Oliver Heaviside and the theory of transmission lines (2021)

It wasn't just Cats. There really is a layer in the ionosphere called the Heaviside Layer, or more formally the Kennelly–Heaviside layer:

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!

Not a religious person, but there's something deeply spiritual about Katalin Karikó type characters, who throughout the ages stuck with their curiosities and craft for the craft's sake.

That video is good for the water like wave explanation that is a very useful lens. If you want a more in-depth explanation, particularly how the field is in the dielectric and the wires/traces are simply the wave guide, this long presentation by Rick Hartley will help move to the next level.

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.

> Controlled impedance took me a long time to wrap my head around (...) 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?

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.

I remember reading about the first cable that was laid across the Atlantic.

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.

That is a great visualisation, yes!

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.

That video (and channel, seemingly) is incredible, thank you for posting! I've never seen anything like the visualizations starting at ~10m.

And Li-ion batteries are good enough: https://en.wikipedia.org/wiki/John_B._Goodenough

Nominal Determinism at its finest

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I doubt it, as pseudovectors are kind of a mess ?

But you can also further compress those 4 equations into just a single one by using slightly more complicated geometry !

http://www.av8n.com/physics/maxwell-ga.htm

> Dirac delta function

and the Heaviside Step function looks like Heaviside's head lol.

Tried skimming the page but couldn't find the answer: do we know if the neural connection impedance is perfectly matched? It looks quite organic in shape, with teardrop connections and so on, but curious how nature did that job?

This looks different, as there is a completely resistive path from source to destination, which is not the case for transmission lines (as that would mean an instantaneous response which isn't possible due to the speed of light limit).

Elk is a type of transmission line conductor. Example - https://www.lzcable.com/acsr-elk-conductor/

Others include moose and drake.

I just finished reading this one. It was fantastic. I particularly enjoyed the spicy editorial excerpts from The Electrician ( https://en.m.wikipedia.org/wiki/The_Electrician ).

Paul Nahins books are so good.

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)

> doesn't omit the math.

"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...

For me, an optics analogy appealed to my intuition. A transmission line is analogous to a periodic crystalline material, perhaps a form of quartz. Impedance is analogous to index of refraction; if two materials of differing index of refraction are juxtaposed, some of the light will reflect back. If the indices of refraction match ("impedance match") then there is no reflection and maximum energy transfer takes place.

https://en.m.wikipedia.org/wiki/Refractive_index

Indeed, if you search for "ceramic antennas" you'll see that they are already being used and smaller than equivalent PCB antennas. They rely on a dielectric material with high e_r, which implies that speed of light is slower there. Lots of portable devices use them nowadays!

Yes! I’ve dabbled in digital electronics and never managed to form an intuitive understanding on ‘impedance’ in signal wires despite reading quite a few ‘basics’ texts about it. I’d ended up accepting that I wouldn’t really understand its basis without learning a lot more about analog electronics, but this explanation really worked for me.

Am partial to the following vintage video on transmission lines from Tektronix:

https://www.youtube.com/watch?v=I9m2w4DgeVk

It's the general theory of waves: whenever some value exists on a continuum, has a position and a velocity at each point, and the acceleration (change in velocity) brings each point towards the average of its neighbours.

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.