Planar PCB Transformer Model for Circuit Simulation

Abstract

An equivalent circuit model for planar printed circuit board (PCB) transformers is presented. The model utilizes the 1-D analysis of Maxwell’s equations to develop a frequency-dependent representation of a multilayer, planar PCB transformer that can be implemented in the circuit simulation software. In this transformer model, each conductor layer is implemented as a complex impedance network, while each insulator layer is implemented as an air-cored inductor. Each magnetic core layer is modeled as a non-linear inductance whose magnetic characteristic is based on a temperature-dependent Jiles–Atherton hysteresis model. These impedances and inductances are then arranged side by side as they are arranged in the layer stack of the actual planar PCB transformer. Through this model, the skin and proximity effect in the conductors and current distribution across windings can be simulated. The developed model also enables the modeling of temperature-dependent hysteresis and saturation effects in the magnetic material. The model provides a simpler method to derive the core and winding loss of the transformer than using a finite-element analysis software. It also enables direct integration to circuit simulation tools. A prototype planar PCB transformer was used to obtain experimental data for model validation. Comparisons made show good agreement between the performance of the model and experimental results.