Two waveform-shaping techniques to reduce or eliminate the switching stresses and switching losses in switching-mode power conversion circuits are developed: the zero-current switching technique and the zero-voltage switching technique. Based on these two techniques two new families of quasi-resonant converters are derived. Since the stresses on semiconductor switching devices are significantly alleviated, these quasi-resonant (QRC) converters are suitable for high-frequency operations with much improved performances and equipment power density. Employing the duality principle, the duality relationship between these two families of quasi-resonant converters are derived. The establishment of the duality relationship provides a framework allowing the knowledge obtained from one converter family to be readily transferred to the other. Further topological refinements are derived through the utilization of parasitic elements in the devices and the circuit. In particular, the two most significant parasitic elements, the leakage inductance of the transformer and the junction capacitances of the semiconductor switch, are incorporated as part of the resonant-tank circuit required by these quasi-resonant converters. Consequently, the detrimental effects due to these parasitic elements are eliminated, and the converters can be operated at very high frequencies. / Ph. D.