GATE EC 2021 Set 1 — Question 32
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Communications → Analog Communications → AM Modulation & Demodulation
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Question
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 ___________.
Correct answer
94.2 to 94.6
Solution
Given:
Modulation index, The total power in a standard AM signal is given by:where is the carrier power.The power in each sideband is:In the modified signal, the carrier and one sideband are suppressed. This results in a Single Sideband Suppressed Carrier (SSB-SC) signal. The power remaining in the signal is the power of the single sideband:The power saved is the difference between the total AM power and the remaining SSB-SC power:The percentage of power saved is:Substituting :Rounding off to one decimal place, the percentage of power saved is 94.4%.
Modulation index, The total power in a standard AM signal is given by:where is the carrier power.The power in each sideband is:In the modified signal, the carrier and one sideband are suppressed. This results in a Single Sideband Suppressed Carrier (SSB-SC) signal. The power remaining in the signal is the power of the single sideband:The power saved is the difference between the total AM power and the remaining SSB-SC power:The percentage of power saved is:Substituting :Rounding off to one decimal place, the percentage of power saved is 94.4%.
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