Question

$\text{When a sinusodial carrier signal is amplitude modulated by a siusodial message signal}{m}_1\left(t\right),\text{the modulation index of the resultant AM signal is 0.80. When this AM signal is}\text{simultaneously modulated by one more sinusoidal message signal}{m}_2\left(t\right)\text{the total power of}\text{the Am signal become double. The modulation index of the Am signal obtained due to}{m}_2\left(t\right)\text{alone will be\_\_\_\_\_\_\_}$

• A. 1.625

Answer 1

The correct option is A 1.625
$P_t=P_c(1+\frac{{\mu }^2}{2})\frac{P_c(1+\frac{{\mu }^2}{2})}{P_c(1+\frac{{\mu }^2}{2})}=2(2+{\mu }^2)=2(2+{\mu }_1^2){\mu }^2-2{\mu }_1^2=2\text{So,}{\mu }_2^2-{\mu }_1^2=2\because {\mu }^2={\mu }_1^2+{\mu }_2^2{\mu }_2^2=2+{\mu }_1^2=2+(0.80{)}^2=2.64{\mu }_1=\sqrt{2.64}=1.625$