Decoupling the magnitude and phase in a constant phase element

Abstract

• Modified CPE impedance using the complex function s α , β = j β ω α instead of s α = ( j ω ) α . • Phase and magnitude are decoupled from each other in modified CPE. • Modified CPE is suitable for fitting non-KK compliant spectral data. The success of fractional-order fractance (FOF) as a modeling tool in (photo)bio(electro)chemical systems can be readily gauged by the large body of research work that has been conducted over the past few years in terms of materials fabrication, building integer-order emulators of their behavior, as well as applications in filter design, controller design, modeling of energy storage devices and biomaterials. The impedance of FOF has the general form Z α ( s ) = k α s α where k α and α are real constant and s = j ω is the complex Laplace number. In this work, we investigate the possibility of decoupling the magnitude and phase properties of a FOF, and the application of this modified circuit element in the modeling of spectral electrochemical data. The proposed modification relies on the complex parametric function j β ω α = j β - α s α which can been viewed as a phase-shifted version of s α = ( j ω ) α by a β -dependent constant angle. This extra degree of freedom is expected to be useful in facilitating the modeling of more complex systems in which the classical FOF fails, and is here verified on the low-frequency response of a lithium-ion battery showing unstationary and/or nonlinear behavior.