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In electric circuit simulation we are confronted with highly nonlinear DAEs with low smoothness properties. They may have index 2 but they do not belong to the class of Hessenberg form systems that are well understood. The classic and the charge‐oriented modified analysis are shown to lead to the same DAE‐index if the circuit models satisfy some natural assumptions. We present a topological criteria for calculating the index. This makes it possible to determine the index also for high‐dimensional circuit equation systems.

The development of integrated circuits requires powerful numerical simulation programs. Naturally, there is no method that treats all the different kinds of circuits successfully. The numerical simulation tools provide reliable results only if the circuit model meets the assumptions that guarantee a successful application of the integration software. Owing to the large dimension of many circuits (about 107 circuit elements) it is often difficult to find the circuit configurations that lead to numerical difficulties. In this paper, we analyse electric circuits with respect to their structural properties in order to give circuit designers some help for fixing modelling problems if the numerical simulation fails. We consider one of the most frequently used modelling techniques, the modified nodal analysis (MNA), and discuss the index of the differential algebraic equations (DAEs) obtained by this kind of modelling. Copyright © 2000 John Wiley & Sons, Ltd.

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