Difference between Charge–Voltage Relations of Ordinary and Fractional Capacitors
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The paper investigates the charge–voltage relations of ordinary capacitors and Constant Phase Elements (CPEs) in the context of time-varying capacitors. The authors conducted experiments involving a time-varying capacitor in parallel with a resistor and found that the response follows a power-law function rather than an exponential one, thus supporting the time-domain multiplication model. This result contrasts with the behaviour of CPEs, suggesting fundamental differences between ordinary capacitors and CPEs in time- and frequency-varying contexts.
The authors provide a clear explanation of the charge–voltage relations of ordinary capacitors and CPEs in the context of time-varying capacitors. This presents a novel contribution to the field. However, the following comments need to be addressed:
Ø Discuss the robustness of the proposed work using a hardware model.
Ø Validate your model under transient conditions.
Ø Compare the cost function involved in the proposed model with that of existing models. Discuss how the proposed model is economically suited for industrial applications.
Ø Include the objective of the proposed work in the abstract.
Ø Avoid citing references in the conclusion. Instead, discuss the outcomes of your proposed work in the conclusion.
Ø Ensure that the paper follows the template provided by the journal.
Author Response
See comments under heading "Reviewer1"
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors
In this paper, a comparison is made between ordinary capacitors and fractional capacitors. Through theoretical analysis and experimental research, the debate whether a time-domain multiplication or a time-domain convolution of capacitance and voltage determines charge is clarified. The result is that the time-domain multiplication is correct for ordinary capacitors and the time-domain convolution is correct for fractional-order capacitors.
There are several questions:
1. Is a fractional-order capacitor a constant phase element?
2. The variable capacitor circuit mimics a time-varying capacitor, what kind of the capacitor? An ordinary one or a fractional-order one? The α-values are calculated using (30), this shows that the capacitor is a fractional-order one. But later, the author states that the response is the power law of (9). Is the power law correct for ordinary capacitor? This is contradictory.
Author Response
See comments under heading "Reviewer2"
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for Authors
This work presents a theoretical and experimental frame for distinguishing the behaviour of a time-varying capacitor and a CPE element. I have many concerns about the theoretical part, detailed in the annotated PDF.
Comments for author File: Comments.pdf
Comments on the Quality of English Language
English is not fluent. Some improvements are needed to make it clearer
Author Response
See comments under heading "Reviewer3"
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Comments and Suggestions for Authors
The manuscript is acceptable.
Author Response
Thanks for finding the manuscript acceptable
Reviewer 3 Report
Comments and Suggestions for Authors
The manuscript has been improved in clarity and quality of the discussion. One last issue is related to equation (4), as marked into the PDF.
Comments for author File: Comments.pdf
Author Response
The reviewer’s question regarding Eq (4):
"Why not defining q(t) = \hat{v(t)} * c(t), so that c(t) remains in [F]?"
Due to the convolution, one of the terms in the equation has to have unit "per second", either the capacitance term with F/s or the voltage term with V/s. Thus one cannot avoid that either the capacitance or the voltage terms will have unusual units. However, letting the voltage term be in V/s rather than V, will create more problems than it solves.
The equation as it is (assuming F/s), is consistent with Eq (20) where the similarity with Eq (4) is remarked. Changing this, would therefore make Eq (4) inconsistent with the analysis of the CPE in Eqs (14)-(20). The CPE analysis is consistent with analyses elsewhere, and therefore we are reluctant to change Eq (4) according to the reviewer's suggestion.
