Analytical winding size optimisation for different conductor shapes using ampère's law

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