Diana Estévez Schwarz, Caren Tischendorf
Structural analysis for electric circuits and consequences for MNA
Preprint series: Fachbereich Mathematik der Humboldt-Universität zu Berlin

MSC:

94C05 Analytic circuit theory

65L05 Initial value problems

Abstract: 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 10⁷ 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.
Keywords: Circuit simulation; differential-algebraic equation; DAE; index; modified nodal analysis; MNA; structural properties; modelling.