Neutron STEM Lab
Virtual engineering lab

Rectangular Waveguide & Cutoff

Explore TE10 cutoff, guided wavelength, phase and group velocity, evanescence, and the onset of higher modes.

Electrical Engineering / RF & MicrowaveintermediateValidated educational model
Learning mode

Guided laboratory

Use the checklist when you want a structured lab. Explore mode leaves the instruments unrestricted.

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Set up your experiment

Read the equations

Start with an example, change one input, then run again. Inactive controls do not apply to the selected model. Results and validation always belong to the last completed run.

Internal broad dimension; must exceed b.
Internal narrow dimension.
unitless
Uniform, lossless, nonmagnetic filling material.
Positive frequency; stored internally in hertz.
Used for the normalized evanescent axial envelope only.

Choose an example or use the default settings, then run the experiment.

Keep this experiment

Your setup stays in this browser. A project file preserves SI inputs, display units, receiver stages, and any imported complex network samples.

Changes are saved on this device when the settings are valid.

Measurements

Instrument readings

TE10 cutoff
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Recorded from the current model setup; rerun after editing inputs.
Next-mode cutoff
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Recorded from the current model setup; rerun after editing inputs.
TE10 phase constant
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Recorded from the current model setup; rerun after editing inputs.
Theory

Equations and model

Mode cutoff

For a > b in a homogeneous nonmagnetic filling, TE10 is the dominant mode. TE modes allow one index to be zero, but not both. TM modes require both indices to be nonzero. A frequency above cutoff permits propagation but does not specify excitation strength.

fc,mn=c2εr(ma)2+(nb)2f_{c,mn}=\frac{c}{2\sqrt{\varepsilon_r}}\sqrt{\left(\frac{m}{a}\right)^2+\left(\frac{n}{b}\right)^2}β=k1−(fcf)2(f>fc)\beta=k\sqrt{1-\left(\frac{f_c}{f}\right)^2}\quad(f>f_c)

Dispersion and evanescence

Above cutoff the phase and group velocities differ. Below cutoff the axial solution is evanescent. A normalized decay envelope alone does not determine transmission through a finite guide section with interfaces.

vp=c/εr1−(fc/f)2,vg=cεr1−(fc/f)2v_p=\frac{c/\sqrt{\varepsilon_r}}{\sqrt{1-(f_c/f)^2}},\qquad v_g=\frac{c}{\sqrt{\varepsilon_r}}\sqrt{1-(f_c/f)^2}α=kc2−k2,A(z)=A(0)e−αz(f<fc)\alpha=\sqrt{k_c^2-k^2},\qquad A(z)=A(0)e^{-\alpha z}\quad(f<f_c)
Validation

Independent checks

Published reference caseNot run

Check the model against a known numerical benchmark.

Expected
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Simulated
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Error
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Tolerance
0.00001%

Run the experiment to perform this check.

Current model applicabilityNot run

Check current assumptions and report any limitations.

Expected
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Simulated
—
Error
—
Tolerance
0%

Run the experiment to perform this check.

Engineering interpretation

Run the experiment to generate an engineering interpretation.

Assumptions and limitations
Assumptions
  • All calculations run locally; frequencies and lengths are stored in SI units.
  • The selected steady-state ideal or approximate model is appropriate to the engineering question.
  • Each experiment states its reference impedance, sign convention, and omitted effects.
Limitations
  • Model benchmarks validate the implementation, not a particular fabricated device.
  • Plots and sweeps have bounded resolution; inspect raw samples and refine a real measurement when required.
  • Guided completion requires current measurements and passing applicability checks. A warning scenario can still be useful for learning.
Local experiment export

Save your measurements and setup

Exports are generated in your browser. No account or server upload is required.

Settings JSON
Current parameters and instrument controls, including waveform, output enable, scope coupling, timebase, trigger, and cursors when present. Data labs also include the dataset, mappings, exclusions, budget, or propagation setup.
Measurements CSV
Completed instrument readings with labels, units, and descriptions.
Plot PNG
The current canvas-based scope, transient, sweep, or statistics visualization when available.
Summary
Markdown report with objectives, setup, measurements, validation, interpretation, assumptions, and graded guided concept-check results.

Ready to export the current local experiment state.

Learning objectives

What this experiment should establish

  • Establish single-mode propagation.
  • Go below cutoff.
  • Explore higher modes.
  • Check velocity interpretation.
Check your understanding

Questions to answer from the experiment

  1. For a > b in a uniformly filled nonmagnetic guide, what sets TE10 cutoff?
  2. Does phase velocity above c imply faster-than-light information transfer?
  3. What does the below-cutoff exponential envelope represent here?
  4. What changes above the next-mode cutoff?
Continue learning
RF & Microwave LabContinue with the other five RF experiments.AC Circuits WorkbenchReview phasors, reactance, and sinusoidal steady state.Data & Uncertainty LabAnalyze exported numerical data and measurement uncertainty.

Sources and model review

Reviewed 2026-09-17. The educational model exposes its assumptions and validation; source references do not imply external certification.