Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel
We present an alternative representation of integer and fractional electrical elements in the Laplace domain for modeling electrochemical systems represented by equivalent electrical circuits. The fractional derivatives considered are of Caputo and Caputo-Fabrizio type. This representation includes...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/9720181 |
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| author | J. F. Gómez-Aguilar J. E. Escalante-Martínez C. Calderón-Ramón L. J. Morales-Mendoza M. Benavidez-Cruz M. Gonzalez-Lee |
| author_facet | J. F. Gómez-Aguilar J. E. Escalante-Martínez C. Calderón-Ramón L. J. Morales-Mendoza M. Benavidez-Cruz M. Gonzalez-Lee |
| author_sort | J. F. Gómez-Aguilar |
| collection | DOAJ |
| description | We present an alternative representation of integer and fractional electrical elements in the Laplace domain for modeling electrochemical systems represented by equivalent electrical circuits. The fractional derivatives considered are of Caputo and Caputo-Fabrizio type. This representation includes distributed elements of the Cole model type. In addition to maintaining consistency in adjusted electrical parameters, a detailed methodology is proposed to build the equivalent circuits. Illustrative examples are given and the Nyquist and Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. The advantage of our representation appears according to the comparison between our model and models presented in the paper, which are not physically acceptable due to the dimensional incompatibility. The Markovian nature of the models is recovered when the order of the fractional derivatives is equal to 1. |
| format | Article |
| id | doaj-art-a223c80a340a47429368ab97facdb149 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-a223c80a340a47429368ab97facdb1492025-02-03T05:51:47ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/97201819720181Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular KernelJ. F. Gómez-Aguilar0J. E. Escalante-Martínez1C. Calderón-Ramón2L. J. Morales-Mendoza3M. Benavidez-Cruz4M. Gonzalez-Lee5CONACYT-Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Colonia Palmira, 62490 Cuernavaca, MOR, MexicoFacultad de Ingeniería Mecánica y Eléctrica, Universidad Veracruzana, Avenida Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, MexicoFacultad de Ingeniería Mecánica y Eléctrica, Universidad Veracruzana, Avenida Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, MexicoFacultad de Ingeniería Electrónica y Comunicaciones, Universidad Veracruzana, Avenida Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, MexicoFacultad de Ingeniería Mecánica y Eléctrica, Universidad Veracruzana, Avenida Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, MexicoFacultad de Ingeniería Electrónica y Comunicaciones, Universidad Veracruzana, Avenida Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, MexicoWe present an alternative representation of integer and fractional electrical elements in the Laplace domain for modeling electrochemical systems represented by equivalent electrical circuits. The fractional derivatives considered are of Caputo and Caputo-Fabrizio type. This representation includes distributed elements of the Cole model type. In addition to maintaining consistency in adjusted electrical parameters, a detailed methodology is proposed to build the equivalent circuits. Illustrative examples are given and the Nyquist and Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. The advantage of our representation appears according to the comparison between our model and models presented in the paper, which are not physically acceptable due to the dimensional incompatibility. The Markovian nature of the models is recovered when the order of the fractional derivatives is equal to 1.http://dx.doi.org/10.1155/2016/9720181 |
| spellingShingle | J. F. Gómez-Aguilar J. E. Escalante-Martínez C. Calderón-Ramón L. J. Morales-Mendoza M. Benavidez-Cruz M. Gonzalez-Lee Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel Advances in Mathematical Physics |
| title | Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel |
| title_full | Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel |
| title_fullStr | Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel |
| title_full_unstemmed | Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel |
| title_short | Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel |
| title_sort | equivalent circuits applied in electrochemical impedance spectroscopy and fractional derivatives with and without singular kernel |
| url | http://dx.doi.org/10.1155/2016/9720181 |
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