Simplified Power Inductor Analytical Model and Optimization With Natural Air Convection Cooling

This paper presents a comprehensive, easy-toimplement model for the design of gapped inductors. The algorithm incorporates a complete analytical model and includes a Litz wire sizing algorithm. The fringing effect is taken into account for sizing and loss calculations. The proposed inductance model uses analytical sizing, loss and thermal models from the scientific literature, as well as a library of ETD-shaped magnetic cores. The goal is to provide a user-friendly model that calculates inductor losses and material volume based on input parameters. Thermal constraints are defined for natural air convection cooling. The application focuses on an inductor for a boost converter, with a current having both DC and AC components, and with a switching frequency ranging from 10 kHz to 100 kHz. The inductance of the inductor realized differs from the theoretical value by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2.9 \%$</tex>, while the electromagnetic and thermal constraints are respected.