# Divider

Model ideal frequency-independent dividers or combiners with S-parameters

Libraries:
RF Blockset / Circuit Envelope / Junctions

## Description

The Divider block models power dividers or combiners in a circuit envelope environment as an S-parameter model. In a power divider, the input power enters at a port, splits, and exits at different ports.

To use a power divider to model and simulate a 66 GHz QPSK RF transmit and receive system with a 32-element hybrid beamforming antenna, see the Transmit Subarrays section in the Modeling RF mmWave Transmitter with Hybrid Beamforming example.

## Parameters

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Divider type, specified as:

• `T power divider`

The S-parameter matrix for `T-power divider ` is :

$\left[\begin{array}{ccc}{s}_{11}& {s}_{21}& {s}_{31}\\ {s}_{21}& {s}_{22}& {s}_{32}\\ {s}_{31}& {s}_{32}& {s}_{33}\end{array}\right]$

where:

• s11 = (z23 –z1) / (z23 + z1)

• s22 = (z13 –z2) / (z13 + z2)

• s33 = (z12 –z3) / (z12 + z3)

• s21 = (1+ s11) * sqrt(z1 / z2)

• s31 = (1+ s11) * sqrt(z1 / z3)

• s32 = (1+ s22) * sqrt(z2 / z3)

• z12 = z1 * z2 / (z1 + z2)

• z13 = z1 * z3 / (z1 + z3)

• z23 = z2 * z3 / (z2 + z3)

• z1 = Z0(1), z2 = Z0(2), z3 = Z0(3)

• Reference Impedances: Z0 = [z1, z2, z3 ]

• `Resistive power divider`

The S-parameter matrix for `Resistive power divider` is :

$\left[\begin{array}{ccc}0& 1/2& 1/2\\ 1/2& 0& 1/2\\ 1/2& 1/2& 0\end{array}\right]$

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

• `Wilkinson power divider`

The S-parameter matrix for `Wilkinson power divider` is:

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

Note

• For DC carrier (0 Hz) frequency, Wilkinson power divider is a zero matrix.

• Starting R2021a, port positions in the Divider block when you select the ```Wilkinson power divider``` component have changed. For more information, see Compatibility Considerations.

• `Tee H-plane (S33=0)`

The `Tee H-plane (S33=0)` is symmetrical, lossless, and reciprocal. The S-parameter matrix is:

$\frac{\left(\begin{array}{ccc}-1& 1& \sqrt{2}\\ 1& -1& \sqrt{2}\\ \sqrt{2}& \sqrt{2}& 0\end{array}\right)}{2}$

• `Tee E-plane`

The `Tee E-plane` is symmetrical, lossless, and reciprocal. The S-parameter matrix is:

$\frac{\left(\begin{array}{ccc}1& 1& \sqrt{2}\\ 1& 1& -\sqrt{2}\\ \sqrt{2}& -\sqrt{2}& 0\end{array}\right)}{2}$

Number of Wilkinson power divider outports, specified as a nonnegative integer in the range (`1`, `65`].

#### Dependencies

To enable this parameter, set Select Component to `Wilkinson power divider`.

Reference impedance of divider, specified as a positive scalar or three-tuple vector.

Select this parameter to ground and hide the negative terminals. To expose the negative terminals, clear the 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

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