The total power content of an AM wave is `2.64` KW at a modulation factor of `80%`. The power content of each side band is

Options

A. 160 w
B. 320 w
C. 480 w
D. 640 w

Answer

To find the power content of each sideband in an amplitude modulated (AM) wave, we can follow these steps:

### Step 1: Understand the given data
- Total power content of the AM wave, \( P_T = 2.64 \, \text{kW} = 2640 \, \text{W} \)
- Modulation factor, \( M = 80\% = 0.8 \)

### Step 2: Calculate the power content of the carrier wave
The power content of the carrier wave \( P_C \) can be calculated using the formula:

\[ P_C = \frac{P_T}{2 + M^2} \]

Substituting the values:

\[ P_C = \frac{2640}{2 + (0.8)^2} \]

Calculating \( (0.8)^2 \):

\[ (0.8)^2 = 0.64 \]

Now substituting back into the equation:

\[ P_C = \frac{2640}{2 + 0.64} = \frac{2640}{2.64} \]

Calculating \( P_C \):

\[ P_C = 1000 \, \text{W} \]

### Step 3: Calculate the power content of each sideband
The power content of each sideband (upper sideband \( P_{USB} \) and lower sideband \( P_{LSB} \)) can be calculated using the formula:

\[ P_{USB} = P_{LSB} = \frac{M^2}{4} P_C \]

Substituting the values:

\[ P_{USB} = P_{LSB} = \frac{(0.8)^2}{4} \times 1000 \]

Calculating \( \frac{(0.8)^2}{4} \):

\[ P_{USB} = P_{LSB} = \frac{0.64}{4} \times 1000 = 0.16 \times 1000 = 160 \, \text{W} \]

### Final Answer
The power content of each sideband is \( 160 \, \text{W} \).

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