance between Two Pairs of Parallel Conductors

50 Crosstalk between Two Pairs of Parallel Conductors

52 Check on the Validity of Crosstalk Figures

53 Energy Current

56 The Theories

57 The capacitor - voltage planes

58 Comparison of the transmission line model with the lumped model of a capacitor in an RC circuit

60 Catt's Anomaly

60 The diode as an energy-controlled, not a charge-controlled device

72 Table 1. Electrical Formulae

Then there were the remarkable researches of Faraday, the prince of experimentalists, on electrostatics and electrodynamics and the induction of currents ... The crowning achievement was reserved for the heaven-sent Maxwell, a man whose fame, great as it is now, has, comparatively speaking, yet to come.

- O. Heaviside, Electromagnetic Theory vol 1 pp 13/14, 1893.


Now, there are spots before the sun, and I see no good reason why the many faults in Maxwell's treatise should be ignored. It is most objectionable to stereotype the work of a great man, apparently merely because it was so great an advance, and because of the great respect thereby induced.

- ibid, p68.


Our electrical theory has grown like a ramshackle farmhouse which has been added to, and improved, by the additions of successive tenants to satisfy their momentary needs, and with little regard for the future. We regard it with affection. We have grown used to the leaks in the roof .... But our haphazard house cannot survive for ever, and it must ultimately be replaced by a successor whose beauty is of structure rather than of sentiment.

- H W Heckstall-Smith, Intermediate Electrical Theory, pub. Dent, 1932, p283.


It was once told as a good joke upon a mathematician that the poor man went mad and mistook his symbols for realities; as M for the moon and S for the sun.

- O. Heaviside, Electromagnetic Theory vol 1 p133, 1893.


... the universe appears to have been designed by a pure mathematician.

- Sir James Jeans, The Mysterious Universe, 1931, p115.






D S Walton

I studied Physics for my first degree at the University of Newcastle and stayed to complete a PhD before embarking on an academic career, being appointed to a Junior Lectureship in Trinity College, Dublin in 1971. In 1974, frustrated with academic life, I left to start a company whose aim was to exploit the rapidly expanding possibilities within digital electronics.

At the time the state of the art technology was represented by Schottky TTL, an evolved form of Transistor-Transistor logic using Schottky 'clamping' diodes in order to prevent device saturation and hence reduce propagation delay. A feature of this technology was that the logic signals had a transition time of 1.5 nS which was to lead to problems when systems were constructed from these devices.

As our fledgling company struggled to build a prototype of the logic analyser, which was to be our first product, I became increasingly frustrated by the difficulties we encountered in trying to build a reliable system. These problems resulted from phenomena like crosstalk and power supply transmitted noise, and I was puzzled by the apparent lack of any design guidelines or processes which would produce systems with predictable levels of reliability. It was clear that no progress would be made towards more reliable systems until we understood these phenomena and could lay down design rules for power supply design and distribution, and logic signal interconnections on printed circuit boards and backplanes.

It was as I was struggling with these issues that I met Ivor Catt during a sales visit I was making to Marconi Elliott Automation at Borehamwood. In the lift after the demonstration Ivor introduced himself to me and we seemed to cover a vast range of subjects from computer architecture to hardware design. Subsequently Ivor wrote to me enclosing information on his computer architecture papers and inviting me to stay with him on my next trip to the area.

Ivor Catt is one of the most original and creative thinkers I have ever had the privilege to know and there is no doubt that the progress we made together was largely dependent on his ability to bring a fresh perspective to familiar situations. I was particularly grateful for his explanation of the development of ECL (Emitter Coupled Logic) with which he was intimately involved as part of Motorola's team in the sixties. He also explained his view on TTL and S-TTL and their shortcomings.

I remember a telephone conversation about the transmission line nature of logic interconnections which established a basis for my future thinking and demonstrated the poverty of most of the contemporary writings on the subject.

At this time also Ivor sent me an unpublished manuscript of his book on logic design. I read this avidly and, I believe, surprised Ivor by finding an error in his technique for assessing the pulse performance of decoupling capacitors. Ivor's key point was that the so called 'stray inductance' attributed to capacitors was a myth. I particularly remember his comment that 'all of the stray inductance is not in series with all of the capacitance. In other words, from the point of view of a step pulse, the capacitor was distributed in space and therefore in time. It was as I reflected on this that I 'saw' that a capacitor was in fact a transmission line and the whole universe began to turn itself inside out with the transmission line becoming the fundamental primitive while other concepts such as inductance, capacitance, and mutual inductance were constructed from it.

I think Ivor's own words recorded at the time are the best history of what happened next;

Then one night, [28 May 1976] as was his wont, Walton phoned Catt and talked about a number of things - how he knew he should get the sine wave out of his [conceptual] system but how difficult it was to do so; how he wondered how the particle came into Faraday's Law of Induction; that perhaps the Law was only an approximation and did not hold exactly at the atomic level. Catt wanted no particles introduced into the argument [!!].

Then Walton raised the point about a 'Faraday's Law loop' with a capacitor as part of the loop. Catt said that if instead of a C you had the end of a very long 50 ohm transmission line it would look just like a resistor. ...... Walton said, "So that gets rid of displacement current". .... Catt and Walton promptly agreed that a capacitor was a transmission line.

The work which Ivor, Malcolm Davidson, and I carried out over the next few years influenced not only the practicalities of designing digital systems but made a significant contribution to the development of electromagnetic theory. It is my sincere hope that a time will come when Ivor's contribution to electromagnetic theory will be accorded the position it deserves in the mainstream of the development of the subject.







Malcolm Davidson

In 1976, long before Personal Computers and microprocessors, when TTL was the de facto designer's building block, I was working on a military program for a large electronics company on the outskirts of London. I was still a fresh face engineer with merely 5 years of post graduate experience under my belt. Nevertheless, I was helping to design some digital test equipment utilising TTL. The system would ultimately interface to a DEC PDP 11. It seemed very interesting, but I was becoming increasingly perplexed that the paper design never seemed to work as planned and the staff appeared incapable of finding the problem. "Noise", "glitches", "race conditions", "spikes" and "flaky chips" were all popular choices to describe the poorly understood problems of the moment. This list soon had "bugs" added when software became part of the system. "Heaven help any military personnel who ever have to use this stuff," I thought.

"What was going on?", I wondered. "Why do all these problems appear to be insurmountable?" Someone suggested I go and talk to a contract engineer, some guy called Catt. He seemed to have a lot of ideas about the problems. So filled with a little hope and a lot of confusion, I set off to find this fellow, little knowing that those first few steps would be the start of a journey that has taken me far beyond circuit boards and logic chips. I found Ivor Catt, and listened intently as he spoke so eloquently and with such enthusiasm about issues that were at the time either half forgotten from college days, or entirely foreign to me.

TEM wave fronts, Oliver Heaviside, Transmission line theory, and Poynting Vectors. What had all this got to do with some paper logic design and a few TTL gates? I quickly found out that it had a tremendous amount to do with it, allowing me to resolve problems and tackle design issues that had hitherto seemed impossible. I decided to devote time to this apparent chasm between theoretical concepts and physical reality. I would feel pretty bad if some plane filled with 300 passengers crashed due to one of these so called "glitches".

With Ivor's good counsel and the help and support of David Walton, I began to uncover a treasure trove of knowledge. My first so-called discovery was in an engineering library at Marconi Elliott Avionics, where I found a book by J A Fleming from 1898. On page 80 he states;

It is important that the student should bear in mind that, although we are accustomed to speak of the current as flowing in the wire in one direction or the other, this is a mere form of words. What we call the current in the wire is, to a very large extent, a process going on in the space or material outside the wire.

There it was, right in front of me in black and white! The current does not flow around a loop setting up a magnetic field as I had, along with countless other engineers, been taught in high school and university. It was the other way round. The electric current is but an artefact of a more fundamental entity. Over the next few years Ivor, David and I wrote numerous articles, gave a lecture series, and tried to have various papers published. I read voraciously, and began to realise that academia and industry based its beliefs, not on accuracy of knowledge, but on a "perceived accuracy", inextricably linked to the ego needs of worried individuals and their desire to retain the status quo.

Everyone has to justify a philosophical position taken by believing that it is the correct one, for to think otherwise would be sheer folly. To be convinced that some basic tenet of electrical engineering is wrong means a complete re-evaluation of the very theoretical structure that one has supported and believed in for many years. Scientific dogma has many fervent allies who continually resist change.

Regardless of challenges by us and especially by Ivor, attempts to cajole the engineering and academic world into rejecting some accepted theories and adopting a coherent set of somewhat different basic axioms have been fruitless. Many projects are still developed using inaccurate physical models, the saving grace being that designs have shrunk so rapidly in the last 10 years that the problems are less than they might have been. Designs that used to be in a rack now may reside on a card, and those once requiring a card now use an LSI chip. However, the problems will not go away, and difficulties still exist as engineers struggle to achieve reliable complex designs at clock rates above 20 MHz.


In the constant pursuit of improvement and quality, this book, outlining both scientific and political issues, is a must for every electronics company and every educational faculty. As a society, we need to spend more time reflecting upon our past and evaluating our progress. This book will stimulate discussion and debate, through which, hopefully, science can at last begin to place digital design on a foundation of solid, appropriate theories and concepts.

Those of you who feel that many of the ideas in this book are not mainstream should find a copy of "Standard Handbook for Electrical Engineers" by Donald G. Fink and H. Wayne Beaty. In all editions up to and including 12 (published in 1987), there is a section entitled "Electromagnetic Wave Propagation Phenomena". This seminal work gives a clear and unambiguous description of the role that conventional electric current plays in energy flow.

The usually accepted view that the conductor current produces the magnetic field surrounding it must be displaced by the more appropriate one that

the electromagnetic field surrounding the conductor produces, through a small drain on the energy supply, the current in the conductor. Although the value of the latter may be used in computing the transmitted energy, one should clearly recognize that physically this current produces only a loss and in no way has a direct part in the phenomenon of power transmission

It should be noted that the 13th edition has deleted this entry, as this excellent description has been replaced by more "up to date material"! As engineers, academics and scientists, are we interested in truth, or do we just pay lip service to it, justifying our actions as not wanting to rock the boat?

To challenge the status quo, to take on the establishment, takes courage, ability, energy and a certain amount of stubbornness. Ivor Catt has all of these qualities in abundance. Hopefully, time will afford him the recognition his contributions to science deserve.



Around 1875, Oliver Heaviside pioneered high speed pulse signalling down a coaxial undersea cable between Newcastle and Denmark. This led to his theory of electromagnetism, which runs to five volumes. His approach is based on the TEM wave travelling at the speed of light down a dielectric guided by two conductors.

Development of the more glamorous wireless signalling around 1900 erased Heaviside's approach. In 1960, when the centre of gravity reverted to Heaviside's problem, this time on the back plane of a digital computer, Heaviside and his earlier approach had disappeared from the record.

A quick check in the indexes of today's text books on electromagnetism will show that, along with Heaviside, the TEM wave has virtually disappeared from today's electromagnetic theory. What little mention there is, is confusing. One book calls the TEM wave a degenerate form!

As data rates increase, wired communication comes more and more into the fore. I adopt the approach appropriate to the new situation, very much centred on the guided TEM wave.

This book comes after a long gap in the author's publications on electromagnetism, which began a quarter of a century ago with a major paper revolutionising the theory of crosstalk in the IEEE Transactions on Computers, December 1967. Previous books are listed in the Cumulative Index at the end of this book.

Text book writers of the last fifty years seem to have fed on each other. Confusion has accumulated as writers with no practical experience of the art have copied and re-copied each other. Generally, a growing welter of dubious and irrelevant mathematics has submerged the subject. Their divorce from practical experience of driven waves (as opposed to the standing waves of wireless and radar) makes the present challenge, to bring the art back to the Heaviside mainstream, difficult but rewarding for the author and for the reader. Bizarre extremes adopted as quick-fixes in 'modern physics' further confuse the subject, which should be reasonably straightforward.


Ivor Catt.

St. Albans, 1994