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I built a little USB powered audio amp (op-amp based) with 3.5mm audio jacks as an output. If I plug something to the audio jack, then during plugin moment there is a small period where the amp output is shorted. This causes my USB connected micro-controller part to reboot. What would be the most elegant counter-measure against that?

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The standard thing to do (for example in a op-amp headphone amplifier) is to AC couple the output jack (that is, go through a blocking capacitor). While this prevents the short circuit problem you have noted and protects the amplifier and headphone circuitry (for example, if you have some DC offset or the D/A is able to put out a DC voltage), the problems with this approach are that:

1) You need a fairly large capacitor for good low-frequency response, since the resistance part of that R-C filter will likely be small (it is an amplifier after all, and you don't want the response to be dominated by the resistance of the headphones).

2) You are putting a capacitor into your audio path, so it needs to be fairly linear, or you will have distortion in your output. A typical choice is to use film capacitors, but they are large and expensive.

Another approach is to use a 'capless' headphone driver, which takes care of all this stuff for you. A highly regarded part is the TPA4411.

See also, this document on capacitor and topology selection if you go the op-amp route: SLOA043

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