Pieter-Tjerk de Boer, PA3FWM web@pa3fwm.nl

(This is an adapted version of an article I wrote for the Dutch
amateur radio magazine Electron, November 2021.)

An antenna cable is not just a piece of wire.
Technically, it’s called a “transmission line”,
with special properties such as its characteristic impedance.
But transmission lines are quite a bit older than radio technology: they date back to the
second half of the 19th century, in the form of (mostly submarine) telegraph cables.
In this article we look at the principles and properties of transmission lines,
with special emphasis on Oliver Heaviside’s contribution to our knowledge of them.

Oliver Heaviside

After secondary school, Oliver Heaviside (1850-1925) started working at the company
which operated the submarine telegraph cable between Newcastle (UK) and Denmark.
At first he worked as a telegraph operator, but soon he also got involved with the
(electro)technical side of the telegraph systems.
One of the things he noticed, was that when water leaked into a submarine cable and
progressively short-circuited it, the signals did not just become weaker (as expected),
but also clearer, less distorted.

In those days, electrical engineering was still in its infancy.
Thanks to the work of physicists like Volta, Ampère, Ørsted and Faraday, there was a decent
understanding of generating electrical currents and moving compass needles using an electromagnet.
Together, that is enough for building a telegraph, at least in principle.
But if one uses as very long cable, and tries to send dots and dashes at a high rate,
it turned out to not work so well.
There was little theoretical understanding of this,
particularly among the more practically minded people who cobbled together telegraph systems.

Heaviside studied physics by himself, and stumbled on the books by James Clerk Maxwell.
Maxwell’s ideas about electromagnetism were, at that time, rather speculative and not widely accepted,
but Heaviside got enthousiastic, studied them, and succesfully applied this theory to telegraph lines.

Thus, Heaviside, who never had studied at a university, rose from being a humble telegraph operator
to a respected physicist.
After quitting his job at the telegraph company at the age of 24, he never had another job.
The rest of his life he lived in relative poverty while working on the theory.
He became one of the so-called Maxwellians: a group of physicists who enhanced Maxwell’s
theory after his untimely death (in 1879 at the age of 48) and popularised it.
One of Heaviside’s achievements is that he converted Maxwell’s twenty mathematical formulas
into a more accessible set of just four, which nowadays are taught at all universities
as “Maxwell’s equations”.
If you want to learn more about this remarkable person, I recommend his biography [1].

Thomson’s model

William Thomson (later Lord Kelvin)
attempted to describe what happens in a long telegraph cable.
His model is sketched in the figure.
He mentally chopped the cable into short pieces, each of which has some resistance and some capacitance.
Next, he calculated what happens if at the left end one suddenly applies a voltage of say 1 volt.
The graphs show the result, for a 4 km long cable having 0.1 ohm of resistance per meter,
and 10 pF of capacitance per meter.
The cable has been divided into 4 pieces of 1 km each, so each having 100 ohm and 10 nF.
We see that the voltage on the first capacitor gradually increases to 1 volt: that’s logical,
as the capacitor gets charged via the first resistor.
The voltage on the second capacitor also gradually increases to 1 volt, but slower:
that makes sense, as it is charged from the first capacitor.
And so on.
At the right end of the cable, the voltage increases only very gradually,
and this slow increases puts a limit on how quickly Morse code signs can be sent.

However, Thomson’s model is wro