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

[tfr000]

So far I have:
V=A_carriersin(2∏F_carriert) (1+C_modsin(2∏F₁t)+C_modsin(2∏F₂t))
which I think is pretty close to correct.
Where: A is amplitude, F is freq, t is time, C_modis 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 C_mod, because if you use 1, you get 200% modulation with two tones... I think.

 

[uart]

So far I have:
V=A_carriersin(2∏F_carriert) (1+C_modsin(2∏F₁t)+C_modsin(2∏F₂t))
which I think is pretty close to correct.
Where: A is amplitude, F is freq, t is time, C_modis 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 C_mod, 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 $x_m(t)$.

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

$$v = A \sin(w_c t) (1 + M \, x_m(t))$$

Where A is the carrier amplitude and M is the modulation index.

 

[tfr000]

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

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

$$v = A \sin(w_c t) (1 + M \, x_m(t))$$

Where A is the carrier amplitude and M is the modulation index.

OK, that makes sense. My equation reduces to yours with x_m = (sin(2∏F₁t) + sin(2∏F₂t)) and M = C_mod... and a bunch of sleight of hand regarding ω and 2∏f. Thanks!