Question:
A carrier wave is used to transmit a message signal. If the peak voltage of modulating signal and carrier signal are increased by \(1\%\) and \(3\%\) respectively, the modulation index is changed by
A carrier wave is used to transmit a message signal. If the peak voltage of modulating signal and carrier signal are increased by \(1\%\) and \(3\%\) respectively, the modulation index is changed by
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In amplitude modulation,
\[
m=\frac{V_m}{V_c}
\]
If carrier voltage increases more rapidly than modulating voltage, the modulation index decreases.
Updated On: Jun 22, 2026
- \(-2\%\)
- \(4\%\)
- \(2\%\)
- \(-4\%\)
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The Correct Option is A
Solution and Explanation
Step 1: Write the expression for modulation index.
In amplitude modulation, \[ m=\frac{V_m}{V_c} \] where \[ V_m=\text{peak voltage of modulating signal} \] and \[ V_c=\text{peak voltage of carrier signal} \]
Step 2: Apply the percentage changes.
The modulating signal increases by \(1\%\), so \[ V_m'=1.01V_m \] The carrier signal increases by \(3\%\), so \[ V_c'=1.03V_c \] Therefore, new modulation index is \[ m'=\frac{V_m'}{V_c'} \] \[ m'=\frac{1.01V_m}{1.03V_c} \] \[ m'=m\left(\frac{1.01}{1.03}\right) \]
Step 3: Find the percentage change.
\[ \frac{m'}{m}=\frac{1.01}{1.03} \] \[ \frac{m'}{m}\approx0.9806 \] Thus, modulation index decreases by approximately \[ (1-0.9806)\times100 \] \[ \approx1.94\% \] \[ \approx2\% \] Hence, the change is \[ -2\% \]
Step 4: Final conclusion.
Therefore, the modulation index changes by \[ \boxed{-2\%} \]
In amplitude modulation, \[ m=\frac{V_m}{V_c} \] where \[ V_m=\text{peak voltage of modulating signal} \] and \[ V_c=\text{peak voltage of carrier signal} \]
Step 2: Apply the percentage changes.
The modulating signal increases by \(1\%\), so \[ V_m'=1.01V_m \] The carrier signal increases by \(3\%\), so \[ V_c'=1.03V_c \] Therefore, new modulation index is \[ m'=\frac{V_m'}{V_c'} \] \[ m'=\frac{1.01V_m}{1.03V_c} \] \[ m'=m\left(\frac{1.01}{1.03}\right) \]
Step 3: Find the percentage change.
\[ \frac{m'}{m}=\frac{1.01}{1.03} \] \[ \frac{m'}{m}\approx0.9806 \] Thus, modulation index decreases by approximately \[ (1-0.9806)\times100 \] \[ \approx1.94\% \] \[ \approx2\% \] Hence, the change is \[ -2\% \]
Step 4: Final conclusion.
Therefore, the modulation index changes by \[ \boxed{-2\%} \]
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