7.1 Introduction

The first 2D and 3D field computation software did not allow coupling with the external electric circuit. However, this coupling quickly becomes essential as soon as a simulation of the actual operation of a device is needed. In certain cases, it is possible and even interesting to characterize a device by a set of static or dynamic simulations without resorting to the coupling. However, this technique can quickly become tiresome, even impossible, in other cases, taking into account the great number of simulations that must be performed for a complete characterization (linked to saturation, to movement, to multiple sources, etc.).

This chapter proposes, without being exhaustive, some examples of coupling with circuit equations in two and three dimensions. After a short review of the various methods for setting up an equation of the electric circuits and of the various possible types of coupling, we will establish the relations allowing the current and the voltage to be linked within the framework of the finite element formulations. Coupling techniques themselves will then be developed successively for two then for three dimensions. If the use of the vector potential is essential in two dimensions, the coupling technique, although very general, proves more disputed in three dimensions where formulations based on scalar potential have appeared. We will show that it is possible to develop very general coupled formulations with magnetic scalar potential.

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7.2 Review of the Various...