Overall solution algorithm for DC Analysis

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.

Figure 3.7: DC solution algorithm flow chart

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.

• check circuit topology (e.g. floating nodes or overdetermining sources)
• check model parameters of non-linear components
• apply nodesets
• choose a more accurate equation system solver
• relax the convergence tolerances if possible
• increase the maximum iteration count
• choose the prefered fallback algorithm

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.