FM demodulation amplifier with saturation I'm trying to understand how FM demodulation works. I read a lot on the internet and as far as I understand, the main process is to extract the phase difference (that is also the output) between a quadrature signal and the input signal, and that use this difference to keep those two signals locked in phase.

However the output signal amplitude depends a lot on the input signal strenght. As I understand, the input of the phase locked loop should be constant in amplitude.

Besides on this article on wikipedia it's written that FM recivers do not need a AGC, but it's enough to use a "high-gain IF amplifier which is intentionally driven into saturation". How can this be right? I mean.. If the amplifier is driven into saturation, the input wave will look more like a square wave and all the quadrature equations won't be true anymore! Can anybody explain me this step?

EDIT 1

I think that the input should be constant in amplitute because(I'm thinking about a PLL):

$ FM_in(t) = A sin( W_c * t + \phi(t) ) \\
 FM_in(t) * cos(W_c*t) = {A \over 2}(sen(\phi(t)) +  cos(2W_c + \phi(t)) ) $

So filtering out the high frequency cosine, I get:

$ DEM_Out(t) = {A \over 2} sen(\phi(t)) \simeq {A \over 2}\phi(t) $

And so far so good, but to keep in lock the loop I should feed this value to the VCO, and if A doubles(as I understand), the phase shift of the VCO doubles, too so that the loop won't be in lock anymore. I hope I have explained what I mean!
The receiver's output does not depend on the input amplitude.  From the point of view of the receiver, the output only depends on the frequency/phase of the input.  

An fm signal in an ideal environment has a constant amplitude.  Another way of putting it is that fm modulation has a constant envelope.  Often this is advantageous because it allows the transmit amplifier to run at saturated output and not impact the modulation since amplitude is not varied as opposed to QAM and other non-constant envelope modulation types.  The same should hold true for the receiving side of the equation.  In practice I imagine you'd still need to watch out for overloading the receiver and causing harmonics and other nasties.

A write-up on my pyFmRadio blog post illustrates FM's amplitude independence from the modulating audio source.