A Common State-Plane Framework for Series Resonant Converters: Forward and Inverse Relationships Between Operating Conditions and Trajectory Geometry

State-plane analysis provides an intuitive geometric description of resonant converters, but the relationship between trajectory geometry and practical operating quantities remains insufficiently established. This paper presents a common state-plane framework for LLC and general CLLC converters. Based on established state-plane relationships, a forward mapping relates operating conditions to the characteristic trajectory radius, while an inverse mapping reconstructs the switching frequency from trajectory information. Simulation results show close agreement between analytical and simulated trajectory radii and validate the inverse reconstruction. Overall, the proposed framework establishes a common analytical connection between operating conditions and trajectory geometry in both forward and inverse directions.