A Bidirectional Symmetrical C4LC-DCX Resonant Converter

2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JESTPE.2021.3099476, IEEE Journalof Emerging and Selected Topics in Power Electronics

Abstract—To achieve the maximum efficiency of resonant

converter under wide voltage conversion gain range, two stageconversion, which adopts the resonant converter operating atresonant frequency to work as a dc-dc transformer (DCX) inisolation stage, is a preferred solution. This paper proposes abidirectional C4LC resonant converter to work as a DCX. Thestructure of the topology is totally symmetrical, and two auxiliaryinductors are used to achieve full load range zero-voltage-switching (ZVS) for all the power switches under bidirectionalpower flow. Unlike conventional ZVS analysis, the ZVS of theproposed converter is analyzed with considerations of all theswitch junction capacitors and load. The clamping diodes arealso combined in the topology which can help achieve naturalpower limitation in case of overload and limit the start-upcurrent. Even though four inductors and one transformer areillustrated in the topology, all these magnetic components can besimplified and manufactured with one external inductor and oneconventional transformer. Meanwhile, the converter operates atfixed frequency and adopts the synchronous Pulse WidthModulation (PWM) modulation, which can achieve constantvoltage gain and automatically change the power directionwithout synchronous rectifier (SR) current detection. Finally, theexperimental results from a 1-kW prototype verify theeffectiveness of the proposed converter.

Index Terms—natural bidirectional power flow, powerlimitation, symmetrical C4LC-DCX resonant converter, ZVS.

I. INTRODUCTION

SOLATED DC/DC converter can provide an interfacebetween power bus and energy storage device [1], and it is

widely used in distributed power system, uninterruptiblepower supply (UPS) and electrical vehicles to realize powerconversion and satisfy the safety requirement [2].

Among the various topologies of isolated DC/DCconverters [3]-[7], resonant converters, such as LLC converter,CLLC converter, etc., have been a preferred solution, due to

Manuscript received February 8, 2020; revised April 16, 2021; acceptedJuly 17, 2021. This work was supported in part by the National NatureScience Foundation of China under Grant 61903382, the StateKey Laboratoryof Power System and Generation Equipment under Grant SKLD21KM06, theNatural Science Foundation of Hunan Province, China under Grant2020JJ5722, the National Science Fund for Young Scholars of China underGrant 51907206. (Corresponding author: Hanbing Dan.)

G. Xu, J. Huang, H. Dan, M. Su and R. Zou are with the School ofAutomation, Central South University and with Hunan Provincial KeyLaboratory of Power Electronics Equipment and Grid, Changsha, 410083,China, (e-mail: [email protected]; [email protected];[email protected]; [email protected]; [email protected]).

their high performance in view of soft switching andelectromagnetic interference (EMI) performance [8].

For LLC resonant converter, within a specific frequencyrange, it can achieve ZVS turn-on of the primary side switchesand zero-current-switching (ZCS) turn-off of the secondaryside switches [9]. When operating at the resonant frequency,the conversion efficiency of LLC resonant converter reachesthe highest. However, if the working frequency is away fromthe resonant point when wide conversion gain range isrequired, the conversion efficiency will decrease because ofthe increasing circulating current [10].

To cope with the contradiction between wide range ofvoltage gain regulation and high conversion efficiency, twostage conversion structure is studied in [11]-[13]. As shown inFig. 1, the first stage is a LLC resonant converter whichoperates at the resonant point to achieve its best efficiency.The conversion gain of the LLC-DCX is unregulated. Thesecond stage usually is a none-isolated DC/DC converter (e.g.,buck converter, boost converter and buck-boost converter)with PWM modulation, which is used as a voltage regulator toadjust the voltage gain [14]-[16]. The feedback loop of thesecond-stage converter doesn’t need to be isolated, thereforethe dynamic response of the voltage regulation module isimproved. The LLC-DCX in the first stage adopts open-loopcontrol, so it is simple to implement.

Fig. 1. The structure of the two-stage conversion.In order to improve the efficiency of LLC-DCX, many

methods have been proposed. In [17] and [18], resonantfrequency tracking methods are applied to make the LLCresonant converter exactly work at the resonant point to obtainthe best efficiency. In [19], a method of multilevel gate driveris proposed, which can boost the efficiency of LLC-DCX byreducing the effect of parasitic inductance to solve the earlySR-switch turn-off problem. However, in the above methods,current sensing or voltage sensing is required for the SRswitches, which increases the cost and makes the controlstrategy more complex. Additionally, in [20], the primary sideof LLC converter is dynamically changed from full bridgestructure to half bridge structure under light load condition,which significantly improves the overall light load efficiency.In [21], a matrix transformer structure and PCB windings are

A Bidirectional Symmetrical C4LC-DCX ResonantConverter with Power Limitation Capability

Guo Xu, Member, IEEE, Junyi Huang, Student Member, IEEE, Hanbing Dan, Member, IEEE, Mei Su,Member, IEEE and Runmin Zou, Member, IEEE

I

Authorized licensed use limited to: Central South University. Downloaded on July 28,2021 at 03:49:45 UTC from IEEE Xplore. Restrictions apply.

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applied in LLC-DCX to reduce the losses of transformer.Although these methods can achieve high efficiency for LLC-DCX, they are not suitable for bidirectional powerapplications.

For bidirectional power applications, symmetrical structureis required to ensure that the operational characteristics of theconverter will not change with the power direction. Asymmetrical bidirectional CLLLC resonant converter isproposed in [22]-[23], which has the same operationcharacteristics in the forward and backward power directions.In [24], a bidirectional L3C resonant converter is proposed,which has a symmetrical resonant tank in bidirectional powerflow. In [25], four diodes are added in the half-bridge LLCconverter to help achieve the same operation characteristics inthe forward and backward modes. However, even if thesemethods [22]-[25] are applied in LLC-DCX, the control logicsneed to be changed according to the direction of power flow,it’s difficult to shift the power direction smoothly.

In [26] and [27], synchronous PWM modulation method isapplied in LLC-DCX to achieve natural bidirectional powerflow. The driving signals for the primary and secondary sideswitches are identical, which avoids SR sensing and logicsexchanging for two sides switches when the power directionchanges. However, only one side switches of the LLCconverter in [26] and [27] can achieve ZVS. In order to boostthe efficiency, a bidirectional LLC resonant converter with anauxiliary inductor is proposed in [28]. In this converter, all theswitches can achieve ZVS under bidirectional power flow.However, one transformer and two external inductors are usedin the hardware circuit, which reduces the power density of thecircuit. In view of ZVS analysis, the effect of load andjunction capacitors of secondary side switches is ignored in[26] and [27], and ZVS is analyzed without consideration ofswitches junction capacitors in [28]. As pointed out in [29],the secondary side junction capacitors can cause theinconsistent charge/discharge time, hence the ZVS analysis in[26]-[28] leads to insufficient accuracy. Even though theresonant converter is working as DCX, the operation modesfor the converter in [26]-[28] are not identical under differentpower directions, which would further increase the complexityof full load range ZVS analysis and achievement whenconsidering the junction capacitors and load.

In addition, over current protection and power limitationcapability are not embedded in these methods [26]-[28]. Whenthe converter is over load or starting up, the current andvoltage stress on the resonant tank is extreme high which maydamage the circuit. To deal with these issues, in [30], a PulseFrequency Modulation (PFM)/PWM hybrid control method isapplied in LLC resonant converter, which can achieve currentlimitation effectively. However, this method requiresadditional circuits to detect the over load conditions.Reference [31] proposes a multi-element resonant tank whichcombines notch filter and band pass filter. In case of overcurrent, the switching frequency is increased to notchfrequency to limit the output current. By this method, thecurrent can be limited inherently by the characteristic ofresonant tank, but sensing devices are required. In [32], anauxiliary circuit is added in the LLC converter, which canclamp the voltage of resonant capacitor by the output voltagethrough a transformer under over current condition. By this

method, inherent current limitation ability is embedded, butthe extra transformer increases the cost and volume of theconverter. In [33], clamping diodes are added to bypass theresonant capacitors in case of over current, which caneffectively reduce the input current ripple, switch current andresonant capacitor voltage stress. This method is simple toimplement and its response is fast. However, the clampingdiodes are only added at one side of the converter, which isonly suited for unidirectional power transfer.

The proposed C4LC-DCX resonant converter has thefollowing advantages:1) The proposed converter with the synchronous PWM

modulation method has identical operation characteristicsunder bidirectional power directions and can achievenatural bidirectional power flow. In addition, the resonantinductor currents in the primary and secondary sides aresymmetrical, which simplifies the analysis of voltageconversion gain and ZVS.

2) Full-load range ZVS can be achieved for all the switchesunder bidirectional power flow due to the two auxiliaryinductors added in the proposed converter. The ZVS isanalyzed with considerations of all the switch junctioncapacitors and load, which provides more accurateguidance for ZVS design. Moreover, a method ofmagnetic components integration is proposed, by whichall the magnetic components can be simplified andmanufactured with one external inductor and oneconventional transformer, and the specific designconsiderations are comprehensively discussed.

3) Power limitation and over current protection can beachieved under bidirectional power flow since theclamping diodes are connected in parallel with theresonant capacitors at both sides of the proposedconverter.

In this paper, a bidirectional symmetrical C4LC-DCXresonant converter with power limitation capability isproposed to achieve natural bidirectional power flow and ZVSwith consideration of load and all the switches junctioncapacitors. The operation principle analysis of the C4LC-DCXresonant converter with the synchronous PWM modulationmethod is given in Section Ⅱ. In Section Ⅲ, the constantvoltage gain, ZVS condition, power limitation and magneticcomponents integration of the C4LC-DCX converter areanalyzed. The experimental results based on a 1-kW prototypeare shown in Section IV to verify the effectiveness of theproposed converter.

II. PRINCIPLE OF OPERATION

A. Topology StructureThe topology of the C4LC-DCX resonant converter is

shown in Fig. 2. In this converter, two active half bridges areapplied to achieve bidirectional power flow. In the primaryside of the transformer, the auxiliary inductor La1 is connectedbetween point A and point B, and in the secondary side, theauxiliary inductor La2 is connected between point C and pointD. The two auxiliary inductors are used to help achieve full-load range ZVS for the switches of the proposed converter,and they affect the resonant frequency and the resonant




process. Clamping diodes are in parallel with the resonantcapacitors to realize power limitation in case of overload andlimit the inrush current when the converter starts up. It shouldbe noted that even though four inductors and one transformerare illustrated in the topology, all these magnetic componentscan be simplified and manufactured with one external inductorand one conventional transformer, which will be explained inPart D of Section Ⅲ.

The turns ratio of the transformer is n. To ensure that thetopology is completely symmetrical, the value of Lr2 referred tothe primary side is equal to Lr1 (Lr1=n2Lr2=Lr), the value of Cr3and Cr4 referred to the primary side is equal to Cr1 and Cr2(Cr1=Cr2=Cr3/n2=Cr4/n2=Cr), and the value of La2 referred to theprimary side is equal to La1 (La1=n2La2=La).

With the synchronous PWM modulation method, thedriving signals of S3 and S4 are the same as those of S1 and S2,respectively. If ignoring the effect of the dead-band, theswitches S1 and S2 in the primary side are switchedcomplementarily with 50% duty cycle (detailed waveforms areshown in Fig. 4). The C4LC-DCX resonant converter operatesat the resonant point. Four resonant capacitors Cr1, Cr2, Cr3, Cr4,two auxiliary inductors La1, La2 and two resonant inductors Lr1,Lr2 build up the resonant tank.

In this paper, the forward mode refers to the transmission ofpower from the V1 side to the V2 side.

Fig. 2. The topology of the C4LC-DCX resonant converter.

B. Mode 1: Forward Power Transmission ModeAs shown in Fig. 3, in the forward power transmission

mode, there are three working stages in a half switching cycle.Fig. 4 shows the key waveforms of the converter in this mode.The proposed converter with synchronous PWM modulationmethod will not work in DCM (Discontinuous ConductionMode) mode since the driving signals for two sides switchesare identical.Stage 1 (t0-t1): Fig. 3(a) shows the equivalent circuit of the

converter in this stage, and it can be equivalently representedby the circuit shown in Fig. 5. At t0, the switches S1 and S3

turn on with ZVS.

(a)

(b)

(c)Fig. 3. The working stages of the converter in the forward power transmission

mode.(a)Stage 1(t0-t1). (b)Stage 2(t1-t2). (c)Stage 3(t2-t3).

Fig. 4. The key waveforms of the converter in the forward power transmissionmode.

In this stage, La1, La2 resonant with Cr1, Cr2, Cr3, Cr4, Lr1 andLr2. According to the relationship between the voltages andcurrents of the circuit shown in Fig. 5, the equations (1), (2)and (3) can be deduced to describe the converter in this stage.

11 3

11

23

( )2 ( ) ( )

( )( )

( )( )

rr C C

Laa C

a LaC

di tL v t nv tdt

di tL v t

dtL di t

nv tn dt

(1)

1 21 1

3 2 41

( ) ( )( ) ( )

( ) ( ) ( )( )+

C Cr r r La

C La Cr r r

dv t dv tC i t C i t

dt dtdv t i t dv t

C n i t C ndt n dt

(2)

1 2 1

3 4 2

( ) ( )( ) ( )

C C

C C

v t v t Vv t v t V

(3)

Where ir1 is the resonant current in the primary side, iLa1 andiLa2 are the currents of La1 and La2 respectively, vC1, vC2, vC3 andvC4 are the voltages across Cr1, Cr2, Cr3 and Cr4 respectively.

For the proposed C4LC-DCX converter, the resonantfrequency is referred to the frequency of the resonant inductorcurrent. According to (1), the current of the resonant inductorin the primary side can be expressed as

1 1 31( ) ( ) ( )

2r C Cr

i t v t nv t dtL

(4)

Based on (4), it can be deduced that the resonant frequency




is equal to the frequency of vC1-nvC3. Hence, the resonantfrequency can be solved according to the frequency of vC1-nvC3.

According to (3), it can be deduced that dvC2(t)/dt=-dvC1(t)/dt and dvC4(t)/dt=-dvC3(t)/dt, then (2) can be simplifiedas

11 1 1

3 2 31

2 = ( ) ( )= ( )

( ) ( )2 ( )

Cr La r s

C La sr r

dvC i t i t i t

dtdv i t i t

C n i tdt n n

(5)

The derivative of the difference between the two equationsin (5) can be expressed as

21 3 1 2 1

2

( ) ( ) ( ) ( ) ( )12 2C C La La rr

d v t nv t di t di t di tC

dt n dt dtdt

(6)

Then, substituting the three equations in (1) into (6), it canbe deduced that

21 3

1 32

( )( ) 0

2C C r a

C Cr a r

d v nv L Lv nv

L L Cdt

(7)

By solving the differential equation in (7), the angularfrequency of vC1-nvC3 can be obtained.

13 2r a

Cr a r

L LL L C

(8)

According to the relationship between the resonant currentir1 and vC1-nvC3 shown in (4), it can be deduced that theresonant angular frequency is equal to the angular frequencyof vC1-nvC3. Therefore, the resonant frequency can beexpressed as

13 12 2 2 2

C r arr

r a r

L Lf

L L C

(9)

The following equations can be deduced by substituting (1)into the derivative of the sum of the two equations in (5).

21 3

1 32

( + ) 1 ( + ) 02

C CC C

a r

d v nvv nv

L Cdt (10)

According to the solutions of the differential equations in(7) and (10), the expressions of vC1 and vC3 can be obtained.Then according to the relationship between switch currentsand resonant capacitor voltages in (5), the expressions ofswitch currents can be deduced. Finally, substituting theinitial values of switch currents and resonant capacitorvoltages at t0, the following equations can be deduced

3010

10 301 0 0

3010

10 302 0 2 0

2

3010

10 303 0 0

3010

( ) sin ( ) cos ( )4 2

sin ( ) cos ( )4 2

( ) sin ( ) cos ( )4 2

4

SS

C CC r r

r r

SS

C C

r

SS

C CC r r

r r

SS

I I V nVnv t t t t tC

I I V nVn t t t tC

I I V nVnnv t t t t tC

I In

10 30

2 0 2 02

sin ( ) cos ( )2

C C

r

V nVt t t t

C

(11)

Where VC10 is the voltage of Cr1 at t = t0, Is10 is the current

of S1 at t = t0, VC30 is the voltage of Cr3 at t = t0, Is30 is thecurrent of S3 at t = t0, ωr=2πfr, and 2 1/ 2 a rL C .

The equation (11) is complex, in order to simplify theanalysis of ZVS condition, the effect of resonance between theresonant capacitors and auxiliary inductors is ignored. Thenthe resonant capacitor voltage is a sine wave with an angularfrequency of ωr, according to the solution of the differentialequation in (7), the voltages of resonant capacitors can beexpressed as

1 1 0 1 0

3 2 0 2 0

( ) sin ( ) cos ( )

( ) sin ( ) cos ( )

C r r

C r r

v t A t t B t t CCv t A t t B t tn

(12)

Where A1, A2, B1, B2 and C are constant quantitiesremaining to be solved. The absolute values of iC1 and iC2 areequal, and the sum of vC1 and vC2 is equal to V1, hence the DCcomponent of vC1, which is C in (12), is equal to V1/2.Substituting (12) into (5), the currents of S1 and S3 in this stagecan be expressed by

s1 1 0 1 02 2

s3 2 0 2 0

( ) 2 cos ( ) 2 sin ( )

( ) 2 cos ( ) 2 sin ( )r r r r r r

r r r r r r

i t C A t t C B t t

i t n C A t t n C B t t

(13)

Then substituting the initial values of switch currents andresonant capacitor voltages at t0 into (12) and (13), theconstant quantities A1, B1, A2 and B2 can be deduced, whichare equal to -IS10/2Crωr, VC10-V1/2, -IS30/2n2Crωr and VC30-V2/2respectively.

Therefore, the currents of S1 and S3 and the voltages of Cr1and Cr3 in this stage can be expressed by

1s1 10 0 10 0

101 11 10 0 0

2 2s3 30 0 30 0

3023 30 0 2

( ) 2 ( )sin ( ) cos ( )2

( ) ( )cos ( ) sin ( )2 2 2

( ) 2 ( )sin ( ) cos ( )2

( ) ( )cos ( ) sin (2 2

r r C r s r

sC C r r

r r

r r C r s r

sC C r r

r r

Vi t C V t t I t t

IV Vv t V t t t t

CV

i t n C V t t I t t

IVv t V t t t

n C

20 )

2V

t

(14)

Fig. 5. The equivalent circuit in stage 1 of the forward power transmission.Stage 2 (t1-t2): At t1, S1 and S3 turn off. As shown in Fig.

3(b), in this stage, the junction capacitors of S1 and S3 arecharged, and the junction capacitors of S2 and S4 aredischarged. At t2, the voltages of S2 and S4 are equal to zero,the body diodes of S2 and S4 conduct.Stage 3 (t2-t3): Fig. 3(c) shows the equivalent circuit of the

converter in this stage. In this stage, current flows through thebody diodes of S2 and S4. At t3, S2 and S4 turn on with ZVS.

Because of the symmetry for both the topology and PWMmodulation, the operation principle of the backward powertransmission mode is the same as that of the forward powertransmission mode.

The initial values of the inductor currents and resonantcapacitor voltages at t0 are solved as follows.




Considering that the dead-time is relatively short comparedwith the switching period, the effect of dead-time is ignored inthe following analysis. During t0 to t1, the input current i1 isequal to is1/2. Based on power conservation law of two sides,it can be deduced that

1

0

21 2

11

( )22

t St

s o

i t Vi dtT R V

(15)

Where Ro is the output resistance. Hence, substituting theexpression of is1 in (14) into (15), VC10 can be expressed as

22 1

1014 2C

s r o

V VVf C R V

(16)

In practical application, the output capacitor Co is designedto be much larger than the resonant capacitor, hence the effectof output capacitor is negligible. The output current i2 is equalto -is3/2 during t0 to t1. The average value of the output currentcan be expressed as

1

0

3 22

( )22

t S

ts o

i t Vi dt

T R (17)

Then substituting the expression of is3 in (14) into (17), VC30

can be deduced.2 2

30 22 4Cs r o

V VV

n f C R (18)

As shown in Fig. 5, during t0 to t1, the voltage across La1 isequal to -vC1, and the voltage across La2 is equal to vC3. SinceIS10 and IS30 are small, their effects on vC1 and vC3 are ignoredin the following analysis. Hence according to (1) and theexpressions of vC1 and vC3 in (14), the following equations canbe deuced.

10 1 11 0 0 10

2( ) sin ( ) ( )

2 2C

La r Laa r a

V V Vi t t t t t I

L L

(19)

2230 2 2

2 0 0 202

( ) sin ( ) ( )2 2C

La r Laa r a

V V n Vi t n t t t t IL L

(20)

Where ILa10 and ILa20 are the currents of La1 and La2 at t0,respectively. ILa10 is equal to -iLa1(Tr/2), and ILa20 is equal to -iLa2(Tr/2). Therefore, according to (19) and (20), it can bededuced that

110 1( )

2 8r r

La Laa

T VTI i

L (21)

22

20 2 ( )2 8r r

La Laa

T n V TI iL

(22)

Where Tr=1/fr. By substituting (16) into the expression ofvC1 in (14), the voltage across Cr1 at t1 can be expressed by(23).

21 2

1 1 11

( ) ( )2 2 4r

C Cs r o

T V Vv t vf C R V

(23)

The C4LC-DCX converter with synchronous PWMmodulation method operates at the resonant frequency, hencethe resonant inductor current at t1 is equal to zero. Since thedead-time is short, the change of vC1 during the dead-time isnegligible. If ignoring the effect of the switch junctioncapacitors, during t1 to t3, the body diode of S2 is conducted,and the voltage of the transformer in the primary side vT1 isnearly equal to -V1/2. Hence the expression of ir1 during t1 to t3

can be expressed as1

1 1 1 11( ) ( ) ( )

2r Cr

Vi t v t t tL

(24)

Then substituting (23) into (24), it can be deduced that

10 1 31

( )4

o deadr r

s r r

P tI i t

f C L V (25)

Where Po is the output power and tdead is the length of thedead-time. Then according to (21), (22) and (25), thefollowing equation can be deduced.

110 10 10

14 8o dead r

S r Las r r a

P t VTI I I

f C L V L (26)

22

30 20 1018 4

o deadrS La r

a s r r

nP tn V TI I nIL f C L V

(27)

The above equations will be used in the convertercharacteristics analysis in Section Ⅲ.

For the conventional LLC converter, the asymmetricstructure leads to different operation characteristics in theforward and backward modes and makes the ZVS analysiscomplex when considering all the switch junction capacitors[34]. The CLLC converter differs from the proposed C4LC-DCX converter in that no auxiliary inductor is added in theconverter, hence ZVS cannot be achieved for the switches. Forthe CLLLC converter [22]-[23], the resonant inductor currentis coupled with the magnetizing inductance current, whichmakes the ZVS analysis with consideration of all the switchjunction capacitors complex. In addition, with the traditionalmagnetizing inductance design method [22], only one sideswitches can achieve ZVS. Even if these converters workunder DCX operation, the above problems still exist.Compared with these converters, the proposed C4LC-DCXconverter has a symmetrical structure and the resonantinductor current waveforms in the primary and secondarysides are symmetrical (ir1=ir2/n), which simplifies the analysisof operation principle and ZVS condition in bidirectionalpower directions. Full-load range ZVS can be achieved for allthe switches in the proposed converter with considerations ofswitch junction capacitors and load under bidirectional powerflow. In addition, bidirectional power limitation capability isembedded in the proposed converter, while power limitationcannot be achieved in the hardware circuits of theconventional LLC, CLLC and CLLLC converters.

C. Mode 2: Forward Power Limitation ModeWhen the converter is overload, the current flowing through

the resonant capacitors is large, and then the converter willwork in the power limitation mode. As it is shown in Fig. 6, inthis mode, there are eight working stages in a half switchingcycle. Fig. 7 shows the key waveforms of the converter in thismode.Stage 1 (t0-t1): Fig. 6(a) shows the equivalent circuit of the

converter in this stage. At t0, S1 turns on with ZVS, while thejunction capacitor of S3 begins to be discharged. This stageends when the voltage across S3 decreases to zero at t1.Stage 2 (t1-t2): As shown in Fig. 6(b), D2 and D3 conduct in

this stage. The input current i1 is less than zero, and the outputis bypassed by D3. The resonant tank does not work, and the




power transmission is interrupted.Stage 3 (t2-t3): Fig. 6(c) shows the equivalent circuit of the

converter in this stage. At t2, iLa2 is equal to ir2, the current ofD3 is equal to zero. Then, D3 turns off.Stage 4 (t3-t4): At t3, iLa1 is equal to ir1, the current of D2

decreases to zero. Then, D2 turns off. This stage is the same asthe stage 1 in Mode 1. The equivalent circuit of this stage isshown in Fig. 3(a).Stage 5 (t4-t5): At t4, vC4 drops to zero, and then D4 conducts.

As shown in Fig. 6(d), Cr3 and Cr4 are bypassed, and thevoltage of La2 is clamped to V2 in this stage.Stage 6 (t5-t6): Fig. 6(e) shows the equivalent circuit of the

converter in this stage. At t5, S1 and S3 turn off, and then thejunction capacitors of S1 and S2 begin to be charged/discharged.iLa2 minus ir2 is less than zero, so the body diode of S3 conductsin this stage.Stage 7 (t6-t7): Fig. 6(f) shows the equivalent circuit of this

stage. At t6, the voltage across S2 drops to zero, and then thebody diode of S2 conducts.Stage 8 (t7-t8): Fig. 6(g) shows the equivalent circuit of this

stage. vC1 decreases to zero at t7, and then D1 conducts. At t8,S2 turns on with ZVS, while the junction capacitors of S3 andS4 begin to be charged or discharged.

(a)

(b)

(c)

(d)

(e)

(f)

(g)Fig. 6. The working stages of the proposed converter in the forward power

limitation mode.(a)Stage 1(t0-t1). (b)Stage 2(t1-t2). (c)Stage 3(t2-t3). (d)Stage 5(t4-t5).

(e)Stage 6(t5-t6). (f)Stage 7(t6-t7). (g)Stage 8(t7-t8).

Fig. 7. The key waveforms of the proposed converter in the forward powerlimitation mode.

It should be noted that the clamping diodes only work in thepower limitation mode. Under normal working conditions, itdoes not participate in the power transmission and will notcause additional loss.

Because of the symmetry for both the topology and PWMmodulation, the operation principle of the backward powerlimitation mode is the same as that of the forward powerlimitation mode.

III. CONVERTER CHARACTERISTICS ANALYSIS

A. Constant Voltage GainFig. 8 shows the key currents waveforms of the converter in

the forward power transmission mode. Without consideringthe dead-band, the average value of iLa1 and iLa2 is equal tozero. Hence, the average value of the input current i1 andoutput current i2 can be expressed by

1 1 121 0

( ) ( )22 2

STr La r

s

i t i t ii dtT

(28)




1 2 122 0

( ) ( )22 2

STr La r

s

ni t i t nii dtT

(29)

Where Ts is the switching period.The output power is equal to input power if ignoring the

losses, so according to (28) and (29), the voltage conversiongain M can be expressed by

2 1

1 2

1V iM

V i n (30)

According to (30), a conclusion is drawn that the voltageconversion gain of the proposed converter is only determinedby the turns ratio n and its value remains unchanged from no-load to full-load.

Fig. 8. The key currents waveforms of the converter in the forward powertransmission mode.

B. ZVS Condition AnalysisAs Fig. 4 shows, to ensure that S1 and S2 can achieve ZVS,

ir1 minus iLa1 should be positive and can charge/discharge thejunction capacitors of S1 and S2 completely during t1 to t3.

During t1 to t3, the voltage of Cr1 can be regarded asunchanged, and the voltage across S1 increases from zero to V1.Hence, it can be deduced that

1

1 1 1 1

1 1 11 1 1 1 3

1( ) ( )

( ) = ( )+ ( ), [ , ]

t

La Cta

CLa

a

i t V v t dtLV v t

t t i t t t tL

(31)

During the dead-time, the voltage of the transformer in theprimary side vT1 decreases from V1/2 to -V1/2, and vT1 plus vds1is less than or equal to V1/2. Hence, ir1 satisfies (32) during t1to t3.

1

11 1 1

11 1 1 1 3

1( ) ( )2

1 ( ) ( ), [ , ]2

t

r Ctr

Cr

Vi t v t dtL

Vv t t t t t tL

(32)

In order to prevent anti-resonance, ir1 minus iLa1 should bepositive during t1 to t3. Hence, according to (31) and (32), anti-resonance will not occur if (33) is satisfied.

1 1 111 3 1 3 1 1

1 1

( )( ) ( ) ( )

2 ( ) 0

dead Cr La C dead

r a

La

t V v tVi t i t v t t

L Li t

(33)

According to (9), it can be deduced that

2 2=8 1

ar

r a r

LL

f L C (34)

Then substituting (21), (23) and (34) into (33), it can bededuced that

21

2 3

(1 4 )16s dead r

adead o r

f V t fL

t P f

(35)

In order to discharge or charge the junction capacitors of S1

and S2 completely during t1 to t3, (36) should be satisfied.

3

11 1 1 1( ) ( ) 2

t

r La ossti t i t dt C V (36)

Where Coss1 is the value of the junction capacitors of theprimary side switches. By substituting (21), (23), (31), (32)and (34) into (36), it can be deduced that

21

2 2 2 31 1

(1 2 )16 8

dead s r deada

oss s r dead r o

V t f f tL

C f f V t f P

(37)

From the analysis above, it can be concluded that ZVS forS1 and S2 will be achieved if the value of the auxiliaryinductors satisfies (35) and (37).

As Fig. 4 shows, in the secondary side, the direction ofresonant current ir2 during the dead time is favorable for S3 andS4 to achieve ZVS. Hence, if (38) is satisfied, the ZVS of thesecondary side switches can be achieved.

3

1

12 2( ) 2

t

La osst

Vi t dt Cn

(38)

Where Coss2 is the value of the junction capacitors of thesecondary side switches.

During the dead-time, the change of the secondary sideauxiliary inductor current iLa2 is negligible. Thus, substitutingthe expression of iLa2(Tr/2) in (22) into (38), it can be deducedthat

2

216dead

ar oss

n tL

f C (39)

Fig. 9 shows the available region of ZVS according to (35),(37) and (39). To achieved ZVS for all the switches in theproposed C4LC-DCX converter, the auxiliary inductorsshould be designed to satisfy (35), (37) and (39).

Fig. 9. The available region of ZVS (V1=400V, n=1, fr=fs=500kHz,Coss1=Coss2=60pF, tdead=50ns).

C. Power Limitation of The ConverterIn the power limitation mode, the power transmission will

be interrupted when the clamping diodes conduct. Themaximum transmission power occurs at the critical momentwhen the load increases to the point where power limitationoccurs, and the waveforms at this moment is shown in Fig. 10.




As shown in Fig. 10, at t0, vC1 is equal to V1, and is1 is equalto 0. During t0 to t1, i1 is equal to is1/2, hence based on theexpression of is1 in (14), the input current can be expressed by

11 0( ) sin ( )

2r r

rC V

i t t t

(40)

At t1, vC1 is equal to 0. If ignoring the influence of the dead-band, according to (14) and (40), the maximum average valueof input current can be expressed as

1

01_ max 1 1

2 ( ) 2t

s rts

i i t dt f C VT

(41)

Hence, the maximum transmission power can be calculatedby

2max 1 1_ max 12 r sP V i C f V (42)

From the analysis above, it can be deduced that themaximum power is related to the value of Cr. Hence, theresonant capacitor can be designed according to the maximumpower.

Fig. 10. The waveforms of the input current and the voltages acrossresonant capacitors at the critical moment when power limitation occurs.

D. Integration of Magnetic ComponentsAs Fig. 2 shows, there are four inductors and one

transformer in the proposed converter. The method ofmagnetic components integration is applied in this paper toreduce the number of magnetic components, and the detailedprocess is shown in Fig. 11.

Fig. 11(a) shows the magnetic components network of theproposed converter, and its equivalent circuit when Lr2 and La2

are referred to the primary side is shown in Fig. 11(b).According to the equivalent replacement principle of delta-starconnection, the circuit in Fig. 11(b) can be transformed intothe T type circuit shown in Fig. 11(c). Then, the cantilevermodel of the transformer can be obtained from the T typecircuit, which is shown in Fig. 11(d). In order to limit themaximum power in a safe range, the value of resonantcapacitors cannot be too large. Hence, large resonant inductorsare used in the proposed converter to meet the requirement ofresonant frequency. Considering that the transformer leakageinductance is small, an external inductor is used to compensatethe inadequate value of the transformer leakage inductance.Hence, Lca is divided into two parts, the external seriesinductor Lk_ext and the transformer internal leakage inductanceLleak. Hence, as Fig. 11(e) shows, the cantilever model of theactual transformer is the circuit in the red dotted box. Finally,convert the actual transformer from cantilever model to Tmodel, which is shown in Fig. 11(f).

The external inductor in Fig. 11(f) can be calculated by (43).

_2

2r a

k est leakr a

L LL L

L L

(43)

Fig. 11. The integration of the magnetic components.After the equivalent transformation, the turns ratio of the

actual transformer nact in Fig. 11(f) is not equal to the turnsratio n in Fig. 2, and it can be calculated by (44). Themagnetizing inductance of the actual transformer in Fig. 11(f)can be calculated by (45).

2 2_

2

2 ( )4 4(2 )(2 )

k ext a rr a r aact

a r ar a

L L LL L L Ln

L L LL L

(44)

2

_ 2( )act a

m acta r

n LL

L L

(45)

The magnetic core of the transformer can be designedaccording to (44) and (45). By this method, the auxiliaryinductors, resonant inductors and transformer of the C4LC-DCX converter can be simplified and manufactured with oneexternal inductor and one conventional transformer withoutchanging the midpoint voltages and switch currents, which isthe meaning of magnetic component integration in this paper.

The final circuit derived by magnetic componentsintegration is shown in Fig. 12, which has the same electricalcharacteristics of resonant tank as the circuit shown in Fig. 2.The reason why discrete magnetic components are used in thetopology shown in Fig. 2 instead of the integrated case is thatthe topology is completely symmetrical, which can simplifythe analysis of operation principle and ZVS condition underbidirectional power flow.

In practical application, the transformer is none-ideal, whichincludes leakage inductance and magnetizing inductance. Theleakage inductance can be used as part of resonant inductor,and the large magnetizing inductance in real transformer hasnegligible influence on the magnetic components network ofthe proposed converter. Therefore, in the process of magneticcomponents integration, the magnetizing inductance is ignoredfor the circuit shown in Fig. 11(a). It should be noted that theproposed C4LC-DCX converter is implemented by the finalcircuit derived by magnetic components integration shown inFig. 12 in the hardware design. In the final circuit, both theleakage inductance and magnetizing inductance of the actual




transformer are considered.The magnetic components network of the CLLLC and

C4LC converters can be equivalently transformed, but thesymmetrical magnetic components network of the proposedconverter shown in Fig. 2 simplifies the analysis of operationprinciple and ZVS condition in bidirectional power directions.

For the resonant tank of conventional CLLLC structure, theparameters in the primary and secondary sides aresymmetrical. If clamping diodes are added to achieve powerlimitation in a safe range, the value of the two resonantinductors will be too large to be implemented by thetransformer leakage inductances. Hence, the magneticcomponents network of the CLLLC converter will beimplemented by two external series inductors and oneconventional transformer. Besides, when the CLLLCconverter operates in resonant point, the voltage conversiongain is equal to the turns ratio. While for the circuit derived bymagnetic components shown in Fig. 12, the inductor in thesecondary side is the small intrinsic leakage inductance oftransformer, hence only one external inductor and oneconventional transformer is required, and the turns ratio can becalculated according to (44).

In many engineering practices, when the transformer is usedin combination with external series inductor, the leakageinductors of transformer are considered to be small and areignored. While for the transformer model applied in the circuitderived by magnetic components integration, the actualleakage inductors in the primary and secondary side are takeninto account, and the addition of external series inductor is tocompensate the inadequate value of the leakage inductors.

Fig. 12. The final circuit derived by magnetic components integration.

IV. PARAMETER DESIGN AND EXPERIMENTAL RESULTS

A. Parameter DesignA 1000W experimental prototype based on GaN devices

which is shown in Fig. 13 is built to verify the above analysisfor the proposed converter. The input voltage V1 and outputvoltage V2 are both 400V, and the switching frequency fs is500kHz.

Fig. 13. The experimental prototype.

To reduce the size of converter, the prototype is designedaccording to the circuit derived by magnetic componentsintegration shown in Fig. 12, in which the four inductors andone transformer of the C4LC-DCX converter shown in Fig. 2is implemented by one external series inductor and oneconventional transformer.

For the C4LC-DCX converter shown in Fig.2, under thecondition of V1=V2=400V, the turns ratio n can be calculatedbased on (30).

1

2

400 1400

Vn

V (46)

The value of the resonant capacitors is related to themaximum transmission power. Under the condition ofPmax=1.23kW and fs=500kHz, the value of resonant capacitorcan be obtained according to (42).

max2 5 2

1

1230 7.72 2 5 10 400r

s

PC nF

f V

(47)

Under the condition of tdead=50ns, fs=fr=500kHz,Coss1=Coss2=60pF and Po=1kW, the constraint conditions of theauxiliary inductor can be deduced based on (35), (37) and (39).

21

2 3

(1 4 )73

16s dead r

adead o r

f V t fL H

t P f

(48)

21

2 2 2 31 1

(1 2 )60

16 8dead s r dead

aoss s r dead r o

V t f f tL H

C f f V t f P

(49)

2 2 9

5 122

1 50 10 10416 16 5 10 60 10

deada

r oss

n tL H

f C

(50)

Hence, the auxiliary inductor La is designed to be equal to60μH to ensure that all the switches can achieve full-loadrange ZVS.

Then, by substituting La=60μH, Cr=7.7nF and fr=500kHzinto (9), the value of resonant inductor can be calculated.

2 2 7.38 1

ar

r a r

LL H

f L C

(51)

The leakage inductance of the actual transformer Lleak is2μH. For the final circuit derived by magnetic componentsintegration, the value of the external series inductor can becalculated by substituting Lr=7.3μH and La=60μH into (43).

_2

9.72

r ak est leak

r a

L LL L H

L L

(52)

By substituting the value of Lr, La and Lk_est into (44), theturns ratio of the actual transformer nact can be calculated.

2 2_

2

2 ( )4 40.84

(2 )(2 )k ext a rr a r a

acta r ar a

L L LL L L Ln

L L LL L

(53)

According to (45), the magnetizing inductance of the actualtransformer Lm_act can be calculated.

2 6 2

_ 6 6

0.84 (60 10 ) 22.52( ) 2 (60 10 7.3 10 )

act am act

a r

n LL H

L L

(54)

TABLE I shows the parameters of the prototype. Theparameters selected according to the above method can makethe converter resonate at the 500kHz switching frequency.




TABLE IPARAMETERS OF THE EXPERIMENTAL PROTOTYPE

Item DetailInput Voltage (V1) 400V

Output Voltage (V2) 400VRated Output Power (Po) 1000WSwitching Frequency (fs) 500kHz

Turns Ratio (n) 1Resonant Capacitance (Cr) 7.7nFResonant Inductance (Lr) 7.3μHAuxiliary Inductance (La) 60μH

External Series Inductor (Lk_set) 9.7μHLeakage Inductance of Actual Transformer (Lleak) 2μH

Turns Ratio of Actual Transformer (nact) 14:17Magnetizing Inductor of Actual Transformer (Lm_act) 22.5μH

Switches GS66508TClamping Diodes G3S06503C

B. Experimental ResultsThe steady-state waveforms of the converter under different

loads are shown in Fig. 14. vgs2 and vgs4 are the driving signalsof S2 and S4 respectively, and irp is the resonant current in theprimary side (irp=ir1-iLa1). It can be seen from Fig. 14(a) andFig. 14(b) that the driving signals for the primary andsecondary bridges are identical under different powerdirections, and the actual resonant frequency is equal to500kHz, which verifies the correctness of (7). Fig. 14(c) is thewaveforms of the converter in forward power limitation mode,it can be seen that the resonant capacitors are clamped by the

conducted diodes in the power limitation mode (1100W),which interrupts the power transmission.

Fig. 15 shows the waveforms of the midpoint voltages (vABand vCD, where Point A, B, C and D are denoted in Fig. 2) andthe resonant currents on both sides of the transformer underdifferent loads in the forward and backward powertransmission modes. As Fig. 15 shows, irs is the resonantcurrent in the secondary side (irs=ir2-iLa2), the voltages acrossthe two auxiliary inductors are nonlinear, and the converteroperates effectively under different loads and different powerdirections.

Fig. 16 shows the soft-switching waveforms of the proposedC4LC-DCX converter under different load conditions. As it isshown in Fig. 16, all the switches in the proposed convertercan achieve ZVS at no-load, half-load and full-load conditionsunder bidirectional power flow.

Fig. 17 shows the dynamic waveforms of the proposedconverter. In Fig. 17(a), the power is changed from +500W to-500W. It can be seen that the direction of power flow can bechanged smoothly. In Fig. 17(b), the power of the proposedconverter switches between 100W and 500W. It can be seenthat the output voltage remains unchanged when the loadchanges in the power transmission mode. The soft-startwaveforms of the proposed converter are shown in Fig. 17(c).It can be seen that the inrush current is limited when theconverter starts up.

(a) (b) (c)Fig. 14. Steady-state waveforms of the proposed converter under different loads.

(a) Full-load of forward power transmission. (b) Full-load of backward power transmission. (c) Over-load of forward power limitation mode.

(a) (b) (c)

(d) (e) (f)Fig. 15. The waveforms of the midpoint voltages and resonant currents. Forward power transmission: (a) no-load; (b) half-load; (c) full-load. Backward power

transmission:(d) no-load; (e) half-load; (f) full-load.




(a) (b) (c)

(d) (e) (f)Fig. 16. The soft-switching waveforms of the C4LC-DCX converter. Forward power transmission: (a) no-load; (b) half-load; (c) full-load. Backward power

transmission: (d) no-load; (e) half-load; (f) full-load.

(a) (b) (c)Fig. 17. The dynamic waveforms of the proposed converter.

(a) Forward mode to backward mode. (b) Load changes between 100W and 500W. (c) The soft-start waveforms.

Fig. 18 shows the measured voltage gain and efficiency ofthe proposed C4LC-DCX resonant converter.

Fig. 18. The measured voltage gain and efficiency.It can be seen from Fig. 18 that the voltage gain of the

proposed converter is almost constant under different loadconditions. The gain drops slightly with the increase of theoutput power, which could be caused by the conductionresistance, the line impedance, etc. The maximum efficiencyof the proposed converter is 97.4% and the full-load efficiencyis 96.5% at 500kHz.

V. CONCLUSION

In this paper, a bidirectional symmetrical C4LC-DCXresonant converter with the synchronous PWM modulation

method is proposed for DCX application. By adding auxiliaryinductors, full load range ZVS considering the effect of loadand switch junction capacitors for all the switches can beachieved. With the method of magnetic componentsintegration, the number of magnetic components is reduced. Inaddition, over current protection and power limitationcapability are embedded in the proposed converter by addingclamping diodes. A 1-kW prototype is designed to verify thetheoretical analysis. The ZVS analysis and parameter designare verified by the experimental results. Meanwhile, theresults have shown that natural bidirectional power flow,constant voltage conversion gain and natural power limitationcapability can be obtained with the proposed solution.

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A Bidirectional Symmetrical C4LC-DCX Resonant Converter