Oliver Heaviside and the theory of transmission lines (2021)
pa3fwm.nl
pa3fwm.nl
William Henry Preece was Engineer-In-Chief at the British Post Office in the late 19th Century (basically heading their telegraphy efforts) and controversially stuck to Thomson's model, or the "KR Law" as it was called back then, relying on poor quality experimental results to direct the organization.
Oliver Heaviside publicly criticized Preece, who in turn blocked publication of Heaviside's writing to preserve his own reputation (according to Wikipedia). When Preece retired in 1899 and received a knighthood, Heaviside wrote in the preface of Volume II of "Electromagnetic Theory":
"It is to be hoped and expected that the late important removals in the British Telegraph Department will lead to much improvement in the quality of official science."
Writing by hand on his own copy, Heaviside suggested that the preface (and thus the book's publication) were "held back" so as to "allow W H Preece to make sure of his knighthood".
https://outsideecho.com/DGT-BIO_files/PDFs/DGT13.pdf
So! On the one hand, we have an esteemed engineer who ran the country's telegraphs and refused to admit he made a mistake, became a knight and faded somewhat from history; on the other hand, we have a self-taught physicist who made massive contributions to our understanding and analysis of electromagnetism, lived in "relative poverty" for fifty years while doing so, didn't shy away from calling out bad science, and he gets the analogue of heaven named after him in the musical "CATS".
https://deadreckonings.com/2007/12/07/heavisides-operator-ca...
https://en.wikipedia.org/wiki/Kennelly–Heaviside_layer
Today this is more commonly known as the E layer or E region, and it is much beloved by ham radio operators because of its intermittent nature.
You never know when sporadic E skip will become available and you can use it to contact hams far away!
Controlled impedance took me a long time to wrap my head around when starting PCB design, the moment when it finally clicked was watching this excellent AlphaPhoenix video https://www.youtube.com/watch?v=2AXv49dDQJw& asking and practically demonstrating the simple question:
When you flip on a switch, to turn on anything, send data, morse something etc, how does the circuit know how much current the load at the other end needs?
Spoiler: Given that information can't travel faster than light, the simple answer is: it doesn't. So it just guesses and adjusts, which you don't want as it gives you exactly the ringing etc Heaviside identified. The video is a nice complement, as it perfectly visualizes the issues at play.
It's a pretty wild bit of understanding to have, even in simple situations like flipping on a light switch.
https://en.wikipedia.org/wiki/Transatlantic_telegraph_cable
They didn't know much about transmission line theory, and even burned out the cable at one point. Heaviside was only about 8 years old when the first cable was laid down.
https://www.youtube.com/live/ySuUZEjARPY
The dramatic shift in behavior above the audio frequency range is where the water wave lens starts to fall down IMHO.
I was looking at my brothers memory card from a Cray 1a the other day and that video popped in my head. They had the timing traces snaking through several flat-pack chips legs. No wonder they had to move from parity to Hamming code even with exclusively using differential twisted pairs between modules.
Understanding waves feels a bit like the bell curve meme for me: you start with the mental water model, and eventually end up with it again.
Or Feynman: you hear him helpfully talk about bouncy rubber balls, then learn a bunch of stuff over the next decade, and randomly listen to the same lecture again, and suddenly all sorts of „aaaah, that’s what he meant“ lightbulbs go off.
The original link side stepped that as to be honest it is to complicated for the intended use case.
All models are wrong, some are useful, and the water wave model is very useful for very real needs.
I personally wasted a lot of time confusing the map for the territory, but yes everyones path will be different. I confused the "electron flow" and water wave model as being absolute ground truth for way longer than I would like to admit.
It's probably more helpful to not use the idea of 'guessing' though - the transition from off to on is a signal with a certain frequency content and that signal is reacting to the capacitance and inductance etc. of the wires and propagating through them basically the only way it can. Once the signal has propagated through and the ringing has all been absorbed it settles on the DC condition.
This kind of thing has always been my hurdle when learning electronics. Whether through tutorials or high-school level physics, all the explanations I read tend to simplify and omit things in exactly the way as to break down when you start asking questions like this. My pet peeve are various equations that people flip around seemingly arbitrarily to calculate just the thing they need at the spot, from the two "knowns" that happen to be unknown at the same spot a moment later. Everything is obviously affecting everything else, but no one thought to mention feedback loops and how to correctly deal with them (even if by simplifying them away).
Or maybe I'm just a naturally imperative thinker, and I don't feel comfortable with declarative explanations which I can't "step through" mentally to understand the underlying process. Which, in case of electronics, involves voltages propagating around the circuit at finite speeds.
In programming, this hit me wrt. non-deterministic programming in Prolog. Usually explained as magic. "You can assume program will compute X, because it's structured so that if it wouldn't, it would hit this 'can never happen' statement, and because that - literally - can never happen, it magically must take the correct path".
Became immediately obvious to me once I realized that the runtime is just hiding a big fat loop that takes every path for you, and the magic instruction just tells it to silently discard the current path and try another one. Overall, the moment I felt I finally understand Prolog was when I realized the runtime is doing depth-first search in the background.
Anyone know of an accessible guide to the translation of Maxwell's quaternions to Heaviside's vectors? Was Heaviside's compression of Maxwell's work — lossless?
But you can also further compress those 4 equations into just a single one by using slightly more complicated geometry !
https://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_14.h...
This is the one that finally made impedance "click" in my head.
OP's, however, treats the subject of "loading coils", which I remember hearing about in the context of telephone lines but never really understood until just now.
and the Heaviside Step function looks like Heaviside's head lol.
I remember one professor mentioning the origin of this theory in undersea cable modeling at some point.
I also skimmed the page and saw that equation 20 is not a wave equation (as the article says, it is a diffusion equation.) Again, I am not sufficiently knowledgeable to say whether that renders the question of impedance matching moot.
Update: I see from the sibling thread and its excellent reference that the refractory period, where the sodium and potassium ions are being pumped back to their starting positions, suppresses reflection.
Hope that clears up any confusion that might possibly arise.
Others include moose and drake.
https://www.electricaldesks.com/2022/09/Types-of-Conductors-...
I did find it an interesting overlap that in the field of transmission lines (electricity lines specifically) there is literally a conductor size names elk :)
My original comment could do with an "also".
See also The Science of Radio And the Mathematical Radio (Similar content but one more focussed at elec eng people and one more at math(s) people)
"The best result of mathematics is to be able to do without it", he said, which seems strange but makes sense coming from the man who came up with functional operators.
I knew this quotation in my undergrad school days; just now checked the net and there is a source: https://hsm.stackexchange.com/questions/7332/a-peculiar-quot...
>His neighbours related stories of Heaviside as a strange and embittered hermit who replaced his furniture with 'granite blocks which stood about in the bare rooms like the furnishings of some Neolithic giant. Through those fantastic rooms he wandered, growing dirtier and dirtier, and more and more unkempt - with one exception. His nails were always exquisitely manicured, and painted a glistening cherry pink'
Genius confirmed.
EDIT: one of the traits of creative genius according to Hans Eysenck is psychoticism which includes an indifference to social norms:
https://philipperushton.net/wp-content/uploads/2015/02/Impur...
PS: he discusses the impossibility of moving signals faster than light. I'm in fact interested in moving them way slower than they do, since that could make it possible to build very short antennas. I'm surely not the first to think of this. Maybe that's not even possible and that theoretical model could help to demonstrate why (even though it applies to transmission lines while I'm concerned about antennas).
In fact, I'd say it's easier to explain optical refraction with an electrical model than the other way around.
That's not just an analogy; impedance is index of refraction, with the same body of modern theory, except that "impedance" derives from the history of analysis of low frequency ("radio") waves whereas "index of refraction" derives from the history of analysis of high frequency ("optical") waves.
When someone waves a skipping rope at one end, they directly move the portion of the rope closest to them, which pulls on the portion next to it, which pulls on the portion next to it, and so on. Some wave-shapes happen to be are sustainable enough to travel along the whole rope with low distortion. (Like when you draw random pixels in Conway's Game of Life and run it, you usually end up with lots of gliders and a few spaceships travelling off in various directions, because those happen to be the simplest travelling patterns and the rest of your scribble died out or turned into things that don't travel. There aren't any non-travelling wave shapes.)
In a rope, the usual wave packet is like a hump, and if the rope is infinitely long, the wave packet can travel forever, as sections at the front of the wave get raised up by the hump just behind them, and sections the hump passed through get pulled down by the rope in its default position behind them. If you now imagine the rope is cut in half and one end is tied to a wall, when the wave gets to this wall, the bit that is tied to the wall does NOT rise up because it's tied to the wall, so the bit just behind it gets pulled down more than it would be in an infinite rope, and after running the simulation for a short time, the net effect is that the back part of the wave doesn't just get pulled down to its equilibrium position like it would if the rope was infinite, but gets pulled down twice that, forming a negative copy of the original wave.
And you can have in-between values, where some section of the rope is harder but not impossible to move, which causes the back part of the wave to be pulled down more than usual, but not twice as much, forming a smaller inverse copy, and the part that is harder to move is pulled up, but less than usual, forming a smaller non-inverse copy.
You can also go the other way, and have a section of the rope that's easier to move than usual (or infinitely easy i.e. an open end), and when the wave gets to this point, the back part of the wave doesn't get pulled down as much as it normally would, leaving it still in the shape of the wave, i.e. a smaller non-inverse copy, instead of returning it fully to equilibrium.
And if you can visualize this with ropes it works similarly for electricity - just replace position by voltage and velocity by current - or any other imaginable system where each piece of a continuum has a second derivative that tries to bring its value back to the average value of its neighbors.