On the Hybrid Description of a Linear n-Port Resulting from the Extraction of Arbitrarily Specified Elements

Consider a given network which contains a few elements, that for some reason require special attention: independent sources, nonlinear devices, time-varying elements, variable parameters, or even just simple resistors in a feedback path. Extract these special elements outside the given network to leave an n-port. It is assumed that the n-port is linear; it may contain, for example, RLCM type of elements, ideal transformers, and linear controlled sources. The proper representation of such an n-port is discussed. Specifically, the hybrid description is explicitly formulated. A simple rule for determining a set of independent variables for the hybrid description is given. It is shown that if the n-port consists of RLCM type of elements only, a hybrid matrix always exists. The necessary and sufficient condition for the existence of the inverse of such a hybrid matrix is also given. In view of the interest in the literature on the A matrix, it is shown that the A-matrix description is a special case of the hybrid description.