= AM modulation index
{c}
{title2=$m$}
In the single-<sinusoid> <AM> voltage model, $m$ is the peak fractional excursion of the signed multiplying factor from its mean value $1$. At $m=0$ there is only the <carrier wave>; at $m=0.5$ its multiplying factor ranges from $0.5$ to $1.5$; at $m=1$ it just touches zero. For $0\leq m\leq1$, the <wave envelope> extrema are
$$
E_{\max}=A(1+m),\qquad E_{\min}=A(1-m),\qquad
m=\frac{E_{\max}-E_{\min}}{E_{\max}+E_{\min}}.
$$
The last equality follows by adding and subtracting the first two. An <oscilloscope> estimate uses local carrier peaks near the message extrema and needs enough carrier cycles to approximate those bounds. Consistent local <peak-to-peak amplitude> readings give the same ratio because their common factor of two cancels. Mixing a peak reading with a peak-to-peak reading does not.
For $A=2\,\mathrm V$ and $m=0.5$, the <wave envelope> ranges from $1$ to $3\,\mathrm V$, giving $(3-1)/(3+1)=0.5$. These are model values. At $m=1.4$, the signed factor has minimum $-0.4$, but the nonnegative <wave envelope> reaches zero at its sign changes; the extrema formula would misleadingly report $1$. It cannot measure the true depth of <overmodulation> from the folded envelope alone.
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