Applying Response Surface Methodology to Small Planar Transformer Winding Design

Planar transformers provide a light-weight and low-profile solution for power electronic converters with highly reproducible parameters and simple manufacturability. Parasitic inductances, capacitances, and resistances in planar magnetics are difficult to model due to the complex interactions between the physical winding arrangement of each layer and the core geometry (track width, air gap, clearance, etc.). These nonlinear and multivariate magnetic devices play a key role in defining the performance of traditional, soft-switching, and resonant converters by ruling behaviors such as ringing, self-resonant frequency, conduction losses, and the current rate of change in these converters. In this paper, a methodology for determining parametric models for leakage and magnetizing inductance, inter- and intrawinding capacitances, and the winding resistance of small planar transformers is presented using a variety of winding arrangements. The models are employed to shape the winding design to control parasitic elements in order to optimize soft-switching and resonant converters. A central composite design based on the design of experiment methodology is employed on finite element simulations to provide the comprehensive models. Results from physical verification on a planar Ferroxcube ER18/3.2/10-3F3 core set are provided and show excellent correlation between models and verification tests. The method is later employed to effectively design an LLC resonant converter, which is also experimentally verified to illustrate the benefits of the proposed method. The methodology can be employed to characterize and design planar transformers and to predict their performances as part of a variety of power electronic converters.