Find transfer function and step function for this circuit
You cannot find a "transfer function" of this circuit as a whole, because it's NOT linear. Even the part directly involved on the \$V_2\$ generation isn't linear because it contains a diode.

You have to reason otherwise: The circuit generating \$V_2\$ is an envelope detector which, if designed correctly, will obtain the envelope of the \$V_3\$ voltage. The value of that envelope is what it's compared by the comparator with the \$V_1\$ voltage obtained by the voltage divider.

Then it's also the 100K resistor connected between the comparator's output and the positive input, which maybe introduces some sort of hysteresis into the comparison.

If \$V_1 &gt; V_2\$, the comparator's output will be LOW, so the inverter output will go HIGH turning the MOSFET ON. Then, presumabily (the whole circuit isn't visible) a positive voltage vill be applied at the upper input of the first "???" block (which I presume it's another comparator identical to the second one), so perhaps its output will go HIGH generating a step that will be detected with the second comparator, which will turn its output ON, which will turn the MOSFET OFF, deactivating the output of the first comparator, making \$V_1 &gt; V_2\$ again but ONLY AFTER SOME TIME....

My guess is that's some kind of oscillator, but built in an unnecessarily complicated way.

As you see, there are many unknown things in this circuit to be able to be more precise in the answer.