Phase modulation

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

  1. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    0
    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....
     
  2. KL7AJ

    AAC Fanatic!

    Nov 4, 2008
    2,040
    287
    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
     
  3. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
    451
    0
    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... :)
     
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