Phase modulation

Discussion in 'Wireless & RF Design' started by mentaaal, Nov 24, 2008.

  1. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
    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:
    where mp = (Δf/fm)
    Which is how my notes and various other sources of information have it....
  2. KL7AJ

    Senior Member

    Nov 4, 2008
    Phase modulation has a greater modulation index at higher modulating'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.

  3. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
    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... :)