# Transfer function of a cascaded op-amp circuit

#### xdarkbee

Joined Dec 9, 2022
11

I have doubts with the following circuit, I have already obtained the transfer function to the circuit but only with resistors, now they have put a capacitor and I don't know how to proceed

#### LvW

Joined Jun 13, 2013
1,760
The calculation procedure is as before when you replace the feedback resistor of the 1st opamp with the capacitive impedance Zc=1/jwC.
However, under real conditions the circuit will not work because of resistive positive feedback. There will be no stable DC operating point and the circuit will go into saturation.

#### xdarkbee

Joined Dec 9, 2022
11
The calculation procedure is as before when you replace the feedback resistor of the 1st opamp with the capacitive impedance Zc=1/jwC.
However, under real conditions the circuit will not work because of resistive positive feedback. There will be no stable DC operating point and the circuit will go into saturation.
The circuit would be fed back with a PID controller that makes it seek its stabilization, do you think that it works?

#### LvW

Joined Jun 13, 2013
1,760
The circuit would be fed back with a PID controller that makes it seek its stabilization, do you think that it works?
No, I dont think so. A PID controller will influence the dynamic behaviour of a circuit but it cannot fix a dc operating point.
In any case - you must avoid DC feedback with two inversions within the loop.
As a working example: The classical state variable filter (universal filter) consists of an integrator stage plus an inverting amplifier (as in your case) plus an additional integrating stage within one loop.

#### xdarkbee

Joined Dec 9, 2022
11
No, I dont think so. A PID controller will influence the dynamic behaviour of a circuit but it cannot fix a dc operating point.
In any case - you must avoid DC feedback with two inversions within the loop.
As a working example: The classical state variable filter (universal filter) consists of an integrator stage plus an inverting amplifier (as in your case) plus an additional integrating stage within one loop.
Before I asked how to convert my plant into a circuit, since I was going to test the PID controller in a physical circuit and they gave me that circuit that has an unstable pole, so how do you recommend I model my function which is 1/ s - 2 in a circuit functional?

#### Papabravo

Joined Feb 24, 2006
21,227
Before I asked how to convert my plant into a circuit, since I was going to test the PID controller in a physical circuit and they gave me that circuit that has an unstable pole, so how do you recommend I model my function which is 1/ s - 2 in a circuit functional?
A voltage-controlled voltage source whose output grows exponentially.

#### xdarkbee

Joined Dec 9, 2022
11
A voltage-controlled voltage source whose output grows exponentially.
Could I make use of an exponential amplifier?

#### Rodrigo0595

Joined Sep 23, 2022
9
Regardless of whether the circuit works or not, the transfer function of the circuit is:

I hope I did not make any mistakes in the analysis.

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#### Papabravo

Joined Feb 24, 2006
21,227
Could I make use of an exponential amplifier?
I don't know what that is.