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jason9
modified 5 months ago

Rapid response resistor

2
2
113
01:02:17
A simple resistor can be made by coiling a long piece of wire. However, this is also how an inductor is constructed, so this resistor will have a large quantity of unwanted inductance. To solve this, after it is coiled, the wire may then turn around and follow itself again backwards, which winds it the opposite way, cancelling the inductance. In effect, it is a long transmission line (two parallel wires) that is terminated at the end by a short and coiled up. However, such a construction will produce ringing at high frequencies as the transmission line resonates since a wave traveling down it will tend to reflect off the shorted end, so it will take a while for the resistor to eventually settle down to a simple 50 ohm response after a DC voltage is suddenly applied. The solution is to specifically tailor the transmission line so that its characteristic impedance at any given point exactly matches the total wire resistance from that point to the shorted end of the transmission line. Here, I have a simulated 50 ohm resistor (made out of a transmission line) forming a voltage divider with an ideal 50 ohm resistor. The wire that the transmission line is composed of has resistance, modeled here as repeated 5.55 or 5.56 ohm resistors, totaling 50 ohms, so under DC conditions, it acts as a 50 ohm resistor. However, the transient behavior is what is important here. The goal is for it to behave as a 50 ohm resistor immediately, well before the EM wave reaches the end of the transmission line. To do this, the transmission line is engineered to have a characteristic impedance of 50 ohms at the start. However, this characteristic impedance changes through the transmission line so that at every point it matches the resistance of the remaining line. So, half way through the line, it has a characteristic impedance of approximately 25 ohms, achieved by increasing the capacitance and reducing the inductance. By the end, the characteristic impedance is very small, achieved using tiny inductance and massive capacitance. The net result is a resistor that responds immediately with a 50 ohm impedance and produces an EM wave propagating down the line that essentially does not reflect at all at the end.
published 5 months ago
zorgrian
5 months ago
You can also bunch-up the windings, such that there are spaces between these. However, no amount of counter-windings will really work. Essentially, you're making an inductor. Real resistors are often made this way, albeit using metal film.
jason9
5 months ago
Yeah, there's always gonna be a lot of parasitic stuff going on. To implement my circuit properly would probably be very expensive since you'd basically need a compact transmission line with properly tailored characteristics along its whole length and coiled up in such a way as to minimize self-interference.

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