Directive Gain versus Wavelength for a Fixed-Size Transmitting Antenna How does the directive gain of a transmitting antenna vary with the operating wavelength (assuming physical aperture/size is fixed)?

Introduction / Context:
The directive gain of an antenna relates to how concentrated its radiation is. For a physically fixed aperture, gain is strongly tied to wavelength.

Given Data / Assumptions:

• Physical aperture is held constant.
• We are varying wavelength only.

Concept / Approach:

For an aperture antenna, gain G ≈ (4 * pi * A_e) / lambda^2. If physical aperture (and thus effective aperture A_e in the high-efficiency case) is fixed, gain varies as 1 / lambda^2.

Step-by-Step Solution:

Verification / Alternative check:

Aperture theory and antenna textbooks consistently show the inverse-square dependence with wavelength for fixed apertures.

Why Other Options Are Wrong:

Options A, B, C, and E contradict the aperture-gain relationship when physical size is fixed.

Common Pitfalls:

Confusing physical aperture with electrical size; neglecting efficiency factors which change the constant but not the lambda^2 dependence.

Final Answer:

Inversely proportional to square of wavelength.