Modeling of planar transformer parasitics using design of experiment methodology

Planar transformer parasitics are difficult to model due to the complex winding geometry and their nonlinear and multivariate nature. This paper provides parametric models for planar transformer parasitics based on finite element simulations of a variety of winding design parameters using the Design of Experiments (DoE) methodology. A rotatable Central Composite Design (CCD) is employed based on a full 2⁴ factorial design to obtain equations for the leakage inductance, inter and intra-winding capacitances, resistance, output current, and output voltage. Using only 25 runs, the final results can be used to replace time-intensive finite element simulations for a wide range of planar transformer winding design options. Validation simulations were performed to confirm the accuracy of the model. Results are presented using a planar E18/4/10 core set and can be extended to a variety of core shapes and sizes.