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Find the given values using the following information:

A sinusoidal carrier has amplitude of 20v and a frequency of 200KHZ. It is amplitude modulated by a sinusoidal voltage of amplitude 6v and frequency 1KHZ.Modulated voltage is developed across 80Ω resistance:

i. Write the equation for modulated wave

ii. Determine the modulation index

iii. Draw the spectrum of modulated wave

iv. Calculate the total average power

1 Answer
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Given: EC= 20V ,fC= 200kHz , Em= 6V , fm=1 kHz ,R = 50Ω

  • Modulation index:

m= Em/Ec = 6/20 = 0.3

  • Equation of modulated wave:

eAM = EC(1+m cosωmt) cos2π fC t =20[1+0.3 cos(2 π *1000t)]

cos (2π 200103)

eAM = 20[1+0.3 cos 2000 πt]cos(2π200103)……….ANS

  • Spectrum of AM wave:

Various spectral components are as follows:

  1. Carrier: fC =200 kHz

  2. USB :( fC+ fm)=201 kHz

  3. LSB: ( fC - fm) = 199 kHz

Amplitude of these spectral components are as follows:

  1. Carrier: EC= 20V

  2. LSB and USB :m EC/2 =(0.3*20)/2 = 3V

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Calculate the total average power

Pt = (1+m2/2)Pc = (1+m2/2) E2c/2R =( 1+0.32/2) 202/(2*50)

= 4.18W…..ANS

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