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Consider a lossless antenna with a directive gain of +6 dB. If 1 mW of input power is fed to the antenna, what will be the total power radiated by the antenna?

Difficulty: Easy

Correct Answer: 1 mW

Explanation:


Introduction / Context:
Antennas are described using different gain measures, such as directive gain, power gain, and efficiency. This question examines the difference between directive gain and radiated power, focusing on the principle that directive gain affects the directional distribution of radiated energy but not the total radiated power for a lossless antenna.


Given Data / Assumptions:

  • Input power to antenna = 1 mW.
  • Directive gain = +6 dB.
  • Antenna is lossless (no ohmic or dielectric losses).


Concept / Approach:
For a lossless antenna, all input power is radiated. Directive gain (in dB) indicates how much stronger the field or power density is in the maximum radiation direction compared to an isotropic radiator. It does not change the total radiated power, only its spatial distribution. Therefore, the total radiated power always equals the input power provided losses are negligible.


Step-by-Step Solution:

Step 1: Convert gain from dB to linear scale. Gd = 10^(6/10) = 10^0.6 ≈ 3.98.Step 2: Interpret directive gain: maximum radiation intensity is 3.98 times that of an isotropic radiator for same power.Step 3: For a lossless antenna, Pin = Prad. Here, Pin = 1 mW.Step 4: Thus Prad = 1 mW.Step 5: Gain affects directivity but does not alter total radiated power.


Verification / Alternative check:

If antenna efficiency = 100%, input power and radiated power are identical regardless of gain. Directive gain only shapes radiation pattern.


Why Other Options Are Wrong:

4 mW: Misinterpretation, assuming gain multiplies power rather than intensity.7 mW: No basis in gain-power relation.1/4 mW: Would imply efficiency < 25%, contradicting given lossless assumption.0.5 mW: Suggests 50% efficiency, not given here.


Common Pitfalls:

Confusing directive gain with power gain; assuming that dB gain changes total radiated power; ignoring lossless assumption.


Final Answer:

1 mW
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