RC Driving-Point Impedance Realization by Linear Transformations

This paper presents a procedure for the realization of an RC driving-point impedance (that hasnpoles, is finite ats = 0, and vanishes for large values ofs) in the form of an (n + 1)- node network with a capacitance and conductance in parallel between every pair of nodes. Element values are found directly from hyperdominant parameter matrices obtained through a linear transformation. Hyperdominancy is achieved by regarding the linear transformation as the product of two transformations, one orthogonal, the other a scaling, which establish the sign pattern and dominance, respectively, of the parameter matrices. The number of either capacitances or conductances can be reduced ton, and further reduction is possible too, although the realization is always noncanonic. Examples are included to illustrate the procedure.