S-Parameters

The S-Parameters (or scattering parameters) are a description of an N-port circuit based upon concepts of input (or incident) power and output (transmitted or reflected, collectively "scattered") power.

The S-parameter description makes use of a reference impedance, Z_0,n, for every port. This can be any positive number; often a value of 50 Ohms is used.

The normalized incident wave variable, A_n at a port is defined as:

The normalized reflected wave variable, B_n, is defined as:

The complex magnitude of A_n is denoted by |A_n|.

|A_n|² is interpreted as the incident power on the port, and |B_n|² is the reflected power. The total power on the port is |A_n|² - |B_n|².

The scattering matrix, S, relates these quantities:

The entries S_ij of the scattering matrix are the individual scattering parameters. An S-parameter value of S_ij = 0 means no power is transmitted from port i to port j. A magnitude of 1 means that all available power is transmitted from port i to port j.

For example, S₃₁ is used to compute the amount of power from the port 1 excitation that is transmitted to port 3. The phase of S₃₁ specifies the phase shift that occurs from port 1 to port 3.

The S-parameters associated with a structure are a function of frequency. Therefore, separate solutions and S-matrices are generated for each frequency point of interest.

All voltage and current sources are ignored when the S-, Y-, and Z- parameters are computed.