Lossless Snubber for GaN-Based Flyback Converter with Common Mode Noise Consideration

The previous lossless snubber for flyback converters, although with a small number of components, simple control and high power conversion efficiency, has no consideration for electromagnetic interference (EMI). This paper proposes a lossless snubber converter with a novel drain voltage rising slew rate control for the main switch of the flyback converter. Compared to traditional topologies, the proposed snubber topology has two advantages: first, only an additional inductor is used. Second, the proposed method can reduce EMI emissions significantly. Finally, a prototype of the proposed snubber is built and verified with two existing similar snubbers.


I. INTRODUCTION
Ideally, the transformer is perfectly coupled without leakage flux between the windings, but the actual transformer always has leakage inductance in its windings. Without a suitable voltage suppression mechanism, leakage inductance can induce a voltage spike over the rating voltage of the power switches, the power switch may be damaged. In order to prevent the power switch from being damaged, a snubber circuit is applied to suppress the voltage spike. The snubber is usually located on the drain of the power switch in Fig. 1. The typical dissipative circuit includes a resistor, a diode, and a capacitor called RCD snubber [1][2]. The RCD snubber has been widely used in industry for a long time.  voltage changes of switching devices and transformer windings, the inter-winding parasitic capacitor (IWPC) of the transformer causes CM conduction noise current between the primary side windings and secondary side windings. CM conduction current flows through the earth ground of the line impedance stabilization network (LISN) to be detected by the EMI receiver. The CM conduction current usually causes more conduction EMI emissions in the frequency range of 1 MHz to 30 MHz in a flyback converter. The IWPC is determined according to the physical structure and material of the transformer. As shown in Fig. 1, the CM current highly depends on the voltage slew rate of the main switch when the transformer is designed and made.
Due to the low switching loss and high switching frequency of gallium nitride (GaN) power switch, there is a strong interest in emerging power electronics converters. However, one of the concerns is that the high switching speed (dv/dt or di/dt) of GaN devices can generate more EMI emissions [3] compared to conventional silicon-based power switches.
The rapid drain voltage slew rate on the main switch is an important source [4] of EMI common mode noise. The snubber can be passive [5]- [7] or active [8], or a mixed active and passive [9]. It can also be dissipative [10]- [12] or nondissipative [5]- [9], [12]- [15]. According to the conclusions in [4], the methods of controlling turned-off dv/dt have a better effect on reducing CM current of a flyback converter, such as [9], [13]- [15], but they use more active switches and passive components, so the circuits are too complicated.
The proposed circuit is shown in Fig. 2, which is a lossless snubber topology. Compared to the basic flyback topology, the proposed circuit has the following two features: first, it needs one additional inductor and one winding. Second, it can be driven by the commercial flyback control IC without any modification. Thus, the proposed circuit is easily commercialized for industrial applications.
There are two similar existing lossless snubber topologies shown in Fig. 3. Fig. 3(a) is the lossless LC snubber, which can recycle the energy of leakage inductance [16] to improve the efficiency. Compared with the first prior topology in Fig.  3(a), the proposed circuit adds an auxiliary winding to the main transformer. As shown in Fig. 3(b), the second prior circuit, named energy regenerative snubber [17]- [20], has the same components as the proposed circuit. The energy regenerative snubber is basically a lossless snubber. With the auxiliary winding of the transformer, the energy stored in the leakage inductor of the transformer can be recycled back to the input capacitor.
The above two existing snubber topologies are similar to the proposed circuits, and have similar operating principles, so these two circuits are described together in this paper. However, the difference from the previous literature is that the previous research did not discuss the behavior of reverse recovery of snubber diodes. However, it is found that the effect of reverse recovery cannot be ignored, and there is still valuable for discussion in this paper. (a) (b) FIGURE 3. Two types of conventional lossless snubber: (a) Lossless LC snubber [16]; (b) Energy regenerative snubber [17]- [20].
The definition list of symbols and variables in this paper is shown in Table I. Reversed recovery charge of D1 and D2 trr1, trr2 Reversed recovery time of D1 and D2 irr1, irr2 Reversed recovery current of D1 and D2 After the first introduction section, the remainder of this paper is organized as follows. Section II describes the proposed circuit. Sections III and IV introduce the operation behavior of the lossless LC snubber and the energy regenerative snubber in the flyback converter. Then, in Section V, the specifications of these three prototypes are mentioned. The design process of the proposed circuit in Section VI. The results of three prototype circuits are discussed and analyzed in Section VII. The performance of the proposed circuit is compared with the others to show its feasibility. Finally, the conclusions are drawn in Section VIII.
Before entering the following circuit discussion in Session II, III, and IV, there are several assumptions as follows.
1) These circuits operate in CCM.
2) The polarity of the Cr is positive at initial voltage.
3) D1 and D2 have no initial current with non-ideal diode behavior of forward conduction voltages VF-D1 and VF-D2, reverse recovery times trr1, trr2 and reverse recovery charge Qrr1, Qrr2, respectively. 4) The turn-on resistance of Q2 is so low that it can be regarded as an ideal rectifier. 5) Q1 has parasitic output capacitor Coss1. 6) The leakage inductance of the winding Np is represented by LLK1, and the transformer magnetizing inductance is expressed by Lm.

7)
The leakage inductance of the winding Nr is represented by LLK2. LLK2 can be ignored in the proposed circuit and lossless LC snubber, because the Lr is much larger than LLK2. However, there is no physical Lr in energy regenerative snubber, and LLK2 has to be considered.

II. PROPOSED CIRCUIT CONFIGURATION
As shown in Fig. 2, the proposed snubber stores leakage inductance energy when Q1 is turned off. When Q1 is turned on, the Nr, Lr, D2, and Cr constitute a resonant tank, which regenerates the energy of the leakage inductor LLK1 to the input terminal. Nr provides a reversed DC superposition voltage on Cr for the soft switching function when Q1 is turned off. In this session, a detailed analysis of the operation states will be carried out. Fig. 4 shows the waveform of each point of the circuit. It can be seen that in the state 1 (t0~t1) interval, vCr will oscillate from positive polarity to negative polarity. Therefore, in state 4 (t3~t4), vds1 can change from a low vclamp and gradually increase upward.   5 is an explanation of the behavior of the proposed circuit, which can be divided into 7 operation states. The relative parameters of the proposed circuit are defined as follows.
And, the initial voltage of Cr is defined as (16).
1) State 1: As shown in Fig. 5(a), Q1 is turned on. Because iLm has an initial value, ids1 rises rapidly, and Vin continues to excite Lm in the forward direction, causing iLm to continue to rise as (18). At the same time, Cr resonates with Lr. At this time, D2 is forward-biased conduction, and reaches the lowest point of vCr(t1) after half a resonant period, as shown in (24). In addition, iD1 and iNs are zero.
2) State 2: As shown in Fig. 5(b). Q1 is turned on, and Vin continues to magnetize Lm in the forward direction, causing iLm to continue to rise as (31). On the other hand, Cr resonates with Lr for half a resonant period. Due to the existence of non-ideal D2 with Qrr2 and trr2, after the resonance half cycle, iCr will be reverse discharged so that Qrr2 of D2 can be discharged and completely reverse biased off. vCr2 can be expressed as (33). At this time, both iD1 and iNs are zero.
3) State 3: As shown in Fig. 5(c), Q1 remains on, and Vin continues to magnetize Lm in the forward direction, causing iLm to continue to rise. At this time, iLr, iD1, and iNs are zero. Lm charges Coss1, and vds1 rises rapidly at the same time. vds1 can be expressed as (56). The voltage rising slew rate of vds1 can be described in (59). LLK1 charges Coss1 and Cr at the same time to increase vCr. Since Cr is much larger than Coss1, vds1 in this interval rises slowly, so iD1 and iCr are positive. In (60), vclamp is the start point of clamping voltage by the proposed snubber on vds1 after Q1 is turned off.
is not an ideal diode, there are Qrr1 and trr1, so Cr will generate a reverse current iD1 to discharge vCr and cut off, which will cause a slight discharge and drop. As Qrr1 is completely discharged and cut off, it enters state 7.
(82) 7) State 7: As shown in Fig. 5(g), Q1 remains off. But Q2 turns on. As described in (83) and (84), Lm continues to be magnetized via the winding Ns to the output terminal. LLK1, D1, Q2, and Cr all reach a steady state as (85) to (88). As Q1 turns on, it returns to state 1.  Fig. 6 shows the waveform of each point of the lossless LC snubber. It can be seen that in the state 1 (t0~t1) interval, the voltage vcr will oscillate from positive polarity to negative polarity. Therefore, in state 4 (t3~t4), the voltage vds1 can rise from a low voltage and gradually increase upward. The related parameters of the lossless LC snubber circuit are defined as (1) to (15), and the initial conditions are as (91) and (92).
Because iLm has an initial value, ids1 rises rapidly, and Vin continues to magnetize Lm in the forward direction, causing iLm to continue to rise. On the other hand, Cr resonates with Lr. At this time, D2 is forward-biased conduction, and will reach the lowest point as shown in (93) after half a resonant period. During this state, iD1 and iNs are zero.
(93) 2) State 2: As shown in Fig. 7(b), Q1 is turned on, and Vin continues to magnetize Lm in the forward direction, causing iLm to continue to rise. On the other hand, Cr will resonate with Lr for half a resonant period. Due to the existence of non-ideal D2 with Qrr2 and trr2, after the resonance half cycle, iCr will be reverse discharged so that Qrr2 of D2 can be discharged and completely reverse biased off. vCr can be expressed as (94). During this state, both iD1 and iNs are zero.
3) State 3: As shown in Fig. 7(c), Q1 remains on, and Vin continues to magnetize Lm in the forward direction, causing iLm to continue to rise. At this time, iLr, iD1, and iNs are zero.
6) State 6: As shown in Fig. 7(f), Q1 remains off, but Q2 is turned on. Because D1 is not an ideal diode, it has Qrr1 and trr1. When LLK1 is completely demagnetized, there is a reverse current iD1 to discharge Cr and cut off after trr1, which causes a slight discharge and drop on vCr. As Qrr1 is completely discharged and cut off, it enters state 7.
State 7: As shown in Fig. 7(g), Q1 remains off, but Q2 is turned on. Lm continues to be demagnetized via the winding Ns to the output terminal. The currents in LLK1, D1, Q1, Cr, D2 and Coss1 are zero. As Q1 turns on, it returns to state 1. It can be seen that in the state 1 (t0 ~ t1) interval, the voltage vCr will oscillate, but still stay positive polarity. Therefore, in state 3 (t2 ~ t3), the voltage of vds1 can increase from a higher voltage vclamp. Due to the voltage vclamp of the proposed snubber is lowest in these three snubbers, the voltage rising slew rate can be controlled during the whole rising duration as Q1 is turned off. The related parameters of the energy regenerative snubber circuit are defined as (4) to (15), and the initial conditions are as (115) and (116). Because there is no Lr in this topology, formulas (1), (2), and (3) are modified as (112), (113), and (114), respectively.
(116) 1) State 1: As shown in Fig. 9(a), Q1 is turned on. Because iLm has an initial value, ids1 rises rapidly, and Vin continues to magnetize Lm in the forward direction, causing iLm to continue to rise. On the other hand, Cr resonates with LLK2. At this time, D2 is forward-biased conduction, and will reach the lowest point shown in (120) after half a resonant period. During this state, iD1 and iNs are zero. In (121), vclamp(ER) is the start point of clamping voltage by the lossless LC snubber on vds1 after Q1 is turned off.
2) State 2: As shown in Fig. 9(b), Q1 remains on, and Vin continues to magnetize Lm in the forward direction, causing iLm to continue to rise. During this state, iNr, iD1, and iNs are zero.
(124) 3) State 3: As shown in Fig. 9(c) 4) State 4: As shown in Fig. 9(d), Q1 remains off status, but Q2 is turned on. Because D1 is not an ideal diode, it has Qrr1 and trr1. When LLK1 is completely demagnetized, there is a reverse current iD1 to discharge Cr and cut off after trr1, which can causes a slight discharge and drop on vCr. As Qrr1 is completely discharged and cut off, it enters state 5.
5) State 5: As shown in Fig. 9(e), Q1 remains off, but Q2 is turned on. Lm continues to be demagnetized via the winding Ns to the output terminal. The currents on LLK1, D1, Q2, and Coss1 are zero. As Q1 is turned on, it returns to state 1.  Table II. It is known that vclamp(ER) > vclamp(LC) > vclamp(prop). It is also known that vds1 rising time and vclamp are positively correlated, so the vds1 rising time of the proposed snubber is related to vclamp. The slower rising slope of vds1 is helpful to reach better EMI performance.

V. CIRCUIT SPECIFICATIONS AND PARAMETERS
These three flyback prototype circuits are modified from an existing business 72 W flyback adapter product. Therefore, the design step of the main transformer is skipped to simplify the design process. The prototype circuits are built with the following specifications and parameters shown in Tables III  and IV. The variables in the design process of the prototype in this paper are listed in Table V.

Maximum duty cycle at low line Vin and high line Vin, respectively
Np-min

Calculated minimum turn of winding Np td-Q2
Turn-on delay time 100ns of Q2 Rcm-chk DC resistance of common choke at low line and high line Vin iD1-pk(LL), iD1-pk(HL) Peak forward current of D1 at low line Vin and high line Vin, respectively iD2-pk(LL), iD2-pk(HL) The system blocks for the conventional lossless LC snubber, the energy regenerative snubber, and the proposed snubber are shown in Fig. 10.

VI. DESIGN of PROTOTYPE
The first design step is to calculate the duty cycle in CCM with high line and low line input voltages.
Then, the DCM/CCM boundary can be obtained. When the load current is above 43% of rated load at the low line input voltage and 63.3% of rated load at the high line input voltage, the converter operates in CCM.
When over 63% of rated load, the converter enters the CCM under high line input voltage. For the reasons above, it can be seen that it operates in CCM when the circuit is fully loaded even at the high line input voltage or low line input voltage.

A. Current calculation for Np and Q1
The formulas of peak current of Q1 in CCM are also shown.
It can be ensured that the peak current in Q1 happens in CCM. Then both iNp-pk(LL) and iNp-pk(HL) can be obtained as (147) and (148). iNp-pk(LL)=1.96 A (147) iNp-pk(HL)=1.829 A (148) Also, the peak current of the secondary winding and rectifier can be calculated as the following equation. iNs-pk(LL)=Nps• iNp-pk(LL)=14.113 A (149) In industrial design, the de-rating of flux density saturation is acceptable 90%. The turn number of winding Np-min is 31.678 as (150). However, it is not a reasonable solution.
Here, the turn number of Np is determined with 36 and the maximum flux density is 0.276 T for the low line input voltage and 0.257 T for the high line input voltage.

B. Current calculation for Ns
Next, the peak-to-peak current ΔiNs(LL) andΔiNs(HL) can be calculated as (157) and (158). Their RMS values are also obtained as (159) and (160). Finally, the average currents values iNs-avg(LL) and iNs-avg(HL) are calculated as (161) The maximum peak value on vds1 appears at the high line and when the circuit is operated at full load.

E. The start point of clamping voltage vclamp
The clamping voltage vclamp(prop) of the proposed circuit is calculated as (171) and (172). After Q1 is turned off, vds1 rises from vclamp(prop). When vds1 reaches vclamp(prop), the slew rate control function will execute, so this voltage should be as low as possible. From (171), it can be seen vclamp(LL) should be -12.8 V at the low line input voltage. However, the body diode of Q1 can clamp the vds1 at -0.9 V. The vclamp(HL) is obtained as (172) at the low line input voltage.

F. Voltage and current calculation of D2
For a sinusoidal wave, the average value is 0.9 times of its RMS value. Therefore, the average value and RMS value of iD2 are obtained as (175) to (178): Cr max HL D pk HL r Cr max HL r r D rms HL r sw And the reverse voltage vD2-pk(LL) and vD2-pk(HL) of D2 are shown as (179) and (180), respectively.

G. Calculation of D1
The calculation formulas of the voltage and current of D1 are shown as (181) to (185): Ns HL on D pk HL in HL sr o 20.05 mA 2 2 Np pk LL LK r D rms LL sw 18.71 mA 2 2 Np pk HL LK r D rms HL sw

I. Loss estimation of T1
Since the Bmax values of T1 provided by the supplier under high line and low line conditions are too close, the core loss is calculated to be the same result. Bmax values of T1 under 100 kHz can be found in the data sheet.
Since the switching frequency is 100 kHz and multistranded wire has been used, in order to simplify the design, the skin effect is not considered here, and the measured DC resistance of each winding is directly used for calculation.
The copper loss of each winding is shown as (194) to (199). The auxiliary winding is only used for powering PWM IC U1, and its operation current is only 1.5 mA, so the winding loss is not included in the calculation:

K. Loss estimation of D1 and D2
The formulas of power loss analysis of D1 and D2 are estimated as (203) to (206): The total power loss of Q2 can be estimated as (214) and (215):

N. Loss estimation of bridge diode
The power loss of the bridge rectifier can be calculated according to the average input current, as shown in (218) and (219):

O. Loss estimation of EMI common choke
The loss of the EMI common mode filter can be calculated according to the input current to have the result of (220) and (221).

P. Total loss estimation
Finally, the loss items above are summed up to obtain the total system loss as (222) and (223)  The loss breakdown charts of low line AC input and high line AC input are shown in Fig. 11(a) and Fig. 11(b), respectively. It can be seen that the copper loss and core loss of T1 are the main sources of loss. However, D2 and Q2 also have significant contributions.

VII. EXPERIMENTAL RESULTS
The proposed circuit is similar to lossless LC snubber and energy regenerative snubber. For the convenience of comparison with [10]- [12] in this paper, these three prototype circuits are made with the same components and the same PCB layout to make a fair comparison as shown in Fig. 12.  Table II is verified.
The experimental results of the energy regenerative snubbers are shown in Figs. 14 and 15. It can be observed that there is no significant change in the rising slope of vds1. Compared with the vds1 rising slope of the energy regenerative snubber in Figs. 15 and 16, the vds1 rising slope of the proposed circuit in Figs. 17 and 18 are significantly slower, which proves that the proposed circuit can indeed achieve a significant switching speed reduction.
After Q1 is turned off and vds1 rises to the highest point, it can be seen that iCr will have a negative current, which is due to the current of the diode recovery charge Qrr to discharge Cr reverse. This behavior occurs in all these three topologies.
The experimental results of conversion efficiency are shown in Fig. 19. Under 80% to 100% of rated load, the efficiency of the proposed topology is about 0.1% higher than the efficiency of the energy regenerative snubber.  Table VI lists vds1 turned-off rising slew rate of these three prototypes. The proposed circuit slows down the turned-off rising slew rate compared to the energy regenerative snubber, but similar to the lossless LC snubber.
The experimental EMI results can also verify the previous waveforms in Fig. 20 to Fig. 22. Even the energy regenerative snubber provides higher efficiency, but its EMI performance is worse than the proposed circuit and the lossless LC snubber. The proposed method significantly reduces conduction EMI emissions in the frequency range of 500 kHz to 2 MHz and radiation EMI emissions up to 6 dBμV in the frequency range of 60 MHz to 230 MHz.

VIII. CONCLUSION
In view of the high frequency and wide bandgap switching devices brought by the miniaturization of power converters, faster switching speeds and EMI problems that come with them, this paper proposes a slope control snubber. It can be applied to the flyback converter. The experimental results show that compared to the previous methods [13]- [15], the proposed snubber significantly improves both conduction and radiation EMI emissions with the same components.