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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

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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