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       Interpolation and Extrapolation of N-Port Data           

Interpolation and Extrapolation of N-Port Data

Data may not be available at each frequency point of the simulation. Consequently, the data may require interpolation or extrapolation to produce information at the necessary frequencies. System designs differ from Nexxim designs in the methods used for interpolation and extrapolation of S-parameter data.

System Designs

For System designs, processing is done for each matrix element for all sweep points independent of the other matrix elements that may be supplied. Several cases arise for data processing:

• Data at a single sweep point is supplied—In this case, the data is considered to remain constant for all frequencies at which the simulation takes place. The frequency entry is optional and is ignored in this case. If the simulation is to take place at a number of frequencies, the frequency value should be omitted.

• Data is supplied without frequencies—For this case, the number of data sets must match the number of sweep points that are used during the simulation. A one-to-one correspondence is assumed between the list of sweep points and the list of data sets: the first data set is used for the first frequency, and the second data set is used for the second frequency, and so on.

• Data is supplied with frequencies—When the data is not supplied precisely at the same frequencies that are used in the circuit simulation a minimum of three data points must be present. In this case the data is interpolated and/or extrapolated to obtain data points for each and every sweep point that is needed for the circuit simulation.

Three methods are available in System Designs for data interpolation and extrapolation: linear, cubic spline, and polynomial. The default method is linear interpolation. These methods work best if the supplied data is at frequency points that are close to the frequencies used in the simulation. Following are some points to keep in mind:

• Extrapolation is based on the end points of the data set and will generate a straight-line function that may generate unexpected results. The program will issue a warning if extrapolation is used for network or noise data.

• Attempts to supply data with large phase changes (for example, more than 180°) may yield unexpected results.

Nexxim Designs

When the S-parameter data has a low top frequency compared to the frequency content of the input signal, Nexxim extrapolates the data. Nexxim’s standard transient solution for S-parameters incorporates a state-space formulation, which is guaranteed causal. This state-space formulation gives a natural extrapolation function, which is also causal. However, Nexxim’s extrapolation function can differ from the functions provided by other simulators. Convolution-based simulators generally provide simple constant, linear, or windowing extrapolation functions. Such simple extrapolation functions are not causal, and therefore can give erroneous transient results.

• The designer can avoid the issue of extrapolation by extending the frequency range of the input S-parameter data well above the traditional signal integrity bandwidth of 0.35/risetime.

• The HIGHPASS and LOWPASS parameters on the S-element model control the extrapolation method. See S-Element Model.

• For interpolation, the S-element model in Nexxim has parameters for selection between LINEAR and STEP interpolation. STEP interpolation takes the interpolated value from the closest table entry that is lower in frequency that the current entry. LINEAR is the default. See S-Element Model.

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