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One three-transistor push-pull (TTPP) converter is proposed in this study. In this TTPP converter, an extra transistor is inserted between the input power supply and midpoint of two primary windings. On the secondary side, a saturable inductor and an extra freewheeling diode are employed. Adopting the proposed pulse-width modulation method for three power switches, two original transistors can achieve zero-voltage-switching (ZVS) easily in a wide range of load current, the extra transistor can also realise ZVS assisted by the saturable inductor. Each operation mode of the proposed TTPP converters is discussed in detail. The soft-switching conditions are explained. One 83.3 kHz, 800W prototype has been built. Its peak efficiency reaches 94.87%. The experimental result is provided to verify the analysis.