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854 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 59, NO. 4, APRIL 2012

Analysis of PWM Z-Source DC-DC Converter inCCM for Steady State

Veda Prakash Galigekere and Marian K. Kazimierczuk, Fellow, IEEE

Abstract—Steady-state analysis of pulse-width modulated(PWM) Z-source dc-dc converter operating in continuous conduc-tion mode (CCM) is presented. Voltage and current waveforms,and their corresponding expressions describing the steady-stateoperation of the PWM Z-source dc-dc converter have been pre-sented. The input-to-output dc voltage transfer functions, bothfor ideal and non-ideal PWM Z-source dc-dc converter havebeen derived. The minimum Z-network inductance required toensure CCM operation is derived. The voltage ripple due to filtercapacitor and its ESR, and their individual effects on the theoverall output voltage ripple have been derived and analyzed.Expressions for power loss in each of the components of the PWMZ-source dc-dc converter has been determined. Using the expres-sions derived to determine the power losses, an expression for theoverall efficiency of the PWM Z-source dc-dc has been derived.An example PWM Z-source dc-dc converter is considered. Alaboratory prototype is built and the theoretical analysis is in goodagreement with the experimental results.

Index Terms—Continuous conduction mode, dc-dc converter,Z-source converter (ZSC).

I. INTRODUCTION

T HE impedance-source or Z-source converter was pro-posed in 2002 [1]. The salient feature of the PWM

Z-source converter is that, when it is operated in the invertermode, it has the unique feature of being a voltage buck-boostinverter as opposed to either being a buck or a boost inverter.This was a significant step in the field of dc-ac power conver-sion and the topic was given due attention by researchers inacademia and the industry [2]–[6]. Majority of the literaturecorresponding to PWM Z-source converter focuses on theinverter mode of operation or the PWM Z-source invertershown in Fig. 1. This paper specifically deals with the dc-dcconverter mode of operation of the PWM Z-source converter.A quasi-Z-source based isolated dc/dc converter is presentedin [11]. Quasi-Z-source based dc-dc converter [11] utilizes analtered impedance or Z-network derived from the impedancenetwork utilized in the original Z-source inverter of [1]. Theauthors in [7] and [8] present a brief analysis of a loss-lessZ-source dc-dc converter aided by simulation results. Theauthors in [9] explore the double input version of the PWMZ-source dc-dc converter. The authors in [10] present a briefanalysis of a loss-less Z-source dc-dc converter in discon-tinuous conduction mode and the simulation results. The

Manuscript receivedMarch 11, 2011; revised June 01, 2011; accepted August25, 2011. Date of publication November 08, 2011; date of current versionMarch28, 2012. This paper was recommended by Associate Editor E. Alarcon.The authors are with the Department of Electrical Engineering, Wright State

University, Dayton, OH 45435 USA (e-mail: [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TCSI.2011.2169742

Fig. 1. PWM Z-source inverter.

Fig. 2. PWM Z-source dc-dc converter.

motivation of this paper is to explore the steady-state operationof PWM Z-source converter in a more elaborate manner, andto present output voltage ripple analysis of the PWM Z-sourcedc-dc converter, which has not been reported yet.Additionally, there has been a renewed interest in isolated and

non-isolated voltage step-up PWM dc-dc converters for renew-able energy and distributed power generation systems [11]–[17].Typically, the low output voltage energy source, like fuel-cellsrequires a PWM dc-dc converter to (1) provide a voltage boostand (2) act as a protective buffer between the load and the en-ergy source. Compared to the conventional boost converter, thePWM Z-source dc-dc converter has a higher input-to-output dcvoltage boost factor for the same duty ratio, isolates the sourceand the load in case of a short-circuit at the load side, and hasa second-order output filter. This makes PWM Z-source dc-dcconverter a potential topology candidate for renewable energyapplications. These features prompt the necessity for a detailedinvestigation of the steady-state behavior of the PWM Z-sourcedc-dc converter in CCM.The PWM Z-source dc-dc converter is a boost converter. The

PWM Z-source dc-dc converter shown in Fig. 2 consists of adiode , two identical inductors denoted by and two iden-tical capacitors denoted by connected in a manner to obtainthe unique impedance or Z-network, an active switch such asa MOSFET/IGBT, a second order low-pass filter formed byand , and the resistive load .The objectives of this paper are to present (1) the equiva-

lent circuits and the associated expressions corresponding to dif-ferent stages of operation of the PWM Z-source dc-dc converterin CCM, (2) the dc input-to-output voltage conversion factorand minimum inductance required to ensure CCM operation (3)for power losses in the components of the PWM Z-source dc-dcconverter and the overall efficiency (4) output voltage ripple

1549-8328/$26.00 © 2011 IEEE

GALIGEKERE AND KAZIMIERCZUK: ANALYSIS OF PWM Z-SOURCE DC-DC CONVERTER IN CCM FOR STEADY STATE 855

across the filter capacitor and its ESR and (4) experi-mental results to validate the theoretical analysis.Section II presents the equivalent circuits and the derivation

of relevant equations of the PWM Z-source dc-dc converter[18]. Section III presents the derivation of DC voltage conver-sion factor for CCM and the minimum inductance required forCCM operation. Section IV presents an analysis of the outputvoltage ripple of the PWM Z-source dc-dc converter. Section Vpresents the derivation of power losses in each of the com-ponents, and the efficiency of the PWM Z-source dc-dc con-verter. Section VI presents experimental and simulation results.Section VII presents conclusions.

II. IDEALIZED WAVEFORMS

The following assumptions are used in the present analysis.1) Inductors, capacitors, and resistors are linear, time-in-variant, and frequency independent.

2) Semiconductor switches, i.e., the MOSFET and the diodeare ideal (except in estimating efficiency).

3) The natural time constant of the converter is much longerthan one switching time period.

Referring to Fig. 2, the MOSFET is switched at a constantfrequency with the duty ratio of given by

, where is the duration when is in the ON position.Since the MOSFET and the diode have complimentaryduty ratios, the duty ratio of the diode is given by .Due to the symmetry of the Z-network, and sinceand , we have ,and .

A. Time Interval:

The equivalent circuit corresponding to this state is shownin Fig. 3. In this state, the voltage across the diode is

, causing the diode to be reverse biased or OFF. Shortingthe output terminals results in the diode being reverse bi-ased, thus isolating the energy source from the rest of thecircuit. The current through the diode and the voltage across theMOSFET are zero, i.e., and . The voltage acrossthe inductor is

(1)

The inductor current is given by

(2)

Hence, the peak inductor current which occurs at isgiven by

(3)

The peak-to-peak value of the inductor current is expressed as

(4)

Fig. 3. Equivalent circuit of the PWM Z-source dc-dc converter when is ONand is OFF.

By KCL, the current through the switch is given by. The output voltage across the load resistor is

maintained by the output capacitor . The voltage across theoutput filter inductor is given by

(5)

The resulting current through is

(6)

By letting in (6), we obtain

(7)

The peak-to-peak value of the current flowing through the filterinductor is

(8)

Using (7) in (8), we have

(9)

B. Time Interval:

The equivalent circuit corresponding to the state when theMOSFET is OFF and the diode is forward biased is shownin Fig. 4. In this state, the Z-network acts as the interface be-tween the source and the load. The voltage across the diodeand the current through the MOSFET are zero. The voltageacross the inductor is given by

(10)

The current through the inductor is given by

(11)


Fig. 4. Equivalent circuit of the PWM Z-source dc-dc converter when is OFFand is ON.

Fig. 5. Voltage and current waveforms of the PWM Z-source dc-dc converterfor CCM.

The inductor current at is given by

(12)

The voltage across is given by

(13)

The resulting current through is given by

(14)

By using (13) and (14), we obtain

(15)

By letting in (15), we obtain the peak output inductorcurrent to be

(16)

The peak-to-peak value of the current through the filter inductoris given by

(17)

Fig. 5 shows the idealized theoretical waveforms for the PWMZ-source dc-dc converter.

III. DC VOLTAGE CONVERSION FACTOR AND MINIMUMINDUCTANCE FOR CCM

A. DC Voltage Conversion Factor for CCM

By the volt-second balance property of the inductor , theaverage voltage across an inductor in steady state is zero. From(1) and (10), the volt-second balance for the inductor can beexpressed as

(18)

Thus,

(19)

which gives

(20)

Equation (20) is the dc input-to-capacitor voltage conversionfactor. Reffering to Fig. 2, by applying KVL to the loop con-taining the Z-network capacitor , the filter inductor , theparallel combination of , and the Z-network inductor ,we obtain

(21)

Since the average values of and , (21) leads to

(22)

Using (20) and (22), we derive the dc input-to-output voltageconversion factor as

(23)

Since for a lossless converter, the dc input-to-output current conversion factor can be expressed as

(24)


Fig. 6. Normalized load current as a function of at theCCM/DCM boundary for PWM Z-source dc-dc converter.

B. Minimum Inductance for CCM

From (1) and (22), the peak inductor current is

(25)

At the boundary between continuous conduction mode and dis-continuous conductionmode (CCM/DCM), we have .Hence, the peak inductor current at the CCM/DCM boundary is

(26)

Since the dc inductor current is equal to the dc input current, atthe CCM/DCM boundary we have

(27)

Using (24) and (27), we derive the output current at theCCM/DCM boundary to be

(28)

The load resistance at the CCM/DCM boundary can be ex-pressed as

(29)

Figs. 6 and 7 show the plots of normalized load currentand normalized load resistance as a function of at theCCM/DCM boundary, respectively. Setting the derivative of

to zero in (28), we obtain

(30)

From (30), the maximum value of occurs at .By substituting in (28), we obtain

(31)

Fig. 7. Normalized load resistance as a function of at theCCM/DCM boundary for PWM Z-source dc-dc converter.

or(32)

Using in (31), we determinethe minimum inductance for CCM operation to be

(33)

IV. OUTPUT VOLTAGE RIPPLE IN PWM Z-SOURCE DC-DCCONVERTER IN CCM

The output circuit of the PWM Z-source dc-dc converter isshown in Fig. 8. Here, the filter capacitor is modeled as anideal capacitor and its equivalent series resistance (ESR). The dc component of the current through the filter inductorflows through the load resistor while the ac componentflows through the filter capacitor. Consider the time interval

. The current through the filter capacitor is given by

(34)

Using (9) and (34), we have

(35)

The voltage across the ESR of the filter capacitor isgiven by

(36)

The voltage across the filter capacitor is given by

(37)

Using (35) in (37), we obtain

(38)


The ac component of the output voltage is the sum of voltagesacross and , and is given by

(39)

Setting the derivative of to zero, the time instant at whichthe maximum value of occurs is

(40)

The maximum value of occurs at , hence by lettingin (40), we obtain

(41)

The maximum value of is equal to the maximum value of. This occurs at aminimum value of , which can be found

from (41), and is

(42)

Consider the time interval . The current throughthe filter capacitor is

(43)

From (17) and (43) we obtain

(44)

The voltage across can be expressed as

(45)

The voltage across the filter capacitor is given by

(46)

Using (44) and (46), we obtain

(47)

The ac component of the output voltage is the sum of the volt-ages across and , and is

(48)

Setting the derivative of with respect to time to zero, wedetermine the time instant corresponding to a minimum valueof , and is expressed as

(49)

The minimum value of is equal to the minimum value of, and it occurs at . Hence, by letting in

(49), we obtain

(50)

The value of corresponding to (50) occurs at a minimumcapacitance given by

(51)

Hence, the peak-to-peak value of the output voltage ripple isindependent of the voltage across the filter capacitor andis determined only by the voltage across the ESR of the filtercapacitor if

(52)

The minimum value of filter capacitances can be segregated as

(53)

and

(54)

If the condition specified in (52) is satisfied, the peak-to-peakoutput voltage ripple is

(55)

If the condition specified in (52) is not satisfied, bothand will contribute to the output voltage ripple. Theoutput voltage ripple and the associated value of the filtercapacitance is estimated as follows. The maximum increaseof the charge stored in the filter capacitor in each switching cycleis

(56)

The peak-to-peak voltage across the capacitor is

(57)

Since is the corner frequency of the outputfilter, then (57) can be expressed as

(58)


Fig. 8. Output circuit of the PWM Z-source dc-dc converter.

Fig. 9. Ripple voltage in PWM Z-source dc-dc converter.

Fig. 10. PWM Z-source dc-dc converter with parasitic resistances.

Hence, the total output voltage ripple is

(59)

where . Fig. 9 shows the voltageand current waveforms associated with the filter capacitorand its ESR .

V. POWER LOSSES AND DC VOLTAGE CONVERSION FACTOROF A NON-IDEAL PWM Z-SOURCE DC-DC CONVERTER

Equivalent circuit of PWM Z-source dc-dc converter withparasitic resistances is shown in Fig. 10. The diode is repre-sented by an ideal switch in series with a resistor repre-senting the forward resistance and a voltage source repre-senting the forward voltage drop. The MOSFET is replaced by

an ideal switch in series with its equivalent drain-source resis-tance represented by . The ESRs of the inductors and capac-itors have been included to account for parasitic resistance of thepassive components. The power loss in the individual compo-nents of the Z-source dc-dc converter are estimated below

A. Losses in Semiconductor Switches

By KCL, and noting that , the current through theMOSFET is

(60)

Using (24) in (60), the root mean square value is

(61)

Hence, the Ohmic power loss in MOSFET is

(62)

where is the MOSFET on-resistance, is output power,and is the load resistance. Assuming the output capacitanceof the MOSFET to be linear, the switching loss in the con-verter is

(63)

where is the output capacitance of the MOSFET . The totalpower loss in the MOSFET is the sum of the switching powerloss and the conduction power loss. By (62) and (63), we obtain

(64)

The current through the diode is

forfor

(65)

The RMS value of the current through the diode is found to be

(66)

Using (24), can be expressed in terms of as

(67)

The conduction loss in the diode forward resistance is

(68)


The average value of the diode current is

(69)

The power loss associated with the forward voltage drop ofthe diode is

(70)

Using (68) and (70), the overall power loss in the diode is

(71)

Power loss in inductors is segregated into core loss andwinding loss. Typically for PWM converters the core lossis negligible. The winding loss is dependent on the windingresistance and the RMS value of the current flowing through it.The RMS value of the currents through the Z-network inductorsis approximated to be

(72)

resulting in a power loss given by

(73)

It should be noted that expression (73) is multiplied by twosince there are two Z-network inductors. The current throughthe Z-network capacitor is

forfor

(74)

Using (24) and (74), the RMS current through is found to be

(75)

The power loss associated with the Z-network capacitors is

(76)

The RMS value of the current through the filter inductor canbe approximated to be

(77)

Power loss in the filter inductor given by

(78)

Using (35), (44), (9), and (17), the RMS value of the currentthrough the filter capacitor is

(79)

The power loss in the filter capacitor is

(80)

Using (23) and (80), the power loss in in terms of the outputpower is found to be

(81)

Hence, from (64), (71), (73), (76), (78), and (80), the total lossesin the PWM Z-source dc-dc converter is

(82)

B. DC Voltage Conversion Factor of Non-Ideal PWMZ-Source DC-DC Converter in CCM

The efficiency of the PWM Z-source dc-dc converter is

(83)

Using (23), (24) and (83), we obtain

(84)

(85)

(86)

In (86), is the dc input-to-output voltage conversionfactor for an ideal converter, and is (82).

VI. EXPERIMENTAL AND SIMULATION RESULTS

An example PWM Z-source dc-dc converter with the speci-fications , , , ,

, , is selected. Theinductors ( and ) are 1433428C manufactured by MurataPower Solutions with a measured dc resistance .The capacitors ( and ) are electrolytic capacitors with mea-sured dc resistances of and ,respectively. International Rectifier Power MOSFET IRF520which is rated for 9.2 A/100 V and has a maximum

and , and a ON Semiconductor manu-factured SWITCHMODE Power Rectifier MBR10100 rated for10 A/100 V and having and areselected. For the example considered, from (33), the minimumvalue of inductance to ensure CCM operation is

(87)


Fig. 11. Predicted efficiency as a function of and .

From (53), the minimum value of filter capacitance beyondwhich the voltage ripple across the filter capacitor is dependentonly on the value of the ESR of is determined to be

(88)

where . It should be noted that the selected valuesof and are in agreement with (87)and (88), respectively.Fig. 11 shows the variation of predicted efficiency as a func-

tion of and for a fixed . The parameters usedto obtain Fig. 11 are as specified by the considered example.The above PWM Z-source dc-dc converter was simulated in

Saber circuit simulator. The parasitics of the passive compo-nents were included and the simulation models of IRF510 andMBR10100 present in the Saber library were employed. Tran-sient simulation was carried out for three different values ofL: , , and

. It can be inferred from Fig. 12, 13 ,and 14 that for the Z-source dc-dc con-verter is in CCM, for the Z-sourcedc-dc converter is at the CCM/DCM boundary, and for

the Z-source dc-dc converter is in DCM, re-spectively. The peak-to-peak inductor current predicted by (4)is in good agreement with the simulated peak-to-peak inductorcurrent shown in Fig. 12, which corresponds to CCM operation.A laboratory prototype was built corresponding to the example.The PWM Z-source dc-dc converter was setup to operate in aopen-loop configuration. IR2110, a high-side MOSFET driverwas employed to drive the MOSFET. The duty ratio wasvaried from to in steps of .Figs. 15–17 present the theoretically predicted and experimen-tally measured , , and respectively. The differencein the measured and predicted output voltage , , andat higher duty ratios can be attributed to the losses inthe converter due to ringing in the MOSFET and non-idealitiesin the setup (stray inductances and capacitances) which have notbeen included in the analysis.Table I presents the theoretically predicted and experimen-

tally measured values of key parameters corresponding to thesteady-state analysis. is obtained by measuringto obtain . The parameters correspondto the example considered. Tektronix P6021 AC current probe

Fig. 12. Simulated inductor current and output voltage forand .



with a conversion factor of 2 mA/mV was employed to obtainthe current measurements. Fig. 18 shows the current waveformthrough obtained for . Differential probe master4231 was employed to obtain the pulsating voltage measure-ments.Fig. 19 shows the waveforms of and of for the

PWMMZ-source dc-dc converter operating in CCM. wasmeasured using a differential probe: Probe Master 4231 witha scaling factor of 20:1. The inductor current waveform was


Fig. 15. as s function of for .

Fig. 16. as s function of for .

Fig. 17. as a function of for .

obtained by measuring the voltage across a sense resistor ofconnected in series with . Fig. 20 shows the steady-state

output voltage for and . The AgilentDS05012A oscilloscope was used to record the waveforms.

Fig. 18. Current through the filter capacitor .

TABLE ITHEORETICAL AND EXPERIMENTAL RESULTS.

Fig. 19. Experimental waveforms- Upper trace: Differential probe scaling20:1, 1 V/div. Lower trace: measured across sense resistor 500mV/div and 1 mA/1 mV.

VII. CONCLUSIONS

A detailed steady-state analysis of PWMZ-source dc-dc con-verter operating in CCM has been presented. The dc input-to-output voltage conversion factor for an ideal PWM Z-sourcedc-dc converter has been derived. Equations for power loss ineach of the components of the PWM Z-source dc-dc converterhave been derived. Based on the power loss expressions derived,expressions for the overall efficiency and the dc voltage con-version factor of a non-ideal PWM Z-source dc-dc converterare determined. TheminimumZ-network inductance requiredto ensure CCM operation has been derived. The output voltageripple due to and have been analyzed, and the deriva-tion of expressions to determine the same are presented. A lab-oratory prototype was built to verify the theoretical analyses.The predicted output voltage was in good agreement with


Fig. 20. Experimental steady-state output voltage for and.

the experimental results for discret points of duy ratio fromto as shown in Fig. 15. The predicted ef-

ficiency was in good agreement with experimental results fordiscrete points of duy ratio from to . How-ever, a discrepancy was noticed for beyond 0.3, as shown inFig. 17. This can be due to the fact that the losses due to high-fre-quency ringing of the MOSFET have not been considered. Thepredicted output voltage ripple was also in good agreememntwith the experimentally measured ripple as shown in Table Iand Fig. 18. The disadvantage of the PWM Z-source dc-dc con-verter as compared to conventional boost converter topology isits higher part count. However, the merits of the PWM Z-sourcedc-dc converter are:• For the same duty ratio and input voltage , PWMZ-source dc-dc converter offers a higher output voltage.

• Since the diode is turned OFF when the MOSFET is ON, ifthere is a short on the load side, the source is isolated fromthe load. This provides inherent immunity to disturbancesat the load side. This can be critical if the fuel or energysource is expensive and is to be protected.

• Since the input-to-output voltage conversion factor isfor , the output voltage

is inverted. It can be employed, where such a feature isdesired

REFERENCES

[1] F. Z. Peng, “Z-source inverter,” IEEE Trans. Ind. Appl., vol. 39, no. 2,pp. 504–510, Mar. 2003.

[2] M. Shen and F. Z. Peng, “Operation modes and characteristics of theZ-source inverter with small inductance or low power factor,” IEEETrans. Ind. Electron., vol. 55, no. 1, pp. 89–96, Jan. 2008.

[3] V. P. Galigekere and M. K. Kazimierczuk, “Small-signal modeling ofPWM Z-source converter by circuit-averaging technique,” in IEEE In-ternational Symposium on Circuits and Systems (ISCAS), May 2011,pp. 1600–1603.

[4] P. C. Loh, D. M. Vilathgamuwa, C. J. Gajanayake, Y. R. Lim, and C.W. Teo, “Transient modeling and analysis of pulse-width modulatedZ-source inverter,” IEEE Trans. Power. Electron., vol. 22, no. 2, pp.498–507, Mar. 2007.

[5] M. Shen, A. Joseph, J. Wang, F. Z. Peng, and D. J. Adams, “Com-parison of traditional inverters and Z-source inverter for fuel cell ve-hicles,” IEEE Trans. Power. Electron., vol. 22, no. 4, pp. 1453–1463,Jul. 2007.

[6] J. Liu, J. Hu, and L. Xu, “Dynamic modeling and analysis of Z-sourceconverter-derivation of ac small signal model and design-oriented anal-ysis,” IEEE Trans. Power. Electron., vol. 22, no. 5, pp. 1786–1796,Sep. 2007.

[7] X. Fang and X. Ji, “Bidirectional power flow Z-source dc-dc con-verter,” in Proc. IEEE Veh. Power Propulsion Conf. (VPPC’08), pp.1–5.

[8] X. Fang, “A novel Z-source dc-dc converter,” in Proc. IEEE Int. Conf.Ind. Technol. (ICIT 2008), pp. 1–4.

[9] F. Sedaghati and E. Babaei, “Double input Z-source DC-DC con-verter,” in Proc. IEEE Power Electron., Drive Syst., Technol. Conf.(PEDSTC), 2011, pp. 581–586.

[10] J. Zhang and J. Ge, “Analysis of Z-source DC-DC converter in dis-continuous current mode,” in Proc. IEEE Power Energy Eng. Conf.(APPEEC), Asia-Pacific, 2010, pp. 1–4.

[11] D. Vinnikov and I. Roasto, “Quasi-Z-source based isolated DC/DCconverters for distributed power generation,” IEEE Trans. Ind. Elec-tron., vol. 58, no. 1, pp. 198–201, Jan. 2011.

[12] Z. Yao and L. Xiao, “Push-pull forward three-level converter with re-duced rectifier voltage stress,” IEEE Trans. Circuits Syst. I, Reg. Pa-pers, vol. 57, no. 10, pp. 2815–2821, Oct. 2010.

[13] E. H. Ismail, M. A. Al-Saffar, and A. J. Sabzalli, “High conversion ratioDC-DC converters with reduced switch stress,” IEEE Trans. CircuitsSyst. I, Reg. Papers, vol. 55, no. 7, pp. 2139–2151, Aug. 2008.

[14] B. Axelrod, Y. Berkovich, and A. Ioinovici, “Switched-capac-itor/switched-inductor structures for getting transformerless hybridDC-DC PWM converters,” IEEE Trans. Circuits Syst. I, Reg. Papers,vol. 55, no. 2, pp. 687–6961, Mar. 2008.

[15] E. H. Ismail, M. A. Al-Saffar, A. J. Sabzali, and A. A. Fardoun, “Afamily of single-switch PWM converters with high step-up conversionratio,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55, no. 4, pp.1159–1171, May 2008.

[16] A. Shahin, M. Hinaje, J. Martin, S. Pierfederici, S. Rael, and B. Davat,“High voltage ratio DC-DC converter for fuel cell applications,” IEEETrans. Ind. Electron., vol. 57, no. 12, pp. 3944–3955, Dec. 2010.

[17] L. S. Yang, T. J. Liang, and J. F. Chen, “Transformerless DC-DC con-verters with high step-up voltage gain,” IEEE Trans. Ind. Electron.,vol. 56, no. 8, pp. 3144–3152, Aug. 2009.

[18] M. K. Kazimierczuk, Pulse-Width Modulated DC-DC Power Con-verters. Hoboken, NJ: Wiley, 2008.

Veda Prakash Galigekere Nwas born in Bangalore,India, on Dec. 19, 1982. He received the B.E fromVTU, Belgaum, India, in 2004 and the M.S degreefrom Wright State University, Dayton, OH, in 2007.Since September 2007, he has been working towardthe Ph.D. degree at Wright State University.His areas of interests are stady state and dynamic

modeling of PWM dc-dc and dc-ac inverters, powersemiconductor devices, and renewable energy sys-tems.

Marian K. Kazimierczuk (M’91–SM’91–F’04)received the M.S., Ph.D., and D.Sci. degrees inelectronics engineering from the Department ofElectronics, Technical University of Warsaw,Warsaw, Poland, in 1971, 1978, and 1984, respec-tively.He was a Visiting Professor with the Department

of Electrical Engineering, Virginia Polytechnic Insti-tute and State University, Blacksburg. Since 1985,he has been with the Department of Electrical Engi-neering, Wright State University, Dayton, OH, where

he is currently a Professor. His research interests are in high-frequency high-efficiency switching-mode tuned power amplifiers, resonant and PWM dc/dcpower converters, dc/ac inverters, high-frequency rectifiers, electronic ballasts,modeling and control of converters, high-frequency magnetics, power semicon-ductor devices.Prof. Kazimierczuk received the IEEE Harrell V. Noble Award for his contri-

butions to the fields of aerospace, industrial, and power electronics, in 1991. Hewas and is an Associate Editor of the IEEE TRANSACTIONS ON CIRCUITS ANDSYSTEMS—PART I: FUNDAMENTAL THEORY AND APPLICATIONS, and served asan Associate Editor for the Journal of Circuits, Systems, and Computers. He wasa member of the Superconductivity Committee of the IEEE Power ElectronicsSociety. He was a chair of the CAS Technical Committee of Power Systems andPower Electronics Circuits in 2001–2002.

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