Understanding S-parameters: S11, S21, S12 and S22

Published: 5 October 2026 · Reading time: about 8 minutes

S-parameters describe how radio-frequency energy enters, leaves and reflects from a network. They are compact and powerful, but easy to misread when a simulated 50-ohm circuit is compared with an active transmitter, a high-impedance probe or a board with an incomplete return path.

Why RF engineers use travelling waves

At low frequencies it is often sufficient to discuss voltage and current at a component. At RF, physical length, phase and impedance become important. A signal travels along a trace or cable; some energy continues through the network and some can return towards its source. S-parameters describe the ratios between those incident and outgoing waves at defined ports.

A two-port network has an input port and an output port. Each S-parameter uses two digits: the first identifies where the result is observed and the second identifies the excited port.

S11 and S22: how well are the ports matched?

S11 is often displayed in decibels. A value near 0 dB means that much of the incident signal is reflected. More-negative values indicate a better match: −10 dB corresponds to roughly ten per cent of the incident power being reflected, while −20 dB corresponds to about one per cent. S22 applies the same idea to the other port.

Return loss is commonly expressed as a positive number even though the plotted S11 magnitude is negative. An S11 magnitude of −15 dB is therefore described as 15 dB return loss. VSWR and reflection coefficient express related information in different forms; the VSWR and Return Loss Calculator converts between them.

S21: transmission, gain and insertion loss

For a passive filter, S21 normally appears at or below 0 dB. If S21 is −2 dB in the passband, the network has 2 dB insertion loss under the stated port conditions. An active amplifier can produce S21 above 0 dB because it draws energy from a power supply.

Do not automatically subtract a transmitter’s programmed power from a probe reading and call the difference S21. The programmed level may not equal available power at the pin, and the probe may not present the same load as a 50-ohm analyser. That difference is still useful measurement data, but it represents the complete source, network, load and instrument arrangement.

Reference impedance is part of the answer

Most RF instruments and Touchstone files use a 50-ohm reference impedance. That does not prove every physical node is a 50-ohm generator or load. A raw power-amplifier pin can require a complex matching network before the antenna side becomes approximately 50 ohms. Changing the reference impedance changes the mathematical wave definitions and therefore the displayed S-parameters.

Why a voltage probe changes the circuit

A probe is another electrical component. Its input resistance, capacitance, bandwidth and ground connection load the node being measured. One picofarad has a reactance of only about 66 ohms at 2.4 GHz, before considering lead inductance and fixture effects. A long oscilloscope ground lead creates an uncontrolled RF return loop and can produce a convincing but inaccurate trace.

Use the shortest practical ground connection, understand the probe’s specified loading and—where possible—compare against a calibrated 50-ohm measurement path. The RF Circuit Studio can add simplified loaded voltage probes to show why the simulated node voltage changes.

Simulation versus a physical board

An ideal inductor has inductance and nothing else. A real part also has series resistance, parallel capacitance, a self-resonant frequency and layout-dependent pads and vias. The same is true for capacitors and transmission lines. At microwave frequencies, a few millimetres of track and a ground via can be material parts of the circuit.

Use ideal simulation to understand topology and trends. Move to manufacturer models, electromagnetic analysis and calibrated measurement when tolerances, loss, power handling or compliance matter. If simulation and measurement disagree, check the measurement reference plane, calibration, connector launch, component orientation, grounding, source impedance and output load before assuming the equation is wrong.

A sensible measurement workflow

1. Record the exact circuit, component values, board revision, frequency range and power setting.
2. Define where port 1 and port 2 are physically located.
3. Record the instrument, calibration plane, probe model and termination.
4. First compare a conventional 50-ohm simulation with a calibrated 50-ohm measurement.
5. Then introduce the actual source, load and probe models to explain in-circuit voltages.
6. Repeat the sweep to distinguish stable behaviour from fixture movement or noise.

Try the RF Filter Designer for ideal filter synthesis and S2P inspection, or assemble a custom network in RF Circuit Studio.