On the cascade connection for time-invariant n-ports

Questions concerning the existence of the scattering matrix for the interconnection of two networks are considered. It is shown that all interconnections can be regarded as a special type of interconnection termed cascade loading. If two networks in the cascade-loading configuration are separately linear, passive, time-invariant and have scattering matrixes, the same is true of the interconnection network. This result is applied to finite networks, and it is shown that any finite network composed of passive resistors, capacitors, inductors, gyrators and transformers has a scattering matrix. Some illustrative examples are also considered, pointing out that the results stated are the best obtainable.