Passive approximations of double-exponent fractional-order impedance functions

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 Pade-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.

Automated summary

Double-exponent fractional-order impedance functions are crucial for modeling various biochemical materials and biological tissues. By selecting different exponents, well-known relaxation models can be obtained as special cases, and an integer-order Pade-based approximation of the Havriliak-Negami function is shown to be possible. Two application examples demonstrate the capabilities of this approach.