In this section an overall solution algorithm for a DC analysis for linear as well as non-linear networks is given. With non-linear network elements at hand the Newton-Raphson (NR) algorithm is applied.
The algorithm shown in fig. 3.7 has been proved to be able to find DC solutions for a large variety of networks. It must be said that the application of any of the fallback convergence helpers indicates a nearly or definitely singular equation system (e.g. floating nodes or overdetermining sources). The convergence problems are either due to an apparently ``wrong'' network topology or to the model implementation of non-linear components. For some of the problems also refer to the facts mentioned in section 15.2 on page . In some cases it may even occur that tiny numerical inaccuracies lead to non-convergences whereas the choice of a more accurate (but probably slower) equation system solver can help. With network topologies having more than a single stable solution (e.g. bistable flip-flops) it is recommended to apply nodesets, i.e. forcing the Newton-Raphson iteration into a certain direction by initial values.
When having problems to get a circuit have its DC solution the following actions can be taken to solve these problems.
The presented concepts are common to most circuit simulators each having to face the mentioned aspects. And probably facing it in a different manner with more or less big differences in their implementation details especially regarding the (fallback) convergence helpers. None of the algorithms based on Newton-Raphson ensures global convergence, thus very few documents have been published either for the complexity of the topic or for uncertainties in the detailed implementation each carrying the attribute ``can help'' or ``may help''.
So for now the application of a circuit simulator to find the DC solution of a given network sometimes keeps being a task for people knowing what they want to achieve and what they can roughly expect.