684 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 5, SEPTEMBER 2002 Unified Steady-State Analysis of Soft-Switching DC–DC Converters Jaber Abu-Qahouq, Student Member, IEEE, and Issa Batarseh, Senior Member, IEEE Abstract—In this paper, based on the switching cell approach, a unified steady state analysis for families of soft-switching dc–dc converters with complete unified design equations will be presented. The concept of the unified approach and step by step procedure for a generalized process are discussed and applied to selected soft-switching families such as zero-voltage-switching (ZVS) and zero-current-switching (ZCS)–quasi-resonant converter families, ZVS-clamped voltage quasi-square-wave (QSW) family, ZCS-clamped-current (CC) QSW family, and zero-voltagetransition and zero-current-transition pulse-width modulation families. Also, it has been noted that all the analyzed families have one generalized transformation table. The basic unified equations will be summarized and the cell-to-cell comparison will be introduced. It will be shown that the unified analysis leads to several advantages such as improving the computer-aided analysis and design, simplified mathematical modeling, and giving more insight into the converter-cell operation. Index Terms—Converter, dc–dc, generalized analysis, softswitching, steady-state, switching-cell, unified analysis, zerocurrent switching, zero-voltage switching. I. INTRODUCTION O VER THE LAST ten years, many soft-switching dc–dc converter families were introduced in the open literature with the objectives of developing high switching converters with high power density and high efficiency [1]–[13]. This was accomplished by adding additional components to the power stage to either limit the resonant period and/or to utilize power device parasitic components. As a result of adding an additional auxiliary circuitry (additional resonant components and auxiliary switches and diodes), the steady-state analysis of soft-switching topologies tend to be cumbersome, time consuming, and provided little insight into the converter switching cell operation. In this paper, it will be shown that the analyses of the soft-switching dc–dc converters can be unified for a given switching network family. As a result, instead of analyzing individual converter topology, only one switching network for each family is needed to be analyzed. By using generalized parameters, it is possible to generate a single transformation table from which the voltage converter ratios and other important design parameters for each converter can be obtained directly. The derivation of the model is obtained from studying the switching network modes of operation and by expressing the switching intervals in terms of the converter design parameters such as Manuscript received February 15, 2001; revised February 16, 2002. Recommended by Associate Editor N. Femia. The authors are with the School of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32816 USA (e-mail: batarseh@mail.ucf.edu). Publisher Item Identifier 10.1109/TPEL.2002.802195. Fig. 1. Block diagram representation for the switching cell. gain, normalized frequency, and normalized load. Using the proposed unified analysis, it is possible to analyze a complete dc–dc converter family as simple as analyzing one converter topology. Moreover, redesign of converter family is made much easier due to the flexibility in generalized parameter variation. Finally, since the analysis is unified and the parameters are generalized for a given switching cell, it is much easier to obtain steady-state design curves using such simpler mathematical models. Such characteristic curves are used to carry out converter design and provide design information about the converter voltage and current stresses. Unified switching cells are derived for selected dc-dc softswitching pulse-width modulation (PWM) families that have three terminal switching cells including the conventional hardswitching PWM topologies and the following: 1) zero-voltage-switching (ZVS) and zero-current-switching (ZCS) quasi-resonant converter (QRC) families [2]; 2) zvs-clamped voltage (CV) quasi-square-wave (QSW) family [3], [4]; 3) zcs-clamped-current (CC) QSW family [5]; 4) zero-voltage-transition (ZVT) and zero-current-transition (ZCT) PWM families [6], [7]. It must be noted that the experimental work for the selected soft-switching families were presented in the literature [2]–[7] and the objective of this paper is to present unified method for analyzing soft-switching dc–dc converter families. The concept and the process of unified cells will be discussed in Section II along with their switching waveforms. In Section III, the generalized parameters and transformation table will be defined and discussed. Section IV gives the summary of the basic unified equations for the selected cells. The cell-to-cell comparison and will be introduced in Section V. A comparison between the theoretical and simulation results will be made in Section VI. 0885-8993/02$17.00 © 2002 IEEE ABU-QAHOUQ AND BATARSEH: ANALYSIS OF SOFT-SWITCHING DC–DC CONVERTERS 685 Fig. 2. Switching cells: (a) Conventional cell, (b) ZVS-QRC cell, (c) ZCS-QRC cell, (d) ZVS-QSW CV cell, (e) ZCS-QSW CC cell, (f) ZVT-PWM cell, and ZCT-PWM cell. II. UNIFIED SWITCHING-CELLS The block diagram representation for a unified three-terminal switching cell is given in Fig. 1. Fig. 2 shows the six softswitching cells for the families mentioned above in addition to the conventional cell, while Fig. 3 shows the basic switching waveforms for the soft switching cells. Since each family uses the same switching network (same modes of operation) and the same waveform shapes, the analysis can be unified using the following steps. 1) Identify the unified switching cell and the generalized parameters for the given family. 2) Identify the unified switching waveforms for the unified switching cell. 3) Analyze the switching network modes of operation. 4) Derive the time interval for each mode. 5) Use the switching network output side to derive the gain. As an example, if the output side is a diode, use the diode voltage or the diode current, whatever available and easier, to derive the gain. Or in general, find another equation that relates the cell output to the cell input. 6) Normalize and unify the resultant equations by defining suitable normalized parameters. 7) Use the unified analysis done in steps 1–6 to derive the stress equations and other design parameters for the converter detailed analysis and design. III. GENERALIZED PARAMETERS TRANSFORMATION TABLE AND Various orientations of any of the cells in Fig. 2 result in a family of converters. Using the three terminals , , and in the switching cells, generalized parameters can be defined and their values can be determined from the orientation of the cell in a specific converter. Let us define the following parameters: : overall input-to-output converter voltage gain, 1) ; : normalized cell-input voltage to the converter input 2) voltage, ; : normalized cell-output current to the converter 3) ; output current, : normalized filter capacitor ( ) voltage to the con4) ; verter input voltage, 686 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 5, SEPTEMBER 2002 Fig. 3. Switching cells basic waveforms: (a) ZVS-QRC cell, (b) ZCS-QRC cell, (c) ZVS-QSW CV cell, (d) ZCS-QSW CC cell, (e) ZVT-PWM cell, and (f) ZCT-PWM cell. 5) : normalized cell-output voltage to the converter ; input voltage, 6) : normalized cell-current entering node ; verter output current, to the con- ABU-QAHOUQ AND BATARSEH: ANALYSIS OF SOFT-SWITCHING DC–DC CONVERTERS TABLE I GENERALIZED TRANSFORMATION TABLE 687 IV. UNIFIED ANALYSIS RESULTS FOR THE SELECTED FAMILIES Table II shows the basic unified equations (the intervals and gain equations) for the selected soft-switching cells. Because of the simplicity of the conventional cell unified analysis, it is not included in the table. However, it can be shown that the unified basic gain equations for the conventional cell under the continuous conduction mode (CCM) and discontinuous conduction mode (DCM) operations are (1) (2) 7) 8) : characteristic impedance, ; : normalized load, , where is the converter load resistor; , where is the 9) : switching frequency, switching period; ; 10) : resonant frequency, ; Where : normalized frequency, ; 11) 12) : duty ratio of the main switch; : duty ratio of the auxiliary switch; 13) , , , 14) , , , : The conduction intervals for the modes of operation. Note that the end of the switching period time is also equal to . The unified equations for each cell shown in Fig. 2 will include one or more of the following previous defined normalized , , , , , ), depending on the parameters ( topology of the switching cell itself. It must be noted that all the voltages are normalized with respect to , while all the current are normalized with respect to . By applying the switching cells of Fig. 2 to the conventional dc–dc converters (Buck, Boost, Buck-Boost, Cuk, Zeta, and SEPIC), a transformation table for each family can be generated. It is interesting to point out that when two or more switching cells share the same normalized parameter, they will have the same transformation quantity for that parameter. So, one transformation table can be generalized for all the families and only the parameter that is applicable for specific family unified equations can be used. It can be shown that the single transformation table given in Table I is complete and applies to all the cells given in Fig. 2. The characteristics of this table can be summarized as follows. 1) As mentioned above, when two or more switching cells share the same generalized parameter, they will have the same transformation quantity for that parameter. 2) By applying the theory of conservation of energy, it can . be shown that 3) By applying KVL and KCL to the cells, we have: . 4) As a result of the above-mentioned characteristics, the generalized parameters of the switching cells of Fig. 2 can be and . reduced to only two generalized parameters: is the ratio of the time when both the switch and where the diode are OFF. It must be noted that the unified analysis of the conventional cell can be extended by including the inductor at node and analyzing the cell for both modes of operation (CCM and DCM). The following assumption have been made when the softswitching cells in Fig. 2 are analyzed. 1) The circuit is under steady-state operation. 2) The transistors and diodes are ideal devices. 3) The reactive elements are lossless, linear, passive, timeinvarient, and do not have parasitic components. passes through is very 4) The filter inductor in which is constant (constant current source). large so that 5) The output and filter capacitors are much larger than the resonant capacitor and can be treated as a constant voltage sources. 6) All inductors are much larger than the resonant inductor and can be treated as constant current sources. 7) The switching frequency is less than the resonant frequency. The unified equations of Table II can be validated to a specific converter by substituting for the generalized parameters from Table I. These equations can be used to plot the characteristic curves for the design purposes. Many other unified equations can be also derived such as component stresses. The next section will include some of these equations. V. CELL-TO-CELL COMPARISON BASED UNIFIED EQUATIONS ON THE The unified equations can be used to make a cell-to-cell comparison. As an example, Table III shows the unified equations for the peak and average current and voltage for the main switch, while Table IV shows the main diode peak voltage and current for the analyzed ZVS and ZCS cells. They show how the QRC, QSW, and soft-switching transition cells voltage and current stresses on the main switch and main diode are compared. As an example, the following can be concluded from these two tables. 1) The peak voltage stress on the main switch for the ZVS-QRC cell is high and load ( ) dependent. The higher the used in the design for the ZVS-QRC cell, the lower the peak voltage stresses on the main switch. Unlike the ZVS-QRC cell, the ZVS-CV QSW cell has the peak . Unfortunately, the peak switch voltage limited to 688 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 5, SEPTEMBER 2002 TABLE II BASIC UNIFIED EQUATIONS SUMMARY TABLE III SOME OF THE MAIN SWITCH UNIFIED STRESS EQUATIONS TABLE IV SOME OF THE DIODE UNIFIED STRESS EQUATIONS current for the ZVS-CV QSW cell is higher than twice of its value in the ZVS-QRC cell and it is load dependent. The ZVT-PWM cell has low peak voltage and peak current stresses on the main switch that is also load independent. 2) The peak current stress on the main switch for the ZCS-QRC cell is high and load dependent. The lower the , the lower the peak current stress is. For the ZCS-CC QSW cell, the peak current stress is reduced and it is load independent, but the peak voltage stress on the main switch is higher than twice of its value for the ZCS-QRC cell. In the ZCT-PWM cell, the peak switch current is high but load independent, while the switch peak voltage stress is kept low. ABU-QAHOUQ AND BATARSEH: ANALYSIS OF SOFT-SWITCHING DC–DC CONVERTERS 689 TABLE V SOME CHARACTERISTICS FOR THE ANALYZED CELLS 3) The average main switch voltage is the same for all the . analyzed switching cells and is equal to 4) The ZVS-CV QSW cell causes the current stress on the diode to increase and to be load dependent by trying to reduce the voltage stress on the main switch. In the ZCS-CC QSW cell, the voltage stress on the diode increases and is load dependent, while the current stress on the main switch is lower. 5) The ZVT-PWM and the ZCT-PWM cells reduce the current and the voltage stresses on the main switch without increasing it on the diode. Table V summarized some characteristics for the analyzed soft-switching cells. Furthermore, the unified analysis can be used to derive other characteristic equations for the unified switching cells such as values as shown below for the the component stresses and ZCT-PWM cell [14], [15]. resonant inductor current 1) Unified equation for ) as seen in the equation shown at the bottom ( of the page. After normalizing by dividing the above equation by , the expression for the normalized resonant inductor current will be the equation shown at the bottom of the next page, which yields (3) 2) Unified equation for peak resonant capacitor voltage ). ( It can be shown that (4) 3) Unified equation for peak resonant inductor current ). ( It can be shown that (5) VI. DESIGN EXAMPLE AND SIMULATION RESULTS After comparing between the cells, an appropriate cell for specific design requirements can be chosen. As an example, 690 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 5, SEPTEMBER 2002 = Fig. 4. Some characteristics curves for the ZCT-PWM boost: (a) dc voltage conversion ratio characteristics for f 0.5, (b) normalized resonant inductor rms 0.5, (c) normalized resonant inductor peak current, and (d) normalized resonant capacitor peak voltage for 0.427. current for f = the ZCT-PWM cell is chosen here. Once a cell is selected, design curves may be plotted using the unified equations along with Table I. Fig. 4 shows some of these design curves for the ZCT-PWM boost converter. V and A 10 W ZCT-Boost DC-DC converter with V is to be designed here for and . A step by step design procedure is given as follows. 1) 2) From the gain equation in Fig. 4(a), we have . 3) The load resistance is , and the A. load current is KHz, and with , the 4) By choosing resonant frequency is KHz. , the characteristics impedance 5) By choosing . becomes = 6) Solve the following two equations and : kHz to yield H and 7) The time interval when culated from , which means that nF should be ON ( ) can be cal- ABU-QAHOUQ AND BATARSEH: ANALYSIS OF SOFT-SWITCHING DC–DC CONVERTERS Fig. 5. ZCT-PWM boost basic waveforms from Pspice simulation results. TABLE VI THEORETICAL AND SIMULATION RESULTS COMPARISON Fig. 5 shows the basic waveforms from the simulation results using Pspice while Table VI shows a comparison between some values from the theoretical results and the Pspice simulation results. This table shows that the theoretical and the simulation results are in good agreement. 691 [2] K. Liu, R. Oruganti, and F. C. Lee, “Resonant switches—Topologies and characteristics,” IEEE Trans. Power Electron., vol. PE-2, pp. 62–74, Jan. 1987. [3] V. Vorpe’rian, “Quasisquare-wave converters: Topologies and analysis,” IEEE Trans. Power Electron., vol. 3, pp. 183–191, Mar. 1998. [4] T. Mizoguchi, T. Ohgai, and T. Ninomiya, “A family of single-switch ZVS-CV DC-DC converters,” in Proc. IEEE APEC’94, vol. 2, 1994, pp. 1392–1398. [5] E. Ismail and A. Sebzali, “A new class of quazi-square wave resonant converters with ZCS,” in Proc. IEEE APEC’97, 1997, pp. 1381–1387. [6] G. Hua, C. Leu, and F. C. Lee, “Novel zero-voltage-transition PWM converters,” in Proc. IEEE PESC’92, 1992, pp. 55–61. [7] G. Hua, E. X. Yang, Y. Jiang, and F. C. Lee, “Novel zero-current-transition PWM converters,” IEEE Trans. Power Electron., vol. 9, pp. 601–606, Nov. 1994. [8] G. Hua and F. Lee, “Evaluation of switched-mode power conversion topologies,” in Proc. 1st Int. Power Electronics Motion Control Conf. (IPEMC), vol. 1, 1994, pp. 12–26. [9] A. B. Carlson, Circuits. Pacific Grove, CA: Brooks/Cole-Thomson Learning, 2000. [10] C. Tseng and C. Chen, “Zero-voltage-transition topologies for Cuk converters,” in Proc. IEEE PESC’98, vol. 2, 1998, pp. 930–935. , “On the ZVT-PWM Cuk converter,” IEEE Trans. Ind. Electron., [11] vol. 45, pp. 674–677, Aug. 1998. [12] D. C. Martins and G. N. de Abreu, “Application of the ZETA converter in switch-mode power supplies,” in Proc. IEEE APEC’93, 1993, pp. 214–220. [13] C. H. G. Treviso, O. C. De Freitas, and V. J. Farias, “A ZVS-ZCS-PWM self-resonant dc-dc sepic converter,” Ind. Electron., Control Instrum., vol. 1, pp. 176–181, 1994. [14] J. Abu-Qahouq, “Generalized analysis of soft-switching dc–dc converter families,” Tech. Rep., Univ. Central Florida, Orlando, 2000. [15] J. Abu-Qahouq and I. Batarseh, “Generalized analysis of soft-switching DC-DC converters,” in Proc. IEEE PESC’00, vol. 1, 2000, pp. 185–192. Jaber Abu-Qahouq (S’01) received the B.Sc. degree in electronics engineering from Princess Sumaya University, Amman, Jordan, in 1998, and the M.S. degree in electrical engineering and electronics from the University of Central Florida, Orlando, in 2000, where he is currently pursuing the Ph.D. degree. He worked as a Test Engineer in the Electronic Services and Training Center, Royal Scientific Society, Amman, Jordan. His research interests include soft-switching power conversion, power factor correction circuits, and low-voltage high-current fast-transient dc–dc converters. His research results in publishing several research papers. Mr. Abu-Qahouq received several awards, including the Royal Watch. VII. CONCLUSION A unified analysis method for families of soft-switching dc–dc converters was developed in this paper. The unified technique is applied to several well-known switching families including QRC, QSW, and PWM converters. It is shown that there exists a single Generalized Transformation Table for all the families. This leads to several advantages such as improving the computer-aided analysis and design, simplified mathematical modeling, and gives more insight into the converter-cell operation. The unified equations for each family can be easily used in the analysis of any new converter that uses the same switching cell. This is done by finding the generalized parameters for the new converter and then substituting in the unified equations. The cell-to-cell comparison was introduced and the theoretical results were compared with the simulation results. REFERENCES [1] E. J. Miller, “Resonant switching power conversion,” in Proc. IEEE PESC’76, 1976, pp. 206–211. Issa Batarseh (SM’93) received the B.S., M.S., and Ph.D. degrees from the University of Illinois, Chicago, in 1983, 1985, and 1990, respectively, all in electrical engineering. He is a Professor in the School of Electrical Engineering and Computer Science, University of Central Florida (UCF), Orlando. He was a Visiting Assistant Professor at Purdue University, West Lafayette, IN, from 1989 to 1990, before joining UCF in 1991. His power electronics research focuses on the development of high frequency power converters to improve power density, power factor, efficiency, and performance. The research includes the analysis and design of high frequency dc-to-dc resonant converter topologies, low-voltage dc-dc converters, small signal modeling and control of PWM and resonant converters, power factor correction techniques, and power electronic circuits for distributed power systems applications. Dr. Batarseh has served as a Chairman of the PE/AES/PEL Chapter, Orlando IEEE Section and currently serves as an ExCom member of the lEEE Orlando Section. He is also an Associate Editor for the IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS and the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS. He is a Reviewer for the National Science Foundation and several IEEE TRANSACTIONS/JOURNALS. He serves on the program committees of IEEE-APEC, PESC, IECON, IAS, and ISCAS. He is a Registered Professional Engineer in Florida.