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

In summary, the conversation discusses the equation for amplitude modulation (AM) and the need to adjust the coefficient of modulation for multiple tones. The equation can be written as v = A*sin(w_c*t)*(1+M*x_m(t)), where A is the carrier amplitude, w_c is the carrier frequency, t is time, and M is the modulation index. The conversation also mentions the importance of normalizing the modulating signal.
  • #1
tfr000
205
21
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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  • #2
tfr000 said:
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.
 
  • #3
uart said:
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! :biggrin:
 

1. What is amplitude modulation (AM)?

Amplitude modulation is a method of encoding information onto a carrier signal by varying its amplitude. This allows for the transmission of audio or other signals through radio waves.

2. How is an AM signal created?

An AM signal is created by combining a carrier signal with a modulating signal, which carries the information to be transmitted. The amplitude of the carrier signal is then varied in proportion to the amplitude of the modulating signal, resulting in an AM signal.

3. What is the formula for calculating the modulation index?

The modulation index, also known as the modulation depth, is calculated by dividing the amplitude of the modulating signal by the amplitude of the carrier signal. This can be represented by the formula m = ΔV/Vc, where ΔV is the amplitude of the modulating signal and Vc is the amplitude of the carrier signal.

4. How does a two-tone AM signal differ from a single-tone AM signal?

In a two-tone AM signal, two different modulating signals with different frequencies are used to modulate the carrier signal. This results in a more complex waveform with multiple frequency components. In contrast, a single-tone AM signal has only one modulating signal and therefore a simpler waveform.

5. What is the advantage of using two-tone AM over single-tone AM?

Using two-tone AM allows for the transmission of more information as two different frequencies can be encoded onto the carrier signal. This can result in a higher quality audio signal in broadcasting applications compared to single-tone AM.

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