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

# Antenna efficiency

Propagation and Antenna · Chapter 2: Antenna Parameters and Arrays

- Asked in: 2075 Bhadra, 3 marks; 2072 Asoj, 4 marks; 2069 Bhadra, 2 marks (asked 3 times)
- Video: [Antenna Radiation Efficiency (Basics, Definition, Calculation & Examples) Explained](https://www.youtube.com/watch?v=WBe0yhpdpcw) — 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-efficiency
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-2

## Question

Explain antenna efficiency.

## Short answer

Radiation efficiency η = P_rad/P_in = R_r/(R_r+R_L). Total efficiency includes mismatch: e0 = e_r·e_c·e_d with e_r = 1-|Γ|². Gain G = ηD. Electrically short antennas have small R_r, thus low efficiency.

## Answer

**Antenna (radiation) efficiency** is the ratio of the power radiated by the antenna to the power accepted at its input terminals. It accounts for conductor and dielectric losses.

```text
η = P_rad / P_in = P_rad / (P_rad + P_loss)
  = Rr / (Rr + RL)
```

where Rr = radiation resistance and RL = loss resistance.

The **total efficiency** also includes mismatch loss:

```text
e0 = e_r · e_c · e_d,   e_r = 1 − |Γ|²
```

(e_r reflection, e_c conductor, e_d dielectric efficiency).

**Example:** Rr = 73 Ω, RL = 2 Ω → η = 73/75 = 0.973 (97.3 %). With |Γ| = 0.2, e_r = 0.96 and total efficiency ≈ 0.934 (93.4 %).

Efficiency links gain and directivity: **G = η D**. Electrically short antennas have very small Rr, so their efficiency is low.

## Check yourself

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

1. What is radiation efficiency?
   A. P_in / P_rad
   B. P_loss / P_in
   C. P_rad / P_in, radiated power over accepted input power
   D. Rr·RL
   Answer: C. η = P_rad/P_in = P_rad/(P_rad + P_loss). (Key point: Definition)

2. Which equals the efficiency in terms of resistances?
   A. Rr/(Rr + RL)
   B. RL/(Rr + RL)
   C. Rr/RL
   D. Rr + RL
   Answer: A. Rr is radiation resistance and RL loss resistance, so η = Rr/(Rr + RL). (Key point: Resistance form)

3. Rr = 73 Ω and RL = 2 Ω. What is the efficiency?
   A. 0.027
   B. 0.973
   C. 0.5
   D. 0.96
   Answer: B. 73/(73 + 2) = 0.973, or 97.3 %. (Key point: Numerical example)

4. What does total efficiency additionally include?
   A. Directivity
   B. Beamwidth
   C. Mismatch (reflection) loss, e_r = 1 - |Γ|²
   D. Polarization
   Answer: C. e0 = e_r·e_c·e_d, where e_r accounts for reflection. (Key point: Total efficiency)

5. Why do electrically short antennas have low efficiency?
   A. Very high Rr
   B. Very small Rr compared with loss resistance
   C. They have no loss
   D. Their gain is infinite
   Answer: B. Their small Rr makes Rr/(Rr + RL) low; gain G = ηD. (Key point: Short antennas)

## Related in Propagation and Antenna

- [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