The number of strands for a minimum-loss litz-wire winding may be found
by evaluating the tradeoff between proximity-effect losses and dc resistance.
Of the factors leading to increased dc resistance in a litz-wire winding,
only the space allocated to strand insulation varies significantly with the
number of strands in a well designed construction. A power law can be used
to model insulation thickness in the region of interest. Combining this with
standard models for eddy-current loss results in an analytic solution for
the optimal number of strands. The simplest model for loss, using only the
first terms of a series expansion can be used since good designs use strands
that are small compared to a skin depth. Experimental results correlate well
with the simple model.
Stranding for minimum loss may lead to many strands of fine wire and thus
excessive expense. Minimum loss designs constrained by minimum strand size
or maximum number of strands have also been derived.