Key Features

  • RF filters, transmission lines, amplifiers, and mixers specified by measurement data, network parameters, or physical properties
  • S-parameter calculation for RF component networks
  • RF Budget Analyzer app for calculating noise figure, gain, and IP3 of RF transceivers and for generating RF Blockset™ test benches
  • Rational function fitting method for building models and exporting them as Simulink® blocks or Verilog-A modules
  • De-embedding of N-port S-parameters measurement data
  • Conversion among S, Y, Z, ABCD, h, g, and T network parameters
  • RF data visualization using rectangular and polar plots and Smith® Charts
Smith Chart showing input (blue) and output (red) stability circles of an amplifier characterized by its S-parameters. The circles with constant available gain (yellow) and constant noise figure (purple) can be used to find the input and output matching conditions for minimizing the noise figure and maximizing gain.

Defining RF Components

A key challenge in RF engineering is accounting for impedance difference and reflection effects that occur when components are configured into a network. RF Toolbox™ represents an RF component by its network parameters, which are sufficient to determine its small signal response. RF Toolbox can determine the network parameters and small signal response of any configuration containing RF components. You can use this capability in the design of matching networks.

RF Toolbox enables you to specify RF filters, transmission lines, amplifiers, and mixers, either directly or by their physical properties. Network parameters can be generated from within MATLAB® or read in from external data. You can read and write industry-standard data file formats, such as Touchstone. You can also specify components, such as lumped RLC elements and transmission lines, by their physical properties. RF Toolbox calculates the corresponding network parameters.

Using RF Toolbox, you can define components in the following ways:

  • General circuit elements using data from Touchstone .snp, .ynp, .znp, and .hnp files
  • RLC elements using their nominal values
  • Transmission lines, using the lines' geometries and electrical properties
Reading measurement data for the linear response of an amplifier from a 2-port Touchstone file and visualizing the data with a plot of S-parameter magnitude.

Working with S-Parameters

RF Toolbox provides functions to transform and manipulate S-parameter data so you can gain insights into it. Measured 2N-port S-parameter data can be de-embedded by removing the effects of test fixtures and access structures. Single-ended measurements can be transformed into differential or other mixed-mode formats. You can also convert and reorder single-ended N-port S-parameters to single-ended M-port S-parameters.

With RF Toolbox you can choose the appropriate format for your task by converting among S, Y, Z, ABCD, h, g, and T network parameter formats. For example, you can choose Y-parameters for calculating network parameters of RLC circuits, T-parameters for the analysis of cascaded elements, and S-parameters for visualizing frequency responses. In addition, you can convert S-parameters to S-parameters with different reference impedances.

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Designing RF Networks

RF Toolbox helps you build networks of RF components. In addition to calculating the small signal frequency response, RF Toolbox calculates input and output reflection coefficients, stability factors, noise figures, and third-order intercept points (IP3) for cascaded components.

With the RF Budget Analyzer app you can build and analyze a cascade of RF components and automatically generate a RF Blockset model and test bench for circuit envelope simulation. The RF Budget Analyzer app lets you rapidly start modeling RF transmitters and receivers for wireless applications and validate simulation results in different operating conditions by comparing them with analytical predictions.

Example of an RF chain analyzed with the RF Budget Analyzer app. Filters described using S-parameters, mixers, and amplifiers are cascaded and the resulting power, gain, noise figure, IP3, and SNR are computed at each stage, taking into account the operating frequency and impedance mismatches.

Modeling with Rational Functions

You can use RF Toolbox to fit data defined in the frequency domain (such as S-parameters) with an equivalent Laplace transfer function. For example, you can model single-ended and differential high-speed transmission lines using rational functions. This type of model is useful in signal integrity engineering, where the goal is the reliable connection of high-speed semiconductor devices using, for example, backplanes and printed circuit boards.

Rational function fitting provides the following advantages over traditional techniques, such as inverse fast Fourier transform:

  • Simpler models for a given accuracy
  • Model order reduction, letting you trade off complexity and accuracy
  • Zero phase on extrapolation to DC, avoiding the need to write elaborate constraint algorithms
  • Physical correspondence between the model and transmission line characteristics, providing greater insight
  • Causal modeling of the system

In the typical signal integrity workflow, you use RF Toolbox after you characterize the backplane with N-port network parameters and before you begin the design of the high-speed semiconductor I/O circuitry. Specifically, you:

  • Measure the network parameters with a vector network analyzer
  • Import the Touchstone data file
  • Convert the single-ended 2N-port S-parameters to N-port differential S-parameters
  • Compute the transfer function of the desired and interfering channel
  • Fit the transfer function to a closed-form rational function model, reducing the order as needed
  • Export the model to Simulink or in Verilog-A format for use as a test environment in a SPICE-like analog circuit simulator, which you use to design the I/O circuitry

Frequency response (left) of a rational function model (blue) created from measured S-parameters (red). The model was used to model a backplane operating at 2 Gbps (center) and to create an eye diagram (right) with Communications Toolbox for analyzing intersymbol interference.