A modulating signal is given by \(V_m=2sin\left(2\pi\times500t\right)\) amplitude modulates a carrier signal given by \(V_C=10sin2\pi\times{10}^6t\), Determine
The expression of Amplitude modulated signal is
\(S\left(t\right)=\left[10sin2\pi\times{10}^6t+40sin\left(2\pi\times500t\right)sin2\pi\times{10}^6t\right]\) … (1)
\(S\left(t\right)=A_c\left[1+\mu x\left(t\right)\right]cos\omega_ct=A_ccos\omega_ct+A_mx\left(t\right)cos\omega_ct\) … (2)
Comparing equation (1) and (2), we have
\(A_c=10\) and \(A_m=2\)
The carrier power \(P_c=\frac{1}{2}{A_c}^2=\frac{1}{2}\times100=50W\)
Total transmitted power \(P_t=P_c\left(1+\frac{\mu^2}{2}\right)=50\times\frac{2.4}{2}=60W\)
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