Cost-constrained selection of strand diameter and number in a litz-wire transformer winding

The design of litz-wire windings subject to cost constraints is analyzed. An approximation of normalized cost is combined with analysis of proximity effect losses to find combinations of strand number and diameter that optimally trade off cost and loss. The relationship between wire size, normalized cost and normalized loss is shown to have a general form that applies to a wide range of designs. A practical design procedure is provided, and applied to an example design, for which it leads to less than half the original loss at lower than the original cost, or under one fifth the original cost with the same loss as the original design.