PropagationHardQuestion 20294
Question
The Friis transmission equation gives received power P_r = P_t G_t G_r (λ/4πd)². For a satellite link at 6 GHz (λ = 5 cm), distance d = 36,000 km, with G_t = G_r = 10⁴ (40 dBi), and P_t = 100 W, the received power is:
- A≈ 4.8 × 10⁻¹⁰ WCorrect
- B≈ 4.8 × 10⁻⁶ W
- C≈ 4.8 × 10⁻¹² W
- D≈ 48 W
Correct answer
≈ 4.8 × 10⁻¹⁰ W
Explanation
Pr = 100 × 10⁴ × 10⁴ × (0.05/(4π × 3.6×10⁷))² = 10¹⁰ × (0.05/4.52×10⁸)² = 10¹⁰ × (1.107×10⁻¹⁰)² = 10¹⁰ × 1.22×10⁻²⁰ ≈ 1.22×10⁻¹⁰ W ≈ 0.12 nW. Even with high-gain antennas and 100 W transmitter, received power is sub-nanowatt — explaining why satellite dishes need LNBs.