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

Authors: İzzet Cem Göknar
Journal: Mathematical Problems in Engineering
 (2018)

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## 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).


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## Body

## 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 t0-) [2].In case of a singular L (C) matrix,Theorem3 gives a necessary and sufficient condition for the energy at t0+ 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 inSection5of paper [1]; they can all be derived simply from the general formulation in [2].For a circuitN consisting of inductors (capacitors) only, anaugmented circuitNa is obtained fromN by including resistors intoN in such a way that all L cut-sets (all C loops) are destroyed and when all resistors are open (short) circuited the topology ofN is obtained.Theorem 4 in [2] shows that all L currents (C voltages) in Na tend to L currents (C voltages) inN as t→∞. Furthermore, the fact that the energy jump inN is equal to the energy consumed on the interval 0,∞ in the resistors of Na is demonstrated inTheorem5 [2], giving a physical interpretation to the energy jump inN.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.



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*Source: 1567645-2018-10-31.xml*