This improvement can be continued until insulation area increases result in a full bobbin. Thus, the minimum-resistance solution fills the bobbin, and we can find this solution by analyzing a full bobbin.
For a full bobbin, the outside diameter of the complete litz bundle is,
where bb is the breadth of the bobbin, h is the height allocated for the particular winding under consideration, N is the number of turns in that winding, and Fp is a turn-packing factor for turns in the winding, expressed relative to perfect square packing (For Fp =1, the litz bundle would occupy of the window area).
Assuming a factor Flp accounting for serving area, bundle packing, any filler area, strand packing, and the effect of twist on diameter, we can find the outside diameter of a single strand
where n is the number of strands in the overall litz bundle.
The diameter of the copper in a single strand can then be written using (4).
We now define a total resistance factor
where Fdc is the ratio of dc resistance of the litz wire to the dc resistance of a single strand winding, using wire with the same diameter as the litz-wire bundle. Using (6) and (7), we can show
Combining (2), (8), and (9) results in
Equation (10) can now be minimized with respect to n$ to find the optimal number of strands.
This will give non-integral numbers of strands; the nearest integral
number of strands can be chosen to minimize ac resistance.