---
title: "Short note: Dominant mode in waveguide"
subject: "RF and Microwave Engineering"
chapter: 4
key: "semester_7/rf_and_microwave_engineering:dominant-mode-waveguide-note"
source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/dominant-mode-waveguide-note
site: BCT Engineering
---

# Short note: Dominant mode in waveguide

RF and Microwave Engineering · Chapter 4: RF and Microwave Components and Devices

- Asked in: 2072 Asoj, 5 marks
- Video: [Dominant Mode of Waveguide in Microwave Engineering by Engineering Funda](https://www.youtube.com/watch?v=w4LtkYdkNdY) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/dominant-mode-waveguide-note
- Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-4

## Question

Write a short note on dominant mode in waveguide.

## Short answer

The dominant mode has the lowest cutoff frequency, enabling single-mode operation without mode conversion. In rectangular waveguide (a>b) TE10 with fc=c/(2a) is dominant; in circular waveguide TE11 (fc=1.841c/(2πa)) is dominant. It offers lowest attenuation and simple field coupling.

## Answer

The **dominant mode** of a waveguide is the propagating mode with the **lowest cut-off frequency** (longest cut-off wavelength). Below its cut-off no energy propagates; between its cut-off and that of the next higher mode, only the dominant mode can travel, which gives clean **single-mode operation**.

**Rectangular waveguide (a > b):**
```text
 fc,mn = (c/2) √((m/a)² + (n/b)²)
 TE10: fc = c/(2a),  λc = 2a   (dominant)
```
TE10 has only Ey, Hx and Hz components; E is maximum at the centre of the broad wall and zero at the side walls. TM modes start at TM11, which is always higher.

**Circular waveguide (radius r):** dominant mode **TE11** (p'11 = 1.841), fc = 1.841c/(2πr), λc = 3.41r. The lowest TM mode is TM01 (λc = 2.61r).

**Why the dominant mode is used:**
- Single-mode operation avoids mode conversion and distortion.
- Lowest attenuation for a given size (in rectangular guides) and simple field pattern for coupling with probes.
- Easy design of components (tees, couplers) for one known field pattern.

**Example:** WR-90 guide (a = 2.286 cm, b = 1.016 cm): fc(TE10) = 6.56 GHz, next mode TE20 at 13.12 GHz. It is used in the X-band (8.2–12.4 GHz), where only TE10 propagates.

## Check yourself

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

1. The dominant mode of a waveguide is the mode with:
   A. Highest cut-off frequency
   B. Lowest cut-off frequency
   C. Highest attenuation
   D. Zero cut-off frequency
   Answer: B. It has the lowest fc (longest λc) and is the first mode to propagate. (Key point: Definition)

2. For a rectangular guide with a > b, the dominant mode and its cut-off are:
   A. TM11, c/(2a)
   B. TE01, c/(2b)
   C. TE10, fc = c/(2a)
   D. TE20, fc = c/a
   Answer: C. TE10 has fc = c/(2a), which is the lowest when a > b. (Key point: Rectangular dominant mode)

3. What is the dominant mode of a circular waveguide?
   A. TM01
   B. TE11
   C. TE01
   D. TM11
   Answer: B. TE11 has root p'11 = 1.841, the smallest, with λc = 3.41r. (Key point: Circular dominant mode)

4. Why is the dominant mode preferred for operation?
   A. Between its cut-off and the next mode's cut-off only it propagates, avoiding mode conversion and distortion
   B. It has the highest cut-off
   C. It carries TEM waves
   D. It needs no waveguide walls
   Answer: A. Single-mode operation gives clean transmission and simple component design. (Key point: Single-mode operation)

## Related in RF and Microwave Engineering

- [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
- [Magic tee, degenerate modes, dominant mode for a = 3b](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Amagic-tee-modes-a-3b) — RF and Microwave Engineering, chapter 4
- [Proof that TE10 is the dominant mode](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Ate10-dominant-mode-proof) — 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×
- [Rectangular waveguide TE mode field equations](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Arectangular-waveguide-te-equations) — RF and Microwave Engineering, chapter 4, asked 11×

## Related in other subjects

- [Define cutoff frequency, dominant mode](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Acutoff-frequency-dominant-mode-define) — Electromagnetism, chapter 6
- [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
- [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
- [Dominant cut-off, dielectric-filled guide](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Awaveguide-dielectric-filled-dominant-cutoff) — Electromagnetism, chapter 6