High step-up converters are crucial in many power electronic interfaces, including for renewable energy sources. As the result of topological variation of high step-up converters, many topologies share similar characteristics. In order to have a clear understanding of an optimized design that makes the best use of components to achieve high gain, it is necessary to devise a generalized comprehension method for high step-up converters. This article presents a novel generalized method for analyzing single-switch step-up converters that can include switched capacitor (SC) cells, a coupled inductor (CI), and/or voltage multiplier cells (VMCs). The proposed method is neither dependent on the position of the CI nor the structure of the VMC, and is not tied to a specific topology. Thus, the proposed generalized method uniquely reveals the unifying theory underlying high step-up converters with any variation of SC/CI/VMC. In order to verify the theoretical analysis, many examples from the literature are investigated. Then, using design tips from the generalized method, a new high step-up converter is designed. A 150-W prototype of the converter shows 97.5% peak efficiency. The proposed converter also compares favorably to other topologies in both a power loss breakdown analysis and a component stress factor analysis.