A Structural Analysis of Field/Circuit Coupled Problems Based on a Generalised Circuit Element

TL;DR

This paper analyzes the differential index of coupled field and circuit systems, introducing a generalized inductance-like element and relating the index to circuit topology, with applications to magnetoquasistatic formulations.

Contribution

It introduces a generalized inductance-like element for coupled systems and relates the differential index to circuit topology, advancing the understanding of field/circuit coupling.

Findings

The index depends on the circuit's topological characteristics.

Both A* and T-Ω formulations lead to inductance-like elements.

The analysis aids in understanding the complexity of coupled DAEs.

Abstract

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.