"Electronics World", May 2009, p16
The Catt Question
Letters in "Electronics World", June 2009
'ALIEN' SINEWAVES CONCEPT?
I was amused to see that Mr Catt had mentioned my article on transmission lines (Letters, May 2009) to launch another tirade against well-known researchers concerning his "Catt Question". Mr Catt criticised my use of sinewaves in the article, which shows that he missed the point entirely. This article was to illustrate the fact that transmission lines can be used to demonstrate that electromagnetic waves can be reflected. This concept was, I found, alien to junior engineers whose experience had been with DC electricity (including AC Mains) which never usually reveals such phenomena.
It is unfortunate that Mr Catt's criticism implied that somethiung else might happen if we discount sinewaves, because these reflections occur even for a single step-function waveform. However, we cannot easily demonstrate a standing wave with single-step waveforms.
Nevertheless, the transmission line model can explain Mr Catt's long-posed question. I thought that the reason most people had given up trying to debate this with Mr Catt is that it turns out to be a non-problem.
Suppose we had a transmission line made up from a parallel pair running from Land's End to John O'Groats. Perhaps this might be a 300-ohm line, exhibiting a propagation delay of maybe 5ns/m then if one were to apply a 250Vdc signal to the wires at Land's End, were another measuring the voltage across the wires at John O'Groats, he would record a delay of about 5ms before the pulse arrived.
Provided the observer had not placed a matched load on the wires, we would also get a reflection. Now consider the charge on the wires. assume that only electrons, for the sake of argument, conveyed the charge. On the negative lead, these electrons would have flowed in along with the pulse, i.e. from Mr Catt's west. On the positive wire, there will be a shortage of electrons, which will have flowed away, towards Land's End, as the pulse arrived. They don't know they have to move until the pulse reaches John O'Groats.
If you prefer, these are from the north. So it seems Mr Catt's question is non-existent in reality: the charge causes the electrons to flow and, for the positive wire, the electrons came from the wire; for the negative, from the supply. This basic principle seems never to have been violated during the many decades Mr Catt has posed his "question".
There are now several electromagnetic solvers available. I suggest |Mr Catt uses one of these 3D Maxwell simulators to see where the electrons come and go. He can then count the electrons before and after his pulse if he wishes. Actually, the spread of the charge in capacitor plates quite pretty images when presented as a movie.
TRANSMISSION LINE TRANSIENTS
[Two diagrams omitted]
Ivor Catt asks the question: "When a voltage step travels down a transmission line at the speed of light guided by two conductors, where does the negative charge come from on the bottom conductor to terminate the electric field between the conductors?"
He declares that two eminent scientists provided completely contradictory answers to that question, but neglects to quote any references which allow readers to check the validity of this assertion.
He then goes on to imply that electromagnetic theory is not capable of analysing the transient phenomena associated with high speed logic, and concludes that it is necessary to introduce a new theor: 'Theory C'.
It would seem that his search for a complex explanation has led Catt up a blind alley. An engineering approach to the problem would be to set up an experiment, observe how the actial line does respond to a step input, then to analyse and assess the results.
So a 15-metre length of 2-core mains cable was purchased and a signal generator used to inject a square wave of 6 micro-seconds duration into one end. Figure 1 is a schematic illustration of the set-up.
The interface circuitry at the near end was designed to provide low value source impedance, whilst the far end of the cable was open circuit. This provided a configuration in which several reflections could be observed for each step of the input waveform.
The input voltage was monitored by one channel of an oscilloscope via a simple potentiometer network, whilst the output current was monitored by the second channel via a current transformer. Waveforms were recorded as accurately as possible.
A circuit model was developed to simulate the assmbly-under-review, and this was subjected to transient analysis.troal-and-error process. It took some time to complete this task, but the eventual response was a fair representation of the waveform displayed on channel 2 of the scope. This simulation is reproduced in Figure 2.
The first step, from zero to 20mv, was exactly as exprcted. This was followed by a flat response for about 180 nano-seconds, the time taken for the front edge of the pulse to arrive back at the near end. Since the distance involved in the round trip was 30 metres, the velocity of propagation had to be about 170 metres per micro-second; about half the speed of light. This was fairly reasonable, since there was quite a lot of dielectric material in the cable.
The trailing edge, from 20mV to -18mV, is probably the most informative feature of the waveform. Textbook theory would predict a step change between these two levels. Instead, the current waveform follows an exponential decay. Only one explanation is possible: current is departing from tha transmission line via capacitive coupling netween cable and environment. Moreover, it must be emanating from the signal conductor, since that is the only conductor that is being energised.
The picture emerges of a current transient propagating along the surface of the signal conductor anhd creating the wavefront of an electromagnetic field. This spreads out in the same way as the bow wave of a ship.
Since the conductors of the transmission line are 2mm apart, the wavefront does not reach the return conductor until the current pulse has progressed at least 2mm along the signal conductor. When the wavefront does reach the return conductor, it creates a return current which flows back towards the near end. During the time taken for this to happen, all the elctromagnetic energy of the pulse is released to the environment. Since this happens for every increment of length, it must happen along the whole length.
Viewing the configuration of Figure 1, it is clear that a conducting path exists along the structure, t6hrough the generator and 4.6-ohm resistor, to the signal conductor. The path acts as an aerial and is the source of the radiated current. There is no aerial-mode current at the far end, since that end is isolated. Hence, the differential-mode current arriving at the far end is balanced. Reflected current must also be balanced. This means that there is minimal radiation from the cable due to reflected current.
Subsequent reflections are of a distributed wavefront. Each incremental step in the forward wave delivers a transient current pulse into the environment. So the qsquare wave gradually changes into a sine wave.
So the answer to the Catt Question is:
Electric charge on a transmission line manifests itself as a current. Current in the lower conductor is created by an electromagnetic field emanating from the upper conductor.
In the experiment outlined above, electric test equipment was used to observe the voltage and current waveforms. Each waveform was recorded in a table of values of amplitude versus time. A circuit model of the cable was derived from electromagnetic theory, and component values calculated using spatial measurements.
The model was extended to simulate the test equipment. Time-step calculations were carried out to determine the transient response. The model was modified to achieve correlation between theoretical and observed waveforms. Cioncepts of electromagnetic theory were used to explain the coupling mechanisms involved.
There was no need to invoke the complexities of time-frequency transformations. There was certainly no need to invent completely new theory.
Ivor Catt’s reply in January 2010 is at http://viewer.zmags.co.uk/publication/b423ad6a#/b423ad6a/40