Symmetry and Extended Duality in Resonant DC-AC Inverters: Open-Input and Closed-Input Operation Below and Above Resonance

This paper develops a symmetry-oriented regime-level framework for resonant DC-AC inverters that extends classical source duality toward a multidimensional representation of inverter operation. The proposed formulation introduces a compact inverter signature vector and associated symmetry operators to organize source-domain, detuning side, commutation, switch-path, and modal correspondences within a unified hierarchy. On this basis, a symmetry-guided workflow is defined using compact screening metrics for stress/circulation balance, phase displacement, and commutation feasibility, enabling early-stage comparison of operating regimes before topology-specific detailed design closure. The framework is demonstrated through an extended-duality pairing of two resonant DC-AC inverter regimes: an open-input super-resonant ZVS-like corridor and a closed-input sub-resonant ZCS-like corridor. The case studies show how the proposed regime signatures and screening metrics support structured reasoning about soft-switching corridors, stress redistribution, and device-class-dependent implications, including wide-bandgap (WBG) design tendencies. The proposed metrics are intended as low-order screening indicators and regime-selection tools rather than substitutes for detailed circuit, thermal, EMI, and device-level validation. Within this scope, the paper contributes an operational symmetry formalism that links duality-based interpretation to practical early-stage design organization and robustness-oriented comparison.