# Practical implementation of a Dual op-amp integrator

#### Sambeet

Joined Feb 13, 2021
5
I found this circuit here on the web. The post claims of improving the open-loop gain of the op-amp by huge margins, which is true. But if we try to analyse this circuit in MATLAB, we find that this has zero phase margin at cross-over, which gives gain peaking. My question is, can we use this circuit for practical usage as it appears to be very close to instability?

#### crutschow

Joined Mar 14, 2008
30,107
Why do you want such a high open-loop gain?
Most op amps have a high open-loop gain that increasing would have no significant effect on the integrator accuracy.

#### Sambeet

Joined Feb 13, 2021
5
It is because I want a high bandwidth opamp like THS4631, but the open-loop gain of that is about 10000. With such a low open loop gain, the low cut off frequency is not enough for my application. So I need to increase my open-loop gain for getting a lower cut-off frequency.

#### crutschow

Joined Mar 14, 2008
30,107
What is the circuit?

#### Sambeet

Joined Feb 13, 2021
5
The circuit is an integrator for PCB Rogowski Coil. With Ri =470 and Ci=1nF, the low-cutoff frequency comes out to be 33Hz. The Ri and Ci are fixed with respect to the application as that also decides the sensitivity. So I want to increase the Aol by a factor of 20, to get a lower cut-off frequency.

#### crutschow

Joined Mar 14, 2008
30,107
If the integrator bode gain/phase plot looks normal, then I would think you could use the two op amps in series as shown without a stability problem.

#### Sambeet

Joined Feb 13, 2021
5
Let me reframe the question. The bode plot shows zero phase margin, but the crossover is at 200MHz.I want to use it till a frequency of 30MHz though (it shows proper gain phase characteristics till that frequency). So the question is can I use this integrator like this, i.e. though the system is unstable, can the use be limited to before crossover for operation?

#### LvW

Joined Jun 13, 2013
1,465
The circuit is an integrator for PCB Rogowski Coil. With Ri =470 and Ci=1nF, the low-cutoff frequency comes out to be 33Hz. The Ri and Ci are fixed with respect to the application as that also decides the sensitivity. So I want to increase the Aol by a factor of 20, to get a lower cut-off frequency.
I found this circuit here on the web. The post claims of improving the open-loop gain of the op-amp by huge margins, which is true. But if we try to analyse this circuit in MATLAB, we find that this has zero phase margin at cross-over, which gives gain peaking. My question is, can we use this circuit for practical usage as it appears to be very close to instability?
To answer your last question - of, course, you can`t!
However, there are many other topologies for "composite" amplifiers (consisting of two opamps) with other stability properties.
Example: S. Michael, W.B. Mikhael, "Inverting intergator and active filter applications of composite opamps" (IEEE Trans., Vol. CAS-34. No 5).

As an alternative, you can improve the stability margin using external phase compensation (suitable R-C-combination across the input terminals of the first opamp). This method leads to a continuous increase of 1/beta (inverse feedback factor) and enables a zero (change to a horizontal line) before 1/beta crosses the open-loop amplifier gain magnitude.

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