# stabilitymu

Stability factor μ of two-port network

## Syntax

``[mu,muprime] = stabilitymu(s_params)``
``[mu,muprime] = stabilitymu(hs)``

## Description

example

````[mu,muprime] = stabilitymu(s_params)` calculates and returns the stability factor, `μ`, and `μ'` for the two-port S-parameters```

example

````[mu,muprime] = stabilitymu(hs)` calculates and returns the stability factor for the two-port network represented by the S-parameter object `hs`.```

## Examples

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Calculate the stability factor of network data from a file.

```S = sparameters('passive.s2p'); s_params = S.Parameters; [mu,muprime] = stabilitymu(s_params);```

Check stability criteria.

```stability_index = (mu>1)|(muprime>1); is_stable = all(stability_index)```
```is_stable = logical 1 ```

List frequencies with unstable S-parameters.

```freq = S.Frequencies; freq_unstable = freq(~stability_index)```
```freq_unstable = 0x1 empty double column vector ```

Create a `sparameters` object from the specified file.

`s_params = sparameters('passive.s2p');`

Calculate the stability factor using `stabilitymu` function.

`[mu,muprime] = stabilitymu(s_params);`

Check the stability criteria.

```stability_index = (mu>1)|(muprime>1); is_stable = all(stability_index)```
```is_stable = logical 1 ```

List frequencies with unstable S-parameters.

```freq = s_params.Frequencies; freq_unstable = freq(~stability_index)```
```freq_unstable = 0x1 empty double column vector ```

## Input Arguments

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Two-port S-parameters, specified as a complex 2-by-2-by-M array. M is the number of two-port S-parameters.

Data Types: `double`

Two-port network, specified as an S-parameter object.

Data Types: `function_handle`

## Output Arguments

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Minimum distance between the center of the unit Smith chart and the unstable region in the load plane, returned as vector equal to the number of frequency or data points.

Minimum distance between the center of the unit Smith chart and the unstable region in the source plane, returned as a vector equal to the number of frequency or data points.

## Algorithms

`stabilitymu` calculates the stability factors using the equations

`$\begin{array}{c}\mu =\frac{1-{|{S}_{11}|}^{2}}{|{S}_{22}-{S}_{11}^{*}\Delta |+|{S}_{21}{S}_{12}|}\\ \mu \prime =\frac{1-{|{S}_{22}|}^{2}}{|{S}_{11}-{S}_{22}^{*}\Delta |+|{S}_{21}{S}_{12}|}\end{array}$`

where:

• S11, S12, S21, and S22 are S-parameters, from the input argument `s_params`.

• Δ is a vector whose members are the determinants of the M 2-port S-parameter matrices:

`$\Delta ={S}_{11}{S}_{22}-{S}_{12}{S}_{21}$`

• S* is the complex conjugate of the corresponding S-parameter.

The function performs these calculations element-wise for each of the M S-parameter matrices in `s_params`.

## References

[1] Edwards, M.L., and J.H. Sinsky. “A New Criterion for Linear 2-Port Stability Using a Single Geometrically Derived Parameter.” IEEE Transactions on Microwave Theory and Techniques 40, no. 12 (December 1992): 2303–11. https://doi.org/10.1109/22.179894.

## Version History

Introduced before R2006a