Product of inductive and capacitive operators

The linear passive time-invariant systems are classified according to the reactive energy sign. Subsequently, overall inductive and capacitive systems and their `products¿ are defined. A key theorem is presented, showing that the product of a pair of linear accretive inductive and capacitive operators corresponds to a linear passive system. The theorem has a broad range of applicability as the proposed proof encompasses lumped as well as distributed networks. In particular `the product¿ of RL and RC n-port open-circuit impedance matrices represents a passive n-port. The same applies to `the product¿ of arbitrary inductive and capacitive RLN n-ports open-circuit impedance or short-circuit admittance matrices.