RECENTLY, newly emerging power-electronics applications

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1 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 54, NO. 8, AUGUST Nonisolation Soft-Switching Buck Converter With Tapped-Inductor for Wide-Input Extreme Step-Down Applications Joung-Hu Park, Member, IEEE, and Bo-Hyung Cho, Senior Member, IEEE Abstract In this paper, a new zero-voltage switching (ZVS) buck converter with a tapped inductor (TI) is proposed. This converter improves the conventional tapped inductor critical conduction mode buck converters that have the ZVS operation range determined by the TI turn ratios. It includes another soft switching range extension method, the current injection method, which gives an additional design freedom for the selection of the turn-ratios and enables the optimal design of the winding ratio of the TI so that the efficiency may be maximized. This soft-switching buck converter is suitable for wide input range step-down applications. The principle of the proposed scheme, analysis of the operation, and design guidelines are included. Experimental results of the 100-W prototype dc dc converter are given for hardware verification also. Finally, based on the proposed soft-switching technique, a new soft-switching topology family is derived. Index Terms DC DC power conversion, hysteretic control, soft switching, tapped inductor (TI). I. INTRODUCTION RECENTLY, newly emerging power-electronics applications such as renewable energy conversion systems, telecommunication power systems, and high-frequency ballast systems require extremely step-down (or step-up) voltage conversion ratios [1]. This extreme conversion ratio causes the duty cycle to also be extremely high or low. In buck converter case, the operation with small duty cycle influences the performance of both steady state and transient state. This small duty cycle degrades the power efficiency and the transient dynamics with the effect of the minimum pulsewidth of MOSFET gate drivers [2], [3]. In order to remove these problems, the increase of duty cycle is introduced by employment of a transformer. The utilization of the transformer has some benefits such that the duty cycle of the converter can be adjusted to a desirable value in order to prevent the extreme duty cycle at the high step-up or low step-down ratios through the proper selection of the winding ratio [4]. This extra degree of freedom enables the switches to avoid high-peak current, and contributes to a reduction of the switching loss and conduction loss of the converters. However, the isolation type converters keep a low efficiency level due to the transformer loss itself and the bulky size with an increasing number of extra components to reset the Manuscript received July 14, 2005; revised December 30, This paper was recommended by Associate Editor A. Ioinovici. The authors are with the Department of Electrical Engineering and Computer Science, Seoul National University, Seoul , Korea ( wait_4_u@hotmail.com; bhcho@snu.ac.kr). Digital Object Identifier /TCSI transformer. To obtain both the extreme voltage conversion and high efficiency, the application of a tapped inductor (TI) has been considered as one of the effective alternatives in previous researches [5] [10] since the tapped inductor operates as an autotransformer without the need of a reset circuit. Furthermore, an autotransformer employment utilizes less copper than an isolation-type transformer [11]. However, there are still some difficulties in applying the TI to converters because the ringing between the leakage inductance of the inductor and the parasitic capacitances in switches leads to higher voltage stress across switching devices and more EMI. These problems prevent the tapped inductor employment from being the optimal solution for extreme conversion ratio applications. In order to remove these problems, it is necessary to apply the soft-switching technique to TI applications. In this paper, a new zero-voltage switching (ZVS) buck converter with the TI is proposed. The proposed converter improves the conventional critical conduction mode (CRM) buck converter that has a ZVS operation range extended by the TI turn ratios [12], [13]. The improvement includes another soft switching technique (named as the current injection (CI) method in this paper) which gives another design freedom for the selection of the turn-ratios and enables the optimal design of the TI so that both the switching loss and the conduction loss may be minimized. This soft-switching converter is suitable for applications with wide input ranges leading to extremely low step-down ratios. The following sections explain the principle of the proposed scheme, analyze the operation, and suggest design guidelines. The results of the 100-W prototype dc-dc converter will be given for hardware verification. II. OPERATION PRINCIPLES OF PROPOSED TI SOFT-SWITCHING CONVERTERS The soft switching operation is so meaningful to the converter employing a tapped inductor, which has a leakage inductance causing serious performance degradation. This is important not only for efficiency, but also in the electromagnetic interference (EMI) viewpoint, because the parasitic leakage inductance causes severe ringing at the switching moment. The soft-switching technique is able to attenuate these problems by removing dissipation loss and enabling the use of a lossless capacitive snubber without paying for efficiency reduction and additional parts except a capacitor [14]. This snubber absorbs the ringing energy of the leakage inductor and significantly reduces the switching-off loss by adapting the switching speed /$ IEEE

2 1810 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 54, NO. 8, AUGUST 2007 Fig. 1. Conventional TI buck converter. the subinterval is. When the subinterval starts, the resonant voltage is enhanced up to. This means that of an untapped CRM buck converter cannot exceed [see Fig. 2(a)] and the soft switching range of the untapped CRM buck is limited where the inputoutput voltage conversion ratio is higher than 0.5. However, if the filter inductor is replaced with a tapped inductor (Fig. 1), soft - switching operation is achieved as shown in Fig. 2(b) even when the conversion ratio is lower than 0.5. That is because the inductor increases the resonant voltage,, up to the input voltage,, through the inductor s autotransformer operation. In order to obtain ZVS operation in all operating ranges, winding ratio of the TI which steps up the secondary voltage ( in Fig. 1) to the primary voltage,, must satisfy the following condition: (1) Fig. 2. Voltage waveforms of V in Fig. 1. (a) Untapped CRM buck converter. (b) Tapped CRM buck converter. (voltage rising time) to an optimal level. Because of these benefits the soft-switching converter with tapped inductor has, this converter is one of the most suitable candidates for extremely step-down applications in spite of the high output current ripple [13]. The following sections introduce a proposed soft switching tapped inductor converter as well as the one proposed in previous research. The proposed approach applies an additional soft-switching technique to the conventional approach, which gives one more design freedom for tapped inductor design with obtaining the soft-switching operation over the entire operation range. A. Operation Principle of Conventional TI Soft-Switching Converters [12], [13] The conventional CRM soft-switching TI buck converter is shown in Fig. 1. For the analysis, it is assumed that the TI is completely coupled and output capacitor is complete voltage sink. This CRM control changes the switching frequency in order that the switching operation may maintain the boundary condition between continuous conduction mode and discontinuous conduction mode. It is a kind of hysteretic current-mode control with a fixed lower boundary (Ground). The hysteretic method was presented as one of current-mode control methods with the most optimized dynamic performances [15], [16]. Fig. 2(a) shows the main switch (source point) voltage waveform of unti buck converter and Fig. 2(b) shows that of the TI converter. There are three operation modes in the soft-switching CRM operation MOSFET conduction mode, diode conduction mode, and resonant subinterval mode shown as the shadowed area in Fig. 2(a) and (b). The equivalent circuit of each operation mode is shown in Fig. 3(a) (c), respectively. In order to consider softswitching mechanism, let us take a look at Fig. 3(c) with a definition of a resonant capacitance,, representing the equivalent capacitance of the parallel connection of with the reflected in Fig. 1. Then, the resonant inductance refers to the same value as, the inductance of. The initial condition of where and. Thus, the extended soft switching condition expressed with voltage gain and turn ratio is established as B. Proposed TI Soft-Switching Converter As shown in the previous section, the conventional strategy utilizes a TI in order to obtain soft-switching operation even for extremely low voltage gain by the enhancement of the resonant voltages. However, when the application has wide input ranges extending from regular (nonextreme) transfer ratio to extreme ones, TIs are not advantageous because the soft switching requires an extremely high turn ratio of the inductor in order to satisfy the ZVS condition, which leads to the increase of the main switch voltage stress and the degradation of performance such as the decrease of the overall efficiency. Furthermore, with high, the employment of synchronous rectifier is not effective to increase efficiency because of the increased peak current of freewheeling mode. In this paper, in order to remove these problems, an additional soft-switching technique, named current injection (CI), is introduced into the conventional TI soft-switching converter by replacing the freewheeling diode with an active switch (synchronous rectifier), as shown in Fig. 4. The proposed soft-switching technique is a hybrid type that combines the TI (voltage-enhancement type) soft-switching technique with the CI technique. This hybrid type soft-switching converter has very similar circuit operation with the conventional TI CRM converter. However, the current injection method extends the soft-switching region not passively depending on the parasitic resonance, but actively storing current in the filter inductor for the resonance of the subinterval. The principle of the CI method has been proposed as a soft-switching technique for some applications in previous researches [14], [17]. This CI method is also a good alternative for wide input range applications although it is not suitable for extreme gain applications. Fig. 5 shows the key waveforms (gating signals,, and in Fig. 4) of the proposed TI soft-switching buck converter (2)

3 PARK AND CHO: NONISOLATION SOFT-SWITCHING BUCK CONVERTE 1811 Fig. 3. Operation mode of the tapped inductor buck converter under CRM (/CI) control. (a) Main switch turn-on mode. (b) Diode (synchronous rectifier) turn-on mode. (c) Resonant mode. rectifier ON period in Fig. 4). Then, when the rectifier turns off, the inductor current,, is released to enhance the resonant voltage by charging switch output capacitors, and shown in Fig. 4. The peak value of the enhanced voltage ( in Fig. 4) is derived from Fig. 4. Proposed ZVS TI buck converter with the current injection (CI) method. Fig. 5. Key waveforms (gating signals, main switch voltage V, and inductor current I ) of the proposed scheme. with the CI method. This is variable switching frequency control for the maintaining of the boundary conducting operation and there exist three operation modes like the conventional TI scheme main switch conduction mode ( period in Fig. 5), synchronous rectifier conduction mode, and resonant mode ( ) from the resonance between parasitic capacitances of the switching devices and the filter inductor. However, in this proposed scheme, the synchronous rectifier maintains turn-on until the freewheeling inductor current turns into slightly negative ( of synchronous thus the greater the inductor current is, the higher the peak of the resonant voltage is. And this voltage is enhanced by TI once more ( in Fig. 4). Thus, the extreme voltage-boost for the soft-switching operation at the main switch is achieved. Since this approach uses a filter inductor instead of parasitic inductors for the resonance, the switching current ( in Fig. 5) required to satisfy the soft-switching is comparably smaller than other switching currents. Thus, this CI method influences very small portion on the major operating parameters such as device stress and switching frequency. From these features mentioned above, the proposed hybrid method has an advantage of achieving the extension of the soft-switching range without depending on the extreme turn ratio of the TI even for the extreme step-down condition. For a detailed description of the resonant subinterval, the equivalent circuit of the resonant mode in Fig. 3(c) is included in the analysis. One of the major differences between the proposed and the conventional subinterval operation is the initial condition. At the moment the subinterval begins, the inductor has some initial current stored by the synchronous rectifier. The initial condition is given as where is positive. Fig. 6 shows the state-plane trajectory of the resonant mode. From the figure, the boosted capacitor voltage is derived as (3) (4)

4 1812 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 54, NO. 8, AUGUST 2007 Fig. 6. State plane trajectory between V and I. For the ZVS operation, the turn ratio N of the TI, which is another boosting source of the resonance voltage, stepping up into primary voltage in Fig. 3, must satisfy the following condition: stress. High means that the switching device processes low power for a given output and the device obtains the alleviation not only of conduction and switching losses, but also of thermal stress, ESR loss, EMI noise, packaging size etc. [18]. Therefore, this parameter is appropriate to the estimation of the converter performance in the viewpoint of power stress and efficiency as a whole. In order to derive the objective function, the voltage gain is derived in (8) with the assumption that the inductor current flowing negatively through the synchronous rectifier is small enough to be negligible and (period of the subinterval) is kept constant as (a half of the resonant period). The detailed description of the derivation procedure is presented in Appendix. The voltage conversion ratio is (see Appendix A) (8) (5) where is the phase angle presented in Fig. 6 which shows the state-plane trajectory between and. Thus, the soft switching condition is satisfied when the peak value of, which is established as This equation shows that the proposed soft-switching method does not require extremely high value of N for the ZVS operation due to the initial inductor current. Also, this result shows that the ZVS condition is not dependent on the load condition. The injected current is very small due to the high inductance, which requires very precise handling on the current information from current sensor to controller. If is too small due to the positive offset voltage of the current sensor, the soft-switching does not occur. On the other hand, if the switching frequency is very high and is too large due to the propagation delay of the current sensor and controller, the loss from the switching action is not negligible any more. However, since it occurs at light load conditions and efficiency is concerned on heavy load condition in general applications, the injected current control is not a serious problem for soft-switching if there is an enough margin for. (6) The switching frequency is implicitly established as (Appendix C) The switching current (turn-off) of the main switch is (Appendix B) (9) (10) For the analysis of the TI effect, the previous parameter is normalized by the untapped inductor case. The normalized switching current is The square of the RMS current of the main switch is (11) III. OPERATION PARAMETER ANALYSIS For the design-oriented operation analysis, an objective function is introduced in this section. The conventional and proposed TI topologies have simple structures and the performances are dominantly affected by the utilization efficiency of the switching device. For example, a power processing parameter (named device utilization factor) for the main switch, is introduced as The normalized main switch current is (12) (7) (13) has a reciprocal relationship with the power stress of the main switch that is proportional to voltage stress and current In the same way, the RMS current stress of the synchronous rectifier is shown in (14), at the bottom of the page.

5 PARK AND CHO: NONISOLATION SOFT-SWITCHING BUCK CONVERTE 1813 The normalized current stress is The normalized synchronous rectifier voltage stress is [12] (15) The normalized main switch voltage stress is [13] (16) Finally, the normalized main switch utilization factor is (17) The normalized rectifier utilization factor is (18) Fig. 7. Utilization factor plots of the TI soft switching converter. (a) Main switch utilization factor (U ) where! = rad/s, R =Z = 0:2. (b) Synchronous rectifier utilization factor (U ) where! = rad/s, R =Z =0:2. (19) Fig. 7 shows the contours of these normalized main switch and synchronous rectifier utilization factors of the TI converter according to N and M. The contours of and in Fig. 7(a) and (b) are used as an objective function to select for the optimization of the converter performance. The axis represents the voltage conversion ratio and axis represents (14)

6 1814 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 54, NO. 8, AUGUST 2007 TABLE I MAJOR COMPONENTS USED FOR THE CONVENTIONAL AND PROPOSED CIRCUIT PROTOTYPES the turn ratio. Each line in the contour represents the group of same operating conditions in the utilization factor. The region bounded by the solid line with the mark represents the soft-switching conditions of the conventional tapped/untapped inductor converters (without CI method), which is presented in (2). In that case, in order to obtain high efficiency through the overall input voltage operating range, all the operating points should exist inside the soft switching operation area in Fig. 7. The figure shows that higher leads to a greater utilization factor in the extremely small region. However, as increases, the utilization factor of high decreases rapidly. Thus, for the wide-input and extreme step-down application design, it is difficult to find an optimal solution for the conventional TI scheme. As a design example, solid line between points C and D marked with (, in Fig. 7) represents a result of the conventional TI converter design for the spec. of a 100-W dc dc converter hardware prototype in chapter IV. The designed parameter is high for the ZVS region of the conventional TI converter. The proposed converter, however, is allowed to set even lower value such as C and D due to the hybrid method including TI and current injection soft-switching methods both (6). This optimized design has higher and than both of the conventional tapped inductor and untapped inductor designs in most of the input voltage range. IV. EXPERIMENTAL RESULTS The results of analysis and design were verified by the prototype hardware test of a 100-W telecommunication equipment power supply. The input voltage range is and the output voltage is. The conversion ratio is from 0.15 to Based on the design results in previous section, the hardware prototype is implemented, and the major components used Fig. 8. Major waveforms of the hardware prototype and measured efficiency comparison between the proposed ZVS Tapped CI converter and the previous ZVS Tapped and untapped soft-switching converters. (a) Major waveforms of the proposed (N =3) converter [Ch.1: gating signal of main switch, Ch.2: gating signal of synchronous rectifier, Ch.3: inductor current, Ch.4: voltage of the main switch)]. (b) Measured efficiency comparison between the proposed (N =3)and conventional (N =1;N =6)converters. for the conventional and proposed hardware prototypes are presented in Table I. The switching frequency varies from around 20 to 70 khz according to the input voltage at full load. The MOSFET gate driver is IR2111 for the three cases. In the conventional tapped circuit [Table I(b)], an ultra-fast rectifier is used instead of synchronous rectifier because the average current loss is lower than RMS current loss due to the higher peak current (Section II-B). Fig. 8 shows the experimental results. In Fig. 8(a), the proposed scheme shows that ZVS operation is achieved in the main switch by CI method (the negative inductor current in Ch.3)

7 PARK AND CHO: NONISOLATION SOFT-SWITCHING BUCK CONVERTE 1815 switch in the conventional converter rises up to 66 C with TO-220 package type, and in the proposed case, the temperature drops into 40 C with the same package type. This loss reduction dominantly contributes the efficiency improvement of the proposed converter. From the experimental results, it is concluded that the proposed scheme is effective to relieve the extremely step-down converters from the severe power stress as the results of the design analysis in previous sections. Fig. 9. Comparison of thermal distributions of the hardware prototypes (Vin = 220 V, full load). (a) Thermal distribution of the conventional untapped CI converters (N =1), (b) Thermal distribution of the proposed tapped CI converters (N =3). and voltage enhancement of tapped inductor. The voltage waveform of the main switch (Ch.4) is different from in Fig. 5 because the main switch and primary tap inductor are swapped to each other in the circuit position in order to use the high-side gate driving circuit for the main switch [19]. In Fig. 8(b), the previous tapped or untapped CRM shows the efficiency below 94%, while the proposed tapped converter employing the CI method maintains an efficiency level above 94% through the overall operating range. For more detailed analysis, temperature distributions of the hardware prototypes were measured and presented in Fig. 9. In this experiment, the conventional CI only method converter and hybrid type TI converter both of which are first two converters with the highest efficiencies in Fig. 8 were investigated. The temperature distributions were measured by the Universal Thermal Imager from IRISYS, the part number IRI1001E. Fig. 9(a) and (b) shows the temperature distribution of the two converters with the same operating condition such as 220-V input voltage and full load. The experiment was done at the ambient temperature, and the MOSFET and synchronous rectifier have no heat sink. When you look at the figures, the spot of heat sources such as inductor, synchronous rectifier and main switch are shown as some white-outlined rectangular. The number shown in the right, upper-side of the window is the temperature measured at the spot of small rectangular in the main switch. The results show that the inductor and synchronous rectifier temperature are not significantly different which means that the absolute loss-relieving portion from these devices are small. On the contrary, the temperature of the main V. TOPOLOGY EXTENSION In order to extend this soft-switching topology, the proposed soft-switching technique combining the CI method to the TI buck converter is applied to other conventional TI converters such as boost or buck boost [4], and the new soft-switching topology family is derived in Fig. 10. In order to apply CI method, a synchronous rectifier is employed to all diode part (a parallel arrow). Each member of the family is able to obtain soft-switching operation covering all input operating ranges by adjusting both the inject current and the tapped inductor winding ratios. Therefore, the topologies avoid extremely high turn-ratios of the tapped inductor and provide more optimal design criteria for device stress, the utilization factor and ultimately efficiency, especially in wide input range application design. The tapped inductor circuit family is categorized with the following three parts. Switch-to-tap type converters in Fig. 10(a), (c), and (f), the synchronous rectifier-to-tap version in Fig. 10(b), (d), and (g), and the power rail-to-tap version in Fig. 10(e) and (h). Each version has a different soft-switching range and it can be derived in the same manner as in Section II. The ZVS range for the boost derived converters in Fig. 10(c) (e) is (20) where is the initial current of inductance of at the resonant subinterval. Also the buck boost derived converters in Fig. 10(f) (h) have a ZVS range as follows: (21) where is and is the initial current of inductance of at the resonant subinterval. VI. CONCLUSION AND FUTURE WORK In this paper, a new ZVS buck converter employing a TI is proposed. In order to obtain the soft-switching operation in extremely step-down applications, the proposed converter utilizes not only the resonant voltage enhancement by the TI, but also the current injection (CI) method that boosts the resonant voltage by the initial inductor current. In spite of use of the variable switching frequency, the CRM control method contributes better performances by eliminating reverse recovery of the freewheeling diode (synchronous rectifier) as well. This hybrid type soft-switching method gives another design freedom to select the turn ratio, and thus it is possible to obtain more optimally designed circuits than the conventional TI or the CI only method

8 1816 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 54, NO. 8, AUGUST 2007 Fig. 10. Topology family of TI DC-DC converters with CI soft-switching technique. (a) Switch to tap (N < 1). (b) Rectifier to tap (N > 1). (c) Switch to tap (N >1). (d) Rectifier to tap (N <1). (e) Rail to tap (0 <N). (f) Switch to tap (N <1). (g) Rectifier to tap (N >1). (h) Rail to tap (0 <N). especially in extremely step-down and wide input range applications. The operation principle and the design-oriented analysis of the proposed converter have been presented. The experimental result with a 100-W hardware prototype is also included to show that the proposed converter has a higher efficiency over 94% than the conventional tapped/untapped buck converters. Based on the proposed soft-switching technique, a new soft-switching topology family is derived. As a future work, it will be worthwhile to make the utilization factor more accurate for the more various specifications such as high frequency applications or high/low voltage/current applications etc. From this equation, the voltage gain is (A.2) B. Switching Current Derive the peak inductor (main switch) current through the derivation of the (total) inductor current in each mode. 1) Main switch conduction mode in Fig. 5). The total current (charge) during this period is A. Voltage Gain APPENDIX The voltage gain for the proposed TI converter is derived easily as a simple term (but accurate enough) with an assumption that (period of the subinterval) is kept constant as (a half of the resonant period). Then, secondary winding of the tapped inductor should satisfy the voltage-second balance in steady state as (A.1) 2) Synchronous rectifier conduction mode in Fig. 5). The total current (charge) is (B.1) (B.2) 3) Resonant mode: As shown in Fig. 5, when a capacitive snubber is added to the main switch, the inductor current in the subinterval increases due to the reduction of the characteristic impedance. Thus, the current in the subinterval should be considered in the operation analysis.

9 PARK AND CHO: NONISOLATION SOFT-SWITCHING BUCK CONVERTE 1817 The equations of follows: in the resonant mode are derived as (B.3) For obtaining more simple and accurate equation, the total inductor current during subinterval is derived by the integral from zero to half period instead of from the in Fig. 6. The total current (charge) is (B.4) Then, from the relationship between inductor current and load current From (B.5) and current (turn-off) of the main switch is C. Switching Frequency (B.5), switching The inductor current during period 1) in Appendix B is (B.6) (C.1) The peak current should be the same as the switching current as REFERENCES [1] Z. Qun, T. Fengfeng, H. Yongxuan, and F. C. Lee, Active-clamp dc dc converters using magnetic switches, in Proc. Appl. Power Electron. Conf. Expo (APEC 01), 2001, vol. 2, pp [2] J. Kingston, R. Morrison, M. G. Egan, and G. Hallissey, Application of a passive lossless snubber to a tapped inductor buck dc/dc converter, IEE Power Electron. Machines and Drives, pp , [3] P. Xu, J. Wei, K. Yao, Y. Meng, and F. C. Lee, Investigation of candidate topologies for 12 V VRM, in Proc. Appl. Power Electron. Conf. Expo (APEC 02), 2002, pp [4] D. A. Grant and Y. Darroman, Extending the tapped-inductor dc-to-dc converter family, Electron. Lett., vol. 37, no. 3, pp , Feb. 1, [5] J. Wei, P. Xu, H.-P. Wu, F. C. Lee, K. Yao, and M. Ye, Comparison of three topology candidates for 12 V VRM, in Proc. Appl. Power Electron. Conf. Expo (APEC 01), 2001, pp [6] T. H. Kim, J. H. Park, and B. H. Cho, Small-signal modeling of the Tapped-Inductor converter under variable frequency, in Proc. IEEE Power Electron. Specialists Conf. (PESC 04), Jun. 2004, vol. 2, pp [7] M. Rico, J. Uceda, J. Sebastian, and F. Aldana, Static and dynamic modeling of tapped-inductor DC-to-DC converters, in Proc. IEEE Power Electron. Specialists Conf. (PESC 87), 1987, pp [8] D. Edry, M. Hadar, O. Mor, and S. Ben-Yaakov, A SPICE compatible model of tapped-inductor PWM converters, in Proc. Appl. Power Electron. Conf. Expo (APEC 94), 1994, vol. 2, pp [9] P. H. Wurm and F. A. Himmelstoss, Application of EXCEL for analyzing dc dc converters, in Proc. 6th Workshop Comput. Power Electron.,, 1998, pp [10] S. Abe and T. Ninomiya, Comparison of active-clamp and ZVT techniques applied to tapped-inductor DC-DC converter with low voltage and high current, J. Power Electron., vol. 2, no. 3, pp , Jul [11] K. Yao, Y. Ren, J. Wei, M. Xu, and F. Lee, A family of buck type dc-dc converters with autotransformers, in Proc. Appl. Power Electron. Conf. Expo (APEC 01), 2003, pp [12] J. H. Park and B. H. Cho, The zero voltage switching (ZVS) critical conduction mode (CRM) buck converter with tapped-inductor, in Proc. Appl. Power Electron. Conf. (APEC 03), Feb. 2003, vol. 2, pp [13] J.-H. Park and B.-H. Cho, The zero voltage switching (ZVS) critical conduction mode (CRM) buck converter with tapped-inductor, IEEE Trans. Power Electron., vol. 20, no. 4, pp , Jul [14] D. M. Sable, F. C. Lee, and B. H. Cho, A zero-voltage-switching bi-directional battery charger/discharger for the NASA EOS satellite, in Proc. Appl. Power Electron. Conf. Expo (APEC 92), 1992, pp [15] J. H. Park and B. H. Cho, Small signal modeling of hysteretic current mode control using the PWM switch model, COMPEL, pp , Jul [16] J. H. Park, T. H. Kim, and B. H. Cho, PWM-switch model of tapped inductor converters under hysteric current-mode control, IECON, pp , Nov [17] S.-G. Yoon, A high efficiency bi-directional dc-dc converter topology and control for HEV system using super-capacitor, Master s thesis, Elect. Eng. Comp. Sci., Seoul National Univ., Seoul, Korea, [18] C.-G. Kim, Topology and control of resonant converter with loosely coupled transformer, Ph.D. dissertation, Elect. Eng. Comp. Sci., Seoul National Univ., Seoul, Korea, [19] K. Yao, F. C. Lee, Y. Meng, and J. wei, Tapped-inductor buck converters with a lossless clamp Circuit, in Proc. Appl. Power Electron. Conf. Expo (APEC 02), 2002, vol. 2, pp From the equation and switching frequency equation is implicitly established as (C.2), the (C.3) Joung-Hu Park (M 07) received the B.S., M.S., and Ph.D. degrees in electrical engineering and computer science from Seoul National University, Seoul, Korea, in 1999, 2001, and 2006, respectively. He is currently a Post Doctoral Researcher at Seoul National University. His interests include analysis and design of high-frequency switching converter, renewable energy systems, and piezoelectric transformer power applications, etc.

10 1818 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 54, NO. 8, AUGUST 2007 Bo-Hyung Cho (M 89 SM 95) received the B.S. and M.E. degrees in electrical engineering from California Institute of Technology, Pasadena, and the Ph.D. degree, also in electrical engineering, from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg. Prior to his research at Virginia Tech, he worked for two years as a member of the technical staff of the Power Conversion Electronics Department, TRW Defense and Space System Group, where he was involved in the design and analysis of spacecraft power processing equipment. From 1982 to 1995, he was a Professor in the Department of Electrical Engineering, Virginia Tech. He joined the School of Electrical Engineering, Seoul National University, Seoul, Korea, in 1995, and he is presently a Professor. He is currently the chairman of the Korean Institute of Power Electronics (KIPE). His main research interests include power electronics, modeling, analysis and control of spacecraft power processing equipment, power systems for space station and space platform, and distributed power systems. Dr. Cho was a recipient of the 1989 Presidential Young Investigator Award from the National Science Foundation. He is a member of Tau Beta Pi.