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Contactless transformer is an essential element in inductive power transfer systems. To improve its efficiency performance, a resonant tank is normally formed at the secondary side by adding an external capacitor in series (SS) or in parallel (SP) with the secondary winding. In this paper, a mathematical analysis based on simplified circuit model is presented. It leads to the theory of the boundary frequency which can be used to determine the optimal operating range for SS and SP mode, respectively, from the efficiency point of view. Calculated and measured results have been given to verify the theory in a case study.