Electronics > Beginners

Deriving Op Amp Output Equations

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TeddyPython:
I'm learning about the basics of op amps - at the moment looking into using them to remove or add offsets. However I'm struggling with deriving a 'general-case' equation for such a circuit for gain and why it offsets the way it seems to in simulation.

Using a standard op amp model I found that, for an inverting amp, applying a voltage, Vx, to the non-inverting input would offset the output by 2Vx without affecting the gain.

I tried deriving the gain equation, as shown in my attachment. When the inverting input is 0V, the Vp terms disappear nicely - but in this case they don't... Instead I am juggling Vout by (5) and have no idea where it goes from here...

Also, as far as it comes to figuring out why the offset is twice the voltage at the +'ve terminal - I have no idea where to start.

Any further explanation would be really appreciated.  ^-^

magic:
Firstly, gain is Vout/Vin rather than Vin/Vout, but that doesn't really matter.
Secondly, you made the mistake of trying to calculate DC gain. Of course if the input is 1V and the offset is 1000V, the DC "gain" of the whole circuit will be about 1000x. That's not really a useful spec to have at all :)

Calculate the AC gain, which is how much the output varies when Vin varies. This is probably what you want to know.

It may be helpful to observe that Vout=Vin+(R1+R2)/R1ยท(Vp-Vin).

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