CASCADE REALIZATION OF A CLASS OF 2-VARIABLE TRANSFER-FUNCTIONS

Realizability conditions have so far been presented for a two-variable rational function of p1 and p2 to be realized as the transfer function of a doubly terminated two-port consisting of a cascade of single-variable lumped, lossless, reciprocal two-ports, each of which depends only on p1 or p2 and has all of its transmission zeros only at infinity or at the origin. In this paper, necessary and sufficient conditions are derived for the realizability of a transfer function of p1 and p2 in a similar but more general case. It is noted that a set of realizability conditions presented as well as the approach to the realization is entirely different from those in the previous contributions. The derived conditions are based on the factorability of three polynomials determined from the denominator and numerator polynomials of the transfer function under consideration. The proposed approach is based on the synthesis of two single-variable driving-point impedance functions, which are defined at the junction of single-variable two-ports, each of which depends only on p1 or p2. Moreover, a realization procedure based on the approach used in the previous contribution is also derived from the viewpoint of reciprocal realization of the transfer function presented in this paper. In addition, a theorem on a cascade realization of multivariable positive real functions is extended.