Transient Analysis of Nonlinear Circuits Based on Waves

Circuit-level simulation of complex systems is a challenging task in terms of memory and CPU time. It is thus of great interest to find more efficient methods for circuit-level simulation. At the core of nonlinear circuit analysis is the solution of a system of nonlinear algebraic equations. Solving this system of equations using Newton method requires the decomposition of a large (normally sparse) matrix for each iteration. This matrix is particularly large in the case of harmonic balance (HB) or techniques based on multiple time dimensions [1]. This paper presents a transient analysis approach that requires only one matrix decomposition for a given time step size. This approach was inspired in the multiple reflections technique [2] and wave digital simulation of circuits [3,4]. Wave digital filters [5] were developed to replace analog filters with a digital structure. Several methods have been proposed for transient simulation using waves but they have limitations handling nonlinearities or do not scale well with the size of the circuit. Felderhoff [3] proposed a convergent relaxation method that can treat several nonlinear devices and is easily parallelizable. The method proposed in this paper is also parallelizable and can handle arbitrary static and dynamic nonlinearities.