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Capacitively coupled contactless power transfer through electric field coupling, also named CPT (capacitive power transfer), has been proposed recently as an alternative non-contact power transfer technology. Compared to existing inductive power transfer (IPT) technology, CPT has many advantages such as metal penetration ability, low standing power losses, and reduced EMI (electromagnetic interference). However, understanding and experience in CPT system analysis and design are still very limited to date. This paper analyzes the basic steady state performance of a typical CPT system. Stroboscopic mapping method is employed to model the system to determine the ZVS (zero voltage switching) frequencies and steady state waveforms. The system switching performance is analyzed against circuit parameter variations, and simulation and experimental results have verified the proposed method.