Topic: Electromagnetics / Antennas
A satellite at a distance of 40000 km from a point on earth's surface radiates a power of 2 W from an antenna with a gain of 17 dBi in the direction of observer. Find the power received by an antenna with an effective area of 10 m².
- A. -110 dBW
- B. 133 dBW
- C. -133 dBW
- D. 110 dBW
Answer: C. -133 dBW
Explanation: Transmit power $P_t = 2$ W. Transmit gain $G_t = 17$ dBi $= 10^{(17/10)} = 10^{1.7} \approx 50.12$. Distance $R = 40000$ km $= 4 \times 10^7$ m. Receiver effective area $A_e = 10~m^2$.
Received power $P_r = \frac{P_t G_t A_e}{4\pi R^2}$.
$P_r = \frac{2 \times 10^{1.7} \times 10}{4\pi (4 \times 10^7)^2} = \frac{20 \times 50.12}{4\pi \times 16 \times 10^{14}} = \frac{1002.4}{201.06 \times 10^{14}} \approx 4.985 \times 10^{-14}$ W.
Converting to dBW: $P_r (dBW) = 10 \log_{10}(4.985 \times 10^{-14}) = 10 \times (-14 + \log_{10}(49.85)) \approx 10 \times (-14 + 0.7) = -133$ dBW.