State-plane technique was adopted for analysis of a class of resonant de to de power converters. A comprehensive method was developed to understand the complex operation of a resonant converter, identify its operating modes along with their regions of occurrence and determine the de characteristics of the converter in each mode. The method was shown by application to a series resonant converter (SRC), a parallel resonant converter (PRC) and the family of quasi resonant converters (QRCs). Several major conclusions were experimentally verified. By suitably modifying the method, the effect of parasitic losses on the performance of a SRC was also studied. The operating regions where significant deviations in de characteristics occurred due to losses were also identified. In addition, from the mode and de analysis of a PRC, a novel resonant buck converter with de gain almost insensitive to load variations was proposed. Generalized mode and de analysis applicable to all QRC topological variations were performed using state-plane diagrams. Four sets of mode and de analyses were shown to be adequate to characterize the steady-state operation of nearly a hundred QRC variations. This simplified the understanding and analysis of these converters. Also, two simple circuit rules were introduced using which several QRC topological variations were generated and evaluated based on relative component stresses. The state-plane technique was also used to understand and evaluate different control methods of a SRC. The occurrence of large, undesirable tank energy surges with analog-signal-to-discrete-time-interval-converter (ASDTIC) control was investigated and explained using state-plane trajectories. A new control method called #optimal trajectory control*, which attempts to achieve the fastest response possible was proposed. By exploiting the structure of SRC state portrait, the tank energy is always kept within bounds with this control. Experimental implementation was discussed in detail along with experimental oscillograms which confirm the predicted fast response. / Ph. D.