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

Abstract

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.

Citation

Tadeusiewicz, M. and Hałgas, S. (2005), "Transient analysis of nonlinear dynamic circuits using a numerical‐integration method", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 2, pp. 707-719. https://doi.org/10.1108/03321640510571192