Op amp feedback math question

Oct 09, 2026 Last reply: 5 hours ago 3 Replies

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Christopher Howard 1 day ago

Hi, I'm looking at the input-output equations for op amps in the inverting amplifier configuration, and the inverting integrator configuration, and also how those are derived. But I am wondering what is the equation for the inverting integrator configuration where an extra feedback resistor is added in parallel with the feedback capacitor. I tried to work through deriving that but am feeling doubt about my result. What I came up with was

`(de_o)/dt = -(1/C)(e_i/R_i + e_o/R_f)` where

e_o is output voltage C is feedback capacitor capacitance e_i is input voltage R_i is input resistor resistance

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JM 23 hours ago

Looks correct. Assuming a perfect Op-Amp

Vo/Vi = -Rf/(Ri(1+sRfC)) which is the same as your expression.

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Edward Rawde 23 hours ago

If AI had existed 50 years ago I'd have done this:

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Then select AI mode if it didn't already.

What you have above looks very similar to what the AI says for the differential equation. I haven't checked in detail.

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someone 19 hours ago

That's right. Your equation is just Kirchhoff's current law stating that sum of currents entering a node is 0. The node in this case is IN(-) of the opamp. C x deo/dt is current through the integration capacitor. It does neglect Ib the opamp bias current from IN(-) which can be a big deal if you don't use a FET input amp. And it neglects Vos, the opamp input offset voltage which adds a DC current component to the node summation too. But what you have is basically correct for an exercise in the case of an ideal opamp.

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