S-Parameter Measurement Library Theory of Operation

Scattering parameter (S-parameter) measurements quantify how energy propagates through a multi-port network.

S-parameter values are complex numbers which contain both amplitude information and phase information.

For an RF signal incident on one port of the DUT, some fraction of that signal gets reflected back out of the incident port, and another fraction of the signal enters the incident port and scatters to other ports. The remaining fraction of the signal dissipates as heat or electromagnetic radiation.

Understanding these characteristics of a device or a system helps you mitigate impedance mismatch issues and compensate for signal attenuations and distortions. With the amplitude and the phase information discovered through S-parameter measurements, you can also quantify the other reflection and the transmission characteristics of devices, such as return loss, impedance, and group delay.

The matrix for a two-port DUT has four S-parameter measurements. Each measurement is named with the following syntax: S<OutputPort><InputPort>. For example, S21 is a measure of the signal coming out of port 2 relative to the RF stimulus entering port 1. Therefore, S21 and S12 are considered transmission parameters, while S11 and S22 are considered reflection parameters. Refer to the following diagram for more information about S-parameter naming.
Figure 1. S-Parameter Overview


In the previous figure, a1 represents a wave incident at Port 1 and b2 represents a wave reflected at Port 2.

The S-parameters in the previous figure are calculated through the following formula.

(b1b2)=(S11S12S21S22)×(a1a2)