A matrix presentation of State-Plane Analysis for a broad class of Series-Resonant Converters

The trend toward higher switching frequencies and higher power densities in DC-DC conversion led the designers to rediscover resonant topologies. However, the analysis of these converters is often limited to a particular operating mode and/or topology. This paper wants to fill the gap by presenting a statespace based analysis for a broad class of series-resonant converters including voltage-fed as well as current-fed topologies, either unidirectional or bidirectional. The proposed solution consists in a mathematical framework that solves the trajectory of state variables in the resonant tank as well as the main characteristic functions like voltage conversion ratio and transferred power. The matrix approach permits a flexible and compact formulation, and easy implementation in computational tools like MATLAB®. The theoretical framework is applied to both voltage-fed and current-fed resonant topologies: the first is used to show the advantages of the proposed model respect to the First Harmonic Approximation, while a detailed analysis in terms of operating mode boundaries, delivered power, and voltage gain is provided for the second. Simulations and measurements on a 300W prototype of the current-fed topology are used to validate the correctness of the proposed solution.