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,
${\mu }_1=\frac{A_m+0.001A_m}{A_c+0.003A_c}$
$=\frac{1001A_m}{1003A_c}=\frac{1001}{1003}\mu$ [From Eq. (i)]
$\Rightarrow \frac{{\mu }_1}{\mu }=\frac{1001}{1003}$
The percentage change in modulation index,
$=\frac{{\mu }_1-\mu }{\mu }\times 100$
$=\frac{1001-1003}{1003}\times 100$
$=-\frac{2}{1003}\times 100\simeq -0.2\%$