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JEE Main 2019 · Physics · Semiconductors and Communication · easy

A carrier wave is amplitude modulated by a single sinusoidal message signal with modulation index 0.6. The fraction of the total transmitted power…

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A carrier wave is amplitude modulated by a single sinusoidal message signal with modulation index 0.60.6. The fraction of the total transmitted power that is carried by the two sidebands together is nearly
  1. A. 18%18\%
  2. B. 30%30\%
  3. C. 8.5%8.5\%
  4. D. 15.3%15.3\%
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Answer: (D) 15.3%15.3\%

For amplitude modulation the total power is Pt=Pc(1+m22)P_t=P_c\left(1+\dfrac{m^2}{2}\right) where PcP_c is the carrier power, and the sidebands together carry Pc m2/2P_c\,m^2/2. With m=0.6m=0.6, m2/2=0.18m^2/2=0.18. The fraction in the sidebands is 0.181.18≈0.153\dfrac{0.18}{1.18}\approx0.153, i.e. 15.3%15.3\%. The value 18%18\% is the sideband power as a fraction of the carrier power, not of the total, and each sideband alone carries about 7.6%7.6\%.
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