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+.

中文翻译：

---

数字波框架中 S 参数分段线性拟合的频域行为

本文介绍了 PWLFIT+，它是 PWLFIT 频域的扩展，它是线性多端口系统时域宏建模的新范式，基于 S 参数阶跃响应的分段线性 (PWL) 行为表示。虽然每个 S 参数的脉冲响应近似为延迟矩形 (rect) 函数的总和，但其频谱被内插为相应延迟基数正弦 (sinc) 函数的总和。利用这种对应关系，通过迭代过程执行模型构建，其中可以确定 PWL 宏模型以满足频谱上定义的精度目标。在运行时，宏模型端口的波是使用数字波模拟器 (DWS) 框架内的分段快速卷积 (SFC) 算法计算的。所提出的方法的特点是简单，稳定性、速度和可扩展性，所有这些特性都是在 DWS 框架中使用时所强调的。在分析了 SFC 在Z域与基于极点和残差的传统宏观建模方法明显不同，提供了两个合适的应用示例来展示 PWLFIT+ 的独特功能。