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Passive approximations of double‐exponent fractional‐order impedance functions
Author(s) -
Kapoulea Stavroula,
Psychalinos Costas,
Elwakil Ahmed S.
Publication year - 2021
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2946
Subject(s) - exponent , electrical impedance , fractional calculus , fractal , emulation , resistor , relaxation (psychology) , discretization , capacitor , mathematics , mathematical analysis , topology (electrical circuits) , physics , combinatorics , social psychology , psychology , philosophy , linguistics , quantum mechanics , voltage , economics , economic growth
Summary Double‐exponent fractional‐order impedance functions are important for modeling a wide range of biochemical materials and biological tissues. Through appropriate selection of the two exponents (fractional orders), the well‐known Havriliak–Negami, Cole–Cole, Cole–Davidson, and Debye relaxation models can be obtained as special cases. Here we show that an integer‐order Padé‐based approximation of the Havriliak–Negami function is possible to obtain and can be realized using appropriately configured Cauer/Foster resistor‐capacitor (RC) networks. Two application examples are subsequently examined: the emulation of the capacitive behavior in a polycrystalline solid electrolyte and the emulation of the impedance of four “fractal” vegetable types.