Variability Analysis via Parameterized Model Order Reduction and Numerical Inversion of Laplace Transform

A fast algorithm is presented for statistical analysis of large circuits with multiple stochastic parameters. The proposed method combines the merits of the parameterized model order-based techniques and numerical inversion of Laplace transform (NILT). The response of the reduced model at any given time point is expressed as a linear combination of the frequency-domain response at a relatively small number of predetermined complex frequency points. This eliminates the necessity for explicit representation of the dynamic model in the form of a set of differential equations. As a result, the moment vectors associated with frequency are excluded while forming the moments' subspace, leading to much smaller reduced models. In addition, evaluation of the time-domain response of the reduced-order models using NILT is more efficient and highly parallelizable compared to time-stepping numerical integration techniques. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.