For a transmitting aperture antenna, the directive gain (directivity) is proportional to which geometric quantity of the antenna, all else equal?

Introduction:
Directivity quantifies how concentrated an antenna’s radiation is in a particular direction. For aperture antennas (dishes, horns), directivity is tied to effective area and wavelength. This question checks awareness of that proportionality.

Given Data / Assumptions:

• Far-field pattern consideration.
• Comparable aperture efficiencies across compared designs.
• Same operating wavelength.

Concept / Approach:

For an aperture antenna, D ≈ 4π * Ae / lambda^2, where Ae is the effective area. If efficiency is held roughly constant, Ae scales with the physical cross-sectional area A, so D ∝ A.

Step-by-Step Solution:

Verification / Alternative check:

Doubling the diameter of a circular aperture quadruples the area and increases directivity by roughly 4×, consistent with D ∝ A.

Why Other Options Are Wrong:

• Square, square-root, cube-root dependencies do not follow from the standard aperture relation.
• Perimeter alone does not determine directivity.

Common Pitfalls:

Confusing gain with directivity. Gain also includes radiation efficiency, but with fixed efficiency the proportionality remains to area.

Final Answer:

its cross-sectional (aperture) area