Lossless Snubber Cell for a Soft-Switched Bidirectional Buck–Boost Converter

In this paper, we propose a lossless snubber cell for a soft-switched bidirectional buck–boost converter (BBC). The proposed snubber cell provides all switches with soft-switching conditions in both the bidirectional power flows of the BBC. In addition, the cell also achieves a relatively low circulating current for the snubber operation over a wide load range. In particular, the reverse recovery problem of the synchronous rectifier can be eliminated with the aid of the snubber inductor. Accordingly, the snubber cell enables high-frequency switching of approximately 60 kHz for all power switches and achieves high efficiency and high power density. Moreover, the proposed snubber cell does not have any auxiliary switch; therefore, complex auxiliary circuits or driving algorithms for the auxiliary switch are not required. Therefore, the proposed snubber cell has a simple structure with high reliability. To confirm the validity of the proposed lossless snubber cell, we provide detailed analyses, design guidelines, and experimental results using a 3-kW laboratory prototype.


I. INTRODUCTION
Recently, battery-fed bidirectional dc-dc converters have been widely used in various applications such as wind power, photovoltaic systems, fuel cells, energy storage systems, and electric vehicles [1]- [6]. In these applications, the role of the bidirectional dc-dc converter is crucial. In particular, the dcdc converter maintains the state of energy storage using power-flow management, dc-dc voltage conversion, and battery charging and discharging. In general, battery-fed systems often employ a bidirectional buck-boost converter (BBC) topology, as shown in Fig. 1, because this topology has specific advantages, such as circuit simplicity, ease of control, good performance, and cost-effectiveness [4]- [6]. However, this conventional BBC is not suitable for achieving the high power density that is required by the latest power conversion circuits. The most straightforward approach to increase the power density is to increase the switching frequency because the size and volume of the incorporated passive components are highly dependent on this frequency [7], [8]. However, The associate editor coordinating the review of this manuscript and approving it for publication was Shihong Ding . the conventional BBC has two general problems that are caused by the power switch characteristics. The first problem is the switching loss. This is due to the hard switching, which is generated by the overlap of the switch current and voltage when the switch is turned on and off. Furthermore, these losses become more serious in low speed switching devices. The other problem is the reverse recovery loss. This is caused by the low speed of the body diode built in the synchronous rectifier (SR) for every switching cycle [9].
Because of these losses, high efficiency is difficult to achieve, and power density decreases due to the limitations of increasing the switching frequency. Therefore, the most effective way of increasing the efficiency in high-frequency power converters is to decrease or eliminate the switching losses of the transistors using soft-switching techniques. These problems can be overcome using either the SiC field-effect transistor (FET) or the GaN FET, which are the wide bandgap (WBG) devices currently in the spotlight. The WBG devices feature a high-speed body diode and a high-speed switching performance [5], [7], [8]. However, the WBG devices need additional gate drive circuits for negative voltage driving because of their low turn-on threshold voltage. Moreover, WBG devices are quite expensive. Thus, various soft-switching techniques for implementing high-frequency driving for a BBC using a general Si-FET have been actively investigated [9]- [35]. Typically, the soft-switching methods for a BBCs can be divided into two categories depending on whether or not an auxiliary switch is used. Regarding the first category, the so-called active snubbers, that use auxiliary switch, were studied in [9]- [31]. However, not all snubbers can provide a soft-switching condition at turn-on and turnoff transients [10], [15]- [19]. Namely, the snubber described in [8] still has a hard-switching issue when the switch is turned off. In [15]- [19], although soft-switching of the main switch was possible, the auxiliary switch operates under the hard-switching condition. On the other hand, the active snubbers described in [11]- [14] and [21]- [25] can provide all switches with the soft-switching condition at turn-on and turn-off transients. However, they have several disadvantages; for example, the snubbers described in [11]- [14] suffer from serious conduction loss because of the high circulating current. Moreover, the snubber described in [21] has a narrow soft-switching range because the soft-switching condition is lost under a duty cycle less than 0.5. The snubbers described in [9] and [22]- [25] can overcome the abovementioned disadvantages, namely, the large circulating current, narrow soft-switching range, and the hard switching of the auxiliary switch. However, they still require two auxiliary switches. Moreover, the snubber described in [9] requires three auxiliary switches.
Despite the advantages of soft switching, these active snubbers require additional auxiliary switches, extra floating gate drivers, and complicated control algorithms, which may increase the cost, size, and complexity of the system. To overcome these disadvantages, active snubbers with a reduced number of auxiliary switches have been proposed in [26]- [31]. However, the methods described still use auxiliary switches. In particular, the methods described in [26]- [28] require numerous components, and their main switches suffer from hard switching at turn-off. Meanwhile, to overcome the above-mentioned disadvantages of the active snubbers, studies on the so-called passive snubbers have been presented in [32]- [35]; these methods fall in the second category. Although the methods described in [32]- [35] are capable of achieving soft switching and do not suffer from the reverse recovery problem, they still exhibit the following drawbacks. In [32] and [33], the root mean square current of the main switch is always large regardless of the load. In addition, a hard-switching operation of the main switch at turn-off is described in [32]. A narrow range of soft switching by the duty cycle is described in [33]. Also, the method described in [35] requires complex frequency control to reduce the circulating current from the auxiliary inductor-capacitor resonant circuit, especially for light load conditions. However, although the method described in [35] can overcome the problems mentioned in [33], [34], it requires an additional auxiliary inductor and a main coupled inductor instead of a single inductor for soft switching. Furthermore, the secondary-side leakage inductance of the coupled inductor also affects the soft-switching condition; therefore, an appropriate leakage inductance must be designed. In particular, a large leakage inductance is required for high-power applications; therefore, an extra inductor may be additionally inserted.
In this paper, a passive lossless snubber cell for a BBC is proposed, as shown in Fig. 2. The proposed snubber cell can achieve high efficiency by providing soft switching for the BBC using only passive components. This allows the BBC to operate at high switching frequency and makes it easy to obtain high power densities. In particular, the proposed snubber cell does not require any auxiliary switch, and it can help all the switches of a BBC to operate under softswitching conditions, such as zero voltage switching (ZVS) and zero current switching (ZCS), over a wide load range. Moreover, the reverse recovery problem of the body diode built in the SR can be eliminated. Additionally, since the proposed snubber cell operates mainly at the switching transition time and its current flows in proportion to the load condition its circulating current and subsequent conduction loss are small. Consequently, the proposed snubber cell can overcome the drawbacks caused by the switching loss and the use of auxiliary switches, which are seen in the conventional approach. To confirm the validity of the proposed snubber, we discuss the operation analysis and design considerations in Sections II and III. In Section IV, the validity of the proposed snubber is examined through experiments using a 3-kW rated prototype. Finally, the conclusions of this paper are presented in Section V.

II. PROPOSED CIRCUIT AND OPERATION ANALYSIS
The equivalent circuit of the BBC with the proposed snubber cell is presented in Fig. 2. The proposed snubber cell consists of one coupled inductor (T 1 ), two capacitors (C s and C c ), and three diodes (D 1 , D 2 and D 3 ). The magnetizing inductance of T 1 (L sb ) serves as a snubber inductor. The operation of the BBC with the proposed snubber is divided into eight stages in one switching period. The assumptions used for the steady-state analysis of the proposed circuit are as follows: 1) C HVS and C LVS are large enough to be considered as constant voltage sources V HVS and V LVS , respectively. 2) All components are ideal except for the body diodes of M 1 and M 2 .
3) The turn ratio of the coupled inductor T 1 is 1: n. 4) C c is large enough to be considered as a constant voltage V HVS -((n − 1)V LVS /n). 5) L bi is large enough to be compared with L sb .

A. DISCHARGING MODE
During the discharging mode of the BBC with the proposed snubber cell, the power-flow direction was from V LVS to V HVS . Therefore, as with the boost converter, M 2 acts as the main switch to regulate the output voltage V HVS , and M 1 operates as the SR. The equivalent circuits of the eight operational stages are shown in Fig. 3, and their key waveforms are illustrated in Fig. 4.
Stage0 [Before t 0 ]: Before t 0 , M 1 and M 2 are switched off, and the energy stored in L bi is transferred to the output through the body diode of M 1 . Since L bi and L sb are connected in series, their currents are the same. At the same time, v Cs is maintained at V Cc = V HVS− ((n − 1)V LVS /n),, which will be determined at stage 7. Since V LVS is applied to L bi by the conduction of M 2 , i Lbi begins to increase linearly as follows: Also, −V HVS is applied to L sb ; therefore, i Lsb begins to decrease to 0 A slowly, as follows: At the same time, since i Lbi is equal to i Lsb in the previous stage, and i ds2 is determined by the Kirchhoff's current law (KCL); therefore, i ds2 increases linearly from 0 A as follows: From (3), it can be observed that the current, which is obtained as the difference between i Lbi and i Lsb , flows through M 2 from 0 A. The slope of i ds2 is limited by L bi and L sb . Therefore, the ZCS turn-on condition of M 2 is satisfied. At the same time, M 1 and L sb are connected in series; therefore, i ds1 gradually decreases to 0 A, as seen in (2). Therefore, the body diode of M 1 can be softly turned off without the occurrence of the reverse recovery problem. When i Lsb is equal to 0 A, this stage ends, and the time duration of this interval is as follows: : When i Lsb becomes equal to 0 A at t 1 , D 1 and D 3 are turned on. Thus, v Cs decreases by the resonance between C s and L sb , as follows: where where v Cs must reach −V LVS within this stage to achieve the ZVS turn-off of M 2 at t 4 . When v Cs becomes equal to −V LVS at t 2 , this stage ends.
When v Cs reaches -V LVS , D 2 is turned on, and v Cs is clamped on -V LVS through M 2 and D 2 . At the same time, (V LVS /n) is applied to L sb via T 1 because the voltage across M 1 becomes V HVS + (V LVS /n), and i Lsb increases linearly toward 0 A, as follows: Therefore, the energy stored in L sb returns to the input battery through the conductive path of L sb -D 1 -D 2 -V LVS -D 3 . When i Lsb becomes equal to 0 A at t 3 , D 1 , D 2 , and D 3 are blocked, and this stage ends. Stage 4 [t 3 , t 4 ]: M 2 is conducting; therefore, i Lbi increases linearly with the slope of V LVS /L bi .

Stage 5 [t 4 , t 5 ]:
When M 2 is turned off at t 4 , i Lbi flows along the conductive path of L bi -C s -D 2 . The time interval of this stage is very short; therefore, it can be assumed that C s is charged with the constant current of L bi . Thus, v Cs , v ds2 , and v ds1 can be expressed as follows: In Stage 2, v Cs reaches −V LVS ; therefore, v ds2 is equal to 0 V at t 4 , as can be seen from (11). Also, the rising slope of v Cs is limited by C s , as described in (10); therefore, v ds2 also increases slowly from 0 V. Therefore, the ZVS turn-off condition of M 2 is achieved at t 4 . When v Cs becomes equal to V HVS -V LVS , and v ds1 reaches 0 V, this stage ends. Stage 6 [t 5 , t 6 ]: When v ds1 becomes equal to 0 V, the body diode of M 1 is turned on, and this stage begins. Therefore, during this stage, v Cs further increases by the resonance between C s and L bi ||L sb . If L bi is assumed to be even larger than L sb , C s resonates with L sb . Therefore, the voltage and current of C s can be determined as follows: v where Consequently, the voltage across M 1 is 0 V, and i ds1 increases slowly from 0 A because of L sb ; M 1 can be turned on under the ZVS turn on condition. When v Cs becomes equal to V Cc at t 6 , D 1 is turned on, and this stage ends.
Stage 7 [t 6 , t 7 ]: When D 1 is turned on at t 6 , v Cs is clamped on V Cc along the conductive path of C s -M 1 -C c -D 1 . By applying Kirchhoff's voltage law (KVL), V Cc can be determined as follows: At the same time, the current i pri = i Lbi− i Lsb flows through D 1 , D 2 , and D 3 via the coupled inductor T 1 , and the turn ratio of T 1 is 1: n according to assumption 3; V LVS /n is applied to L sb . Thus, i Lsb increases linearly toward i Lbi as follows: Also, −V Cc is applied to L bi , and i Lbi decreases slowly as follows: To guarantee the ZCS turn-on of M 2 at t 0 , i Lsb must reach i Lbi within this stage. When i Lsb becomes equal to i Lbi , all snubber VOLUME 8, 2020 diodes are turned off, and this stage ends. The duration of this stage is as follows: After t 7 , the converter operates in the same way as it did in stage 0, and a new cycle begins.
Also, V HVS is applied to L sb by the conduction of M 1 ; therefore, i ds1 begins to increase linearly from 0 A, as follows: The slope of i ds1 is limited by L sb , and i ds1 increases from 0 A; therefore, the ZCS turn-on condition of M 1 is satisfied. At the same time, by applying KCL, i ds2 can be determined as follows: From (22), it can be observed that the current, which is obtained from the difference between i Lbi and i Lsb , flows through M 2 . Thus, i ds2 decreases gradually to 0 A. As a result, the body diode of M 2 can be softly turned off without the occurrence of the reverse recovery problem. When i Lsb becomes equal to i Lbi , this stage ends. The time duration of this stage is as follows: Stage2 [t 1 , t 2 ]: This stage begins when i Lsb becomes equal to i Lbi at t 1 . During this stage, v Cs increases because of the resonance between C s and L bi ||L sb . If L bi is assumed to be even larger than L sb , C s resonates with L sb . Thus, v Cs and v ds2 can be determined as follows: v To achieve the ZVS turn-off of M 1 at t 4 , v Cs must reach V Cc within this stage. When v Cs becomes equal to V Cc at t 2 , D 1 is turned on, and this stage ends. Stage 3 [t 2 , t 3 ]: When D 1 is turned on at t 2 , v Cs is clamped on V Cc along the conductive path of C s -M 1 -C c -D 1 . Also, by applying KVL, V Cc can be determined as the voltage described in (16). At the same time, i pri = i Lsb -i Lbi flows through D 1 , D 2 , and D 3 via T 1 , and the turn ratio of T 1 is 1: n according to assumption 3; therefore, −V LVS /n is applied to L sb . Thus, i Lsb decreases linearly toward i Lbi , as follows: Also, since V Cc is applied to L bi , i Lbi increases slowly as follows: When i Lsb becomes equal to i Lbi , all the snubber diodes are turned off and this stage ends. Stage 4 [t 3 , t 4 ]: M 1 is conducting; therefore, i Lbi increases linearly with the slope of (V HVS -V LVS )/L bi .
Stage 5 [t 4 , t 5 ]: When M 1 is turned off at t 4 , i Lbi flows along the conductive path of L sb -D 1 -C s -L bi -D 3 . The time interval of this stage is very short, and L sb is connected with L bi in series. Therefore, using assumption 5, we can assume that C s is charged with the constant current of L bi . Thus, v Cs , v ds1 , and v ds2 can be expressed, respectively, as follows: In stage 2, v Cs reaches V Cc ; therefore, v ds1 is equal to 0 V at t 4. Also, the rising slope of v Cs is limited by C s (as described in (28)); therefore, v ds1 also increases slowly from 0 V. Therefore, the ZVS turn-off condition of M 1 is achieved at t 4 . From (30), we can see that when v Cs becomes equal to −(n−1)V LVS /n, and v ds2 reaches 0 V, this stage ends. Stage 6 [t 5 , t 6 ]: When v ds2 becomes equal to 0 V at t 5 , the body diode of M 2 is turned on, and this stage begins. Therefore, in this stage, v Cs further increases by the resonance between C s and L sb via T 1 . The voltage and current of C s can be determined as follows: v Cs (t) = V Cs (t 5 ) cos(ω 1 t) + i Lbi (t 5 )Z 1 sin(ω 1 t), (31) i Consequently, the voltage across M 2 is 0 V, and i ds2 increases slowly from 0 A by the current obtained as the difference between i Lbi and i Cs . Therefore, M 2 can be turned on under the ZVS condition. When v Cs becomes equal to −V LVS at t 6 , D 2 is turned on, and this stage ends. Stage 7 [t 6 , t 7 ]: When v Cs reaches −V LVS , D 2 is turned on, and v Cs is clamped on −V LVS through M 2 and D 2 . At the same time, −V LVS /n is applied to L sb via T 1 ; therefore, the voltage across M 2 becomes V HVS + (V LVS /n), and i Lsb decreases linearly toward 0 A as follows: To guarantee the ZCS turn-on of M 1 at t 0 , i Lsb must become equal to 0 A within this stage. Also, −V LVS is applied to L bi ; therefore, i Lbi decreases slowly, as follows: During this time, the energy stored in L sb returns to the output battery along the conductive path of L sb -D 1 -D 2 -V LVS -D 3 . Finally, when i Lsb becomes equal to 0 A at t 7 , all the snubber diodes are turned off, and this stage ends. The duration of this stage is given as After t 7 , the converter operates in the same way as in stage 0, and a new cycle begins.

III. DESIGN CONSIDERATIONS
The purpose of the proposed lossless snubber cell is to achieve high efficiency, high-frequency operations, and (subsequently) high power density by ensuring soft-switching.
In this section, the design guidelines of the proposed snubber cell will be presented considering soft-switching and power losses. The design guidelines obtained for one of the two operation modes can also guarantee the proper operation of the other mode; therefore, we describe the design considerations, which are mainly based on the discharging mode.

A. TURN RATIO OF THE COUPLED INDUCTOR
The turn ratio of the coupled inductor is crucial with respect to the ZCS turn-on of the main switch and the soft turn-off of the SR. Moreover, it also determines the voltage stresses of all power semiconductors. Therefore, we present the design considerations for the turn ratio of the coupled inductor. Initially, we need to ensure the simultaneous ZCS turn-on of M 2 and soft turn-off of M 1 . For this purpose, the equivalent circuit shown in Fig. 7 must be maintained during the discharging mode in stage 1. To limit the rising or falling slopes of i ds1 and i ds2 using L bi and L sb , i Lsb must flow through the body diode of M 1 by blocking D 3 . Therefore, assuming that the body diode of M 1 is conducting at the turn-on of M 2 , D 3 must be blocked. Thus, the relationship between V Cc and v sec should be satisfied as follows: Moreover, by applying KVL on the loop of M 2 -M 1 -v pri -V HVS , the following relationship can be obtained: From (37) and (38), we obtain the following: The average value of v sec and v pri is 0 V in the steady state; therefore, the following relationship can be obtained by applying KVL on the loop of D 3 -v sec − C c − v pri − V HVS : where < · > means the average value of ''·.'' If the forward voltage drop of D 3 is assumed to be 0 V, < v D3 > is always 0 or higher. Therefore, from (39) and (40), we obtain that the turn ratio of the coupled inductor should be equal to or greater than 1 to ensure simultaneous ZCS turn-on of M 2 and soft turn-off of M 1 . The turn ratio of the coupled inductor also determines the voltage stresses of all the power semiconductors. When n ≥ 1, the voltage stress of each device is determined with respect to the turn ratio, as follows: Assuming that the snubber interval (i.e., t 4 -t 6 ) is very short as compared with the switching period T s , the voltage conversion ratio of V HVS /V LVS can be approximated as 1/ (1−D), where the duty ratio D of M 2 is defined as (t 0− t 4 )/T s . Therefore, from (41) and (44), the voltage stress of each device with respect to the turn ratio can be illustrated as shown in Fig. 8. Finally, to ensure the ZCS turn-on of M 2 and the soft turn-off of M 1 , the turn ratio of the coupled inductor can be appropriately selected as n ≥ 1, considering the voltage stresses of all the semiconductors shown in Fig. 8.

B. OPTIMAL VALUES OF L sb AND C s
In the proposed snubber, L sb and C s are not only important in soft-switching, but they also affect the additional conduction losses caused by the circulating resonant current. Therefore, both the soft-switching condition and power losses must be considered in the design of L sb and C s . Initially, to ensure the ZCS turn-on of M 2 during the discharging mode, the duration of stage 7 described in (19) should be smaller than the turn-off time of M 2 , that is, (1−D)T s . Therefore, the maximum value of L sb required during the discharging mode considering (19) is given as follows: where I Lbi is roughly equal to i Lbi (t 6 ), but it can be approximated by the average current of L bi at full load as the worstcase scenario. Similarly, to ensure the ZCS turn-on of M 1 during the charging mode, the maximum value required for L sb considering (36) is where I Lbi is roughly equal to i Lbi (t 6 ) but can be approximated by the average current of L bi at full load as the worst-case scenario. Therefore, L sb for the ZCS turn-on of both M 1 and M 2 should be designed to be less than the maximum values given in (45) and (46). To ensure the ZVS turn-off of M 2 during the discharging mode, C s should be designed such that the sum of the time durations in stages 1 and 2 is less than the turn-on time of M 2 , that is, DT s . Therefore, assuming that the duration of stage 2 is half that of the resonant period, the maximum value of C s considering (4) can be determined as follows: where I Lbi is equal to i Lbi (t 0 ) but can be approximated by the average current of L bi at full load as the worst-case scenario. Similarly, to ensure the ZVS turn-off of M 1 during the charging mode, the maximum value of C s considering (23) can be determined as follows: where I Lbi is equal to i Lbi (t 0 ) but can be approximated by the average current of L bi at full load as the worst-case scenario. Therefore, C s for the ZVS turn-off of both M 1 and M 2 should be designed to be smaller than the maximum values given in (47) and (48).
Finally, the optimal values of L sb and C s satisfying (45)-(48) should be selected such that the power conversion loss of the overall system becomes minimum. The power losses during the charging and discharging modes are almost the same; therefore, the theoretical power loss in the discharging mode is presented in Fig. 9. This is obtained according to the input-to-output conditions specified in Table 1. As shown in Fig. 9 (a), although the proposed snubber can significantly reduce switching losses, the power loss from the snubber cannot be ignored. Therefore, the optimal values of L sb and C s should be designed by considering the overall power conversion efficiency, as shown in Fig. 9 (b). From these results, the optimal values for the minimum power loss can be chosen as L sb = 9 µH, C s = 4 nF, which shows the minimum power loss as P loss = 51.05 W.
C. CLAMP CAPACITOR C c As described in Section II, the proposed snubber cell provides M 1 and M 2 with soft switching based on the resonance between L sb and C s . Therefore, C s should be designed with a small enough value to be able to resonate with L sb during the short switching interval. However, the function of C c is to provide the voltage source determined by (41) for clamping v Cs on V Cc . Therefore, the value of C c must be large enough to be maintained at a constant voltage for one switching cycle. Therefore, as a design recommendation, it is considered appropriate to design C c such that it is approximately 10 times higher than C s .

D. DEADTIME FOR ZVS TURN-ON
The BBC requires two totem-pole switches operating complementarily; therefore, the dead time (T dead = t 4 − t 5 ) between these switches is essential to avoid having a short arm. In addition, T dead also affects the soft-switching of the SR at stage 6. The ZVS turn-on of the SR can be achieved only if the SR is turned on after the voltage across the SR becomes 0 V at t 5 .
In particular, C s begins charging by i Lbi (t 4 ) after the main switch M 2 is turned off at t 4 during the discharging mode.
After v Cs reaches V HVS− V LVS at t 5 , v ds1 becomes equal to 0 V. Therefore, the ZVS turn-on of the SR switch M 1 can be achieved as long as M 1 is turned on at any time between t 5 and t 6 . Thus, the duration of stage 5 during the discharging mode must be long enough to ensure that v ds1 becomes equal to 0 V. The minimum T dead is given as follows: Similarly, C s begins discharging by i Lbi (t 4 ) after the main switch M 1 is turned off at t 4 during the charging mode. After v Cs reaches −(n − 1)V LVS /n at t 5 , v ds2 becomes equal to 0 V. Therefore, the ZVS turn-on of the SR switch M 2 can be achieved as long as M 2 is turned on any time between t 5 and t 6 . Thus, the duration of stage 5 during the charging mode must be long enough to ensure that v ds2 approaches 0 V. The minimum T dead is also given in (49). The minimum T dead values that ensure the ZVS turn-on of the SR according to the load conditions in each mode are shown in Fig. 10. These values were obtained according to the input-to-output conditions specified in Table 1. When C s = 4 nF and P out = 300 W (at 10% load), the appropriate T dead for ZVS turn-on of the SR can be selected in the range of 250-300 ns for both the charging and discharging modes.

IV. EXPERIMENTAL RESULTS
The prototype of the BBC equipped with the proposed snubber cell was implemented using a two-phase interleaved BBC (see Fig. 11). Its specifications are listed in Table 1.  A photograph of the prototype is shown in Fig. 12. The experimental waveforms for a 3-kW fully loaded condition during the charging and discharging modes are shown in Figs. 13 and 14, respectively. These waveforms coincide well with the theoretical key waveforms (see Figs.4 and 6). In particular, the voltage and current of the main switch during the switching transient are shown in detail in Figs. 13(b) and (c) and Figs. 14(e) and (f), respectively. The overlap between the current and voltage can be negligible during both the turn-on and turn-off transients, as shown in these figures; therefore, we can confirm that  the soft-switching conditions of the main switches are satisfied. Also, Figs. 13(e) and (f) and Figs. 14(b) and (c) show that the soft-switching conditions of SRs can be guaranteed during the turn-on and turn-off transients. In addition, the current decreases slowly to 0 A; therefore, the reverse recovery problems of SRs can be effectively overcome. However, as shown in these experimental results, the voltage stress of the switches M 1 and M 2 was approximately 540 V. This result is relatively higher than the voltage stress of semiconductor devices in the conventional BBC. Also, Figs. 13(a) and 16(a) show that the soft turn-off of D 3 is satisfied. As compared with the conventional BBC, the proposed snubber cell increases the high-voltage stress beyond the conventional BBC, as shown in Section III.
The measured efficiencies of the BBCs with and without the proposed snubber cell are shown in Fig. 15. These efficiencies were measured using the power meter WT18042 from YOKOGAWA. The efficiencies of the BBCs without the snubber could not be measured at more than P out = 2 kW because of a heat explosion of the power switch. These results prove that the efficiencies of the BBCs using the proposed snubber cell are more than 96.66% and 95.26% for a wide load range during the charging and discharging modes, respectively. The highest efficiencies measured were 98.20% and 98.27% during the charging and discharging modes, respectively. However, the BBC with the snubber has lower efficiency than the BBC without the snubber at P out = 500 W. This is because the BBC operates  in the discontinuous conduction mode (DCM) at that load, and the DCM operation can provide the main switch with the ZCS turn-on even in the absence of the snubber. The BBC without the snubber does not have additional losses caused by the snubber; therefore, it has higher efficiency than the snubber for light loads. Nevertheless, the proposed snubber can improve the switching performance of the switch and the reverse recovery characteristics of the diode. Therefore, it can provide high efficiency in the continuous conduction mode. Consequently, the proposed snubber can achieve high efficiency despite the high switching frequency; therefore, it can significantly improve the power density of the BBC.

V. CONCLUSION
In this paper, a lossless snubber cell for soft-switched BBC was proposed to improve the switching performance of the switch and the reverse recovery characteristics of the diode. Therefore, this cell enables the BBC to operate at high switching frequencies with high efficiency.
We present a detailed analysis and discuss the design considerations; the optimal parameters of the snubber were derived from the loss analysis. The validity of the proposed snubber was confirmed by the experimental results using a 3-kW prototype. The experimental results demonstrated that the proposed snubber could achieve the soft switching of all power switches; it could also overcome the reverse recovery problem of the body diode of SR without auxiliary switch and any complex control strategy. Moreover, the efficiencies of the BBCs with the proposed snubber cells were over 96.66% and 95.26% for a wide load range during the charging and discharging modes, respectively. The maximum measured efficiencies were as high as 98.20% and 98.27% during the charging and discharging modes, respectively. These results prove that the proposed snubber is well suited for high power density and high-efficiency bidirectional converters; it is applicable in various systems using a battery.
In this paper, our experimental results show that the proposed snubber cell significantly reduces switching loss but increases the voltage stress more than the conventional BBC. Recently, however, to achieve high efficiency for high powered battery-fed systems, high-voltage batteries are being increasingly used. In this case, applying the proposed snubber cell to the BBC may be somewhat burdensome to the voltage stress of the switch. In addition, the feasibility of the proposed snubber cell was discussed by applying the snubber cell only to the BBC where the metal-oxide-semiconductor FET (MOSFET) was used. However, the application of proposed snubber cells can be expanded in various ways. Therefore, in our future research, we propose to investigate the following areas.
• We will investigate how the proposed circuit can reduce the voltage stress of the semiconductor required for high-voltage battery applications.
• For extending the application of the proposed snubber cell, the validity for applying the proposed snubber cell to the bidirectional inverter can be investigated (see Fig. 16).
• The performance of the BBC using insulated-gate bipolar transistor (IGBT) instead of MOSFET can be investigated. Especially for IGBT, high-frequency switching is difficult because of the switching loss arising as a result of the tail current during turn-off [36]. Therefore, for the high-frequency drive of the BBC using IGBT, the softswitching method using the proposed snubber cell is an efficient solution.