Area Product Equations for Inductor Energy Density Scaling Law With Input Design Parameter Variability

Abstract

The design of inductors is a complex and demanding task that often requires trial and error iterations, particularly in terms of size optimization. Typically, the design process starts with an initial core shape and size, followed by iterative “trial and error” adjustments to the core size to achieve optimal dimensions. The proposed method is purely analytical for the case of inductors non-limited by saturation (NLS) and for the cases that are limited by saturation (LS), typically requiring calculation iterations. The proposed method is intended as a scoping and scaling tool, so it can also be used as a scaling law for the energy density of inductors for comparing volumes for different specifications. The method includes the variability of input design parameters to account for the deviation between theoretical designs and actual implementations. Finally, a workflow is presented consisting of two iterations: the second iteration recalculates input parameters based on the initial core selection from the first pass, significantly reducing deviation from experimental results. The maximum deviation for the proposed method is improved from around 20%–35% on the first iteration to around 4%–20% for the second iteration.