A Quadratic Buck Converter with Lossless Commutation

264 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 igh 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. Index Terms Pulsewidth modulated power converters, resonant power conversion. Fig. 1. Circuit diagram of the quadratic buck SR-PWM converter. I. INTRODUCTION FOR 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. igh switching frequency operation is a way to obtain converters with these characteristics. owever, 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. owever, 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. owever, 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

PACECO et al.: A QUADRATIC BUCK CONVERTER WIT LOSSLESS COMMUTATION 265 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 and 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. (1) (2)

266 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 47, NO. 2, APRIL 2000 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 current sources and respectively, the voltages across and present no ripple, all components are treated as being ideal, and the currents and flow through the freewheeling diodes and until the auxiliary switches are turned on at It is assumed that all stages 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. 1) First Stage : This stage begins when the auxiliary switches are turned on under ZCS condition. At this time, the currents across and increase linearly from zero. The voltages across and are zero due the conduction of and This stage ends at the instant in which the currents and reach and, respectively. 2) Second Stage : This is the resonant stage. After the freewheeling diode turns off, resounds with The capacitor is charged while continues to increase. The resonance between and happens in the same way described above when turns off. When the voltages across and reach and respectively, diode is turned on, which ends this stage. 3) Third Stage : The conduction of diode allows the main switch to turn on under soft switching (ZVS condition) at when the gate signal is applied. Due to the association between two resonant networks, currents and voltages across the resonant inductors and capacitors keep oscillating. The voltage becomes higher than while voltage becomes lower than The oscillation finishes when and reach and again, in which values are clamped. At this moment, the stage ends. 4) Fourth Stage : In this stage, the voltages and remain clamped and the currents and decrease linearly and the diode conducts the difference between and When falls to the main switch begins to conduct. The current across increases linearly from zero to At when and fall to zero, this stage ends. 5) Fifth Stage : The auxiliary switches and 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. 6) Sixth Stage : This stage begins when is turned off. and discharge linearly in and in the load, respectively. During this stage, every semiconductor is turned off. At, the stage finishes when the voltages and fall to zero. 7) Seventh Stage : When the resonant capacitor voltages fall to zero, and turn on. This stage ends at 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.

PACECO et al.: A QUADRATIC BUCK CONVERTER WIT LOSSLESS COMMUTATION 267 TABLE I RELEVANT EXPRESSIONS FOR EAC OPERATION STAGE OF QUADRATIC BUCK SR-PWM Definitions are as follows: (3) (4) Fig. 6. 400-W experimental quadratic buck SR-PWM converter. (5) Fig. 4 shows that, due to the quasi-square shape for current, the maximum current through the main switch is the load current This means that the conduction loss is minimized in this converter. The current peak through the auxiliary switches can be minimized by choosing and, which makes it as small as possible. (6) (7) IV. CIRCUIT ANALYSIS In this section, the analytical expressions describing the operation of the proposed quadratic buck converter are presented. (8)

268 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 47, NO. 2, APRIL 2000 (9) (10) (11) (12) (13) (14) (15) (16) (17) Table I shows the relevant expressions according to each operation stage. The intervals correspond to 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 following expressions in the calculation of and must be used: (18) (19) Fig. 7. Simulation waveforms of the quadratic buck SR-PWM converter. (a) V and i : (b) V and i : (c) V and i : (d) V and i : (e) V and i :

PACECO et al.: A QUADRATIC BUCK CONVERTER WIT LOSSLESS COMMUTATION 269 (20) From Table I, by calculating the average voltage in and the dc voltage conversion ratio is obtained. The third stage can be overlooked. Then, considering, thus (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 V A nf nf F F V V kz. 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 V A nf nf F F kz Fig. 8. Oscillograms of the 400-W experimental quadratic buck SR-PWM. (a) V (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).

270 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 47, NO. 2, APRIL 2000 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. For a given duty ratio quadratic duty ratio yields a 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 inadequate 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. First Stage In this stage, voltages across and are constants and equal to and, respectively. The resonant inductors voltage equations are (22) 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 main switch operates under ZVS condition and there is no current peak across this switch. The current through the waveform is very close to square wave, as in 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. (23) Second Stage According the equivalent circuit shown in Fig. 3, the following equations can be obtained: (24) VII. CONCLUSION (25) Third Stage The equations for the equivalent circuit are (26) (27) (28) (29)

PACECO et al.: A QUADRATIC BUCK CONVERTER WIT LOSSLESS COMMUTATION 271 and and (30) (31) Fourth Stage In this stage, voltages across and are clamped and the currents across and decreases linearly, falling to zero. The resonant inductors current equations are (32) [2] F. C. Lee, igh-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.,. L. ey, 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, O, 1992, pp. 229 235. [5], A high-power high-frequency ZCS-ZVS-PWM buck converter 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. ua, C. S. Leu, and F. C. Lee, Novel zero-voltage-transition PWM converter, in Proc. IEEE PESC 92, Toledo, O, 1992, pp. 55 61. Fifth Stage Voltages across and and the currents across and continue unaltered. (33) Vinicius Miranda Pacheco was born in Uberlândia, Brazil, in 1970. e 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. is research interest is power electronics, in particular, inverters, UPS s, and soft-switched converters. Sixth Stage Resonant capacitors and discharge linearly in and in the load, respectively. The resonant capacitors voltage equations are (34) Acrísio José do Nascimento, Jr., was born in Uberlândia, Brazil, in 1972. e 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. is research interest is power electronics, in particular, parallel converters in the current-sharing mode and high-frequency power conversion. (35) ACKNOWLEDGMENT The Power Electronics Research Group, Federal University of Uberlândia, gratefully acknowledges the contributions of TORNTON-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. e 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 orizonte, Brazil, and the Ph.D. degree from the State University of Campinas, Campinas, Brazil, in 1975, 1981, and 1989, respectively. e is currently a Professor in the Electrical Engineering Department, Federal University of Uberlândia. e has authored numerous published papers. is 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).

272 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 47, NO. 2, APRIL 2000 João Batista Vieira, Jr. (M 88) was born in Panamá-Go, Brazil, in 1955. e 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. e is currently a Professor. e has authored numerous published papers. is 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. e 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. e is currently a Professor in the Electrical Engineering Department, Federal University of Uberlândia. e has authored numerous published papers and has two Brazilian patents pending. is 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).