# gammams

Source reflection coefficient of 2-port network

## Syntax

```coefficient = gammams(s_params) coefficient = gammams(hs) ```

## Description

`coefficient = gammams(s_params)` calculates the source reflection coefficient of a 2-port network required for simultaneous conjugate match. `s_params` is a complex 2-by-2-by-M array, representing M 2-port S-parameters. `coefficient` is an M-element complex vector.

`coefficient = gammams(hs)` calculates the source reflection coefficient of the 2-port network represented by the S-parameter object `hs`.

## Examples

collapse all

Calculate the source reflection coefficient using network data from a file.

```ckt = read(rfckt.amplifier,'default.s2p'); s_params = ckt.NetworkData.Data; coefficient = gammams(s_params)```
```coefficient = 191×1 complex -0.7247 + 0.4813i -0.7324 + 0.4723i -0.7401 + 0.4632i -0.7478 + 0.4541i -0.7554 + 0.4449i -0.7630 + 0.4357i -0.7704 + 0.4264i -0.7778 + 0.4170i -0.7850 + 0.4075i -0.7921 + 0.3980i ⋮ ```

## Algorithms

The function calculates `coefficient` using the equation

`${\Gamma }_{MS}=\frac{{B}_{1}±\sqrt{{B}_{1}{}^{2}-4|{C}_{1}{}^{2}|}}{2{C}_{1}}$`

where

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