Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 1567645, 2 pages
https://doi.org/10.1155/2018/1567645

Letter to the Editor

Comment on “Storage and Dissipation Limits in Resonant Switched-Capacitor Converters”

İzzet Cem Göknar

EE Department, Işık University, Şile, Istanbul 34980, Turkey

Correspondence should be addressed to İzzet Cem Göknar; cem.goknar@isikun.edu.tr

Received 2 February 2018; Accepted 18 July 2018; Published 31 October 2018

Academic Editor: J.-C. Cortés

Copyright © 2018 İzzet Cem Göknar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The purpose of this note is (i) to point to a reference missing in the paper (Mayo-Maldonado et al., 2018) and (ii) to show that some of its content is covered in a more general setting by the results in that reference (Göknar, 1972).

1. Introduction

As explained in the sequel, some of the results developed for specific circuits in Sections 5 and 7 of the paper given in [1] can simply be obtained as applications of results in [2] presented for arbitrary passive circuits containing inductor only cut-sets and/or capacitor only loops.

2. Comments

With Theorem 1 (typo, first Theorem 2 should be Theorem 1) in [2], a measure for the jump in energy is given for a general circuit consisting of inductors (L) and/or capacitors (C) at a time of discontinuity and shown to be positive.

With Theorem 2 for a nonsingular L (C) matrix, it is shown that the necessary and sufficient condition for the jump in energy to be zero is that L currents (C voltages) satisfy Kirchhoff Laws before the jump (at ) [2].

In case of a singular L (C) matrix, Theorem 3 gives a necessary and sufficient condition for the energy at to be zero showing how essential is the nonsingularity of L (C) matrix.

Thus there is no need for all the lengthy derivations for a circuit consisting of two capacitors in Section 5 of paper [1]; they can all be derived simply from the general formulation in [2].

For a circuit N consisting of inductors (capacitors) only, an augmented circuit is obtained from N by including resistors into N in such a way that all L cut-sets (all C loops) are destroyed and when all resistors are open (short) circuited the topology of N is obtained.

Theorem 4 in [2] shows that all L currents (C voltages) in tend to L currents (C voltages) in N as . Furthermore, the fact that the energy jump in N is equal to the energy consumed on the interval in the resistors of is demonstrated in Theorem 5 [2], giving a physical interpretation to the energy jump in N.

It is expected that results in Section 7 of paper [1] can profit from Theorems 4 and 5 of [2].

3. Conclusions

Referring to paper [2] will do justice to it and profiting from its results may shorten the paper [1]. Also, it is quite possible that these results open new horizons for developing further outcomes.

Conflicts of Interest

The author declares that he has no conflicts of interest.

References

J. C. Mayo-Maldonado, T. M. Maupong, J. E. Valdez-Reséndiz, and J. C. Rosas-Caro, “Storage and Dissipation Limits in Resonant Switched-Capacitor Converters,” Mathematical Problems in Engineering, vol. 2018, Article ID 1054179, 10 pages, 2018.

I. C. Göknar, “Conservation of Energy at Initial Time for Passive RLCM Network,” lEEE Transactıons on Circuit Theory, vol. 19, pp. 365–367, 1972.