Circular Waveguide Modes: Identify the Dominant (Lowest-Cutoff) Mode True or False: In a circular waveguide, the TE21 mode has the lowest cutoff frequency.
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ATrue
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BFalse
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CTrue only for very large diameters
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DTrue when the guide is partially filled with dielectric
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EFalse because TM01 is always dominant
Answer
Correct Answer: False
Explanation
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:
1) List candidates: TE11, TM01, TE21, etc.2) Compare normalized cutoff constants: the smallest corresponds to TE11.3) Conclude: TE21 does not have the lowest cutoff; the statement is false.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