DC analysis of circuits with idealized diodes considering reverse bias breakdown phenomenon

The resistive circuits containing idealized diodes are considered in this paper. The diodes are represented by three-segment characteristics enabling us to take into account the effect of reverse bias breakdown phenomenon. A parametric representation is developed leading to a well-defined description of the circuits. It is shown that this equation always has at least one solution and a region containing all the solutions can be easily determined. The necessary and sufficient conditions for uniqueness of the solution are also developed. The problem of finding a unique or multiple dc solutions of the circuits is considered in detail. It is shown that the Newton-Raphson algorithm can be used, in a very effective way, to determine a unique solution. The structure of the Jacobian matrix makes it possible to considerably improve the process of solving linear simultaneous equations at each iteration. Exploiting some properties of the parametric equation an algorithm is developed enabling us to determine all the dc solutions of this class of circuits. Moreover, some suggestions are given concerning computation of circuits including more realistic models of diodes and transistors. Several numerical examples are presented conforming usefulness of the proposed approach