RC Driving-Point Impedance Realization by Linear Transformations

This paper presents a procedure for the realization of an RC driving-point impedance (that has poles, is finite at , and vanishes for large values of ) in the form of an ( )- 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 to , and further reduction is possible too, although the realization is always noncanonic. Examples are included to illustrate the procedure.