Physical reasons for gain compression of amplifier?

Hi everyone, as we know that amplifiers suffer from ?gain compression? because of its nonlinearity. Assume the input of ampllifier is "

=cos(

t)", the amplitude of the output fundamental wave can be expressed by the following formula "k1

[1+

(k3/k1)

]" (or, you can clearly see in the following fig.).

When ?k3>0?, it is called ?gain expansion?; while ?k3<0?, it is called ?gain compression?. Well, we know that gain compression is the real case for amplifiers. But what are the physical reasons for gain compression of amplifiers? Or, anyone can physically explain why ?gain expansion (k3>0)? cannot happen for amplifiers? Thanks!

I read the book <Microwave Engineering(2011_4th) David Pozar>. It simply explain the physical reason for the "gain compression".
But I still cannot understand it. Anyone can give me some comments?

"This effect is called gain compression, or saturation. Physically, this is usually due to the fact that the instantaneous output voltage of an amplifier is limited by the power supply voltage used to bias the active device."

What do you think is not clear? In any amplifier, output voltage swing across the load impedance is limited by the DC voltage power supply. If the AC or RF voltage becomes larger than the DC voltage of the power supply, limiting effect occurs. This limiting breaks the linear response of output voltage (power) to the input voltage (power). We observe the gain reduction (some call it compression), and we quantify it by 1- dB gain reduction : this is the P-1dB point.

Gain expansion can indeed occur for amplifiers. In power amplifiers biased in deep class-AB or class B, gain expansion occurs.

Check : "Effect of gain expansion of MMIC power amplifier for high order modulation OFDM portable system" in IEEE or the Steve Cripps book for the whole deal...