Circular Waveguide Modes: Identify the Dominant (Lowest-Cutoff) Mode True or False: In a circular waveguide, the TE21 mode has the lowest cutoff frequency.

Introduction / Context:
Circular waveguides support discrete TE and TM modes, each with a specific cutoff frequency determined by boundary conditions and Bessel function roots. Identifying the dominant mode is crucial in design.

Given Data / Assumptions:

• Uniform, air-filled circular waveguide.
• Standard mode nomenclature TE_mn, TM_mn.

Concept / Approach:

The dominant (lowest-cutoff) mode in a circular waveguide is TE11, not TE21. The cutoff for each mode is proportional to the corresponding root divided by the diameter. TE21 has a higher-order root and therefore a higher cutoff frequency than TE11.

Step-by-Step Solution:

Verification / Alternative check:

Mode charts show TE11 as dominant with λ_c ≈ 1.706 * D; TE21 has a larger constant and thus higher cutoff.

Why Other Options Are Wrong:

“True” variants contradict standard charts. “TM01 always dominant” is also incorrect; TM01 usually has higher cutoff than TE11 in air-filled circular guides.

Common Pitfalls:

Confusing circular with rectangular guides (dominant TE10 in rectangular) or mixing TE/TM ordering.

Final Answer:

False