Neutron STEM Lab
Virtual engineering lab

Impedance Matching & Bandwidth

Design low-pass or high-pass L networks and quarter-wave transformers, then test their frequency dependence.

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.

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.

Real resistance or reference impedance.
Real resistance or reference impedance.
Positive frequency; stored internally in hertz.
Positive frequency; stored internally in hertz.
unitless
Wave speed divided by the speed of light in vacuum.

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

Power accepted at probe
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Recorded from the current model setup; rerun after editing inputs.
Probe reflection magnitude
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Recorded from the current model setup; rerun after editing inputs.
Theory

Equations and model

L-network synthesis

For positive resistive terminations, the smaller resistance sets the series reactance and the larger resistance sets the shunt susceptance. Place the shunt element on the higher-resistance side. Low-pass and high-pass forms use opposite reactive signs.

Q=RhighRlow−1Q=\sqrt{\frac{R_{\mathrm{high}}}{R_{\mathrm{low}}}-1}∣Xs∣=QRlow,∣Bp∣=QRhigh|X_s|=Q R_{\mathrm{low}},\qquad |B_p|=\frac{Q}{R_{\mathrm{high}}}XL=ωL,XC=−1ωC,BC=ωC,BL=−1ωLX_L=\omega L,\quad X_C=-\frac{1}{\omega C},\quad B_C=\omega C,\quad B_L=-\frac{1}{\omega L}

Quarter-wave transformer

A quarter-wave line inverts a resistive load. Choosing its characteristic impedance as the geometric mean gives a match at the design frequency. The physical section remains fixed as frequency changes.

Zt=RsRLZ_t=\sqrt{R_sR_L}ℓ=c VF4f0\ell=\frac{c\,\mathrm{VF}}{4f_0}Zin(f0)=Zt2RL=RsZ_{\mathrm{in}}(f_0)=\frac{Z_t^2}{R_L}=R_s
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
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Error
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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

  • Synthesize a reference match.
  • Read the topology.
  • Probe away from design.
  • Compare matching methods.
Check your understanding

Questions to answer from the experiment

  1. What transformer impedance matches a 50 Ω source to a 200 Ω resistive load at a quarter wavelength?
  2. Why does a perfect match at one frequency not guarantee a broadband match?
  3. Which elements form the high-pass L network used here?
  4. What is required to match two equal positive resistances in this ideal model?
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.