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Series Elastic Actuation (SEA) is a widely-used approach for interaction control, as it enables high fidelity and robust force control, improving the safety of physical human-robot interaction (pHRI). Safety is an imperative design criterion for pHRI that limits the interaction performance since there exists a fundamental trade-off between stability robustness and rendering performance. The safety of interaction necessitates the closed-loop stability of a pHRI system when coupled to a wide range of unknown operators and environments. In this study, we provide the necessary and sufficient conditions for two-port passivity of series damped elastic actuation under velocity-sourced impedance control within the frequency-domain passivity framework. Based on the newly established conditions, we derive non-conservative passivity bounds for a virtual coupler and rigorously prove the necessity of a dissipative element parallel to the series elastic component and the necessity of a virtual coupler with dissipation for the absolute stability and two-port passivity of the system. The additional dissipative elements in the physical filter and the virtual coupler enable the system to render virtual stiffness values higher than that can be rendered using a pure SEA. Our results extend earlier studies on coupled stability by presenting the necessary and sufficient conditions for all passive terminations. We validate our results through a set of physical experiments and systematic numerical simulations.