From trig,  A₁.cos(θ) + A₂.cos(θ+δ) = A.cos(θ+φ)

where φ = tan^-1[A₂.sin(δ) /(A₁+A₂.cos(δ))], and A is the hypotenuse of the corresponding right triangle.

As long as A₁ and A₂ are constant, the phase shift φ is static and an FM demodulator can't tell it from propagation delay. The case of A₂ ≪ A₁ is obvious. But if you have some amplitude fluctuations prior to clipping, then there'll be a time varying φ due to AM-PM conversion.

The effect of a time varying φ on FM can be difficult to calculate - depends on whether the FM is for analog (voice) or digital (FSK/GMSK/CPSK). If you have CPSK with modulation memory and a trellis coding layer, it becomes a serious question for a communications theorist. In my understanding, FM and PM are the same beast - in one the message is integrated, in the other it is not. In an FM demodulator you need to count periods to tell what the frequency is, so you end up integrating somewhere.

M.G.Rajan
www.eecalc.com

Hi Mr. Rajan,

thanks for your help.

regarding the formula you derived, I have a slight correction...

A = √(A₁² + 2A₁A₂cosδ + A₂²)

cheers,
Aaron