Analysis of polarization dynamics by singularity decomposition method |
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Authors: | H Sun A Charef Y Y Tsao B Onaral |
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Institution: | (1) Biomedical Engineering and Science Institute, Drexel University, 19104 Philadelphia, PA |
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Abstract: | The driving point immittance (impedance or admittance) function is commonly used in electrical characterization of polarized
materials and interfaces. The immittance function typically attenuates following a power function dependence on frequency.
This fact has been recognized as a macroscopic dynamical property manifested by strongly interacting dielectric, viscoelastic
and magnetic materials and interfaces between different conducting substances. Linear interfacial polarization processes which
occur at metal electrode-electrolyte interfaces have been represented by the Fractional Power Pole FPP] function in single
or multiple stages. The FPP function is referred to as the Davidson-Cole function in the dielectrics literature. A related
function widely used in mathematical modeling of dielectric and viscoelastic polarization dynamics is the Cole-Cole function.
The fractional power factor which parametrizes the FPP or the Davidson-Cole function has been shown earlier to equal the logarithmic
ratio of the locations of the pole-zero singularities. In this paper we first review a modified form of the singularity decomposition
of the FPP function accomplished within a prescribed error range. The distribution spectrum and the corresponding simulation
by a cascadeR-C network, as opposed to the synthesis by a ladderR-C network, are readily obtained as the next step in the simulation. The method is then applied to decompose the Cole-Cole function;
the pole-zero placement of the singularity function is determined and the equivalent cascadeR-C network is synthesized. |
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Keywords: | Fractal dynamics Self-similarity Power law attenuation |
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