The Realization of RC N-Ports

Given an
n \times n
matrix,
Z(s)
composed of elements which are the ratio of polynomials in the complex quantity
s
, necessary and sufficient conditions of a general nature are found which are required for the existence of a common-ground network of resistors and capacitors that possesses
Z(s)
as its open-circuit impedance matrix. Based on these conditions, we consider a form of this problem in which the main restriction is the requirement that the elements of
Z(s)
have no more than
n + 1
poles. The solution presented provides a practical procedure for determining whether a given nth-order matrix with no more than
n + 1
poles can be realized, and if it can be, then an economical set of resistors and capacitors is derived. Further, a complete class of equivalent realizations is also presented.