An analytical synthesis method is described which is capable of generating the complete set of switching converters which possess given attributes. This leads to a number of useful new converter topologies, as well as to a more fundamental understanding of switched-mode conversion. Two examples are considered. It is found that the class of single-inductor two-topology converters contains seven basic members. In addition, a class of converters with nonpulsating input and output currents also contains seven members. Zero input or output current ripple may be obtained in three of these converters.