# VLSI Macromodeling and Signal Integrity Analysis via Digital Signal Processing Techniques

Linear macromodeling has been applied to highfrequency circuit simulations to accelerate the global interconnect system simulation process. By approximating tabulated structure response data, reduced macromodels can be generated. However, conventional macromodeling approaches suffer from numerical robustness and convergence problems. This paper aims to apply digital signal processing techniques to facilitate the macromodeling process. Besides improving the existing widely adopted framework (called VFz) through introducing a robust discrete-time domain (z-domain) computation, alternative macromodeling methodology (called VISA) has also been developed, which signiﬁcantly simpliﬁes the computation procedure. Furthermore, universal pre-processing technique (frequency warping) is introduced for a numerically favorable computation of the macromodeling process. These techniques have been shown to signiﬁcantly improve the robustness and convergence of the modeling process.

WITH the increasing operation frequency and decreasing feature size of very-large-scale integration (VLSI) circuits, high-frequency effects, such as signal delay, crosstalk and simultaneous switching noise, have become a dominant factor limiting integrated circuit (IC) system performance. Accurate and efﬁcient simulation is required during the IC design phase to capture the high-frequency behaviours of electronic systems. Linear macromodeling, in this context, refers to replacing a high-order system by a small-order linear model with similar input-output responses, for computationally efﬁcient simulation and timecritical design. Macromodels can be generated by ﬁtting tabulated data from measurement/simulation, as shown in Fig. 1. There is a number of stringent modeling constraints in the non-linear computation for high-frequency and/or large scale systems systems, such as accuracy, computation complexity, manual intervention and numerical robustness. Some macromodeling approaches have been developed only very recently. In particular, Vector Fitting (VF) is regarded as a robust and simple broadband macromodeling technique and widely adopted in the signal integrity community. However, it suffers from convergence problem in the iterative calculation framework with initial pole assignment. Due to the strict requirements of the modeling problem and development Fig. 1. Common Macromodeling Flow in the Signal Integrity Process. of emerging technologies, there is no optimal algorithm so far, making macromodeling a challenging problem and a high value research topic. Furthermore, pre- and postprocessing techniques and improvements from non-controltheoretic perspectives have been less explored. With “sampled response is a sampled and discretized signal sequence” as the fundamental concept, this research study [1] explores the feasibility and beneﬁts of applying DSP techniques to the macromodeling process, focusing on: 1) improving the functionality and automation of the approximation process;

2) increasing the ﬁtting accuracy of the approximation process;

3) reducing the computation time of the macromodeling procedure.

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