Transient analysis of nonlinear dynamic circuits using a numerical-integration method

摘要

Purpose - Developing an efficient second-order integration method of transient analysis of nonlinear dynamic circuits which overcomes the main drawback of the trapezoidal rule. Design/methodology/approach - Dynamic circuits including transistors and operational amplifiers are considered. A new family of two-step, second-order numerical integration algorithms has been developed using a polynomial approximation. Findings - The algorithms have been worked out which are implicit, A -stable and they depend on a parameter which is allowed to be changed during the computation process according to a proposed strategy. Also the variable step-size formula has been derived enabling us to eliminate a restarting procedure. The method has been implemented and tested using several representative circuits. It has been compared, both theoretically and via numerical examples, with the alternative well known algorithms: the trapezoidal rule and the backward differentiation formula of order two. Research limitation/implications - The algorithms developed in the paper are two-step and second-order, consequently the step size cannot be too large and the algorithms are not L-stable. Originality/value - A new family of two-step implicit integration algorithms is developed. It can be useful for the analysis and design of electronic circuits.