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. 2020 Dec 31;11(1):101-105.
doi: 10.2478/joeb-2020-0015. eCollection 2020 Jan.

Time Domain Characterization of the Cole-Cole Dielectric Model

Sverre Holm  1
Affiliations

Time Domain Characterization of the Cole-Cole Dielectric Model

Sverre Holm. J Electr Bioimpedance. .

Abstract

The Cole-Cole model for a dielectric is a generalization of the Debye relaxation model. The most familiar form is in the frequency domain and this manifests itself in a frequency dependent impedance. Dielectrics may also be characterized in the time domain by means of the current and charge responses to a voltage step, called response and relaxation functions respectively. For the Debye model they are both exponentials while in the Cole-Cole model they are expressed by a generalization of the exponential, the Mittag-Leffler function. Its asymptotes are just as interesting and correspond to the Curie-von Schweidler current response which is known from real-life capacitors and the Kohlrausch stretched exponential charge response.

Keywords: Cole-Cole; Constant phase element; Curie-von Schweidler; Kohlrausch.

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Conflict of interest statement

Conflict of interest The author states no conflict of interest.

Figures

Figure 1
Figure 1
The Cole-Cole response function or current response to a step voltage and its approximations for α = 0.7.
Figure 2
Figure 2
The Cole-Cole relaxation function which is related to the charge response to a step voltage, and its approximations for α = 0.7.
See this image and copyright information in PMC

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