Question

A sinusoidal carrier voltage is amplitude modulated The resultant amplitude modulated wave has maximum and minimum amplitude of $120 \, V$ and $80\, V$ respectively The amplitude of each sideband is:

• A. $10\, V$
• B. $5 \, V$
• C. $20 \, V$
• D. $15 \, V$

Answer 1

The Correct Option is A

To solve for the amplitude of each sideband in an amplitude modulated (AM) wave, we start by understanding the relationship between the maximum and minimum amplitudes of the AM wave.

Given:

• Maximum amplitude, \( A_{\text{max}} = 120 \, \text{V} \)
• Minimum amplitude, \( A_{\text{min}} = 80 \, \text{V} \)

The modulation index \( m \) is defined in terms of these amplitudes by the formula:

\(m = \frac{A_{\text{max}} - A_{\text{min}}}{A_{\text{max}} + A_{\text{min}}}\)

Substituting the given values, we have:

\(m = \frac{120 - 80}{120 + 80} = \frac{40}{200} = 0.2\)

The amplitude of each sideband, \( A_{\text{sideband}} \), in an AM wave is given by:

\(A_{\text{sideband}} = \frac{m \cdot A_{\text{carrier}}}{2}\)

The carrier amplitude, \( A_{\text{carrier}} \), is the average of the maximum and minimum amplitudes:

\(A_{\text{carrier}} = \frac{A_{\text{max}} + A_{\text{min}}}{2} = \frac{120 + 80}{2} = 100 \, \text{V}\)

Now, substituting the values into the sideband amplitude formula:

\(A_{\text{sideband}} = \frac{0.2 \times 100}{2} = \frac{20}{2} = 10 \, \text{V}\)

Thus, the amplitude of each sideband is 10 V, which corresponds to the given correct answer.