Frequency domain behavior of S-parameters piecewise-linear fitting in a digital-wave framework

This paper describes PWLFIT+, an extension to the frequency domain of PWLFIT, a new paradigm in time-domain macromodeling for linear multiport systems, based on a piecewise-linear (PWL) behavioral representation of the S-parameters step response. While the impulse response of each S-parameter is approximated as sum of delayed rectangles (rect) functions, its spectrum is interpolated as sum of the corresponding delayed cardinal sine (sinc) functions. Exploiting this correspondence, the model building is performed by an iterative procedure where the PWL macromodels can be determined in order to meet defined accuracy goals on the spectrum. At runtime, waves at macromodels ports are calculated using the Segment Fast Convolution (SFC) algorithm within the Digital Wave Simulator (DWS) framework. The proposed method is characterized by its simplicity, stability, speed and scalability, all features that are emphasized when it is used in the DWS framework. After an analysis of the excellent numerical features of SFC in the Z-domain, clearly differentiated with respect conventional macromodeling methods based on poles and residues, two suitable application examples are presented to demonstrate the unique features of PWLFIT+.