Comparing the characteristic frequencies of the transmissive and reflexive finite-length Warburg diffusion processes

Abstract

This manuscript revisits the Warburg impedances and relate the characteristic frequencies of the finite-length diffusion processes under both transmissive and reflexive conditions. A novel study on the characteristic frequency of the reflexive finite-length diffusion process is presented by isolating the purely capacitive behaviour from the reflexive impedance. It is well-known that 2.54065 is the characteristic frequency of the transmissive diffusion impedance. Here, it is numerically found the value 11.6087 as the characteristic frequency of the reflexive one. Approximate analytical expressions for the characteristic frequencies are also obtained and compared from the series development into partial and continued fractions of both impedances.