This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

S-Parameter Notation

Define S-Parameters

RF Toolbox™ software uses matrix notation to specify S-parameters. The indices of an S-parameter matrix correspond to the port numbers of the network that the data represent. For example, to define a matrix of 50-ohm, 2-port S-parameters, type:

s11 = 0.61*exp(j*165/180*pi);
s21 = 3.72*exp(j*59/180*pi);
s12 = 0.05*exp(j*42/180*pi);
s22 = 0.45*exp(j*(-48/180)*pi);
s_params = [s11 s12; s21 s22];
RF Toolbox functions that operate on s_params assume:

  • s_params(1,1) corresponds to the reflection coefficient at port 1, S11.

  • s_params(2,1) corresponds to the transmission coefficient from port 1 to port 2, S21.

  • s_params(1,2) corresponds to the transmission coefficient from port 2 to port 1, S12.

  • s_params(2,2) corresponds to the reflection coefficient at port 2, S22.

RF Toolbox software also supports three-dimensional arrays of S-parameters. The third dimension of an S-parameter array corresponds to S-parameter data at different frequencies. The following figure illustrates this convention.

Refer to S-Parameters Using Character Vector

RF Toolbox software uses character vector to refer to S-parameters in plotting and calculation methods, such as plot. These character vector have one of the following two forms:

  • 'Snm' — Use this syntax if n and m are both less than 10.

  • 'Sn,m' — Use this syntax if one or both are greater than 10. 'Sn,m' is not a valid syntax when both n and m are less than 10.

The indices n and m are the port numbers for the S-parameters.

Most toolbox objects only analyze 2-port S-parameters. The following objects analyze S-parameters with more than two ports:

You can get 2-port parameters from S-parameters with an arbitrary number of ports using one or more of the following steps: