Product-type phase detector question

I am looking for more information (derivations, equations) about detector gain differences when fed with 2 sinusoidal or 2 square wave inputs. Also how sinusoidal distortion can affect useful operation range.

I have searched on the web but could not find anything useful yet.

To find equations and functional description of the circuit posted, search for Foster-Seeley Discriminator which has similar behavior.

I looked at the FS but the book I found this circuit describe the two to be different in operation.

I want to know if the gain equation will be different when driven with sine waves as opposed to be driven with square waves. I found conflicting information and want to know which is correct.

One source say gain is 2V/Π for square waves and just V when driven with sine.

Another source say both are the same with gain V/Π

Edit:

I found what I agree with and believe is correct:

When driven with sine sources amplitude A&B, Kd will be -(AB/2)*Sinθ

When driven with squarewaves amplitude A&B, Kd will be 2AB/Π