100 Ω load on a 50 Ω line
Expected: |Γ| = 1/3; VSWR = 2; delivered fraction = 8/9
Observed: |Γ| = 0.3333333333333333; VSWR = 1.9999999999999998; delivered = 0.8888888888888888
passRF & Microwave Engineering Laboratory
Follow reflections around a Smith chart, build a matching network, inspect measured two-port data, or explore the geometry that controls a microwave circuit. Every experiment connects the result to its equations, assumptions, and numerical checks.
No account, no installation, and no uploads to a server. Projects and imported network data remain in your browser unless you export them.
Choose an experiment
Use the examples first, then vary one input at a time. Guided mode adds procedures and automatically graded concept questions.
Transmission Lines & Smith Chart
See how mismatch, line length, and attenuation change input impedance, standing waves, and delivered power.
Impedance Matching & Bandwidth
Design low-pass or high-pass L networks and quarter-wave transformers, then test their frequency dependence.
S-Parameters & Virtual Network Analyzer
Sweep ideal two-port networks or import a Touchstone .s2p file. Inspect reflection, transmission, group delay, reciprocity, and passivity.
Receiver Gain & Noise Budget
Build and reorder a receiver chain, identify dominant noise contributions, and compare sensitivity with small-signal headroom.
Microstrip Geometry & Impedance
Analyze a thin PCB trace or synthesize its width for a target impedance, with effective permittivity and guided wavelength exposed.
Rectangular Waveguide & Cutoff
Explore TE10 cutoff, guided wavelength, phase and group velocity, evanescence, and the onset of higher modes.
Learn what a good RF result looks like
Low reflection, low insertion loss, low noise, and wide bandwidth are different design goals. A lossy line can hide a bad load match. An exact match at one frequency can be narrowband. A high-gain receiver can still have poor sensitivity if loss appears ahead of the first amplifier.
The lab keeps those distinctions visible through power fractions, complex impedance, sampled network diagnostics, stage-by-stage noise contributions, and geometry limits. Plots include numerical tables and downloadable data, so you can independently inspect the evidence.
Use measured data and keep your work
The network analyzer imports the two-port S-parameter subset of Touchstone 1.x. Real/imaginary, magnitude/angle, and dB/angle formats are supported with a common real reference impedance. It preserves the original complex samples, shows the actual probe frequency, and exports standard .s2p data.
Save project JSON to move between browsers. Use data CSV for further work in the Measurement, Data Analysis & Uncertainty Lab. Shared experiment exports include plots, current measurements, validation, and guided answers. Changing an input requires a fresh run before results can be exported.
Numerical validation6/6 published reference checks passReviewed 2026-09-17
View benchmark details
Quarter-wave impedance inversion
Expected: 50 Ω source to 200 Ω load: transformer 100 Ω; input 50 Ω
Observed: Transformer 100 Ω; input 50 + j-4.592425496802574e-15 Ω
passSeries 100 Ω element between 50 Ω ports
Expected: S11 = S21 = 0.5; maximum singular-value squared = 1
Observed: S11 0.5; S21 0.5; power bound 1
passTwo-stage Friis reference
Expected: F1 = 2, G1 = 10, F2 = 4: total F = 2.3
Observed: Total F = 2.3
passAir dielectric and impedance synthesis
Expected: εeff = 1 in air; synthesized 50 Ω line resolves within 10⁻⁸ Ω
Observed: Air εeff 1; synthesized 50.00000000000001 Ω
passWR-90 TE10 reference
Expected: Cutoff 6.557140376 GHz; vp·vg = c² at 10 GHz
Observed: Cutoff 6.557140376202975 GHz; vp·vg/c² = 1
passModel scope and limits
These are bounded steady-state educational models. They do not include full-wave field solving, antenna radiation, nonlinear transistor models, fabrication tolerances, or a calibrated measurement instrument. The microstrip model is quasi-static and assumes zero conductor thickness; the waveguide model uses perfect conductors. Receiver budgets assume matched linear stages and exclude mixer sideband noise.
The two-port analyzer checks sampled passivity and reciprocity; it does not certify causality, stability, or accuracy of an imported measurement. Group delay needs adequate frequency resolution. Each experiment includes its governing equations, source references, and specific assumptions.