In circular waveguides, which mode has the lowest cutoff frequency (i.e., is the dominant mode)?

Introduction:
Waveguides support discrete modes with specific cutoff frequencies. The mode with the lowest cutoff is called dominant and determines basic design and bandwidth considerations. This question asks for the dominant mode in a circular waveguide.

Given Data / Assumptions:

• Geometry: circular metallic waveguide of radius a
• Mode families: TE_nm and TM_nm with Bessel-function roots determining cutoff

Concept / Approach:
The cutoff frequency f_c for TE_nm/TM_nm modes in a circular guide is proportional to the corresponding Bessel-function root divided by radius a. The smallest root among propagating modes corresponds to TE11, making it the dominant mode in circular waveguides (analogous to TE10 dominance in rectangular guides).

Step-by-Step Reasoning:

Verification / Alternative check:
Standard tables show TE11 cutoff parameter (approximately 1.841/a for k_c) lower than other TE/TM modes.

Why Other Options Are Wrong:

• A/C/D: Their cutoff parameters are larger than that of TE11, so they require higher frequencies to propagate.

Common Pitfalls:
Confusing rectangular (TE10) dominance with circular; mixing TE01 (often used for low-loss bends) with dominant status.

Final Answer:
TE11