Question

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

• A. \(\frac{3}{2}\)
• B. 5
• C. 1
• D. 2

Hint:

Remember the formulas for maximum and minimum amplitude in AM: A_max = A_c +A_m and A_min =A_c−A_m.

Answer 1

The Correct Option is A

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 \( \frac{3}{2} \).