The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Faster, parametric trajectory-based macromodels via localized linear reductions
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
Fast, non-Monte-Carlo estimation of transient performance variation due to device mismatch
Proceedings of the 44th annual Design Automation Conference
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
SiSMA-a tool for efficient analysis of analog CMOS integrated circuits affected by device mismatch
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Hermite Polynomial Based Interconnect Analysis in the Presence of Process Variations
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Proceedings of the 47th Design Automation Conference
A Fast Non-Monte-Carlo Yield Analysis and Optimization by Stochastic Orthogonal Polynomials
ACM Transactions on Design Automation of Electronic Systems (TODAES)
A new uncertainty budgeting based method for robust analog/mixed-signal design
Proceedings of the 49th Annual Design Automation Conference
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To cope with an increasing complexity when analyzing analog mismatch in sub-90nm designs, this paper presents a fast non-Monte-Carlo method to calculate mismatch in time domain. The local random mismatch is described by a noise source with an explicit dependence on geometric parameters, and is further expanded by stochastic orthogonal polynomials (SOPs). This forms a stochastic differential-algebra-equation (SDAE). To deal with large-scale problems, the SDAE is linearized at a number of snapshots along the nominal transient trajectory, and hence is naturally embedded into a trajectory-piecewise-linear (TPWL) macromodeling. The TPWL is improved with a novel incremental aggregation of sub-spaces identified at those snapshots. Experiments show that the proposed method, is TPWL, is hundreds of times faster than Monte-Carlo method with a similar accuracy. In addition, our macromodel further reduces runtime by up to 25X, and is faster to build and more accurate to simulate compared to existing approaches.