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Capacitively coupled contactless power transfer (CCPT) technology has been proposed as a new contactless/wireless power transfer method recently. By employing electric field as the energy transfer medium, CCPT has advantages of being able to transfer power across metal barriers and reduced electromagnetic interference. However, there is very limited understanding and experience in the CCPT system modelling and analysis. This study models a typical CCPT system and analyses its performance under steady-state operations. An accurate non-linear circuit model is established and the stroboscopic theory is extended to determine the zero-voltage switching (ZVS)-operating frequency of the system. The tuning inductance for achieving exact ZVS operation is derived, and the effects of the coupling and load variations on the system performance are analysed. A prototype CCPT circuit is built, and practical measurements show that the steady-state time domain waveforms and efforts of coupling and load variations calculated from the theoretical model are in good agreements with experimental results. The power efficiency predicted is slightly higher than the practical results, particularly at heavy loads, because ideal power semiconductor switches and wires are used in the theoretical model.