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Using LLC Resonant Converter for Designing Wide-Range Voltage Source

Article  in  IEEE Transactions on Industrial Electronics · June 2011

DOI: 10.1109/TIE.2010.2052537 · Source: IEEE Xplore

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1746 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 5, MAY 2011

Using LLC Resonant Converter for DesigningWide-Range Voltage SourceReza Beiranvand, Student Member, IEEE, Bizhan Rashidian,

Mohammad Reza Zolghadri, Member, IEEE, and Seyed Mohammad Hossein Alavi

Abstract—LLC resonant converter with significant resonant in-ductance is proposed for designing an adjustable wide-range reg-ulated voltage source. Large resonant inductance increases outputvoltage adjustment range and conversion efficiency, particularly atlight loads. Soft switching is achieved for all power devices underall operating conditions by choosing the dead time and maximumswitching frequency properly and operating in the converter’sinductive region. Using a power-factor-correction (PFC) converterreduces the resonant converter’s output voltage dependence to thevariations of the main ac input voltage. Thus, the compensation ofthe load variations and the wide-range adjustment of the regulatedoutput voltage can be achieved by using small switching frequencyvariations. The proposed method has been used to implement anadjustable wide-range voltage source (35–165 V dc), as an ionimplanter arc power supply. An almost flat efficiency curve withmaximum value of 94% has been achieved for the converter. Itsoutput current can change from no load to 3 A dc.

Index Terms—Dead time, LLC resonant converter, wideadjustable range, zero-current switching (ZCS), zero-voltageswitching (ZVS).

I. INTRODUCTION

ION SOURCES used in ion implanters need an adjustableregulated voltage and current sources for adjusting the arc

voltage and filament current. The main features of the ion im-plantation are controlled by subsystems such as the following:1) Ion source; 2) mass analyzer; 3) accelerator; 4) scanner;and 5) high-precision ion counter. All of the processes aredone in high vacuum for getting a controlled ion beam witha specific energy. The arc voltage and the filament currentmust be adjusted properly for achieving a controlled thermionicemission and a stable ion beam which is implanted into thewafers for doping the semiconductor devices. Fig. 1 showsthe block diagram of the designed circuit as part of the ionimplanter ion source. Lee et al., provide good descriptions foreach stage and the whole system [1]. In this structure, theelectromagnetic interference (EMI) filter prevents the switchingnoises propagation in the main ac input. The power-factor-correction (PFC) unit improves the input power factor and tosome extent regulates the resonant converters’ dc input voltage.

Manuscript received November 15, 2009; revised February 8, 2010 andApril 24, 2010; accepted May 20, 2010. Date of publication June 14, 2010;date of current version April 13, 2011.

The authors are with the Department of Electrical Engineering, SharifUniversity of Technology, Tehran 11365-8639, Iran (e-mail: r.beiranvand@yahoo.com; rashidia@sharif.edu; zolghadr@sharif.edu; mhalavi@sharif.edu).

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

Digital Object Identifier 10.1109/TIE.2010.2052537

A regulated voltage is provided for the control unit by theauxiliary switched-mode power supply. The resonant convertersprovide adjustable and regulated current and voltage sourcesfor ion implanter filament and arc sections, respectively. In thispaper, the arc resonant converter is discussed for providinga wide-range regulated voltage source. In our ion implantersystem, the output voltage of the arc power supply must beadjustable from 35 to 165 V dc. Its output load changes fromno load to 3 A dc. The LLC resonant topology is proposed toachieve this purpose. This converter has many advantages. Itcan regulate the output voltage over wide input voltage andload variations with a relative small variation of switchingfrequency. Additionally, all essential parasitic elements, in-cluding the metal-oxide-semiconductor field-effect transistors(MOSFETs) output capacitances and the transformer leak-age and magnetizing inductances are utilized to achieve soft-switching and high-frequency operation.

Series resonant converter and series-parallel load-resonantconverter have been used for designing arc power supplies[2], [3]. Also, CLL resonant converter has been proposed toachieve very high efficiency at very high switching frequencydc–dc power conversion [4]. Many authors have used theLLC resonant converters for designing constant output voltagesources by using diode or synchronous rectifier at their outputstages [5], [6]. Also, an integrated solution of the LLC resonantconverter (based on the silicon-on-insulator power MOSFETsand using an integrated transformer) at switching frequenciesin the range of 1 MHz has been presented by De Groot et al.,to achieve a constant output voltage [7]. Some other usefulanalyses, discussions, and verifications of the LLC resonantconverters for constant output voltage applications can be per-ceived in [8]–[11]. But, using merely the transformer’s primaryreferred leakage inductance cannot be used for wide outputvoltage with wide dynamic loading applications.

In summary, the LCC and parallel resonant converters canbe used for wide dynamic load applications. These convertersexhibit large circulating tank currents in their inductive regionsparticularly at light load. In complex three-level topologies withcareful design, these converters can operate efficiently and canachieve very high power density for certain wide dynamic loadapplications, as can be concluded from [12] and [13]. On theother hand, the series resonant converter has low circulatingtank currents at light loads but it cannot be used for wide loadvariations [14].

As mentioned before, lots of researches have been doneon this concept, having “constant output voltage and variableloads” as their main scopes. Particularly in low-load conditions,

0278-0046/$26.00 © 2010 IEEE

BEIRANVAND et al.: USING LLC RESONANT CONVERTER FOR DESIGNING WIDE-RANGE VOLTAGE SOURCE 1747

Fig. 1. Block diagram of the designed circuit as part of the ion source of the ion implanter system.

the load variations of such designs are often limited, due tovery wide-range frequency changes needed for regulating theoutput voltage. Most of the resonant converters controllers donot afford these wide frequency variations; also, the induc-tive components cannot be designed optimally for such widevariations.

In this paper, LLC resonant converter with a significantresonant inductance, is proposed for an adjustable wide-rangeregulated voltage source. Wide output voltage adjustment range(35–165 V dc) is achieved, independent of input voltage oroutput load variations. The output current changes from 0 to3 A dc and the converter can operate in low-load conditionsperfectly. Using frequency control, LLC resonant converter canhandle wide regulated output voltages even in the case of wideinput voltage or output load variations.

LLC resonant converter topology is discussed in Section II.Its ac equivalent circuit, transfer function, and frequency re-sponse are studied in Sections III and IV, respectively. De-signing the converter passive elements to satisfy the worstcase conditions is discussed in Section V. Elimination of thestresses at the startup transient time and converter losses aredescribed in Sections VI and VII, respectively. Dead time andupper limit of the maximum switching frequency for realizingthe zero-voltage switching (ZVS) operation are calculated inSection VIII. Experimental results are presented in Section IX.Conclusions are made in Section X.

II. LLC RESONANT CONVERTER TOPOLOGY

LLC resonant converter is one of the most suitable circuittopologies which have been introduced for designing con-stant output voltages switched-mode power supplies (SMPSs).Using this topology, a low-noise high-efficiency SMPS canbe designed. In this paper, the LLC resonant converter witha significant resonant inductance is achieved by adding anexternal inductor in series with the transformer’s primary sideof the LLC resonant converter, and is proposed for an adjustablewide-range regulated voltage source (35–165 V dc) for usingas ion implanter arc power supply. The output load changesfrom no load to full load. This case is much more general thanthe constant output voltage situations. Obtaining soft switchingfor all input/output voltages and load conditions is much moredifficult. One of the most important topics for designing ahigh-frequency converter is related to its generated EMI noises.For reducing these noises, the LLC resonant converter with

Fig. 2. LLC resonant converter (a) circuit topology and (b) typical waveforms.

soft switching has been used. The switching losses have beenreduced effectively due to the soft switching; thus, by increas-ing the switching frequency, the size of the converter can bereduced. In this converter, frequency control is used for adjust-ing and regulating the output voltage. In resonant converters,pulsewidths of the gate control signals are equal [15].

Circuit topology of the LLC resonant converter has beenillustrated in Fig. 2(a) and its typical waveforms have beenshown in Fig. 2(b). These waveforms are associated with theinductive region, where the switching frequency is larger thanthe converter’s resonant frequency. In half-bridge topology, anyasymmetry in gate control signals causes dc current whichcan saturate the transformer core. But resonant capacitor Cr

in Fig. 2(a) prevents this unpleasant event by deleting theaforesaid component. Forming a resonant circuit, which hasan important role in the resonant converter, is the main role ofthis capacitor. In Fig. 2, n = Np/Ns is the transformer turnsratio. Np and Ns are the turn numbers of the primary andsecondary windings of the transformer, respectively. Lm is thetransformer’s magnetizing inductance and Lr is the summationof the transformer’s primary referred leakage inductance andan inductance which has been added to the LLC topology at thetransformer’s primary side.

1748 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 5, MAY 2011

Fig. 3. AC equivalent circuit of the LLC resonant converter.

III. AC EQUIVALENT CIRCUIT OF THE LLC RESONANT

CONVERTER AND ITS VOLTAGE GAIN

Based on the first-harmonic approximation (FHA) approach,the converter’s nonlinear circuit is replaced by a linear- andtime-invariant circuit, as illustrated in Fig. 3. Ro is equivalentof the load and rectifier stage and is expressed as follows [16]:

Ro =8π2

V 2out

Pout=

8π2RL. (1)

This approximation model simplifies the analysis of the maincomplex circuit and illustrates variations of the output voltageby changing the load and frequency. Transfer function of the acequivalent circuit can be expressed as follows:

Hac(s) =Vo

Vi=

n2RoLms

n(n2Ro + Lms)Zin(s). (2)

Here, Vi and Vo are the first components of the ac input andoutput voltages, respectively. Zin(s) is the input impedance ofthe circuit and it is equal to

Zin(s) =1Crs

+ Lrs+n2RoLms

n2Ro + Lms. (3)

For calculating the transfer function in the frequency domain,the following parameters are defined:

a =Lr

Lm, fn =

fs

fr, Q =

1n2Ro

√Lr

Cr, fr =

12π

√LrCr

. (4)

Here, fn, fr, fs, andQ are the normalized frequency (dimen-sionless), resonant frequency (in hertz), switching frequency(in hertz), and the quality factor, respectively. From (2)–(4),the magnitude of the converter voltage gain can be expressedas follows:

|Hac(Q, a, fn)|= 1

n√

(Qfn (1 − 1/f2n))2 + (1 + a− a/f2

n)2.

(5)

Magnitude of the voltage gain is a function of the qualityfactor and a parameter, as represented in (5). The quality factordepends on the load and it is equal to zero at no-load condition.To study the dependence of the dc output voltage on the dc inputvoltage, we can write

Vi =√

2πVin, Vo =

2√

2π

Vout. (6)

Here, Vin and Vout are dc input and output voltages, respec-tively. From (5) and (6), we can write

Vout =Vo

2√

2/π=

|Hac(Q, a, fn)|2√

2/π

√2πVin. (7)

Thus, the dc output voltage can be expressed as follows:

Vout =12|Hac(Q, a, fn)|Vin. (8)

If dc voltage gain is defined as follows:

HDC(Q, a, fn) =Vout

Vin. (9)

Then, from (8) and (9), the dc transfer function of theresonant converter versus the voltage gain of its ac equivalentcircuit can be expressed as follows:

HDC(Q, a, fn) =12|Hac(Q, a, fn)| . (10)

Thus, the dc transfer function is obtained

HDC(Q, a, fn)=1

2n√

(Qfn (1 − 1/f2n))2+(1+a−a/f2

n)2.

(11)

We define the normalized dc input and output voltages,respectively, as follows:

VinN =Vin

VinNorm, VoutN =

Vout

Vin Norm. (12)

Here, Vin Norm = (Vinmin + Vinmax)/2 is the normal valueof the dc input voltage. Vinmin and Vinmax are the minimumand maximum values of the converter input voltage, respec-tively. Thus, the normalized dc output voltage is derived

Vout N (Q, a, fn)=VinN

2n√

(Qfn (1−1/f2n))2+(1+a−a/f2

n)2.

(13)

Using (13), the resonant converter behavior can be studied.

IV. FREQUENCY RESPONSE OF THE

LLC RESONANT CONVERTER

Output voltage of the converter depends on its input voltage.According to Fig. 1, a PFC converter has been used. So, the in-put power factor is improved and the resonant converter’s inputvoltage is almost regulated. Therefore, the resonant converter’soutput voltage dependence on the main ac input voltage hasbeen reduced. Thus, switching-frequency variations are onlyused for compensating the load variations and adjusting theregulated output voltage in a wide range.

The normalized dc output voltage of the LLC resonant con-verter (13) versus normalized switching frequency and Q hasbeen plotted in Fig. 4. By controlling the switching frequency,the output voltage can be adjusted at a desired value and it can

BEIRANVAND et al.: USING LLC RESONANT CONVERTER FOR DESIGNING WIDE-RANGE VOLTAGE SOURCE 1749

Fig. 4. Normalized dc output voltage of the LLC resonant converter versus fn

and Q (n = 2.3, a = 1.51) (a) minimum output voltage, Vout min N = 0.1when Vin N = 1.057 and (b) maximum output voltage, Vout max N = 0.47when Vin N = 0.914.

be regulated against input voltage or output load variations.Considering (12), the normalized maximum and minimumoutput voltages (corresponding to Voutmax = 165 Vdc andVoutmin = 35 Vdc, respectively) have been plotted in Fig. 4,too. In this figure, maximum and minimum values of the inputvoltage (370–320 V dc) have been applied to the converter toidentify the maximum and minimum values of the normalizedswitching frequency, respectively. These switching frequenciesare occurred under the light load at minimum output voltageand under the full load at maximum output voltage, respec-tively. When there is a little power consumption or at no-load condition, the minimum output voltage cannot be adjustedin a wide range by controlling the switching frequency. Theadjustable range of the output voltage depends on the valueof the inductance ratio (Lr/Lm) and it can be increased byincreasing the value of this quantity [see (11)–(13)]. The LLCresonant converter normalized dc output voltage versus nor-malized switching frequency at different conditions has beenplotted in Fig. 5. Using this figure, regulation of the differentvalues of the output voltage by frequency control (from no loadto full load) can be understood.

Fig. 5. Typical LLC resonant converter normalized dc output voltage versusfn at different conditions (a) Vin N = 1.057, Q = Qmin = 9 × 10−3

(b) Vin N = 0.914, Q = Qmax L = 0.539, and (c) Vin N = 0.946, Q =Qmax H = 2.54.

For high output voltages VoutmaxN , small normalized fre-quency variations Δfn1 = fn1 − fnmin are enough to compen-sate the output load and input voltage changes. But for lowoutput voltages VoutminN , we need wide normalized frequencyvariations Δfn2 = fnmax − fn2, as shown in Fig. 5.

It is necessary to mention that in the PFC stage, there is abasic conflict between the input power factor and the outputvoltage regulation [17]. Thus, a tradeoff between these parame-ters must be considered. In this case, it has been preferred toimprove the input power factor instead of the output voltageregulation, due to the ability of the next stage to more easilyregulate the output voltage. Under the worst case conditions(considering the 100-Hz ripple in the output voltage of thePFC converter and wide output load and input voltage changes),output voltage of this stage varies less than 10%. For increasingthe confidence coefficient and operating the resonant converterproperly, this converter is designed to compensate more than15% of the variation in its input voltage (320–370 V dc).

Changing the pulsewidth is used for regulating the outputvoltage against the input voltage or the load variations in thepulsewidth modulation (PWM) converters [18], [19]. But, inthe resonant converters, frequency variation is used for com-pensating the aforesaid changes. Power MOSFETs of the LLCresonant converter or their antiparallel diodes are always turnedon and off with duty cycle = 0.5 − ΔT ′fs, which slightly de-pends on the input voltage or load variations. Here, ΔT ′ isthe time duration which the effective capacitance appeared inparallel with drain sources of the power MOSFETs is chargedor discharged. This time interval depends on the input andoutput voltages and load. ΔT ′ should be always smaller thanthe converter dead time ΔT to achieve ZVS operation in theconverter’s inductive region.

The arc voltage must be adjusted in a wide range. We preferto design the converter to operate in the inductive region, dueto the ZVS operation and the simplicity of its controller, whichmust be able to regulate the output voltage against the outputload and input voltage variations in steady states and under thetransient conditions. This controller must be able to adjust theregulated output voltage in a wide range.

In the LLC resonant converter, the primary referred leakageinductance of the transformer is small, which leads to a smallvalue for the coefficient of a. Due to this problem, increasingthe switching frequency even in a wide range cannot be useful

1750 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 5, MAY 2011

for achieving an adjustable wide-range regulated output volt-age. This subject can be understood as well by considering (13)at light-load condition which can be written as follows:

VoutN (Q ≈ 0, a, fn) =VinN

2n (1 + a− af−2n )

. (14)

As illustrated in (14), for small values of a, by increasingthe switching frequency, the output voltage moves toward aconstant value. This constant value is high for small values of a.Thus, low output voltages cannot be regulated under the light-load conditions. On the other hand, increasing the transformerturns ratio to achieve low output voltages even under thelight-load conditions causes high voltages and currents on thecomponents at maximum output voltage under the full-loadconditions. Thus, a and nmust be chosen properly to overcomethese problems. Larger values for a and wider output voltageadjustment range can be obtained by using higher values ofresonant inductance, achieved by adding an external inductorin series with the primary side of the transformer. This inductorincreases not only the output voltage adjustment range, butalso the input impedance particularly at high frequencies. Thehigher input impedance causes the smaller circulating tank cur-rents and higher efficiency, especially at light loads. Therefore,the converter can operate between no load and full load, andits regulated output voltage can be adjusted in a wide range, bychoosing values of a and transformer turns ratio properly.

V. DESIGNING THE CONVERTER PASSIVE

ELEMENTS TO SATISFY THE HIGHEST

VOLTAGE AND CURRENT STRESSES

Considering (3) and doing some simple straightforwardalgebraic calculations, the resonant capacitor’s ac voltage canbe obtained as follows:

VCr(s) =

IinCrs

=Vi

1 + n2Ro

Lms

LrCrs2+(1+ Lr

Lm

)n2RoCrs+1+ n2Ro

Lms

. (15)

By substituting (1), (4), (6), and s = j2πfs into (15), thisvoltage as a function of Vin, a, Q, and fn is derived

|VCr| =

√2Vin

πf2n

√1 + χ

χ (1 − f−2n )2 + (1 + a−1 − f−2

n )2(16)

where χ = (Qfn/a)2. According to the simulations, the reso-nant capacitor’s highest voltage stress is occurred at point A inFig. 5. So, the resonant capacitor must be chosen to undergo ahigh ac voltage VCr max which is identified as follows:

VCr max =√

2Vinmin

πf2nmin

×√

1 + χm

χm

(1 − f−2

nmin

)2 +(1 + a−1 − f−2

nmin

)2 (17)

where χm = (QmaxLfnmin/a)2. By substituting (1) into (4)and considering Fig. 5, QmaxL is given

QmaxL =π2Ioutmax

8n2Voutmax

√Lr

Cr. (18)

In (17), we assume that the input voltage is reduced to Vinmin

when the maximum output voltage delivers maximum outputcurrent to the output load. According to Figs. 2, 3, and 5, andusing (4), (15), and (17), the power MOSFETs’ peak currentcan be expressed as follows:

Iinmax =Vinmin

fnmin

√8f2

rC2r (1 + χm)

χm

(1 − f−2

nmin

)2+(1 + a−1 − f−2

nmin

)2 .

(19)

According to (17) and (19), higher values of the normalizedminimum switching frequency fnmin cause lower circulatingcurrents and lower voltage and current stresses on the com-ponents. Considering Fig. 2 and calculating the input powerbased on the FHA approach, the resonant converter peak currentIinmax can also be derived as follows:

Iinmax =πVoutmaxIoutmax

ηcVinmin cosψ1. (20)

Here, ηc is the efficiency of the converter by ignoring powerdissipations of the MOSFETs. ψ1 is the converter resonantcurrent’s first-harmonic phase shift relative to the drain sourcesquare-wave voltage first harmonic (corresponding to point Ain Fig. 5). As shown in Fig. 5, for the desired output voltageadjustable range, we need to obtain proper values of a andQ parameters to satisfy the worst case conditions. As illus-trated in Fig. 5, these conditions can be considered as follows:(A) Minimum input voltage, minimum switching frequency,maximum desired output current for maximum output voltage,(B) maximum input voltage, minimum desired output currentfor maximum output voltage, (C) minimum input voltage, max-imum desired output current for minimum output voltage, and(D) maximum input voltage, maximum switching frequency,minimum desired output current for minimum output voltage.

According to Fig. 5, maximum output voltage must beachievable even when minimum input voltage is applied tothe converter. LLC resonant converter’s available input voltagerange to achieve maximum output voltage is determined byits peak voltage gain. Thus, the resonant network should bedesigned so that the gain curve has enough peak value tocover the input voltage range. ZVS operation is lost belowthe peak gain point in the LLC resonant converter capacitiveregion [15]. Therefore, some margin is required to determinethe maximum gain to guarantee a stable ZVS operation duringthe load transient and startup.

The same is true for the output voltage transient during itsadjustment in a new desired value. Typically, 10%–20% of themaximum gain is required as a margin for practical design.Thus, when output voltage is adjusted at its maximum value,normalized switching frequency varies between fnmin and fn1

to compensate input voltage changes (Vinmin − Vinmax) andload variations (from full load to no load), as illustrated in

BEIRANVAND et al.: USING LLC RESONANT CONVERTER FOR DESIGNING WIDE-RANGE VOLTAGE SOURCE 1751

Fig. 5. Normalized frequency changes between fn2 and fnmax

to regulate the minimum output voltage, as depicted in Fig. 5.According to Fig. 4, for a specified value of a parameter,

changing the variation range of Q changes the frequency varia-tion range for regulating the output voltage. Thus, the frequencyvariation range can be properly controlled by choosing thevalue of a and the variation range of Q versus load. Smallerfnmax − fnmin values need larger values of a. As mentionedbefore, Δfn2 = fnmax − fn2 is the normalized frequency vari-ation for regulating the minimum output voltage. Larger valuesof fn2 reduce the circulating currents and improve performanceof the converter at minimum output voltage. This is occurreddue to the higher values of the input impedance at higherfrequencies. In practice, normalized frequency variations forregulating different values of the output voltage depend onthe load regulation of the input voltage source. In this case,the input voltage source is a PFC stage, as shown in Fig. 1.Considering (1), (4), (18), and Fig. 5, QmaxH is derived

QmaxH =π2Ioutmax

8n2Voutmin

√Lr

Cr=Voutmax

VoutminQmaxL. (21)

From (13) and Fig. 5 at point A, maximum value of thenormalized output voltage can be expressed as follows:

VoutmaxN

=VinminN/2n√

Q2maxLf

2nmin

(1−f−2

nmin

)2+(1+a−af−2

nmin

)2. (22)

Similarly, at points D and C, we can write

VoutminN (Qmin ≈ 0, a, fnmax) =VinmaxN

2n (1 + a− af−2nmax)

(23)

VoutminN =VinminN

2n√Q2

maxHf2n2

(1−f−2

n2

)2+(1+a−af−2

n2

)2.

(24)

In practice, we prefer to design the converter with smallfrequency variation range. So, small values of fnmax are de-sirable and the aforesaid analysis gives quite accurate results.For high values of fnmax, this approach is less accurate butstill valid. Because for analyzing the converter based on theFHA approach, the higher harmonics (third, fifth, . . .) have beenignored. Thus, for applications which large values of fnmax areunavoidable, using a circuit simulator besides this analysis isuseful.

VI. ELIMINATION OF THE STARTUP STRESSES

The SMPSs startup currents are high due to the incorrectinitial conditions and the voltage gain mismatch. These highcurrents saturate the transformer core and increase the currentsfurther which cause extremely high voltages and currents onthe power devices. These high stresses can damage the devicesseriously. Proper air gap is required to avoid core saturation.But it leads to more turn numbers and generates more fringing

Fig. 6. LLC resonant converter input impedance under the no-load and short-circuited conditions versus normalized switching frequency.

fluxes. For reducing these high tensions, PWM controllersincrease the duty cycle slowly during the startup transient time[18], [19]. Different overcurrent protection methods have beendiscussed in [20] and [21] for the LLC resonant converter.

For an adjustable wide-range LLC resonant converter, sim-ple frequency increasing method [20] is efficient for currentlimiting during the startup. Unlike the constant output LLCresonant converter, large resonant inductor is used in adjustablewide-range LLC resonant converter. Therefore, at switchingfrequencies higher than its resonant frequency, the voltage gaincharacteristic is not flat, as shown in Fig. 5. As a result, thecurrent can be limited by increasing the switching frequencyabove the resonant frequency. The converter is turned on withits maximum switching frequency. Then, during the startuptransient time, the switching frequency is reduced to a valuewhich is necessary for regulating the output voltage at thedesired value. The switching frequency depends on the giveninput voltage and output load, too.

VII. LOSSES OF THE DESIGNED CONVERTER

Since zero-current switching (ZCS) operation does not ad-dress the switching loss mechanisms that dominate in MOSFETresonant converters, improvements in efficiency are typicallynot observed in this operation mode. In general, amplitudes ofthe resonant currents in the ZVS region of the LLC resonantconverter at light load are lower than their value under the full-load conditions, contrary to the situation that occurred in theZCS operation area. So, in the ZVS region, higher efficiencycan be achieved at light load. This can be concluded by plot-ting the LLC resonant converter’s input impedance (3) versusnormalized switching frequency under the output open- andshort-circuited conditions, as depicted in Fig. 6, typically. Theconverter operation modes have been illustrated in this figure,too. fnoc and fnsc are the normalized switching frequencieswhich lead to zero-input impedance under the output open- andshort-circuited conditions, respectively. Between these frequen-cies, the operation mode depends on the output load. Circu-lating energy and power factor concepts in resonant convertershave been analyzed in [22]. The inductive region of the resonantconverter transfer function has been used for controlling theoutput voltage; therefore, the input current of the resonantcircuit always lags from the square-wave voltage (see iin andein waveforms in Fig. 2). This is a necessary condition for ZVSoperation in the LLC resonant converter.

1752 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 5, MAY 2011

Diodes of the output rectifier stage are always turned onand off at zero current in the whole load, input, and outputvoltages variations ranges, and switching losses are ignored[8], [15]. At no-load condition, the converter operates in burstmode for reducing power dissipation. In this operation mode,the converter operates at high frequencies in a short time,then the switching operation is stopped for a long time de-pendent on the output voltage, and this duration is repeated.The presented methods in [23] and [24] cannot be implementeddirectly for wide output voltage with wide dynamic loading ap-plications. For example, by implementing these methods, whenthe output voltage is adjusted at its low values, the converteroperates in the burst mode even when large output current isdelivered to the output load. More investigations are neededto achieve an efficient burst mode for wide output voltageapplications.

Transformer and inductor must be designed based on thehigh-frequency cores such as ferrite or nanocrystalline alloycores due to the high switching frequency. Litz wires havebeen used for reducing the skin effect. In high-frequencyapplications, the winding losses are minimized when thecurrents are sine wave without any harmonics. In this converter,the high-frequency harmonics of the transformer currents aresmall enough due to the transformer quasi-sine-wave currents.Thus, its windings losses are very close to the minimum value.This subject is roughly true about the transformer core losses,too [25]. Thus, the transformer can be designed optimally. Thesplit-winding technique is used for reducing the transformerlosses [25].

VIII. DEAD TIME AND UPPER LIMIT OF THE

MAXIMUM SWITCHING FREQUENCY FOR

REALIZING THE ZVS OPERATION

Realizing the ZVS operation even under the worst caseconditions is one of the most important topics that must besatisfied for using the LLC resonant converter as a wide-rangeadjustable voltage source. To achieve ZVS operation at theprimary side of the converter at power MOSFETs’ “turn-ontimes,” the converter should operate in the inductive region;also during the dead time, the resonant inductor current mustbe high enough to charge or discharge voltage of the effectivecapacitance which appeared in parallel with the drain sourcesof the power MOSFETs [15].

The gate drive circuit must be able to sink MOSFETs gate-source capacitors charges and turn off them fast before theirdrain-source voltages rise significantly above zero. The circu-lating current amplitude should be reduced as low as possible tominimize the conduction losses of the converter; but this subjectmay lead to no-ZVS operation. By choosing the dead time andmaximum switching frequency properly in the inductive regionof the LLC resonant converter, soft switching is achieved for allpower devices even under the worst case conditions.

During the dead time, both power MOSFETs are off. Aproper dead time should be used to realize the ZVS operationat light- or no-load conditions, even when the output voltage isadjusted at its minimum value and maximum input voltage isapplied to the converter. Under these conditions, the switching

frequency is increased to its maximum allowed value for reg-ulating the output voltage, as illustrated in Fig. 5. Thus, underthe aforesaid conditions, the resonant current is minimized andthe maximum value of the dead time is required to chargeor discharge the effective capacitance Cp. Under the light- orno-load conditions, the output rectifying stage can be ignoredfor simplicity. Thus, the switch network (M1 and M2) drivesa linear time-invariant (LTI) resonant tank network (Cr, Lr,and Lm).

The FHA approach gives an overestimated dead time valuedue to the ignored higher harmonics in this approach. Ignoringthe dead time intervals for simplicity, the switch network gen-erates a symmetrical square-wave output voltage which can beexpressed in the Fourier series as follows:

vs(t) =Vinmax

2+

2πVinmax

∑k=1,3,5,...

1k

sin(kωst). (25)

Considering the dead time intervals to derive the Fourierseries of the switch network symmetrical square-wave outputvoltage leads to intricate calculations for calculating the nor-malized dead time and cannot be written in the closed form.It can be concluded intuitively that ignoring this interval doesnot introduce significant error in the obtained Fourier series,if the dead time is much smaller than the minimum switchingperiod, i.e., ΔT � Tsmin. This condition is always satisfiedpractically. Considering the superposition, in the aforesaid LTIcircuit, the input current at maximum switching frequency isobtained

iin(t) =2π

∑k=1,3,5,...

Vinmax

k |Zin(jkωsmax)| sin(kωsmaxt− ψk).

(26)

From (3) and (4), the converter’s input impedance atωsmax = 2πfrfnmax and under the no-load condition can bewritten as follows:

Zin(j2πfrfnmax) = jfnmax

√Lr

Cr

(1 +

1a− f−2

nmax

). (27)

Also, we have

ψk = arg [Zin(j2kπfrfnmax)] = π/2. (28)

Ignoring the dead time and current sign, resonant peak cur-rent is occurred at t = 0. So, this peak value is obtained

Iinp =2πVinmax

∑k=1,3,5,...

1k |Zin(j2kπfrfnmax)| . (29)

From (27), for k ≥ 3 and fnmax〉1, under the no-load condi-tion, we can write

Zin(j2kπfrfnmax) ≈ jkfnmax

√Lr

Cr

(1 +

1a

). (30)

BEIRANVAND et al.: USING LLC RESONANT CONVERTER FOR DESIGNING WIDE-RANGE VOLTAGE SOURCE 1753

Fig. 7. Converter’s primary-side simulated waveforms at minimum outputvoltage Vout = 35 V dc and maximum input voltage Vin max = 370 V dcunder the light-load condition Iout = 50 mA (vDS−M2; 50 V/Div., iCr ;0.5 A/Div., vGS−M1, vGS−M2; 5 V/Div., Time; 100 ns/Div.).

Substituting (27) and (30) into (29) and doing some algebraiccalculations, the current peak value is obtained

Iinp =2Vinmax

πf ′nmax

√a

1 + a

√Cr

Lr

⎡⎣ 1

1 − f ′−2nmax

+∑

k=3,5,7,...

1k2

⎤⎦ .

(31)

Equation (31) can be simplified as follows:

Iinp ≈ 2Vinmax

πf ′nmax

√a

1 + a

Cr

Lr

[1

1 − f ′−2nmax

+π2

8− 1

]. (32)

Here,

f ′nmax =√

1 + a−1fnmax. (33)

Under the no-load condition, resonant inductor’s currentapproximately reaches to its peak value at the beginning of thedead time ΔT . For simplifying the analysis, we assume thatthis current remains constant during the dead time period andit charges or discharges the effective capacitance Cp in parallelwith the power MOSFETs drain sources. Ignoring the voltagedependence of this parasitic capacitor, we can write

Iinp ≈ −CpΔVΔT

= CpVinmax

ΔT. (34)

Inserting (32) into (34), we have

ΔT =πf ′nmaxCp

√Lr/Cr/2

π2/8 − 1 + (1 − f ′−2nmax)

−1

√a+ 1a

. (35)

The normalized maximum switching frequency is obtainedfrom (33) and (35) by equating the power MOSFETs minimumrequired dead time under the full-load conditions and the con-verter’s necessary dead time for achieving the ZVS operation.Fig. 7 provides the simulation verification results for illustratingthe ZVS operation under the light-load condition at minimumoutput voltage (here, Lr = 160 μH, Cr = 9.9 nF, fnmax =2.53, a = 1.51, and Cp ≈ 530 pF). Scales of voltages, current,and time have been written for each waveform in the subscript,as shown in Fig. 7. The calculated and simulated dead times areequal to 335 and 350 ns, respectively.

IX. EXPERIMENTAL RESULTS

Fig. 8 shows the circuit topology of the designed adjustablewide-range voltage source and a photograph of its prototype.

Fig. 8. LLC resonant converter (a) circuit topology and (b) prototype of thedesigned voltage source (dimensions: 15 cm × 11 cm × 6 cm).

In general, lower dv/dt leads to lower common mode noiseand ZVS converters are better than ZCS converters. However,the generated noises highly depend on the circuit design andEMI noise suppression techniques. EMI noise transferring pathand EMI model of the LLC resonant converters have beenstudied and several noise reduction approaches have been pre-sented in [26] and [27]. For reducing the generated noise andimproving the performance of the designed voltage source, allof the high-frequency high-current paths on the printed circuitboard (PCB) of the converter must be as wide and short aspossible. Low equivalent series resistance (ESR) and high-frequency capacitors must be used on the main input and outputbuses. Due to the generated fringing flux by the air gaps of thetransformer and inductor cores, windings losses are increasedand noises are radiated into the environment. Thin copper foilsare wound around these devices to prevent the radiations. Thelarge signals in the power stage can influence the control circuit.These undesirable effects can be reduced effectively by choos-ing a good elements configuration on a two-layer PCB. Theconverter and the adjacent systems interplays must be tried to beminimized for improving the EMI performance. The developedprototype of the converter has been tested under different loads(0–3 A dc) and input voltage conditions (320–370 V dc).

The experimental results confirm high performance of thedesigned wide-range regulated voltage source even under theworst case conditions. These results are presented in this sec-tion, shortly. Due to the soft switching, the frequency can beincreased for reducing the passive components sizes. It shouldbe reminded that synchronous rectifiers (SR) are widely appliedat the secondary side of the dc–dc LLC resonant converters inthe high output current applications. Conduction losses can bereduced tremendously by using SRs instead of diode rectifiers[28], [29]. For our purpose (35 < Vout < 165 V dc and 0 <Iout < 3 A dc), using the SR at the secondary side is still

1754 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 5, MAY 2011

Fig. 9. Converter experimental different waveforms under the full-load con-dition Iout max = 3 A, and minimum input voltage Vin,min = 320 V dc,Time; 1 µs/Div. (a) (up) vDS−M2; 100 V/Div., (middle) iDS−M2; 10 A/Div.,and (down) vGS−M2; 10 V/Div., (b) (up) Vout max = 165.8 V dc, (middle)vCA−D3; 50 V/Div., and (down) iD3; 5 A/Div.

Fig. 10. Converter experimental different waveforms under the light-load con-dition Iout min = 50 mA, and maximum input voltage Vin,max = 370 V dc,Time; 1 µs/Div. (a) (up) vDS−M2; 100 V/Div., (middle) iDS−M2; 10 A/Div.,and (down) vGS−M2; 10 V/Div., (b) (up) Vout max = 166.5 V dc, (middle)vCA−D3; 50 V/Div., and (down) iD3; 500 mA/Div.

Fig. 11. Converter experimental different waveforms under the maximumoutput current Iout max = 3 A, and input voltage is equal to Vin = 331 V dc,Time; 1 µs/Div. (a) (up) vDS−M2; 100 V/Div., (middle) iDS−M2; 5 A/Div.,and (down) vGS−M2; 10 V/Div., (b) (up) Vout min = 35.5 V dc, (middle)vCA−D3; 10 V/Div., and (down) iD3; 5 A/Div.

beneficial and it can improve the converter efficiency particu-larly at low output voltages, while it is not so effective for highoutput voltages. Thus, we have used diode rectifier at the sec-ondary side for simplicity. The converter different waveformscorresponding to points A, B, C, and D in Fig. 5 have beenshown in Figs. 9–12, respectively. Scales of voltage, current andtime have been written for each waveform in the subscripts.

Fig. 9 shows the primary- and secondary-side waveforms ofthe resonant converter at maximum output voltage under thefull-load condition, when minimum input voltage is applied tothe converter. The converter waveforms at maximum outputvoltage under the no- load condition, when maximum inputvoltage is applied to it, have been plotted in Fig. 10. Also,the corresponding waveforms at minimum output voltage havebeen shown in Figs. 11 and 12. As identified in the subscript ofFig. 11, the converter input voltage reduces to 331 V dc.

Fig. 12. Converter experimental different waveforms under the light-load con-dition Iout min = 50 mA, and maximum input voltage Vin,max = 370 V dc,Time; 500 ns/Div. (a) (up) vDS−M2; 100 V/Div., (middle) iDS−M2; 1 A/Div.,and (down) vGS−M2; 10 V/Div., (b) (up) Vout min = 36.07 V dc, (middle)vCA−D3; 50 V/Div., and (down) iD3; 100 mA/Div.

As illustrated in Figs. 9–12, in wide input voltage and widedynamic load variation ranges, the MOSFETs switching lossesat turn on times are almost zero and can be ignored dueto the ZVS operation. In practice, driving capability is veryimportant to decrease turnoff switching losses. The gate-drivecircuit must be able to sink MOSFETs gate-source capacitorscharges and turn off them fast. If the MOSFETs “turnoff times”are sufficiently fast, then they are switched fully off beforetheir drain-source voltages rise above zero significantly. Thus,MOSFETs drain source’s larger parasitic capacitances can playan important role for reducing the turnoff time losses.

To assist the transistor turnoff process, small capacitor maybe introduced in parallel with the power MOSFETs [14].Therefore, the switching stresses on MOSFETs at “turnofftimes” in the inductive region of the LLC resonant convertercan be reduced. This can be achieved by using a properMOSFET driver and introducing enough delay into the gatedrive signals. From Fig. 12(a), the experimental necessary deadtime is approximately equal to 350 ns for realizing the ZVSoperation even under the light-load conditions, which is in goodagreement with the calculated and simulated values (335 and350 ns, respectively, as mentioned before).

Diodes of the output rectifying stage are always turned onand off at zero current, as illustrated in Figs. 9–12. Due tothe ZCS operation of the rectifier stage, its switching lossescan be ignored and only its conduction losses are important.When this rectifying stage operates in discontinuous conduc-tion mode (DCM), transformer’s secondary-side leakage in-ductance and rectifying stage parasitic capacitance cause someringing, as shown in Figs. 9, 10, and 12(b). These ringingcan be removed by adding an external capacitor in parallelwith the transformer’s secondary side. But, it changes the ZCSoperation of this stage to ZVS; also, it changes the converter’scharacteristics. This subject is under investigation. Efficiency ofthe prototype voltage source versus output voltage at differentconditions has been illustrated in Fig. 13.

Comparing Figs. 9(a) and 11(a) illustrates that for loweroutput voltages, the converter operates at higher switching fre-quencies under the maximum output current. This subject leadsto lower circulating currents and dissipations. In practice, thegenerated loss terms (including switching loss, conduction loss,core loss, etc.) vary such that approximately, a flat efficiencycurve is achieved for the wide adjustable range LLC resonantconverter. In this converter, the circulating currents do not

BEIRANVAND et al.: USING LLC RESONANT CONVERTER FOR DESIGNING WIDE-RANGE VOLTAGE SOURCE 1755

Fig. 13. Efficiency of the adjustable wide-range LLC resonant converterversus output voltage for different output currents.

TABLE IKEY PARAMETERSAND POWER DEVICES OF THE DESIGNED

LLC RESONANT CONVERTER PROTOTYPE

vary proportional to the output load. This is the main reasonof decreasing the converter efficiency at low output currents.Increasing the input voltage of the resonant converter decreasesits resonant input current and improves its efficiency. Amongthe problems that limit maximum value of the input voltage arethe power MOSFETs’ breakdown voltages. Key parameters andpower devices of the LLC resonant converter prototype havebeen tabulated in Table I.

Litz wire, used in the transformer and external resonantinductor is made from 50 strands of 0.08-mm- diameter copperwires, as denoted in this table. L′

r = Lr − Lσi is the externalinductance which must be added to the converter and Lσi is thetransformer’s primary referred leakage inductance.

For output currents lower than 0.05Ioutmax, the burst-modeoperation is under investigation to improve the converter’slight-load performance and to reduce the required maximumswitching frequencies for regulating lower values of the output

voltage even under the light-load conditions. Transient behaviorand the control design of the LLC resonant converter forconstant output voltage applications have been discussed bymany authors [7], [24], and [30]–[34]. But, for wide outputvoltage applications, more investigations are necessary.

X. CONCLUSION

The LLC resonant converter with a significant resonantinductance has been proposed for designing adjustable wide-range regulated voltage source (35–165 V dc). This inductorincreases not only the output voltage adjustment range, but alsothe input impedance particularly at high switching frequencies.The higher input impedance causes the smaller circulatingtank currents and higher efficiency at light loads. Maximumoutput current of 3 A dc and maximum efficiency of 94%has been achieved. Input voltage of the resonant converter hasbeen regulated by a PFC converter. Thus, with small switchingfrequency variations, compensation of the load variations andadjustment of the regulated output voltage in a wide range hasbeen achieved. Soft switching is achieved for all power devicesunder all operating conditions. Due to this feature, switchinglosses and EMI noises have been reduced effectively, and theconverter size has been reduced by increasing the switching fre-quency. This voltage source has been used as an ion implanterarc power supply. Removing the ringing at output rectifyingstage in its DCM operation mode, optimization, burst-modeoperation, control design, and transient analysis of the converterare under investigation.

ACKNOWLEDGMENT

The authors would like to thank the Nanoelectronics Lab-oratory, Sharif University of Technology, with ion implanterproject for their support.

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Reza Beiranvand (S’08) received the M.Sc. de-gree in electrical engineering from Sharif Universityof Technology, Tehran, Iran, in 1999, where he iscurrently working toward the Ph.D. degree in theCollege of Electrical Engineering.

From 1999 to 2007, he was a Senior Engineer atthe R&D Centers of Parselectric and Shahab MFGs,Tehran, where he was engaged in designing theCRT and liquid crystal display (LCD) TVs based onMicronas, Philips Semiconductors (now Next eXPe-rience (NXP) Semiconductors), and ST components,

and also on high-power factor resonant converters for ballasts applications. Hiscurrent research interests include topologies and control circuits of the resonantconverters and soft switching, synchronous rectifier, and ballast techniques.

Bizhan Rashidian received the B.Sc. and M.Sc.(highest honors) degrees in electrical engineeringfrom Tehran University, Tehran, Iran, in 1987 and1989, respectively, and the Ph.D. degree in electricalengineering from Georgia Institute of Technology,Atlanta, in 1993.

Since 1994, he has been with the College of Elec-trical Engineering, Sharif University of Technology,Tehran, where he is currently a Professor and theFounding Director of the Microtechnology and Pho-tonics Laboratories. His current research interests

include optics, micromachining, microelectronics, and ultrasonic.

Mohammad Reza Zolghadri (M’01) received theB.Sc. and M.Sc. degrees in electrical engineeringfrom Sharif University of Technology, Tehran, Iran,in 1989 and 1992, respectively, and the Ph.D. de-gree in electrical engineering from the Institute Na-tional Polytechnique de Grenoble, Grenoble, France,in 1997.

Since 1997, he has been with the College of Elec-trical Engineering, Sharif University of Technology.From 2000 to 2003, he was a Senior Researcher inthe Electronics Laboratory, SAM Electronics Com-

pany, Tehran. From 2003 to 2005, he was a Visiting Professor at the NorthCarolina, A&T State University, Greensboro. He is the author or coauthor ofmore than 50 publications in power electronics and variable speed drives. Hiscurrent research interests include application of power electronics in renewableenergy systems and hybrid electric vehicle, variable speed drives, and modelingand control of power electronic converters.

Seyed Mohammad Hossein Alavi received theM.Sc. degree from Karlsruhe University of Tech-nology, Karlsruhe, Germany, in 1974, and the Ph.D.degree in electrical engineering from Stuttgart Uni-versity of Technology, Stuttgart, Germany, in 1993.

In 1974, he joined the Department of Electri-cal Engineering, Sharif University of Technology,Tehran, Iran, where he returned as an AssistantProfessor in 1993. From 1979 to 1985, he was theDirector of the Electronic Laboratory, Iran Telecom-munication Research Center. He was a member of

the technical staff at Siemens Instrumentations Laboratory, Wagner ComputerIndustry, WSW Transformatoren Fabrik, and Adler SMPS-Manufacturing forseveral years, all in Germany. His current research interests include switchingpower supplies and general electronic systems.

Dr. Alavi was a recipient of the 1998 Distinguished Faculty Award.

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