Circular waveguide – Cutoff wavelength for TE11 mode in terms of diameter If D is the inner diameter of a circular waveguide, what is the cutoff wavelength λc for the TE11 mode, expressed as a multiple of D?

Introduction:
Designing circular waveguides requires accurate cutoff relations for allowed TE/TM modes. TE11 is usually the dominant mode in circular guides (lowest cutoff), analogous to TE10 in rectangular guides. Expressing λc in terms of the physical diameter D helps in quick sizing and band allocation.

Given Data / Assumptions:

• Air-filled, perfectly conducting circular waveguide.
• TE11 mode uses the first root of the derivative of the Bessel function: x′11 ≈ 1.841.
• Radius a = D/2.

Concept / Approach:

For circular guides, the cutoff frequency is f_c = (c / 2π) * (x′mn / a). The corresponding cutoff wavelength is λ_c = 2πa / x′mn. Substituting TE11 data yields λc relative to diameter.

Step-by-Step Solution:

Verification / Alternative check:

Cutoff charts for circular WG list TE11 with λc/D ≈ 1.706; higher modes have smaller λc multiples and thus higher cutoff frequencies.

Why Other Options Are Wrong:

2.11 D corresponds to other roots/modes; 0.82 D and 0.41 D are too small for dominant TE11; 3.54 D is roughly 2× the correct value.

Common Pitfalls:

Confusing TE versus TM roots (x′mn vs xmn) or using radius a where the formula expects diameter D.

Final Answer:

1.706 D.