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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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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 else than at the intended place, because Signal-to-Noise-Power!-Ratio is important.
    Examples are radio receivers (not only for very short wavelengths). In an 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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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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