Passivity and its Relation to Stability in LRTI N-Ports

Among the properties of Linear Resistive Time Invariant (LRTI) N-port networks, passivity plays a crucial role. In fact, passivity has a strong relation to stability of the corresponding Linear Dynamic Time Invariant (LDTI) circuit, where a positive dynamic element, i.e. a capacitor or an inductor, is connected to each port. This relation is less intuitive than expected and requires a more formal and in depth approach than that normally found in circuit theory textbooks. Passivity is also very important to characterize AC N-ports, even if, in this case, it takes a somewhat different meaning. Passivity in AC is important in applications, especially those concerning power grids. Reciprocity of these elements will also be considered.