So I am working on a soft limiter problem where I am supposed to plot V_out vs V_in. I have the answer in front of me but I have no idea where the answer came from.

What I know how to get so far is the middle section of the graph. When the voltage is low the diodes act like a short and all you are left with is an inverting amplifier.

What I don't know how to get is where the limiting takes place. This limiter is symmetrical so it should just be a mirror image on the positive and negative ends. I don't understand how the slope of V_out vs V_in is determined and at what value the limiting takes place.

Thanks for your help!

 

Assume everything is ideal and that Vin is initially zero. Then, Vout will be zero too and both diodes are reversed biased.

If Vin increases, Vout decreases and so does Va. When Va decreases just below zero D1 conducts because the voltage at the inverting input is held at 0V and R4 is in parallel with R2.

If Vin decreases, Vout increases and so does Vb. When Vb increases just above zero D2 conducts and R6 is in parallel with R2.