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

# Antenna gain and directivity

Propagation and Antenna · Chapter 2: Antenna Parameters and Arrays

- Asked in: 2076 Baisakh, 2 marks
- Video: [Relationship Between Gain, Directivity & Efficiency | Antenna Performance Explained](https://www.youtube.com/watch?v=f-rQ5l6LOuk) — WaveRes
- 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-and-directivity
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-2

## Question

Explain antenna gain and directivity.

## Short answer

Directivity D = 4πU_max/P_rad depends only on pattern shape. Gain G = 4πU_max/P_in = η D includes losses (η = radiation efficiency). Example: λ/2 dipole D=1.64, with η=0.97 G≈1.59 (2.0 dBi).

## Answer

**Directivity (D)** is the ratio of maximum radiation intensity to the average radiation intensity: D = 4πU_max/P_rad. It depends only on the pattern shape.

**Gain (G)** is the same ratio but referred to the **input power**, so it includes losses: G = 4πU_max/P_in = η·D, where η is the radiation efficiency. Hence G ≤ D. Example: λ/2 dipole D = 1.64; with η = 0.97, G ≈ 1.59 (2.0 dBi).

## Check yourself

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

1. Directivity depends only on what?
   A. The ohmic losses of the conductor
   B. The shape of the radiation pattern
   C. The input power
   D. The efficiency η
   Answer: B. D = 4πU_max/P_rad compares radiated power only, so it is independent of losses. (Key point: Directivity depends on)

2. Why is gain always less than or equal to directivity?
   A. Gain uses the average intensity while D uses the maximum
   B. Gain is measured in dB and D is not
   C. Gain is referred to input power, so it includes losses: G = ηD with η ≤ 1
   D. Gain ignores the pattern shape
   Answer: C. Since P_rad = ηP_in, G = ηD ≤ D. (Key point: Why G is at most D)

3. A λ/2 dipole has D = 1.64 and η = 0.97. What is its gain?
   A. About 1.59 (2.0 dBi)
   B. About 1.64 (2.15 dBi)
   C. About 1.69
   D. About 0.97
   Answer: A. G = 0.97 × 1.64 ≈ 1.59. (Key point: Dipole example)

## Related in Propagation and Antenna

- [Gain, efficiency and directivity](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Again-efficiency-directivity) — Propagation and Antenna, chapter 2
- [Antenna directivity](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Adirectivity) — Propagation and Antenna, chapter 2, asked 3×
- [Antenna gain](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aantenna-gain) — 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 beamwidth](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Again-efficiency-beamwidth) — Propagation and Antenna, chapter 2

## Related in other subjects

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