---
title: "Dominant mode and 2.254 cm waveguide at 6 GHz"
subject: "RF and Microwave Engineering"
chapter: 4
key: "semester_7/rf_and_microwave_engineering:waveguide-dominant-mode-2-254cm"
source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/waveguide-dominant-mode-2-254cm
site: BCT Engineering
---

# Dominant mode and 2.254 cm waveguide at 6 GHz

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

- Asked in: 2080 Bhadra, 1+1+2 marks
- Video: [Rectangular Waveguide (Basics, Modes, Cut-Off Frequency, Wave Impedance, Phase & Group Velocity)](https://www.youtube.com/watch?v=Y3szgmhuXeg) — 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/waveguide-dominant-mode-2-254cm
- Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-4

## Question

What is dominant mode in a waveguide? What are the dominant modes for rectangular and circular waveguides? Does a rectangular waveguide of width 2.254 cm support the propagation of a signal having frequency 6 GHz?

## Short answer

The dominant mode has the lowest cutoff frequency. Rectangular guide: TE10 with fc=c/(2a); circular guide: TE11 with fc=1.841c/(2πr). For a=2.254 cm, TE10 cutoff is 6.655 GHz, so a 6 GHz signal is below cutoff and does not propagate.

## Answer

#### Dominant mode
The **dominant mode** of a waveguide is the mode with the **lowest cut-off frequency** (longest cut-off wavelength). It is the first mode to propagate as frequency rises, so a guide is normally operated where only this mode can travel.

#### Dominant modes of rectangular and circular waveguides
- **Rectangular waveguide (a > b):** **TE10**, with fc = c/(2a), λc = 2a.
- **Circular waveguide (radius r):** **TE11**, with fc = 1.841c/(2πr), λc = 3.41r.

#### Does a 2.254 cm wide guide pass 6 GHz?
For the dominant TE10 mode, with a = 2.254 cm = 0.02254 m:
```text
 fc = c/(2a) = (3 × 10⁸)/(2 × 0.02254)
    = 6.655 × 10⁹ Hz = 6.655 GHz
```
The signal frequency f = 6 GHz is **below** the cut-off frequency (6 < 6.655 GHz). Equivalently, λ0 = 5 cm > λc = 2a = 4.508 cm.

**Answer: No. The lowest cut-off of the guide is 6.655 GHz, so a 6 GHz signal is evanescent (attenuated) and does not propagate.**

## Check yourself

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

1. The dominant mode of a circular waveguide is
   A. TE10
   B. TM01
   C. TE01
   D. TE11, with fc = 1.841c/(2πr)
   Answer: D. TE11 has the smallest root of J'n and the lowest cut-off. (Key point: Dominant mode)

2. The cut-off of the TE10 mode in a guide with a = 2.254 cm is
   A. 6.655 GHz
   B. 13.31 GHz
   C. 3.33 GHz
   D. 6.00 GHz
   Answer: A. fc = 3×10^8/(2×0.02254) = 6.655 GHz. (Key point: Cut-off calculation)

3. Does a 6 GHz signal propagate in this guide?
   A. Yes, because 6 GHz exceeds 2.254 cm
   B. No, 6 GHz is below the 6.655 GHz cut-off, so it is evanescent
   C. Yes, with a higher guide wavelength
   D. No, because TE11 is dominant here
   Answer: B. Only f > fc propagates; equivalently λ0 = 5 cm exceeds λc = 4.508 cm. (Key point: Propagation decision)

## Related in RF and Microwave Engineering

- [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
- [Air-filled 3 cm waveguide at 6 GHz; coupler parameters](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Awaveguide-3cm-6ghz-directional-coupler) — RF and Microwave Engineering, chapter 4
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- [TE field components; 1 GHz in 5 cm waveguide](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Ate10-1ghz-5cm-waveguide) — 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

## 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
- [Modes in rectangular waveguide](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Amodes-supported-rectangular-waveguide) — Electromagnetism, chapter 6, asked 4×
- [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