46 Even More Oliver Heaviside

The purpose of this post is to mop up a few bits and bobs that turned up whilst I was researching the previous two posts 44 and 45.

Just as electrical concepts had not fully revealed themselves in the 1800s, the language for discussing these things had not evolved. I read in the Kelvin biography that at the time that the first Atlantic cable was laid, the names of the electrical units had not been agreed on.

Heaviside invented the word “impedance” in 1886. This word seems so normal to us today, but to learned latinists it seemed barbaric at the time.

Even in the 1920s when Henry Fowler wrote “Modern English Usage”, “Impedance still had the power to raise the philologist’s ire. In that work, Fowler had three entries that mentioned “impedance”, and they were all negative. Here is an example:

Although Heaviside was not the sort of bloke to pander to the sensibilities of latinists, other were more inclined to take care. Michael Faraday, for instance.

In the Wren Library at Trinity College Cambridge there is a collection of the correspondence of William Whewell. Librarian Nicholas Bell read from a letter from Whewell to Michael Faraday on a recent radio program. There is an MP3 at:

It ran (in part) like this…

“My Dear Sir,

I still think anode and cathode the best terms beyond comparison for the two electrodes. The terms which you mention … show that you have come to the conviction that the essential thing is to express a difference and nothing more. This conviction is nearly correct but I think one may say that it is very desirable in this case to express an opposition: a contrariety, as well as a difference. The terms you suggest are objectional in not doing this.”

Whewell was responsible for the coining of “anode”, “cathode” and “electrode”.

It interests me that Fowler should get so hot under the collar about “impedance”, yet ignore other electrical terms that seem (on the face of it) to be worse. He does not mention “voltage” for instance. OED2 (The second edition of the Oxford Dictionary) records the first use of the word “voltage” in 1890 in Pall Mall magazine.

Wikipedia says: The Pall Mall Magazine was a monthly British literary magazine published between 1893 and 1914. Started by William Waldorf Astor as an offshoot of the Pall Mall Gazette, the magazine included poetry, short stories, serialized fiction, and general commentaries, along with extensive artwork.

In other words, this was a source for a new technical term coining that was about as technologically sophisticated as Women’s Weekly. It seems that at the time, the word would have been about as acceptable amongst those who took an interest in electrical matters as “amperage” is today. Yet “voltage” somehow has become widely acceptable. Why would this be?

In the 1800s two distinct concepts crystallized which had the same unit: the volt. The first was “electromotive force”, and the second was “potential”. A year or so ago, I wrote a regular magazine column that had a tutorial aspect for some who needed to strengthen their understanding of electrical matters. I invented a circuit to help make the distinction between electromotive force and potential clear. It had four 1.5 volt primary cells and four incandescent lamps in series.

The emf in this circuit is six volts, and yet if you poke around with a volt meter, you will not find a potential difference anywhere that exceed 1.5 volts.

As conceptualization advanced, this distinction between emf and potential came to be seen differently. Now, we speak of a Thevenan equivalent circuit. When we do this, we mean (of course) “Linear Circuit Model”. In this context, we speak of the circuit’s “Open Circuit Voltage”, or the voltage at the terminals”. We do somehow need this more general concept “voltage”, and then use other words to set the details and show what we really mean by voltage. “Amperage” has no corresponding utility.

As I indicated in recent posts, in the early days of telegraphy, the speed were so low that transmission lines could be modelled with (distributed) resistance and (distributed) capacitance, and that inductance could be ignored entirely. It was Heaviside who first worked out the significance of inductance where it did have to be taken into account, and how to address it. He worked out the criterion for distortionless transmission.

I find it interesting that in the early days of transmission line research, the inductance was completely ignored. It wasn’t until telephony made its demands that inductance became important. Here is a note about the properties of a transmission line in which inductance can be ignored. This is from “Life of Lord Kelvin by Silvanus Thompson P329:

You don’t hear much about this “square law” these days!

Back to the Present.

(My mate Cyril complains that this Blog dwells too much on the “very old”.)

The modelling of a transmission line in which inductance does not appear at all, is not common. There are circumstances in which it is still completely appropriate. One example is in the probes used to measure the electrical potential inside a living cell. This interesting electrical measurement problem is mentioned in ADALPAD (P845), where it is stated that “high impedance is essential in these applications, since living cells are destroyed by the passage of quite minute currents”, but that is only a part of the story. The electrical activity in living cells involves the movement of ionized molecules. It does matter exactly what these molecules are, as every species of molecule will have its own characteristic preponderance to take up or dispose of charge. The introduction of a metallic probe, would involve the doping of the cell interior with metal ions, which would invalidate the investigation.

For this reason, probes are made of very fine glass tubes which are filled with an aqueous liquid charged with ionized molecules to match or mimic the liquid in the cell where the potential is to be measured. A metal electrode is installed in the other end of the tube, but the tube life is limited to the time before metal contaminants reach the active end.

This construction gives a probe with a very high series resistance, which is in itself a reason for a very high input impedance on the attached equipment. As well as that the shunt capacitance in the glass tube wall is distributed along the probe resistance. Here in the most up-to-date biological research work, we find an analogue for the submarine cables of 160 years ago.

I first read about design solutions to the problem of such a high impedance probe in the lamented Wireless World magazine. (This was very different from its successors in that design details and the design process were discussed.) The idea that I read about there was to apply a negative capacitor to the probe to partially cancel the probe capacitance. This was done with a non-inverting amplifier (I think the voltage gain was 3) with a capacitor to apply capacitative positive feedback.

When I try this now, I find evidence that the old idea of modelling the line by assuming lumped capacitance all in one spot doesn’t look that good.

Years ago, before I had either circuit modelling or filter design software available, I did some work on ladder networks in which R(series, C(shunt) networks are strung together in cascade. Of course, for any particular RC, the subsequent members of the cascade provide loading and spoil the simple determination of a pole frequency. A usual trick here is to make the impedance of each stage, higher than the preceding. If a stage is ten times the impedance of its predecessor, it will not make a significant impact on the pass response of the earlier one.

In the following picture, I show the amplitude and phase responses for three networks. The green lines represent a network with three stages or RC low pass filter with RC = 100us. Corner frequency = 1591 Hz. The stages are isolated from each other with unity gain buffers. That is, each stage suffers no loading from following stages.

The Blue lines represent a “ladder network” with three stages of RC low pass filter. These are directly coupled, but the second and third stages have an impedance that is 10 times the previous stage. The Blue line is a little less sharper in the knee than the green one, but the difference is not great.

The red line represents a “ladder network” with three identical RC low pass filters. The second and third stages impose a load on the previous stage. For the red line, the three poles are “spread out”, and the result is a much less clearly defined knee in the response.

I have taken an interest in extending this to the situation where there are a very large number of identical RC stages. Such a circuit might serve as a model for a transmission line with distributed resistance, and distributed capacitance, such as a glass biological probe discussed above.

Maybe I will go into this a little more in a later post.

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