Estimate the approximate half-power beamwidth (HPBW) in degrees for a 1 m diameter parabolic antenna operating at 10 GHz.
Electronics and Communication Engineering
Microwave Communication
Difficulty: Medium
Choose an option
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A1°
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B5°
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C50°
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D100°
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E0.2°
Answer
Correct Answer: 1°
Explanation
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°