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

# Antenna directivity

Propagation and Antenna · Chapter 2: Antenna Parameters and Arrays

- Asked in: 2079 Chaitra, 3 marks; 2072 Asoj, 4 marks; 2070 Bhadra, 2 marks (asked 3 times)
- Video: [Directivity of Antenna (Basics, Definition, Calculation & Examples) Explained in Antenna Parameters](https://www.youtube.com/watch?v=UeaGoCoxZAU) — 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/directivity
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-2

## Question

Explain the directivity of an antenna.

## Short answer

Directivity (D) is the ratio of maximum radiation intensity to the average intensity: D = U_max / U_avg = 4π U_max / P_rad. It depends only on the shape of the radiation pattern, not on losses. Example: isotropic D=1, λ/2 dipole D=1.64 (2.15 dBi).

## Answer

**Directivity (D)** is the ratio of the radiation intensity of an antenna in a given direction to the radiation intensity averaged over all directions. Usually the maximum value is quoted:

```text
D = U_max / U_avg = 4π U_max / P_rad
```

where U = radiation intensity (W/sr) and U_avg = P_rad/4π (isotropic source).

- It depends only on the **shape of the pattern**, not on losses.
- Isotropic antenna D = 1 (0 dBi); short dipole 1.5 (1.76 dBi); λ/2 dipole 1.64 (2.15 dBi).
- For a pencil beam with half-power beamwidths θ1, θ2:

```text
D ≈ 4π / (θ1 θ2)   (radians)
  ≈ 41253 / (θ1° θ2°)
```

**Example:** θ1 = θ2 = 30° → D ≈ 41253/900 ≈ 45.8 (16.6 dBi).

Relation with gain: G = η D, where η is the radiation efficiency.

## Check yourself

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

1. What is directivity?
   A. Ratio of input power to radiated power
   B. Ratio of radiation intensity in a given direction to the intensity averaged over all directions
   C. Ratio of loss to radiated power
   D. Beam angle
   Answer: B. D = U_max/U_avg = 4πU_max/P_rad, with U_avg = P_rad/4π. (Key point: Definition)

2. What does directivity depend on?
   A. Ohmic losses
   B. Mismatch
   C. Shape of the radiation pattern only, not losses
   D. Feeder length
   Answer: C. Directivity depends only on pattern shape; gain includes efficiency. (Key point: Dependence)

3. Which set of directivities is correct?
   A. Isotropic 0, short dipole 1, λ/2 dipole 2
   B. Isotropic 1, short dipole 1.64, λ/2 dipole 1.5
   C. Isotropic 1, short dipole 1.5, λ/2 dipole 1.64
   D. All equal 1
   Answer: C. Isotropic 1 (0 dBi), short dipole 1.5 (1.76 dBi), λ/2 dipole 1.64 (2.15 dBi). (Key point: Reference values)

4. A pencil beam has HPBWs of 30° and 30°. Approximate directivity?
   A. About 45.8 (16.6 dBi)
   B. About 900
   C. About 1.5
   D. About 4.58
   Answer: A. D ≈ 41253/(30×30) ≈ 45.8, which is 16.6 dBi. (Key point: Beamwidth estimate)

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