Statistical model order reduction for interconnect circuits considering spatial correlations

Authors:
Jeffrey Fan;Ning Mi;Sheldon X.-D. Tan;Yici Cai;Xianlong Hong
Affiliations:
University of California, Riverside, CA;University of California, Riverside, CA;University of California, Riverside, CA;Tsinghua University, Beijing, China;Tsinghua University, Beijing, China
Venue:
Proceedings of the conference on Design, automation and test in Europe
Year:
2007

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Abstract

In this paper, we propose a novel statistical model order reduction technique, called statistical spectrum model order reduction (SS-MOR) method, which considers both intra-die and inter-die process variations with spatial correlations. The SSMOR generates order-reduced variational models based on given variational circuits. The reduced model can be used for fast statistical performance analysis of interconnect circuits with variational input sources, such as power grid and clock networks. The SSMOR uses statistical spectrum method to compute the variational moments and Monte Carlo sampling method with the modified Krylov subspace reduction method to generate the variational reduced models. To consider spatial correlations, we apply orthogonal decomposition to map the correlated random variables into independent and uncorrelated variables. Experimental results show that the proposed method can deliver about 100x speedup over the pure Monte Carlo projection-based reduction method with about 2% of errors for both means and variances in statistical transient analysis.