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.
Next: Converting Network Parameters