Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel
| Autor: | C. Calderón-Ramón, J. E. Escalante-Martínez, Mario Gonzalez-Lee, José Francisco Gómez-Aguilar, Luis J. Morales-Mendoza, M. Benavidez-Cruz |
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| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Article Subject
Laplace transform Applied Mathematics Physics QC1-999 Mathematical analysis General Physics and Astronomy Electrical element 02 engineering and technology 021001 nanoscience & nanotechnology 01 natural sciences Transfer function Fractional calculus law.invention Integer law Electrical network 0103 physical sciences Equivalent circuit 0210 nano-technology Representation (mathematics) 010301 acoustics Mathematics |
| Zdroj: | Advances in Mathematical Physics, Vol 2016 (2016) |
| ISSN: | 1687-9139 1687-9120 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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