From Commutation to Modal Symmetry: Half-Cycle Symmetry, Detuning Duality, and Symmetry Breaking in LLC Resonant DC–DC Converters

Inductor–inductor–capacitor (LLC) resonant converters can produce nearly symmetric waveforms without achieving low-loss switching. This paper separates these properties, using a common framework for a resonant circuit containing two inductive elements and one capacitor. An analytical gain model is combined with a time-domain model that distinguishes positive secondary conduction, an open secondary circuit, and negative secondary conduction. The framework compares the two switching half-cycles, their conduction sequences, the gain at reciprocal normalized frequencies, and the current available for zero-voltage switching (ZVS). Finite magnetizing inductance breaks reciprocal gain symmetry, while a balanced converter can retain close half-cycle correspondence. Controlled bridge, timing, and rectifier asymmetries increase the waveform mismatch. Independent LTspice checks reproduce three representative mode families and agree with the low-order gain within 0.45–3.55%. They also confirm that a high-gain operating point can fail ZVS despite good waveform symmetry. Highlighted current paths, a datasheet-informed semiconductor-loss budget, and input/output ripple spectra connect the descriptors to practical design questions. The loss estimates are conditional analytical scenarios, and the filtering study uses a separate coupled reduced-order model. The framework supports reproducible design screening; it does not replace detailed device simulation or hardware validation.