Question

An AM transmitter radiates $9kW$ when the carrier is unmodulated, and $10,125kW$ when the amplitude of the carrier is modulated by a sinusoidal message signal. if another sinusoidal message signal is simultaneously transmitted with an individual modulation index of $0.4$, then the total radiated power is equal to

• A. $10.125kW$
• B. $10.845kW$
• C. $10.50kW$
• D. $11.88kW$

Answer 1

The correct option is B $10.845kW$

$P_t=P_c(1+\frac{{\mu }^2}{2})$
With first sinusoid alone,
$10.125=9(1+\frac{{\mu }_1^2}{2})$
With second sinusoid along, ${\mu }_2=0.4$
To calculate the total radiated power.
${\mu }^2={\mu }_1^2+{\mu }_2^2$
$P_t=9(1+\frac{{\mu }_1^2}{2}+\frac{{\mu }_2^2}{2})=10.125+\frac{9{\mu }_2^2}{2}kW$
$=10.125+(9\times 0.08)=10.125+0.72=10.845kW$