How do I find the closed loop output impedance of an op-amp in terms of R,L,C parameters?

Question

How do I model the closed loop output impedance of an op-amp with R,L,C parameters? Is there a definite method using simulations? And is it possible to relate it with individual transistor configuration/sizing inside the op-amp? I have been told by my professor to do the same but I could not find any good resource on the internet regarding the same.

Answer 1

How do I model the closed loop output impedance of an op-amp with R,L,C parameters?

The closed-loop output impedance of an opamp can be found using the loop gain. From sysytem theory we know that the ouput impedance r2 of the "naked" opamp alone is reduced due to negative feedback by a factor of (1-loop gain):

r_out=r2/(1-loop gain).

Note that for negative feedback the loop gain LG has a negative sign_: LG=-k(s) * Ao(s)

with k(s)=feedback factor (can be frequency-dependent) and Ao=open-loop gain of the opamp.

The output impedance can be simulated when a test current i_test is injected into the opamp output (loop closed) with signal input Vin=0 (grounded): r_out=v_out/i_test

Answer 2

How do I model the closed loop output impedance of an op-amp with R,L,C parameters?

Solve the circuit for the output vs inputs.

Is there a definite method using simulations?

A spice package can give you an AC analysis, which can be converted to a transfer function with control system ID tools

And is it possible to relate it with individual transistor configuration/sizing inside the op-amp?

No, there are too many parameters. You would have to know the configuration of the transistors and processes with reverse engineering.