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The magnetic coupling of filter inductors is widely utilized in various power electronics application fields, including most commonly implemented dc-dc converters in electric vehicle charger systems, in order to enhance the filtering performance while maintaining the minimal filter size. The optimal distribution of self and mutual inductance of the coupled inductor is regarded as one of the important design tasks with respect to the coupling factor. This article proposes an explicit mathematical form of the optimized coupling factor design of a generalized n-winding coupled inductor, which generates the least size of inductor current ripple in phase-staggered multiparalleled dc-dc converters. The general equations for the n-winding coupled inductor are verified through the example case of the three-winding coupled inductor. The experimental results successfully confirmed the newly proposed method of obtaining the optimal coupling factor. [ABSTRACT FROM AUTHOR]