An impedance of an antenna is 40 Ω. An unmodulated AM signal produces a current of 5 A. Assuming total power of 1295 W, determine the sideband power:

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Explanation:

Given Problem:

An antenna has an impedance of 40 Ω. An unmodulated AM signal produces a current of 5 A. The total power of the AM signal is given as 1295 W. The task is to determine the sideband power (PSB).

Solution:

In amplitude modulation (AM), the total power (PT) is the sum of the carrier power (PC) and the sideband power (PSB). Mathematically, this can be expressed as:

PT = PC + PSB

Where:

• PT = Total power
• PC = Carrier power
• PSB = Sideband power

To solve the problem, let us calculate the carrier power first.

Step 1: Calculate the Carrier Power (PC)

The carrier power is given by the formula:

PC = I² × R

Where:

• I = Carrier current (in amperes)
• R = Impedance of the antenna (in ohms)

Substitute the given values:

PC = 5² × 40

PC = 25 × 40

PC = 1000 W

Thus, the carrier power is 1000 W.

Step 2: Calculate the Sideband Power (PSB)

The total power (PT) is provided as 1295 W. From the total power formula, we know:

PT = PC + PSB

Rearranging for PSB:

PSB = PT - PC

Substitute the known values:

PSB = 1295 - 1000

PSB = 295 W

Thus, the sideband power is 295 W.

Final Answer:

The sideband power is 295 W, which corresponds to Option 4.

Additional Information

To further analyze the correctness of the other options, let's review them based on the solution:

Option 1 (800 W):

This option is incorrect. The sideband power (PSB) is calculated as 295 W, not 800 W. The value of 800 W is far too high and does not match the given total power or the calculated carrier power.

Option 2 (2800 W):

This option is also incorrect. A sideband power of 2800 W exceeds the given total power (1295 W), which is not feasible. Such a value is physically inconsistent with the problem's parameters.

Option 3 (2295 W):

This option is incorrect as well. A sideband power of 2295 W is unrealistic and does not align with the calculated values. The total power is only 1295 W, so the sideband power cannot exceed this value.

Option 4 (295 W):

This is the correct option. As derived above, the sideband power is 295 W, which matches the calculations based on the given data.

Option 5 (No value provided):

This option is invalid as it does not provide any numerical value for the sideband power.

Conclusion:

In amplitude modulation, the total power is the sum of the carrier power and the sideband power. Using the given data, the carrier power was calculated as 1000 W, and the sideband power was determined to be 295 W. Therefore, the correct answer is Option 4.

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