A Note on the Scattering Matrix of an Active Linear Two-Terminal Pair Network

By separating the scattering matrix into matrix factors, a cascade of partial two-terminal pair networks is obtained, which represents the general nonreciprocal two-terminal pair network. Using a matrix factor to represent a source, the active circuit properties are separated from the passive ones and it is demonstrated that this source, which is simply related to the determinant can be moved to the terminal ends of the total network, where it may be combined with an external source. The derived equivalent circuits do not employ gyrators but contain, besides the source mentioned, 2 two-terminal circuit elements, which characterize loss as well as inherent stability, and 2 "ideal transformers" rendering measures of amplitude and phase transfer. An application to the transistor results in a novel equivalent circuit for that device.