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

Given: $E_C$= 20V ,$f_C$= 200kHz , $E_m$= 6V , $f_m$=1 kHz ,R = 50Ω

• Modulation index:

m= $E_m$/$E_c$ = 6/20 = 0.3

• Equation of modulated wave:

$e_{AM}$ = EC(1+m cos$ω_m$t) cos2π $f_C$ t =20[1+0.3 cos(2 π *1000t)]

cos (2π 200103)

$e_{AM}$ = 20[1+0.3 cos 2000 πt]cos(2π200103)……….ANS

• Spectrum of AM wave:

Various spectral components are as follows:

1. Carrier: $f_C$ =200 kHz

2. USB :( $f_C$+ $f_m$)=201 kHz

3. LSB: ( $f_C$ - $f_m$) = 199 kHz

Amplitude of these spectral components are as follows:

1. Carrier: $E_C$= 20V

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

Calculate the total average power

$P_t$ = (1+$m^2$/2)$P_c$ = (1+$m^2$/2) $E_c^2$/2R =( 1+${0.3}^2$/2) ${20}^2$/(2*50)

= 4.18W…..ANS