Topological index calculation of DAEs in circuit simulation

Electric circuits are present in a number of applications, e.g. in home computers, television, credit cards, electric power networks, etc. The development of integrated circuit requires numerical simulation. Modern modeling techniques like the Modified Nodal Analysis (MNA) lead to differential algebraic equations (DAEs). Properties like the stability of solutions of such systems depend strongly on the DAE index. The paper deals with lumped circuits containing voltage sources, current sources as well as general nonlinear but time-invariant capacitances, inductances and resistances. We present network-topological criteria for the index of the DAEs obtained by the classical and the charge oriented MNA. Furthermore, the index is shown to be limited to 2 for our model-class.