S-parameters are employed to characterize any N- port linear electrical network as an N×N matrix of complex numbers. This matrix is used to express reflected wave amplitudes at each port as a linear combination of the incident wave amplitudes at all ports.

In a two-port network, S-parameters help express the scattered waves b_1 and b_2 as linear combinations of incident waves a_1 and a_2 as follows

The figure below illustrates the concept of “reflected” and “transmitted” waves when “incident” wave (stimulus) is directed towards port 1 of a two-port DUT. Setting a_2=0, equation 9 states that S_11 is the ratio of reflected and incident waves, while S_21 is the ratio of transmitted and incident waves

Assuming a_1=0, S_22 can be interpreted as the ratio b_2/a_2, and S_12 can be interpreted as the ratio b_1/a_2.

In the context of a two-port DUT S11 and S21, are sometimes referred to as forward S-parameters because the incident signal originates from the RF source on port one. With the incident source on port two, S22 and S12 are called the reverse S-parameters.

S-Parameter Direction Description
S11 Reflected The ratio of the voltage reflected at port one to the incident voltage placed on port one.
S21 Transmitted The ratio of the voltage transmitted through the DUT present at port two to the incident voltage placed on port one.
S22 Reflected The ratio of the voltage reflected at port two to the incident voltage placed on port two.
S12 Transmitted The ratio of the voltage transmitted through the DUT present at port one to the incident voltage placed on port two.

Generalizing to N-port DUTs, S-parameters are represented using the notation S_ij and can be interpreted as the ratio of the voltage transmitted to port i to the voltage incident on port j assuming that incident waves at all other ports are 0, as represented in the following equation: