# Coupler

Model ideal frequency-independent couplers with S-parameters

**Libraries:**

RF Blockset /
Circuit Envelope /
Junctions

## Description

The Coupler block models four port directional
couplers in a circuit envelope environment as an ideal S-parameter
model. The four ports of the coupler are `Input port`

(Port
1), `Through port`

(Port 2), `Isolated port`

(Port
3), `Coupled port`

(Port 4).

Directional couplers are used to sample forward and reflected waves propagating along a transmission line. Directional couplers find uses in many RF design applications such as line power sensors and transmitter automatic level controls.

Hybrid couplers are used to split or combine signals with specific phase relations.

## Parameters

**Select component** — Coupler type

`Directional coupler`

(default) | `Coupler symmetrical`

| `Coupler antisymmetrical`

| `Hybrid quadrature (90 deg)`

| `Hybrid rat-race`

| `Magic tee`

Coupler type, specified as:

`Directional coupler`

The default option is

`Directional coupler`

. The S-parameters matrix for the`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:

r

_{l}= 10^{(-ReturnLoss/20)}i

_{l}= j10^{(-InsertionLoss/20)}i

_{s}= j10^{(-(Coupling+Directivity)/20)}c = 10

^{(-Coupling/20)}

**Note**In release 2019a, the S-parameters representation of the Directional Coupler block is altered to permit a valid implementation for all specified mask values. This implementation adds a 90 degree phase shift to s12, s13, s21, s24, s31, s34, s42, and s43 terms. In addition, a -180 phase shift is added to the s14, s23, s32 and s41 terms.

Use this option to model coupler parameters from data sheets.

`Coupler symmetrical`

The S-parameters matrix for the

`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)

`Coupler antisymmetrical`

The S-parameters matrix for the

`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)

`Hybrid quadrature (90deg)`

The S-parameters matrix for the

`Hybrid quadrature(90deg)`

is:$$\left[\begin{array}{cccc}0& -j/\sqrt{2}& 0& -1/\sqrt{2}\\ -j/\sqrt{2}& 0& -1/\sqrt{2}& 0\\ 0& -1/\sqrt{2}& 0& -j/\sqrt{2}\\ -1/\sqrt{2}& 0& -j/\sqrt{2}& 0\end{array}\right]\text{\hspace{0.05em}}$$

`Hybrid rat-race`

The S-parameters matrix for the

`Hybrid rat-race`

is:$$\left[\begin{array}{cccc}0& -j/\sqrt{2}& 0& -j/\sqrt{2}\\ -j/\sqrt{2}& 0& j/\sqrt{2}& 0\\ 0& j/\sqrt{2}& 0& -j/\sqrt{2}\\ -j/\sqrt{2}& 0& -j/\sqrt{2}& 0\end{array}\right]\text{\hspace{0.05em}}$$

`Magic tee`

The S-parameters matrix for the

`Magic tee`

is:$$\frac{\left[\begin{array}{cccc}0& 0& 1& 1\\ 0& 0& 1& -1\\ 1& 1& 0& 0\\ 1& -1& 0& 0\end{array}\right]}{\sqrt{2}}$$

The Divider block uses the `ispassive`

function to test the passivity of the S-parameters
matrix.

**Coupling (dB)** — Fraction of input signal power coupled to output port

0 (default) | nonnegative and real scalar

Fraction of input signal power coupled to output port of the ```
Directional
coupler
```

, specified as a nonnegative and real scalar. The
default value is `0`

dB.

#### Dependencies

To enable this parameter, select `Directional coupler`

in **Select
component** tab.

**Directivity (dB)** — Ratio of power at coupled port to power at isolated port

`inf`

(default) | nonnegative and real scalar

Ratio of power at coupled port to power at isolated port of
the `Directional coupler`

, specified as a nonnegative
and real scalar. The default value is `inf`

.

#### Dependencies

To enable this parameter, select `Directional coupler`

in **Select
component** tab.

**Insertion loss (dB)** — Loss of signal power between input and output ports

`inf`

(default) | nonnegative and real scalar

Loss of signal power between input and output ports of the ```
Directional
coupler
```

, specified as a nonnegative and real scalar. The
default value is `inf`

.

#### Dependencies

To enable this parameter, select `Directional coupler`

in **Select
component** tab.

**Return loss (dB)** — Loss of signal power due to impedance mismatch

`inf`

(default) | nonnegative and real scalar

Loss of signal power due to impedance mismatch of the ```
Directional
coupler
```

, specified as a nonnegative, and real scalar. The
default value is `inf`

.

#### Dependencies

To enable this parameter, select `Directional coupler`

in **Select
component** tab.

**Power transmission coefficient** — Transmitted signal power

0 (default) | real scalar

Transmitted signal power of the `Directional coupler`

,
specified as a real scalar. The default value is 0.

#### Dependencies

To enable this parameter, select ```
Coupler
symmetrical
```

or ```
Coupler
antisymmetrical
```

in **Select
component** tab.

**Reference impedances (Ohm)** — Reference impedance of coupler

`50`

(default) | positive scalar | three-tuple

Reference impedance of coupler, specified as a scalar or three-tuple.
The default value is `50 Ohms`

.

**Ground and hide negative terminals** — Ground RF circuit terminals

`on`

(default) | `off`

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

By default, this option is selected.

## Version History

**Introduced in R2014a**

## See Also

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