Structural analysis for electric circuits and consequences for MNA

The development of integrated circuits requires powerful numerical simulation programs. Of course, 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 the successful application of the integration software. Because of the large dimension of many circuits (about $10^7$ circuit elements) it is often difficult to find the circuit configurations that lead to numerical difficulties. In this paper, we analyze 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 technique, the modified nodal analysis (MNA), and discuss the index of the differential algebraic equations (DAEs) obtained by this kind of modelling