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Comparing rectangular vs circular waveguides: which statement about modal families is correct?

Difficulty: Easy

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)

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