Either I suck at searching or there is not a lot information about calculating values of bypass caps for opamps(I found a bunch on the topic in general). The question is, what it says in the title, say I have an audio range circuit with variable gain with an op amp run off of +/- 4.5V ( voltage divider on a 9V cell ) output current is probably under 50mA, now how would I go about calculating the values for the supply bypass caps?
Batteries are a special case because their internal resistance increases as they discharge.
Probably something like 100uF/16V in parallel with 1uF/16V ceramic. Here's what the impedance vs. frequency of a 100uF capacitor with 5 ohm ESR in parallel with a 1uF ideal capacitor looks like from 100Hz to 5MHz:
So, it's pretty low over the entire audio range (so it will prevent unnecessary changes in the battery voltage if you draw reasonable current) and very low up to where the audio op-amp gain should be below 1. 1000uF would be even better but they're physically large, and 100uF/16V is quite small.