Difference between charge-voltage relations of ordinary and fractional capacitors

TL;DR

This paper investigates the charge-voltage relationship in ordinary and fractional capacitors, confirming that ordinary capacitors follow a multiplication model while fractional capacitors like CPEs differ fundamentally.

Contribution

It experimentally demonstrates the difference in charge-voltage relations between ordinary and fractional capacitors, clarifying the fundamental nature of CPEs.

Findings

Ordinary capacitors follow a multiplication model in charge-voltage relations.

Fractional capacitors like CPEs exhibit fundamentally different behavior.

Power-law response observed in fractional capacitors over multiple decades.

Abstract

In an ordinary time-varying capacitor, there is debate whether a time-domain multiplication or a time-domain convolution of capacitance and voltage determines charge. A time-varying capacitor in parallel with a resistor was implemented by a motor-driven potentiometer and op-amps. The response matched a power-law function over about two decades of time, and not an exponential, for several sets of parameters. This confirms the time-domain multiplication model. This result is the opposite of that obtained for a Constant Phase Element (CPE) in its common time- and frequency-varying capacitor interpretation. This demonstrates that a CPE is fundamentally different from an ordinary time- and frequency-varying capacitor.