Someday, I wish I could understand electrical impedance.
I understand DC resistance. After designing and building my own Tube based electric guitar amplifier, I head to learn the relation between DC resistance and current _intimately_.
What I still didn't have a grasp on is the concept of impedance. While I was able to calculate correct values for my guitar amp, I didn't know _why_ I was doing it which is a bit frustrating. For instance, I still don't understand the output transformer that "matches the impedance of the speaker to the output tube". Le sigh.
I'm no expert but FWIW, I find thinking about it as a resistance is unhelpful. It's much closer to a sort of "resonance coefficient". Sure it's measured in ohms but a 50 ohm cable will not "resist" the flow of signal like a 50 ohm resistor because a resistor is a load (can simulate an antenna) while the cable is just resonant with the load. What makes a given line/cable "50 ohm" is largely capacitance driven because it needs to be resonant with a 50 ohm load at one end and a 50 ohm source at the other.
I find amateur radio literature to be pretty good for this kind of stuff. It's a very central issue to them.
I think the OP is talking about input/output impedances of amplifiers/guitar pickups, while you're talking about transmission line characteristic impedance.
Impedance of a transmission line is weird: in some ways, it acts exactly like a resistor, and in some ways it doesn't.
In contrast to a resistor, an ideal transmission line doesn't convert electrical energy to heat. Ideally, 100% of electrical energy put in one end of the line will make it to the other end of the line intact.
However, just like an ideal resistor, an ideal transmission line will have a real-valued impedance, not a capacitive (negative imaginary values) or inductive (positive imaginary values) impedance; nor will an ideal transmission line have any frequency dependence in its impedance: 50 ohms is 50 ohms.
One way I like to think of characteristic impedance is that it's the temporary impedance a change in signal will see until current/voltage wave reflections make it back from the other end:
For a 50-ohm ideal transmission line one light-second long (pretending we have velocity factor 1.0 to make the math easy), your ohmmeter would read 50 ohms for two seconds, and after that it would read whatever resistance is connected to the other end. If the other end is an open circuit, the ohmmeter would measure 50 ohms then infinite resistance; if the other end is a short circuit, the ohmmeter would see 50 ohms then 0 ohms; if the other end is terminated with a 50-ohm resistor, the ohmmeter would measure 50 ohms indefinitely.
If you have an infinitely long ideal transmission line with 50 ohm impedance, and hooked up an ohmmeter to it, it would measure 50 ohms. If you hooked up an LCR meter, it would show 0 impedance and 0 capacitance.
This indistinguishability between an infinitely long transmission line and a resistor is why a matched termination resistor prevents signal reflections: If you have some finite length of transmission line, and you attach either a matched resistor or an infinitely long transmission line with the same impedance to the end, the first length of transmission line cannot tell which you have attached - its behavior will be the same in either case: all the energy is passed into the next section.
Do you mean impedance the concept (it's just resistance, in the frequency domain), the fact that amplifiers have an "output" impedance, maximum power transfer, or how a transformer works to convert output impedance?
There's a lot of inter-layered things behind "why do tube amps need an output transformer." The concept of impedance is pretty simple and doesn't really deal with that, other than being the 0th layer.
Impedance is basically the resistance of the change in current direction. In DC systems, you almost never deal with this. You deal with this constantly in AC systems and LC circuits.
"Impedance" as used by audio people is completely different from "impedance" as used by RF people.
In audio, it's about the equivalent resistance of an input or load. If you put a dummy resistor in place of a load, how would the output/driver treat it? How do you choose what value of resistor to use, to stand in for a given load/input? That's the impedance.
In RF, it's about the equivalent resistance of the transmission line itself, because at high enough frequencies the speed-of-light prevents you from even seeing the far end. That phenomenon is well treated here:
I don't believe this is true, AF and RF have significant overlap on the frequency domain, AF is just baseband RF when it's on the wire. RF very much can work with a resistive load, a 50ohm dummy load will ohm out as 50 ohm DC on any cheap multimeter.
The distinction is when the transmission line is "electrically short" relative to the wavelength of the highest harmonic of interest (typical in audio unless your speaker wires are 40km long), and thus its impedance doesn't play much of a role (and therefore you "see" the load directly), or if the transmission line is "electrically long" (typically the case in RF), so your source is driving the line rather than driving the load directly.
I understand DC resistance. After designing and building my own Tube based electric guitar amplifier, I head to learn the relation between DC resistance and current _intimately_.
What I still didn't have a grasp on is the concept of impedance. While I was able to calculate correct values for my guitar amp, I didn't know _why_ I was doing it which is a bit frustrating. For instance, I still don't understand the output transformer that "matches the impedance of the speaker to the output tube". Le sigh.