Beamwidth vs. gain: Compared with a 17.34° earth-coverage antenna, what is the total increase in relayed signal (gain factor) for an INTELSAT-IV narrow-beam 4.5° antenna?

Introduction / Context:
Antenna directivity (and hence gain) increases as beamwidth narrows. For similar apertures and efficiencies, gain scales approximately with the inverse square of the beamwidth (in radians or degrees, to first order for small angles).

Given Data / Assumptions:

• Earth-coverage beamwidth ≈ 17.34°.
• Narrow-angle beamwidth ≈ 4.5°.
• Assume comparable aperture efficiency and illumination.

Concept / Approach:

Gain ratio ≈ (θ_wide / θ_narrow)^2. Substituting 17.34° and 4.5° gives a straightforward numeric factor indicating how much stronger the narrow beam is relative to the wide beam.

Step-by-Step Solution:

Verification / Alternative check:

Dish gain G ∝ D^2/λ^2 and half-power beamwidth approximately inversely proportional to D/λ; thus G ∝ 1/(beamwidth)^2 for similar apertures.

Why Other Options Are Wrong:

• 3.85: that is the linear beamwidth ratio, not the power (gain) ratio.
• 78 or 220: far too high for these beamwidths.

Common Pitfalls:

• Using a linear instead of squared relationship between beamwidth ratio and gain ratio.

Final Answer:

14.85