Estimate the approximate half-power beamwidth (HPBW) of a 1 m diameter parabolic antenna operating at 1 GHz. (Use HPBW ≈ 70 * (lambda / D) degrees; lambda ≈ 0.3 m at 1 GHz.)

Introduction:This problem evaluates your ability to estimate the beamwidth of a parabolic reflector from its diameter and operating frequency. Such quick estimates are vital in link budgeting and antenna siting.

Given Data / Assumptions:

• Parabolic antenna, diameter D = 1 m.
• Operating frequency f = 1 GHz ⇒ lambda ≈ 0.3 m.
• Empirical HPBW rule: HPBW ≈ 70 * (lambda / D) degrees for typical illumination.

Concept / Approach:

The beamwidth of a large-aperture antenna is inversely proportional to its electrical size (D / lambda). Increasing diameter narrows the beam; increasing wavelength (lower frequency) widens it.

Step-by-Step Solution:

Verification / Alternative check:

Some texts use constants between 58 and 70 depending on taper and efficiency. Using 58 * (lambda / D) gives ≈ 17°. Both figures are of the same order, confirming that ≈ 21° is a reasonable estimate for typical illumination.

Why Other Options Are Wrong:

• 12°/18°/24°: plausible but deviate from the commonly used 70 * (lambda / D) estimate for a 1 m dish at 1 GHz.
• 5°: far too narrow for such a small dish at 1 GHz.

Common Pitfalls:

Confusing HPBW with first-null beamwidth (FNBW), which is roughly ~2 * HPBW. Choosing a constant without considering illumination taper can also skew results.

Final Answer:

21°