IEEJ Journal of Industry ApplicationsVol.10 No.6 pp.682–687 DOI: 10.1541/ieejjia.21000624

Paper

Analysis of Switching Frequency Characteristics of Single-switch HighStep-up DC–DC Converter with Three-winding Coupled Inductor

Masataka Minami∗a)Member, Genki Hase∗ Non-member

(Manuscript received Jan. 18, 2021, revised March 16, 2021)J-STAGE Advance published date : April 23, 2021

Recently, high step-up DC–DC converters have been widely used in several applications. Previously, we proposeda novel high step-up DC–DC converter, which consisted of a single-switch and a three-winding coupled inductor. Ourprevious report only highlighted the CCM operation and steady state principle of the proposed converter. This studyaimed to investigate the switching frequency characteristics including the CCM and DCM operations of the proposedconverter.

Keywords: high step-up DC–DC converter, three-winding coupled inductor, single-switch

1. Introduction

A photovoltaic (PV) source is widely used in several ap-plications. However, as the output voltage of the PV sourceis relatively low, DC–DC converters in Fig. 1 are required toboost the low PV voltage to a high voltage for grid connec-tion owing to their high step-up gain and high efficiency (2).

Ideally, a conventional boost converter can achieve highstep-up gain with an extreme duty ratio. In practice, thestep-up gain is limited by effects of the active switch, thediode, and the parasitic resistor of the inductor and capacitor.In addition, an extreme duty ratio causes a serious reverse-recovery problem and conduction losses. Qun Zhao and FredC. Lee (3) added an additional diode and a small capacitor tothe boost converter and introduced a family of DC–DC con-verters with a high step-up gain and high efficiency. Sincethen, several studies on converters have reported about circuittopologies, control methods, design, and optimization (4)–(8).However, DC–DC converters become complicated and thedrive circuits become large if the converters contain sev-eral switches. Thus, we previously proposed a novel highstep-up DC–DC converter that has only one active switch (9).The proposed high step-up DC–DC converter based on theconverter (10) combines the Cockcroft-Walton (CW) circuit (11).In addition, it uses a three-winding coupled inductor. Al-though previous studies (12)–(15) proposed different topologieswith the single-switch and three-winding coupled inductor,the proposed converter achieves a higher step-up gain thanthat obtained in other studies. Therefore, the proposed highstep-up DC–DC converter can achieve the highest boost ra-tio among previously proposed converters in the CCM operation (9).

This paper is based on Reference (1), which published in theICEMS-Hamamatsu (2020) c©2020 IEEJ.

a) Correspondence to: Masataka Minami. Email: minami@kobe-kosen.ac.jp∗ Kobe City College of Technology

8-3, Gakuenhigashi, Nishi, Kobe 651-2194, Japan

Fig. 1. Diagram of grid-connected PV system

Our previous study (9) revealed only the CCM operationof the proposed high step-up DC–DC converter at onlyone switching frequency. Our subsequent study (16) revealedonly the DCM operation of the proposed converter at onlyone switching frequency. The present study investigatedthe switching frequency characteristics of the proposed highstep-up DC–DC converter. In addition, the experimental re-sults show the DCM and CCM operations.

The remainder of this paper is organized as follows. Sec-tion 2 illustrates a circuit configuration and describes the op-erating principle of CCM and DCM in the proposed highstep-up DC–DC converter. In particular, the section demon-strates that the boost ratio of the proposed high step-up DC–DC converter is the highest compared to other circuit topolo-gies (12)–(15) in the CCM operation. In addition, an equation forthe boost ratio of the DCM is derived, and the BCM opera-tion, which is the boundary between the DCM and CCM, isdiscussed. Section 3 presents the theoretical switching fre-quency characteristics of the boost ratio in the proposed highstep-up DC–DC converter for each duty ratio. Numerical andexperimental verifications are presented in Section 4. Section5 summarizes the study and the main findings.

2. Proposed High Step-up DC–DC Converter

This section presents the circuit configuration and opera-tions of the proposed high step-up DC–DC converter. Thetheoretical switching frequency characteristics are discussedbased on the circuit operations.

c© 2021 The Institute of Electrical Engineers of Japan. 682

High Step-up DC–DC Con with 3-winding Inductor（Masataka Minami et al.）

Fig. 2. Proposed high step-up DC–DC converter (9)

2.1 Circuit Configuration Figure 2 shows the pro-posed high step-up DC–DC converter (9). The proposed highstep-up DC–DC converter consists of a power supply Vin; anactive switch S ; a three-winding coupled inductor with wind-ings L1, L2, and L3; five diodes D1, · · · ,D5; six capacitorsC1, · · · ,C5 and Co; and a load R. Here, the coupled inductorturns are N1, N2, and N3, respectively, and the turn ratios aredefined as ni = Ni/N1, i ∈ {1, 2, 3}†.

The active switch S and the three-winding coupled induc-tor with windings L1, L2, and L3 are inserted into the 3-stageCW circuit of the converter. Each time the input voltage po-larity changes owing to the active switch S , the diodes turnON and OFF alternately. Consequently, the proposed highstep-up DC–DC converter generates a high voltage due to themulti-stage connection of capacitors.

The following conditions are assumed to simplify the cir-cuit analysis for CCM, DCM, and BCM operations:• The active switch S and the diodes D1, · · · ,D5 work ide-

ally.•All capacitors, C1, · · · ,C5 and Co, are sufficiently large.

Thus, all voltages of capacitors: VC1, · · · ,VC5, and Vout

are considered as constant voltages.• Equivalent series resistances (ESRs) of all capacitors, all

diodes, and the three-winding inductor are ignored.• The leakage inductors are also ignored. Thus, the fol-

lowing equation holds:v

jLi = niv

jL1, i ∈ {1, 2, 3}, j ∈ M, · · · · · · · · · · · (1)

where M denotes a mode set (explained in subsections2.2 and 2.3).• The turns are similar: N1 = N2 = N3. Thus, the turn

ratios become n2 = n3 = 1.2.2 CCM Operation This subsection explains the

CCM operation of the proposed high step-up DC–DC con-verter. The relationship of all voltages of capacitors is usedto derive the boost ratio of the proposed high step-up DC–DC converter in the CCM operation. Our previous paper (9)

had already reported the detailed description of the expres-sion transformation.

To simplify the analysis of the CCM operation, only twomodes are considered, although the proposed high step-upDC–DC converter in the CCM operation has multiple modes.One mode is the ON mode of the active switch S , whereasthe other mode is the OFF mode. Then, the mode set M is{on, off | at CCM} in (1).

When the active switch S is turned on, the diodes D2 andD4 are turned on while the diodes D1, D3, and D5 are turned

† n1 = N1/N1 = 1

Table 1. Comparison between high step-up DC–DCconverters using single-switch and three-winding cou-pled inductor in terms of boost ratio in CCM operation

Converter Type αCCM = Vout/Vin

Converter in (12) (2 − d) + dn2 + (1 − d)n3

1 − d

Converter in (13) 1 + n2 + dn3

1 − d

Converter in (14) (2 − d) + (1 − d)n2 + n3

1 − d

Converter in (15) 2 + n2 + n3

1 − d

Proposed converter3 + 2n2 + n3

1 − d

Fig. 3. Comparison between high step-up DC–DC con-verters using single-switch and three-winding coupledinductor in terms of boost ratio in CCM operation atn2 = n3 = 1

off. Capacitor C2 is charged to VC2 = VC1 + vonL2 from capaci-

tor C1 and inductor L2. Similarly, capacitor C4 is charged toVC4 = VC3 + v

onL3 from capacitor C3 and inductor L3.

Meanwhile, when the active switch S is turned off, diodesD2 and D4 are turned off while diodes D1, D3, and D5 areturned on. Capacitor C3 is charged to VC3 = VC2 − voffL2from capacitor C2 and inductor L2. Similarly, capacitor C5

is charged to VC5 = VC4 − voffL3 from capacitor C4 and inductorL3.

In addition, the voltage of capacitor C1 is expressed asVC1 = (1/(1 − d))Vin because a part of the circuit contain-ing input Vin, inductor L1, active switch S , diode D1, andcapacitor C1 is regarded as the general boost converter.

The relationship of all voltages of capacitors and (1) yieldsthe output voltage Vout = VC1 + VC3 + VC5. The boost ratioof the proposed high step-up DC–DC converter in the CCMoperation αCCM is expressed as follows:

αCCM =3 + 2n2 + n3

1 − d. · · · · · · · · · · · · · · · · · · · · · · · · · · · (2)

The (2) shows that the boost ratio of the proposed highstep-up DC–DC converter in the CCM operation αCCM is in-dependent of the switching frequency f .

Table 1 compares the boost ratio in the CCM operation ofconventional converters (12)–(15) with that of the proposed con-verter. Consequently, the proposed high step-up DC–DCconverter boosts higher than conventional converters (12)–(15).Figure 3 illustrates the boost ratio in the CCM operation fromTable 1 at n2 = n3 = 1.2.3 DCM Operation This subsection explains the

DCM operation of the proposed high step-up DC–DC con-verter. Similar to the previous subsection, the relationship of

683 IEEJ Journal IA, Vol.10, No.6, 2021

High Step-up DC–DC Con with 3-winding Inductor（Masataka Minami et al.）

Fig. 4. Current waveform of the three-winding coupledinductor in DCM operation

all voltages of capacitors is used to derive the boost ratio ofthe proposed high step-up DC–DC converter in the DCM op-eration αDCM. Our previous paper (16) had already reported anapproximate description of the expression transformation. Inthis subsection, we derive the boost ratio αDCM in detail.

To simplify the analysis of the DCM operation, only threemodes are considered, although the proposed high step-upDC–DC converter in the DCM operation has multiple modes.One mode is the ON mode of the active switch S , whereas theother modes are the OFF1 and OFF2 modes. Therefore, themode setM is {on, off1, off2 | at the DCM} in (1).

Figure 4 illustrates the current waveform of the three-winding coupled inductor. Here, the inductor current iL de-notes iL1 + iL2 + iL3 because of n2 = n3 = 1.

In the ON mode, diodes D2 and D4 are turned on whilediodes D1, D3, D5 are turned off. Capacitor C2 is charged toVC2 = VC1+v

onL2 from capacitor C1 and inductor L2. Similarly,

capacitor C4 is charged to VC4 = VC3 + vonL3 from capacitor C3

and inductor L3.Second, in the OFF1 mode, diodes D2 and D4 are turned

off while diodes D1, D3, and D5 are turned on. Capacitor C3

is charged to VC3 = VC2 − voff1L2 from capacitor C2 and induc-

tor L2. Similarly, capacitor C5 is charged to VC5 = VC4 − voff1L3

from capacitor C4 and inductor L3. When the inductor cur-rent iL = iL1+iL2+iL3 becomes zero in Fig. 4, the OFF1 modeends and changes to the OFF2 mode.

Finally, in the OFF2 mode, all diodes D1, · · · ,D5 are turnedoff. The OFF2 mode has no inductor current. Then, voff2

Li = 0,i ∈ {1, 2, 3}.

The following operations are summarized. Because theaverage value of the inductor voltage is zero, the followingequation holds:

1T

{∫ dT

0von

L1 dt +∫ dT+dLT

dTvoff1

L1 dt +∫ T

dT+dLTvoff2

L1 dt

}= 0

dVin − dL(VC1 − Vin) + 0 = 0 · · · · · · · · · · · · · · · · · · · · (3)

Therefore, the voltage of capacitor C1 is expressed as VC1 =

(1 + d/dL)Vin from (3). The voltage of the other capac-itor becomes VC2 = VC1 + v

onL2 = VC1 + n2 Vin, VC3 =

VC2 − voff1L2 = (VC1 + n2 Vin) + n2(VC1 − Vin) = (1 + n2)VC1,

VC4 = VC3+vonL3 = (1+n2)VC1+n3 Vin, and VC5 = VC4−voff1

L3 =

(1 + n2)VC1 + n3 Vin + n3(VC1 − Vin) = (1 + n2 + n3)VC1.The relationship of the capacitor voltage is used to derive

the output voltage as follows: Vout = VC1 + VC3 + VC5 =

(1 + d/dL)(3 + 2n2 + n3)Vin. Solving this equation for dL

yields the following equation:

dL =(3 + 2n2 + n3)Vin

Vout − (3 + 2n2 + n3)Vind · · · · · · · · · · · · · · · · · · (4)

Here, we focus on D5. A linear current iL3 flows throughD5 at OFF1, and the average value of the current is the loadcurrent Vout/R:

1T

(12

ILmp

2 + n2 + n3dLT

)=

Vout

R

12

ILmp

2+n2+n3

d(3+2n2+n3)Vin

Vout−(3+2n2+n3)Vin=

Vout

R· · · · · · · · (5)

The current distribution at the moment of turn-off is basedon the flux conservation law: ILmp = Vind/(Lm f ), where Lm

denotes an exciting impedance of the three-winding coupledinductor. Additionally, the normalized inductor time constantis defined as τLm = Lm f /R. In addition, the boost ratio of theproposed high step-up DC–DC converter in the DCM opera-tion αDCM is Vout/Vin. From (5), the following equations arederived as follows:

d2(3 + 2n2 + n3)2(2 + n2 + n3){αDCM − (3 + 2n2 + n3)} = αDCMτLm

α2DCM − 2 · 3 + 2n2 + n3

2αDCM − d2(3 + 2n2 + n3)

2(2 + n2 + n3)τLm

= 0

From these equations, the boost ratio of the proposed highstep-up DC–DC converter in the DCM operation αDCM is ex-pressed as follows:

αDCM =3 + 2n2 + n3

2

+

√(3 + 2n2 + n3)2

4+

d2(3 + 2n2 + n3)2(2 + n2 + n3)τLm

,

· · · · · · · · · · · · · · · · · · · (6)

(6) shows that the boost ratio of the proposed high step-upDC–DC converter in the DCM operation αDCM depends onnot only the duty ratio d but also on the switching frequencyf , exciting impedance of the three-winding coupled inductorLm, and load R.2.4 BCM Operation This subsection derives the

BCM operation and its condition. The previous subsections2.2 and 2.3 expressed the boost ratios: αCCM and αDCM.In the BCM mode, the boost ratio of the BCM becomesαBCM = αCCM = αDCM because the BCM mode is the bound-ary between CCM and DCM. (2) and (6) lead to the BCMnormalized inductor time constant τLmBCM as follows:

τLmBCM =d(1 − d)2

2(3 + 2n2 + n3)(2 + n2 + n3), · · · · · · · · · (7)

where τLmBCM is defined as (Lm fBCM)/R. Here, fBCM is aBCM switching frequency as follows:

fBCM =d(1 − d)2R

2Lm(3 + 2n2 + n3)(2 + n2 + n3). · · · · · · · · · (8)

The BCM switching frequency fBCM is the boundary be-tween CCM and DCM in the switching frequency character-istics.

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High Step-up DC–DC Con with 3-winding Inductor（Masataka Minami et al.）

Fig. 5. Switching frequency characteristics of theoreti-cal boost ratio for each duty ratio

3. Theoretical Switching Frequency Characteris-tics

In this section, we present the switching frequency charac-teristics of the theoretical boost ratio. In the previous section2, we derived the theoretical boost ratios of the proposed highstep-up DC–DC converters αCCM and αDCM. In this section,the parameters are set to Lm = 82.6 μH and R = 1 kΩ. Here,the inductor is designed as 100 μH to achieve CCM opera-tion at about 50 kHz, which is half of the available frequencyrange. Then, the inductor parameter was the measured value.The optimal design of the inductor, e.g. (17)–(19), is left for thefuture work. In addition, as an experiment in later section toverify the principle of the proposed converter, the load resis-tance was set to 1 kΩ at several tens of watts. The future workis left evaluating the characteristics of the proposed converterby changing the load.

Figure 5 describes the switching frequency characteristicsof the theoretical boost ratio for each duty ratio d. The hor-izontal axis represents the switching frequency f , whereasthe vertical axis represents the boost ratios αCCM and αDCM.The black broken line represents the BCM operation. Thefrequency higher than the black broken line is the CCM op-erating region, whereas the frequency lower than the blackbroken line is the DCM operating region. In addition, theduty ratio d becomes higher or lower, and the CCM region islarge. The boost ratio significantly changes when the duty ra-tio d is varied. From (8), the BCM switching frequency fBCM

depends on the load resistance R and the excited impedanceLm: fBCM ∝ R/Lm. Therefore, the black broken line in Fig. 5become higher as Lm becomes smaller or R becomes higher.The result of (8) is useful for designing the proposed con-verter to achieve the desired behavior: CCM or DCM opera-tions.

Consequently, the proposed high step-up DC–DC con-verter has a 10 times boost ratio at the CCM operation ind ≥ 0.4. The proposed high step-up DC–DC converter caneasily achieve a 10 times higher boost ratio.

Based on these results, the next section presents results ford = 0.5 through the numerical simulation and experiment ofthe prototype.

4. Numerical and Experimental Results

This section analyzes the numerical and experimental

results of the proposed high step-up DC–DC converter. First,the numerical and experimental conditions are set. Next, theswitching frequency f characteristics of the output voltageVout and boost ratios αCCM and αDCM are used to demon-strate the validity of the theoretical results (Fig. 5) in the pre-vious section 3. Finally, by measuring the current and volt-age waveforms of the changing behavior in DCM and CCMat each switching frequency, it is clarified that the theoreticalderivation process is appropriate.4.1 Conditions To analyze the proposed high step-up

DC–DC converter, the following conditions are set:• Input DC voltage Vin = 20 V• Switching frequency f : from 10 to 100 kHz•Duty ratio d = 0.5: it implies no control.• Three-winding coupled inductor: L1 = 88.2 μH, L2 =

87.3 μH, L3 = 87.5 μH, and ESRs are 1.8 mΩ• Coupled coefficients of the three-winding coupled in-

ductor: k12 = 0.952, k23 = 0.961, k31 = 0.914• Capacitors C1, · · · ,C5 = 30 μF, Co = 590 μF†• Load resistor R = 1 kΩ•Active switch S and diodes D1, · · · ,D5: ideal for numer-

ical simulation, that is, no on-resistor, no forward volt-age, and no switching delay time.•Active switch S and diodes D1, · · · ,D5: SiC MOS-

FET(SCT2120AF, 650 V, 29 A, ROHM Co. Ltd.) andSi SBD(DSS2x101-02A, 200 V, 100 A, IXYS Corpora-tion) in the experimental system††• Circuit Simulator: PLECS 4.3.6

Here, the three-winding coupled inductor parameters weremeasured in advance.

In addition, the following experimental equipment are usedfor the experimental prototype system.• Input power supply: PWR400L (Kikusui Electronics

Corporation)•Digital oscilloscope: WaveRunner 204MXi (Teledyne

LeCroy Corporation)• Three-winding coupled inductor: custom-made product

(Union Electric Co., Ltd.)•Voltage and current probes: PP011-1 (input voltage),

PPE2 kV (output voltage), and CP030 (inductor current)(Teledyne LeCroy Corporation)

4.2 Switching Frequency Characteristics of OutputVoltage and Boost Ratio Figure 6 shows the switchingfrequency characteristics of the output voltage Vout and boostratios αCCM and αDCM in the proposed high step-up DC–DC converter. The horizontal axis represents the switchingfrequency f , whereas the vertical axis represents the outputvoltage Vout and the boost ratios αCCM and αDCM. Figure 6includes the theoretical results from the previous section 3(pink line), numerical results (red line), and experimental re-sults (blue points). Although the numerical and experimentalresults are lower than the theoretical results, they exhibit analmost similar trend.

† The value of capacitors has a significant effect on the operating wave-forms. The previous experiments (1) used the 2.2 μF for the capacitorsC1, · · · ,C5 and 10 μF for the capacitor Co. At that time, the output voltagewas almost unaffected, but the operating waveforms of the inductor currentare affected. Then, we increase the value of capacitors in this paper.†† This paper experiments with a 20 V input to verify the principle of the

proposed converter, but this study has chosen this design because we plan toincrease the input to several hundred V in the future.

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High Step-up DC–DC Con with 3-winding Inductor（Masataka Minami et al.）

Fig. 6. Vout- f characteristics under R = 1 kΩ. Pink line,red line, and blue points respectively indicate the theoret-ical, numerical, and experimental results

In the experimental results, the output voltage Vout is ap-proximately 220 V between 16 kHz ≤ f ≤ 100 kHz. Theproposed high step-up DC–DC converter works in the CCMmode in this region. The theoretical output voltage shouldbecome 240 V, but the experimental result is about 220 V.Since the purpose of proposed converter is to boost the volt-age more than 10 times, the purpose itself is achieved.

The output voltage Vout increases as the switching fre-quency f decreases under 20 kHz because the operationchanges from the CCM mode to DCM mode. In compari-son with the BCM switching frequency fBCM, the theoreticalBCM switching frequency is 31.51 kHz; the numerical re-sult is 22 kHz, and the experimental result is approximately16 kHz. These differences may have been obtained becausethe leakage inductance, ESRs, and forward voltages of thediodes, and the on-resistor were not considered when deter-mining the theoretical relationship equation. Although thereare some differences, the results are roughly the same.4.3 Voltage and Current Waveforms in DCM and

CCM Operations Figures 7, 8, 9 show the measuredvoltage and current waveforms: Vout, iL1, iL2, iL3, and iL =iL1 + iL2 + iL3, of the proposed high step-up DC–DC con-verter in the experimental prototype system at d = 0.3, 0.5,and 0.7. Figures 7(a), 8(a), 9(a) and 7(b), 8(b), 9(b) respec-tively illustrate the DCM and CCM operations at the switch-ing frequency f = 10 kHz and 100 kHz. Figures 6 and 7, 8,9 confirm that the proposed high step-up DC–DC converterworks effectively in the DCM and CCM operations. In par-ticular, the inductor current iL waveforms indicate the DCMand CCM operations in Figs. 7, 8, 9.

In addition, the output voltage Vout includes a surge be-cause the proposed converter uses a hard switching in theactive switch. Generally, increasing the value of capacitorCo will suppress voltage fluctuations. However, since thesurge contains high frequency, it is not enough to increasethe capacitance. The larger the capacitance, the worse the fre-quency response of the capacitor, so there is concern that thecapacitor will not be able to fully suppress surges. The opti-mization of the value of capacitors is left for a future work.

5. Summary

This study investigated the switching frequency charac-teristics of our proposed high step-up DC–DC converter.The CCM, DCM, and BCM operations were derived, and

(a) DCM at f = 10 kHz

(b) CCM at f = 100 kHz

Fig. 7. Waveforms of output voltage and inductor cur-rent. iL = iL1 + iL2 + iL3 at d = 0.3

(a) DCM at f = 10 kHz

(b) CCM at f = 100 kHz

Fig. 8. Waveforms of output voltage and inductor cur-rent. iL = iL1 + iL2 + iL3 at d = 0.5

the theoretical switching frequency characteristics were dis-cussed. The theoretical results were verified through numeri-cal and experimental analyses. Consequently, the proposedhigh step-up DC–DC converter operated in the DCM andCCM modes at the switching frequencies f = 10 kHz and100 kHz.

As the boost ratio is also dependent on the duty ratio, futurework will involve analyzing the characteristics of the boost

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High Step-up DC–DC Con with 3-winding Inductor（Masataka Minami et al.）

(a) DCM at f = 10 kHz

(b) CCM at f = 100 kHz

Fig. 9. Waveforms of output voltage and inductor cur-rent. iL = iL1 + iL2 + iL3 at d = 0.7

ratio relative to the other value of the duty ratio.AcknowledgmentThe authors would like to thank Prof. M. Michihira and

Prof. S. Motegi for their insightful advice on this paper.

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Masataka Minami (Member) received his Bachelor’s, Master’s, andPh.D. degrees from Kyoto University, Kyoto, Japan,in 2008, 2010, and 2013, respectively. In 2013,he joined the Department of Electrical Engineering,Kobe City College of Technology (KCCT), where heis currently an Associate Professor. From April 2018to March 2019, he was an Academic Visitor in theSchool of Engineering, Ecole Polytechnique Federalede Lausanne (EPFL), Lausanne, Switzerland. Hisresearch interests include power conversion systems

and power systems engineering. He is a member of the Institute of Elec-tronics, Information and Communication Engineers (IEICE) and Institute ofSystem, Control and Information Engineers (ISCIE).

Genki Hase (Non-member) joined the Department of Electrical Engi-neering, Kobe City College of Technology (KCCT) inApril 2015. He joined the power electronics labora-tory in October 2018, where Prof. Masataka Minamiwas his supervisor. He received the Associate’s de-gree from KCCT in March 2020. Since April 2020,he is a Bachelor candidate in KCCT. His research in-terests include DC–DC converters, energy-harvestingsystems, and control applications. He is a member ofthe Japan Institute of Power Electronics (JIPE).

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