Comparing rectangular vs circular waveguides: which statement about modal families is correct?
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ABoth support an infinite set of TE and TM modes (no true TEM mode)
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BRectangular has infinite TE/TM but circular does not
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CCircular has infinite TE/TM but rectangular does not
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DNeither supports TE or TM families
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EBoth primarily support TEM only
Answer
Correct Answer: Both support an infinite set of TE and TM modes (no true TEM mode)
Explanation
Introduction:Hollow metallic waveguides guide energy as TE or TM modes. Understanding which modal families exist in rectangular and circular geometries is basic to microwave engineering.
Given Data / Assumptions:
- Air-filled hollow metallic guides.
- No internal center conductor (hence not coax).
- Standard boundary conditions on perfect conductors.
Concept / Approach:
Hollow guides do not provide a return path needed for TEM fields. Therefore, they support TE (transverse electric) and TM (transverse magnetic) modes only. Both rectangular and circular cross-sections produce an infinite discrete set of TE and TM modes, each with its own cutoff frequency.
Step-by-Step Solution:
1) Apply boundary conditions: Ez or Hz must satisfy homogeneous Helmholtz equations with metallic boundaries.2) Solutions form countably infinite sets: TE_mn/TM_mn (rectangular) and TE_lm/TM_lm (circular).3) No TEM solution exists in a single-conductor hollow guide.Verification / Alternative check:
Mode charts show infinitely many cutoff points for both geometries; TEM appears in two-conductor structures like coax or parallel-plate.
Why Other Options Are Wrong:
- Claims denying one geometry having infinite modes are incorrect.
- TEM dominance is false in hollow guides.
Common Pitfalls:
Equating “dominant mode” with “TEM.” The dominant mode in rectangular is TE10; in circular it is TE11.
Final Answer:
Both support an infinite set of TE and TM modes (no true TEM mode)