For achieving a specified high directivity, how does the required physical size (aperture) of an antenna vary as the operating wavelength decreases?

Introduction / Context:
High-directivity antennas concentrate radiated energy into narrow beams. Dishes, horn antennas, and phased arrays are common examples. Designers often ask how physical dimensions scale when changing frequency (or wavelength) for a target directivity and beamwidth.

Given Data / Assumptions:

• Comparing antennas of the same type and efficiency.
• Goal: maintain the same directivity while changing operating wavelength λ.
• Free-space conditions; mutual coupling and platform constraints are ignored.

Concept / Approach:

For an effective aperture antenna, directivity D is approximately D ≈ 4π * A_e / λ^2, where A_e is effective aperture (proportional to physical area A times efficiency). Holding D constant implies A_e ∝ λ^2. Therefore, as λ decreases (frequency rises), the required area drops with λ^2.

Step-by-Step Solution:

Verification / Alternative check:

Practical systems demonstrate this scaling: a 1 m dish at X-band provides far greater directivity than at L-band; conversely, the same directivity at X-band needs a much smaller dish than at L-band.

Why Other Options Are Wrong:

• Increases: Opposite of aperture scaling for fixed D.
• Unaffected: Ignores λ^2 dependence in aperture theory.
• Depends only on polarization: Polarization does not set required physical aperture for D.
• Oscillates with wavelength: No such periodic relation in basic aperture theory.

Common Pitfalls:

Mixing up gain scaling with frequency-dependent efficiency; comparing dissimilar antenna types; overlooking edge-taper and blockage effects which slightly modify constants but not the λ^2 law.

Final Answer:

It decreases as wavelength decreases