S-Parameter Rational Fit

Implement rational fit approximation to S-parameter description of linear system

Since R2024b

• 

Libraries:
Simscape / Electrical / Passive

Description

The S-Parameter Rational Fit block implements a rational approximation of a linear system characterized with scattering parameters (S-parameters). S-parameters describe the frequency behavior of a system. For more information about the S-parameters format, see Data Import and Network Parameters (RF Toolbox). For more information about how to calculate S-parameters, see sparameters (RF Toolbox).

The S-Parameter Rational Fit block operates with passband signals. If you need to simulate a baseband signal, a frequency band limited signal superimposed on a carrier frequency, use the S-Parameters (RF Blockset) block with other blocks in the RF Blockset™ Circuit Envelope library instead. For more information about the relationship between baseband and passband signals, see the Passband Signal Representation in Circuit Envelope (RF Blockset) example. For more information about using blocks in the Circuit Envelope library, see Circuit Envelope Simulation (RF Blockset).

You define the rational fit by specifying a value for the Rational fit object parameter. There are two ways to construct a rational fit object:

• You can fit a rational function object to the component data using the rational (RF Toolbox) function.

• You can use the rfmodel.rational (RF Toolbox) constructor to specify the pole-residue representation of the component directly. Use the rationalfit (RF Toolbox) function to return an rfmodel.rational object.

Note

rational (RF Toolbox) is recommended over rationalfit because it enables faster simulation and has improved fitting controls.

For testing purposes, you can also specify the rational fit object as:

• The empty set [] — This option creates a nonreflective rational system with no cross-coupling between ports. All ports present an impedance to the external circuit equal to the value of the Reference impedance (Ohm) parameter.

• A square constant matrix with dimensions equal to the number of ports — This matrix defines the constant term connecting the ports. A matrix of zeros is equivalent to the empty set option and an entry of 1 in the (i,j) element implies a direct feedthrough from port j to port i.

Note

In this context, a "port" refers to a pair of terminals connecting two electrical networks. This definition is common in the telecommunications industry. By this definition, a single "port" represents two "conserving ports" in the Simscape™ family of products.

You can specify the number of ports by setting the value of the Number of ports parameter. Limit this value to 33. Higher values significantly increase compilation and simulation time. Higher order rational fits also increase the compilation and simulation time. If the rest of your model is linear or switched linear, avoid including delay terms in the rational fit object so that the S-Parameter Rational Fit block also uses linear equations. For more information about checking your model for blocks with nonlinear equations, see simscape.findNonlinearBlocks.

Equations

This figure shows the four-element S-parameter matrix for a two-port device.

In this figure:

• a_i is the incident power wave from port i.

• b_i is the reflected power wave from port i.

• S_ij is the transmission coefficient that indicates how much of the signal that enters the network at port j transmits to port i.

The block assumes that all the reference impedances are equal and have a real scalar value. These equations describe the relationship between the incident power wave and the reflected power waves at each port over a range of frequencies,

$$\begin{array}{l}{b}_1=S_{11}{a}_1+S_{12}{a}_2\\ b_2=S_{21}{a}_1+S_{22}{a}_2\end{array}$$

$$a_i=b_i=\frac{1}{2}\left(V_i+\sqrt{Z_0}{I}_i\right)$$

where:

• V_i is the voltage at port i relative to the ground.

• Z₀ is the value of the Reference impedance (Ohm) parameter.

• I_i is the current through port i.

The rational object approximates the frequency responses S_ij by rational transfer functions of the form,

$$F(s)={\displaystyle \sum _{k=1}^n\frac{C_k}{s-A_k}+D},$$

where:

• s is the angular frequency.

• C_k are the residues.

• A_k are the poles.

• D is the direct term.

Ports

Conserving

pk — k^th positive terminal

electrical

Electrical conserving port associated with the positive terminal of the k^th port.

The number of ports of this type is equal to the value of the Number of ports parameter.

nk — k^th negative terminal

electrical

Electrical conserving port associated with the negative terminal of the k^th port.

The number of ports of this type is equal to the value of the Number of ports parameter.

Dependencies

To enable this port, clear the Ground and hide negative terminals parameter.

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Number of ports — Number of electrical connection pairs

2 (default) | positive integer

Number of electrical connection pairs. The term "port" in the name of this parameter refers to a pair of terminals connecting two electrical networks. This definition is common in the telecommunications industry.

If you clear the Ground and hide negative terminals parameter, the number of Simscape "conserving ports" that the block exposes is twice the value of the Number of ports parameter.

If you select the Ground and hide negative terminals parameter, the number of Simscape "conserving ports" that the block exposes is equal to the value of the Number of ports parameter.

Reference impedance (Ohm) — Reference line impedance

50 (default) | real scalar

Reference line impedance Z₀, in ohms.

Rational fit object — Rational fit object

[] (default) | square matrix | rational object | rfmodel.rational object

Rational fit object. Use the rational (RF Toolbox) function to fit a rational function object to the component data.

The default value of [] indicates that there is no cross-coupling and all ports have an impedance equal to the value of the Reference impedance parameter. Use the default value of [] for early testing and building models when you do not have the rational object.

Ground and hide negative terminals — Option to ground and hide negative terminals

Off (default) | On

Option to ground and hide the negative terminals.

Clear this parameter to enable the nk ports associated with the negative terminals of the block.

Select this parameter to ground all the electrical connection pair negative terminals. The block models the connections to the ground inside the S-Parameter Rational Fit block using Electrical Reference blocks.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2024b