The electrodynamics of high-frequency magnetics in power electronics

The electromagnetic behavior of magnetic devices used in power electronics circuitry, is studied in order to predict their performance within a context of desirable circuit parameters. Past efforts have focused on simplifications widely used in electric machinery applications. Due to the greatly increased operating frequencies of today's circuits (in the upper kHz and lower MHz region), the operation and design of magnetic components greatly differs from those of 60 Hz machinery. A set of models based on assumptions that are unique to the these devices used in power electronics are put forth. The entire approach is based on deriving models from solutions of the field equations, rather than using older, less accurate circuit analogies. More importantly, models are needed for accurate design and optimization processes of complete power electronic systems, in which the magnetic components form a small part. Solutions are sought without using the popular simplifications at very low and very high frequencies, since they are not accurate at intermediate frequencies encountered in power electronics. The conductors used in transformers and inductors are modelled in these high frequency regions. They include twisted wire, Litz wire and foils. Their limiting behavior and advantages are determined at high switching frequencies. The more complicated problem of fields and currents in transformers is approached in a two-dimensional fashion, a major improvement over traditional one-dimensional solutions. The solutions are effected by approximating the coupled eigenfunctions of the magnetic vector potential by decoupled ones by using multiple eigenfunctions. The procedure allows a two-dimensional model to be formed without the need for any numerical solutions. Many transformer properties not previously predictable using one-dimensional models can be accounted for. These include end-effects, the location of windings with respect to the magnetic core, winding asymmetries and imbalances, the inherent two-dimensional behavior of foils when mixed with wires, etc. These properties are illustrated by the magnetic field and current density solutions obtained from the model along with power loss and energy storage calculations, all showing strong improvements over one-dimensional models.