A 1-kW Step-Up

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 7, JULY 2013 3329

A 1-kW Step-Up/Step-Down Switched-CapacitorAC–AC Converter

Romero L. Andersen, Member, IEEE, Telles B. Lazzarin, Member, IEEE, and Ivo Barbi, Fellow, IEEE

Abstract—This paper proposes a new ac–ac static power con-verter based on the switched-capacitor (SC) principle, intended toreplace the conventional autotransformer in commercial and resi-dential applications. The principle of operation, a qualitative andquantitative analysis, the design methodology, and an example aredescribed in this paper. The main advantages of the proposed ac–acconverter are the absence of magnetic elements, the stress voltagesin all components being equal to half of the high-side voltage, thecommon reference between input and output voltages, the employ-ment of a single SC leg, the ability to be bidirectional, the highefficiency, and the high power density. In order to demonstratethe performance of this converter in the laboratory, a prototype of1-kW, 220-Vrm s high-side voltage, 110-Vrm s low-side voltage, andswitching frequency of 100 kHz was designed and fabricated. Therelevant experimental results are reported herein. The maximumand rated power efficiencies obtained in the laboratory were 98%and 96%, respectively.

Index Terms—AC–AC converter, bidirectional, switched-capacitor (SC).

I. INTRODUCTION

THROUGHOUT the world, it is common to find com-mercial and domestic appliances that work with differ-

ent voltages from those available on the electrical grid andthe most popular solution is the employment of a low-power/low-voltage autotransformer. However, like any electromagnetictransformer, the autotransformer efficiency is poor and it pro-duces considerable audible noise. Moreover, the global demandfor copper, utilized in the autotransformer winding construction,has been continuously increasing and is nowadays exceeding thesupply [1].

The switched-capacitor (SC) converters have been a very im-portant research topic for many years, basically in relation tononisolated dc–dc static power conversion [2]–[7]. Some ap-plications that already benefit from the SC principle includepower supplies for mobile electronics systems, electric vehi-cles, battery equalizer circuits, voltage-balancing circuits formultilevel inverters, etc. [8]–[20]. As SC power converters arecomposed only of capacitors and switches, without magnetic de-vices, they can achieve significant size reduction in comparisonwith the converters generally used in conventional switched-

Manuscript received June 4, 2012; revised August 9, 2012; acceptedSeptember 20, 2012. Date of current version December 24, 2012. Recom-mended for publication by Associate Editor J. A. Pomilio.

The authors are with the Department of Electrical Engineering, Power Elec-tronics Institute, Federal University of Santa Catarina, Florianopolis 88040-970, Brazil (e-mail: [email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPEL.2012.2222674

mode power supplies. Furthermore, the behavior of these cir-cuits can be described by simple equivalent circuits [21]–[27]and it is possible to fabricate these converters on a semiconduc-tor IC chip [21]–[26].

A recent publication [1] extended for the first time the switch-ing capacitor principle to ac–ac static conversion, where a briefanalysis and experimental results for a step-down/step-up con-verter with rated power of 600 W, high-side voltage of 220 Vrms ,low-side voltage of 110 Vrms , line frequency of 60 Hz, andswitching frequency of 50 kHz were presented. The main char-acteristics of the converter are the stress voltages in all compo-nents being equal to half of the high-side voltage, the differentialoutput voltage, the employment of two SC legs, and eight uni-directional switches. The results presented in [1] are promisingand show that the employment of an SC in an ac–ac convertercan contribute with new and efficient solutions for the ac–acarea, as, for example, in low-power/low-voltage systems aimedat replacing the conventional autotransformer in commercialand domestic applications.

The purpose of this paper is to introduce a new SC-basedac–ac static power converter topology. The main characteristicsof the proposed ac–ac converter that are also present in [1]are the absence of magnetic elements and the stress voltageson the switches being equal to half of the high-side voltage.In addition, there are also the new characteristics of having acommon reference between input and output voltages, no dccomponent in the capacitor voltages, and the employment of asingle SC leg and four bidirectional switches. A detailed analysisof the converter, equivalent circuits, the design methodology,and experimental results are reported herein.

II. PROPOSED SC AC–AC CONVERTER

The proposed SC ac–ac converter is presented in Fig. 1. Thisconverter operates as a step-down converter when configured asshown in Fig. 1(a) or as a step-up converter when configuredaccording to Fig. 1(b). The only difference is that the pointswhere the source and the load are connected have to be in-verted. The circuit has four bidirectional switches representedas S1 , S2 , S3 , and S4 and three capacitors represented as C1 , C2 ,and C3 . Fig. 1(c) and (d) shows the proposed gate signals andthe practical implementation of a bidirectional switch using twoconventional MOSFETs, respectively.

In this topology, one half of the high-side voltage (vH /2)is applied to C2 and C3 . Capacitor C1 , being connected toC2 and after this to C3 in each switching period, equalizestheir voltages to vL = vH /2. Each bidirectional switch seriesresistance is considered, and despite being needed for thecapacitor charge/discharge process, they also cause losses.These losses are minimized for D = 0.5, as will be discussed ina later section, which is the proposed duty cycle.

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3330 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 7, JULY 2013

Fig. 1. Proposed SC ac–ac converter: (a) step-down configuration, (b) step-up configuration, (c) gate drive signals, and (d) bidirectional switch model and itspractical implementation using two MOSFETs.

Fig. 2. Theoretical waveforms of the proposed ac–ac converter: (a) input andoutput voltages; (b) voltages across the capacitors; and (c) voltage across theswitches.

III. PRINCIPLE OF OPERATION

This section presents the principle of operation of the pro-posed SC ac–ac converter in two steps: the first analyzes the maincharacteristics of the converter at low frequency (frequency ofthe input voltage) and the second studies the operation stages ofthe converter in a switching period (high-frequency analysis).

A. Low-Frequency Analysis

The low-frequency analysis presents the principle of opera-tion, the main waveforms, and voltage stresses on the compo-nents of the proposed converter in a period of the input source.

The SC C1 in the ac–ac converter shown in Fig. 1(a) and (b)ensures the voltage balance between the capacitors C2 and C3 .Consequently, it operates as a step-down or step-up converterand the voltage stresses on the capacitors and on the switchesare one-half of high voltage vH . For both operation modes, theexpected waveforms of the proposed converter are illustrated inFig. 2, where the input and output voltages are in Fig. 2(a), thevoltages across the capacitors are in Fig. 2(b), and the voltagesacross the switches are in Fig. 2(c), Vkp being the peak value ofthe high voltage vH .

B. High-Frequency Analysis

An SC converter can operate in three modes, which are de-fined by the charge of the SC. These modes are complete charge(CC), partial charge (PC), and no charge (NC) [25]. The best op-eration regions are in PC and NC modes. The NC mode usuallyrequires a high operation frequency and large capacitances, andthe advantages in relation to PC mode are not significant; thus,the PC mode is considered for the proposed converter. There-fore, the waveforms described in this section, in the operationstages, relate to the converter operating in PC mode.

The proposed ac–ac converter operating as a step-down con-verter presents two operation stages per switching period. Dur-ing the positive half of the grid voltage, with the converter inthe step-down configuration, these stages can be described asfollows.

First stage starts when switches S1 and S3 are turned ON.Capacitor C2 discharges and capacitor C3 charges during thefirst part of this stage (Δt1A ). When their currents reach zero,C2 starts to charge and C3 starts to discharge until the end of thestage (Δt1B ). Capacitor C1 charges throughout this stage andthe power source vH delivers energy to the circuit. SwitchesS1 and S3 are turned OFF at the end of the first stage. Thistopological stage is shown in Fig. 3(a).

Second stage starts when switches S2 and S4 are turned ON.Initially, the power source receives energy from the circuit, ca-pacitor C2 discharges, and capacitor C3 charges until their cur-rents reach zero (Δt2A ). After this, the power source deliversenergy to the circuit, capacitor C2 charges and capacitor C3discharges until the end of the stage (Δt2A ). Capacitor C1 dis-charges throughout this stage. Switches S2 and S4 are turnedOFF at the end of the second stage. This topological stage isshown in Fig. 3(b).

After the second stage, another switching period starts fromthe first stage.

In the negative half-cycle of the grid, the converter has similaroperation stages with different current directions, as can be seenin Fig. 3(c) and (d). The main theoretical waveforms for thepositive and the negative half-cycles of the grid are shown inFig. 4(a) and (b), respectively.

ANDERSEN et al.: 1-kW STEP-UP/STEP-DOWN SWITCHED-CAPACITOR AC–AC CONVERTER 3331

Fig. 3. Topological stages for step-down configuration. Positive half-cycle of the grid voltage: (a) First stage. (b) Second stage. Negative half-cycle of the gridvoltage: (c) First stage. (d) Second stage.

IV. QUANTITATIVE ANALYSIS

A. Ideal Voltage Gain

The ideal voltage gain of the proposed SC ac–ac convertercan be understood by examining Fig. 1(a) and (b), where the ca-pacitor voltages C1 , C2 , and C3 are the same and are defined by

vC 1 = vC 2 = vC 3 =vH

2. (1)

When the converter operates in a step-down configuration, itsoutput voltage is the voltage across the capacitor C3 (vC 3) andthe ideal voltage gain is defined by

GvSD ideal =vL

vH=

12. (2)

When the converter operates as a step-up configuration, itsoutput voltage is the voltage across the capacitors C2 and C3(vC 2 + vC 3) and the ideal voltage gain is defined by

GvSU ideal =vH

vL= 2. (3)

B. Equivalent Resistance

The proposed ac–ac converter has an SC cell, as shown inFig. 5(a). Previous studies on dc–dc converters have demon-strated that this SC cell can be represented by an equivalentresistance, as illustrated in Fig. 5(b), which is calculated using(4) for different duty cycle values and (5) for a duty cycle of50% [21], [22]. The model in Fig. 5(b) describes the equivalent

resistance of the SC ac–ac converter “seen” through its highside; nevertheless, it can also be represented through its lowside employing the relation defined in (6).

Expression (4) considers the capacitor voltages C2 and C3to be constant. The proposed converter allows this approachbecause capacitors C2 and C3 are always connected to the inputvoltage. When the SC C1 is connected in parallel with C2 [seeFig. 3(a) and (c)], capacitor C2 supplies energy to C1 onlypart of the time [ΔT1A in Fig. 3(a) and (c)]. During the timeΔT1B , both capacitors C1 and C2 receive energy. The processis similar when the SC C1 is connected in parallel with C3 [seeFig. 3(b) and (d)]. This characteristic makes the voltage ripplesin capacitors C2 and C3 lower than that in capacitor C1 , eventhough the order of magnitude of the capacitors is same. Thus,it is possible to consider the voltage ripples in C2 and C3 tobe constant in order to obtain the equation for the equivalentconduction resistance.

ReqH =1

fs · C

· (1 − e−1/fs ·2·Ro n ·C )[1−(e−(D )/fs ·2·Ro n ·C +e−(1−D )/fs ·2·Ro n ·C )+e−1/fs ·2·Ro n ·C ]

(4)

ReqH (D=0.5) =1

fs · C· (1 + e−1/2·fs ·2·Ro n ·C )(1 − e−1/2·fs ·2·Ro n ·C )

(5)

ReqL =14· ReqH (6)


Fig. 4. Main theoretical high-frequency waveforms. (a) Positive half-cycle ofthe grid voltage. (b) Negative half-cycle of the grid voltage.

Fig. 5. (a) SC ac–ac converter. (b) Equivalent resistance of SC ac–ac converter“seen” through its high side vH .

Fig. 6. Normalized equivalent resistance (a) versus fs τ and (b) versus D.

A normalized equivalent resistance is defined by (7) for dif-ferent duty cycle values and by (8) for a duty cycle of 50%.These expressions are obtained through manipulation of (4) and(5), and τ is defined in (9)

ReqH =ReqH

8 · Ron=

14 · fs · τ

·(1 − e−1/fs ·τ

)[1 −

(e−(D )/fs ·τ + e−(1−D )/fs ·τ

)+ e−1/fs ·τ

]

(7)

ReqH (D=0.5) =ReqH (D=0.5)

8 · Ron=

14 · fs · τ

·(1 + e−1/2·fs ·τ

)(1 − e−1/2·fs ·τ

)

(8)

τ = 2 · Ron · C (9)

ReqH (D=0.5) min = lim ReqH (D=0.5)fs →∞

= 8 · Ron . (10)

Expression (8) shows the behavior of the normalized equiva-lent resistance in relation to fsτ (product of switching frequencyand τ ) when D is fixed (D = 0.5), which is presented in Fig. 6(a).It indicates that an increase in frequency provides a decrease inReqH . Thus, the equivalent resistance value is lower when theswitching frequency tends to infinite (or it is very high) and thisvalue is defined in (10).

The behavior of the normalized equivalent resistance in re-lation to the duty cycle can be verified in Fig. 6(b) when fsτis fixed (fsτ = 0.5). The curve was drawn employing (7) andit demonstrates that the equivalent resistance value is lower atclose to D = 0.5. Therefore, an SC ac–ac converter with a lowequivalent resistance can be obtained through the proper design-ing of the parameters D, fs , and τ . Consequently, its efficiencywill be high.

C. Equivalent Capacitance

The SC C1 of the proposed ac–ac converter remains con-nected DTs in parallel with C2 and (1 – D)Ts in parallel withC3 in each switching period. This operation works as two equiv-alent capacitors, one in parallel with C2 which has a value ofD · C1 and another in parallel with C3 which has a value of(1 − D) · C1 , as represented in Fig. 7(a). The analysis of thiselectrical circuit (considering D = 0.5 and three equal capac-itors) enables an equivalent capacitance to be found for theac–ac converter which, when seen through the high side, is de-fined in (11) and has the configuration shown in Fig. 7(b). The


Fig. 7. (a) Model employed to obtain the equivalent capacitance. (b) Equiva-lent capacitance of SC ac–ac converter “seen” through high side vH .

same capacitance can be represented by the low side, as givenby (12). The equivalent capacitance allows the reactive powerflow required by the ac–ac converter and its power factor to beestimated.

CeqH =34· C (11)

CeqL = 3 · C (12)

D. Switching Losses

The converter proposed in Fig. 1 employs bidirectionalswitches implemented by MOSFETs. The switching loss in oneMOSFET due to its parasitic capacitance is given by (13), whereCOSS is the output capacitance of a MOSFET, fs is the switch-ing frequency, and vs is the voltage across the switch that isshown in Fig. 2(c) and defined by (14). Equation (13) calculatesthe power supplied to the MOSFET capacitance in a switchingperiod. The sum of the supplied power in all switching peri-ods during one period of input voltage provides the total powersupplied to the MOSFET capacitance, which is given by (15).As the converter uses eight switches, the total switching lossesdue to parasitic capacitances of MOSFETs are expressed by(16). This equation demonstrates that increasing the switchingfrequency of the ac–ac converter also increases the switchinglosses

Psl1S = E · fs =12· COSS · (vS )2 · fs (13)

vS =vH

2=

Vpk

2· sin (θ) (14)

Psl1S =12· COSS · fs ·

12π

∫ 2π

0

Vpk

2· sin (θ) dθ

=116

· COSS · fs · V 2pk (15)

Psl8S = 8 · Psl1S =12· COSS · fs · V 2

pk . (16)

An equivalent resistance that describes the switching lossesof the ac–ac converter on the high side can be obtained from(17). On substituting (16) into (17), this equivalent resistance isdependent only on Coss and fs , as shown by (18). This equivalent

Fig. 8. Equivalent circuit of SC ac–ac converter. (a) Model “seen” by highside. (b) Model “seen” by low side.

resistance can be reflected to the low side by (19).

RslH =v2

H

Psl8S(17)

RslH =1

COSS · fs(18)

RslL =1

4 · COSS · fs. (19)

E. Equivalent Circuit

Based on Sections IV-B, IV-C, and IV-D, an equivalent circuitfor the ac–ac converter is proposed, as presented in Fig. 8.Its variables can be represented by the high side, as shown inFig. 8(a), or by the low side, as shown in Fig. 8(b). The elementsthat compose the equivalent circuit are as follows:

RslH or RslL : parallel resistance that indicates the switchingloss due to intrinsic capacitances of the MOSFETs;

ReqH or ReqL : series resistance that indicates conductionloss in switches and capacitors;

CeqH or CeqL : parallel capacitance that indicates reactivepower flow required by ac–ac converter.

The study in Sections IV-A and IV-D demonstrated that theresistances ReqH and Rsl decrease when the switching fre-quency increases; therefore, the conduction loss decreases andthe switching loss increases. As the total loss of the ac–ac con-verter is the sum of both losses, there is a range of switchingfrequency that minimizes the total loss and, consequently, in-creases the efficiency of the converter.

The analysis of the equivalent circuit allows simple equationsto be found that are employed to examine and design the pro-posed ac–ac converter. These equations are shown in Table I andthey provide the main information on the ac–ac converter. Thevariable f in the equations is the frequency of the input voltage.

V. DESIGN EXAMPLE

A. Specification

After the theoretical analysis, some design specificationswere defined with the objective of simulating the converter and


TABLE IEQUIVALENT CIRCUIT EQUATIONS

implementing a prototype. These specifications are: Po = 1000-W output power; Qi ≤ 0.3Po -VAR input reactive power; vH =220-V high-side voltage; vL = 110-V low-side voltage; fi =60-Hz frequency of ac voltage; η > 95% expected efficiency;and D = 0.5 duty cycle.

The proposed ac–ac converter is designed to operate with lowequivalent resistance. This requires that fsτ ≥ 0.2 and D ∼= 0.5in Fig. 6(a) and (b). Thus, an adequate design sets the duty cycleat 0.5, calculates the capacitor according to the desired reactivepower, and chooses the switches and the switching frequencyto maintain fsτ higher than 0.2 while still keeping the switchconduction resistance low (Ron) and the switching frequencyfs achievable in the practical implementation. In the followingsections, the choice of components, the choice of switchingfrequency, and an analysis of the results are discussed.

B. Capacitance Calculation

Based on the specification and the equation for the inputreactive power in Table I, the maximum capacitance for C1 , C2 ,and C3 is obtained using

C ≤ 2 · (0.3 · Po)3 · π · v2

H · f ≤ 21.9μF. (20)

Two 10-μF/400-V parallel-connected were chosen for eachcapacitor (C = 20 μF). Thus, the expected power factor is 0.969in full load.

C. Switching Frequency and Choice of Switches

The MOSFETs that implement the bidirectional switches arechosen with the aim of obtaining the appropriate fsτ and a low

Fig. 9. Efficiency versus switching frequency.

conduction resistance. Thus, the MOSFET FQA62N25C, whichhas a RDS(on) value of 35 mΩ at 25 ◦C (or 60 mΩ at 100 ◦C),was selected. Its maximum drain–source voltage is 250 V.

The total conduction resistance of a bidirectional switch(Ron) is twice the resistance of a MOSFET, and therefore, theresistance Ron is 120 mΩ at 100 ◦C.

Applying the values of C and Ron in the efficiency equationin Table I allows the efficiency of the ac–ac converter to be pre-dicted for the switching frequency selected, as shown in Fig. 9.This curve demonstrates that the converter is most efficient atbetween 80 and 120 kHz. Thus, the switching frequency se-lected was 100 kHz, as identified in the figure. At this operationpoint, the expected efficiency is 97.3%.


TABLE IIMAIN PARAMETERS OF EQUIVALENT CIRCUIT

TABLE IIIDESIGN EXAMPLE RESULTS

D. Equivalent Circuit

The definition of the values of C,Ron ,D, and fs allows theparameters for the equivalent circuit to be calculated, as shownin Table II.

E. Main Results of Design Example

The expected results for the design example were obtainedby applying the equations in Table I and by simulation of theproposed ac–ac converter. Both sets of results are shown inTable III, those obtained from the equations in the first columnand from the simulation in the second column.

The results in Table III indicate that the specification of thedesign example could be extended as it has an expected effi-ciency of 97.4%. The results also allow it to be estimated thatfor this converter the conduction loss is around 24.8 W and theswitching loss is around 4.6 W.

The results in the two columns are very similar, which val-idate the equations presented in Table I, determined throughan analysis of the proposed equivalent circuit. Therefore, theequations in Table I and the equivalent circuit can be used inthe study of the proposed ac–ac converter to produce consistentresults.

VI. PROTOTYPE IMPLEMENTATION AND

EXPERIMENTAL RESULTS

After the analysis, design, and simulations, a prototype wasbuilt to verify the operation of the proposed converter in lab-oratory. The main specifications and components used in theprototype are presented in Table IV. The schematic of the im-plemented circuit and a photo of the prototype are presented

TABLE IVMAIN SPECIFICATIONS AND COMPONENTS OF THE PROTOTYPE

in Figs. 10 and 11, respectively. The experiments were carriedout with the converter fed by the electric grid. As the converterprovides a significant level of power, the input filter needs to beeither an inductive L or an inductive-capacitive LC filter. Thefrequency of the current ripple is high (100 kHz), and thus, asmall filter is sufficient to filter the input current. An L filter wasselected in order to employ the line inductance as a filter ratherthat add an external inductor. However, an LC filter could beused, and in cases of high power, this may be a more appropri-ate choice. An input inductance changes slightly the shape ofthe current ripple in capacitors and switches because the high-frequency component circulates only through C2 and C3 . Thisdifference slightly decreases the efficiency of the converter, butthis is not significant. The line inductance during the test wasaround 10 μH.

The prototype uses a simple gate drive circuitry. The gatesignals were generated using a UC3525 PWM modulator, twointegrated drivers UCC27424, and two small gate drive trans-formers with a 1:1:1 turns ratio. A commercial 15-W 12-Vauxiliary power supply was included in the prototype to feedthe ICs and the overall size is much reduced.

First, the prototype was tested for the step-down configurationand the basic waveforms were acquired. Fig. 12 shows the inputand output voltages in this situation. The output voltage followsthe shape and phase of the grid voltage and the small voltagedrop compared to the ideal value of vH /2 is caused by the totalequivalent resistance. Fig. 13 shows the voltage across a switchand the output voltage; as expected, the low-side voltage isapplied to the switches. This is an advantage of the topologywhich allowed the use of low-resistance low-voltage (250 V)MOSFETs.

The voltages across the capacitors can be seen in Fig. 14. Theirvalue is around vH /2 and the ripple is almost imperceptiblefor the chosen parameters. The current through capacitor C1is shown in Fig. 15 and its shape is similar to that shown inFig. 4.

The input current leads the voltage by approximately 14.4◦

as can be seen in Fig. 16, which is expected for the capacitivecircuit. Its profile is near sinusoidal with some distortion whichis reproduced from the grid voltage. The grid series inductancewas able to filter most of the high-frequency component. Themeasured power factor for rated power was 0.9687.

The operation with different types of loads can be seen inFigs. 17 and 18 for an RL load and a nonlinear load, respectively.In both figures, the voltage distortion that is present in the grid


Fig. 10. Schematic of the implemented circuit.

Fig. 11. Photo of the prototype.

Fig. 12. Experimental waveforms: Input vH and output vL voltages.

Fig. 13. Experimental waveforms: Voltage across switch S1 and output volt-age vL .

voltage appears in the output voltage. The output current inFig. 17 lags the voltage as expected by around 60◦ and hassinusoidal profile (R = 10 Ω and L = 45 mH). The outputcurrent in Fig. 18 is caused by a single-phase rectifier with acapacitive filter of 300 μF, a line inductance of 1.4 mH, and aresistor of 20 Ω. In both situations, the converter presents normaloperation.

Second, the same procedure was followed for the step-upconfiguration. The waveforms acquired for the input and outputvoltages shown in Fig. 19, the low-side voltage and the voltageacross a switch shown in Fig. 20, and the capacitor voltagesshown in Fig. 21 are similar to those presented for the step-down configuration. The only difference is that in this case,the power source is connected to the low side and the load is


Fig. 14. Experimental waveforms: Voltages across capacitors C1 , C2 , andC3 .

Fig. 15. Experimental waveform: Current through capacitor C1 (iC 1 ). Scale:10 A/div. and 2 μs/div.

Fig. 16. Experimental waveforms: Input voltage vH and input current iH .

Fig. 17. Experimental waveforms: Input voltage vH , output voltage vL , andoutput current iL for RL load.

Fig. 18. Experimental waveforms: Input voltage vH , output voltage vL , andoutput current iL for nonlinear load.

Fig. 19. Experimental waveforms: Input vL and output vH voltages.


Fig. 20. Experimental waveforms: Voltage across switch S1 and low-sidevoltage vL .

Fig. 21. Experimental waveforms: Voltages across capacitors C1 , C2 , andC3 .

connected to the high side. The input current, shown in Fig. 22,also leads the voltage by around 13.5◦, as expected, and themeasured power factor for the rated power was 0.9724. Thehigh-frequency component is more filtered in this case than itis in the step-down configuration because the input current ishigher.

Finally, the experimental curves for the efficiency, regula-tion, and power factor were compared to the theoretical curvesobtained through calculation using the equations presented pre-viously in the analysis.

The efficiency curves plotted in Fig. 23 show that for a wideload range, the experimental efficiency is higher than 96% forboth the step-down and step-up configurations. The experimen-tal efficiency at rated power was 96.2% for the step-down [seeFig. 23(a)] and 95.6% for the step-up [see Fig. 23(b)] con-figuration. The efficiency peaks were 97.8% (step-down) and97.2% (step-up), and occurred at 400 W. The theoretical andsimulation curves are above the experimental curves, due to theexperimental setup wires and connections having resistances

Fig. 22. Experimental waveforms: Input voltage vL and input current iL (lowside).

that were not taken into account in the theoretical analysis, andconsequently, the losses were greater than those considered inthe calculations. Fig. 23(a) also shows a theoretical curve wherethe experimental setup resistance was considered as an additionof 50% in the equivalent resistance (from 259 to 388 mΩ). In thiscase, the calculated efficiency is much closer to the experimentalresult.

The output regulation curves can be seen in Fig. 24. Fig. 24(a)shows the calculated output voltage regulation, the theoreticalregulation where the experimental setup resistances were con-sidered, and the experimental regulation for step-down opera-tion. Fig. 24(b) shows a comparison between the simulated andthe experimental regulation for step-up operation. A voltagedrop of less than 3.5% was noted for rated power compared tothe no-load output voltage. Again, this voltage drop is higherthan expected based on the calculations and the simulationsbecause the experiment had more resistances. The cables andconnections used to install the measurement instruments typi-cally have resistances of the order of a few tens of milliohms,which can cause this difference.

The curves in Fig. 24 also verify the switching losses ofthe proposed model (19). The converter has switching lossesdue to the intrinsic capacitances of MOSFETs even when theconverter is under no-load conditions (0 kW in output power).Nevertheless, the regulation is 100% at this operation point,verifying that there is no drop in the output voltage due to thecharge/discharge of the intrinsic capacitances of the MOSFET.This energy is supplied by the input voltage and it does not affectthe output voltage. However, it is present and it is responsiblefor the low efficiency under the low-load conditions shown inFig. 23.

The input power factor curves in Fig. 25 show very goodagreement between the calculations and experimental measure-ments. The power factor is close to 1 at rated power but itdrops considerably for low power. This is a consequence of thecapacitive circuit and the parameters chosen. Nevertheless, thecapacitive characteristic can be beneficial in some scenarios andcontribute to increasing the overall power factor where most ofthe loads are inductive.


Fig. 23. Measured efficiency. (a) Theoretical A (calculation); theoretical B (calculation considering prototype resistances) and experimental step-down.(b) Simulation step-up and experimental step-up.

Fig. 24. Output voltage regulation. (a) Theoretical A (calculation); theoretical B (calculation considering prototype resistances) and experimental step-down.(b) Simulation step-up and experimental step-up.

Fig. 25. Input power factor. Theoretical (calculation); experimental step-downand experimental step-up.

VII. CONCLUSION

A new ac–ac static power converter based on the SC princi-ple has been proposed. The following conclusions can be drawnfrom the theoretical analysis and the experimental results re-ported in this paper:

1) the proposed ac–ac static power converter employs onlycapacitors and switches;

2) the converter employs a single SC and has a commonreference between output and input voltages;

3) the converter operating in open loop with a con-stant duty cycle of 0.5 presents better voltage regula-tion than its autotransformer counterpart with the samespecifications;

4) the topology does not require complex control algorithms,the conversion efficiency is high, and the power factor isclose to 1 for rated power;

5) the circuit can operate as a step-down converter (staticgain of 0.5) or a step-up converter (static gain of 2), and


in both modes, only one-half of the high-side voltage isapplied to the switches and the capacitors;

6) the theoretical analysis results were corroborated by theexperimental results;

7) the proposed converter is a potential candidate for sub-stituting the conventional autotransformer in low-powerapplications.

REFERENCES

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Romero L. Andersen (M’11) was born in Floriano-polis, Santa Catarina, Brazil, in 1980. He receivedthe B.S., M.S., and Ph.D. degrees in electrical engi-neering from the Federal University of Santa Cata-rina, Florianopolis, Brazil, in 2003, 2006, and 2010,respectively.

He is currently a Postdoctoral Researcher at thePower Electronics Institute, Federal University ofSanta Catarina. His interests include dc–dc powerconversion, power converter modeling, and renew-able energy sources.

Telles B. Lazzarin (S’09–M’12) was born inCriciuma, Santa Catarina, Brazil, in 1979. He re-ceived the B.Sc., M.Sc., and Ph.D. degrees in electri-cal engineering from the Federal University of SantaCatarina (UFSC), Florianopolis, Brazil, in 2004,2006, and 2010, respectively.

He is currently a Professor at the Federal Instituteof Santa Catarina, Florianopolis, and he also works asa Guest Researcher at the Power Electronics Institute(INEP), UFSC. In 2007, he was a Research Assistantat the University Center of Jaragua do Sul, Brazil. In

2010 and 2011, he was a Postdoctoral Fellow at INEP, UFSC. His interestsinclude inverters, parallel operation of inverters, UPS, high-voltage dc-dc con-verters, ac–ac power converters, and switched-capacitor converters.

Dr. Lazzarin is a Member of the Brazilian Power Electronic Society, theIEEE Power Electronics Society, and the IEEE Industrial Electronics Society.

Ivo Barbi (M’78–SM’90–F’11) was born in Gaspar,Santa Catarina, Brazil, in 1949. He received the B.S.and M.S. degree in electrical engineering from theFederal University of Santa Catarina, Florianopolis,Brazil, in 1973 and 1976, respectively, and the Dr.Ing.degree from the Institut National Polytechnique deToulouse, Toulouse, France, in 1979.

He founded the Brazilian Power Electronics So-ciety and the Power Electronics Institute of the Fed-eral University of Santa Catarina. He is currently aprofessor of the Power Electronics Institute, Federal

University of Santa Catarina.

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A 1-kW Step-Up