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In this study, an analytical optimisation of the foil, strip, square and solid-round-wire winding inductors conducting sinusoidal current is performed. The Ampère law is used to derive analytical equations for the AC-to-DC winding resistance ratio of different shape inductor windings valid at low and medium frequencies. These equations are used to perform optimisation of windings to obtain the global minimum of the winding AC resistance of the foil and strip wire windings and the local minimum of the winding AC resistance for the square and solid-round-wire windings. Derivations of AC-to-DC winding resistance ratio and winding AC resistance based on Ampère's law for the solid-round-wire windings are compared to Dowell's equation. Results of the predicted winding AC resistance based on Ampère's law for the solid-round-wire windings are validated by experimental results.

Foil Winding Resistance and Power Loss in Individual Layers of InductorsThis paper presents an estimation of high-frequency winding resistance and power loss in individual inductor layers made of foil, taking into account the skin and proximity effects. Approximated equations for power loss in each layer are given and the optimal values of foil thickness for each layer are derived. It is shown that the winding resistance of individual layers significantly increases with the operating frequency and the layer number, counting from the center of an inductor. The winding resistance of each foil layer exhibits a minimum value at an optimal layer thickness. The total winding resistance increases with the total number of layers.

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