Before revision:  In this study, we extend the one-port passivity analyzes provided in the literature and provide the necessary and sufficient condition for two-port passivity of SEA under velocity-sourced impedance control  . Based on the newly established conditions, we derive non-conservative passivity bounds for a virtual coupler . We also prove the need for a physical damping term in parallel to the series elastic element to ensure two-port passivity , even when a virtual coupler is present.
After revision:  In this study, we extend the one-port passivity analyzes provided in the literature and provide the necessary and sufficient condition for two-port passivity of SEA under velocity-sourced impedance control . 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 element to ensure two-port passivity , even when a virtual coupler is present.