# Documentation

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# Z-Parameters Passive Network

Model passive network using Z-parameters

## Library

Black Box Elements sublibrary of the Physical library

## Description

The Z-Parameters Passive Network block models the two-port passive network described in the block dialog box, in terms of its Z-parameters and their associated frequencies.

In the Z-Parameters field of the block dialog box, provide the Z-parameters for each of M frequencies as a 2-by-2-by-M array. In the Frequency field, specify the frequencies for the Z-parameters as an M-element vector. The elements of the vector must be in the same order as the Z-parameters. All frequencies must be positive. For example, the following figure shows the correspondence between the Z-parameters array and the vector of frequencies.

The Z-Parameters Passive Network block uses the RF Toolbox™ `z2s` function to convert the Z-parameters to S-parameters, and then interpolates the resulting S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See Map Network Parameters to Modeling Frequencies for more details.

## Parameters

### Main Tab

Z-Parameters

Z-parameters for a two-port passive network in a 2-by-2-by-M array. M is the number of Z-parameters.

Frequency (Hz)

Frequencies of the Z-parameters as an M-element vector. The order of the frequencies must correspond to the order of the Z-parameters in Z-Parameters. All frequencies must be positive.

Interpolation method

The method used to interpolate the network parameters. The following table lists the available methods describes each one.

MethodDescription
`Linear` (default)Linear interpolation
`Spline`Cubic spline interpolation
`Cubic`Piecewise cubic Hermite interpolation

### Visualization Tab

For information about plotting, see Create Plots.

## Examples

### Plotting Parameters with the Z-Parameters Passive Network Block

The following example specifies Z-parameters [0.13 - 5.93i, .03-3.16i; 0.03-3.16i, .13-5.93i] and [0.27-2.86i, -.09-5.41i; -.09-5.41i, .27-2.86i] at frequencies 2.0 GHz and 2.1 GHz respectively. It uses the MATLAB® `cat` function to create the 2-by-2-by-2 Z-parameters array.

```cat(3,[0.13-5.93i, .03-3.16i; 0.03-3.16i, .13-5.93i],... [0.27-2.86i,-.09-5.41i; -.09-5.41i, .27-2.86i]) ```
1. Type the following command at the MATLAB prompt to create a variable called `zparams` that stores the values of the Z-parameters.

```zparams = cat(3,... [0.13-5.93i,.03-3.16i; 0.03-3.16i,.13-5.93i],... [0.27-2.86i,-.09-5.41i; -.09-5.41i,.27-2.86i])```

2. Set the Z-Parameters Passive Network block parameters on the Main tab as follows:

• Set the Z-Parameters parameter to `zparams`.

• Set the Frequency (Hz) parameter to `[2.0e9,2.1e9]`.

Click . This action applies the specified settings.

3. Set the Z-Parameters Passive Network block parameters on the Visualization tab as follows:

• In the Source of frequency data list, select `User-specified`.

• Set the Frequency data (Hz) parameter to `[1.9e9:1.0e8:2.2e9]`.

• In the Y parameter1 list, select `S12`.

Click . This action creates an X-Y plane plot of the S12 parameters in the frequency range 1.9 to 2.2 GHz.

## See Also

`z2s` (RF Toolbox)

`interp1` ( MATLAB)

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