Nonlinear charge-voltage relationship in constant phase element

The constant phase element (CPE) or fractional-order capacitor is an electrical device that has an impedance of the form Z(s) = 1/C alpha S alpha, where C-alpha is the CPE parameter and alpha is a fractional dispersion coefficient of values between 0 and 1. Here we show that in the time-domain the classical linear charge-voltage relationship of ideal capacitors, q = C.nu, is not valid for CPEs. In fact the relationship is nonlinear and can be expressed as q = C(nu; C-alpha, alpha) .nu. We verify our findings using (i) circuit simulations of an integer-order emulator of a CPE, and (ii) experimental results from a commercial supercapacitor as well as an in-house fabricated device based on carbon film materials. (C) 2020 Elsevier GmbH. All rights reserved.