---
title: "Short note: Waveguides"
subject: "Electromagnetism"
chapter: 6
key: "semester_3/electromagnetism:short-note-waveguides"
source: https://www.bctengineer.com/q/semester_3/electromagnetism/short-note-waveguides
site: BCT Engineering
---

# Short note: Waveguides

Electromagnetism · Chapter 6: Wave guides

- Asked in: 2068 Baisakh, 3 marks
- Video: [Waveguides Explained](https://www.youtube.com/watch?v=r9-m17IPOco) — Jordan Edmunds Chetty
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electromagnetism/short-note-waveguides
- Whole chapter: https://www.bctengineer.com/md/semester_3/electromagnetism/chapter-6

## Question

Write a short note on waveguides.

## Short answer

A waveguide is a hollow conducting tube that guides microwaves via wall reflections, supporting only TE and TM modes above a cutoff frequency; the dominant mode is TE10. It is dispersive (v_p > c, v_g < c), offers low loss and high power, but is bulky and cannot transmit DC. Widely used in radar, satellite, and microwave links.

## Answer

A **waveguide** is a hollow, conducting tube (rectangular, circular or elliptical) used to guide electromagnetic waves, mainly at microwave frequencies (about 1 to 100 GHz). The wave travels along the guide by repeated reflection from the inner walls.

Key features:
- **Modes:** only TE (E_z = 0) and TM (H_z = 0) modes; a hollow guide cannot support TEM.
- **Cut-off:** each mode propagates only above its cut-off frequency f_c = (c/2)√[(m/a)² + (n/b)²]; the dominant mode in a rectangular guide is TE₁₀ with f_c = c/2a.
- **Dispersion:** guide wavelength λ_g = λ₀/√(1 − (f_c/f)²), v_p = c/√(1 − (f_c/f)²) > c, v_g = c√(1 − (f_c/f)²) < c, and v_p v_g = c².
- **Impedance:** Z_TE = η/√(1 − (f_c/f)²), Z_TM = η√(1 − (f_c/f)²).

Advantages: very low loss, high power handling, good shielding.
Disadvantages: bulky and costly, no DC or low-frequency transmission, dispersive.

Applications: radar, satellite and microwave links, feed lines to horn and dish antennas, microwave ovens, and connections between microwave components.

## Check yourself

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

1. Which modes can a hollow waveguide carry?
   A. TEM only
   B. TEM and TE
   C. TE and TM only
   D. Any mode including TEM, from DC
   Answer: C. A hollow guide cannot support TEM, so only TE and TM modes exist. (Key point: Modes in waveguide)

2. How do phase and group velocities relate to c in a waveguide?
   A. v_p < c, v_g > c, v_p v_g = c^2
   B. v_p > c, v_g < c, v_p v_g = c^2
   C. Both equal c
   D. Both greater than c
   Answer: B. v_p = c/√(1 − (f_c/f)²) > c, v_g = c√(1 − (f_c/f)²) < c, and their product is c^2. (Key point: Velocities)

3. Why can a waveguide not carry DC or low-frequency signals?
   A. The walls are too thick
   B. Every mode has a cut-off frequency below which it does not propagate
   C. It has too much loss
   D. It only supports TEM
   Answer: B. Propagation occurs only above f_c, so low frequencies are blocked. (Key point: Cut-off operation)

4. Which is an advantage of waveguides over other lines at microwave frequencies?
   A. Low cost and small size
   B. Works at DC
   C. Very low loss and high power handling
   D. Non-dispersive
   Answer: C. They offer low loss, high power handling and good shielding, though they are bulky, costly and dispersive. (Key point: Advantages)