A new approach to overcome the overflow problem in computer‐aided analysis of nonlinear resistive circuits

Abstract This paper is addressed to the so‐called overflow problem commonly encountered in the computer simulation of nonlinear resistive circuits containing rapidly varying nonlinearities—such as exponentials found in the models of diodes and transistors. A novel approach which makes use of the arc‐lengths of the nonlinear characteristic curves as the variables of iteration is proposed. It is proved, under rather mild conditions, that the arc‐length approach not only overcomes the overflow problem, but also leads to a more rapid rate of convergence. Moreover, it is proved that for most practical diode‐transistor circuits, the region of convergence associated with the arc‐length approach is larger and the convergence of the Newton‐Raphson algorithm is not sensitive to the initial guess. Since it is more difficult to make good initial guesses when the size of the network is large, in so far as choosing the initial guess is concerned, the advantage for using the arc‐length approach over the conventional approach increases with the size of the network. Extensive numerical experiments confirm the superior convergence property of this approach even for circuits which violate the sufficient conditions invoked by the rigorous mathematical proofs. Although the approach is applicable to a much wider class of nonlinear networks, particular emphasis is focused on diode‐transistor networks in this paper.