High Power Density, High-Voltage Parallel Resonant Converter Using Parasitic Capacitance on the Secondary Side of a Transformer

electronics

Article High Power Density, High-Voltage Parallel Resonant Converter Using Parasitic Capacitance on the Secondary Side of a Transformer

Jaean Kwon and Rae-Young Kim *

Department of Electrical and Biomedical Engineering, Hanyang University, Seoul 04763, Korea; [email protected] * Correspondence: [email protected]; Tel.: +82-2-2220-2897

Abstract: High-voltage DC power supplies are used in several applications, including X-ray, plasma, electrostatic precipitator, and capacitor charging. However, such a high-voltage power supply has problems, such as a decrease in reliability, owing to an increase in output ripple voltage, and a decrease in power density, owing to an increase in volume. Therefore, this study proposes a method for improving the power density of a parallel resonant converter using the parasitic capacitor of the secondary side of the transformer. Due to the fact that high-voltage power supplies have many turns on the secondary side, a signiﬁcant number of parasitic capacitors are generated. In addition, in the case of a parallel resonant converter, because the transformer and the primary resonant capacitor are connected in parallel, the parasitic capacitor component generated on the secondary side of the transformer can be equalized and used. A parallel cap-less resonant converter structure developed using the parasitic components of such transformers is proposed. Primary side and secondary side equivalent model analyses are conducted in order to derive new equations and gain waveforms. Citation: Kwon, J.; Kim, R.-Y. High Finally, the validity of the proposed structure is veriﬁed experimentally. Power Density, High-Voltage Parallel Resonant Converter Using Parasitic Keywords: Capacitance on the Secondary Side of cap-less parallel resonant converter; high power density; high-voltage power supply; a Transformer. Electronics 2021, 10, parasitic capacitance; equivalent model analysis 1736. https://doi.org/10.3390/ electronics10141736

Academic Editor: 1. Introduction Giambattista Gruosso High-voltage DC power supplies are used in several applications, including X-ray generators, plasma generators, electrostatic precipitators, and capacitor charging. However, Received: 14 June 2021 such a high-voltage power supply has problems, such as a decrease in reliability owing to Accepted: 9 July 2021 an increase in output ripple voltage and a decrease in power density owing to an increase Published: 19 July 2021 in volume. Consequently, several studies have been conducted in order to reduce the output voltage ripple or improve the power density and to ensure the miniaturization, Publisher’s Note: MDPI stays neutral high efficiency, and reliability of high-voltage DC power supplies [1–7]. with regard to jurisdictional claims in In high-voltage DC power supplies, soft-switching-based resonant converter topolo- published maps and institutional affil- gies, such as a series resonant converter, parallel resonant converter, and LCC resonant iations. converter, are mainly used to increase system efficiency. However, owing to the characteristics of the high-voltage output, a high rated voltage and a large current are induced in the resonant network on the primary side of the topology. Accordingly, a resonant capacitor comprising the resonant network also requires a high rated voltage and a large current. The Copyright: © 2021 by the authors. resonant capacitor is applied as a bank, comprising several capacitors connected in series or Licensee MDPI, Basel, Switzerland. parallel, in order to satisfy these required characteristics. This configuration of the resonant This article is an open access article capacitor bank is a major cause of the deterioration of the power density of the resonant distributed under the terms and converter in a high-voltage DC power supply. In addition, in a high-voltage DC power conditions of the Creative Commons supply, increasing the output voltage is an important factor. Therefore, in many current Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ high-voltage DC power supply applications, voltage multiplier circuits are frequently used 4.0/). to increase the output voltage itself. However, in the case of the voltage multiplier circuit,

Electronics 2021, 10, 1736. https://doi.org/10.3390/electronics10141736 https://www.mdpi.com/journal/electronics Electronics 2021, 10, 1736 2 of 13

the number of diodes and capacitors increases as the output voltage increases; therefore, the power density of the entire system decreases [2]. Several studies have been conducted in order to increase the switching frequency and power density of the system. However, if the switching frequency is increased, the efficiency of the system generally decreases, owing to the high switching loss, and the heat dissipation design becomes difficult. In [7,8], the authors proposed methods to reduce the size of passive components, such as resonant inductors, transformers, and capacitors, by increasing the switching frequency through applying wide-bandgap (WBG) switching components. In this case, the switching loss did not increase significantly, owing to the fast-switching characteristics of the WBG switching element. However, applying such an element to an actual system is not favorable because it leads to an increase in the price of the switching device used in the system. To increase the power density of the system, some studies [9,10] proposed a method that uses the leakage inductance of a transformer as a resonant inductor. In [10,11], the power density was improved by applying a planar transformer. However, it is difficult to implement a large number of windings when the frequency increases, owing to the structure of a planar transformer that forms windings using a PCB pattern. Consequently, it is difficult to apply a high-voltage DC power supply that requires several turns on the secondary side of the transformer. Applying a conventional device, such as using the planar transformer and WBG switching components, to a high-voltage DC power supply is difficult because the transformer turns are limited and the cost increases. This paper proposes a method for improving the power density of a parallel resonant converter by employing the secondary side parasitic capacitor of the transformer without using a resonant capacitor on the primary side. Due to the fact that high-voltage power supplies have many turns on the secondary side, a significant number of parasitic capacitors are generated. In addition, in the case of a parallel resonant converter, because the transformer and the primary resonant capacitor are connected in parallel, the parasitic capacitor component generated on the secondary side of the transformer can be used. Primary side and secondary side equivalent model analyses are performed in order to derive new equations and gain waveforms. Finally, the validity of the proposed structure is verified experimentally.

2. Proposed Parallel Resonant Converter 2.1. Structure of the Proposed Parallel Resonant Converter Figure1a shows the structure of a conventional parallel resonant converter applied with a voltage multiplier circuit on the secondary side, and Figure1b shows the structure of a parallel resonant converter in which the primary resonant capacitor is equalized to the secondary side of the transformer. The conventional parallel resonant converter shown in Figure1a is composed of switching components S1–S4, a resonant inductor Lr, a magnetizing inductance Lm existing in the transformer primary side, a resonant capacitor Cr, a high-frequency transformer Tr, capacitors C1 − C4n and rectifier diodes D1 − D4n forming the secondary side voltage multiplier circuit, and a load Ro. However, after considering the rated voltage and current that flows in the resonant inductor, the resonant capacitor is configured in series or parallel, which increases the size of the system. Consequently, a resonant capacitor on the primary side is not used in the proposed converter (Figure1b), and a resonant circuit can be constructed through the secondary side parasitic capacitance of a high-frequency transformer. Thus, it is possible to improve the power density compared to that of the conventional structure. Electronics 2021, 10, x FOR PEER REVIEW 3 of 13

side of the transformer, owing to the higher number of turns on the secondary side. Con- sequently, in contrast to the conventional parallel resonant converter, the proposed parallel resonant converter uses a resonant capacitor to replace the parasitic capacitance generated in the transformer. In Equation (1), the resonant capacitor 퐶푟 on the primary side is equalized to the secondary side by considering the ratio of the number of turns of the transformer. In the proposed parallel resonant converter, the resonant capacitance is 2 푛 ∙ 퐶푝 instead of 퐶푟 [12,13]. Consequently, the resonant inductor 퐿푟 and the secondary side parasitic capacitor 퐶푝 of the transformer resonate, and the resonant frequency can be expressed using Equation (2). In addition, when the secondary side parallel structure is used, the upper voltage multiplier circuit produces a voltage of +50 kV and the lower Electronics 2021, 10, 1736 voltage multiplier circuit produces a voltage of −50 kV, resulting in an output voltage3 of 13of 100 kV.

Full Bridge

Voltage Multiflier Transformer

(a)

(b)

FigureFigure 1. SystemSystem structure structure of of the the parallel parallel resonant resonant converter converter applied applied with with a voltage a voltage multiplier multiplier:: (a) (caonventional) conventional system system structure structure;; (b) ( bp)roposed proposed system system structure structure..

In the proposed structure, if the high-voltage2 DC output characteristic is used, the C푟 = 푛 ∙ C푝 (1) secondary side has a signiﬁcant amount of parasitic capacitance compared to the primary side of the transformer, owing to the higher number of turns on the secondary side. Consequently, in contrast to the conventional parallel resonant converter, the proposed parallel resonant converter uses a resonant capacitor to replace the parasitic capacitance generated in the transformer. In Equation (1), the resonant capacitor Cr on the primary side is equalized to the secondary side by considering the ratio of the number of turns of the transformer. In the proposed parallel resonant converter, the resonant capacitance is 2 n · Cp instead of Cr [12,13]. Consequently, the resonant inductor Lr and the secondary side parasitic capacitor Cp of the transformer resonate, and the resonant frequency can be expressed using Equation (2). In addition, when the secondary side parallel structure is used, the upper voltage multiplier circuit produces a voltage of +50 kV and the lower voltage multiplier circuit produces a voltage of −50 kV, resulting in an output voltage of 100 kV. 2 Cr = n · Cp (1) 1 fr = q (2) 2 2π Lr · n Cp Electronics 2021, 10, x FOR PEER REVIEW 4 of 13

1 푓푟 = (2) 2휋√퐿 ∙ 푛2C Electronics 2021, 10, 1736 푟 푝 4 of 13

2.2. Operating Principle 2.2. Operating Principle Figures 2 and 3 show the operating principle and key waveforms of the proposed parallelFigures resonant2 and 3converter show the, respectively operating principle. For an andanalysis key waveformsof the operation of the of proposed the converter, par- allelthe parasitic resonant components converter, respectively. generated at For the an primary analysis side of the of operationthe transformer of the converter,and the com- the parasiticponents componentsgenerated at generated the capacitor at the of primary the voltage side multiplier of the transformer circuit stage and the are components not consid- generatedered. at the capacitor of the voltage multiplier circuit stage are not considered.

(a)

(b)

(c)

Figure 2. Cont.

Electronics 2021, 10, x FOR PEER REVIEW 5 of 13 ElectronicsElectronics 20212021,, 1010,, 1736x FOR PEER REVIEW 55 of 1313

((dd)) FigureFigure 2.2. OperationOperation mode mode of of the the proposed proposed parallel parallel resonant resonant converter converter:: (a) (MODEa) MODE 1 [푡 10 −[t 푡1−]; t(b];) Figure 2. Operation mode of the proposed parallel resonant converter: (a) MODE 1 [푡0 − 0푡1]; (1b) MODE 2 [푡1 − 푡2]; (c) MODE 3 [푡2 − 푡3]; (d) MODE 4 [푡3 − 푡4]. (MODEb) MODE 2 [푡 21 [−t1푡−2];t 2(c];() MODEc) MODE 3 [ 3푡2[t−2 −푡3]t;3 ](;(d)d MODE) MODE 4 4[푡[3t3−−푡4t]4.] .

Figure 3. Key waveforms of the proposed parallel resonant converter. Figure 3. Key waveforms of the proposed parallel resonant converter.converter.

Electronics 2021, 10, 1736 6 of 13

MODE 1 [t0 − t1]: this mode starts when S1 and S4 are conducting. During this period, the primary side resonant current ILr flows in the positive direction and flows through the transformer to the secondary side parasitic capacitor Cp. In this operation period, because the capacitor voltage VC1 at the voltage multiplier circuit is greater than the voltage on the secondary side of the transformer Vsec, diode D1 becomes reverse biased so that all currents flowing in the secondary side flow toward the secondary side parasitic capacitor Cp. Consequently, the rectifier diodes D1 − D4n at the voltage multiplier circuit do not conduct, and the resonant inductor Lr at the primary side and Cp at the secondary side participate in resonance. In addition, the current path is formed by the voltage charged in the capacitor at the voltage multiplier. This mode ends as soon as the voltage across the secondary side parasitic capacitor becomes greater than the capacitor voltage VC1 at the voltage multiplier circuit. MODE 2 [t1 − t2]: in mode 2, S1 and S4 are still conducting, and this mode starts when Vsec becomes higher than VC1 at the voltage multiplier circuit. At this time, the current flows to diodes D1 − D4n and becomes forward biased, making the diodes at the upper and lower voltage multiplier conduct. Consequently, no current flows to the secondary side Cp, and the transformer voltage Vsec is clamped at Vout. In addition, because the output voltage is clamped at Cp, the primary side magnetizing inductor Lm connected in parallel assumes a voltage. This results in the resonant inductor Lr, the secondary-side Cp, and the primary side magnetizing inductor Lm not participating in resonance, and the primary side resonant current ILr being linearly decreased. This mode ends when the switching components S1 and S4 are turned OFF.

di V = L m (3) pri m dt

MODE 3 [t2 − t3]: this mode represents a dead time period and starts when S1 − S4 are turned OFF. Consequently, power is not transferred from the primary side to the secondary side. In addition, S1 − S4 do not conduct; thus, ILr and the rectiﬁer diode current ID decrease signiﬁcantly. This mode ends when S2 and S3 conduct. MODE 4 [t3 − t4]: after the switching half cycle is complete at t3, a new half cycle starts when S2 and S3 conduct.

3. Analysis of Equivalent Circuit of the Proposed Parallel Resonant Converter The fundamental harmonic approximation (FHA) is used to analyze the primary and secondary sides of the proposed parallel resonant converter and to obtain the voltage gain [14]. For the analysis, only the ﬁrst-order harmonic component of the square wave of the input voltage is considered; thus, it is easy to analyze the proposed parallel resonant converter. In addition, the structure of the proposed parallel resonant converter comprises a parallel voltage multiplier at the secondary side and produces a total output voltage of 100 kV. However, in this study, only one voltage multiplier stage producing a 50 kV output voltage is considered. Equation (4) considers several harmonic components of the primary side voltage. In Equation (5), the equation used for FHA, only the ﬁrst-order harmonic component is considered; that is, other harmonic orders are not considered. Thus, Equation (5) is used to calculate the voltage gain of the proposed converter.

4V 1 V = in sin(n ωt) (4) pri π ∑ n 1 n1=1,3,5··· 1

4V VF = in sin(ωt) (5) pri π Figure4 shows the circuit for deriving the equivalent load resistance value. The component on the primary side is replaced by a sinusoidal current source, and the input voltage on the secondary side is expressed as a square wave component. In addition, the Electronics 2021, 10, 1736 7 of 13

average value of the sinusoidal current is the output current, expressed by Equation (6). Equation (7) represents the voltage across the secondary transformer. In the voltage multiplier circuit, this voltage is 1/8 times that of the output voltage. In addition, by dividing Equation (9) by the current component Equation (6), the equivalent load resistance Equation (10) can be obtained.

π · I I = out sin(ωt) (6) Electronics 2021, 10, x FOR PEER REVIEW ac 2 7 of 13

1 1 V = + V if sin(ωt) > 0V = − V if sin(ωt) < 0 (7) sec 8 out sec 8 out 4V 1 age on the secondary sideV is= expressedout as asin square(n ωt) wave component. In(8) addition, the av- sec π ∑ n 1 erage value of the sinusoidal currentn1=1,3,5 ···is the1 output current, expressed by Equation (6). Equation (7) represents the voltage4 Vacrossout the secondary transformer. In the voltage mul- VF = sin(ωt) (9) tiplier circuit, this voltage is 1/8sec timesπ that of the output voltage. In addition, by dividing VF 8 V 8 Equation (9) by the current component= sec = Equationout = (6), the equivalent load resistance Equa- Rac 2 2 Ro (10) tion (10) can be obtained. Iac π Iout π

Rectifier

Figure 4. 4.Circuit Circuit diagram diagram to derive to derive the equivalent the equivalent load resistance. load resistance.

In high-voltage applications, the secondary side of the transformer has a higher turn ratio than the primary side. If the turn ratio is equalized휋 ∙ 퐼표푢푡 to the primary side, the equivalent 퐼 = sin (ωt) (6) load resistance can be expressed by Equation푎푐 (11). Therefore,2 the equivalent resistance equation can be derived, and the voltage gain of the converter can be obtained through the Equations (5) and (9). When the secondary side1 voltage Vsec is equalized to the primary side, we obtain the voltage gain Equation푉 (12).= + When푉 the primaryif sin(ω sidet) > and0 secondary side 푠푒푐 8 표푢푡 voltages are calculated, the voltage gain can be expressed as Equation (13). (7) 1 푉푠푒푐 = −8 푉표푢푡 if sin(ωt) < 0 Rac = Ro (11) n2 · π82

1 · VF = n4푉 sec 1 M 표푢푡F (12) 푉푠푒푐 = Vpri ∑ 푠푖푛 (푛1휔푡) (8) 휋 푛1 푛1=1,3,5∙∙∙ 4Vout sin(ωt) 1 V = nπ = out M 4V (13) in ( ) n Vin π sin ωt 4푉 푉퐹 = 표푢푡 푠푖푛 (휔푡) (9) Figure5 shows the AC equivalent circuit푠푒푐 of the proposed휋 parallel resonant converter. In order to derive the necessary equation for the parallel resonant converter, it is necessary to calculate the characteristic impedance Z using퐹 the resonant inductor L , magnetizing o 푉푠푒푐 8 푉표푢푡 8 r 2 · inductance Lm, equivalent resistance R푅ac,푎푐 and= the equivalent= 2 resonant= 2 푅 capacitance표 n Cp. (10) These resonance tank components can be expressed퐼푎푐 as휋 follows.퐼표푢푡 휋

In high-voltage applications, the 2secondary side of the transformer has a higher turn Lm n · Cp Rac M = (14) ratio than the primary side. If the turn ratio 2 is equalized to the primary side, the equivalent Lr + Lm n · Cp Rac load resistance can be expressed by Equation (11). Therefore, the equivalent resistance equation can be derived, and the voltage gain of the converter can be obtained through the Equations (5) and (9). When the secondary side voltage 푉푠푒푐 is equalized to the primary side, we obtain the voltage gain Equation (12). When the primary side and secondary side voltages are calculated, the voltage gain can be expressed as Equation (13). 8 푅 = 푅 (11) 푎푐 푛2 ∙ 휋2 표

1 ∙ 푉퐹 푛 푠푒푐 (12) 푀 = 퐹 푉푝푟푖

4푉표푢푡 푠푖푛 (휔푡) 1 푉 푀 = 푛휋 = 표푢푡 4푉 (13) 푖푛 푠푖푛 (휔푡) 푛 푉푖푛 휋 Figure 5 shows the AC equivalent circuit of the proposed parallel resonant converter. In order to derive the necessary equation for the parallel resonant converter, it is necessary to calculate the characteristic impedance 푍표 using the resonant inductor 퐿푟, magnetizing

Electronics 2021, 10, x FOR PEER REVIEW 8 of 13

inductance 퐿푚 , equivalent resistance 푅푎푐 , and the equivalent resonant capacitance 2 푛 ∙ 퐶푝. These resonance tank components can be expressed as follows. 2 (퐿푚||푛 ∙ 퐶푝||푅푎푐) 푀 = 2 (14) 퐿푟 + (퐿푚||푛 ∙ 퐶푝||푅푎푐)

1 푍표(푠) = (푠퐿푟|| 2 ||푅푎푐) (15) 푠푛 ∙ 퐶푝 In the case of a parallel resonant converter, the impedance of the inductor, which can be expressed as |푍표(푠)|| ≅ 휔퐿푟, is more dominant at a low frequency, whereas the imped- 1 ance of the capacitor component, which can be expressed as |푍표(푠)|| ≅ 2 , is more 휔푛 퐶푟 Electronics 2021, 10, 1736 dominant at a high frequency. In addition, the resonant inductance and8 of 13resonant capacitance are canceled at the resonant frequency, as shown in Equation (16). The resonant inductor and resonant capacitor values of1 the proposed parallel resonant converter can be ( ) = Zo s sLr 2 Rac (15) derived from Equations (17)–(19). sn · Cp

Primary Side Equivalent Secondary Side

FigureFigure 5. 5.AC AC equivalent equivalent circuit circuit of the proposedof the proposed parallel resonant parallel converter. resonant converter.

In the case of a parallel resonant converter, the impedance of the inductor, which Figure 6 shows the∼ voltage gain curve for an output voltage of 50 kV. This curve is can be expressed as |Zo(s)||= ωLr , is more dominant at a low frequency, whereas the

obtained using the equivalent circuit shown in Figure 5 and the c∼alculated1 Equations (14) impedance of the capacitor component, which can be expressed as |Zo(s)| = 2 , is ωn Cr moreand (17 dominant)–(19). at a high frequency. In addition, the resonant inductance and resonant capacitance are canceled at the resonant frequency, as shown in1 Equation (16). The resonant inductor and resonant capacitor( values) of the proposed parallel resonant converter can be ||푍표 푠 ||푠=푗휔푠 = = 푅푎푐 1 2 (16) derived from Equations (17)–(19). + 푗휔표 ∙ 푛 ∙ 퐶푝 + 푅푎푐 Figure6 shows the voltage gain curve for an output푗휔표퐿푟 voltage of 50 kV.This curve is obtained using the equivalent circuit shown in Figure5 and the calculated Equations (14) and (17)–(19). 1 휔표퐿푟 =1 2 = 푍표 (17) ||Zo(s)|| = = 휔표 ∙ 푛 ∙ 퐶푝= Rac (16) s jωs 1 + jω · n2 · C + R jωo Lr o p ac

1 푍표 = 퐿=푟 = (18) ωo Lr 2 Zo (17) ωo · n · Cp 휔표

Zo Lr = 1 (18) ωo 퐶푝 = 2 (19) 1 휔표 ∙ 푛 ∙ 푍표 Cp = (19) ω · n2 · Z o o 1 1 Electronics 2021, 10, x FOR PEER REVIEW = 휔표퐿푟 = = 2 = 푍표 9 of 13 (20) ωo Lr 2 휔 Z∙ 푛o ∙ 퐶 (20) ωo · n · Cp 표 푝

Figure 6. Gain curve of the proposed parallel resonant converter.

4. Analysis of the Secondary Side Voltage Multiplier In high-output-voltage applications, a voltage multiplier circuit is used to obtain a much higher output voltage by using a rectifier diode and a capacitor [15–19]. For example, in the case of a parallel resonant converter used in high-output-voltage applications such as medical devices, because the output voltage is greater than 5 kV, voltage multiplier circuits are mostly used at the rectifier stage of the converter. Consequently, in this study, four stages and a parallel-structure voltage multiplier are used to obtain an output voltage greater than 100 kV. The voltage at the secondary side transformer 푉푠푒푐 is required in order to increase the output voltage 푉표. Based on the resonant inductor 퐿푟 on the primary side and the parasitic capacitor 퐶푝 on the secondary side, as shown in Figure 1, the voltage applied to the secondary side of the transformer 푉푠푒푐 has a pulse waveform with a peak value of 6.25 kV. In addition, this voltage is applied to the capacitor at the voltage multiplier circuit

퐶1 when the rectifier diode is turned ON. With this principle, the voltage 푉퐶2 of 12.5 kV

is applied, and 푉퐶2푛, the current from the four-stage voltage multiplier circuit, is obtained as 50 kV. With this principle, the proposed parallel resonant converter can obtain a final output voltage of 100 kV, with a voltage ranging from −50 kV to 50 kV, using upper and lower voltage multiplier circuits. The pulsed voltage waveforms can be expressed as shown in Figure 7.

(a) (b) (c) Figure 7. (a) Voltage at the secondary side of the transformer. (b) Voltage after 1st voltage multiplier. (c) Voltage after 4th voltage multiplier.

5. Experimental Results Experiments are conducted to verify the effectiveness of the proposed parallel resonant converter. The operating conditions for the experiment are listed in Table 1. Figure 8 shows the experimental setup of the parallel resonant converter comprising the AC–DC stage, controller, DC–DC primary side, and DC–DC secondary side. It receives an input

Electronics 2021, 10, x FOR PEER REVIEW 9 of 13

Figure 6. Gain curve of the proposed parallel resonant converter. Electronics 2021, 10, 1736 9 of 13 4. Analysis of the Secondary Side Voltage Multiplier

4. AnalysisIn high of-output the Secondary-voltage Sideapplications, Voltage Multiplier a voltage multiplier circuit is used to obtain a much higher output voltage by using a rectifier diode and a capacitor [15–19]. For exam- In high-output-voltage applications, a voltage multiplier circuit is used to obtain a ple, in the case of a parallel resonant converter used in high-output-voltage applications much higher output voltage by using a rectifier diode and a capacitor [15–19]. For example, insuch the as case medical of a parallel devices, resonant because converter the output used voltage in high-output-voltage is greater than applications 5 kV, voltage such multi- asplier medical circuits devices, are mostly because used the at output the rectifier voltage stage is greater of the thanconverter. 5 kV, voltageConsequently multiplier, in this circuitsstudy, four are mostly stages usedand a at parallel the rectifier-structure stage ofvoltage the converter. multiplier Consequently, are used to obtain in this study,an output fourvoltage stages greater and a than parallel-structure 100 kV. voltage multiplier are used to obtain an output voltage greaterThe than voltage 100 kV. at the secondary side transformer 푉푠푒푐 is required in order to increase the outputThe voltage voltage at the푉표. secondaryBased on sidethe resonant transformer inductorVsec is required퐿푟 on the in primary order to side increase and the theparasitic output capacitor voltage V퐶o푝. on Based the onsecondary the resonant side, inductoras shownL inr on Figure the primary 1, the voltage side and applied the to parasiticthe secondary capacitor sideC ofp onthethe transformer secondary 푉 side,푠푒푐 has as a shown pulse inwaveform Figure1, with the voltage a peak appliedvalue of 6.25 tokV. the In secondary addition, sidethis voltage of the transformer is applied Vtosec thehas capacitor a pulse waveform at the voltage with amultiplier peak value circuit of 6.25 kV. In addition, this voltage is applied to the capacitor at the voltage multiplier 퐶1 when the rectifier diode is turned ON. With this principle, the voltage 푉퐶2 of 12.5 kV circuit C1 when the rectifier diode is turned ON. With this principle, the voltage VC of is applied, and 푉퐶 , the current from the four-stage voltage multiplier circuit, is o2btained 12.5 kV is applied,2 and푛 V , the current from the four-stage voltage multiplier circuit, is as 50 kV. With this principle,C2n the proposed parallel resonant converter can obtain a final obtained as 50 kV. With this principle, the proposed parallel resonant converter can obtain aoutput final output voltage voltage of 100 of kV 100, with kV, with a voltage a voltage ranging ranging from from −50− 50kV kV to to 50 50 kV kV,, using using upper upper and andlower lower voltage voltage multiplier multiplier circui circuits.ts. The The pulsed voltage voltage waveforms waveforms can can be expressed be expressed as as shownshown inin FigureFigure7. 7.

(a) (b) (c)

FigureFigure 7. (a) Voltage 7. (a) Voltage at the at secondary the secondary side sideof the of transformer. the transformer. (b) (Voltageb) Voltage after after 1st 1st voltage voltage multiplier. multiplier. (c ()c )Voltage Voltage after after 4th 4th voltagevoltage multiplier. multiplier. 5. Experimental Results 5. Experimental Results Experiments are conducted to verify the effectiveness of the proposed parallel resonant Experiments are conducted to verify the effectiveness of the proposed parallel reso- converter. The operating conditions for the experiment are listed in Table1. Figure8 shows nant converter. The operating conditions for the experiment are listed in Table 1. Figure 8 the experimental setup of the parallel resonant converter comprising the AC–DC stage, controller,shows the DC–DC experimental primary setup side, of and the DC–DC parallel secondary resonant side. converter It receives comprising an input voltagethe AC–DC ofstage, 220 controller, V from the DC AC–DC–DC primary terminal side, and convertsand DC– itDC to secondary a DC voltage side. of It 380 receives V, and an the input converted value, using the transformer and voltage multiplier circuits on the secondary side of the DC–DC converter, ﬁnally results in an output voltage of 100 kV, as shown in Figure8. In addition, in the experimental setup, the transformer stage and voltage

multiplier circuits are separated from the primary side for high-voltage insulation using insulating oil. In addition, a constant current electronic load was applied and operated in a constant current mode. Electronics 2021, 10, x FOR PEER REVIEW 10 of 13

voltage of 220 V from the AC–DC terminal and converts it to a DC voltage of 380 V, and the converted value, using the transformer and voltage multiplier circuits on the secondary side of the DC–DC converter, finally results in an output voltage of 100 kV, as shown in Figure 8. In addition, in the experimental setup, the transformer stage and voltage multiplier circuits are separated from the primary side for high-voltage insulation using insulating oil. In addition, a constant current electronic load was applied and operated in a Electronics 2021, 10, 1736 constant current mode. 10 of 13

Table 1. System parameters. Table 1. System parameters. Symbol Quantity Value (Unit) Symbol Quantity Value (Unit) 푉푖푛 Input voltage 385 (V) V Input voltage 385 (V) 푉표푢푡in Rated output voltage 100 (kV) Vout Rated output voltage 100 (kV) 푃표푢푡 Rated output power 1.7 (kW) Pout Rated output power 1.7 (kW) 퐼Iout표푢푡 OutputOutput currentcurrent 1.7 (mA)(mA) L퐿r푟 ResonantResonant inductorinductor 106 ((µ휇H)H) L Magnetizing inductance 1000 (µH) 퐿m푚 Magnetizing inductance 1000 (휇H) Cp Parasitic capacitance 0.134 (nF) 퐶푝 Parasitic capacitance 0.134 (nF) n1 : n2 Turns ratio 1:12 푛 : 푛 Turns ratio 1:12 1fs 2 Switching frequency 98 (kHz) 푓푠 Switching frequency 98 (kHz)

FigureFigure 8.8. Experimental setup forfor thethe proposedproposed parallelparallel resonantresonant converterconverter system.system.

FigureFigure9 9 shows shows thethe experimentalexperimental resultsresults ofof thethe proposedproposed parallelparallel resonantresonant converter.converter. FigureFigure9 9aa showsshows thethe input gate gate voltage voltage 푉푔푠Vgs of ofthe the switching switching components components and and voltage voltage 푉푑푠 Vacrossds across the switch the switch component component.. The drain The– drain–sourcesource voltage voltage is zero isbecause zero because switching switching compo- componentsnents 푆1 andS 1푆4and areS conducting4 are conducting.. In addition, In addition, the input the voltage input voltage푉푖푛 is appliedVin is appliedto the volt- to theage voltage푉푑푠 whenVds 푆1when and S푆14 andare notS4 areconducting not conducting.. Figure 9b Figure shows9b the shows primary the primary side resonant side I resonantinductor current inductor 퐼퐿푟 current under theLr under rated load the rated condition load. condition.Therefore, the Therefore, proposed the parallel proposed res- parallelonant converter resonant has converter 1.7 kW has output 1.7 kW power, output with power, an output with anvoltage output of voltage100 kV and of 100 an kV output and ancurrent output of current1.7 mA. of In 1.7 addition, mA. In addition,a comparison a comparison with the withkey wave the keyform waveformss analyzed analyzed (Section (Section2) reveals2) revealsthat the that experimental the experimental waveform waveformss of the ofproposed the proposed converter converter are similar are similar to the toanalyzed the analyzed waveform waveform,, as a resonance as a resonance between between the resonant the resonant inductor inductor and andthe theparasitic parasitic ca- capacitance occurs in t0 − t . Figure9c shows the primary side resonant inductor current pacitance occurs in 푡0 − 푡1.1 Figure 9c shows the primary side resonant inductor current ILr at a 50% load. In this case, the current ﬂowing to the secondary side decreases because 퐼퐿푟 at a 50% load. In this case, the current flowing to the secondary side decreases because thethe outputoutput currentcurrent isis lessless thanthan thatthat ofof thethe ratedrated loadload condition.condition. UnderUnder thesethese conditions,conditions, thethe proposedproposed converterconverter operatesoperates effectivelyeffectively atat aa 50%50% load;load; however, thethe primaryprimary sideside resonantresonant currentcurrent waveformwaveform becomesbecomes relativelyrelatively small,small, owing to the difference in the output current. Figure 10 shows the feedback-sensing waveforms of the output voltage and output current at the rated output voltage. Using these voltage waveforms, it is conﬁrmed that the proposed parallel resonant converter has a rated output voltage of 100 kV and an output current of 17 mA. In addition, in high-voltage applications, especially in medical X-rays, because the machines operate for a short time, a constant current load is usually used. Consequently, the sensed output voltage and output current waveforms are different. Electronics 2021, 10, x FOR PEER REVIEW 11 of 13 Electronics 2021, 10, 1736 11 of 13

(a)

(b)

(c) 푉 FigureFigure 9.9. ExperimentalExperimental test test waveforms waveforms;; (a) ( ag)ate gate input input voltage voltage 푔푠 Vandgs and switching switching drain drain–source–source voltage 푉푑푠; (b) resonant inductor current 퐼퐿푟 at full-load condition; (c) resonant inductor current 퐼퐿푟 voltage Vds;(b) resonant inductor current ILr at full-load condition; (c) resonant inductor current ILr at half-load condition. at half-load condition.

Electronics 2021, 10, x FOR PEER REVIEW 12 of 13

Figure 10 shows the feedback-sensing waveforms of the output voltage and output current at the rated output voltage. Using these voltage waveforms, it is confirmed that the proposed parallel resonant converter has a rated output voltage of 100 kV and an output current of 17 mA. In addition, in high-voltage applications, especially in medical X- rays, because the machines operate for a short time, a constant current load is usually Electronics 2021, 10, 1736 used. Consequently, the sensed output voltage and output current waveforms are 12differ- of 13 ent.

FigureFigure 10.10. FeedbackFeedback voltagevoltage forfor predictingpredicting thethe outputoutput voltagevoltage andand outputoutput current.current. 6. Conclusions 6. Conclusions In this paper, a novel parallel resonant converter structure using parasitic capacitor In this paper, a novel parallel resonant converter structure using parasitic capacitor components on the secondary side of the transformer is proposed. The proposed parallel components on the secondary side of the transformer is proposed. The proposed parallel resonant converter uses the parasitic capacitance of the secondary side transformer instead resonant converter uses the parasitic capacitance of the secondary side transformer in- of using the resonant capacitor on the primary side, which can secure the space on the stead of using the resonant capacitor on the primary side, which can secure the space on primary side and so the power density of the parallel resonant converter can be improved. the primary side and so the power density of the parallel resonant converter can be im- The effectiveness of the proposed structure is confirmed through the analysis of the equiv- proved. The effectiveness of the proposed structure is confirmed through the analysis of alent model, derivation of new equations, and analysis of the voltage multiplier circuits. the equivalent model, derivation of new equations, and analysis of the voltage multiplier In addition, the operation of the proposed parallel resonant converter is verified through circuits. In addition, the operation of the proposed parallel resonant converter is verified an experiment in which the system has an output power, voltage, and current of 1.7 kW, 100through kV, and an 1.7experiment mA, respectively. in which the system has an output power, voltage, and current of 1.7 kW, 100 kV, and 1.7 mA, respectively. Author Contributions: Conceptualization, J.K.; methodology, J.K.; software, J.K.; validation, J.K.; formalAuthor analysis, Contribution J.K.; investigation,s: Conceptualization, J.K.; writing—original J.K.; methodology, draft J.K. preparation,; software, J.K.; J.K. writing—review; validation, J.K.; andformal editing, analysis, J.K. J.K. and; R.-Y.K.;investigation, visualization, J.K.; writing J.K. and—original R.-Y.K.; draft supervision, preparation, R.-Y.K. J.K.; All writing authors—review have readand editing, and agreed J.K. toand the R. published-Y.K.; visualization, version of theJ.K. manuscript. and R.-Y.K.; supervision, R.-Y.K. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest. References References 1. Ou, Z.; Gao, F.; Zhao, H.; Zhu, L.; Dang, S.; Hu, Y. Design and analysis of LLC resonant converter for X-ray high-voltage power. 1. InOu, Proceedings Z.; Gao, F.; of Zhao, the 2019 H.; Zhu, IEEE L.; 4th Dang, Advanced S.; Hu, Information Y. Design and Technology-Electronic analysis of LLC resonant and Automation converter for Control X-ray Conference high-voltage (IAEAC), power. Chengdu,In Proceedings China, of 20–22 the December 2019 IEEE 2019; 4th pp.Advanced 505–510. Information Technology-Electronic and Automation Control Conference 2. Chakraborty,(IAEAC), Chengdu, S.S.; Patnala, China, S.; 20 Bhawal,–22 December S.; Hatua, 2019; K. pp. Selection 505–510. procedure of resonant tank parameters for an SiC MOSFET based 2. DC/DCChakraborty, series S.S.; resonant Patnala, converter. S.; Bhawal, In Proceedings S.; Hatua, K. of Selection the 2018 procedure IEEE International of resonant Conference tank parameters on Power for Electronics-Drives an SiC MOSFET based and EnergyDC/DC Systemsseries resonant (PEDES), converter. Chennai, In India, Proceedings 18–21 December of the 2018 2018; IEEE pp. International 1–5. Conference on Power Electronics-Drives and 3. Hsu,Energy W.C.; Systems Chen, (PEDES), J.F.; Hsieh, Chennai, Y.P.; Wu, India, Y.M. Design 18–21 December and steady-state 2018; pp. analysis 1–5. of parallel resonant DC-DC converter for high-voltage 3. powerHsu, W.C.; generator. Chen,IEEE J.F.; Trans.Hsieh, PowerY.P.; Wu, Electron. Y.M.2017 Design, 312 and, 957–966. steady [-CrossRefstate analysis] of parallel resonant DC-DC converter for high- 4. Zhang,voltage Z.;power Tang, generator. Z. Pulse IEEE frequency Trans.modulation Power Electron. LLC 2017 series, 312 resonant, 957–966 X-ray. power supply. In Proceedings of the 2011 Inter- national Conference on Consumer Electronics-Communications and Networks (CECNet), Xianning, China, 16–18 April 2011; pp. 1532–1535. 5. Li, F.; Wang, S.; Hou, W.; Qin, X. Design and research on high voltage power supply of medical X-ray machine. In Proceedings of the 2016 IEEE International Conference on Mechatronics and Automation, Harbin, China, 7–10 August 2016; pp. 943–947. 6. R ˛abkowski,J.; Łasica, A.; Zdanowski, M.; Wrona, G.; Starzyński,J. Portable DC Supply Based on SiC Power Devices for High-Voltage Marx Generator. Electronics 2021, 10, 313. [CrossRef] 7. Liu, Y.; Du, G.; Wang, X.; Lei, Y. Analysis and design of high-efficiency bidirectional GaN-based CLLC resonant converter. Energies 2019, 12, 3859. [CrossRef] Electronics 2021, 10, 1736 13 of 13

8. Hu, Y.; Shao, J.; Ong, T.S. 6.6 kW high-frequency full-bridge LLC DC-DC converter with SiC MOSFETs. In Proceedings of the 2019 IEEE Energy Conversion Congress and Exposition (ECCE), Baltimore, MD, USA, 29 September–3 October 2019; pp. 6848–6853. 9. Jung, J. Bifilar winding of a center-tapped transformer including integrated resonant inductance for LLC resonant converter. IEEE Trans. Power Electron. 2013, 28, 615–620. [CrossRef] 10. Fei, C.; Lee, F.C.; Li, Q. High-efficiency high power density LLC converter with an integrated planar matrix transformer for high output current applications. IEEE Trans. Power Electron. 2016, 64, 9072–9082. [CrossRef] 11. Wang, Y.F.; Chen, B.; Hou, Y.; Meng, Z.; Yang, Y. Analysis and design of a 1-MHz bidirectional multi-CLLC resonant DC-DC converter with GaN devices. IEEE Trans. Power Electron. 2020, 67, 1425–1434. [CrossRef] 12. Liu, J.; Sheng, L.; Shi, J.; Zhang, Z.; He, X. Design of high voltage, high power and high frequency transformer in LCC resonant converter. In Proceedings of the 2009 24th Annual IEEE Applied Power Electronics Conference and Exposition, Washington, DC, USA, 15–19 February 2009; pp. 1034–1038. 13. Liu, J.; Sheng, L.; Shi, J.; Zhang, Z.; He, X. LCC resonant and converter operating under discontinuous resonant current mode in high voltage, high power, and high-frequency applications. In Proceedings of the 2009 24th Annual IEEE Applied Power Electronics Conference and Exposition, Washington, DC, USA, 15–19 February 2009; pp. 1482–1486. 14. Ericson, R.; Maksimovic, D. Fundamentals of Power Electronics, 2nd ed.; University of Colorado: Boulder, CO, USA, 2001; pp. 715–722. 15. Leu, C.; Huang, P. A novel voltage doubler rectifier for high output voltage applications. In Proceedings of the 2010 International Power Electronics Conference (ECCE), Sapporo, Japan, 21–24 June 2010; pp. 2082–2085. 16. Mao, S.; Popovic, J.; Ferreira, J. High voltage pulse speed study for high voltage DC-DC power supply based on voltage multipliers. In Proceedings of the 2015 17th European Conference on Power Electronics and Applications, Geneva, Switzerland, 8–10 September 2015; pp. 1–10. 17. Katzir, L.; Shmilovitz, D. A high voltage split source voltage multiplier with increased output voltage. In Proceedings of the 2015 IEEE Applied Power Electronics Conference and Exposition (APEC), Charlotte, NC, USA, 15–19 March 2015; pp. 3272–3275. 18. Lin, B.-R.; Lin, G.-H.; Jian, A. Resonant Converter with Voltage-Doubler Rectifier or Full-Bridge Rectifier for Wide-Output Voltage and High-Power Applications. Electronics 2019, 8, 3. [CrossRef] 19. Uno, M.; Nakane, T.; Shinohara, T. LLC Resonant Voltage Multiplier-Based Differential Power Processing Converter Using Voltage Divider with Reduced Voltage Stress for Series-Connected Photovoltaic Panels under Partial Shading. Electronics 2019, 8, 1193. [CrossRef]