Origin of the Curie–von Schweidler law and the fractional capacitor from time-varying capacitance

Abstract

Most dielectrics of practical purpose exhibit memory and are described by the century-old Curie–von Schweidler law. Interestingly, the Curie–von Schweidler law is the motivation behind an unconventional circuit component called fractional capacitor which due to its power-law property is extensively used in the modeling of complex dielectric media. Unfortunately, the empirical nature of the Curie–von Schweidler law plagues the applications of the fractional capacitor. Here, we derive the Curie–von Schweidler law from a series combination of a resistor and a capacitor with a linear time-varying capacitance. This may possibly be its first derivation from physical principles. However, this required a modification of the classical charge–voltage relation of a capacitor to account for the time-varying capacitance. The limitation of the classical charge–voltage relation and its subsequent modification are justified using appropriate circuit modeling. Consequently, the parameters of the Curie–von Schweidler law and the fractional capacitor gain physical interpretation. The Debye response of dielectrics emerges naturally from the limiting case of the power-law response at short timescales. The obtained results are validated by matching them with the published experimental reports.