Question

A message signal $m\left(t\right)=2\cos \left(200\pi t\right)+\cos \left(600\pi t\right)DSB-SC$ modulates the carrier signal $c\left(t\right)=100\cos \left(2000\pi t\right)$. The average power carried by the 1300 Hz sideband of the modulated signal will be ____ W.

• A. 1250

Answer 1

The correct option is A 1250

$s\left(t\right)=c\left(t\right)m\left(t\right)$

$=100\cos \left(2000\pi t\right)\left[2\cos \right(200\pi t)+\cos (600\pi t\left)\right]$

$=200\left[\cos \right(2000\pi t\left)\cos \right(200\pi t\left)\right]+100\left[\cos \right(2000\pi t\left)\cos \right(600\pi t\left)\right]$

$=100\left[\cos \right(2200\pi t)+\cos (1800\pi t\left)\right]+50\left[\cos \right(2600\pi t)+\cos (1400\pi t\left)\right]$

The sideside of 1300 Hz will be,

$s_1\left(t\right)=50\cos \left(2600\pi t\right)$

The average power carried by this 1300 Hz sideband will be,
$P_1=\frac{{\left(50\right)}^2}{2}=1250W$