Question

A message signal of frequency \(20~\text{kHz}\) and peak voltage \(20~\text{V}\) is used to modulate a carrier of peak voltage \(100~\text{V}\). The modulation index is

• A. \(1\)
• B. \(0.4\)
• C. \(0.2\)
• D. \(0.1\)

Hint:

Modulation index \( \mu = \frac{V_m}{V_c} \), where \(V_m\) = message voltage, \(V_c\) = carrier voltage.

Answer 1

The Correct Option is C

Modulation index in amplitude modulation is given by: \[ \mu = \frac{V_m}{V_c} \] Where:
- \(V_m = 20~\text{V}\) (peak voltage of message signal)
- \(V_c = 100~\text{V}\) (peak voltage of carrier signal)
\[ \mu = \frac{20}{100} = 0.2 \]

Answer 2

Step 1: Understand the given parameters
- Message signal frequency = 20 kHz (This is not directly needed for modulation index calculation)
- Peak voltage of message signal (\(V_m\)) = 20 V
- Peak voltage of carrier signal (\(V_c\)) = 100 V

Step 2: Recall the formula for modulation index
Modulation index (\(m\)) in amplitude modulation is defined as:
\[ m = \frac{V_m}{V_c} \]

Step 3: Calculate the modulation index
Substitute the values:
\[ m = \frac{20}{100} = 0.2 \]

Step 4: Final Conclusion
The modulation index is 0.2, which means the carrier amplitude varies by 20% due to the message signal.