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.

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

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

General equation

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.

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.