Divider

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

• Library:

• RF Blockset / Circuit Envelope / Junctions

• 

Description

The Divider block models power dividers or combiners in a Circuit Envelope environment as a S-parameter model. For power dividers, the input power enters at a port, splits, and exits at other ports.

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

Parameters

Select component — Divider type

T power divider (default) | Resistive power divider | Wilkinson power divider | Tee H-plane (S33=0) | Tee E-plane

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 = (z_{23 –}z₁) / (z₂₃ + z₁)

  • s₂₂ = (z_{13 –}z₂) / (z₁₃ + z₂)

  • s₃₃ = (z_{12 –}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:

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

Reference impedances (Ohm) — Reference impedance of divider

50 (default) | positive scalar | three-tuple vector

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

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 the parameter. By exposing these terminals, you can connect them to other parts of your model.

By default, this option is selected.

Model Examples

Modeling RF mmWave Transmitter with Hybrid Beamforming

Illustrates a methodology for system-level modeling and simulation of a 66 GHz QPSK RF transmit and receive system with a 32-element hybrid beamforming antenna. The system includes RF imperfections, transmit array radiation effects, a narrowband receive array and a baseband receiver with corrections for system impairments and message decoding. The antenna beamforming direction is defined using azimuth and elevation angles and it is estimated in the RF receive antenna using a Root Music DOA algorithm.

Compatibility Considerations

Port positions of Wilkinson power divider component in Divider block changed

Behavior changed in R2021a

Starting R2021a, the port positions in the Divider block when you select the Wilkinson power divider component have changed. Prior to this release, Ports 1 and 3 were on the same side opposite that of Port 2. This release, Ports 2 and 3 appear on one side together opposite the side of Port 1.

Existing models using the Divider block with the Wilkinson power divider component might need to be updated to ensure that there are no broken connections. Use the RF Blockset check in the Simulink^® Upgrade Advisor to identify and rewire the broken port connections in your existing models. For more information, see Check model for RF Blockset Divider blocks using Wilkinson power divider component with broken connections.