---
title: "Free space loss (LFS)"
subject: "Propagation and Antenna"
chapter: 5
key: "semester_6/propagation_and_antenna:free-space-loss"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/free-space-loss
site: BCT Engineering
---

# Free space loss (LFS)

Propagation and Antenna · Chapter 5: Propagation between Antennas

- Asked in: 2081 Chaitra, 3 marks
- Video: [6 - Free Space Path Loss](https://www.youtube.com/watch?v=-R4ljyNamlc) — GTHillWiFi
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/free-space-loss
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-5

## Question

Explain the antenna parameter: free space loss (LFS).

## Short answer

Free space loss is the power ratio between two isotropic antennas due to spherical spreading only: LFS=(4πd/λ)^2, or LFS(dB)=32.44+20log d(km)+20log f(MHz). It increases 20 dB per decade (6 dB when distance or frequency doubles) and serves as the reference in link budgets.

## Answer

**Free space loss (LFS)** is the loss in signal power between two isotropic antennas in free space, caused only by the spreading of the radiated energy over a growing sphere. It is not a loss of energy in the medium (free space is lossless); the receiving antenna simply intercepts a smaller fraction of the total power as distance increases.

#### Expression

From the Friis equation Pr = Pt·Gt·Gr·(λ/4πd)², putting Gt = Gr = 1:

```text
LFS = Pt/Pr = (4πd/λ)²

LFS(dB) = 20 log(4πd/λ) = 22 + 20 log(d/λ)

LFS(dB) = 32.44 + 20 log d(km) + 20 log f(MHz)
```

#### Key features

- Increases by **6 dB** each time distance doubles (20 dB per decade).
- Increases by 6 dB each time frequency doubles, because a higher-frequency isotropic antenna has a smaller effective aperture (Ae = λ²/4π).
- It is the reference loss used in every link budget: Pr = Pt + Gt + Gr − LFS − other losses.

**Example:** For d = 50 km and f = 10 GHz, LFS = 32.44 + 20 log 50 + 20 log 10000 = 146.4 dB.

## Check yourself

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

1. Free space loss is caused by:
   A. Absorption in the medium
   B. Spreading of energy over a growing sphere
   C. Rain
   D. Ground reflection
   Answer: B. Free space is lossless; the receiver just intercepts a smaller fraction. (Key point: Nature of LFS)

2. Why does LFS rise 6 dB when frequency doubles?
   A. The isotropic effective aperture lambda^2/4pi shrinks
   B. The distance doubles
   C. Absorption increases
   D. Gain doubles
   Answer: A. Higher frequency means a smaller Ae and so less power captured. (Key point: Frequency dependence)

3. LFS for d = 50 km and f = 10 GHz is about:
   A. 92.4 dB
   B. 126.4 dB
   C. 146.4 dB
   D. 186.4 dB
   Answer: C. 32.44 + 33.98 + 80 = 146.4 dB. (Key point: Calculation)

## Related in Propagation and Antenna

- [Friis equation and free space path loss](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afriis-path-loss-free-space) — Propagation and Antenna, chapter 5, asked 2×
- [Free space path loss: 6 GHz, 10,500 km](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afspl-derivation-6ghz-10500km) — Propagation and Antenna, chapter 5
- [Friis equation and LFS = 22 + 20 log(d/λ)](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afriis-free-space-loss-22-20log) — Propagation and Antenna, chapter 5
- [Free space propagation and Friis derivation](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afree-space-friis-complete) — Propagation and Antenna, chapter 5, asked 2×
- [10 GHz LOS link loss and Friis derivation](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Alos-link-10ghz-100km-friis) — Propagation and Antenna, chapter 5
- [Friis, path loss and LOS distance](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afriis-path-loss-los-distance) — Propagation and Antenna, chapter 5

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