Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 50%. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is .
Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 50%. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is .
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Correct Answer: 2
Solution and Explanation
The modulation index \( m \) is 50%, or \( m = 0.5 \). In amplitude modulation, the total power \( P_t \) is given by: \[ P_t = P_c \left( 1 + \frac{m^2}{2} \right) \] where \( P_c \) is the carrier power. When one of the sidebands is suppressed, the power saving occurs due to the absence of one sideband. The percentage of power saved is: \[ \text{Power saved} = \frac{m^2}{1 + \frac{m^2}{2}} \times 100 \] Substituting \( m = 0.5 \): \[ \text{Power saved} = \frac{(0.5)^2}{1 + \frac{(0.5)^2}{2}} \times 100 \approx 94.2\% \] Thus, the percentage of power saved is \( 94.2 \% \).
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