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Can microcontroller work like switches for low voltage analog signal. I mean when press the button signal (less than 300 mV, very low amperage) pass unchanged through microcontroller (one analog input, one analog output), than by software disable input and output or simply turn off power (same button)? I want to solve that without external switches and relays. Thanks.

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No, a microcontroller will generally not include an analogue switching element. The analogue input is implemented as an analogue to digital convertor (with limited resolution and sampling frequency) and the analogue output is a digital to analogue convertor (with again limited resolution and sampling frequency).

So it is possible to pass an analogue signal in and out, but there will be latency, voltage quantisation and timing quantisation introduced. It will also require you to continuously transfer data from one peripheral to another.

An external analogue switch is likely to work much better...

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