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The word 'pad' in audio is derived from Passive Attenuation Device. 'Passive' refers to an electronic circuit that requires no power to operate. 'Attenuation' means making the level of the signal smaller.
'Device' means that it was invented by someone who was extremely clever!
You will commonly find a switchable pad in a capacitor microphone, and also in a microphone preamplifier. There isn't much use for pads anywhere else in the audio signal chain.
The value of a pad is in its passive nature. This means that it can accept any signal level without distortion, right up to the point where the circuit components burn out (which would be a very high level indeed).
A capacitor microphone contains an internal amplifier, which is an active (not passive) device. All active circuits have an upper limit on the level of the signal they can handle correctly. If the signal attempts to go above this level, it will be clipped at peak level until it drops back down again. This causes very serious distortion.
So if a capacitor microphone is exposed to sound of very high level, the internal amplifier might clip. To prevent this, a pad can be switched in that comes before the amplifier, lowering the signal level before it can cause clipping.
The same can happen in a microphone preamplifier. If the input signal is very high in level, the very first input stage can clip. Once again, if a pad is switched in before the first active stage, clipping can be prevented.
So if the sound level is very high, the pad in the microphone should be switched in. If this is switched in, then the pad in the preamp will probably not be necessary, but it's there just in case.
Pads can be used in both studio and live recording.