IT is well known that the boost converter topology is highly

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1 320 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 2, MARCH 2006 Analysis and Design of a Low-Stress Buck-Boost Converter in Universal-Input PFC Applications Jingquan Chen, Member, IEEE, Dragan Maksimović, Member, IEEE, and Robert W. Erickson, Fellow, IEEE Abstract In converters for power-factor-correction (PFC), the universal-input capability, i.e., the ability to operate from any ac line voltage world-wide, comes with a heavy penalty in terms of component stresses and losses, and with restrictions on the dc output voltage. In this paper, we propose a new two-switch topology, boost-interleaved buck-boost (BoIBB) converter, which can offer significant performance improvements over single-switch buck-boost converters (including flyback, SEPIC, or Cuk topologies) or other two-switch buck-boost converters in universal-input PFC applications. The paper presents an analysis of the converter operation and component stresses, as well as design guidelines. High efficiency (over 93%) throughout the universal-input ac line voltage range is demonstrated on an experimental 100-W, 200-V dc output, universal-input BOIBB PFC rectifier. Index Terms Boost-interleaved buck-boost (BoIBB) converter, power-factor-correction (PFC), root-mean-square (RMS). I. INTRODUCTION IT is well known that the boost converter topology is highly effective in power factor correction (PFC) rectifier applications, provided that the dc output voltage is close to, but slightly greater than, the peak ac line voltage [1]. In universal-input applications, with the root-mean-square (RMS) input line voltage in the V range, the output voltage of the boost converter has to be set to about 400 V. At low line (90 V ), the switch conduction losses are high because the input RMS current has the largest value, and because the largest step-up conversion is required. The inductor has to be oversized for the large RMS current at low line input, and for the highest volt seconds applied throughout the input-line range. As a result, a boost converter designed for universal-input PFC applications is heavily oversized compared to a converter designed for a narrow range of input ac line voltages. Furthermore, because of the large energy storage filter capacitor at the output, the boost converter has the inrush current problem that can only be mitigated using additional components. In universal-input PFC applications, the capability of providing both step-up and step-down conversion is attractive because the output dc voltage can be set to any value. However, conventional single-switch buck-boost topologies, including the buck-boost, flyback, SEPIC, and Cuk converters, have greatly Manuscript received July 25, 2002; revised October 10, This paper was presented in part at IEEE APEC 01. Recommended for publishing by Associate Editor Y.-F. Liu. J. Chen is with the FyreStorm Inc., Sunnyvale, CA USA ( jingquan.chen@ieee.org). D. Maksimović and R. W. Erickson are with the Colorado Power Electronics Center, Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO USA. Digital Object Identifier /TPEL increased component stresses and component sizes compared to the boost converter [2] [6]. In general, if their conversion characteristics meet the input/output specifications, the boost converter (for voltage step-up) or the buck converter (for voltage step-down) feature the smallest component stresses. This is a result of the direct energy transfer path from the input to the output in one of the switching subintervals in these two converter topologies. The boost and the buck converters require the minimum indirect energy delivery and therefore have the minimum component stresses for a given voltage conversion ratio. Based on this observation, it is of interest to investigate buck-boost converter topologies with two independently controllabe switches that can operate as boost (for voltage step-up) or as buck (for voltage step-down) converters during portions of an ac line cycle. Fig. 1 shows (a) the standard buck-boost converter and the two well-known two-switch buck-boost configurations, (b) the buck-cascaded buck-boost (BuCBB) converter, and (c) the boost-cascaded buck-boost (BoCBB) converter. When the two active switches are operated independently, the two-switch converters can achieve buck or boost operation with minimum indirect energy processing. As a result, at the expense of additional switches and controls, the two-switch buck-boost topologies can offer reduced component stresses. It has been shown that a number of other two-switch buck-boost configurations can be constructed. In [7], complete families of two-switch buck-boost converters that can achieve minimum indirect energy delivery have been generated through the synthesis method based on the equivalent ac and dc circuits [8]. A comparison of the two-switch buck-boost converter topologies in terms of the switch and the inductor stresses can be found in [7]. In particular, the boost-interleaved buck-boost (BoIBB) converter shown in Fig. 2 has been identified as a configuration with potentials for significantly smaller switch stresses compared to the more conventional cascaded buck-boost converters of Fig. 1(b) and (c), and with lower conduction losses and reduced inductor stresses compared to the boost converter. In power factor correction applications, further advantages of this configuration include the ability to choose the output dc voltage arbitrarily, and the absence of the inrush current problem. The purpose of this paper is to present a detailed analysis of the operation and the component stresses in the BoIBB converter, as well as design guidelines and practical implementation techniques in universal-input PFC applications. Operating modes and basic steady-state characteristics of this converter are described in Section II. Operation of the BoIBB converter as a PFC rectifier together with an analysis of the switch and /$ IEEE

2 CHEN et al.: ANALYSIS AND DESIGN OF A LOW-STRESS BUCK-BOOST CONVERTER 321 Fig. 1. (a) Standard buck-boost converter, (b) the buck-cascaded buck-boost (BuCBB) converter, and (c) the boost-cascaded buck-boost (BoCBB) converter. Fig. 2. Boost-interleaved buck-boost (BoIBB) converter. inductor stresses and conduction losses are discussed in Section III, in comparison with the converters shown in Fig. 1. Section IV describes an experimental 100-W, 200-V dc output, universal-input BoIBB PFC rectifier, with experimental results shown over the universal-input ac line voltage range. II. OPERATING MODES AND STEADY-STATE CHARACTERISTICS OF THE BOOST-INTERLEAVED BUCK-BOOST CONVERTER The proposed boost-interleaved buck-boost (BoIBB) converter with two controllable switches is shown in Fig. 2. In contrast to the cascaded topologies, such as the converters of Fig. 1(b) and (c), where the buck and the boost converter are simply connected in series, in the BoIBB converter the boost switch cell ( and ) is effectively interleaved with the buck switch cell ( and ). Let and be the duty ratios of the switches and, respectively. In continuous conduction mode (CCM), the volt second balance relations for the two inductors yield the overall dc voltage conversion ratio for the BoIBB converter (1) Fig. 3. Operating modes of the BoIBB converter: (a) boost and (b) buck. If is always on, 1, 1 1, and the converter operates in the boost mode, which is shown in Fig. 3(a). The average voltage across is zero. In this mode, the input current is divided through and. If is always off, 0,, the converter operates in the buck mode, as shown in Fig. 3(b). and form a lowfrequency filter. The average current through and is zero and the voltage across is equal to the difference between the input and the output voltage. The inductor in the buck mode has the same role as the inductor in the simple buck converter. The basic steady-state results for the two modes of operation are summarized in Table I.

3 322 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 2, MARCH 2006 TABLE I STEADY-STATE RESULTS FOR THE BOIBB CONVERTER IN THE BOOST AND THE BUCK MODES OF OPERATION III. OPERATION OF THE BOIBB CONVERTER AS AN IDEAL RECTIFIER In this section, we analyze operation of the BoIBB converter as an ideal PFC rectifier. Expressions for the switch and the inductor RMS currents, and the volt-seconds applied to the inductors are derived, so that conduction losses and magnetic sizes can be evaluated. We also compare the total switch and inductor RMS currents of the BoIBB converter with the three converters shown in Fig. 1. In PFC rectifier applications, the rectified input voltage is In an ideal PFC rectifier, the output voltage is regulated at a constant value, and that the input current is proportional to the input voltage where the emulated resistance is constant for a given output power. Fig. 4(a) shows the waveforms of the input and the output voltage in one half of a line period, for the case when the dc output voltage is chosen to be lower than the peak of the input voltage. The converter operates in the boost or the buck modes according to the condition of the input voltage and the output dc voltage, as shown in Fig. 4(b). In Section V, we show that the switchover between the boost and buck modes can be accomplished automatically using a relatively simple PWM controller, without the need to compare the input and the output voltage to facilitate the mode switching. Since the input voltage waveform is periodic with the period of 2 (half line cycle) and symmetric with respect to 4, the analysis can be restricted to the time interval [0 4]. Operation in continuous conduction mode (CCM) is assumed. A. Analysis of Stresses 1) Boost Mode: In the time interval 0, as shown in Fig. 4, the input voltage is lower than the output voltage, and the converter operates in the boost mode: the boost switch cell is active, while the buck cell is inactive ( is always on). In the case when the output voltage is higher than the peak of the input voltage, the converter operates in the boost mode always. In this case, the results of this section still apply. One only needs to replace with 4. The converter switching frequency is much higher than the ac line frequency. (2) (3) Fig. 4. (a) Waveforms of the rectified input voltage v (t) and the dc output voltage V and (b) duty ratios of the boost and the buck cells in the BoIBB converter operated as an ideal PFC rectifier. Therefore, we can assume quasi steady-state operation, which means that the switch duty ratios as functions of time can be found from the steady-state dc conversion results in Section II The average inductor currents in a switching period are When is conducting, its current is the sum of the two inductor currents, while conducts the same current as. In the buck mode, is always off, and the current through equals a small current ripple. Therefore, the total RMS currents of and can be found from (4) and (5), and (6) and (7), shown at the bottom of the next page. The volt seconds applied to and during a switching period are the same as the volt-seconds applied to the inductor in a simple boost converter, and are given by where is the switching period. 2) Buck Mode: In the time interval [ 4], where is the line period, the instantaneous input voltage is greater than the output voltage, and the converter operates in the buck mode: the buck cell is active and the boost cell is inactive ( is always off). and form a low frequency filter between the input (4) (5) (8)

4 CHEN et al.: ANALYSIS AND DESIGN OF A LOW-STRESS BUCK-BOOST CONVERTER 323 and the output, and have insignificant effects in quasi steadystate operation. The duty ratios of and can be expressed as: TABLE II COMPARISON OF COMPONENTRMS CURRENTS AT LOW LINE (120 VRMS) AND HIGH LINE (240 VRMS) FOR A PFC RECTIFIER WITH THE DC OUTPUT VOLTAGE V = 200 V AND THE OUTPUT POWER P = 100 W (9) The average inductor currents in a switching period are (10) Both and are conducting currents in both boost and buck modes, and the RMS currents are found from (4), (5), and (10) as (11) and (12), shown at the bottom of the page. The volt seconds applied to during a switching period are the same as the volt-seconds applied to the inductor in the buck converter The volt seconds applied to buck mode. (13) are approximately zero in the B. Comparison of Stresses It is of interest to compare the switch and inductor RMS currents of the BoIBB converter to the three converters of Fig. 1, in PFC applications. We assume that the two-switch BuCBB and BoCBB converters are operated in the same way as the BoIBB converter, with the switch and duty cycles shown in Fig. 4. In the BoCBB converter of Fig. 1(c), the energy storage is at the output. Equations (14) (16), shown at the bottom of the next page, summarize the results for the standard buck-boost converter of Fig. 1(a), the BuCBB converter of Fig. 1(b), and the BoCBB converter of Fig. 1(c), respectively. As an example, Table II compares the component RMS currents in a 100-W BoIBB PFC rectifier with the dc output voltage 200 V, to the RMS currents in the three converters of Fig. 1 for the low ac line input (120 Vrms) and the high ac line input (240 Vrms). At the low-line input, in this example, the two-switch buckboost converters always operate in the boost mode. According to (6) (7) (11) (12)

5 324 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 2, MARCH 2006 (6), (15) and (16), the RMS current of the switch in this mode is the same for all three two-switch configurations. The RMS currents for the switch, which always stays on in the boost mode, are different. In the BoIBB and the BoCBB, the switch conducts the inductor current. In the BuCBB, conducts the inductor current, which is significantly higher at the low-line input. At low line, the rms currents in the BoCBB, which is equal to the dc load current, is somewhat lower than in the BoIBB due to the filtering action of. For the high-line input, the three two-switch buck-boost converters operate in either the boost mode or the buck mode during different portions of a line cycle. In the buck mode, according to (11), (15), and (16), the switch has the same RMS current in all three two-switch converters. The switch currents in the boost mode are different, with the BoIBB having the lowest RMS current stress at high line. In the boost mode, the two inductors in the BoIBB share the input current, which is not the case in other two-switch buck-boost converters. Furthermore, in the buck mode, conducts zero dc current in the BoIBB converter. As a result, in the example of Table II, the BoIBB has the lowest total RMS inductor current. In the example of Table II, it can be observed that the component RMS current stresses in the two-switch converters are significantly smaller than in the standard buck-boost converter. However, the standard buck-boost converter has only one inductor and only one transistor switch. Let us assume that the on-resistance of the transistor switch in the standard buck-boost converter is two times lower that the on-resistance of and in the two-switch buck-boost converters. Similarly, let us assume that the inductor series resistance in the standard buckboost and the BuCBB is two times smaller than the series resistances of and in the BoCBB or BoIBB. Under these assumptions, Fig. 5 shows the switch and inductor conduction losses normalized to the losses in the standard buck-boost, as functions of the conversion ratio. At high line, i.e.,atlow, the BoIBB switch conduction losses are the lowest of the three two-switch configurations. At low line, i.e., for, the switch conduction losses in the BoIBB are somewhat higher than in the BoCBB, but lower than in the standard buckboost. It should be noted that the switch voltage stresses in the two-switch converters are lower than in the standard buck-boost, resulting in an even more favorable comparison in terms of the transistor switch utilization in the BoIBB and the BoCBB compared to the standard buck-boost converter. The BuCBB converter has higher RMS current stresses because the buck switch has to conduct the input current in both buck and boost modes. The inductor conduction losses in the BoIBB and the BuCBB are substantially smaller than in the standard buck-boost both at low line and at high line. Furthermore, volt seconds applied to the inductors are significantly smaller than in the conventional buck-boost converter, leading to reduced size of the magnetics. Notice, however, that the BuCBB advantages in terms of the inductor utilization are offset in part by the penalties in the switch conduction losses. In conclusion, the BoIBB converter features the most favorable results for the switch conduction losses and the inductor RMS current stresses over the universal-input voltage range. IV. DESIGN CONSIDERATIONS In this section, we address some of the design considerations related to the selection of,,, and the dc output voltage in the BoIBB converter. (14) (15) (16)

6 CHEN et al.: ANALYSIS AND DESIGN OF A LOW-STRESS BUCK-BOOST CONVERTER 325 Combining (17) (19) and using the results for from (4) yields the CCM condition (20), the CCM condi- Defining tion in the boost mode becomes (21) In order to operate in CCM throughout the line cycle, and under all input voltages and output power levels, from (21) we have (22) where is the emulated input resistance for the largest ac input voltage, and the lowest load power. 2) Buck Mode: In the buck mode, only the inductor current ripple is relevant for operation in CCM. The CCM condition can be derived from where which yields (23) (24) (25) The right-hand side expression in (25) has a maximum that depends on the ratio of the peak input voltage and the output voltage. For 1.5 V, we have Fig. 5. Comparison of (a) the total switch conduction losses in the two-switch converters normalized to the buck-boost converter, (I + I )=(I =2) and (b) the inductor conduction losses in the two-switch converters normalized to the buck-boost converter, (I + I )=(I =2). and for 1.5 V, we have (26) A. Conditions for CCM Operation The inductor current ripples are affected by the choice of and. In this section we derive conditions for operation in continuous conduction mode (CCM). 1) Boost Mode: In the boost mode, when the diode is on, it conducts the sum of and. Therefore, the CCM condition can be written as (17) where and are the peak inductor current ripples (18) (19) (27) From (25) (27), the conditions for CCM operation throughout the line cycle are if if. (28) The results of this section can be used to select the inductance values to achieve CCM operation over the entire line cycle, or over a desired portion of the line cycle, and over desired ranges of input voltages and loads. B. Selection of We select the capacitance so that the input voltage variations do not affect the output voltage or the input current through the, path when the converter operates in the buck mode,

7 326 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 2, MARCH 2006 i.e., so that the natural resonant frequency of and is well above twice the line frequency (29) The value of also affects the capacitor voltage ripple in the boost mode. The peak-to-peak capacitor voltage ripple can be found as (30) where is the output power. The ripple in (30) has the maximum value when (31) when. The worst case is at the maximum power and the minimum input line voltage. Finally, it should be noted that there is no need for to act as a low-frequency energy storage element. As a result, the value selected according to (29) or (30), or according to the capacitor RMS current stress, is typically much smaller compared to the energy-storage capacitance. C. Selection of the dc Output Voltage Compared to a boost PFC rectifier, an advantage of the BoIBB converter is that the output dc voltage does not have to be greater than the peak ac line voltage. For universal-input operation, is in the range from approximately 125 V to approximately 370 V. If, for example, we select the dc output voltage 200 V, the ratio varies from 0.54 at high line to 1.6 at low line. In this range, according to the results of Fig. 5, the component stresses in the BoIBB are significantly lower compared to the standard buck-boost converter. However, for PFC applications where a low dc output voltage (e.g., 0.5) is required, the BoIBB converter may not be the best solution, as shown by the stress analysis and the comparison in Fig. 5. V. EXPERIMENTAL RESULTS An experimental prototype (Fig. 6) has been built to verify feasibility and performance of the BoIBB converter. In our experimental setup, 4 mh, 4 mh, 2.25 F, 150 F, and the switching frequency is 100 KHz. The dc output voltage is set to 200 V. and are International Rectifier IRF840 [500-V, 8-A metal-oxide semiconductor field-effect transistors (MOSFETs)] and and are Philips Semiconductor BYM26C (600-V, 2.4-A ultra-fast diodes). A. Controller Implementation In the experimental prototype shown in Fig. 6, the input current shaping and the output voltage regulation are achieved using a standard average current-mode PFC controller chip (UC3854 [9]). The input voltage, the input current and the output voltage are sensed and scaled to the proper levels following the usual practices with the UC3854 average current mode controller. To achieve proper operation of the switches and in the boost and the buck modes, the pulse-width Fig. 6. Experimental BoIBB rectifier (L = 4 mh, L = 4 mh, C = 2.25 F, C = 150 F, f = 100 KHz, V = 200 V). Fig. 7. Dual PWM generator using TL1451. modulator (PWM) in UC3854 is not used. Instead, the output of the average current-mode compensator on the UC3854 chip is fed to a dual PWM chip (TL1451 [10]) to produce the switch control signals with the duty ratios and. These signals are then sent to a high and low side gate driver (IR2110 [11]) to control the high-side buck switch and the low-side boost switch. Fig. 7 shows a diagram of the TL1451 dual PWM generator controlled by the voltage, which is generated by the average current-loop compensator. TL1451 uses two dead-time comparators, such that it is possible to generate two independently controlled PWM signals. The two comparators compare the control inputs and to the same triangle modulation signal. As a result, the two PWM signals are synchronized. The triangle waveform has a valley of 1.45 V and a peak of 2.05 V. The duty cycle of the output PWM signal can be expressed as (32) where 600 mv, and is or. The two amplifiers, which are included in the TL1451 chip

8 CHEN et al.: ANALYSIS AND DESIGN OF A LOW-STRESS BUCK-BOOST CONVERTER 327 Fig. 8. Output duty ratios as functions of v (t). for the purpose of constructing voltage-loop compensators, are used for level-shifting of the control signal to achieve the desired duty-cycle modulation according to Fig. 4 Fig. 9. v (t) (solid curve) and v (t) (dashed curve) during one half of a line cycle. (33) We assign PWM channel 1 to control the boost switch and channel 2 to the buck switch. The buck/boost mode transition occurs when the boost switch is completely off while the buck switch is fully on, or when and. In order to have a smooth mode transition, these two conditions should occur at the same time, which can be accomplished by designing the circuit according to the following: (34) (35) Another consideration in the selection of the two offset voltages is to ensure that falls into the proper output range of UC3854. If we define or equivalently (36) (37) the output duty cycles and as functions of the control voltage can be expressed as and (38) (39) The results in (38) and (39) are plotted in Fig. 8. In quasi steady-state operation, (solid curve) as a function of time is shown in Fig. 9 for one half of an ac line cycle. Notice that the BoIBB converter operates in the boost mode when and in the buck mode when. The transition between the boost mode and the buck mode occurs at. The experimental Fig. 10. Rectified input voltage v (t) (top) and the ac portion of the control voltage v (t) (bottom): (a) low-line input (120 Vrms) and (b) high-line input (240 Vrms). Ch2: 100 V/div, Ch3: 500 mv/div.

9 328 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 2, MARCH 2006 Fig. 12. Efficiency of the experimental BoIBB PFC rectifier as a function of the input line voltage. The efficiency is 93.8% and the total current harmonic distortion is 4.6%. Fig. 12 shows the rectifier efficiency as a function of the input line RMS voltage. In contrast to conventional PFC rectifiers where the efficiency is significantly lower at low line, the efficiency remains greater than 93% throughout the line voltage range (90 Vrms 264 Vrms). VI. CONCLUSION A new two-switch topology, named boost-interleaved buck-boost (BoIBB) converter, is proposed for universal-input PFC applications. A comparison with conventional buck-boost or two-switch buck-boost converters shows that the BoIBB converter has advantages of lower switch voltage stresses, potentials for lower switch and inductor conduction losses, and reduced size of the magnetics. Experimental results are provided to verify the validity of the new topology. High efficiency (over 93% throughout the whole ac line voltage range), and low current harmonic distortion at both high and low line inputs are demonstrated. REFERENCES Fig. 11. Rectified input voltage v (t) (top) and the input ac line current i (t): (a) 120-V low-line input and (b) 240-V high-line input. Ch2: 100 V/div, Ch4: 0.5 A/div. results of are reported in Fig. 10, which correspond well to the ideal waveforms in Fig. 9. B. Experimental Results Experimental waveforms are shown in Fig. 11. The output power is 100 W. In Fig. 11(a), the input line voltage has a lowline RMS value of 120 Vrms and the converter operates in the boost mode always. The efficiency is 93.7% and the total current harmonic distortion is 1.9%. The waveforms of Fig. 11(b) are for the high-line input (240 Vrms). The converter operates in the boost or the buck modes in different parts of the line period. [1] R. W. Erickson and D. Maksimović, Fundamentals of Power Electronics, 2nd ed. Norwell, MA: Kluwer, [2] R. Watson, G. C. Hua, and F. C. Lee, Characterization of an active clamp flyback topology for power factor correction applications, IEEE Trans. Power Electron., vol. 11, no. 1, pp , Jan [3] M. Brkovic and S. Cuk, Input current shaping using Cuk converter, in Proc. Intelec, 1992, pp [4] R. Erickson, M. Madigan, and S. Singer, Design of a simple high power factor rectifier based on the flyback converter, in Proc. IEEE Applied Power Electron. Conf., 1990, pp [5] R. Zane and D. Maksimović, Nonlinear-Carrier control for high-powerfactor rectifiers based on up-down switching converters, IEEE Trans. Power Electron., vol. 13, no. 2, pp , Mar [6] D. S. L. Simonetti, J. Sebastian, F. s. dos Reis, and J. Uceda, Design criteria for SEPIC and Cuk converters as power factor prerequlators in discontinuous conduction mode, in Proc. IEEE IECON, 1992, pp [7] J. Chen, D. Maksimović, and R. Erickson, Buck-Boost PWM converters having two independently controlled switches, in Proc. IEEE Power Electron. Specialists Conf., 2001, pp [8] D. Zhou, Synthesis of PWM dc-to-dc power converters, Ph.D. dissertation, California Inst. Technol., Pasadena, [9] UC 3854 Datasheet, Tech. Rep., Texas Instruments, [10] TL1451A Datasheet, Tech. Rep., Texas Instruments, [11] IR2110 Datasheet, Tech. Rep., International Rectifier, 2005.

10 CHEN et al.: ANALYSIS AND DESIGN OF A LOW-STRESS BUCK-BOOST CONVERTER 329 Jingquan Chen (M 02) received the B.S. degree in electrical engineering from Tsinghua University, Beijing, China, in 1995, the M.S. degree in power electronics from the Chinese Academy of Sciences, Beijing, in 1998, and the Ph.D. degree in electrical engineering from the University of Colorado, Boulder, in From 2002 to 2003, he was a Senior Member of Research Staff at Philips Research, Briarcliff Manor, NY. Since 2003, he has been with FyreStorm, Inc., Sunnyvale, CA, where he is currently a Principal Engineer in the Advanced Research and Development Group. His current research interests include synthesis, modeling, and the digital control of switching power converters. Dragan Maksimović (M 89) received the B.S. and M.S. degrees in electrical engineering from the University of Belgrade, Belgrade, Yugoslavia, in 1984 and 1986, respectively, and the Ph.D. degree from the California Institute of Technology, Pasadena, in From 1989 to 1992, he was with the University of Belgrade. Since 1992, he has been with the Department of Electrical and Computer Engineering, University of Colorado, where he is currently an Associate Professor and Co-Director of the Colorado Power Electronics Center (CoPEC). His current research interests include power electronics for low-power, portable systems, digital control techniques, and mixed-signal integrated circuit design for power management applications. Dr. Maksimović received the NSF CAREER Award and a Power Electronics Society TRANSACTIONS Prize Paper Award in Robert W. Erickson (F 00) received the B.S., M.S., and Ph.D. degrees in electrical engineering from the California Institute of Technology, Pasadena, in 1978, 1980, and 1982, respectively. Since 1982, he has been a member of the Faculty of Electrical and Computer Engineering, University of Colorado, Boulder, where he is currently Professor and Chairman. He established and co-directs the Colorado Power Electronics Center, which is helping the industry in low-harmonic rectifiers, dc dc converters for battery-powered systems, and magnetics modeling for multiple-output converters. He is the author of the textbook Fundamentals of Power Electronics, now in its second edition. He is the author of approximately 60 journal and conference papers in the area of power electronics. Dr. Erickson received the IEEE Power Electronics Society Transactions Prize Paper Award, for the paper Nonlinear Carrier Control for High-Power-Factor Boost Rectifier in 1996.