Question

A message signal is used to modulate a carrier frequency. If the peak voltages of message signal and carrier signals are increased by $0.1 \%$ and $0.3 \%$ respectively, then the percentage change in modulation index is

• A. 0.4
• B. 0.0
• C. -0.4
• D. -0.2

Answer 1

Answer: (D)

We know that, the modulation index is given by
$\mu=\frac{A_{m}}{A_{c}}\,\,\,...(i)$
where, $A_{m}=$ maximum amplitude of message
signal and $A_{c}=$ maximum amplitude of carrier-signal.
Given, $A_{m}$ and $A_{c}$ are increased by $0.1 \%$ and $0.3 \%$, then the modulation index becomes,
$\mu_{1}=\frac{A_{m}+0.001 \,A_{m}}{A_{c}+0.003\, A_{c}}$
$=\frac{1001 \,A_{m}}{1003\, A_{c}}=\frac{1001}{1003} \mu$ [From Eq. (i)]
$\Rightarrow \frac{\mu_{1}}{\mu} =\frac{1001}{1003}$
The percentage change in modulation index,
$=\frac{\mu_{1}-\mu}{\mu} \times 100 $
$=\frac{1001-1003}{1003} \times 100 $
$=-\frac{2}{1003} \times 100 \simeq-0.2 \%$