modulation index am
Hi friends,
Let’s consider a general AM signal with many sinusoidal modulating signals:
s(t) = {A + SUM[a_i*sin(2*pi*fm_i*t+phi_i)]} * sin(2*pi*fc*t+phiC)
The power of such a signal is
P = A^2/2 * {1 + SUM[m_i^2]}
where m_i = |a_i/A| .
In that sense, the multi-modulating-sinusoid AM signal has a power equivalent of a single-tone AM with modulation index
meff = sqrt(SUM[m_i^2]) .
For this reason can be helpful to define an “effective modulation index” meff. It can be used in signal-to-noise calculations, but not for overmodulation calculations.
The condition to prevent overmodulation in general is what I stated above, i.e.: SUM(m_i)<1 .
Here I say “in general”, and in my previous post I said “regardless of the tone frequencies”, because in the case that the modulating frequencies are harmonically related, then it is possible that the peak of the sum is less that the sum of the peaks.
In “real world”, overmodulation must me avoided because its transmission would cause spectral contamination and severe distortion in the received signal.
Regards
Z