Difficulty: Easy
Correct Answer: 1 watt
Explanation:
Introduction / Context:Horn antennas are directive antennas often characterized by high gain values in dB. This question clarifies the relationship between input power, gain, and total radiated power, highlighting that gain shapes directivity but does not amplify the actual radiated power beyond the input for a matched, lossless antenna.
Given Data / Assumptions:
Concept / Approach:Power gain (in dB) indicates how power is concentrated in certain directions relative to isotropic radiation, not an increase in total power. For a lossless, matched antenna, Prad = Pin. The 10 dB gain indicates 10× more power density in the main lobe direction than an isotropic radiator of equal total power.
Step-by-Step Solution:
Step 1: Convert 10 dB gain to linear: G = 10^(10/10) = 10.Step 2: Interpret: Maximum directional intensity is 10× isotropic, but integrated power over all space remains equal to Pin.Step 3: Input Pin = 1 W. Lossless antenna → Prad = Pin = 1 W.Step 4: Thus total power radiated is 1 W.Verification / Alternative check:
Compare with directive gain example: Same principle as earlier; gain affects pattern, not total power.Why Other Options Are Wrong:
10 W: Misinterpretation that gain multiplies total power.0.1 W or 0.01 W: Suggest reduced power, contradicting matched, lossless assumption.5 W: Arbitrary scaling; no basis in antenna theory.Common Pitfalls:
Confusing antenna gain with amplifier gain; assuming gain increases actual power rather than concentrating it.Final Answer:
1 watt
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