Thermal analytical winding size optimization for different conductor shapes

The aim of this paper is to derive an analytical equations for the temperature dependent optimum winding size of inductors conducting high frequency ac sinusoidal currents. Derived analytical equations are useful designing tool for research and development engineers because windings made of foil, square-wire, and solid-round-wire windings are considered. Temperature dependent Dowell's equation for the ac-to-dc winding resistance ratio is given and approximated. Thermally dependent analytical equations for the optimum foil thickness, as well as valley thickness and diameter of the square-wire and solid-round-wire windings are derived from approximated thermally dependent ac-to-dc winding resistance ratios. Minimum winding ac resistance of the foil winding and local minimum of the winding ac resistance of the solid-round-wire winding are verified with Maxwell 3D Finite Element Method simulations.