Question:
An audio signal $\mathrm{v}_{\mathrm{m}}=20 \sin 2 \pi(1500 \mathrm{t})$ amplitude modulates a carrier $\mathrm{v}_{\mathrm{c}}=80 \sin 2 \pi(100,000 \mathrm{t})$. The value of percent modulation is
Solution:
Given : $v_{m}=20 \sin \left[100 \pi t+\frac{\pi}{4}\right]$
$v_{\mathrm{C}}=80 \sin \left[10^{4} \pi \mathrm{t}+\frac{\pi}{6}\right]$
we know that, modulation index $=\frac{A_{m}}{A_{c}}$
from given equations, $A_{m}=20$ and $A_{c}=80$
percentage modulation index $=\frac{A_{m}}{A_{c}} \times 100$
$\Rightarrow \frac{20}{80} \times 100=25 \%$
The value of percentage modulation index is
$=25$
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