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A sinusoidal carrier has an amplitude of 20v and frequency of 200KHz. It is amplitude modulated by a sinusoidal voltage of amplitude 6v and 1 frequency 1KHz modulated voltage is developed across a 80 resistance.
1] Write the equation of modulated wave.
2] Determine modulation index.
3] Draw the spectrum of modulated wave.
4] Calculate total average power.
Solution:
Given:
Ec = 20v
Fc = 200 KHz
Em = 6v
Fm = 1KHz
R = 80
Find:
1] Eam
2] M
3] LSB/ USB/ Carrier
4] PT
1] Eam = Ec (1+ m cos wmt) cos wct
20 (1 + m cos wmt) cos wct
$m = \frac{Em}{Ec}$
$\frac{6}{20}$
m = 0.3
$Wm = 2 \pi \ fm$
$= 2 \times \pi \times 10^3$
$\therefore$ $eam = 20(1 + 0.3 cos 2 \pi \times 10^3 t) \ cos \ 400 \times \pi \times 10^3 \ t $
2] M = modulation index.
$m = \frac{Em}{Ec}$
$m = \frac{6}{20}$
m = 0.3
3] Spectrum
flsb = fc - fm = 200 - 1 = 199KHz
fusb = fc + fm = 20 + 1 = 201KHz
Amplitude of sidebands
$flsb = fusb = \frac{mEc}{2}$
$= \frac{0.3 \times 20}{2}$
= 3V
$\therefore$
4] Total average power.
$p_t = Plsb + Pusb + P_c$
$P_E = [ 1 + \frac{m^2}{2}] P_c$
$\because$ $Pc = \frac{Ec^2}{2R}$
$= \frac{20^2}{2 \times 80} = 2.5$
$plsb = pusb = \frac{m^2}{4} \times P_c$
$= \frac{(0.3)^2}{4} \times 2.5$
= 0.05625
$\therefore$ Pt = Pusb + Pc + Plsb
= 0.05625 + 2.5 + 0.05625
Pt = 2.6125