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?s?, where C? is the CPE parameter and ? 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·v, is not valid for CPEs. In fact the relationship is nonlinear and can be expressed as q=C(v;C?,?)·v. 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. © 2020 Elsevier GmbH


Fouda M.E., Allagui A., Elwakil A.S., Das S., Psychalinos C., Radwan A.G.


Charge-voltage relation; Constant phase element; Fractional-order capacitor; Supercapacitor

Document Type



AEU – International Journal of Electronics and Communications, Vol. 117, Art. No. 153104, Doi: 10.1016/j.aeue.2020.153104

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