# stabilityk

Stability factor K of two-port network

## Syntax

``[k,b1,b2,delta] = stabilityk(s_params)``
``[k,b1,b2,delta] = stabilityk(hs)``

## Description

example

````[k,b1,b2,delta] = stabilityk(s_params)` calculates and returns the stability factor, `k`, and the conditions `b1`, `b2`, and `delta` for the two-port network.```
````[k,b1,b2,delta] = stabilityk(hs)` calculates and returns the stability factor and stability conditions for the two-port network represented by the S-parameter object `hs`.```

## Examples

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Examine the stability of network data from a file by first calculating the stability factor.

```S = sparameters('passive.s2p'); s_params = S.Parameters; [k,b1,b2,delta] = stabilityk(s_params);```

Check stability criteria.

```stability_index = (k>1)&(abs(delta)<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 S-parameters object from a specified file. .

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

Calculate the stability using `stabilityk` function.

`[k,b1,b2,delta] = stabilityk(s_params);`

Check the stability criteria.

```stability_index = (k>1)&(abs(delta)<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`

## Algorithms

Necessary and sufficient conditions for stability are `k`>`1` and `abs(delta)`<`1`. `stabilityk` calculates the outputs using the equations

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

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:

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

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

 Gonzalez, Guillermo. Microwave Transistor Amplifiers: Analysis and Design. 2nd ed. Upper Saddle River, N.J: Prentice Hall, 1997.