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In this article, a quasi-resonant (QR) flyback converter has been proposed for capacitor charging in a pulsed plasma thruster (PPT) of a nano-satellite. The energy in the transformer leakage inductance can be recycled to the resonant capacitor, suppressing the switch-off voltage spikes on the semiconductor power switch. The power switch is turned on with a hybrid switching mode. In this mode, valley-voltage-switching (VVS) is applied until the zero-voltage stress on the power switch is obtained, and zero-voltage-switching (ZVS) is used in the remaining charging process. Consequently, the switching-on loss is reduced, and charging efficiency is improved. When a capacitor bank of $2\mu \text{F}$ is charged to 1.5 kV (i.e., 2.25 J), the switching loss contribution of QR flyback converter using hybrid switching approach is reduced significantly to 0.61% while a flyback converter using hard-switching technique has a switching loss contribution of 15.24%. As a result, the proposed QR flyback converter improves the charging efficiency by 2.43%, from 72.69% to 75.12%. Moreover, the diode in the secondary side can be turned-on with zero-voltage and off with zero-current. Hence, the turn-on overshoot voltage and recovery loss are reduced. [ABSTRACT FROM AUTHOR]