ISRO EC 2025 Q.22: solution and answer

ISRO 2025 · ECQ.22 · 1 mark · MCQ

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 m^2.

(A)
-110 dBW
(B)
133 dBW
(C)
-133 dBW
(D)
110 dBW

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Answer and solution

ANSWER

The received power is about $- 133 dBW$ (option C).

Official answer: CSource: ISRO's final answer key of 15 May 2026

Received power is $P_{r} = \frac{P _{t} G _{t}}{4 π R ^{2}} A_{e}$ : the transmitted power times the antenna gain (EIRP) spreads over a sphere of area $4 π R^{2}$ , and the receiving antenna collects the part falling on its effective area $A_{e}$ .
EIRP in dB: $10 lo g_{10} 2 + 17 = 3.01 + 17 = 20.01 dBW$ , which is about $100 W$ .
Spreading loss: $4 π R^{2} = 4 π (4 \times 1 0^{7} m)^{2} = 2.01 \times 1 0^{16} m^{2}$ , so $10 lo g_{10} (2.01 \times 1 0^{16}) = 163.03 dB$ .
Effective area: $10 lo g_{10} 10 = 10 dB$ (relative to $1 m^{2}$ ).
$P_{r} (dBW) = 20.01 - 163.03 + 10 = - 133.02 dBW$ .
Check in linear form: flux density $= 100.2/ (2.01 \times 1 0^{16}) \approx 4.98 \times 1 0^{- 15} W/m^{2}$ , so $P_{r} = 4.98 \times 1 0^{- 15} \times 10 \approx 4.98 \times 1 0^{- 14} W$ , and $10 lo g_{10} (4.98 \times 1 0^{- 14}) \approx - 133 dBW$ .
The received power must be far below the $2 W$ transmitted, so the positive options $133$ and $110 dBW$ are impossible. $- 110 dBW$ is $23 dB$ (about 200 times) larger than the computed value, so the answer is $- 133 dBW$ .

KEY IDEA

Add the dB terms: received power = EIRP (transmit power plus gain) minus the spreading loss $10 lo g_{10} (4 π R^{2})$ plus $10 lo g_{10} A_{e}$ . Keep $R$ in metres and the units consistent (dBW, dB relative to $1 m^{2}$ ).

WATCH OUT FOR

Using $R = 40000$ instead of $4 \times 1 0^{7} m$ (a $60 dB$ error), forgetting the $4 π$ in the spreading loss, or leaving the answer positive. Received power at such a distance is always far below the transmitted power, so the sign must be negative in dBW.

From the ISRO EC 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 4 ISRO Antennas questions, with notes

ISRO EC 2025 Q.22: solution and answer

Answer and solution

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