Efficient DC and transient analyses in nonlinear circuits by interval arithmetic and tensor decomposition techniques

Abstract

Nonlinear electronic devices are pervasive in modern integrated circuits. However, there are few existing approaches in the electronic design automation (EDA) community, which can meet the growing requirements of the nonlinear circuit analysis. This thesis is comprised of two themes in the context of the nonlinear circuit analysis, namely, the nonlinear direct current (DC) analysis and the nonlinear transient analysis. Accordingly, two novel approaches are proposed for bridging the gap between modern nonlinear circuit problems and existing analytical methods. They employ the power of new computational techniques, such as interval arithmetic (IA) and tensor decomposition, to achieve efficient nonlinear circuit modeling and simulation.

Specifically, the first part of the dissertation proposes a unifying framework for the DC analysis of general nonlinear circuits. The framework is robust and provides a generic approach for finding all DC operating points, as roots of a system of nonlinear equations, within a user-prescribed interval. A superposition-based linear interval model (SLIM) for general nonlinear multivariate systems is presented to demonstrate the utility of the approach for various nonlinear device models, together with guaranteed global convergence. The simple formulation of this algorithm, leveraging on IA, permits a significant speedup in nonlinear root finding.

In the second part, a novel symmetric tensor-based order-reduction method (STORM) is presented for the fast transient simulation of large-scale nonlinear systems. The multidimensional data structure of symmetric tensors, as the higher order generalization of symmetric matrices, is utilized for the effective capture of high-order nonlinearities and the efficient generation of compact models. Compared to the previous tensor-based nonlinear model order reduction algorithm, STORM shows advantages in two aspects. First, STORM avoids the assumption of the existence of a low-rank tensor approximation for the original nonlinear system. Second, with the use of the symmetric tensor decomposition, STORM allows significantly faster computation and less storage complexity.