A carrier wave of amplitude 15 V modulated by a sinusoidal base band signal of amplitude 3 V. The ratio of maximum amplitude to minimum amplitude in an amplitude modulated wave is
Show Hint
Remember the formulas for maximum and minimum amplitude in AM: Amax = Ac +Am and Amin =Ac−Am.
\(\frac{3}{2}\)
- 5
- 1
2
The Correct Option is A
Solution and Explanation
Calculation of Amplitude Modulation Parameters:
Step 1: Formula for Maximum and Minimum Amplitude
The maximum amplitude (\( A_{\text{max}} \)) and minimum amplitude (\( A_{\text{min}} \)) are given by:
- \( A_{\text{max}} = A_c + A_m \)
- \( A_{\text{min}} = A_c - A_m \)
Where:
- \( A_c \): Carrier amplitude
- \( A_m \): Modulating signal amplitude
Step 2: Substitute the Given Values
Given \( A_c = 15 \, \text{V} \) and \( A_m = 3 \, \text{V} \):
\[ A_{\text{max}} = 15 + 3 = 18 \, \text{V} \]
\[ A_{\text{min}} = 15 - 3 = 12 \, \text{V} \]
Step 3: Ratio of Maximum to Minimum Amplitude
The ratio is calculated as:
\[ \frac{A_{\text{max}}}{A_{\text{min}}} = \frac{18}{12} = \frac{3}{2} \]
Conclusion:
The ratio of maximum amplitude to minimum amplitude is \( \frac{3}{2} \).
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