# s2t

Convert S-parameters to T-parameters

## Syntax

``t_params = s2t(s_params)``

## Description

````t_params = s2t(s_params)` converts the scattering parameters to the chain scattering 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. ```

example

## Examples

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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 S-parameters to T-parameters.

`t_params = s2t(s_params)`
```t_params = 2×2 complex 0.1385 - 0.2304i 0.0354 + 0.1157i -0.0452 + 0.1576i -0.0019 - 0.0291i ```

## Input Arguments

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2N-port S-parameters, specified as a 2N-by-2N-by-M array for the complex numbers (since R2023a), where M represents the number of frequency points of 2N-port S-parameters.

## Output Arguments

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2N-port T-Parameters, returned as a 2N-by-2N-by-M array of complex numbers (since R2023a), where M represents the number for the frequency points of 2N-port T-parameters.

## References

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

[2] D. A. Frickey. "Conversions between S, Z, Y, H, ABCD, and T parameters which are valid for complex source and load impedances". IEEE Transactions on Microwave Theory and Techniques, vol. 42, no. 2, pp. 205-211. Feb. 1994, doi: 10.1109/22.275248.

## Version History

Introduced before R2006a

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