Coupler

Model ideal frequency-independent couplers with S-parameters

• Library:

• 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:

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

• Hybrid rat-race

  The S-parameters matrix for the Hybrid rat-race is:

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

• 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.

Model Examples

Modeling RF Front End in Radar System Simulation

In a radar system, the RF front end often plays an important role in defining the system performance. For example, since the RF front end is the first section in the receiver chain, the design of its low noise amplifier is critical to achieving the desired signal-to-noise ratio (SNR). This example shows how to incorporate an RF front end behavior into an existing radar system design.

Digital Predistortion to Compensate for Power Amplifier Nonlinearities

Use digital predistortion (DPD) in a transmitter to offset the effects of nonlinearities in a power amplifier. We use models of a power amplifier that were obtained using the Power Amplifier Characterization (Communications Toolbox) example to simulate two cases. In the first simulation, the RF transmitter sends two tones. In the second simulation, the RF transmitter sends a 5G-like OFDM waveform with 100 MHz bandwidth.