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This article presents an analytical method to derive an optimum converter topology for a specified voltage conversion ratio (G). An optimum topology for any given G can be identified after obtaining the comprehensive pool of converter topologies. This gain-oriented converter synthesis is formulated as an inverse problem around the principle of inductor flux balance. A step-by-step method is proposed to solve the inverse problem and obtain a comprehensive set of non-redundant converter topologies for any given voltage conversion ratio. Consequently, the number of possible converter topologies for a specified voltage conversion ratio is also identified. The optimum converter topology is chosen from the comprehensive set based on three selection criteria, viz., ground-referenced output, a minimum number of switches, and minimum peak inductor current. The proposed solution methodology is illustrated with quadratic boost and quadratic buck gains as case studies. A comprehensive set of non-redundant topologies is identified in both cases. The steady-state operations of all the topologies are studied with PLECS simulation. Based on the selection criteria, an optimum topology is selected in each case, and their steady-state operation is verified experimentally using lab-developed prototypes. [ABSTRACT FROM AUTHOR]

The inverse problem for the dc–dc converters refers to synthesizing converter topologies from a specified voltage gain expression. Though the flux balance principle is widely used in the analysis of dc–dc converters, its application as a synthesis tool has not been explored. This letter describes a mathematical approach to synthesize converter topologies from a required voltage gain expression by utilizing the principle of inductor flux balance. At first, the general form of gain expression for second-order converters is derived. From the general form of gain expression, the inverse problem is formulated by identifying the governing equations. The mathematical formulation of the inverse problem and highlighting challenges involved in solving it are the primary subjects of this article. To outline these challenges, a probable solution strategy of this inverse problem is presented. In order to derive a converter topology, at first, the appropriate flux balance equations are determined, and then the circuit topology is derived to establish the required flux balance. In contrast to the forward problem, the solution to the inverse problem is neither direct nor unique. Hence, getting the optimum closed-form solution to this inverse problem is an open-ended challenge with many possible approaches. [ABSTRACT FROM AUTHOR]