| Summary: | <italic>LLC</italic> resonant DC-DC converter has been widely used in high power density and high efficiency applications. Pulse frequency modulation (PFM) is commonly applied due to its wide soft-switching range. In some special cases, phase shift modulation (PSM) is applied to widen voltage regulation range, improve light-load efficiency, or implement a soft start-up process. Because <italic>LLC</italic> is with 2 control degrees of freedom (2DOFs), switching frequency and duty ratio, a unified analysis and optimization for <italic>LLC</italic> with 2DOFs is desired. This paper makes an effort to present a unified time domain operation stage trajectories (OSTs) analysis of <italic>LLC</italic>. On this basis, a unified numerical optimization method is proposed with arbitrarily designed optimization objectives. With the proposed optimization method, the optimized <italic>LLC</italic> with 2DOFs is with better performance compared to conventional PFM and PSM, which is verified by the experimental results.
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