---
title: "Receiving antenna gain"
subject: "Propagation and Antenna"
chapter: 2
key: "semester_6/propagation_and_antenna:receiving-antenna-gain"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/receiving-antenna-gain
site: BCT Engineering
---

# Receiving antenna gain

Propagation and Antenna · Chapter 2: Antenna Parameters and Arrays

- Asked in: 2081 Chaitra, 3 marks
- Video: [What are Antenna Gain, EIRP, and Friis Equation?](https://www.youtube.com/watch?v=mHo2-f5V8V4) — Iain Explains Signals, Systems, and Digital Comms
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/receiving-antenna-gain
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-2

## Question

Explain the antenna parameter: receiving antenna gain (Gr).

## Short answer

Receiving antenna gain Gr expresses how well an antenna captures power from an incoming wave compared with an isotropic antenna. By reciprocity it equals transmitting gain and relates to effective aperture as Gr = 4πAe/λ². A 1.2 m dish at 12 GHz with 55% efficiency gives about 41.0 dBi.

## Answer

**Receiving antenna gain (Gr)** expresses how well an antenna captures power from an incoming wave in its direction of maximum response compared with an isotropic antenna. By reciprocity it equals the transmitting gain, and it is related to the **effective aperture** Ae:

```text
Gr = 4π Ae / λ²
Ae = η_a × A_physical  (aperture antennas)
Pr = PFD × Ae = Pt Gt Gr (λ / 4πd)²
```

**Example:** 1.2 m dish at 12 GHz (λ = 0.025 m), η_a = 0.55:
Ae = 0.55 × π(0.6)² ≈ 0.622 m²; Gr = 4π × 0.622/0.025² ≈ 12 507 ≈ 41.0 dBi.

Gr is higher for larger aperture and higher frequency; it appears in the receiver term G/T of satellite links.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is receiving gain related to effective aperture?
   A. Gr = Ae/(4πλ²)
   B. Gr = 4πAe/λ²
   C. Gr = 4πλ²/Ae
   D. Gr = Ae·λ²
   Answer: B. Gain grows with effective area and falls with wavelength squared. (Key point: Gain from aperture)

2. For the same dish, what happens to Gr if the frequency is increased?
   A. It increases, since λ becomes smaller
   B. It decreases, since Ae falls
   C. It stays the same
   D. It becomes zero
   Answer: A. With fixed Ae, Gr = 4πAe/λ² rises as λ falls. (Key point: Effect of frequency)

3. Which expression gives received power?
   A. Pr = PFD / Ae
   B. Pr = PFD × λ²
   C. Pr = PFD × Ae
   D. Pr = Ae / (4πd²) only
   Answer: C. The antenna collects the power flux density over its effective aperture. (Key point: Received power)

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