Analytical Method for Generalization of Numerically Optimized Inductor Winding Shapes

—A method is developed to use a single set of two-dimensional numerical optimizations of inductor winding shapes to simply calculate the optimal winding configuration for any design on the same core without repeating the computationally intensive numerical optimization. For transformer windings, the results are consistent with previous one-dimensional optimizations, but for inductor windings, analysis of two-dimensional effects allows significant performance improvements. I. INTRODUCTION In an inductor winding, the core, and particularly the air gap, strongly affect the field in the winding area, and thus determine proximity-effect losses in the winding. Conventional one-dimensional analyses of proximity-effect losses and the associated design methodologies developed for transformers [1-10] do not account for the true field of a gapped inductor, and do not allow accurate prediction of inductor ac resistance [11]. High-frequency winding losses are particularly important in applications with high ac currents, such discontinuous-mode converters, popular for high-power-factor converters, and resonant soft-switching converters. Low ac resistance is essential for efficient operation and thermal management. In [12], numerical computation and optimization methods accounting for two-dimensional field effects were developed, and the resulting winding shapes were shown to provide significant reductions in losses, allowing the performance of a lumped-gap inductor to not only equal, but