If I have a circuit like this, how can I obtain the loop gain, since the capacitors and resistors are not either in series or parallel? If the feedback resistance is \$R_f\$, then I have something similar to the inverting configuration:

$$ V_o = \cfrac{R_f}{Z_{eq}}V_I $$

Where \$Z_{eq}\$ is the equivalent impedance in the input. But how can I get the expression for that input impedance for this configuration?

I know that the result should be:

$$G(s) = \cfrac{s^3R^2C^3R_f}{3s^2R^2C^2+4sRC+1}$$

enter image description here


1 Answer 1


The key here is that the inverting input of the OpAmp is a "virtual ground". When the circuit is in regulation (closed-loop), the OpAmp regulates the voltage at the inverting input to be equal to that on the non-inverting input, which is connected to ground.

With that, your input impedance turns into this circuit:


simulate this circuit – Schematic created using CircuitLab

From there on, it's just a simple series / parallel configuration.

Note that you'll have to compute the current through C3, not the overall input impedance, because some of the current drawn from point X drains to ground before it reaches the OpAmp (and therefore contributes to lowering the input impedance while not contributing to the gain). The equivalent circuit remains the same, though.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.