---
title: "Define cutoff frequency, dominant mode"
subject: "Electromagnetism"
chapter: 6
key: "semester_3/electromagnetism:cutoff-frequency-dominant-mode-define"
source: https://www.bctengineer.com/q/semester_3/electromagnetism/cutoff-frequency-dominant-mode-define
site: BCT Engineering
---

# Define cutoff frequency, dominant mode

Electromagnetism · Chapter 6: Wave guides

- Asked in: 2069 Chaitra, 2+2 marks
- Video: [Dominant and Degenerate modes | TE and TM | Microwave Engineering | Lec-27](https://www.youtube.com/watch?v=DUgzqpZHkqk) — Education 4u
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electromagnetism/cutoff-frequency-dominant-mode-define
- Whole chapter: https://www.bctengineer.com/md/semester_3/electromagnetism/chapter-6

## Question

Define cutoff frequency and dominant mode for a rectangular waveguide.

## Short answer

Cutoff frequency f_c is the minimum frequency for mode propagation; below it, the mode is evanescent. In a rectangular guide, f_c = (c/2)√[(m/a)²+(n/b)²]. The dominant mode has the lowest f_c, TE10 with f_c = c/(2a) when a>b.

## Answer

#### Cut-off frequency

The **cut-off frequency** f_c of a mode is the lowest frequency at which that mode can propagate in the waveguide. For a rectangular guide of width a and height b,

f_c = (c/2)√[(m/a)² + (n/b)²]

For f > f_c, β is real and the mode propagates; for f < f_c, β becomes imaginary (an attenuation constant) and the field dies out quickly (evanescent). At f = f_c the guide wavelength is infinite.

#### Dominant mode

The **dominant mode** is the mode with the lowest cut-off frequency. For a rectangular guide with a > b it is **TE₁₀**:

f_c(TE₁₀) = c/(2a),  λ_c = 2a

It is preferred in practice because it gives single-mode operation over the band c/2a < f < c/a (for a = 2b), has simple field patterns, and needs the smallest guide for a given frequency.

## Check yourself

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

1. What is the cut-off frequency of a mode?
   A. The highest frequency at which it propagates
   B. The frequency at which the wave becomes TEM
   C. The lowest frequency at which the mode can propagate
   D. The frequency where losses are zero
   Answer: C. Below f_c the mode is evanescent; above it, it propagates. (Key point: Cut-off definition)

2. For f < f_c, what happens to β?
   A. It becomes imaginary, giving attenuation
   B. It stays real but small
   C. It becomes infinite
   D. It equals β0
   Answer: A. β turns imaginary (an attenuation constant), so fields die out quickly. (Key point: Below cut-off behaviour)

3. What is the dominant mode of a rectangular guide with a > b?
   A. TM11 with f_c = c/(2a)
   B. TE01 with f_c = c/(2b)
   C. TE10 with f_c = c/(2a)
   D. TE20 with f_c = c/a
   Answer: C. The dominant mode has the lowest cut-off, TE10, with f_c = c/(2a). (Key point: Dominant mode)

4. Why is TE10 preferred in practice?
   A. It has no cut-off
   B. It offers single-mode operation over c/2a < f < c/a (for a = 2b) with simple fields and smallest guide size
   C. It supports DC signals
   D. It has the highest attenuation
   Answer: B. It gives a clean single-mode band and the smallest guide for a given frequency. (Key point: Why TE10 is preferred)

## Related in Electromagnetism

- [Cut-off of TM11 and dominant mode](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Awaveguide-tm11-cutoff-dielectric-1-07) — Electromagnetism, chapter 6
- [Modes in rectangular waveguide](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Amodes-supported-rectangular-waveguide) — Electromagnetism, chapter 6, asked 4×
- [Dominant cut-off, dielectric-filled guide](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Awaveguide-dielectric-filled-dominant-cutoff) — Electromagnetism, chapter 6
- [Cut-off of dominant and TE11, 2.5×1.2 cm](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Awaveguide-2-5x1-2-cutoff-te11) — Electromagnetism, chapter 6
- [Define TM mode; TM11 cut-off 5×3 cm](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Atm-mode-define-cutoff-5x3-guide) — Electromagnetism, chapter 6
- [Cut-off and single-mode range, 4×2 cm](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Awaveguide-4x2cm-cutoff-single-mode-range) — Electromagnetism, chapter 6

## Related in other subjects

- [Dominant mode and 2.254 cm waveguide at 6 GHz](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Awaveguide-dominant-mode-2-254cm) — RF and Microwave Engineering, chapter 4
- [Circular waveguide TM field strength and dominant mode](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Acircular-waveguide-tm-field) — RF and Microwave Engineering, chapter 4
- [Short note: Dominant mode in waveguide](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Adominant-mode-waveguide-note) — RF and Microwave Engineering, chapter 4
- [Rectangular waveguide TM mode field equations](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Arectangular-waveguide-tm-equations) — RF and Microwave Engineering, chapter 4, asked 11×