Difference between charge-voltage relations of ordinary and fractional capacitors

Eirik Brenner Marthins; Sverre Holm

doi:10.3390/fractalfract7110781

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arXiv · 2309.01701

Difference between charge-voltage relations of ordinary and fractional capacitors

Eirik Brenner Marthins·Sverre Holm

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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.

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Eirik Brenner Marthins, Sverre Holm. 2023-09-04. Difference between charge-voltage relations of ordinary and fractional capacitors. https://doi.org/10.3390/fractalfract7110781

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