A quadratic buck converter with lossless ... - Semantic Scholar

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 47, NO. 2, APRIL 2000

A Quadratic Buck Converter with Lossless Commutation Vincius Miranda Pacheco, Acrísio José do Nascimento, Jr., Valdeir José Farias, João Batista Vieira, Jr., Member, IEEE, and Luiz Carlos de Freitas, Member, IEEE

Abstract—High switching frequency associated with soft commutation techniques is a new trend in switching converters. Following this trend, the authors present a buck pulsewidth modulation converter, where the dc voltage conversion ratio has a quadratic dependence on duty cycle, providing a large step-down. By introducing two resonant networks, soft switching is attained, providing highly efficient operating conditions for a wide load range at high switching frequency. Contrary to most of the converters that apply soft-switching techniques, the switches presented are not subjected to high switch voltage or current stresses and, consequently, present low conduction losses. The authors present, for this converter, the principle of operation, theoretical analysis, relevant equations, and simulation and experimental results.

Fig. 1. Circuit diagram of the quadratic buck SR-PWM converter.

Index Terms—Pulsewidth modulated power converters, resonant power conversion.

I. INTRODUCTION

F

OR many years, researchers have been working in order to reduce the weight and size of switching converters to attend the technological advance which demands equipment with high power density. High switching frequency operation is a way to obtain converters with these characteristics. However, the increase of switching frequency results in an increase in switching losses and, consequently, decreases the efficiency of the pulsewidth modulation (PWM) switch-mode converters. Quasi-resonant converters (QRC’s) were introduced in [2] to overcome the disadvantage presented by the PWM switch-mode converter operating at high switching frequency. In these converters, zero voltage or zero current in the switches can be achieved during switching. However, the problems of this principle are the high switch voltage or current stress, operation with variable frequency, and load limitations. Although the QRC-PWM converters work with fixed frequency, they present all the other disadvantages of the QRC converters. In the converters proposed in [3], the disadvantages indicated above are not present. However, the switching frequency is limited by resonant capacitor discharge. In the converters presented in [4], this problem was overcome. Recently, there was introduced in [5] and [6] an improved version of these converters. In applications that require a large step-down or a large range of input or output, the minimum on time of the switch limits the operation at low switching frequency. Manuscript received March 6, 1998; revised June 29, 1999. Abstract published on the Internet December 23, 1999. The authors are with the Departamento de Engenharia Elétrica, Universidade Federal de Uberlândia, 38400-902 Uberlândia, Brazil. Publisher Item Identifier S 0278-0046(00)02516-8.

Fig. 2. Quadratic buck SR-PWM converter using the output voltage of each buck stage as auxiliary voltage source.

In the quadratic buck converters presented in [1], the dc voltage conversion ratio has a quadratic dependence on duty cycle, and they are electrically equivalent to two basic buck converters in a cascade with the advantage of using only one switch. These converters allow the high switching frequency operation with a significantly lower minimum conversion ratio for the same on time of the conventional PWM converter, eliminating the use of transformers where isolation is not required. This paper proposes a buck converter with the following characteristics: quadratic dc conversion ratio, high switching frequency, and lossless commutation II. QUADRATIC BUCK SELF-RESONANT (SR) PWM CONVERTER The proposed quadratic buck converter, shown in Fig. 1, utilizes the resonance principle to attain the lossless commutation although it presents a PWM characteristic.

0278–0046/00$10.00 © 2000 IEEE

PACHECO et al.: A QUADRATIC BUCK CONVERTER WITH LOSSLESS COMMUTATION

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Fig. 3. Quadratic buck SR-PWM equivalent circuits for different operation stages.

Two resonant networks are introduced in a quadratic buck converter (corresponding to two buck converters in cascade, but presenting only one active switch). Each resonant network is composed of an auxiliary voltage source, a resonant inductor, a resonant capacitor, an auxiliary switch, and a diode. The two auxiliary switches operate under zero-current switching (ZCS) due to the placement in series with the resonant inductors. The charging of the resonant capacitors permits the main switch to operate under zero-voltage switching (ZVS). It is known that voltage across a capacitor in a resonant network can reach twice the voltage which feeds the network.

Therefore, the minimum auxiliary voltage source values must be (1) and (2) There are many ways to achieve the auxiliary voltage sources. One of them is to use the output voltages of each buck stage, as shown in Fig. 2.

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To attend the minimum auxiliary voltage source values mentioned above, the minimum duty cycle of the main switch must be equal to 0.5.

III. PRINCIPLE OF OPERATION To simplify the analysis, the indutances filter and are assumed large enough to be considered as ideal and respectively, the voltages across current sources and present no ripple, all components are treated and flow through as being ideal, and the currents and until the auxiliary the freewheeling diodes It is assumed that all stages switches are turned on at of the two networks begin and finish at the same time. According to Fig. 1, the seven operational stages illustrated in Fig. 3 are described as follows. : This stage begins when the auxil1) First Stage iary switches are turned on under ZCS condition. At this time, and increase linearly from zero. the currents across and are zero due the conduction The voltages across and This stage ends at the instant in which the of and reach and , respectively. currents : This is the resonant stage. After 2) Second Stage turns off, resounds with the freewheeling diode The capacitor is charged while continues to increase. and happens in the same way The resonance between turns off. When the voltages across described above when and reach and respectively, diode is turned on, which ends this stage. : The conduction of diode allows 3) Third Stage to turn on under soft switching (ZVS conthe main switch when the gate signal is applied. Due to the asdition) at sociation between two resonant networks, currents and voltages across the resonant inductors and capacitors keep oscillating. becomes higher than while voltage The voltage becomes lower than The oscillation finishes when and reach and again, in which values are clamped. At this moment, the stage ends. : In this stage, the voltages 4) Fourth Stage and remain clamped and the currents and deconducts the difference becrease linearly and the diode and When falls to the main switch tween begins to conduct. The current across increases linearly from At when and fall to zero, this stage zero to ends. : The auxiliary switches and 5) Fifth Stage are turned off with soft commutation. At this stage, only the source transfers energy to load. The turning off instant of the establishes the end of this stage, giving to the converter a PWM characteristic. : This stage begins when is turned 6) Sixth Stage and discharge linearly in and in the load, off. respectively. During this stage, every semiconductor is turned , the stage finishes when the voltages and off. At fall to zero. : When the resonant capacitor 7) Seventh Stage and turn on. This stage ends at voltages fall to zero,

Fig. 4.

Theoretical waveforms of quadratic buck SR-PWM converter.

Fig. 5. State-space phase. (a) State-space phase for resonant circuit composed by C and L : (b) State-space phase for resonant circuit composed by C and L :

when the auxiliary switches are turned on again, beginning a new switching cycle. From the study of the stages described above, the relevant theoretical waveforms are drawn, and the state-space phase of the proposed converter, as shown in Figs. 4 and 5, respectively.


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TABLE I RELEVANT EXPRESSIONS FOR EACH OPERATION STAGE OF QUADRATIC BUCK SR-PWM

Definitions are as follows: (3)

(4)

Fig. 6.

400-W experimental quadratic buck SR-PWM converter.

Fig. 4 shows that, due to the quasi-square shape for current, the maximum current through the main switch is the load curThis means that the conduction loss is minimized in rent this converter. The current peak through the auxiliary switches and , which makes it as can be minimized by choosing small as possible.

(5)

(6)

(7) IV. CIRCUIT ANALYSIS In this section, the analytical expressions describing the operation of the proposed quadratic buck converter are presented.

(8)

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(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17) Table I shows the relevant expressions according to each correspond to intervals operation stage. The intervals of the first buck stage composed of and while the intervals correspond to intervals of the second buck stage composed of and In the seventh stage, all the voltage and current values in the resonant components are zero. In order to obtain the same time intervals shown in Fig. 4, the and following expressions in the calculation of must be used: (18)

Fig. 7.

(19)

V V

Simulation waveforms of the quadratic buck SR-PWM converter. (a) and i : (b) V and i : (c) V and i : (d) V and i : (e) and i :


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(20) and From Table I, by calculating the average voltage in the dc voltage conversion ratio is obtained. The third stage , thus can be overlooked. Then, considering

(21)

where

switching frequency; resonant frequency. V. SIMULATION RESULTS In order to illustrate the operation of the quadratic buck SR-PWM converter, a simulation of the converter presented in Fig. 1 has been accomplished with the following parameter set: V H

V

A H

H nF F V

H nF F V

kHz.

According to the simulation waveforms obtained in Fig. 7, one can see that the switches operate under soft-switching conditions. The resonant interval is small compared to the operating cycle. Thus, the operation of this converter can be considered as a PWM operation. The switches are subjected to low voltage and current stresses. VI. EXPERIMENTAL RESULTS To verify the theoretical and simulated results of the quadratic buck converter, a 400-W prototype has been built and tested by using the circuit presented in Fig. 6 with the following specifications and components values: V H H nF F kHz

V

A H H nF

Fig. 8.

F

Oscillograms of the 400-W experimental quadratic buck SR-PWM. (a) (40 V/div) and i (2 A/div). (b) V (40 V/div) and i (2 A/div). (c) V (25 V/div) and i (2 A/div). (d) V (10 V/div) and i (2 A/div). (e) V (80 V/div) and i (4 A/div).

V

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equate and where isolation is not necessary, in high switching frequency operations and for a wide load range. The experimental and simulation results validate the analysis of the converter proposed. APPENDIX In this section, the converter circuit analysis will be presented. The relevant expressions according to each operation stage shown in Table I was obtained by the following analysis. Fig. 9. Efficiency of experimental quadratic buck SR-PWM converter.

switches and MOSFET IRF 740 MOSFET IRFP 460 diodes MUR 1620.

Fig. 8 shows the most relevant experimental waveforms obtained for the quadratic buck converter prototype. As was expected, all the waveforms agree well with the theoretical analysis and simulation results. The auxiliary switches and turn on and turn off under ZCS condition while the operates under ZVS condition and there main switch is no current peak across this switch. The current through waveform is very close to square wave, as in the the hard-switching PWM converters. Fig. 9 shows the measured efficiency as a function of the output current, maintaining the output voltage at 60 V. The full-load efficiency (400 W) is 91.5%. Even for low output currents, the efficiency exceeds 80%, which proves that the operation for a wide load range maintains the lossless commutation.

First Stage and are constants and In this stage, voltages across and , respectively. equal to The resonant inductors voltage equations are

(22)

(23)

Second Stage According the equivalent circuit shown in Fig. 3, the following equations can be obtained:

(24)

(25)

VII. CONCLUSION In comparison to converters already proposed, such as QRC and QRC-PWM, the new quadratic buck SR-PWM converter offers their advantages but does not present their disadvantages. This converter also offers a significantly wider conversion ratio. The introduction of the resonant networks in the quadratic converter allows for a better operating performance than obtained with hard-switching PWM converters for high switching frequencies. The switches are not submitted to over voltages and currents. The maximum current through the main switch is equal to the load current, presenting low conduction loss. The current peaks across the auxiliary switches can be limited to desired values by choosing suitable resonant capacitors and inductors. quadratic duty ratio yields a For a given duty ratio larger conversion ratio, for the same on time of the conventional PWM converter. The proposal and intention of this converter is that it be applied where conventional, single-stage buck converters are inad-

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(27) Third Stage The equations for the equivalent circuit are

(28)

(29)


and (30) and

(31)

Fourth Stage and are clamped and In this stage, voltages across and decreases linearly, falling to the currents across zero. The resonant inductors current equations are

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[2] F. C. Lee, “High-frequency quasiresonant converter technologies,” Proc. IEEE, vol. 76, pp. 151–157, April 1988. [3] L. C. Freitas, “Two new lossless commutation pulse-width modulated cells using resonant disconnecting circuit and the corresponding families of dc-to-dc converters,” in Conf. Rec. IEEE-IAS ANnu. Meeting, 1991, pp. 959–964. [4] L. C. de Freitas, V. J. Farias, P. S. Caparelli, J. B. Vieira, Jr., H. L. Hey, and D. F. da Cruz, “An optimum ZVS-PWM dc-to-dc converter family: Analysis, simulation and experimental results,” in Proc. IEEE PESC’92, Toledo, OH, 1992, pp. 229–235. , “A high-power high-frequency ZCS-ZVS-PWM buck converter [5] using a feedback resonant circuit,” in Proc. IEEE PESC’93, 1993, pp. 330–336. [6] L. C. de Freitas, D. F. da Cruz, and V. J. Farias, “A novel ZCS-ZVS-PWM DC–DC buck converter for high power and high switching frequency: Analysis, simulation and experimental results,” in Proc. IEEE APEC’93, Mar. 1993, pp. 693–699. [7] L. C. de Freitas, D. F. da Cruz, and V. J. Farias, “A novel ZCS-ZVS-PWM dc-dc buck converter for high power and high switching frequency: Analysis, simulation and experimental results,” in Proc. IEEE APEC’93, Mar. 1993, pp. 693–699. [8] E. Morad, P. D. Ziogas, and G. Joos, “A dc bus commutated high frequency half bridge forward PWM dc/dc converter,” in Proc. IEEE PESC’91, 1991, pp. 216–222. [9] G. Hua, C. S. Leu, and F. C. Lee, “Novel zero-voltage-transition PWM converter,” in Proc. IEEE PESC’92, Toledo, OH, 1992, pp. 55–61.

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Fifth Stage and Voltages across and continue unaltered.

and the currents across

Vinicius Miranda Pacheco was born in Uberlândia, Brazil, in 1970. He received the B.S. degree in electrical engineering, the Safety Engineering Specialist degree, and the M.S. degree in 1994, 1996, and 1998, respectively, from the Federal University of Uberlândia, Uberlândia, Brazil, where he is currently working toward the Ph.D. degree in the Power Electronics Research Group. His research interest is power electronics, in particular, inverters, UPS’s, and soft-switched converters.

Sixth Stage and discharge linearly in Resonant capacitors and in the load, respectively. The resonant capacitors voltage equations are

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Acrísio José do Nascimento, Jr., was born in Uberlândia, Brazil, in 1972. He received the B.S. degree in electrical engineering in 1997 from the Federal University of Uberlândia, Uberlândia, Brazil, where he is currently working toward the M.S. degree. His research interest is power electronics, in particular, parallel converters in the current-sharing mode and high-frequency power conversion.

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ACKNOWLEDGMENT The Power Electronics Research Group, Federal University of Uberlândia, gratefully acknowledges the contributions of THORNTON-INPEC ELETRÔNICA LTDA., SIEMENS S. A., FAPEMIG, CNPq, CAPES, and the anonymous reviewers for their helpful suggestions and comments.

REFERENCES [1] D. Maksimovic and S. Cuk, “Switching converters with wide dc conversion range,” IEEE Trans. Power Electron., vol. 6, pp. 377–390, Jan. 1991.

Valdeir José Farias was born in Araguari, Brazil, in 1947. He received the B. S. degree in electrical engineering from the Federal University of Uberlândia, Uberlândia, Brazil, the M. S. degree in power electronics from the Federal University of Minas Gerais, Belo Horizonte, Brazil, and the Ph.D. degree from the State University of Campinas, Campinas, Brazil, in 1975, 1981, and 1989, respectively. He is currently a Professor in the Electrical Engineering Department, Federal University of Uberlândia. He has authored numerous published papers. His research interest is power electronics, in particular, soft-switching converters and active power filters. Prof. Farias is a member of the Sociedade Brasileira de Automática (SBA) and the Brazilian Society of Power Electronics (SOBRAEP).

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João Batista Vieira, Jr. (M’88) was born in Panamá-Go, Brazil, in 1955. He received the B. S. degree in electrical engineering from the Federal University of Uberlândia, Uberlândia, Brazil, and the M. S. and Ph.D. degrees from the Federal University of Santa Catarina, Florianópolis, Brazil, in 1980, 1984, and 1991 respectively. In 1980, he joined the Electrical Engineering Department, Federal University of Uberlândia, as an Instructor. He is currently a Professor. He has authored numerous published papers. His research interests include high-frequency power conversion, modeling and control of converters, power-factor-correction circuits, and new converter topologies. Prof. Vieira is a member of the Sociedade Brasileira de Automática (SBA) and the Brazilian Society of Power Electronics (SOBRAEP).

Luiz Carlos de Freitas (S’90–M’91) was born in Brazil in 1952. He received the B. S. degree in electrical engineering from the Federal University of Uberlândia, Uberlândia, Brazil, and the M.S. and Ph.D. degrees from the the Federal University of Santa Catarina, Florianópolis, Brazil, in 1975, 1985, and 1992, respectively. He is currently a Professor in the Electrical Engineering Department, Federal University of Uberlândia. He has authored numerous published papers and has two Brazilian patents pending. His research interests include high-frequency power conversion, modeling and control of converters, power-factor-correction circuits, and new converter topologies. Prof. de Freitas is a member of the Sociedade Brasileira de Automática (SBA) and the Brazilian Society of Power Electronics (SOBRAEP).