Field Guide · term

Also known as: scattering parameters, S-matrix

S-parameters (scattering parameters) describe a linear RF network entirely by how it scatters incident waves at its ports into reflected and transmitted waves.1 Each Sij is a complex number — magnitude and phase — giving the wave emerging at port i per unit wave injected at port j, with all other ports terminated in the reference impedance. For the ubiquitous two-port device, S11 is the input match, S21 the forward transmission (gain or loss), S12 the reverse transmission (isolation), and S22 the output match.

2-port network port 1 port 2 a1 in S11·a1 reflected S21·a1 out a2 in S11 in-match · S21 gain · S12 isolation · S22 out-match
A two-port's behaviour is captured by four scattering parameters: S11 and S22 are the port reflections, S21 the forward transmission, and S12 the reverse leakage.

How it works

At radio frequencies you cannot easily hold a port open or shorted to measure the voltages and currents that classic impedance (Z) or admittance (Y) parameters require — the reactances of test leads dominate and open/short standards misbehave. S-parameters sidestep this by working with travelling waves and terminating every port in a well-defined reference impedance, usually 50 Ω. Each port has an incoming wave a and an outgoing wave b, and the network is fully described by the matrix equation b = S·a. For a two-port that expands to:

  • b1 = S11·a1 + S12·a2
  • b2 = S21·a1 + S22·a2

To measure one parameter you drive a single port and terminate the rest, so their incoming waves are zero. With port 2 terminated, S11 = b1/a1 is just the input reflection coefficient, and S21 = b2/a1 is the forward transmission. Swap the drive to the other port for S22 and S12.

In practice

Because each parameter is complex, S-data carries both how much a signal is attenuated or amplified and the phase shift it undergoes — essential for cascading stages, designing matching networks, and building filters. Common derived readings:

  • S11 and S22 in dB give the return loss at each port.
  • S21 in dB gives insertion loss for a passive part or gain for an amplifier.
  • |S12| in dB gives reverse isolation; a large negative value means the device is well unilateral (little leakage backward).

S-parameters are conventionally exported as Touchstone (.s2p) files listing each parameter’s magnitude and phase across frequency, which circuit simulators read directly. They are defined for linear, time-invariant behaviour, so they characterise small-signal operation; strongly nonlinear effects like compression and intermodulation need additional measurements.

Relevance to SDR

The building blocks of an SDR front end are specified in S-parameters: a low-noise amplifier is quoted by its S21 gain and S11 input match, an RF filter by its S21 passband shape and stopband rejection, and connectors and cables by their return and insertion loss. Designers measure all of these on a vector network analyzer, which sweeps a known incident wave and ratios the reflected and transmitted waves to recover each Sij in magnitude and phase.

GopherTrunk is a software decoder that operates after the analog chain, so it neither produces nor consumes S-parameters — they belong to the hardware layer that delivers IQ samples. The concept is still worth knowing for GopherTrunk users choosing an antenna, filter, or amplifier, because those parts’ datasheets speak in S-parameters, and a good S11/S21 profile at the frequency of interest is what ultimately hands the decoder clean samples.

Sources

  1. Scattering parameters — Wikipedia, the S-matrix definition, two-port S11/S21/S12/S22 meanings, and reference-impedance conventions. ↩

See also