Applying Response Surface Methodology to planar transformer winding design

Planar transformers provide a light-weight and low profile solution for power electronic converters with highly reproducible parameters. Their parasitic inductances, capacitances, and resistances are difficult to model due to the complex winding arrangement along with their nonlinear and multivariate nature. This paper provides a methodology for determining parametric models for the leakage inductance, inter and intra-winding capacitances, and resistance of planar transformers using a variety of winding arrangements. A Central Composite Design based on the Design of Experiment (DoE) methodology is employed to provide the parametric models using a small number of experimental runs. Results from physical experimentation on a planar ER18/3.2/10 core set are provided and show excellent correlation between modeled results and confirmation testing. The methodology can be employed to characterize and design planar transformers for specific applications (for example soft switching or resonant converters), and to predict their performance as part of different power electronics topologies.