D-shaped toroidal cage inductors

The toroidal cage coil is a robust and simply constructed inductor that has applications in railway traction and other high current power electronics circuits. A new series of prototypes have the Shafranov D-shape coils, replacing the rectangles presently used. They are more economical in use of copper and significantly easier to wind. Inductance formulas are derived: they show good agreement with measurements, and provide an improved method of design to required values. Loss formulae are derived, using a comprehensive study of mutual proximity losses in bunched conductors, and a systematic dependence of loss on coil shape parameter is found.<>