Realization of generalized Warburg impedance with RC ladder and transmission lines

A systemat ic way of const ruct ing resist ive-capacit ive ladder networks and t ransmiss ion l ines that have a general ized Warburg impedance A(j~o)- " has been developed, where A is independent of the angular f requency to, j = ~ and 0 < n < 1. These rea l izat ions are be l ieved to be usefu l for unders tand ing the phys ica l p rocesses respons ib le for the above f ract iona l-power- law dependence on f requency, wh ich is of ten observed in interrac ia l and bu lk ac response of many materials. The Warburg impedance (1) has an in teres t ing frac-t iona l-power- law dependence on angu lar f requency o Zw(r = A(jr 1/2 [1] where j = ~ and A is independent of o~. Th is imped-ance may appear t an e lec t rode/e lec t ro ly te in ter face i f the charge t ranspor t is cont ro l led by d i f fus ion (2). I t may also appear i f the e lec t rode is b lock ing and porous, and the pores are in form of long channe ls (3). I t is, therefore, somet imes used in equ iva lent c i rcui ts to exp la in exper i