# Coupler

Model ideal frequency-independent couplers with S-parameters

Junctions

## Description

Use the Coupler block to model four port directional couplers in a circuit envelope environment as an ideal S-parameter model.

## Dialog Box and Parameters

### Main Tab

Select component
• `Directional coupler`

The default option is `Directional coupler`. The s-parameter matrix for `Directional coupler` is:

$\left[\begin{array}{cccc}{r}_{l}& {i}_{l}& {i}_{s}& c\\ {i}_{l}& {r}_{l}& c& {i}_{s}\\ {i}_{s}& c& {r}_{l}& {i}_{l}\\ c& {i}_{s}& {i}_{l}& {r}_{l}\end{array}\right]$

where:

• rl = 10(-ReturnLoss/20)

• il = 10(-InsertionLoss/20)

• is = 10(-(Coupling+Directivity)/20)

• c = 10(-Coupling/20)

When you select this option, the following parameters are available:

• Coupling (dB)

Specify the coupling factor of `Directional coupler`. The valid value is nonnegative and real. The default value is ```0 dB```.

• Directivity (dB)

Specify the directivity of `Directional coupler`. The valid values are nonnegative and real. The default value is `inf`.

• Isolation (dB)

Specify the isolation of `Directional coupler`. The valid values are nonnegative and real. The default value is `inf`.

• Return loss (dB)

Specify the return loss of `Directional coupler`. The valid values are nonnegative and real. The default value is `inf`.

• Reference impedance (Ohm)

Specify the reference impedances of `Directional coupler` as scalar or three-tuple. The default values are `50 Ohms`.

• `Coupler symmetrical`

The s-parameter matrix for `Coupler symmetrical` is:

$\left[\begin{array}{cccc}0& \alpha & 0& j\beta \\ \alpha & 0& j\beta & 0\\ 0& j\beta & 0& \alpha \\ j\beta & 0& \alpha & 0\end{array}\right]$

where:

• |α| ≤ 1 = Power transmission coefficient

• β = sqrt(1– α*α)

When you select this option, the following parameters are available:

• Power transmission coefficient

Specify the power transmission coefficient of ```Coupler symmetrical```. The valid values are real. The default value is `0`.

• Reference impedance (Ohm)

Specify the reference impedances of `Coupler symmetrical` as scalar or three-tuple. The default values are `50 Ohms`.

• `Coupler antisymmetrical`

The s-parameter matrix for `Coupler antisymmetrical` is:

$\left[\begin{array}{cccc}0& \alpha & 0& \beta \\ \alpha & 0& -\beta & 0\\ 0& -\beta & 0& \alpha \\ \beta & 0& \alpha & 0\end{array}\right]$

where:

• |α| ≤ 1 = Power transmission coefficient.

• β = sqrt(1– α*α)

When you select this option, the following parameters are available:

• Power transmission coefficient

Specify the power transmission coefficient of ```Coupler antisymmetrical```. The valid values are real. The default value is `0`.

• Reference impedance (Ohm)

Specify the reference impedances of `Coupler antisymmetrical` as scalar or three-tuple. The default values are `50 Ohms`.

• `Hybrid quadrature (90deg)`

The s-parameter matrix for `Hybrid quadrature(90deg)` is:

$\left[\begin{array}{cccc}0& -j/\sqrt{2}& 0& -1/\sqrt{2}\\ -j/\sqrt{2}& 0& -1/\sqrt{2}& 0\\ 0& -1/\sqrt{2}& 0& -j/\sqrt{2}\\ -1/\sqrt{2}& 0& -j/\sqrt{2}& 0\end{array}\right]\text{ }$

When you select this option, the following parameter is available:

• Reference impedance (Ohm)

Specify the reference impedances of `Hybrid quadrature(90deg)` as scalar or three-tuple. The default values are `50 Ohms`.

• `Hybrid rat-race`

The s-parameter matrix for `Hybrid rat-race` is:

$\left[\begin{array}{cccc}0& -j/\sqrt{2}& 0& -j/\sqrt{2}\\ -j/\sqrt{2}& 0& j/\sqrt{2}& 0\\ 0& j/\sqrt{2}& 0& -j/\sqrt{2}\\ -j/\sqrt{2}& 0& -j/\sqrt{2}& 0\end{array}\right]\text{ }$

When you select this option, the following parameter is available:

• Reference impedance (Ohm)

Specify the reference impedances of `Hybrid rat-race` as scalar or three-tuple. The default values are `50 Ohms`.

Ground and hide negative terminals

Select this option to internally ground and hide the negative terminals. Clear the option to expose the negative terminals. By exposing these terminals, you can connect them to other parts of your model.

By default, this option is selected.