The concept of optimum shape of inductors is discussed. The optimum shape is defined to be that of the inductor which has the smallest volume for a given set of electrical specifications. This definition has the widest application and can be used to calculate the optimum shape. A dimensionless function of the proportions of the inductor is related to the definition and is used to calculate the optimum shapes of three types of core: toroidal, E, and pot cores. Equations are developed to help the reader calculate the optimum shapes of other types of core.
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B. Astle (1969) studied this question.