Passive approximations of double‐exponent fractional‐order impedance functions

Abstract

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.

Model reduction of fractional impedance spectra for time–frequency analysis of batteries, fuel cells, and supercapacitors

“…These efforts can be summarized as follows: (i) A Padé approximant is the best approximation of a function near specific points by means of a rational function at a given order. Using this method, Kapoulea et al 54 obtained a rational transfer function for double‐exponent fractional‐order impedance models. (ii) With the inverse Laplace transform, the Warburg element can be transformed back into the time domain.…”

Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method

“…The importance and the very wide range of applications of the fractional models (described by the fractional derivatives) directed mathematicians and physicians to study the numerical and approximate solutions for fractional differential equations (FDEs) using many approximate techniques. We have a lot of examples for the applications of such kind of equations in our life as in fluid mechanics, [1][2][3] image processing, 4 biology, [5][6][7][8][9][10][11][12] engineering, [13][14][15] physics, [16][17][18][19][20] electrical circuits and filters, [21][22][23][24][25][26][27][28][29][30][31][32] and others. [33][34][35][36] Definition 1.…”