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# How to Find Circuit Gain?

Circuit Gain

Suppose I have Vin = V1 + V2*sin(wt) and Vout = V3 + V4*sin(wt). How do I calculate gain? I know it's Vout/Vin, but my lab handout tells me it's a constant (the lab handouts are garbage, though, so it could be wrong). I have zero background in circuits, I'd already spent 40+ hours on this lab before I even got to the circuit gain part, it took me hours to figure out what the "Z" in my handout stood for and I've spent even more hours running in circles around Google trying to figure out how to calculate it, I just need to finish this lab report. Please help.

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### Replies to This Discussion

Gain, as you said, is calculated by Vout/Vin.  You gave Vin = V1 + V2 SINwt and Vout as V3 + V4 SINwt.  So we substitute and we get (V3 + V4 SINwt)/( V1 + V2 SINwt).  Now you cannot really do anything further here unless you know something about the four voltages that you provided.  If they have some sort of relationship, you can do further substitution.

For the heck of it let’s say that V1 = V2 = Vx and that V3 = V4 = Vy.

Now we substitute and we get (Vy + Vy SINwt)/( Vx + Vx SIN wt).

Now we factor out the common factor of both to get:

Vy(1+SINwt)/Vx(1+SINwt)

The common terms cancel and leaves us with Vy/Vx