A flyback type of transformer-coupled dc/dc converter supplies a train of current pulses to charge an energy-storage capacitor to a desired high voltage, converting input de power obtained from a lower voltage de source, The energy-storage capacitor is charged to a specified voltage within a specified time with minimum peak and rms currents in the transistor, the rectifier diode, the transformer windings, and the de power source, minimizing the i(2)R losses, This is done by generating 1) energy-storage current pulses in the power transistor and the transformer primary winding in which the current increment from the beginning to the end of a pulse is only a small fraction of the final (peak) value and 2) energy-delivery flyback current pulses in the capacitor and the transformer secondary winding in which the current decrement from the beginning to the end of a pulse is only a small fraction of the initial (peak) value, Recommended methods are: 1) hysteretic current-mode control with current sensing in both transformer windings; 2) peak-current-commanding current-mode control with switching frequency or transistor-nonconducting time varying in a prescribed way during the charging; or 3) valley-current-commanding current-mode control with switching frequency or transistor-conducting time varying in a prescribed way during the charging, Compared with one nonoptimal method, peak currents are reduced by a factor of about 2 and i(2)R power losses are reduced by a factor of about 1.33.