A circuit has excess elements when it contains capacitor loops – closed contours containing only ideal capacitors and (possibly) ideal independent voltage sources, and/or inductor cut-sets – closed surfaces cutting only ideal inductors and (possibly) ideal independent current sources. For such circuits it is not possible to chose all capacitor voltages and all inductor currents as state variables, as they are not mutually independent. Therefore, sub-sets of essential capacitor voltages and essential inductor currents are selected as state variables. The remaining capacitor voltages and inductor currents are considered dependent variables, as they can be expressed in terms of the essential variables.

Keywords: State variable equations, Systematic equation formulation, Excess circuit elements, Essential circuit elements