In this paper, a comprehensive method is proposed to derive the boost DC–DC converter from a given gain formula. The given gain formula is obtained by analyzing, generalizing, and summarizing previous boost structures in the literature. The analysis is based on the volt-second balance theory of inductors. Thus, the gain formula is only related to two elements, the connection between components and the duty cycle of the switches. Therefore, the topology corresponding to the gain can be derived and synthesized according to the connection of the inductors and the capacitor components during the commutation of the switch to meet the demand for different boost converters in different applications. Meanwhile, all the three-order gain formulas generated by this method are analyzed and three of them are selected for topology simplification and focus analysis, and the correctness of the selected topologies is verified by the simulation results and experimental results.