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Vector Fitting (VF) has been introduced as a partial-fraction basis response fitting methodology for over a decade. Because of its reliability and versatility, VF has been applied and extended to a number of areas. In this book chapter, we will discuss the applications of VF in the context of macromodeling of linear structures in signal/power integrity analyses. We will also discuss main features of VF along three directions: data, algorithms and models. Two practical examples are given to demonstrate the merits of VF. An alternative P-norm approximation criterion is proposed to enhance the accuracy of the macromodeling process.

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Circuits with delay elements are very popular and important in the simulation of very-large-scale integration (VLSI) systems. Neutral systems (NSs) with multiple constant delays (MCDs), for example, can be used to model the partial element equivalent circuits (PEECs), which are widely used in high-frequency electromagnetic (EM) analysis. In this paper, the model order reduction (MOR) problem for the NS with MCDs is addressed by moment matching method. The nonlinear exponential terms coming from the delayed states and the derivative of the delayed states in the transfer function of the original NS are first approximated by a Padé approximation or a Taylor series expansion. This has the consequence that the transfer function of the original NS is exponential-free and the standard moment matching method for reduction is readily applied. The Padé approximation of exponential terms gives an expanded delay-free system, which is further reduced to a delay-free reduced-order model (ROM). A Taylor series expansion of exponential terms lets the inverse in the original transfer function have only powers-of-s terms, whose coefficient matrices are of the same size as the original NS, which results in a ROM modeled by a lower-order NS. Numerical examples are included to show the effectiveness of the proposed al-