Optimum shapes for multilayered toroidal inductors

Optimum shapes and windings, defined by the greatest achievable inductance with a given length of round wire, are known for most standard geometries. The optimum shape for windings on a nonmagnetic toroidal core, which was hitherto only known approximately, has been calculated using a genetic-algorithm method. The maximum possible inductance scales are similar to the Brooks solenoid, as the five-thirds power of the wire length, but is much smaller, essentially because the toroid completely contains the magnetic energy but the solenoid uses the surrounding space. Optimum shapes have also been found for toroids with linear magnetic cores. Using penalty functions, the optimisations have been extended to toroids that must fit into given confined spaces