What is the formula for two (or more) tone amplitude modulated signal?

  1. So far I have:
    V=Acarriersin(2∏Fcarriert) (1+Cmodsin(2∏F1t)+Cmodsin(2∏F2t))
    which I think is pretty close to correct.
    Where: A is amplitude, F is freq, t is time, Cmodis the coefficient of modulation, i.e. 1=100% modulation.
    I can find plenty of websites offering 1-tone AM, but not 2 or more tones.
    You actually have to mess with Cmod, because if you use 1, you get 200% modulation with two tones... I think.
  2. jcsd
  3. uart

    uart 2,776
    Science Advisor

    It's perhaps easier to consider it terms of a general modulating (message) signal [itex]x_m(t)[/itex].

    If we normalize the modulating signal such that [itex]-1 \le x_m(t) \le 1[/itex] then the AM signal can be written as:

    [tex] v = A \sin(w_c t) (1 + M \, x_m(t))[/tex]

    Where A is the carrier amplitude and M is the modulation index.
  4. OK, that makes sense. My equation reduces to yours with xm = (sin(2∏F1t) + sin(2∏F2t)) and M = Cmod... and a bunch of sleight of hand regarding ω and 2∏f. Thanks! :biggrin:
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