RF Toolbox

Modeling with Rational Functions

You can use RF Toolbox to 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

In the typical signal integrity workflow, you use RF Toolbox after you characterize the backplane with 4-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 4-port S-parameters to 2-port differential S-parameters
  • Compute the transfer function
  • 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 the SPICE-like analog circuit simulator, which you use to design the I/O circuitry

Frequency response (left) of a rational function model created from measured S-parameters. The model was used to create the eye diagram (right) for analyzing intersymbol interference.

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