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I was trying to derive the transfer function of a simple inverting op amp topology, incorporating the output impedance, Ro, of the non-ideal op amp, to see how it, when combined with a load capacitance can induce oscillations (or at least ringing). I haven't been able to get a valid answer --could be bookkeeping errors with the math, or just that my set up is incorrect for deriving the circuit's transfer function. Refer to the attached picture.

Using Laplace, the xfer function I end up with is:

[itex]\frac{vo(s)}{vi(s)}[/itex]=[itex]\frac{-A*RF}{(R1+RF)*(s*CL*Ro*RF+(Ro+RF))+A*R1}[/itex]

If A is really big...this simplifies to -RF/R1, which is sort-of expected for negligible Ro. However, I expected the frequency dependent component (which includes RO) to be part this result even as A is big, so I must be doing something wrong somewhere.

I suspect it has to do with the derivation of the xfer function using A(Vp-Vn). Basically, I obtain Vn via superposition of the contributions from Vin and Vo as [itex]\frac{(V1*RF +Vo*R1)}{(R1+RF)}[/itex], Vp =0, and then use KVL at the Vo node....That is...

[itex]\frac{-A*Vn-Vo}{Ro}[/itex]+ [itex]\frac{(Vn-Vo)}{RF}[/itex]=Vo*s*CL....I then sub in the equation for Vn above and solve for Vo/Vin.....

Any help is appreciated...

Jorge

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# Op amp transfer function incorporating output impedance

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