Circular Waveguide Dominant Mode Identification In a uniform, air-filled circular waveguide of radius r, which mode is dominant (i.e., has the lowest cutoff frequency)?

Introduction / Context:
Each circular waveguide mode has a specific cutoff determined by Bessel-function roots. The dominant mode is the one with the lowest cutoff frequency and is preferred for low-loss, single-mode operation.

Given Data / Assumptions:

• Air-filled circular waveguide.
• Standard TE/TM mode nomenclature.

Concept / Approach:

The dominant mode in circular waveguide is TE11. Its cutoff depends on the first root of the derivative of J1 (often denoted x'11 or x′11 ≈ 1.841), giving a cutoff wavelength λc ≈ (2π * r) / 1.841 and hence λc ≈ 3.41 * r (equivalently λc ≈ 1.706 * D, where D = 2r). TE11 has a lower cutoff than TM01 or TE01 for the same radius.

Step-by-Step Solution:

Verification / Alternative check:

Mode charts and design tables for circular waveguides universally show TE11 as dominant for air-filled uniform guides.

Why Other Options Are Wrong:

TM01 and TE01 have higher cutoff constants; TM11 is not the lowest either.

Common Pitfalls:

Confusing circular with rectangular guides (dominant TE10 in rectangular) or misreading TE/TM orderings.

Final Answer:

TE11