gain calculations

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You would use normal op-amp gain calculations, Rf/Ri for inverting, 1+Rf/Ri

to get the gain in dB , 20Log(gain)

In the case of Rods amp ( I assume you were reffering to his P3A?)

It looks like Rf=22k and Ri = 1k which gives the voltage gain of 27dB
 
The AVERAGE power into a load of resistance R for a sinewave is (Vpeak)^2/(2R).
So you work out the Vpeak you need for the average power you want (sometimes average power is incorrectly refered to as "RMS power" by the way - "RMS power" doesn't exist), then divide this by the Vpeak you have available at the input and this is the voltage gain you need.

Example: You want 100W average into 8-ohms at full volume and your CD player gives 2V peak as an input. The output peak voltage needs to be at least SQRT(100*16) = 40. So the voltage gain must be at least 40/2 = 20.

A voltage gain of between 20 and 50 is usual for domestic power amps.
 
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