Extension of Simple and Accurate Inductance Estimation for Rectangular Planar Windings

TL;DR

This paper extends existing inductance estimation equations from square to rectangular planar windings by using the generalized mean value, optimizing accuracy through data-driven p-norm selection, and validating with simulations and laboratory measurements.

Contribution

It introduces a generalized method for inductance estimation of rectangular windings using the p-norm of the mean value, improving accuracy over traditional equations.

Findings

Optimal p-norm improves estimation accuracy.

Method validated with over 2600 simulations.

Laboratory measurements confirm the method's effectiveness.

Abstract

This paper proposes a method to generalize the equations estimating the inductance of square-shape planar windings to rectangle shape. This is done by utilizing the optimal p-norm of the Generalized Mean Value or Power Mean (PM). Three well-established equations with verified accuracy are examined, namely Wheeler, Rosa, and the Monomial, which by definition consider only regular polygons. One critical parameter of the original equations is the outer-side length of the winding, which for the rectangle case, can be substituted by the PM of the two outer-side lengths, without the need for any further modifications. A methodology to select the optimal p-norm for the PM is presented in terms of achieving the best accuracy for this estimation. The selection of the optimal p is based on results from datasets containing more than 2600 simulations of different rectangle-shaped windings. Finally, the estimation accuracy is verified by laboratory measurements for a selection of planar inductors.