Question

An amplitude modulated signal is given by,
$s\left(t\right)=[10+5\cos (3000t)+4\cos (2500t\left)\right]\cos \left(2\pi f_{c}t\right)$
The modulation efficiency of this AM signal is equal to

• A. 17%
• B. 33.33%
• C. 11.11%
• D. 7.40%

Answer 1

The correct option is A 17%

The modulation efficiency of an AM signal can be given as,

%$\eta =\frac{P_{SB}}{P_{total}}\times 100=\frac{{\mu }^2}{2+{\mu }^2}\times 100$

Where, $\mu =$modulation index
For a multi-tone modulation,
$\mu =\sqrt{{\mu }_1^2+{\mu }_2^2}$

For the given AM signal
${\mu }_1=0.5and{\mu }_2=0.4$

so ${\mu }^2={\mu }_1^2+{\mu }_2^2={\left(0.5\right)}^2+{\left(0.4\right)}^2=0.41$

%$\eta =\frac{0.41}{2+0.41}\times 100=17$%