# s2t

Convert S-parameters to T-parameters

## Syntax

`t_params = s2t(s_params)`

## Description

`t_params = s2t(s_params)` converts the scattering parameters `s_params` into the chain scattering parameters `t_params`. The `s_params` input is a complex 2-by-2-by-M array, representing M 2-port S-parameters. `t_params` is a complex 2-by-2-by-M array, representing M 2-port T-parameters.

This function uses the following definition for T-parameters:

$\left[\begin{array}{c}{a}_{1}\\ {b}_{1}\end{array}\right]=\left[\begin{array}{cc}{T}_{11}& {T}_{12}\\ {T}_{21}& {T}_{22}\end{array}\right]\left[\begin{array}{c}{b}_{2}\\ {a}_{2}\end{array}\right],$

where:

• a1 is the incident wave at the first port.

• b1 is the reflected wave at the first port.

• a2 is the incident wave at the second port.

• b2 is the reflected wave at the second port.

## Examples

Convert S-parameters to T-parameters:

```%Define a matrix of S-parameters 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]; %Convert to T-parameters t_params = s2t(s_params)```

## References

Gonzalez, Guillermo, Microwave Transistor Amplifiers: Analysis and Design, 2nd edition. Prentice-Hall, 1997, p. 25.