Extension of Simple and Accurate Inductance Estimation for Rectangular Planar Windings

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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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> -norm of the Generalized Mean Value or Power Mean (PM). Three well-established equations with verified accuracy are examined, namely Wheeler's, Rosa's, 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> -norm for the PM is presented in terms of achieving the best accuracy for this estimation. The selection of the optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> 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.