I think i must ask the most questions on this forum!

I'm trying to where the phase modulation index fits into the equation for a PM modulated wave.

The index is clear for the derivation for FM:
ωi = ωc(1+kωcCos(ωmt+θ)
θi = ωct+(kωc/ωm)sin(ωmt+θ)
Vfm = AcCos(ωct+(kωc/ωm)sin(ωmt+θ))

Where kωc/ωm = mf = modulating index

Applying this logic to PM:

θi = ωct+kωcCos(ωmt+θ) (phase varies linearly with modulating signal)

Vpm = AcCos(ωct+kωcCos(ωmt+θ)
I dont see how Vpm can be described as:
Ac(ωct+kmpCos(ωmt+θ)
where mp = (Δf/fm)
Which is how my notes and various other sources of information have it....

 

Phase modulation has a greater modulation index at higher modulating frequencies....it's like FM with pre-emphasis. Actually, it's a very useful phenomenon in terns of S/N ratio (over the whole system).

Tersely put, in phase modulation, the deviation is directly proportional to frequency.

eric

 

Thanks eric, but would you know where i could find a mathematical derivation for it? a bit like for the fm one that i initially posted, it would make a lot of sense to me that way...