Distinguishability of equivalent circuits containing CPEs: Part I. Theoretical part

Constant phase elements (CPEs) with impedance Z_CPE=1/(Qs^α_f) are widely used to explain electrochemical impedance spectroscopy (EIS) data. It has long been known that different circuits can explain EIS data in an equivalent manner because they exhibit identical impedance for all frequencies (two-terminal non-distinguishable (TTND) circuit). Equivalent circuits containing two CPEs are considered here. TTND circuits containing two CPEs become distinguishable, at least theoretically, if the CPE exponents are different. The experimental distinguishability of these circuits is discussed. The 12 transformation formulae between the four circuits containing two CPEs and two resistors are given for CPEs with equal exponents.