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.

Additional Metadata
Keywords Numerical inversion of Laplace transform (NILT), parametric model order reduction (MOR), time-domain simulation, transmission lines, variability analysis
Persistent URL dx.doi.org/10.1109/TCPMT.2016.2642199
Journal IEEE Transactions on Components, Packaging and Manufacturing Technology
Citation
Tao, Y. (Ye), Nouri, B. (Behzad), Nakhla, M.S, Farhan, M.A. (Mina A.), & Achar, R. (2017). Variability Analysis via Parameterized Model Order Reduction and Numerical Inversion of Laplace Transform. IEEE Transactions on Components, Packaging and Manufacturing Technology, 7(5), 678–686. doi:10.1109/TCPMT.2016.2642199