The designs specified in the preceding section were constructed with two types of litz wire: 130 strands of 48 AWG and 50 strands of 44 AWG. The primary and secondary windings were made from a single length of litz wire, wound on the bobbin in opposite directions. This is magnetically equivalent to having a shorted secondary, but it reduces potential problems with interconnect resistance. In order to evaluate skin effect in the absence of external proximity effect litz wire was also measured outside of a winding. The resistance was measured with an HP 4284A LCR meter, using a custom built test jig for low impedance measurements. The measurements are shown in Fig. 7.

Fig. 7. Experimental ac resistance factor, Fr, as a function of frequency. Top graph is for litz wire with 50 strands of 44 AWG wire; bottom graph is 130 strands of 48 AWG wire. Both are in the example transformer described in the text. Total measured resistance factor in the transformer is marked with stars. Measured skin effect in a straight piece of litz wire is marked with xs. The difference, equal to proximity-effect losses, is marked with circles. These correspond closely to the predicted proximity-effect losses (solid line).

Although the overall litz-wire diameter was small enough to limit bundle-level skin-effect losses to a few percent, the fine strands in the optimal solution also limit proximity-effect losses to similar levels. Fortunately, the losses are orthogonal [15] and the measured skin effect losses (for a litz wire outside of the winding) can be subtracted from the measured losses in the transformer in order to isolate proximity-effect losses. When this is done, the proximity-effect losses predicted by (2) match the measured proximity-effect losses very closely.

Because the exact construction of one of the samples was not known, the expected bundle skin effect could not be predicted accurately. However, the 50-strand bundle of 44 AWG wire was believed to be simply twisted. It exhibited considerably lower loss than would be expected on this basis, indicating that there may be some more complex transposition of the strands, even if the manufacturing process did not deliberately introduce this construction. While these effects merit further experiments, the experiments reported here confirm the validity of the model used in our optimization.