High-Order and Stable Time-Domain Simulation of Nonlinear Circuits - Bandali, Bardia (Université d'Ottawa / University of Ottawa, 2025)
This thesis presents a novel and eﬃcient time-domain simulation methodology for nonlinear electronic circuits, addressing the computational challenges associated with traditional approaches. The core innovation lies in the development of a high-order, stable time-stepping scheme predicated on the Numerical Inversion of Laplace Transform (NILT). This method facilitates the accurate simulation of general circuits by employing a partitioned approach, wherein the circuit is decomposed into linear and nonlinear sub-networks. A key contribution is the matching of time-domain derivatives at the interface between these sub-networks, achieved through the use of the NILT and Rooted Trees (RT) methods. Furthermore, this research utilizes an advanced formulation of NILT, designated as NILTn, which signiﬁcantly enhances the accuracy per time step compared to conventional NILT (referred to as NILT0). By leveraging higher-order derivatives, NILTn greatly reduces truncation errors, thereby allowing simulation with larger step sizes enhancing overall performance. The eﬀectiveness of the proposed methodology is demonstrated through comprehensive numerical simulations, showcasing substantial speed improvements and enhanced accuracy compared to traditional time-domain simulation methods. This advancement enables the eﬃcient and accurate simulation of nonlinear circuits, facilitating advancements in areas such as power electronics, Radio Frequency (RF) design, and mixed-signal systems.
Keywords: NILT; Time-domain; Circuit Simulation; A-stability; L-stability; High-order integration methods; Numerical solution of differential equations; Nonlinear