Network theory without circuit elements

Network methods are by no means limited to lumped systems. Once the ports of a generalized physical structure are defined by use of a modal decomposition of signals, the structure can be analyzed using network techniques which extend beyond the domain of RLC systems and rational network functions. If the physical system is observed as a black box at its ports and various physical time-domain postulates such as linearity, energy, and power conservation theorems are applied in network terms, a variety of realizability relations are obtained for linear, passive, time-invariant structures. For example, one is led to generalizations of bounded real and positive real functions for distributed systems. The network technique also results in a number of interesting theorems for lossless structures such as a generalization of Foster's reactance theorem, and restrictions on minimum phase realizability, and on signal transmission and group delay in distrributed, lossless networks. These results apply in structures containing gyrotropic, dispersive media as well as in the reciprocal, nondispersive case.