During the design and fabrication process of electronic systems, one of the major concerns is predicting the effect of the variability of their geometrical and physical parameters on the general performance of the designed circuits.
To address the above difficulty, this thesis presents a new Hermite-based approach to circuit variability analysis using the Polynomial-Chaos (PC) paradigm. The new approach is aimed at limiting the growth of the computational cost of variability
analysis with the increase in the number of random variables and the number of Hermite coefficients used to
represent the circuit response in each random variable. The proposed method is based on deriving a closed-form for the structure of augmented matrices generated by the PC approach. An algorithm is then developed to decouple the large augmented matrices into independent matrices that can be factorized in parallel. Additionally, the model-order reduction is applied to circuit stochastic analysis using the proposed PC approach.