Optimal designs for multilayer air-cored toroidal inductors with circular windows

The problem of winding the greatest possible inductance with a given length of wire is solved for multilayered air-cored toroids with circular window sections. Calculations indicate significant improvements over single-layer designs, and are confirmed by measurements on devices using two different fabrication methods. The optimum designs are robust against fabrication errors, provided the wire length is correctly measured, accurate inductance is assured. To achieve the same inductance, multilayer devices use significantly less wire and are much more compact. A theory is developed for the optimum multilayer toroid, which is shown to scale similarly to the Brooks solenoid, but requires more wire for the same inductance