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This paper presents a new methodology for synthesis of high-gain step-up DC-DC converters. This methodology is based on the differential connection of two basic non-isolated DC-DC converters, in which the output voltages are respectively positive and negative with reference to a common terminal. Any load connected between these positive and negative terminals is subjected to a differential voltage equivalent to the sum of the voltages individually synthetized by each basic converter. When only non-isolated basic DC-DC converters (boost, buck-boost, Cuk, single-ended primary-inductor converter, and Zeta) are considered, six differential converters may be derived by the proposed methodology; nevertheless, voltage lifting techniques based on gain cells can also be applied to further extend the gain, resulting in others high-gain topologies. Besides the proposition of the methodology, the paper investigates the operating principle of the derived converters under different modulation strategies, evaluates the possibility of eliminating redundant components after integration, and correlates the obtained converters with already existing topologies. In fact, it is demonstrated that several high-gain step-up DC-DC converters previously published could be addressed as particular cases of differential connections of basic converters. Experimental results are presented to validate the methodology herein proposed.