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

# Antenna gain

Propagation and Antenna · Chapter 2: Antenna Parameters and Arrays

- Asked in: 2074 Bhadra, 2 marks
- Video: [Gain of Antenna (Basics, Definition, Calculation & Examples) Explained in Antenna Parameters](https://www.youtube.com/watch?v=YrKvIbx_u1w) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/antenna-gain
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-2

## Question

Explain antenna gain.

## Short answer

Gain (G) is the ratio of radiation intensity in a given direction to that of an isotropic radiator with the same input power: G = 4πU/P_in = η D, where η is efficiency. It accounts for losses. Expressed in dBi or dBd (dBd = dBi - 2.15).

## Answer

**Antenna gain (G)** is the ratio of the radiation intensity in a given direction to the intensity that would be produced if the **power accepted by the antenna** were radiated isotropically:

```text
G = 4π U(θ,φ) / P_in = η · D
```

It includes the antenna's losses through the efficiency η. Gain is given in **dBi** (vs isotropic) or **dBd** (vs λ/2 dipole; dBi = dBd + 2.15). Example: λ/2 dipole 2.15 dBi; parabolic dish G = η_a(πD/λ)², often 30–50 dBi.

## Check yourself

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

1. Antenna gain is the ratio of radiation intensity in a direction to that of an isotropic radiator fed with what power?
   A. The power accepted by (input to) the antenna
   B. Only the power actually radiated
   C. The power of the transmitter's DC supply
   D. The reflected power
   Answer: A. Gain uses input power, so it includes antenna losses; directivity uses radiated power. (Key point: Definition of gain)

2. If an antenna has directivity D = 10 and efficiency η = 0.8, what is its gain?
   A. 12.5
   B. 8
   C. 10
   D. 0.8
   Answer: B. G = η·D = 0.8 × 10 = 8. (Key point: Gain and directivity)

3. A gain of 5 dBd is how many dBi?
   A. 2.85 dBi
   B. 5 dBi
   C. 7.15 dBi
   D. 10 dBi
   Answer: C. dBi = dBd + 2.15, since the half-wave dipole has 2.15 dBi. (Key point: dBi and dBd)

## Related in Propagation and Antenna

- [Antenna gain and directivity](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aantenna-gain-and-directivity) — Propagation and Antenna, chapter 2
- [Receiving antenna gain](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Areceiving-antenna-gain) — Propagation and Antenna, chapter 2
- [Gain, efficiency and polarization](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Again-efficiency-polarization) — Propagation and Antenna, chapter 2
- [Gain, efficiency and directivity](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Again-efficiency-directivity) — Propagation and Antenna, chapter 2
- [Gain, efficiency and beamwidth](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Again-efficiency-beamwidth) — Propagation and Antenna, chapter 2
- [Radiation pattern, gain and power flux density](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Apattern-gain-power-flux-density) — Propagation and Antenna, chapter 2

## Related in other subjects

- [Numerical: Okumura median path loss (unity gain)](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aokumura-median-loss-unity-gain) — Wireless Communication, chapter 3, asked 3×