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Question:
Published on: 20 June, 2022

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

  • Modulation index
  • Frequency present in the modulated signal
  • Total transmission power
Answer:

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 modulation index \(\mu=\frac{A_m}{A_c}=\frac{2}{10}=0.2\)
  • The carrier frequency \(f_c={10}^6Hz and the modulating frequency f_m=500Hz\)
  • 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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