Constant argument immittance realization by a distributed RC network

he driving point properties of a ladder type distributed RC network, characterized by the distributions r (x) = r_{o} exp (-ax) and c(x) = c_{o} exp (- bx) , are investigated. It is shown that the infinite length network exhibits, at one of the ports, a constant argument impedance of the form s^{-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 impedance s^{-1/2} , irrespective of the values of a and b .