# Equivalent input and output load of OpAmp with feedback network

#### Junus2012

Dear friends,

This is a MFB filter circuit, basically an opamp with feedback network,

I am interested to have an expression of the effective load in term of capacitor and resistor in the outputs and inputs terminal

For example, R(vout+)= R2A||R1A+ R3A and C(out+) = C1A+C2A||C2B ................... (for sure my equations are not right but giving an idea about the expression I need)

The knowledge of these values will help me to design the OpAmp that suits my network values

Regards

##### Full Member level 6
Its tedious but if you write the Z equations by stiming one input with a V source
(the other input grounded) and solving for its current, then use PFE on expression,
you can get the equivalent RLC expression for equivalent values of the effective values
with fdbk. Note you can do this assuming OpAmp is perfect or incorporate its pole
zero response as well. Thats more tedious especially if its a two pole response. You
can always throw away a pole if its far enough removed from dominant pole. To
make life easier. Like I said its tedious but deep insight pops out of this work. Like
why the output looks L as freq rises. And how it rises.

For load stim output with a current and solve for V, inputs grounded.

There is also signal flow graphs where you can write T(s) by inspection. I have never done
it for Z analysis though, although the branches are all Z specified.

Regards, Dana.

Last edited:
Junus2012

### Junus2012

points: 2

#### FvM

##### Super Moderator
Staff member
Some simplification suggested.

Presume you are looking for differential mode impedances. Then it's sufficient to analyse the upper circuit halve.
Secondly, assume infinite OP gain, otherwise the equations become even more complicated.

Sapwin circuit for analyzing input impedance

Zin =

( + R1)
( + C1 R2 R3 + C1 R1 R3 + C1 R1 R2) s
( + C2 C1 R1 R2 R3) s^2
------------------------------------------------------------------------------
( +1)
( + C1 R3 + C1 R2) s
( + C2 C1 R2 R3) s^2

OP output current should be calculated as a function of filter input voltage

Results in this transconductance function

Iout/Vin =

( +1)
( + C1 R3 + C1 R2) s
------------------------------------------------------------------------------
( + R1)
( + C1 R2 R3 + C1 R1 R3 + C1 R1 R2) s
( + C2 C1 R1 R2 R3) s^2

Junus2012

points: 2