# How is gain changed in this op-amp integrator?

I am simulating this circuit for personal development. The gain of the integrator can be calculated using the following formula:

Gain = -Rf/R1 (1/(1+(2 x pi x f x C1 x Rf)))

How can I calculate the gain of this circuit when diodes are introduced for rectification?

I tried for some time, but couldn't get the result I see on simulation. How can I calculate the gain of this circuit and the output voltage (both Vrms and Vdc) with that gain?

It would also help if someone could explain how this circuit works.

• Ignore the capacitors. Analyze the circuit assuming the op amp output is positive. Analyze the circuit assuming the op amp output is negative. The op amp negative terminal is always at ground potential. Assume the diodes are shorts when forward biased and opens when reversed biased. Commented Dec 10, 2020 at 5:07
• @user69795, can you be more specific?
– CNA
Commented Dec 10, 2020 at 12:59
• the circuit as far as R5 is called a precision half wave rectifier. You can search on that and find explanations,it is a well known circuit. Then you have a simple CR circuit on its output. Commented Feb 6 at 15:06