EMQS Field Formulations of Darwin-Type

Project description

The regime of quasistatic electromagnetic field models is applicable, if the structures under consideration are small w.r.t. to the wave lengths of the highest operational frequency for a given problem, i.e., if radiation affects can be neglected.

This model regime includes the limit case of static field configurations, where merely capacitive, resistive or inductive effects need to be considered in electrostatic or stationary direct current and corresponding magnetostatic field configurations. More generally, it also covers slowly varying electric or magnetic fields: the electro-quasistatic (EQS) field model covers problems governed by capacitive and resistive effects, whereas magneto-quasistatic (MQS) field models describe resistive-inductive field problems. The majority of these established submodels of Maxwell’s equations are based on mathematical formulations in terms of electric and/or magnetic scalar and vector potentials.

Electromagneto-quasistatic (EMQS) field problems, where resistive, inductive and capacitive effects need to be considered simultaneously, have recently gained interest related to the modeling of high-frequency coils e.g. in transformer or in inductive wireless power transfer systems and also w.r.t. electromagnetic compatibility issues of power electronic systems.

Geometric multiscale aspect ratios of such systems often result in lumped parameter circuit formulations (RLC circuit descriptions based on the Kirchhoff model), hybridized field-circuit formulations or circuit-type formulations as e.g. the partial-element equivalent circuit (PEEC) methods to be the preferred method of modelling.

Rather recently, electromagneto-quasistatic (EMQS) field formulations of such application problems have come into the focus of interest: these field-oriented formulations are developed to consider local nonlinear material behavior and a fine grained description of local inductive and capacitive coupling effects combined with the ability to model transient effects.

Based on the original electromagneto-quasistatic (EMQS) field model of Darwin which was originally devised to describe the electromagnetic field of moving charged particles in free space without wave propagation effects, the development, analysis and extension of electromagneto-quasistatic (EMQS) field formulations of Darwin-type which are capable of including electrically conductive, dielectric and ferromagnetic material behavior simultaneously is a topic of ongoing research efforts in electromagnetic field theory and computational electromagnetics.

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