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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 Strings

RF Toolbox software uses strings to refer to S-parameters in plotting and calculation methods, such as plot. These strings 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:

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