---
title: "Define MUF"
subject: "Propagation and Antenna"
chapter: 4
key: "semester_6/propagation_and_antenna:define-muf"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/define-muf
site: BCT Engineering
---

# Define MUF

Propagation and Antenna · Chapter 4: Propagation and Radio Frequency Spectrum

- Asked in: 2074 Bhadra
- Video: [Maximum Usable Frequency (MUF) (Definition, Basics, Derivation, Formula & Calculation) Explained](https://www.youtube.com/watch?v=0Houq2d-Jtk) — 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/define-muf
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-4

## Question

Define MUF (maximum usable frequency).

## Short answer

MUF is the highest frequency returned to earth by an ionospheric layer for a given angle of incidence (distance). f_MUF = fc sec θi = fc √(1+D²/4h²) (flat earth), where fc = 9√Nmax is the critical frequency. OWF ≈ 0.85 MUF.

## Answer

The **maximum usable frequency (MUF)** is the highest frequency that is reflected (returned) to earth by an ionospheric layer for a given angle of incidence, that is, for a given distance between the transmitter and receiver. Above the MUF the wave passes through the layer and is lost.

```text
f_MUF = fc sec θi = fc √(1 + D²/4h²)   (flat earth)
```
where fc = 9√Nmax is the critical frequency, θi the angle of incidence, D the distance and h the virtual height. MUF is always greater than fc; for a single hop it can reach about 3–4 times fc. In practice the optimum working frequency OWF ≈ 0.85 MUF is used.

## Check yourself

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

1. MUF is the:
   A. Highest frequency returned by the layer for a given angle of incidence / distance
   B. Lowest frequency that can be used
   C. Frequency at zero skip distance
   D. Highest frequency reflected at vertical incidence only
   Answer: A. Above the MUF the wave passes through the layer. (Key point: MUF definition)

2. MUF compared with fc is:
   A. Always smaller
   B. Equal
   C. Always greater, up to 3-4 times fc for a single hop
   D. Half of fc
   Answer: C. f_MUF = fc sec(theta_i) with sec >= 1. (Key point: MUF vs fc)

3. For flat earth, the MUF is:
   A. fc sqrt(1 - D^2/4h^2)
   B. fc sqrt(1 + D^2/4h^2)
   C. fc D/2h
   D. fc (1 + D/h)
   Answer: B. From sec(theta_i) = sqrt(1 + tan^2) with tan = D/2h. (Key point: Formula)

## Related in Propagation and Antenna

- [MUF, critical frequency and skip (curved earth)](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Amuf-fcr-skip-curved-earth) — Propagation and Antenna, chapter 4
- [Refractive index, critical frequency and MUF](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Arefractive-index-fc-muf) — Propagation and Antenna, chapter 4
- [Critical frequency; MUF and skip distance (flat earth)](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Acritical-frequency-skip-muf-flat) — Propagation and Antenna, chapter 4, asked 2×
- [MUF and critical frequency relation](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Amuf-critical-frequency-relation) — Propagation and Antenna, chapter 4
- [Duct propagation; critical frequency and MUF](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aduct-critical-frequency-muf) — Propagation and Antenna, chapter 4
- [Skip distance and MUF (curved earth)](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Askip-muf-curved-earth) — Propagation and Antenna, chapter 4

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