Question

When a carrier signal is amplitude modulated by a sinusoidal signal, the antenna current of the transmitter is increased by 50% from that of unmodulated case. The modulation index of the AM signal is equal to

• A. 1.58

Answer 1

The correct option is A 1.58
The antenna current of an AM transmitter can be given as,

$I_t=I_c\sqrt{1+\frac{{\mu }^2}{2}}$


Given that, $I_t=\left(1.5\right)I_c$

So, $1.5=\sqrt{1+\frac{{\mu }^2}{2}}$

$\frac{{\mu }^2}{2}=(1.5{)}^2-1$

${\mu }^2=2\left(1.25\right)=2.50$

$\mu =\sqrt{2.50}=1.58$