Distributed and lumped RC realization of a constant argument impedance

Abstract

The driving-point properties of the distributed RC ( RC ) network are utilized for realizing an impedance approximating (jw) − 1 2 over a wide frequency range ω 0< ω ∞, where ω 0 depends on the parameters of the RC network and those of the terminating impedance. We show that with suitable termination, the value of ω 0 can be reduced by a factor of ten from the value for open or short-circuit conditions. Thin film or semiconductor realization is possible for the resulting networks, but they can also be approximated by combinations of lumped R's and C's. Two types of lumped-element approximations are suggested: one employs a finite ladder to approximate the three-terminal RC network while the other is based on truncation of the partial-fraction expansion of the two terminal RC impedances. It is found that the former type of structure gives better results than the latter type.