[myth2018]

Thank you very much for sharing this. I've been trying to form a mental model of why reflection in transmission lines is a thing and never found a theoretical foundation that satisfied me. I've read a number of publications that just state that as fact, without further explanation. I'll spend some time sketching my own graphs and formulas to fully absorb the fine article.

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).

[basementcat]

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

[DougMerritt]

> Impedance is analogous to index of refraction

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.

[myth2018]

Thanks. I found experiments like this [0] helpful to visualize reflections and standing waves, but, like a sibling comment said, although these are similar phenomena and show what happens with the energy inside the wire, I couldn't see why these effects manifested at the electrical level.

[0] - https://youtu.be/1PsGZq5sLrw

[marcosdumay]

Yeah, that's easy to work with so it's a great working model. But as an explanation, it leaves a lot to be desired.

In fact, I'd say it's easier to explain optical refraction with an electrical model than the other way around.

[gzalo]

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!

[myth2018]

I had never heard about them. Will do some research right away, thanks

[immibis]

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.

[myth2018]

Those are interesting insights, thanks for the extensive reply

[jrmg]

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.

[nereye]

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

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