# t2s

Convert T-parameters to S-parameters

## Syntax

``s_params = t2s(t_params)``

## Description

example

````s_params = t2s(t_params)` converts the chain scattering parameters to the scattering parameters. ```

## Examples

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Define a matrix of T-parameters.

```t11 = 0.138451095405929 - 0.230421317393041i; t21 = -0.0451985986689165 + 0.157626245839348i; t12 = 0.0353675449261375 + 0.115682026931012i; t22 = -0.00194567217559662 - 0.0291212122613417i; t_params = [t11 t12; t21 t22];```

Convert T-parameters to S-parameters.

`s_params = t2s(t_params)`
```s_params = 2×2 complex -0.5892 + 0.1579i 0.0372 + 0.0335i 1.9159 + 3.1887i 0.3011 - 0.3344i ```

## Input Arguments

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

This function defines the T-parameters as

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

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.

## Output Arguments

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