Performance evaluation of homogenization techniques for proximity losses in PCB coils applied to inductive devices

Energy efficiency is the primary objective in optimal design of inductive power components. This goal is totally aligned with the minimization of power losses in the coils. Typically, coils have been constructed by wire winding but, more recently, the utilization of printed circuit board (PCB) constructions has become more common due to their advantages, i. e. low profile and ease of fabrication, among others. At the operating frequencies of magnetic power devices, multi-conductor cabling with litz structure is required to reduce losses. PCB loss optimization procedure involves determining the number and size of the tracks. Numerical simulation is a very powerful tool to obtain the parameters of magnetic devices. However, including the internal structure of multi-track wiring in the numerical simulation implies a very high computational cost and a low accuracy of the results, because the size of the tracks is very small. Techniques of homogenization of the cabling are used to overcome such difficulty, disregarding the internal structure in order to determine the fields in the system and their electrical equivalent by means of computational simulation. The coil losses are further determined on the basis of the characteristics of the cabling as well as of the surrounding fields. The preceding procedure has proven to be suitable for cables composed of strands of circular cross-section, but should be adjusted to apply to tracks of rectangular cross-section. In this paper, different homogenization techniques for PCB coils have been proposed and evaluated. A highly symmetric reference system is selected to reduce the computational cost of numerical modeling, but the conclusions can be applied to more complicated geometries without loss of generality. Finally, the results of the different homogenization techniques have been validated by comparison with experimental results.