Satellite communication link budget: identify the incorrect statement about free-space path loss and antenna apertures Which of the following statements about link loss (free-space path loss plus antenna effects) in a satellite link is incorrect? Consider fixed geometry and line-of-sight conditions, with standard definitions of antenna effective aperture and gain.
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AFor fixed antenna sizes (physical apertures), free-space path loss increases with frequency approximately as f^2, not decreases.
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BFor a fixed frequency, the received power scales with the product of the transmitting and receiving antenna effective aperture areas; therefore, link loss decreases (improves) as that product increases.
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CFor a given satellite range and given frequency, using higher-gain antennas reduces the required transmit power by lowering the effective link loss.
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DFor fixed frequency and gains, link loss grows with the square of the slant range between the ground station and satellite.
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ELoss in the downlink is always negligible compared with the uplink, regardless of design choices.
Answer
Correct Answer: For fixed antenna sizes (physical apertures), free-space path loss increases with frequency approximately as f^2, not decreases.
Explanation
Introduction / Context:Satellite link budgets balance transmitted power, antenna gains, and propagation losses to predict received power. Understanding how free-space path loss varies with frequency, distance, and antenna aperture is fundamental to designing reliable satellite links.
Given Data / Assumptions:
- Line-of-sight space link (free-space propagation).
- Standard relationships: FSPL = (4 * pi * R * f / c)^2 in linear terms.
- Antenna effective aperture A_e relates to gain G via A_e = (G * lambda^2) / (4 * pi).
Concept / Approach:In free space, path loss grows with frequency squared and distance squared. However, when physical antenna apertures are fixed, their gain increases with f^2 (since G ∝ A_phys * (4 * pi / lambda^2)), which can compensate the frequency dependence if apertures are constant. Confusion often arises between holding gain constant versus holding physical size constant.
Step-by-Step Solution:FSPL (linear) = (4 * pi * R * f / c)^2 ⇒ increases as f^2 and R^2.Received power Pr ∝ Pt * Gt * Gr / FSPL.For fixed frequency, increasing A_e,t and A_e,r increases G and raises Pr, effectively reducing link loss.For fixed gains and f, Pr falls as 1/R^2; thus link loss grows as R^2.Therefore, any statement claiming link loss is inversely proportional to f^2 for fixed apertures is incorrect.
Verification / Alternative check:Using the Friis equation in linear form, Pr = Pt * Gt * Gr * (lambda / (4 * pi * R))^2. Since lambda = c/f, higher f reduces (lambda)^2 term, lowering Pr if gains are held constant.
Why Other Options Are Wrong:Option B: Correct: Pr grows with A_e,t * A_e,r at fixed f, so effective link loss falls.Option C: Correct: Higher gain reduces required Pt for the same Pr.Option D: Correct: FSPL grows as R^2.Option E: Incorrect as a general rule; downlink loss is not inherently negligible and depends on EIRP, G/T, and frequency bands.
Common Pitfalls:Mixing up fixed-aperture versus fixed-gain scenarios; forgetting that higher frequency also allows higher gain for a given physical size.
Final Answer:For fixed antenna sizes (physical apertures), free-space path loss increases with frequency approximately as f^2, not decreases.