A transmission line feeds 1 watt of power to a horn antenna with a gain of 10 dB. The antenna is matched to the transmission line. What is the total power radiated into free space?

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:

• Input power Pin = 1 W.
• Antenna gain = 10 dB.
• Matched system, no reflections or mismatches.

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.

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