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We present a detailed analytical study of rotational eddy-current couplers. We provide a field solution by the variable separation method, and we analyze radial geometry structures. The couplers consist of a permanent-magnet stator and a multilayer conductive rotor. We present different analytical solutions in order to study single- and double-sided permanent-magnet frames. We validate the models by two-dimensional and three-dimensional (3-D) finite-element studies, and we perform an exhaustive parametric analysis to estimate the influence of the dimension parameters of the two structures. Finally, we present an analytical approach to a 3-D correction.