A structural analysis of field/circuit coupled problems based on a generalised circuit element

In some applications, there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system of equations describing the circuit (modified nodal analysis) which yields a system of differential algebraic equations (DAEs). This paper deals with the differential index analysis of such coupled systems. For that, a new generalised inductance-like element is defined. The index of the DAEs obtained from a circuit containing such an element is then related to the topological characteristics of the circuit's underlying graph. Field/circuit coupling is performed when circuits are simulated containing elements described by Maxwell's equations. The index of such systems with two different types of magnetoquasistatic formulations (A* and T-omega) is then deduced by showing that the spatial discretisations in both cases lead to an inductance-like element.