{"title":"Time Domain Characterization of the Cole-Cole Dielectric Model.","authors":"Sverre Holm","doi":"10.2478/joeb-2020-0015","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":38125,"journal":{"name":"Journal of Electrical Bioimpedance","volume":" ","pages":"101-105"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7851980/pdf/","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Electrical Bioimpedance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/joeb-2020-0015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2020/1/1 0:00:00","PubModel":"eCollection","JCR":"Q3","JCRName":"Biochemistry, Genetics and Molecular Biology","Score":null,"Total":0}
引用次数: 7
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.
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