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I know that my problem with this is some flaw in my logic, I just need someone to point out to me where that flaw is. According to the Wikipedia article, there are different formulas because power gain is proportional to the square of the voltage (amplitude) gain. I can accept that and it makes sense except that the formula for voltage gain is only true when the input impedance is equal to the output impedance. That contradicts what I think I know about gain stages - that is, that the input impedance should be very high and the output impedance should be very low in order to drive the next stage.
So my question is, what's wrong with the way I'm thinking about this? And does the formula for voltage gain in decibels change when input impedance does not equal output impedance?