The Warburg Impedance is a Constant-Phase Element

In the high-overpotential region, j is an exponential function of the overpotential, hence the differential Faiadaic resistance also depends exponentially on potential. 

Combining the last two equations one has, for the high-overpotential region 

In the low overpotential region, where the current is linearly related to the overpotential 

The diffusion equations have been solved for the low amplitude sine wave perturbation. It is found that the Warburg impedance is given by 

This equation can be simplified if it is assumed that the two diffusion coefficients are equal, and the bulk concentrations of the oxidized and the reduced species are also equal, yielding 

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