Constant phase element

A constant phase element is an equivalent electrical circuit component that models the behaviour of a double layer, that is an imperfect capacitor.

The electrical impedance can be calculated:

$Z_{CPE}=\frac{1}{Y_{CPE}}=\frac{1}{Q_0\omega^n}e^{-\frac{\pi}{2}ni}$

where the CPE admittance is: $Y_{CPE}=Q_0(\omega i)^n$ and Q₀ and n (0<n<1) are frequency independent.^[1]

Q₀ = 1/|Z| at ω = 1 rad/s

The constant phase is always −(90*n)°, also with n from 0 to 1. The case n = 1 describes an ideal capacitor while the case n = 0 describes a pure resistor.

A constant phase element also appears currently in modeling the behaviour of the imperfect dielectrics. The generalization in the fields of imperfect electrical resistances, capacitances and inductances leads to the general "Phasance" concept : http://fr.scribd.com/doc/71923015/The-Phasance-Concept

Constant phase elements are also used in equivalent circuit modelling and data fitting of electrochemical impedance spectroscopy data.

References

1. Kochowski, S; K. Nitsch (21 May 2002). "Description of the frequency behaviour of metal-SiO₂-GaAs structure characteristics by electrical equivalent circuit with constant phase element" (PDF). Thin Solid Films 415: 133–137. Bibcode:2002TSF...415..133K. doi:10.1016/s0040-6090(02)00506-0. Retrieved 22 October 2012.