A Step-Superposition-Based Analysis Approach to Modeling Resonant Converters

This paper introduces a new analysis approach to modeling resonant converters that can be used to determine closed-form expressions for the exact resonant network waveforms. This approach, based on superposition of step responses to inverter and rectifier imposed steps, can easily be applied to resonant converters with high-order resonant networks, multiple inverters, and/or rectifiers. The usefulness of the proposed analysis approach is demonstrated first by applying it to a series-resonant converter, wherein it is used to determine accurate closed-form expressions for its tank current in different operating modes. These expressions are utilized to draw insights that help identify the converter's operating mode, and determine associated expressions for its output voltage and the switching frequency required to achieve a desired output power. The proposed approach is also applied to the multi-inverter multi-element impedance control network (ICN) resonant converter, wherein it is used to derive closed-form expressions for the converter's currents. These expressions are utilized to evaluate the behavior and optimize the design of an ICN resonant converter. A prototype 200-W 500-kHz ICN resonant converter optimized using the proposed approach is used to validate the modeling results. It is shown that there is an excellent agreement between the experimental and modeled waveforms during steady-state operation as well as during startup transients.