# In a sinusoidal amplitude modulation scheme (with carrier) the modulated signal is given by Am(t) = 100 cos(ωct) + 50 cos(ωmt) cos(ωct), where ωc is t

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In a sinusoidal amplitude modulation scheme (with carrier) the modulated signal is given by Am(t) = 100 cos(ωct) + 50 cos(ωmt) cos(ωct), where ωc is the carrier frequency and ωm is the modulation frequency. The power carried by the sidebands in % of total power is _________%.

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Concept:

The standard equation of AM is given by

y(t) = Ac(1 + μ cos ωmt) cos ωct

$\frac{{{P_{SB}}}}{{{P_C}}} = \frac{{{\mu ^2}}}{{{\mu ^2} + 2}}$

Calculation:

Converting the given equation into standard equation of AM.

<!--[if gte msEquation 12]>yt=Ac1+μcosωmtcosωct<![endif]--><!--[if !msEquation]--><!--[if gte vml 1]> <![endif]--><!--[if !vml]-->$y\left( t \right) = {A_c}\left( {1 + \mu cos{\omega _m}t} \right)\cos {\omega _c}t$

${A_m}\left( t \right) = 100\left( {1 + \frac{1}{2}cos{\omega _m}t} \right)\cos {\omega _c}t$

Here μ = 0.5

μ = 0.5

$\frac{{{P_{SB}}}}{{{P_C}}} = \frac{{{{0.5}^2}}}{{{{0.5}^2} + 2}} \times 100\;\% = 11.11\%$

<!--[endif]--><!--[endif]-->