>Is it only because of the need of lower back-off to avoid peak clipping?
But a C-Class amplifier is operated way beyond the linear region. It is already clipping.
the drain of a Class C amplifier conducts less than half a sinuisodal period, thus, most of the time, the transistor is switch off, thus saving energy.
>What if we go through the math and actually look at a nonlinear amplifier?
You could represent the PA with a series, for example y(t)=c1*x(t)+c2*x(t)^2+c3*x(t)^3....
yes, the output of a class c amplifier creates lots of IMP and harmonics, that's why there is a resonator/filter at the output of class c amplifier. the final output will be a clean amplified x(t)
>I think you GENERALLY have much more spectral components coming out if the amplitude of your incoming signal-amplitude
also variies: x(t)=[A*cos(w1*t)]*cos(w2*t)
the expression give above consist of amplitude modulation, a constant amplitude signal has the expression like this:
x(t)=cos(w1*t+ s(t))
s(t) represent the phase function. the bandwidth of x(t) is determine by d/dt(s(t)). for FM, s(t) is a linear function.
as for reference, search for amplifier linearisation.