Synthesis Using Distributed RC Networks

Abstract

This paper presents necessary and sufficient conditions for a function to be the driving point impedance of a network composed of uniform RC lines all having the same RC product connected in an arbitrary manner. Foster type realizations are developed for an impedance function satisfying these conditions. Analogous to the vector approach for the s plane analysis of lumped circuits, a method for determining the frequency response of driving point impedance and transfer functions in the P = cosh x1s.R- plane is considered. A transfer function synthesis procedure based upon a ladder realization is developed which is capable of realizing transmission zeros along the real axis of the P plane between +1 and - \infty . By locating a zero at P = -11.6 using this procedure, a zero can be obtained on the j \omega axis of the s plane. The use of lattice networks and negative immittance converters for obtaining complex conjugate P plane poles and zeros is also discussed. Finally, it is pointed out that the foregoing work is applicable to three terminal networks that are both symmetrical and reciprocal. These networks may consist of lumped as well as distributed elements.