Understanding TE10 in a rectangular waveguide Which statement best describes the physical nature of TE10 propagation in a hollow rectangular waveguide?
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AIt is the vector sum of three independent TEM waves along the guide
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BIt is one TEM wave along the guide plus one TEM wave in the transverse plane
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CIt is one TEM wave along the guide and two TEM waves forming the pattern
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DNone of the above descriptions are correct because TE10 is a true TE mode, not a combination of TEM waves
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EIt is equivalent to a coaxial TEM mode at a different cutoff
Answer
Correct Answer: None of the above descriptions are correct because TE10 is a true TE mode, not a combination of TEM waves
Explanation
Introduction / Context:Waveguides do not support TEM modes unless multiple conductors are present. Rectangular waveguides are single-conductor enclosures; their propagating solutions are TE or TM, each with cutoff. The TE10 mode is the dominant mode in a standard rectangular waveguide and is a genuine TE solution to Maxwell’s equations with boundary conditions, not a superposition of TEM modes.
Given Data / Assumptions:
- Single hollow PEC rectangular guide, air-filled.
- TE10 is dominant with cutoff f_c = c/(2a).
- No center conductor → no true TEM mode exists.
Concept / Approach:
TEM waves require at least two conductors to define a transverse E field with zero longitudinal components everywhere. In a single-conductor hollow guide, boundary conditions enforce solutions with nonzero longitudinal components (either Ez or Hz). TE10 has Hz ≠ 0 with Ez = 0, exhibiting a standing variation across the broad wall and propagating along z with phase constant β above cutoff.
Step-by-Step Solution:
1) Recognize geometry → single conductor → no pure TEM mode.2) Solve for fields → TE and TM families only.3) TE10 arises from transverse boundary conditions; not expressible as a finite sum of TEM modes.Verification / Alternative check:
Mode charts and derivations show Ez = 0 for TE modes, Ez ≠ 0 for TM modes, and neither equals the TEM condition (Ez = Hz = 0).
Why Other Options Are Wrong:
Options A–C attempt to reinterpret TE10 as combinations of TEM, which is physically incorrect in a single-conductor guide.
Common Pitfalls:
Assuming “all waves are TEM” or importing transmission-line intuition to waveguides without considering boundary conditions and cutoff behavior.
Final Answer:
None of the above descriptions are correct because TE10 is a true TE mode, not a combination of TEM waves.