# User talk:Kevin Brunt

Did you know you can use this page for private(except everyone can see them) conversations (to do with WP of course) and that you dont have to do it all on the Article talk page?--Light current 00:48, 10 February 2006 (UTC)

## Theory D

This argument can resolved by noting that Catt's Theories N, H and C are only part of the story. Theory N deals with charge moving in an "empty" conductor at the velocity of propagation; Theory H deals with energy moving likewise. Catt's own Theory C attempts to detach the energy from the conductor, but without a properly worked-out replacement for the concepts of current flow in the conductor. Instead Catt attempts to tie his version of Heaviside's energy currents to Maxwell's definition of a transverse electromagnetic wave. This is utter nonsense, because Catt is trying to describe current flow in terms of something which by definition is not current flow.
Catt has left out (at least) two theories; I will call them Theory D and Theory Q. Theory D (for Drude Model) says that the "empty" conductor is actually stuffed full of negatively-charged electrons (with a sufficent number of positively-charged nuclei to balance.) The observed "abstract charge" of Theory N is, in Theory D, due to the addition or removal of electrons from a volume of the conductor, resulting in a imbalance of charge in that volume. Theory D does not require that charge move through the conductor at the velocity of propagation, because the electrons that enter at one end of the conductor need not be the same as the ones that leave at the other; instead all the electrons move - there are so many per unit volume that no electron has to move very far (or very fast) to satisfy the flow of current in term of coulombs per second. Likewise, Theory D does not require that energy move at the velocity of propagation because the "empty" conductor is filled with the energy that was needed to bring the electrons together against their mutual repulsion. (In fact, the energy is provided by the electrons moving towards the positive nuclei.) As the electrons move relative to each other energy is transferred between the electric fields. Theory D unifies Theories N and H in a single theory based on the properties and motions of electrons. Theory Q (for Quantum Theory) translates the Drude Model, which is dealing with the motions of electrons using classical mechanics, into a more "correct" model which incorporates the principles of Quantum Mechanics, such as the Heisenberg Uncertainty Principle. The Drude model is an intermediate stage in the evolution of QM - the Drude Model produces the right answers for the wrong reasons. QM was created to deal with the gap between the classical theory and the observed facts. -- Kevin Brunt 18:43, 13 March 2006 (UTC)
The "touching electrons" description is a gross simplification of Theory D which contains enough of the "truth" to derive the equations for the DC behaviour of Theory N and Theory H. Since Catt only discusses the pulse propagation issues, the touching electrons model, (which cannot, without modification, explain capacitance) is of limited use. Catt's Theory C, by rejecting charge and current, rejects Theory D. Theory C (unlike its parent Theory H) is incompatible with observed fact. Nigel's assertion that Nobody has ever proposed a mechanism where by energy travelling at light speed can magically stop when a transmission line charges up, and magically restart when it is allowed to discharge is irrelevant, because Theory D does not require that the energy be travelling at light speed (or indeed at the velocity of propagation of the TL, which is not necessarily the same thing) in the first place. It is worth pointing out that Catt has never explained his "TEM steps" come into existence with the right properties in the first place. Nor, indeed, how they magically reverse their velocity when they are reflected. Catt's energy waves always have equal amounts of energy in their magnetic and electric fields, which means that he has to claim that there is an error in the equation for the energy stored in a capacitor. Theory D says that the energy of the magnetic field associated with the current flow into a capacitor is converted into energy in the electric field of the capacitor as the current stops flowing. Theory D produces the same answers as Theory C (whenever Theory C agrees with reality), but Theory D also explains resistance better; when Theory D predicts that no current flows, Theory C has equal-but-opposite energy currents flowing and has to have an extra bit added so that the currents "magically" cancel out. -- Kevin Brunt 19:13, 13 March 2006 (UTC)
Incidentally Nigel, since Theory D (and Theory N) say that there is no current flowing in a charged (as opposed to charging) capacitor, the energy stored in your charged TL is entirely in the (capacitive) electrical field, and so is equal to 1/2 CV². When the charged TL is discharged, the solution of the Telegrapher's Equations for the step voltage that is propagated require that the magnetic (inductive) and electric (capacitive) energy must be equal. Since it is necessary to conserve charge, we have two statements describing the (travelling) pulse resulting from the discharge of the TL; 1) the energy stored in the capacitance of the travelling pulse is half that of the stationary charge and 2) the charge in the two capacitances is identical. This is a simple pair of simultaneous equations for which the only solution is that the travelling pulse is twice as "wide" and half the voltage of the charged TL. The rate of discharge is dictated by the characteristic velocity of the TL. -- Kevin Brunt 21:12, 13 March 2006 (UTC)

### Capacitors and displacement current

Catt's work on equating capacitors to transmission lines came as a result of his work in trying to provide adequate fast decoupling to the power supplies for very fast (sub nanosecond rise time) logic circuits at Motorola. He was apparently one of the first people to realise that parallel power planes (in common use today) needed to be treated as transmission lines rather than as simple "lumped" capacitances. Ultimately, in 1979 he coauthored (with Malcom Davidson and David Walton) a book "Digital Hardware Design" [1], which applies transmission line principles to the design of high-speed digital electronic circuits.

Almost as a "spin-off" of this book, an article by Catt, Davidson and Walton was published in the December 1978 edition of Wireless World under the title of "Displacement Current (and how to get rid of it)". [2] This is an extremely important article, as Catt evidently regards it as his "master paper" on which much of his later work is built.

The article consists of a five paragraph discussion of displacement current and a somewhat longer Appendix analysing a particular transmission line configuration. Specifically, the Appendix demonstrates if a voltage source is applied to a transmission line through a resistance much larger than the characteristic impedance of the transmission line, the voltage waveform at the "input end" increases in a stepwise manner, in a way that approximates the smooth exponential curve that would be obtained if the transmission line were replaced with a capacitor equal to the total capacitance distributed along the transmission line.

The difficulty that the article presents does not lie with this result, which is entirely reasonable. Rather it lies with the authors' evident belief that the result of itself disproves the existence of displacement current, because the article

From this realisation he developed his equivalence theory. Following on from this, he claims that Maxwell's displacement current term is not in fact needed to explain capacitor operation because displacement current is not needed in a transmission line.

However, the article is highly indicative and suggestive of stepwise charging of capacitors [3]. Catt has championed the Heaviside case of two conductors propagating a slab of energy current.

Another part of Catt's thinking on capacitors was that they do not contain any internal ESL and that the ESR quoted by manufacturers is simply the characteristic impedance of the TL formed by the capacitor plates. These ideas have to some extent gained credence in the high frequency modelling of chip capacitors, where the transmission line model appears to give closer representation than the RLC model.[4] [5] [6]

## Energy Current

"Energy current" is a somewhat informal term that is used, on occasion, to describe the process of energy transfer in situations where the transfer can usefully be viewed in terms of a flow. It is particularly used when the transfer of energy is more significant to the discussion than the process by which the energy is transfered. For instance, the flow of fuel oil in a pipeline could be considered as an energy current, although this would not be a convenient way of visualising the fullness of the storage tanks.

The units of energy current are those of power.

### Energy Current in Electromagnetism

A specific use of the concept of energy current was promulgated by Oliver Heaviside in the last quarter of the 19th Century. Building on the concept of the Poynting Vector, which describes the flow of energy in a transverse electromagnetic wave as the vector product of its electric and magnetic fields (E×H), Heaviside sought to extend this by treating the transfer of energy due to the flow of electric current in a conductor in a similar manner. In doing so he reversed the "normal view" of current flow, so that the electric and magnetic fields due to the current are the "prime movers", rather than being a result of the motion of the charge in the conductor.

Heaviside's approach had some some adherents at the time - enough, certainly, to quarrel with the "traditionalists" in print. However, the "energy current" view presented a number of difficulties, most notably that in asserting that the energy flowed in the electric and magnetic fields around the conductor the theory is unable to explain why the charge appears to flow in the conductor.

After the discovery of the electron in 1897, the Drude_Model, which describes electrical conduction in metals, was developed very quickly. By associating the somewhat abstract concept of moving charge with the rather more concrete motion of the charged electrons, the Drude Model effectively deals with the traditional "charge current" and the Heaviside "energy current" views simultaneously. (The subsequent evolution of Quantum_Mechanics has, of course, rather complicated the idea of an electron in motion.)

With this achievement of "unification", the energy current approach has largely lost favour, because in omitting the concepts related to conduction it has no direct model for (for example) Ohms_Law. In consequence it is less convenient to use than the "traditional" charge current approach, which defines the concepts of current, voltage, resistance, etc, as commonly used for electrical work.

Of recent years Heaviside's original conception of energy current has been resurrected by Ivor Catt who has appropriated it for his own ideas on electromagnetism. Catt avoids the question of the association of energy current and charge current by insisting that there is no charge, although he has never offered a complete alternative explanation for the observed phenomena that are conventional ascribed to charge. He also insists that his version of an energy current is "TEM"; since the behaviour of the electric and magnetic fields simply cannot be fitted into the definition of a "transverse electromagnetic wave" as is universally accepted by scientists, Catt's writing on this point has created a great deal of confusion.

## Energy current page

Kevin, you may (or may not) be plaesed to know that I have included your well written piece above on energy current into the Energy current article. You are now a published author! 8-)--Light current 21:51, 20 May 2006 (UTC)

## Catt on Calculus

An article by Catt appeared in the March 1980 issue of Wireless World under the the title "Maxwell's Equations Revisited" [7]. Unsurprisingly, Catt came to the conclusion Maxwell was wrong, as indeed were Mach, Einstein and Newton (although there is some ambiguity in the latter case.) Faraday is explicitly exempted from Catt's strictures. It is possible that this is because Faraday was notably an experimentalist, rather than a theorist; certainly the main thrust of the article was an attack on "the bogus nature of comtemporary mathematical operations in electromagnetic theory", with a great deal of use of words such as "absurdity", "slovenly", "false", "ludicrous" and "garbage" being levelled at various aspects of theory. However, even though Catt produced a second Wireless World article advancing the same argument in November 1985, and referred to both articles in a letter to Electronics World in April 2004, his entire premise is fatally flawed, doomed by a fundamental mathematical error on Catt's part.

Catt's central argument actually has very little connection either with "contemporary" or with "electromagnetic theory". The only "contemporary" part is the use of the streamlined profile of the then recently-introduced British Rail Intercity 125 locomotive in his scenario, and the only association with Maxwell's Equations is that Faraday's Law contains a term in which a derivative is subtracted. Shorn of irrelevant detail, Catt's argument reduces to this:

• Take a piece of graph paper and draw conventional Cartesian axes on it.
• Label the horizontal axis "x" and the vertical "h". Mark divisions 0 to 10 on each axis.
• Draw a straight line between the "10" on each axis. Obviously this is the line ${\displaystyle h=10-x}$
• Take a straight-edge in your left hand and hold it over the paper, parallel to the h-axis close to ${\displaystyle x=10}$
• Grasp the paper in your right hand and pull it sideways under the straight-edge.
• Note that as the graph moves under the edge, the value of h where the line ${\displaystyle h=10-x}$ passes under the edge is increasing. Thus ${\displaystyle dh/dt>0}$

Catt's reasoning goes: ${\displaystyle {\frac {dh}{dt}}}$ is negative (by observation), ${\displaystyle {\frac {dh}{dx}}}$ is negative (basic differentiation of ${\displaystyle h=10-x}$), ${\displaystyle {\frac {dx}{/}}{dt}}$ is positive (obviously, it's the velocity of the graph paper under the straight-edge. Now, by the chain rule (which Catt does not actually refer to by name) ${\displaystyle {\frac {dh}{dx}}\cdot {\frac {dx}{dt}}={\frac {dh}{dt}}}$, which presents a problem, since ${\displaystyle positive\cdot negative\neq positive}$.

Catt, of course, claims that this is an "anomaly" in the mathematics. However, it is really the exposure of a weakness in Catt's "moving train" formulation, namely that serious difficulties exist in painting the x-axis on the side of the locomotive without provoking the intervention of the British Transport Police. Working with graph paper it is perfectly clear that as the paper moves under the straight-edge, the value of x at which the edge crosses the x-axis is decreasing. Catt has made a basic error in his co-ordinate systems and has confused the velocity of the train relative to the observer with the velocity of the observer relative to the train. This is simply a failure on Catt's part to pay proper attention to detail, and by rights much of his name-calling against the mathematicians ought to be redirected back to him.