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What SunnySkyguy says plus audio device such as a low impedance microphone can be used into a preamp with a low impedance input, while a high impedance microphone would not work at all. So there is a rough impedance match required. Likewise for the audio power amplifiers, they are designed to put their rated power into a loudspeaker with a certain impedance (now a days its 8 ohms). They will work with a different loudspeaker and still meet all of their specifications EXCEPT the power output.
The most critical matching is for high power transmitter circuits. if the matching to the aerial is not spot on and 2% of the power is reflected. because this reflected power can be kilowatts and the output circuits cannot absorb this power, very high voltages will be present and cause real flash overs and the demise of an expensive transmitting valve (tube). High power solid state amplifiers also suffer from this problem. At lower power levels optimum noise factors cannot be realised and frequency responses become "tilted" due to the reflected part of the input signal setting up standing waves on the lines connecting circuits.
Methods of matching and their tuning can only be described as per that one equipment. Obviously the matching circuit is meant to transform one impedance to appear to be another. i.e. a 75 ohm aerial may be matched to a 200 ohm transistor input impedance. In general the match and loss should be within specification across the frequency band required. So there are many variables that may have to be balanced out against each other.
Audio circuits almost always do not have matched impedances so that the voltage loss is low.
The output impedance of an audio power amplifier is extremely low at 0.04 ohms or less so that it damps the resonances of a 4 ohm or 8 ohm speaker.
Matched impedances are not used for many circuits where other factors are critical.
In both power supplies and audio amps and some logic circuits, the voltage attenuation of 50% of a matched impedance can cause poor dampening factor in low frequency response of subwoofers so the source impedance is often 1 to 0.1% of the load impedance.
In CMOS's logic the source impedance depends on selection of driver which can vary from 25 Ohms or modern low voltage chips to 150 Ohms for older CMOS technology and high fan out to multiple loads is required for signal sources so low capacitance and high input impedance is desirable.
For DC power supplies the load regulation is also a ratio of load to source impedance so a1% load regulation spec for a switched load requires that the source impedance is <1% of the load. This applies to both the ESR of a stabilizing source capacitor and the series regulator which may drop V/A with load which determines the regulation and source impedance requirements.
This method of analysis is different from matched impedance as the requirements for reflections at high frequency >1MHz is less important than lower frequency distortion, or regulation is more important , as a true voltage source at 0 Ohms never exists.
Signal traces for high speed data with transmission line "characteristic impedance" is considered important as well as matching load to source impedance such as 200 Ohms for differential pairs or 75 Ohm for video cables or 50 Ohms for most Engineering test equipment etc.