Optimum electromagnetic energy converters

This paper investigates the optimal shape of electromagnetic devices in terms of volume. An entangled pair of a coil and a core is considered. The dimensionless volume characteristic zV of this transformer design is defined, which is a measure for the volumetric efficiency of electromagnetic devices. The description of the design is considerably simplified using symmetry arguments. Based on electromagnetic laws, a mapping between the contours of the core and the coil is found. Consequently, the volume characteristic is expressed in terms of the core contour only. The core contour is then discretized using Bézier segments and Fourier modes, and the minimization of the volume characteristic is carried out numerically. While previous engineering efforts brought down zV to approximately 11.6, this paper presents an optimized transformer design characterized by zV = 10.07365 ± 10−5. To the best of the authors' knowledge, this is the most efficient shape of a simple coil‐core assembly in terms of volume published up to now. Copyright © 2009 John Wiley & Sons, Ltd.