Some optimum shapes for toroidal inductors

The paper shows how to calculate the cross-section of a toroidal air-cored inductor that has maximum inductance for a given DC resistance. The calculations are extended to give families of sections that are optimum for arbitrary mixtures of DC and eddy-current loss. The method is extended, with outline results, to toroids with solid cores, and the theory is given to maximise inductance for total coil mass. Preliminary results are given for a toroidal cage coil having a computed optimum cross-section.