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 current rate of change in these converters. In this work, a methodology for determining parametric models for leakage and magnetizing inductance, inter and intra-winding capacitances, and winding resistance of small planar transformers is presented using a variety of winding arrangements.;First, finite element analysis is investigated for the extraction of planar transformer parasitics from 3D designs. Then a Central Composite Design based on the Design of Experiment (DoE) methodology is employed on finite element simulations to provide comprehensive parasitic models based on winding geometry. Results from physical verification on a planar ER18/3.2/10 core set are provided and show excellent correlation between models and verification tests. The method is later employed to effectively design an LLC (inductor-inductor-capacitor) 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.
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