Necessary and sufficient conditions on the poles and zeros of the reflection coefficient for low-pass ladder networks

Abstract
A method by which the element values can be expressed for a class of linear lumped passive resistively terminatedLCnetworks, in terms of the poles and zeros of the reflection coefficient, is described. The driving-point impedance of the networks belonging to this class has the property that the zeros of its even part are all located at infinity in thepplane. The method to be described is broken down into two distinct steps: the first step consists of finding the element values in terms of the power series coefficients of the drivingpoint function and the second step consists of expressing the power series coefficients of the driving-point impedance in terms of the poles and zeros of the corresponding reflection coefficient or the Taylor series coefficients of the return loss function. A numerical example is provided to illustrate the method. The method can be easily extended to the cases in which all the even-part zeros lie at the origin or at any other finite frequency on thej \omegaaxis.