DC-DC Converter Synthesis: An Inverse Problem

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.