The theory and design of switched-mode power transformers for minimum conductor loss

A comprehensive and general analysis of the electromagnetic fields, power dissipation, and energy storage within transformer windings is presented. Emphasis is placed on applications in switched-mode power conversion. One-dimensional radial variation of the field quantities is assumed.

The first phase of the investigation is for sinusoidal excitation; solutions for the current density and magnetic field intensity are derived and studied in order to develop a fundamental understanding of the basic phenomena. Expressions for the power dissipation and energy storage in both single- and multi-layer windings are then derived which, upon investigation, yield a technique for minimizing the power dissipation by choosing an optimum conductor thickness. Several levels of accuracy, ranging from exact solutions to very simple and physically meaningful series approximations, are defined and examined to determine their usefulness and range of validity.

The time-harmonic treatment is generalized to arbitrary periodic exoitation by means of Fourier analysis, resulting in a powerful extension of its applicability to any possible converter topology. Results for several representative waveshapes are presented from which a fundamental dependence cn the waveform bandwidth is discovered.

Practical application of the theoretical analysis is considered by developing models for several couon winding types: single and multi-filar round wire, litz wire, and sheet conductors. Experimental results are presented and compared with the theoretical results for each of these cases. Finally, a design procedure is outlined for switched—mode pour transformers which is based on this work.