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

by tfr000
Tags: amplitude, formula, modulated, signal, tone
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tfr000
#1
Jan30-14, 02:53 PM
tfr000's Avatar
P: 119
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.
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uart
#2
Jan30-14, 03:45 PM
Sci Advisor
P: 2,751
Quote Quote by tfr000 View Post
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.
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.
tfr000
#3
Jan30-14, 03:58 PM
tfr000's Avatar
P: 119
Quote Quote by uart View Post
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.
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!


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