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98% Efficient Single-StageAC/DC Converter TopologiesA new Hybrid Switching Method is introduced in this article which for the first time makes possible AC/DCpower conversion in a single power processing stage providing both Power Factor Correction and isolationat high switching frequency. This single-phase rectifier is extended to a three-phase rectifier, which for thefirst time enables direct conversion from three-phase input power to output DC power resultingsimultaneously in the highest efficiency and lowest size. Slobodan Ćuk, President TESLAco, Irvine, USA

The goal of developing AC/DCconverters with Isolation and Power FactorCorrection (PFC) feature in a single powerprocessing stage and without a mandatoryfull-bridge rectifier has for years eludedpower electronics researchers (see coverimage). Present AC/DC convertersoperated from a single-phase AC line arebased on conventional Pulse WidthModulation (PWM) switching and processthe power through at least three distinctpower processing stages: full-bridgerectifier followed by boost PFC converterand another cascaded isolated full-bridgeDC/DC converter stage, which togetheruse a total of 14 switches and threemagnetic components resulting incorresponding efficiency, size and costlimitations. The new Hybrid Switching Method

enables new Single-Stage AC/DC convertertopology, the True Bridgeless PFCConverter* consisting of just three switchesand a single magnetic component albeit ata much higher efficiency approaching98%, having a 0.999 power factor and1.7% total harmonic distortion. Three-Phase Rectifier* consisting of three suchSingle-Phase Rectifiers* (*US and foreign

patents pending) takes for the first time afull advantage of Tesla’s three-phasetransmission system to convert constantinstantaneous input power of a three-phase system directly to a constant DCoutput power, albeit isolated at highswitching frequency, with near unity powerfactor (0.999), low total harmonicdistortion (1.7%), smaller size and lowercost but at ultra high efficiency of 98% [6].Serbian-American inventor Nikola Tesla

in 1879 invented the three-phase)transmission system, which together ACthree-phase motors and AC generatorsenabled a very efficient worldwide electricpower transmission and utilization, which isstill unsurpassed today. One of the keyproperties of Tesla’s three-phase system isthat it consists of three AC voltages eachdisplaced from the other by 120 degrees.When each phase is delivering the currentin phase and proportional to its respectiveAC line voltage (unity power factoroperation on each phase), theinstantaneous power from each phase ispositive (active) and is time varying.Nevertheless, the sum of the powers of allthree phases is constant in time (seeFigure 1). As this property is available on

both three-phase AC generator side andthree-phase AC load side there is noelectrical energy storage needed in such athree-phase long distance transmissionsystem. Yet, availability of the AC voltageson each side, make possible use of thethree phase AC transformers for steppingup the AC voltage on generator side andstepping-down AC voltage on the usersload side.

New boost converter topologiesThe new Hybrid Switching Method canbest be explained by way of an example.Shown in Figure 2a is the Ćuk converter[1,2] modified by the insertion of thecurrent rectifier CR1 in series with theoutput inductor which is now designatedas Lr where index r signifies a qualitativelychanged role of that inductor: from a PWMinductor in Square-Wave switching Ćukconverter to the resonant inductor. Theelimination of the PWM inductor alsoeliminates the inherent step-downconversion characteristic of the Ćukconverter and leaves only its step-up DCvoltage gain, albeit with the polarityinversion of the Ćuk converter remainingintact. Thus, the new DC voltage gain is

Figure 1: In Tesla’sthree-phase systemthe sum of the powerof all three phases isconstant in time

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according to equation 1:

(1)

Thus, we already obtained a newpolarity inverting type of the boostconverter, which did not exist before. Letus now examine a more closely theoperation of the polarity inverting boostconverter. First, it consist of three switches,one active controlling switch S (MOSFET)and two current rectifiers CR1 and CR2. Thisis already in contrast to all existingconventional Square-wave PWM switchingconverters which explicitly exclude oddnumber of switches such as 3 in this case,

as the switches must come incomplementary pairs, hence 2, 4, or morebut even number of switches. Note a dual role of the controlling switch

S: it is the controlling switch for the booststage highlighted in Figure 2b but at thesame time also a controlling switch for thetranslation stage highlighted in Figure 2c.Note also the role of the resonantcapacitor Cr connecting two stages, theboost and transferring stage: as an outputPWM capacitor of the boost stage charginglinearly during the OFF-time interval by theinput inductor current source, and as aresonant capacitor discharging resonantlyduring the subsequent ON-timetransferring stage into the load. Figure 3 shows the resonant circuit

model and corresponding resonantcapacitor waveform for entire switchingperiod. The instantaneous resonantcapacitor voltage is continuous at theswitching instants (no jump in voltages atthose instances) with a superimposed DCvoltage level equal to VCr. As the resonanceof this capacitor is clearly containedexclusively during the ON-time discharging interval DTS the resonant circuit model imposes that flux balance onthe resonant inductor must be fulfilledduring this interval alone, resulting insteady-state condition according toequation 2:

(2)

This now also puts a spotlight on thesignificance of the role of the resonantinductor. In its absence, this transfer ofcharge will be taking place but in adissipative way thus resulting in muchreduced efficiency and in additional spikevoltages on switches. The resonantinductor Lr solves both of these problems.From (2) the resonant capacitor voltage

in Figure 3 has a DC voltage VCrsuperimposed on the AC ripple voltage�vCr. As the output capacitor C is muchlarger then resonant capacitor Cr theirseries connection results in a resonantmodel of Figure 4, which has resonantcapacitor Cr only left in the resonantmodel. Moreover, the net voltage on thisresonant capacitor is a ripple voltage �vCras the DC voltages subtract as per (2). Thecorresponding time domain waveform ofthe resonant capacitor current is as inFigure 4.From Figure 2a the capacitor resonant

discharge current has a diode CR1 in the

Figure 2: Hybrid Switching Method with (a) Ćuk converter modified by the insertion of the currentrectifier in series with the output inductor, (b) controlling switch S for the boost stage, and at thesame time also a controlling switch for the translation stage (c)

Figure 3: Resonantcircuit model and

correspondingresonant capacitorwaveform for theentire switching

period

Figure 4:Corresponding timedomain waveform of

the resonantcapacitor current

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discharge loop. This diode permits only thepositive flow of current in the directiondictated by the diode. Moreover, the diodecannot turn-OFF until the resonantinductor current is reduced to zero at theend of ON-time interval, hence resonantcapacitor current is also zero as illustratedin the resonant capacitor current waveformin Figure 4. Since the resonant current isfull-wave sinusoidal waveform, theresonant capacitor current also must startat zero current level at the beginning of theON-time interval as illustrated in Figure 4as well. From the resonant AC circuit model in

Figure 5 the solutions for resonant currentand voltage are according to equations3/4:

(3)

(4)

A companion polarity non-invertingboost converter can be easily obtained bysimply inverting the polarity of the twooutput current rectifiers in Figure 2a andrelocating Lr to result in the converter ofFigure 5a. Note that current rectifiers arealso changing designation since CR2rectifier is now conducting during OFF-timeinterval just as in conventional boostconverter. The flux balance on resonantinductor and PWM inductor as shown inFigure 5b results according to equations5/6 in:

(5)

(6)

Yet another converter topology is shownin Figure 6a in which the input voltagesource has a negative polarity resulting inpositive polarity of the output DC voltageand corresponding AC flux balance shownin shaded areas in Figure 6b. Note that thisconverter topology is analogous to theoriginal polarity inverting boost topology ofFigure 2a but with the source voltagebeing negative. Therefore the same resultsas previously derived are obtained forsteady-state DC voltages. Note the changeof the placement of the resonant inductorto the branch with the rectifier CR2. As the

resonant capacitor ripple voltage �vr is anorder of magnitude smaller than DCvoltage Vr, the flux of the resonant inductoris some 50 times smaller than that ofPWM inductor as seen by comparingshaded areas of the PWM inductor andresonant inductor. Clearly this results inresonant inductor physical size and losses

being negligible compared to PWM inputinductor.

True bridgeless PFC convertertopology Comparison of the converter topologies inFigures 2a/6a reveals that the polaritychange of the input source voltage results

Figure 5: Companion polarity non-invertingboost converter with (a) relocated resonanceinductor and (b) flux balance on resonant and

PWM inductor

Figure 6: Inverting boost topology of Figure 3abut with the source voltage being negative (a)and AC flux balance shown in shaded areas (b)

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in positive and equal output DC voltagesgiven by (1) and (6), respectively.However, only one obstacle remains tomake these two topologies invariantrelative to the polarity change of the inputvoltage source and that is switching of theresonant inductor Lr placement from onediode branch to another. This problem canbe solved by placing resonant inductor forboth cases in branch with the resonantcapacitor Cr as illustrated in the converterof Figure 7. This now results intopologically invariant converter of Figure 7,which does not change its structureirrespective of the polarity of the sourcevoltage. Therefore, the source voltage canbe an AC voltage vAC which changes itspolarity as shown in Figure 7. Note how the polarity of the input

source automatically dictates which of thetwo rectifiers should be conducting duringwhich interval. Stated alternatively, the full-bridge rectifier on the front end is notneeded any more since the new convertertopology operates as the first true AC/DCconverter with the same DC voltage gainfor either polarity of input voltage. As theresult we obtained an AC/DC single-stageTrue Bridgeless PFC converter which canoperate directly from the AC line andwithout front-end bridge rectifier commonto conventional PFC boost converters. Asthe controlling switch S must change itscurrent direction and voltage blockingcapability depending on the polarity of theAC line voltage, it is implemented by aseries back-to-back connection of twoMOSFET switches. In conventional boost converters there

are no good ways to introduce the isolation.The most popular is the Full-Bridge IsolatedBoost converter, which consists of fouractive controlling MOSFET switches on theprimary side and four-diode bridge on thesecondary side. The isolation transformer inthe True Bridgeless PFC converter, however,is introduced in Figure 8 which preservesthe original three-switch configuration andother advantageous of the original non-isolated configurations, such as low voltagestresses on all switches. By controlling the input AC line current

(at 50/60Hz) so that it is in phase and

Figure 7:Topologically

invariant converterwhich does not

change its structureirrespective of the

polarity of the sourcevoltage

Figure 8: True Bridgeless PFC Converter with isolation

proportional to input AC line voltage(Figure 8), the unity power factor and lowtotal harmonic distortion can be obtained.Note also that the PFC IC controller mustalso be a True Bridgeless PFC controller, asit needs to accept as its inputs the full-wave AC line voltage and full-wave AC linecurrents. Current PFC IC controllers, onthe other hand have as input rectified ACline voltage and rectified AC line current.These conventional PFC IC controllerscould still be used but with additionalsignal processing circuitry converting full-wave AC voltage and full-wave AC linecurrent into half-rectified ac waveform foruse with standard PFC IC controller.The isolation transformer is of the best

kind (single-ended transformer of the Ćukconverter type) having magnetic core withthe BH loop as illustrated in Figure 9 with

Figure 9: Isolation transformer having magneticcore with bi-directional flux capability and

square-loop characteristic

bi-directional flux capability and square-loop characteristic, as there is no DC-biasin the transformer operation. Therefore,the design could be scaled up to high

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power without the degradation of theperformance or the large size of magneticcore. In fact, the isolation transformer hasAC flux, which is at least four times lowerthan the flux in, for example, forwardconverter and bridge-type isolatedconverters. This directly translates inproportionally reduced size of themagnetics and increased efficiency.Further improvements are obtained by

integration of the input inductor onto acommon core with the isolationtransformer [1,2,3, 5]. The placement ofthe air-gap on the magnetic leg withisolation transformer winding results inshifting of the input inductor high switchingfrequency ripple to the isolationtransformer resulting in ripple-free inputcurrent as seen in Figure 8 in addition toreduction of magnetics size to onemagnetic core only and further efficiencyimprovements.The PFC performances is measured on

the prototype of a 400W, AC/DC BridgelessPFC converter and the measurement resultsobtained at a 300W power level shown inFigure 10 exhibit a low total harmonicdistortion of 1.7% and a power factor of0.999. The efficiency measurements inFigure 11 show near 98% efficiency at highline of 240V AC. Most important is that at

120V AC line (US main) efficiency is alsovery high (97.2%) as the usual efficiencydegradation of 2% to 3% at low line due tothe two-diode drops of the front-end bridgerectifiers are eliminated.

Three-Phase Bridgeless RectifierAll present AC/DC converters are based onthe cascade of at least two powerprocessing stages. The first stage convertsthe three-phase input voltage tointermediate high 400V DC voltage bus byuse of 6 or more controllable switches.The second Isolated DC/DC converterstage then provides isolation andconversion to lower DC voltages, such as48V or 12V. Unfortunately, all presentisolated DC/DC converters must store theDC output energy in the form of outputfiltering inductor carrying DC load current. The problem lies in the premature

rectification of the AC line into anintermediate 400V DC voltage. Theinstantaneous power delivered to DC loadis constant. Therefore, there is noconceptual reason, why the constantinstantaneous three-phase input powercould not be converted directly into aconstant DC output power. The obviousadded advantage is that such AC/DCconversion will completely eliminate need

for energy storage. Furthermore, the powerconversion will take place in a single powerprocessing stage as seen in the newThree-Phase Rectifier illustrated in Figure12 which consists of three IsolatedBridgeless PFC converters, one for eachphase, of the type shown in Figure 8. Additional important efficiency and size

advantages are obtained as well. Forexample, the total power is deliveredthrough three parallel paths so that eachphase processes only one third of totaloutput power. The overall efficiency staysthe same at 98% as the efficiency ofisolated converters in each phase. Similarlythe same low THD distortion and highpower factor of 0.999 of each phase isalso preserved.Finally, the instantaneous output currents

of each phase are positive and fluctuatingin time in sinusoidal manner. However, dueto 120-degree displacement of the inputline currents of each phase, all fluctuatingoutput currents of each phase add up toconstant output current as illustrated inFigure 1. Any remaining ripple current is onthe order of 5% of the DC load current andcomes at the filtering frequency, which issix times higher than the fundamental60Hz frequency. This clearly results inmuch reduced size of filtering capacitorsneeded, hence in reduced size and cost ofthe three-phase rectifier.

Alternative isolated bridgeless PFCconverter topologies The converter topology of Figure 8 is notthe only True Bridgeless PFC convertertopology with isolation. Another Single-stageAC/DC converter topology with PFC andisolation is shown in Figure 13 which can beused either as a Single-phase Rectifier orimplemented in converter of Figure 12 as aThree-Phase Rectifier. This converter has thesame DC voltage gain of the boost typesuch as [1] and has only one magneticpiece, the two winding isolation transformer,which does have a DC bias and is therefore

Figure 10: PFC performances measured on the prototype of a 400W, AC/DC Bridgeless PFC converterand the measurement results obtained at 300W power level

Figure 11: Efficiencymeasurements shownear 98% efficiencyat high line of 240VAC

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suitable for low to medium power. Inaddition, the input current is pulsatingrequiring the use of the separate highfrequency filter on input to reduce ripplecurrents at high switching frequency.The applications above have highlighted

the use of the new boost converter

topologies, the inverting and non-invertingones, for a single-stage True BridgelessAC/DC power conversion and theirapplication for single- and three-phaserectifiers which include galvanic isolation athigh switching frequency. However, thenew boost converter topologies have alsosignificant advantages when applied to

isolated DC/DC conversion. Shown in Figure 14 is the new isolated

boost DC/DC converter [4] used forconverting solar cell input power into ahigh voltage 400V DC bus. It canaccommodate the wide range of the inputvoltage of 15V to 100V (created by thevariation of solar cells voltages during theday) and generate regulated high DCvoltage isolated output of 400V withefficiencies of over 97%. In current automotive applications for

hybrid and electric vehicles, the auxiliary1kW to 2kW converters are needed toconvert the 400V battery voltage of thehigh voltage DC bus to 14V auxiliarybattery voltage and vice versa. Therefore abi-directional buck-boost converter isneeded. The converter of Figure 14implemented with MOSFET switchesinstead of current rectifiers on the output iscapable of such bi-directional power flowin a single power processing stage and iswell suited for these applications. Onceagain, the use of three switches onlyinstead of eight switches of conventionalconverters results in increased efficienciesand reduced cost at the same time.

Literature[1] Slobodan Ćuk, “Modeling,

Analysis and Design of SwitchingConverters”, PhD thesis, November1976, California Institute of Technology,Pasadena, California, USA.[2] Slobodan �uk, R.D. Middlebrook,

“Advances in Switched-Mode PowerConversion, “ Vol. 1, II, and III, TESLAco1981 and 1983.[3] Slobodan Ćuk, articles in Power

Electronics Technology, describingSingle-Stage, Bridgeless, Isolated PFCConverters published in July, August,October and November 2010 issues. [4] Slobodan Ćuk and Zhe Zhang,

Voltage Step-up Switching DC-DCConverter, US patent No. 7,778,046,August 17, 2010.[5] 99% Efficient AC/DC Converter

Topologies, Power Electronics Europe3/2011[6] Slobodan Ćuk, “Single-Stage,

AC-DC Converter Topologies of 98%Efficient Single Phase and Three-PhaseRectifiers”, Keynote at PCIM Europe2011, May 17, Nuremberg, Germany

Figure 12: Three-Phase Rectifier consisting of three Isolated Bridgeless PFC converters, one for eachphase, of the type shown in Figure 9

Figure 14: Isolated Boost DC/DC converter for converting solar cell input power into a high voltage400V DC bus

Figure 13: True Bridgeless isolated PFC Converter featuring two winding isolation transformer

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