---
title: "Critical frequency"
subject: "Propagation and Antenna"
chapter: 4
key: "semester_6/propagation_and_antenna:critical-frequency"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/critical-frequency
site: BCT Engineering
---

# Critical frequency

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

- Asked in: 2076 Baisakh, 4 marks; 2070 Magh, 2 marks (asked 2 times)
- Video: [Critical Frequency (Definition, Basics, Derivation, Formula & Calculation) Explained](https://www.youtube.com/watch?v=A7WNqtKj-YA) — 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/critical-frequency
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-4

## Question

Define critical frequency for ionospheric region.

## Short answer

Critical frequency is the highest frequency a layer reflects at vertical incidence. It is fc = 9 sqrt(Nmax) Hz, with Nmax the maximum electron density per m^3. Frequencies above fc penetrate the layer at vertical incidence.

## Answer

The **critical frequency (fc)** of an ionospheric layer is the highest frequency that is reflected back to earth by that layer when the wave is sent **vertically upward** (normal incidence). Any frequency above fc penetrates the layer and escapes at vertical incidence.

It depends on the maximum electron density Nmax of the layer:
```text
fc = 9 √Nmax      (fc in Hz, Nmax in electrons per m³)
```
This comes from the refractive index n = √(1 − 81N/f²); at vertical incidence the wave turns back where n = 0, i.e. f² = 81Nmax.

- Typical values: E layer ≈ 3–4 MHz, F2 layer ≈ 5–12 MHz.
- It is higher by day and in high sunspot years.
- For oblique incidence, the highest returnable frequency is MUF = fc sec θi.

Example: Nmax = 1.24 × 10¹² /m³ gives fc = 9 × √(1.24 × 10¹²) ≈ 10 MHz.

## Check yourself

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

1. The critical frequency of a layer is:
   A. The lowest frequency that reaches the layer
   B. The highest frequency reflected by the layer when sent vertically upward
   C. The highest frequency reflected at any angle of incidence
   D. The frequency absorbed most by the layer
   Answer: B. Frequencies above fc penetrate the layer at normal incidence; at oblique incidence higher frequencies (MUF) can be returned. (Key point: Definition)

2. The critical frequency depends on:
   A. The minimum electron density
   B. The transmitter power
   C. The square root of the maximum electron density: fc = 9 sqrt(Nmax)
   D. The height of the antenna
   Answer: C. At vertical incidence the wave turns back where n = 0, i.e. f^2 = 81 Nmax. (Key point: Formula)

3. Why does the wave return at vertical incidence when f^2 = 81 Nmax?
   A. Because n becomes infinite
   B. Because n becomes 1
   C. Because N becomes zero
   D. Because the refractive index n = sqrt(1 - 81N/f^2) becomes zero there
   Answer: D. At n = 0 the wave can go no further upward and is turned back. (Key point: Why n = 0)

4. When is the critical frequency higher?
   A. At night
   B. By day and in high sunspot years
   C. In low sunspot years
   D. Only in winter
   Answer: B. More ionisation raises Nmax and so fc. (Key point: Variation)

## Related in Propagation and Antenna

- [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×
- [Critical frequency and skip distance (flat earth)](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Acritical-frequency-skip-distance-flat) — Propagation and Antenna, chapter 4, asked 2×
- [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
- [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