Satellite link budgeting: If the downlink frequency is constant and the satellite antenna diameter is reduced by half, by what factor must the RF output power be increased to keep the same EIRP over the larger coverage area?

Introduction / Context:
In satellite communications, the Effective Isotropic Radiated Power (EIRP) sets the downlink signal strength perceived by Earth stations. EIRP equals the transmitter RF power multiplied by the antenna gain. If the dish size changes while frequency remains the same, antenna gain changes and the RF power must be adjusted to keep EIRP constant.

Given Data / Assumptions:

• Downlink frequency is fixed (thus wavelength is constant).
• Antenna diameter is reduced by a factor of 2.
• Antenna efficiency remains approximately the same.
• We want the same EIRP at the edge of coverage.

Concept / Approach:

Parabolic dish gain G scales as G ∝ (D/λ)^2 * η where D is diameter, λ is wavelength, and η is efficiency. With constant λ and η, halving D reduces gain by a factor of (1/2)^2 = 1/4. To keep EIRP = P_tx * G constant, transmitter power must increase in the inverse ratio of the gain change.

Step-by-Step Solution:

Verification / Alternative check:

If the antenna beamwidth roughly doubles when diameter halves, coverage area increases and peak gain drops accordingly. Operators compensate with higher RF power or accept lower link margins; keeping EIRP constant requires a 4× power increase.

Why Other Options Are Wrong:

• 2: Underestimates the quadratic dependence on diameter.
• 8 or 16: Overestimates; diameter-halving leads to 4×, not 8× or 16×.
• None: The precise factor is 4 under the given assumptions.

Common Pitfalls:

• Assuming gain scales linearly with diameter; it scales with D^2 at constant frequency.

Final Answer:

4