Estimate the approximate half-power beamwidth (HPBW) in degrees for a 1 m diameter parabolic antenna operating at 10 GHz.

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Parabolic reflectors concentrate energy into a narrow main lobe. A common quick estimate for HPBW is used by antenna engineers for link budgeting and pointing accuracy. Given Data / Assumptions: Antenna diameter D = 1 m. Frequency f = 10 GHz ⇒ wavelength λ ≈ 0.03 m. Rule-of-thumb for HPBW in degrees: HPBW ≈ 70 * (λ / D). Concept / Approach:The HPBW of a well-illuminated parabolic reflector is inversely proportional to aperture size and directly proportional to wavelength. Quick formulas give a practical estimate, adequate for exam problems and early design. Step-by-Step Solution: Compute λ = c / f ≈ 3×10^8 / 10×10^9 = 0.03 m.HPBW ≈ 70 * (λ / D) = 70 * (0.03 / 1) = 2.1 degrees.Among the given discrete choices, 1° is the nearest practical choice (far closer than 5°). Verification / Alternative check:Some texts use 58–70 factor depending on illumination efficiency; with 58 the HPBW ≈ 1.74°, still closer to 1° than to 5°. Why Other Options Are Wrong: 5°, 50°, 100°: too wide for a 1 m dish at 10 GHz.0.2°: unrealistically narrow given the aperture and frequency. Common Pitfalls: Confusing first-null beamwidth (about 2× HPBW) with HPBW, leading to larger estimates. Final Answer: 1°

Estimate the approximate half-power beamwidth (HPBW) in degrees for a 1 m diameter parabolic antenna operating at 10 GHz.

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