Uncertainty Quantification in Large Scale Systems Design

Abstract

One of the main challenges facing designers of high-speed integrated circuits and interconnects is predicting the effect of the variability of geometrical and physical parameters on the circuit performance. Monte Carlo (MC) simulation has been traditionally used in commercial circuit and electromagnetic (EM) simulators for predicting the statistical distribution of circuit and system performance metrics. However, the high computational cost associated with the MC simulation is a significant limiting factor especially for large circuits.In this thesis, an algorithm based on Parametric Model Order Reduction (PMOR) is presented for statistical analysis of large microwave and high-speed circuits with multiple stochastic parameters. Using the proposed algorithm, a set of local reducedorder parameterized circuits are derived based on adaptive frequency sampling and implicit multi-moment matching projection techniques. The local models preserve the stochastic parameters as symbolic quantities. As a result, stochastic response of the circuit can be obtained by simulating the local reduced models instead of the original large system leading to significant reduction in the computational cost compared to traditional Monte-Carlo techniques.In addition, a method is presented for high-dimensional variability analysis. This algorithm is based on two main concepts, namely node tearing for parameter partitioning and sparse grid interpolation. Node-tearing is used to localize the parameters I would also like to thank the staff at department of Electronics in Carleton University, especially Mrs. Blazenka Power. Their constantly and patiently supports made this adventure so much easier and for that, I am thankful.In the end, I would like to express my deep love to my parents for their love and care. Without their encouragement, I could not have reached this far. What they have sacrificed, I could not forget. Their courage, always inspires me. To them, I dedicate this thesis. vi