# Constant phase element

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In [electronics](/source/Electronics), a **constant phase element** is an [equivalent electrical circuit](/source/Equivalent_electrical_circuit) component that models the behaviour of a [double layer](/source/Double_layer_(electrode)), that is, an imperfect [capacitor](/source/Capacitor) (see [double-layer capacitance](/source/Double-layer_capacitance)).

Constant phase elements are also used in equivalent circuit modeling and data fitting of [electrochemical impedance spectroscopy](/source/Electrochemical_impedance_spectroscopy) data.

A constant phase element also currently appears in modeling the imperfect [dielectrics](/source/Dielectric)' behavior. The generalization in the fields of imperfect [electrical resistances](/source/Electrical_resistance), [capacitances](/source/Capacitance), and [inductances](/source/Inductance) leads to the general "**phasance**" concept: [http://fr.scribd.com/doc/71923015/The-Phasance-Concept](http://fr.scribd.com/doc/71923015/The-Phasance-Concept)

## General equation

The electrical [impedance](/source/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](/source/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)°, with n from 0 to 1. The case n = 1 describes an ideal capacitor while the case n = 0 describes a pure [resistor](/source/Resistor).

## 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"](https://www.sciencedirect.com/science/article/abs/pii/S0040609002005060). *Thin Solid Films*. **415** (1–2): 133–137. [Bibcode:2002TSF...415..133K](https://ui.adsabs.harvard.edu/abs/2002TSF...415..133K). [doi:10.1016/s0040-6090(02)00506-0](https://doi.org/10.1016/s0040-6090(02)00506-0). Retrieved 22 October 2012.

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