Antenna Diameter and Maximum Radar/Link Range If the antenna diameter D is increased fourfold (D → 4D) while other parameters remain unchanged, the maximum detectable/usable range increases by what factor?

Introduction / Context:
This question examines how the physical aperture of an antenna influences maximum range in systems governed by the basic radar/link equation. Understanding how gain scales with diameter helps predict range improvements from larger dishes.

Given Data / Assumptions:

• Dish efficiency and transmit power remain the same.
• Carrier frequency (hence wavelength λ) is constant.
• Receiver sensitivity/threshold does not change.

Concept / Approach:

For an aperture antenna, gain G ∝ (D/λ)^2 (assuming constant efficiency). In the basic radar equation, maximum range R_max ∝ (Pt * G^2 * σ / S_min)^(1/4) for monostatic radar, implying R_max ∝ G^(1/2) when other terms are fixed. Therefore, if G ∝ D^2, then R_max ∝ (D^2)^(1/2) = D.

Step-by-Step Solution:

Verification / Alternative check:

Link-budget style reasoning for a receive-only long-haul link similarly shows SNR improving with G, which when mapped to threshold produces the same linear-in-D range scaling for fixed λ and thresholds.

Why Other Options Are Wrong:

2 (either entry): Underestimates improvement; it would imply R_max ∝ sqrt(D), which is incorrect for this setup. 0.2: Nonsense direction (range would not decrease when increasing diameter). 1: Would suggest no improvement, contrary to gain scaling.

Common Pitfalls:

Confusing field strength (∝ 1/R) with power (∝ 1/R^2), or mixing aperture efficiency changes with pure diameter changes.

Final Answer:

4