The realization of a immittance matrix by R, C elements and one controlled source

In this investigation the necessary and sufficient conditions are established for a matrix of real rational functions to be realizable as a short-circuit admittance matrix of a transformerless active three-terminal two-port network utilizing either or networks and one controlled source. An existence theorem on this general class of networks is presented, but no general synthesis procedure is developed. For the special case when the matrix has only simple real axis poles, a synthesis procedure is developed to realize the admittance matrix that satisfies these sufficient conditions as a twoport network. As an application of the synthesis procedure, an equivalent circuit is developed from a set of short-circuit admittance functions which are obtained by approximating a set of experimentally determined magnitude and phase characteristics using the half-line approximation technique. This application provides a method for obtaining general equivalent circuits for a transistor or any other similar active device, valid over any desired frequency range with any degrees of predetermined accuracy by synthesis.