Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Design and analysis of power distribution networks in PowerPC microprocessors
DAC '98 Proceedings of the 35th annual Design Automation Conference
Hierarchical analysis of power distribution networks
Proceedings of the 37th Annual Design Automation Conference
Proceedings of the 37th Annual Design Automation Conference
Proceedings of the 37th Annual Design Automation Conference
Random walks in a supply network
Proceedings of the 40th annual Design Automation Conference
Design and Analysis of Power Distribution Networks with Accurate RLC Models
VLSID '00 Proceedings of the 13th International Conference on VLSI Design
A stochastic approach To power grid analysis
Proceedings of the 41st annual Design Automation Conference
Parametric yield estimation considering leakage variability
Proceedings of the 41st annual Design Automation Conference
Statistical Verification of Power Grids Considering Process-Induced Leakage Current Variations
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Modeling Within-Die Spatial Correlation Effects for Process-Design Co-Optimization
ISQED '05 Proceedings of the 6th International Symposium on Quality of Electronic Design
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Accurate power grid analysis with behavioral transistor network modeling
Proceedings of the 2007 international symposium on Physical design
Analysis of Power Supply Noise in the Presence of Process Variations
IEEE Design & Test
Stochastic extended Krylov subspace method for variational analysis of on-chip power grid networks
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Proceedings of the 2008 international symposium on Physical design
Proceedings of the 2009 Asia and South Pacific Design Automation Conference
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Statistical analysis of large on-chip power grid networks by variational reduction scheme
Integration, the VLSI Journal
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For statistical timing and power analysis that are very importantproblems in the sub-100nm technologies, stochastic analysis of power grids that characterizes the voltage fluctuations due to process variations is inevitable. In this paper, we propose an efficient algorithm for the variational analysis of large power grids in the presence of a significant number of Gaussian intra-die process variables that are correlated. We consider variations in the power grid's electrical parameters as spatial stochastic processes and express them as linear expansions in an orthonormal series of random variables using the Karhunen-Loéve(KLE) method. The voltage response is then represented as an orthonormal polynomial series and the coefficients are obtained optimally using the Galerkin method. We propose a novel method to separate the stochastic analysis for the random variables that effect only the inputs (e.g, drain currents) and for those that effect the system parameters as well (e.g., conductance, capacitance). We show that this parallelism can result in significant speed-ups in addition to the speed-ups inherent to Galerkin-based methods. Our analysis has been applied to several industrial power grids and the results show speed-ups of up to two orders of magnitude over Monte Carlo simulations for comparable accuracy.