Power converters having reduced body diode conduction loss, reduced reverse recovery loss and lower switching noise, among other benefits, have a resonant capacitor Cr connected across an unfiltered output. The resonant capacitor Cr resonates with the leakage inductance Lk of the transformer. The resonant capacitor and leakage inductance are selected such that 1/2 a LC resonance period is equal to an ON time of each secondary switch S1 S2. The resonance provides zero current switching for secondary switches S1 S2, eliminates zero body diode conduction during dead times, and eliminates reverse recovery losses in the secondary switches. The present invention is applicable to many different circuit topologies such as full bridge, active clamp forward, push-pull forward, and center-tap secondary. The present converters provide high energy conversion efficiency and high frequency operation.