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Say I have a signal driver operating at 50 ohm output impedance, driving something with high (hundred kilo-ohm) input impedance. If the wavelength I'm using (a few kilohertz) is much longer than my chord length (a couple feet), then I understand that standing waves cannot develop..

But, do I need to worry about the reflection causing damage to my driver? I guess a back-reflection always occurs if you have an impedance mismatch. Why do we usually only worry about this sort of thing when standing waves are possible, typically at 'high' (RF) frequency?

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One starts to worry about reflections at high frequency because the disturbance caused by such reflections (which are high frequency as well) will interfere with the signal. At low frequency, the first capacitor down the road will filter those disturbances out.

Reflections may happen regardless of the useful frequency of the signal. If the signal happens to have sharp edges (short rise / fall times), you may end up with twice the voltage at the end of the line.

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It's all to do with signal wavelength and the lengths of the signal paths, either within a circuit or in the cables connecting various parts of a circuit or system. Reflections only occur when the length of a signal path or transmission line is significant compared to the wavelength of the signal - such systems are called 'distributed systems'. eg at 100MHz the wavelength is 3m and a transmission line of, say, 20m is significant. At an audio frequency of, say, 10kHz, the wavelength is 30,000m and a 2m length of speaker cable is insignificant. In this case the system would be called 'lumped'.

At microwave frequencies, the lengths of the signal paths (e.g. copper tracks) on the PCB become critical, e.g. at 100GHz, the wavelength is 3mm

To avoid refelections, the impedance of the source, transmission line, and load should be equal.

In the case of your driver, a (straightforward) load mismatch may cause problems. Generally, output stages do not like working into open circuits.

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No matter how long the transmission line compared to wavelength is, impedance matching is important whenever transport of power is relevant.
(in contrast to e.g. just transmitting a signal as voltage level).

Transport of power is relevant in following two (opposite) situations:

  • There is so much power involved that you have a problem if power is not only transported to its intended destination but is wasted somewhere else. Problems that arise are e.g. heat dissipation or low efficiency. Examples are any power amplifiers. E.g. in an audio PA you want the power to get to the speaker and not to make your transistors hotter.
  • There is so little power involved that you can not afford to waste it anywhere, because Signal-to-Noise-(or Signal-to-Disturbance) Power!-Ratio is important.
    Examples are any communication systems that fight against unwanted signals, e.g. radio receivers (not only for very short wavelengths). In a receiver the received signal has to be amplified very much to be used. Amplification per se is not difficult, but it inevitably introduces noise; so much noise that the received signal may get lost in noise; unless you take a lot of care to have efficient transport of signal power between antenna, filter, amplifier, mixer, etc. stages.

Both situation may be the case even if the wavelength is much longer than the transmission line.

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  • \$\begingroup\$ In text books, I find the "transmission line length" rule of thumb. I'm struggling with your criterion "impedance matching is important whenever transport of power is relevant". Are you saying that high speed digital data connections do not need impedance matching as they transmit information ("signal as voltage level") and no power? And in contrast to that, do (low frequency) AC power lines need impedance matching as their only objective is to transport power? \$\endgroup\$ – Daniel K. Aug 26 '19 at 15:57
  • \$\begingroup\$ I'd classify high speed data connections as belonging to the second group: for high speed communication SNR becomes the limiting factor. And concerning LF power distribution: impedance matching is quite important! That's why electric power companies want your SMPS to have PFC and invest a lot effort in matching their transmission lines using huge inductors/capacitors (even though large distribution networks are still tiny compared to wavelength @50/60Hz). \$\endgroup\$ – Curd Aug 27 '19 at 16:47
  • \$\begingroup\$ I don't agree that for high speed communication generally "SNR becomes the limiting factor". In the discussed domain, signal distortion (e.g., generated by reflections due to impedance discontinuities) is the dominant limiting factor. At the receiver, reflections distort the signal and if the distortion is large enough, the signal cannot be detected reliably. I've just checked a simple unmatched digital line where I send a rectangular pulse with a (relatively) sharp edge (~2 ns rise time) and I see textbook reflections like here but no noise. \$\endgroup\$ – Daniel K. Aug 28 '19 at 12:54
  • \$\begingroup\$ You are correct insofar as reflected power strictly speaking is not noise (in the sense of random signal). If you allow me (just now) to count those reflections as noise (in the sense of unwanted disturbance) it is again the SNR that matters. My point is that ratio of transmission line length to wavelength is by far not a sufficient criterion; and also not a necessary criterion (because there are situations where there are reflections caused by mismatching but they just don't cause any problems). \$\endgroup\$ – Curd Aug 28 '19 at 16:41
  • \$\begingroup\$ Curd, I see the point you are making regarding the "transmission line length" rule of thumb. I agree that it is not be a perfect criterion. But so is your " transport of power" criterion. You seem to promote it as a fundamental rule. I just don't agree with that. See my earlier example of high speed digital data connections where it is not about transmission of power but all about information represented by voltage levels. Finally, if you have to change definitions to make a rule work, that's cheating :-) \$\endgroup\$ – Daniel K. Oct 22 '19 at 13:48
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But, do I need to worry about the reflection causing damage to my driver? I guess a back-reflection always occurs if you have an impedance mismatch. Why do we usually only worry about this sort of thing when standing waves are possible, typically at 'high' (RF) frequency?

If your transmission line is electrically short, then the reflected signal is not going to be very far out of phase from what the driver is driving. If "a few kilohertz" is 5kHz, "a couple feet" is 0.6m, and Vf is 0.9, then the returning signal will be about 0.006° out of phase, and the mismatch voltage is a sine with an amplitude no more than about 1/1000 of the driving amplitude. Doesn't sound like something that should be causing damage to me.

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