Circular Waveguide – TE11 Mode Visualizer
Interactive field plots for the dominant TE11 mode.
Mode: TE11 | fc = ... | Propagating
Electric Field (E) – Cross‑section
Arrows show (Ex, Ey) direction & magnitude.
Magnetic Field (H) – Cross‑section
Arrows show (Hx, Hy) direction & magnitude.
E‑field in x‑z plane (y=0)
Arrows: (Ex, Ez). Color = |E|.
H‑field in x‑z plane (y=0)
Arrows: (Hx, Hz). Color = |H|.
Surface Current Density (Js) on Wall
Current magnitude along circumference (θ = 0 to 2π).
📐 TE11 Field Equations
Ez = 0
Hz = H0 J1(kcr) cosφ e-jβz
Eφ ∝ J1'(kcr) cosφ e-jβz
Er ∝ (1/r) J1(kcr) sinφ e-jβz
Cutoff: kc = p'11/R, p'11 ≈ 1.841
Hz = H0 J1(kcr) cosφ e-jβz
Eφ ∝ J1'(kcr) cosφ e-jβz
Er ∝ (1/r) J1(kcr) sinφ e-jβz
Cutoff: kc = p'11/R, p'11 ≈ 1.841
📝 Description & Applications
Circular waveguides are used where rotationally symmetric structures are beneficial. TE11 is the dominant mode, with a cutoff wavelength λc ≈ 3.41R.
Applications: Rotary joints, antennas, high‑power transmission.
Advantages: Lower loss than rectangular for same cutoff, easier to fabricate.
Disadvantages: Polarization instability, mode degeneracy.
💡 Interview Questions
What is the cutoff frequency of the TE11 mode in a circular waveguide?
Why is the TE11 mode often used in practice despite degeneracy?
How does the field pattern change as frequency increases?