Constant argument immittance realization by a distributed RC network

he driving point properties of a ladder type distributed RC network, characterized by the distributionsr (x) = rₒ exp (-ax)andc(x) = cₒ exp (- bx), are investigated. It is shown that the infinite length network exhibits, at one of the ports, a constant argument impedance of the forms-a/(a+b), in an asymptotic manner. With a finite length, the approximation is found to be valid over a finite frequency band only, while the asymptotic behavior is that of an impedances-1/2, irrespective of the values ofaandb.