A Modified High-Efficiency LLC Converter With Two Transformers for Wide Input-Voltage Range Applications

1946 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 4, APRIL 2013

A Modified High-Efficiency LLC Converter WithTwo Transformers for Wide Input-Voltage

Range ApplicationsHaibing Hu, Member, IEEE, Xiang Fang, Student Member, IEEE, Frank Chen, Student Member, IEEE,

Z. John Shen, Fellow, IEEE, and Issa Batarseh, Fellow, IEEE

Abstract—This paper proposed a modified LLC converter withtwo transformers in series, which has four operation configura-tions, covering the range of four times the minimum input voltage.To optimize the proposed LLC converter in an attempt to achievegood efficiency, a numerical method is developed based on the LLCconverter’s steady-state equations. In order to minimize the mag-netizing current and thus minimize the conduction and core losses,an optimal objective is proposed to find the maximum magnetizinginductance. An optimization procedure and a design example aregiven. A 250-W 210-V output prototype with input voltage rang-ing from 25 to 100 V is built to verify the developed numericalmodel and optimal design method. The dc gain obtained from ex-perimental data agrees pretty well with that from the developednumerical model. Two conventional LLC converters are designedusing fundamental harmonic approximation and the proposed op-timal design, respectively, to make comparison with the proposedLLC converter and validate the proposed optimal design. Exper-imental results show that the proposed converter with proposedoptimal design can achieve the peak efficiency up to 98%, whilemaintaining a very wide input voltage range.

Index Terms—DC Gain, LLC converter, microinverter,optimization.

I. INTRODUCTION

PHOTOVOLTAIC (PV) is the fastest growing energy tech-nology in the world, with more than 30% annual increase

in cumulative installed capacity over past 15 years [1]. Amongsolar PV systems, PV panel is a key element, which not onlydetermines the overall cost but also the connected inverter’sspecifications as well. Based on the current PV technologies,the currently commercial PV panels are typically classified intotwo basic groups: 1) crystalline silicon PV panel; 2) thin film PVpanel. The crystalline PV panels with production share reaching

Manuscript received September 13, 2011; revised January 17, 2012 andApril 23, 2012; accepted May 12, 2012. Date of current version October 26,2012. This work was supported in part by the United States Department of En-ergy under Award DE-EE0003176 and in part by the National Natural ScienceFoundation of China under Grant 51177070. Recommended for publication byAssociate Editor Y.-M. Chen.

H. Hu is with the Nanjing University of Aeronautics and Astronautics, Nan-jing 210016, China, and also with the University of Central Florida, Orlando,FL 32826 USA (e-mail: [email protected]).

X. Fang, F. Chen, Z. J. Shen, and I. Batarseh are with the Universityof Central Florida, Orlando, FL 32826 USA (e-mail:[email protected];[email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2012.2201959

up to 83% in 2009 [2], whose power ratings commonly rangefrom 160 to 280 W, have low open-circuit and optimum operat-ing voltages varying from 22 to 65 V. In this paper, the proposedconverter aims for the crystalline PV applications.

Currently, there are three commonly used grid-tied PV invert-ers: the centralized PV inverters, the string PV inverters, and thePV microinverters [3]. The PV microinverters are small grid-tiedinverters of 150–300 W that convert the output of a single PVpanel to the ac grid. The PV microinverters have gained consid-erable attraction in recent years due to their unique advantagesover the conventional centralized inverters and the string in-verters in both commercial and residential rooftop applications,where low dc voltage or ac voltage wiring, easy installation,and mitigation of the partial shading effect are emphasized.With these advantages, the PV microinverter technology hasbecome the trend for future PV systems, but many challengesremains in its way including high efficiency, low cost, long lifeexpectancy, low profile, and multifunctions. For PV microin-verters, efficiency is a top priority, because converters with highefficiency can reduce the size and volume due to less powerdissipation needed to be processed, and further reduction of theinitial cost with more energy harvested. Many studies have beencarried out to improve the efficiency of PV microinverter, in-cluding soft-switching techniques, single-stage architecture, andcontrol techniques [4]–[6]. In addition, these converters shouldhave high step-up capability to convert the low voltage fromPV panels to the voltage compatible to that in ac grid as well.Meanwhile, they should be designed with wide input-voltagecapability to interface a single PV panel featuring wide voltagevariations by nature.

Basically, PV microinverters can be categorized into threeclasses [4]: 1) microinverter architecture with dc bus (so-calledtwo-stage microinverter); 2) microinverter architecture withpseudo dc bus (so-called one-stage microinverter); 3) microin-verter architecture without dc bus. In this research, the front-enddc/dc converter for the PV microinverters in the first category ismainly focused. Among dc/dc converters, the LLC converter, ca-pable of soft switching and achieving high switching frequencywhile maintaining high efficiency, has become a hot researchtopic in recent decades [7]–[29], which could be a good candi-date for PV microinverter applications. However, LLC convert-ers can achieve high efficiency and high power density only ifoperating around the resonant frequency, resulting in a very nar-row input voltage range and limited voltage regulation capabil-ity. This limitation previously kept the LLC topology from being

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HU et al.: MODIFIED HIGH-EFFICIENCY LLC CONVERTER WITH TWO TRANSFORMERS FOR WIDE INPUT-VOLTAGE RANGE APPLICATIONS 1947

Fig. 1. Reconfigured LLC topology from full bridge to half bridge.

used on PV microinverters, for which a very wide input voltagerange is typically expected. For fixed resonant parameters andload condition, the peak dc gain decreases as the magnetizinginductance increases. To maintain the high dc gain, capable ofwide input dc voltage range, the magnetizing inductance has tobe set to a small value, which incurs high magnetizing current,resulting in higher conduction and core losses. It is very chal-lenging for the conventional LLC converters to achieve high dcgain, while maintaining a very high overall efficiency.

Several pieces of research have been conducted to mitigatethe problem of the conventional LLC converter [8]–[14]. In [8],the authors proposed a hybrid scheme to achieve high dc gainby simply changing full bridge to half bridge as shown in Fig. 1.In this manner, the dc gain will be doubled.

However, the normalized dc gain for both full-bridge and half-bridge operations has to be designed at least as high as 2 in orderto cover all the input-voltage range, whose dc gain is still a littlebit high to achieve high efficiency as demonstrated in [8], whereto obtain two times dc gain a wide operating frequency rangefrom 40 to 130 kHz is designed. In this scenario, the optimalmagnet design would be very challenging. For a 2-kW prototypewith input voltage ranging from 125 to 550 V and output voltagefixed at 550 V, a weighted CEC efficiency 97.7% was achieved in[8]. Liang proposed a modified LLC converter to create anotherresonant frequency so as to improve the efficiency at light load[9]. However, the gain curve in Mode 1 still has to be designedto meet wide input-voltage range. Meantime, in its design, thefundamental harmonic approximation (FHA) method is adoptedto design the circuit parameters, which would incur huge dcgain error when it applies to LLC converter design with widefrequency variations. Another solution to achieve high dc gainis to change the transformer turns ratio according to differentinput voltage as shown in Fig. 2 [10]. Although this approachcan improve the dc gain, it suffers from the following two majordrawbacks. As input voltage increases and the transformer atsecondary side changes to the winding W1, 1) the flux in thetransformer will increase, resulting in higher core losses; 2)the magnetizing current at primary side will increase as well,which leads to higher current at the primary side and thus resultsin higher conduction losses and higher core losses in resonantinductor.

To overcome the drawbacks of the LLC converter, achievinghigh dc gain and meantime maintaining high conversion effi-ciency, this paper proposed a novel configuration of the LLCconverter by adaptively changing the magnetizing inductance

Fig. 2. LLC converter with an electronic transformer tap.

Fig. 3. Proposed LLC converter.

based on the input voltage to reduce the magnetizing currentwhile preserving high dc gain.

This paper is organized as follows. In Section II, the oper-ation principle of the proposed topology is given. In SectionIII, the accurate dc gain calculation is given based on the nu-meric method. In Section IV, the optimal criterion and optimaldesign procedure are presented. A design example is as wellgiven in this section. Following Section IV, experimental re-sults are given to demonstrate the efficiency improvement bythe proposed topology and dc gain accuracy achieved by theproposed numeric method. Finally, some conclusions are drawnin Section VI.

II. PROPOSED TOPOLOGY

As shown in Fig. 3, transformer T2 is inserted into the resonanttank in series connection with Lr , Cr , and T1; a bidirectionalswitch, configured by S5 and S6, is paralleled with the primarywinding of transformer T2 to enable or disable T2 by controllingthe bidirectional switch. The secondary sides of transformers T1and T2 are connected in parallel through two rectifier circuits toshare the load. When the input voltage is less than the thresholdVth , the bidirectional switch keeps ON and transformer T2 isdisabled so that it automatically blocks rectifier 2. In this case,the LLC converter operates as a conventional one. When theinput voltage is greater than the threshold Vth , the bidirectionalswitch turns OFF and the total magnetizing inductance in theprimary side will increase from Lm 1 to Lm 1+Lm 2 , reducing themagnetizing currents. In this way, the dc gain range is extendedwhile keeping magnetizing current low. In addition, by keepingS4 conducted and turning OFF S3 permanently, the full-bridge


Fig. 4. Different operation configurations. (a) Configuration 1. (b) Configura-tion 2. (c) Configuration 3. (d) Configuration 4.

structure will change to half-bridge structure, which will fur-ther double the dc gain. In summary, there are four operationconfigurations in this proposed topology illustrated as follows.

Configuration 1: As shown in Fig. 4(a), transformer T2 isdisabled by turning ON the bidirectional switch and rectifier 2is blocked. In this case, the converter operates as a conventionalLLC converter.

Configuration 2: As shown in Fig. 4(b), the bidirectionalswitch is OFF and two transformers operate in series at theprimary side and in parallel at the secondary side. In this manner,the total magnetizing inductance is the sum of two transformers’magnetizing inductance, Lm 1+Lm 2 .

Configuration 3: As shown in Fig. 4(c), the full bridge ischanged to half-bridge operation by switching OFF S3 and keep-ing S4 always ON. Meanwhile, transformer T2 is disabled by thebidirectional switch. In this manner, the dc gain will be halvedcompared to that in Configuration 1.

Configuration 4: As shown in Fig. 4(d), the converter operatesin half bridge and transformer 2 is enabled by turning OFF thebidirectional switch. Similar to Configuration 3, the dc gain ishalf of that in Configuration 2.

III. DC GAIN ANALYSIS

A. Current DC Gain Analysis

Obtaining the accurate dc gain will help guiding the designof LLC converters. However, as the characteristics of LLC con-verters are complicated by the nonlinear relationship betweenoutput voltage with excitations (input voltage and switchingfrequency) and load, obtaining a mathematical expression ofthe accurate dc gain becomes almost impossible. To simplifythe analysis of the characteristics of LLC converters, FHA hasbeen developed, where the voltages and currents are assumedto be sinusoidal waveforms, thereby permitting the traditionalac circuit analysis to be employed, and thus the approximateddc gain in mathematical expression can be easily derived [15].However, the inaccuracy in dc gain of the FHA technique maymislead the design, since the dc gain in FHA is much lower thanthat in real circuits, especially when the switching frequencydeviates far away from the resonant point. It clearly indicatesthat the design based on FHA leads to setting the magnetizinginductance lower than necessary to meet the desired dc gainrange, thus resulting in higher magnetizing current and higherconduction losses. Although there are several other techniques,such as describing function, Fourier series expansion, etc., toimprove the dc gain accuracy [16]–[25], they still cannot givean accurate dc gain due to some approximations assumed inthese techniques. In an efficiency-oriented design, an accuratedc gain is necessary in choosing the right magnetizing induc-tance to reduce the magnetizing current while meeting the dcgain range.

B. Numerical DC Gain Calculation

It is straightforward to obtain accurate dc gain character-istics by using simulation tools, such as Pspice, Saber, andPsim. However, applying this method to a recursive optimization


Fig. 5. LLC converter equivalent circuit.

algorithm in finding the optimal parameters will be time con-suming and unbearable. Another method is to use steady-stateequations which accurately describe resonant circuit behav-iors [26]–[29]. Thanks to the great advance in numerical calcu-lation tools, such as MATLAB, this approach becomes practical.

For a conventional LLC converter, the circuit in the secondaryside can be easily reflected to the one in the primary side andthe equivalent circuit can be described as shown in Fig. 5.

Assuming the transformer turns ratio is n, the equivalent out-put voltage and equivalent resistance in the primary side areVo/n and RL/n2 , respectively. As aforementioned, the pro-posed LLC converter may operate as both full-bridge and half-bridge types, and the analysis presented here will cover eithercase by setting

⎧⎨

⎩

Vin = Vg , for full bridge

Vin =Vg

2, for half bridge

(1)

where Vg is the amplitude of the input square wave. As forthe resonant components Cr and Lr , it is easy to describe theirbehaviors using the following differential equations:

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

ir = Crduc

dt

uLr = Lrdirdt

Vin = uLr + uc + uLm .

(2)

Describing the magnetizing inductance circuit behavior is a littlebit complicated as it may operate in following two differentscenarios. 1) When the load current il is greater than zero, thevoltage across the magnetizing inductance Lm is clamped to±Vo/n, in which case the resonant components are Lr and Cr ,and the circuit behavior on the magnetizing inductance can beexpressed as

Lmdimdt

= ±Vo

n. (3)

2) As the load current il decreases to zero, the circuit before therectifier will disconnect the one after the rectifier, in which casethe resonant components will be Lr , Lm , and Cr and the voltageacross Lm can be given as

uLm = Lmdirdt

. (4)

In summary, at any moment, the LLC converter will fall into oneof the six operation modes as summarized in Table I

The circuit behaviors in each operation mode can be describedusing the aforementioned equations. However, to solve these

TABLE ISIX OPERATION MODES

equations, the initial conditions or constraints should be applied.Owing to the symmetric operation, the end values of ir , iLm , anduc should be opposite to their initial values in a half switchingcycle for a steady state, whose constrains can be given as

⎧⎪⎨

⎪⎩

ir(0) = −ir(0+T s/2)

iLm (0) = −iLm (0+T s/2)

uc(0) = −uc(0+T s/2)

(5)

where Ts is the switching period. In addition, between eachoperation modes the inductor currents, ir , and iLm , and thecapacitor voltage, uc , should be continuous, which providesmore constraints on the operation equations. Also, there areconstraint conditions at the transition between different modes:at the end of Modes 1, 2, 4, and 5 the currents ir , and iLm , shouldconverge in order to enter the other mode; at the end of Modes 3and 6 the magnetizing inductor voltage um should reach ±Vo/nto change to the next mode. For a lossless converter, the inputand output power should be balanced, which will derive anotherconstraint expressed as

TS

2

∫ T s/2

0Vin [ir (t) − im (t)]dt =

V 2o

RL. (6)

If the LLC’s circuit parameters and the operating conditionare known, the mode equations for the dc gain can be solvedbased on the aforementioned equations and constraints. Al-though these equations are nonlinear, we can take advantageof numerical tools to find the solutions and obtain the precisecurrent and voltage functions and dc gain curves for differentoperating frequency and load conditions.

An example is given to demonstrate aforementioned numericanalysis. Modes 1, 3, 5, and 6 in one switching cycle, whichare common operation modes under normal load and belowresonant frequency condition, are chosen to present the numericcalculation procedure. Due to symmetric circuit operation, theoperations of Modes 1 and 3 are symmetric to those of Modes5 and 6. Therefore, only Modes 1 and 3 are analyzed here andModes 5 and 6 can be easily obtained. For Mode 1, the resonanttank behavior based on expression (2) can be described as

ir1(t) = Ir1 sin(2πfr t + θ1) (7.1)

im1(t) = Im1 +Vot

nLr (m − 1)(7.2)


vC 1(t) = − Vo

n√

Lr/Cr

Ir1 cos(2πfr t + θ1) −Vo

n+

nVin

Vo

(7.3)

where Ir 1 is the amplitude of ir and Im 1 is the initial currentvalue of im , θ1 is the initial phase angle in Mode 1, and m is theinductors’ ratio (Lm +Lr )/Lr . In Mode 3, the resonant currentand voltage would become

ir3(t) = im3(t) = Ir3 sin(

2πfr t√m + θ3

)

(8.1)

vC 3(t) = − Vo√

m

n√

Lr/Cr

Ir3 cos(

2πfr t√m + θ3

)

+nVin

Vo(8.2)

where Ir 3 is the amplitude of ir and im , and θ3 is the initialphase angle in Mode 3. From (5) and the continuity conditions,it can be derived that

Ir1 sin(θ1) = −Ir3 sin(

2πfr t3√m + θ3

)

(9.1)

Im1 = −Ir3 sin(

2πfr t3√m + θ3

)

(9.2)

− Vo

n√

Lr/Cr

Ir1 cos(θ1) −Vo

n+

nVin

Vo

=Vo

√m

n√

Lr/Cr

Ir3 cos(

2πfr t3√m + θ3

)

− nVin

Vo(9.3)

Ir1 sin(2πfr t1 + θ1) = Ir3 sin(θ3) (9.4)

Im1 +Vot1

nLr (m − 1)= Ir3 sin(θ3) (9.5)

− Vo

n√

Lr/Cr

Ir1 cos(2πfr t1 + θ1) −Vo

n

= − Vo√

m

n√

Lr/Cr

Ir3 cos(θ3) (9.6)

where t1 and t3 are the duration of Modes 1 and 3 respectively,and t1+t3 = Ts /2. In total, there are seven unknown variables:Ir 1 , Im 1 , θ1 , t1 , Ir 3 , θ3 , and dc gain. From the aforementionedsix equations and the power balance condition (6), there wouldbe right equations to solve these variables.

Regarding other operating conditions, similar numeric calcu-lation procedures can be applied through numerically solvingthe transcendental equations. The detailed mode analysis can befound in [24].

C. DC Gain of the Proposed Converter

As mentioned in Section II, the proposed converter has fouroperation configurations, each of which has its own dc gaincurve. As the converter configuration changes from full bridgeto half bridge, either from Configurations 1 to 3 or from Config-urations 2 to 4, the dc gain will be automatically halved. If thedc gain curves in Configurations 3 and 4 can be achieved, by

Fig. 6. Equivalent circuit of the proposed LLC converter.

halving those in Configurations 1 and 2, all four dc gain curvescan be easily drawn. Referring to Fig. 5, it is a conventional LLCconverter, whose accurate dc gain curve can be calculated outusing the technique mentioned in Section III-B.

As shown in Fig. 3, where additional transformer T2 is addedin series, combining these two transformers, the equivalent cir-cuit can be redrawn as shown in Fig. 6. (The equivalent param-eters are derived in the Appendix.)

As shown in Fig. 6, the magnetizing inductance increasesfrom Lm 1 to Lm 1+Lm 2 and the equivalent voltage and resis-tance in the secondary side change as well. The dc gain curve canbe achieved as well by using the numerical technique by rewrit-ing the differential (3)–(4) with the new magnetizing parameterLm 1+Lm 2 .

IV. OPTIMAL DESIGN

A. Optimal Criterion

As LLC converter operates in zero-voltage switching, switch-ing losses are greatly minimized and thus conduction and corelosses are dominant. For high voltage step-up applications,where the input voltage is relatively low, the current in theresonant tank will mainly determine the conduction and corelosses. The current in the resonant tank can be decomposed intotwo elements: load current and magnetizing current. Regard-ing the load current, it is completely determined by the loadcondition, while the magnetizing current depends on the circuitparameters and can be changed and minimized through choosingsuitable circuit parameters. As known, the magnetizing currentcan be expressed in (10) as the voltage across the primary sideis clamped to Vo /n

ΔILm =Vo

nLmTD (10)

where TD is the time duration of voltage clamped to Vo /n.Normally, both the output voltage and the switching frequencyrange are predetermined in an LLC converter design. On onehand, from (10), the only way to minimize the magnetizingcurrent iLm is to choose nLm as large as possible. On the otherhand, the magnetizing inductance Lm will largely determinethe maximal dc gain: the smaller the ratio of the magnetizinginductance to the resonant inductance, the higher the dc gainand the wider the input-voltage range. From the aforesaid twoscenarios, the magnetizing inductance will have an upper limit tomeet the dc gain range. Therefore, to minimize the magnetizingcurrent, the optimal design turns to finding the maximal nLm

under the constraint of dc gain range requirement.


Fig. 7. Expected gain curve.

B. Optimal Design Procedure

For the conventional LLC converter, the optimal design proce-dure is not so complicated. The turns ratio n is easily determinedby the output voltage Vo and input voltage at the resonant fre-quency. As n and the resonant frequency are determined, thenext step is to search the maximal inductance Lm using thenumerical model introduced in Section III. However, for theproposed LLC converter, the optimization process becomes alittle bit more complicated as determination has to be made atwhat input voltage the additional transformer should be insertedto achieve optimal performance.

Determination of dc gain curves of the proposed topologywill help to facilitate the optimization analysis. Two expecteddc gain curves in Configurations 1 and 2 are drawn as in Fig. 7.To smoothly and consecutively operate all these four configura-tions, the total dc gain range in these two configurations shouldat least be equal to 2, which can be expressed as

GRpeak mode1 ∗ GRpeak mode2 = 2 (11)

where GRpeak mode1 and GRpeak mode2 are the dc gain rangesin Configurations 1 and 2, respectively. It is known that the largerthe magnetizing inductance, the lower the peak dc gain. Since themagnetizing inductance Lm 1+Lm 2 in Configuration 2 is largerthan that in Configuration I, the peak dc gain in Configuration2 will be lower than that in Configuration I. Based on this, thepeak dc gains in Configurations 1 and 2 can be expressed as

GRpeak mode1 =Vth

Vmin

GRpeak mode2 =Vmax

Vth

GRpeak mode1 > GRpeak mode2 . (12)

Thus, the threshold Vth has the following constraint:

Vth >√

VminVmax . (13)

To avoid the reverse recovery losses of the secondary diodes, theswitching frequency is limited below resonant frequency fr . Atthe resonant frequency, the normalized dc gain is 1. Therefore,the turns ratio n1 in Configuration 1 can be expressed as

n1 =Vth

Vo. (14)

In this proposed topology, the voltage threshold Vth is a crucialparameter as it determines the turns ratios and the dc gainsfor each configuration. However, although the threshold Vth isconstrained by (13), it is still undetermined. Therefore, the firststep is to preset the threshold Vth . According to expression (14),the turns ratio n1 is determined. Since the threshold Vth and theturns ratio n are set, a parameter of Lm 1 is swept using thesearching technique to find a local maximum Lm 1 that meetsthe input-voltage range and frequency range requirements. Bychanging threshold Vth , a new local maximum Lm 1 can be foundby applying the same searching procedure. By repeating theaforesaid procedure, all these local maximum Lm 1 are obtainedand then from them a global maximum n1Lm 1 can be found. Inthis manner, all parameters except the secondary transformer’smagnetizing inductance Lm 2 are determined. The next step isto find the maximum Lm 2 to meet the dc gain requirementin Configuration II. By setting the range of Lm 2 , using thesearching method is relatively easy to find the maximum n2Lm 2 .(n2 is the turns ratio of T2.)

Where n2 is related to Lm 1 , Lm 2 and n1 and can be calculatedas

n2 =n1Lm1

Lm2. (15)

The optimal design procedure can be summarized as follows:1) specify threshold voltage range Vth = [Vth min Vth max ],

according to constraint (13), resonant capacitance rangeCr = [Cr min Cr max ], and the magnetizing inductancerange Lm 1 = [Lm 1 min Lm 1 max ];

2) set the initial threshold voltage and determine the turnsratio n1 for Configuration I and two peak gain rangesGRpeak mode1 and GRpeak mode2 according to expres-sions (14) and (11);

3) sweeping the resonant capacitance and applying the nu-merical model to find the local maximum Lm 1 ;

4) if the threshold voltage is less than Vth max , increase thethreshold voltage and go to Step 2; otherwise go to thenext step;

5) from local maximums, find a global maximum nLm 1 ;6) specify the search range of Lm 2 = [Lm 2 min Lm 2 max ];7) search the maximum n2Lm 2 under gain constraint of ex-

pression (12).Fig. 8 demonstrates the flowchart of the optimal design

procedure.

C. Optimal Design Example

A design example is given to illustrate the optimal procedure.Table II shows the specifications of the proposed converter.

According to the constraint of (12), the threshold voltagerange is set to [35.5 50 V]. The resonant capacitance Cr and themagnetizing inductance Lm 1 are set to [300 600 nF] and [Lr

5Lr ], respectively. Under the guidance of optimal design pro-cedure, the developed numerical model is applied to searchingoptimal parameters. A local maximum n1Lm 1 searching resultis shown in Fig. 9, where the threshold voltage is fixed. As theresonant capacitance Cr changes, the inductance Lm 1 to meetthe desired gain GRpeak mode1 changes as well and has a local


Fig. 8. Flowchart of the optimal design procedure.

TABLE IISPECIFICATIONS OF THE PROPOSED CONVERTER

TABLE IIIOPTIMAL PARAMETERS

maximum. For each given threshold voltage, the local maximumn1Lm 1 curve has similar shapes. Fig. 10 shows the magnetiz-ing RMS currents change as load and magnetizing inductancevary, which indicates that the lowest RMS current is achievableby choosing a right magnetizing inductance. It is interesting tonote that the local maximum n1Lm 1 increases as the thresholdvoltage decreases from 50 V as shown in Fig. 11, but when thethreshold voltage reaches to 37.5 V, no local maximum n1Lm 1can be found to meet both peak gains in Configurations 1 and2. The optimal parameters achieved for the proposed LLC con-verter are listed in Table III.

As seen from Fig. 12, the dc gain consists of four segments,each of which has a relatively narrow dc gain range and rep-resents one of the four configurations. As the frequency andconfiguration change, the dc gain can sweep from 2.2 up to 8.8.

Fig. 9. Optimized result of a local maximum n1 Lm 1 .

Fig. 10. Magnetizing RMS currents versus load and inductance.


Fig. 11. Relationship between threshold voltage, resonant capacitance, and magnetizing inductance.

Fig. 12. DC gain margin with optimized inductance.

Fig. 13. 250-W LLC prototype.

V. EXPERIMENTAL VERIFICATION

To verify the proposed LLC topology and design method-ology, a 250-W, 210-V output converter prototype is built asshown in Fig. 13.

The circuit key parameters are listed in Table III. The topologyoperation is verified first and then the accuracy of the developed

TABLE IVKEY CIRCUIT PARAMETERS

numerical model should be verified before it can be appliedto optimal design. The power devices, core sizes, and resonantcapacitors are listed in Table IV.

A. Topology Operation Verification

Fig. 14 shows the resonant current when switching frequencyis less than resonant frequency, while in Fig. 15 the resonant cur-rent presents pure sinusoidal shapes since the converter operatesat resonant frequency. To smoothly charge the output capacitorsduring the start-up stage, a soft start scheme is employed asshown in Fig. 16 by gradually reducing the switching frequen-cies, whose initial frequency is far above the resonant frequency,until the output voltage reaches the set value.

To stabilize the output voltage, a PID controller is appliedto regulate the switching frequency. Fig. 17 demonstrates thedynamic responses as load steps up from 10% nominal load to70%, while Fig. 18 shows the step-down responses (note: theoutput voltages in these two figures have been set to a 210-Voffset position.). As shown in these two figures, the undershootand overshoot voltages are tightly regulated under 10 V, whichis stable enough for the subsequent dc/ac stage.

As aforementioned, four topology configurations exist in thisproposed topology, to make the transitions between differentconfigurations smooth; a scheme similar to the soft start is ap-plied to avoid large inrush current during configuration tran-sitions. Fig. 19 shows the transition from Configurations 1 to2. During configuration transition, all four switches are turned


Fig. 14. Resonant current during steady state at fs <fr .

Fig. 15. Resonant current at fs = fr .

Fig. 16. Qaveforms during soft start-up.


Fig. 17. Dynamic responses during load step-up from 10% to 70% nominal load.

Fig. 18. Dynamic responses during load step-down from 70% to 10% nominal load.

Fig. 19. Transition from Configurations 1 to 2.


Fig. 20. Transition between Configurations 2 and 3. (a) Transition from Configurations 3 to 2 (half bridge to full bridge) and (b) transition from Configurations2 to 3 (full bridge to half bridge).

OFF for a short period to ensure that the resonant current goesto zero before new switching cycle starts. After configurationtransition, the switching frequency will jump from the origi-nal low frequency to far above the resonant frequency to avoidthe inrush current. As shown in Fig. 19, during the configura-tion transition, the output voltage is well maintained due to thelarge output capacitance support. Fig. 20 shows the configura-tion transitions from Configurations 3 to 2 and vice versa. Asshown from the experimental waveforms, the smooth transitionsbetween different configurations can be easily achieved.

B. Numerical Model Verification

The dc gains in Configuration 1 are measured from the proto-type to compare with the ones obtained in numerical calculationunder different load conditions. The dc gain curves obtainedfrom the mathematical calculation agree pretty well with theones measured in the experiment as shown in Fig. 21, which in-dicates that the numerical model has a good accuracy to guide theoptimization design for the proposed LLC converter. In Fig. 21,the solid lines are the dc gain curves obtained by the proposed

Fig. 21. Gain curves obtained from mode analysis (solid lines), FHA (dashlines), and experiment (markers), and estimated peak gain trajectory (dash-dot lines) with “Δ” markers showing the experimental peak gain points atcorresponding loads.

numerical model, while the dash lines are the dc gain curvescalculated using the FHA model. The dash–dotted line is theestimated peak gain trajectory. The square, parallelogram, and


TABLE VKEY CIRCUIT PARAMETERS IN THESE THREE CASES

circle marks are gain points measured in the experiment un-der 150, 100, and 50 W, respectively, which agree with the solidlines obtained by the proposed numerical model pretty well. Thetriangle markers are the peak gain points, which were measuredin the experiment by adjusting the LLC converter operating inthe boundary between zero-voltage switching and zero-currentswitching conditions, which as well match the estimated gaintrajectory fairly well. When the switching frequency is closeto the resonant frequency fr , the gains obtained from FHA arealmost the same as the ones obtained from the numerical model.However, if the operation frequency deviates away from fr , thegain difference from two methods tends to become larger. For awide input-voltage range, FHA fails to provide an accurate gainprediction. It is feasible that a great penalty on overall efficiencywill be incurred by using FHA to design LLC converters.

C. Efficiency Comparison

To verify the efficiency improvement of the proposed LLCconverter and the validity of the proposed design methodology,three cases, whose circuit specifications are the same as listedin Table II, are chosen to carry out the efficiency comparisonstudies. The first case is a conventional LLC topology, whosecircuit parameters are determined using the FHA model, whichis widely used to guide LLC design. The second case uses thesame topology, but the accurate numerical model proposed inthis paper is applied to design the circuit key parameters. Thethird case is the proposed topology with the proposed opti-mal design method. The circuit parameters for all three casesas shown in Table V are obtained by using the same optimalcriterion proposed in this paper, which is to find maximal mag-netizing inductance, while maintaining the dc gain requirement.It should be noted that for the determination of the turns ratiosin Case 3 the reader can refer to the Appendix.

Fig. 22 shows the efficiency curves of the three cases withdifferent input voltages. As seen from Fig. 22, the overall ef-ficiency in the proposed LLC converter is the highest amongthree cases, while the overall efficiency from the FHA case isthe lowest. Since the magnetizing inductance of the proposedLLC converter is the largest, the efficiency improvement at lightload where the magnetizing currents are dominant is obvious. InFig. 22(a), where the input voltage is 25 V, the efficiency curvesin three cases converge under the heavy load condition becauseload currents are much higher than magnetizing currents andmainly determine the conduction losses. It should be noted that

Fig. 22. Efficiency comparison at different input voltages: (a) at input voltage25 V; (b) at input voltage 40 V; (c) at input voltage 60 V; (d) at input voltage100 V.


Fig. 23. Measured efficiency versus magnetizing inductance under differentload and input-voltage conditions: (a) at 10% rated load and (b) at 20% ratedload.

the measured efficiency does not include the driving power,which varies from 0.5 to 0.8 W depending on the switching fre-quency. The efficiency data are acquired by a power analyzer(PZ4000). The peak efficiency of the proposed LLC converter,reaching up to 98%, can be further improved by using loweron-resistance MOSFETs.

To validate the effectiveness of the proposed optimal crite-rion, the efficiency under 10% and 20% rated load conditionswas measured by adjusting the magnetizing inductance. Fig. 23shows that the efficiency curves go high as the magnetizinginductance increases, which indicates that the proposed opti-mal criterion holds true at different input voltages and underdifferent load conditions.

VI. CONCLUSION

This paper proposes a modified LLC converter with two trans-formers in series in an attempt to achieve high conversion effi-ciency while maintaining a wide input-voltage range. To opti-mize the design, a numerical calculation with high accuracy isdeveloped and the method is verified by experimental results.Optimization criterion and procedure are given on guiding theLLC converter design. An example is given to illustrate the op-timal design using the developed numerical model and optimaldesign procedure. The developed numerical model is verifiedby experiment and three design cases are carried out as well

Fig. A.1 Derivation of key equivalent parameters.

to make efficiency comparison. The experimental results showthat the proposed LLC converter, operating from 25 to 100 V,can achieve up to 98% peak efficiency.

APPENDIX

As seen in Fig. A.1, where two transformers operate in series,when the voltages across the primary sides of T1 and T2 areclamped by the output voltage Vo , they can be expressed asfollows:

⎧⎪⎨

⎪⎩

UT 1 =Vo

n1

UT 2 =Vo

n2.

(A.1)

Since the outputs of T1 and T2 are paralleled, n1 and n2 havethe following constraint:

n2 =n1Lm1

Lm2. (A.2)

Combining (A.1) and (A.2), the voltage across T1 and T2 canbe expressed as

Ueq = UT 1 + UT 2 =(Lm1 + Lm2)

n1Lm1Vo. (A.3)

Therefore, the equivalent resistance reflecting to the trans-former primary side is as follows:

Req =(

Lm1 + Lm2

n1Lm1

)2

RL. (A.4)

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Haibing Hu (M’09) received the B.S. degree from theHunan University of Technology, Zhuzhou, China, in1995, and the M.S and Ph.D. degrees in electrical en-gineering from Zhejiang University, Zhejiang, China,in 2003 and 2007, respectively.

From 2007 to 2009, he was an Assistant Professorin the Department of Control Engineering, NanjingUniversity of Aeronautics and Astronautics, Nanjing,China, where he is currently an Associate Professor.In 2009, he joined the Department of Electrical En-gineering, University of Central Florida, Orlando, as

a Postdoctoral Research Fellow. His research interests include digital controlin power electronics, multilevel inverter, digital control system integration forpower electronics, and applying power electronics to distributed energy systemsand power quality. He has authored or coauthored more than 70 technical paperspublished in journals and conference proceedings.

Xiang Fang (S’11) received the B.S. degree in elec-trical engineering from Tsinghua University, Beijing,China, in 2007. He is currently working toward thePh.D. degree in power electronics from the Univer-sity of Central Florida, Orlando.

He is a Research Assistant with Florida PowerElectronics Center, University of Central Florida,where he is involved in the modeling and designof dc/dc resonant converters. His research interestsinclude renewable energy conversion, dc/dc conver-sion, and resonant power conversion.

Frank Chen (S’11) received the B.S. degree in elec-trical engineering from Tongji University, Shanghai,China, in 1999. He is currently working toward thePh.D. degree in electrical engineering at the Univer-sity of Central Florida, Orlando.

He was with Delta Power Electronics Center,Shanghai, China, as a Research and DevelopmentEngineer from 2001 to 2005. In 2006, he joined theSTMicroelectronics Greater China as a Senior Ap-plication Engineer. His research interests include themodeling and design of dc/dc converters, renewable

energy, and soft-switching techniques. He holds one U.S. Patent. He has au-thored or coauthored more than ten technical papers published in journals andconference proceedings.


Z. John Shen (S’90–M’94–SM’02–F’11) receivedthe B.S. degree from Tsinghua University, Beijing,China, in 1987, and the M.S. and Ph.D. degrees fromRensselaer Polytechnic Institute, Troy, NY, in 1991and 1994, respectively, all in electrical engineering.

Between 1994 and 1999, he held a number of tech-nical positions, including Senior Principal Staff Sci-entist with Motorola Semiconductor Products Sec-tor, Phoenix, AZ. Between 1999 and 2004, he waswith the University of Michigan-Dearborn, Dearborn.Since 2004, he has been with the University of Cen-

tral Florida, Orlando, where he is currently a Professor of electrical engineering,the Director of the Power Semiconductor Research Laboratory, and the Asso-ciate Director of Florida Power Electronics Center. His current research interestsinclude power semiconductor devices and integrated circuits, power electronics,automotive electronics, nanotechnology, and renewable-energy systems. He hasauthored or coauthored more than 100 journal and referred conference publi-cations. He is the holder of 12 issued and several pending or provisional U.S.patents. He is the inventor of the world’s first submilliohm power metal–oxide–semiconductor field-effect transistor.

Dr. Shen served as an Associate Editor of the IEEE TRANSACTIONS ON

POWER ELECTRONICS between 2006 and 2009. He served as the Technical Pro-gram Chair of the second IEEE Energy Conversion Congress and Expo in 2010,the 38th IEEE Power Electronics Specialists Conference in 2007, and the firstIEEE Vehicle Power and Propulsion Conference in 2005. He currently servesas the Vice President of Products of the IEEE Power Electronics Society. Hehas also served on numerous IEEE conference and workshop organizing com-mittees, and international editorial boards. He received the 2003 U.S. NationalScience Foundation CAREER Award, the 2006 Transaction Prize Paper Awardof the IEEE TRANSACTIONS ON POWER ELECTRONICS from the IEEE PowerElectronics Society, the 2003 IEEE Best Automotive Electronics Paper Awardfrom the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, and the 1996Motorola Science and Technology Award.

Issa Batarseh (F’06) received the B.S.E.E. degreein electrical and computer engineering, and the M.S.and Ph.D. degrees in electrical engineering, in 1983,1985, and 1990, respectively, all from the Universityof Illinois, Chicago, IL.

He is currently a Professor of Electrical Engi-neering with the School of Electrical Engineeringand Computer Science, University of Central Florida(UCF), Orlando. From 1989 to 1990, he was a Vis-iting Assistant Professor with Purdue University,Calumet, IN, before joining the Department of Elec-

trical and Computer Engineering, UCF, in 1991. His research interests includepower electronics, developing high-frequency energy conversion systems toimprove power density, efficiency, and performance, the analysis and design ofhigh-frequency solar and wind energy conversion topologies, and power factorcorrection techniques. He is the author or coauthor of more than 60 refereedjournals and 300 conference papers in addition to 14 U.S. patents. He is alsothe author of a textbook entitled Power Electronic Circuits (New York: Wiley,2003).

Dr. Batarseh is a Registered Professional Engineer in the State of Florida anda Fellow of the Institution of Electrical Engineers. He has served as a Chairmanfor the IEEE PESC’07 conference and was the Chair of the IEEE Power Engi-neering Chapter and the IEEE Orlando Section.

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A Modified High-Efficiency LLC Converter With Two Transformers for Wide Input-Voltage Range Applications