Statistical model order reduction for interconnect circuits considering spatial correlations
Proceedings of the conference on Design, automation and test in Europe
Distribution arithmetic for stochastical analysis
Proceedings of the 2008 Asia and South Pacific Design Automation Conference
IEEE Transactions on Circuits and Systems Part I: Regular Papers
A fast symbolic computation approach to statistical analysis of mesh networks with multiple sources
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
An improved RC model for VLSI interconnects with applications to buffer insertion
Analog Integrated Circuits and Signal Processing
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Correlated interval representations of range uncertainty offer an attractive solution to approximating computations on statistical quantities. The key idea is to use finite intervals to approximate the essential mass of a probability density function (pdf) as it moves through numerical operators; the resulting compact interval-valued solution can be easily interpreted as a statistical distribution and efficiently sampled. This paper first describes improved interval-valued algorithms for asymptotic wave evaluation (AWE)/passive reduced-order interconnect macromodeling algorithm (PRIMA) model order reduction for tree-structured interconnect circuits with correlated resistance, inductance, and capacitance (RLC) parameter variations. By moving to a much faster interval-valued linear solver based on path-tracing ideas, and making more optimal tradeoffs between interval- and scalar-valued computations, the delay statistics roughly 10× faster than classical Monte Carlo (MC) simulation, with accuracy to within 5% can be extracted. This improved interval analysis strategy is further applied in order to build statistical effective capacitance (Ceff) models for variational interconnect, and show how to extract statistics of Ceff over 100× faster than classical MC simulation, with errors less than 4%.