We thank Prof. I. C. Göknar [
We hope this letter could better emphasize both our contributions and their possible relationship with his work. We now elaborate a comprehensive answer to the points raised.
This issue of existing contributions on this topic had been already pointed out by a reviewer during the reviewing process. For this reason, we already acknowledged those contributions that developed relevant and similar conclusions in energy quantification such as
We are always happy to quote the work of other authors in similar topics as a way to enrich the literature review. In this case, we were unfortunately unaware of Prof. Goknar’s contribution published in 1972, perhaps because he deals with electrical circuits with jumps, rather than resonant switched capacitor converters
It is also important to point out that we cited one of Prof. Goknar’s more recent contributions, which we believe is much closer to the topic under study:
Different from the 1972’s contribution,
We must say that even now that we are aware of the existence of the aforementioned 1972’s contribution, we still believe that his contribution
Since there are several approaches to energy quantification of switching electrical circuits, as also pointed out by Prof. Göknar, it had already been necessary to point out the contributions in our manuscript, to prove that other important novelties that deserve publication were also proposed.
The main purposes of our manuscript, rather than finding an alternative route to develop similar results or drawing equivalent conclusions, consist in introducing a modeling framework for switched capacitor and resonant converters. This framework is the pivotal figure of a systematic analysis that involves quadratic functionals. In particular, we introduce polynomial algebra tools based on the calculus of showing the relationship between the energy transfer mechanism between switched capacitor and resonant switched capacitor structures. Please see Prop. 3, p. 6, and Lemma 1, p. 7. Please note that the circumvention of energy losses associated with redistribution of charge not only is associated with the fact that an inductor is included in the loop or that parasitic resistances are neglected, but also follows from a zero current switching technique: e.g., if the switch is arbitrarily open when the resonant inductor is charged, energy losses will occur and, moreover, if the switch occurs exactly when the inductor reaches its maximum voltage level, the loss will be equal to that of its pure SC counterpart. This paper aims at clarifying these type issues; introducing a mathematical formula to compute resonant inductances on the basis of maximum peak current specifications, rather than resorting to trial and error designs (see, e.g., providing a relative loss factor to characterize the efficiency of the converters. Please see equation (21), p. 7.
Given the reasons pointed out above, regarding the relevance of the 1972’s contribution with respect to our particular publication “Storage and Dissipation Limits in Resonant Switched-Capacitor Converters”, we beg to disagree with the suggestion of using a different approach to obtain the same results. The reasons are the following: Our approach is also general and exemplified using simple (resonant) switched capacitor cells only for illustration purposes, since (resonant) switched capacitor converters are usually constructed in a modular way using such cells. Changing our approach (based on switched linear differential systems and quadratic differential forms, as a Following the scope of the MPE Journal, we developed a mathematical framework to provide practical solutions to engineering problems, in particular, modeling and design specifications. Consequently, although one can find an alternative mathematical route using the 1972’s contribution, one would need to develop a systematic modeling technique for power converters and a way to associate an efficient parametric exploration with performance and benchmarking specifications, as we illustrated in our paper.
We conclude that Prof. Göknar’s contribution can be used as an alternative route to develop some of our technical results that though original, they are not the main contribution in our published paper. The 1972’s contribution is not about resonant switched capacitor converters, but electrical circuits with jumps. Although concepts such as energy quantification of capacitors and inductors can be expressed in mathematical terms in both (his and ours) settings, there is still a considerable amount of nontrivial work to do based on such contribution in order to involve the technicalities of power converters. We already cited Prof. Göknar’s contribution (see Accepting to change our mathematical framework by the one in the 1972 paper would leave aside the main contribution in our manuscript, which is the introduction of a switched linear differential system approach to model and study the overall properties of power converters. We believe that, though interesting, showing that using an alternative route to develop some of our results would immediately raise the critiques that we faced during the reviewing process, since doing so was not considered as a publishable contribution. Our proposed modeling framework, the developed power converter analyses, and design tools were, on the other hand, considered as such.
The authors declare that they have no conflicts of interest.