Neutron STEM Lab
Virtual engineering lab

Transmission Lines & Smith Chart

See how mismatch, line length, and attenuation change input impedance, standing waves, and delivered power.

Electrical Engineering / RF & MicrowaveintroductoryValidated educational model
Learning mode

Guided laboratory

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

Explore a model

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.

Positive frequency; stored internally in hertz.
Real resistance or reference impedance.
Used for the complex-load termination.
Positive is inductive; negative is capacitive. Used for the complex-load termination.
At most 100 wavelengths; plot resolution adapts to the length.
unitless
Wave speed divided by the speed of light in vacuum.
dB/m
Uniform attenuation per metre at this frequency; not return loss.

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

Input reflection magnitude
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Recorded from the current model setup; rerun after editing inputs.
Power delivered to load
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Recorded from the current model setup; rerun after editing inputs.
Theory

Equations and model

Incident and reflected waves

Impedance mismatch creates a reflected wave. With a real reference impedance, its squared magnitude gives the reflected-power fraction. The input reflection includes the full round-trip attenuation and phase.

ΓL=ZL−Z0ZL+Z0\Gamma_L=\frac{Z_L-Z_0}{Z_L+Z_0}Γin=ΓLe−2(α+jβ)ℓ\Gamma_{\mathrm{in}}=\Gamma_L e^{-2(\alpha+j\beta)\ell}Zin=Z01+Γin1−ΓinZ_{\mathrm{in}}=Z_0\frac{1+\Gamma_{\mathrm{in}}}{1-\Gamma_{\mathrm{in}}}

Match, loss, and delivered power

A perfect match has Γ = 0 and infinite return loss. Total reflection has |Γ| = 1 and infinite VSWR. These limits are displayed explicitly. Uniform line attenuation uses a real characteristic impedance and a matched source.

VSWR=1+∣Γ∣1−∣Γ∣\mathrm{VSWR}=\frac{1+|\Gamma|}{1-|\Gamma|}RL=−20log⁡10∣Γ∣\mathrm{RL}=-20\log_{10}|\Gamma|PLPinc=e−2αℓ(1−∣ΓL∣2)\frac{P_L}{P_{\mathrm{inc}}}=e^{-2\alpha\ell}(1-|\Gamma_L|^2)
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
—
Tolerance
0.00001%

Run the experiment to perform this check.

Current model applicabilityNot run

Check current assumptions and report any limitations.

Expected
—
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 a matched reference.
  • Create a mismatch.
  • Change electrical length.
  • Separate match from attenuation.
Check your understanding

Questions to answer from the experiment

  1. What changes when the length of an ideal lossless line is varied?
  2. Why can a lossy cable make the input return loss look better?
  3. At its design frequency, what does a lossless quarter-wave line do to a short circuit?
  4. A load has |Γ| = 0.5. What fraction of incident power is reflected?
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.