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

Difficulty: Medium

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°
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