EE 499 · Week 7 · Lab
Look Inside a Waveguide
A hollow metal tube can carry a radio signal, but only if the frequency is high enough. Slide the frequency and watch what the electric field does.
Part of Week 7 · Fields Inside the Waveguide. Prefer the full engineering view? Open the engineering explorer →
A standard X-band waveguide (WR-90)
Above cutoffDrag to rotate · scroll to zoom · Home resets the view
Looking into the guide from the source side, at a slice mm from the entrance
Below cutoff: drag Slice position into the guide to watch the field shrink with distance.
This 3D view needs WebGL, which is not available in this browser.
The engineering explorer shows the same fields in 2D and works without WebGL.
- Below cutoff
- At cutoff
- Above cutoff
The signal travels. Each arrow is the electric field at one spot. It points up or down between the metal plates, and a longer arrow means a stronger field. The whole pattern slides along the guide, and it is strongest down the middle.
At cutoff the signal stops travelling. The same pattern appears all along the guide and just pulses up and down together. This is the dividing line: below it the field fades with distance, above it the field travels.
Below cutoff the field cannot travel. It fades very quickly with distance from the entrance, and the arrows only pulse up and down in place. Farther along the field is still there, just far too small to draw.
Reduced-motion setting detected. The animation starts paused. Press Play to start it.
Advanced: numbers, equations and assumptions
- Cutoff fc
- GHz
- f / fc
- β
- rad/m
- α (decay)
- Np/m
- Field falls by 1/e every
- mm (below cutoff)
- Guided λg
- mm
- Phase velocity
- Group velocity
f_c = c / (2a) (TE10, a = 22.86 mm) above cutoff: E_y ∝ sin(πx/a) · cos(ωt − βz) β = √(k² − (π/a)²) at cutoff: E_y ∝ sin(πx/a) · cos(ωt) β = 0 (the same in every cross-section) below cutoff: E_y ∝ sin(πx/a) · e^(−αz) · cos(ωt) α = √((π/a)² − k²)
- Perfectly conducting walls, air-filled, lossless. The field values come from the same validated physics module as the engineering explorer.
- Arrow length is Ey divided by its peak value at the entrance. Arrows shorter than 4 % of that peak are not drawn, so a very small field looks absent although it is not zero. Only the electric field is drawn in this version; the engineering explorer also shows the magnetic field.
- The source block is a simplified symbol. The model assumes the TE10 pattern is applied across the entrance plane; it does not simulate a particular probe, coaxial feed or antenna.
- The guide is drawn 4.5a long with its output end open and nothing reflected. At the slice in the cross-section view the same field is cut at one position along the guide.
- Time is slowed enormously: a real 10 GHz field completes ten billion cycles every second.
- Below cutoff the field stores energy but carries no average power along the guide.
- The frequency is used exactly as selected. A frequency counts as “at cutoff” only when it is within one part in a million of the cutoff, which you select with the cutoff marker; a frequency even slightly above it is shown as propagating, with a very long guided wavelength.