Generalization of the Passivity Criterion for One-Port Devices Presenting Negative Real Part Admittances

The physical validation of devices must comply with the principles of causality, passivity, and stability. For linear and time-invariant devices, it can be proved that passivity implies a causal transfer function. In this sense, it is understood that causality is a consequence of the passivity condition. Moreover, if the real part of the admittance is non-negative, it can also be demonstrated that the device is passive. The main subject of this work is a novel class of one-port passive devices presenting negative real part admittances on certain frequency ranges. Thus, the equations expressing the passivity condition, as far defined, are not applicable and the causality condition must also be checked. A theoretical model able to explain this effect and a generalization of the passivity condition, which fully address the applicability of the passivity-causality theorem are provided. The experimental verification of a specific device having this property is also shown. In this way, we report the results of a practical realization of a resonant circuit having negative real part values and a tunable positive to negative real part transition. As a possible outcome, novel passive circuits, such as oscillators and phase modulators covering the full trigonometric circle may be constructed. We also discuss the causality condition, show that negative real part admittances are causal and provide a new causality test that is in full consistence with the Kramers-Kronig relations.