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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**