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This paper unifies the underlying concepts of all basic single-switch, two-state, dc-to-dc voltage-sourced converters, by duality, as generic related current and voltage-sourced converters. By using ac and dc circuit theory, the three basic converters can be transformed to yield all known transfer functions and realizes a proliferation of 33 topologies, three being previously unidentified topologies with unique characteristics. The circuit based systematic unifying approach offers new insight and an alternative interpretation to the origin of the 33 topologies including the Zeta, Cuk, ±Luo, CSC, Landsman, and Sepic converters. Converter time-domain simulations and corresponding practical results of the three new topologies extol and culminate the concepts and analysis presented.