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  4. If a carrier wave c(t) = A sin ωc t is amplitude modulated by a modulator signal m(t) = A sin ωm t then the equation of modulated signal [Cm(t)] and its modulation index are respectively

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Q. If a carrier wave $c(t) = A \,sin\, \omega_{c} t$ is amplitude modulated by a modulator signal $m(t) = A \,sin \omega_{m} t$ then the equation of modulated signal $[C_m(t)]$ and its modulation index are respectively

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Solution:

Modulation index
$m_{a} = \frac{E_{m}}{E_{c}} = \frac{A}{A} = 1$
Equation of modulated signal $\left[C_{m}\left(t\right)\right]$
$= E_{\left(c\right)} + m_{a}E_{\left(c\right)}\,sin\,\omega_{m} \,t$
$= A\left(1+sin\,w_{c} t\right)sin\,\omega_{m} t$
$\left(As\,E_{\left(c\right)} = A\,sin\omega_{c}t\right)$