Pulse Width and Frequency Hybrid Modulated LLC Converter Adapted to Ultra Wide Voltage Range

Umar Khalid 1,*, Muhammad Mansoor Khan 1, Muhammad Zahid Khan 1, Muhammad Ahmad Usman Rasool 1 and Jianming Xu 2 1 School of Electronic, Information and Electrical Engineering (SEIEE), Shanghai Jiao Tong University, Shanghai 200240, China; mansoor@sjtu.edu.cn (M.M.K.), zahid@sjtu.edu.cn (M.Z.K.); iamahmedusman@sjtu.edu.cn (M.A.U.R.) 2 Changzhou Power Supply Company, Changzhou 213000, China; czxjm@sohu.com * Correspondence: umarkhalidd@outlook.com


Introduction
Recently, hybrid, plug-in hybrid and electric vehicles (HEVs, PHEVs, and EVs) have gained popularity as promising automotive products due to numerous advantages, such as increased vehicle performance and fuel economy.They also help in reducing environmental pollution by controlling the emissions of greenhouse gases [1].EVs connected to the grid may be utilized as an ancillary service provider as they can be instrumental in reactive power support and load balancing [2].As EVs are gaining popularity, researchers are trying to address the three main issues, including cost of batteries, optimal design of chargers and improved charging infrastructure [3].EV chargers are typically classified as off-board charges and on-board chargers with or without bidirectional capability.While designing EV on-board chargers, size and weight are major constraints [2].
DC-DC converters are an integral part of EVs onboard chargers [2].The DC-DC stage of Plugin EVs chargers mainly consist of LLC resonant topology [4][5][6].LLC resonant topology has a simple structure and reduced EMI.Moreover, switching losses can be decreased by extending the zero voltage switching (ZVS) and zero current switching (ZCS) range of MOSFETs and power diodes respectively [7][8][9].Hence, LLC is regarded as the more suitable structure opted for EVs chargers [10][11][12].An EV charger needs to operate at higher efficiency at the wide voltage variation range.If the LLC converter has to meet such a wide voltage range, the switching frequency (f s ) needs to be varied and deviates from resonant frequency (f r ) as demonstrated in Figure 1 where voltage gain requirements are met by varying the switching frequency.This variation in fs degrades the converter efficiency and thus it is desired that either the converter operates at its resonant frequency under all load conditions or f s doesn't deviate a lot from f r .Thus, the converter operational frequency range should be minimized [6,13,14].
If low voltage gain is required, the converter has to operate in region 2 as shown in Figure 1.In this region, power diodes will lose ZCS, leading to an increased switching loss.If high voltage gain is required, LLC converter has to operate at much lower frequency than resonance.This leads to the problems in designing optimal circuit magnetics such as transformer core [6].
If low voltage gain is required, the converter has to operate in region 2 as shown in Figure 1.In this region, power diodes will lose ZCS, leading to an increased switching loss.If high voltage gain is required, LLC converter has to operate at much lower frequency than resonance.This leads to the problems in designing optimal circuit magnetics such as transformer core [6].Numerous techniques to narrow down the LLC converter operation frequency have been proposed in the literature [8,[15][16][17][18].In [8], the designed LLC converter is incorporated with a twophase interleaved boost circuit.However, the converter power density is severely affected by additional circuit components.In [16][17][18], burst mode (BM) approach is engaged under low load conditions.However, electromagnetic interference (EMI) issues have been reported due to some high frequency oscillations.In order to eliminate such EMI issues, pulse frequency modulation (PFM) and phase shift (PS) control are combined in [19].But efficiency degrades due to high circulating currents when phase shift is utilized for a wide voltage range.In [20], asymmetric pulse width modulation (APWM) is adopted at the primary side in order to boost the conversion ratio, but voltage gain is still strongly dependent on load.
In [17,[21][22][23][24] various operation modes like synchronous rectification (SR), BM, PS, APWM, Pulse-width modulation (PWM) are studied for resonant converter to work with PFM control.Although proposed operational modes in the literature extend the gain requirements and narrow down the switching frequency range, they have their own limitations.BM presents a severe EMI problem, while the conversion ratio of SR, APWM and PWM are not independent of the load conditions.Promising techniques for wide voltage range DC applications have been discussed in [25], but topology structure and control is complicated.
In this paper, a LLC topology with PWM and PFM hybrid modulation have been proposed.PWM is introduced to the secondary side auxiliary switch to make the voltage regulation independent of the load.Therefore, the main LLC topology is designed to work at its resonant frequency under most of the load conditions and thus never lose ZVS under light load conditions.Furthermore, by making the auxiliary switch constantly on/off, the secondary sides switch networks can reconfigure between half and full bridges structures.This helps to further extend the voltage gain range.Last but not the least, in extreme voltage scenarios, frequency modulation can be activated to extend the voltage gain range even further.To summarize, the benefits of the proposed topology include: (1) an ultra-wide voltage gain range; (2) wide soft-switching range; and (3) load independent PWM based voltage regulation.

Topology Description
In this paper, a LLC topology is proposed, as shown in Figure 2.This DC-DC resonant converter topology has been derived from the full-bridge LLC topology with voltage doubler structure at the secondary side of the transformer.In comparison with the orthodox voltage doubler configuration, Numerous techniques to narrow down the LLC converter operation frequency have been proposed in the literature [8,[15][16][17][18].In [8], the designed LLC converter is incorporated with a two-phase interleaved boost circuit.However, the converter power density is severely affected by additional circuit components.In [16][17][18], burst mode (BM) approach is engaged under low load conditions.However, electromagnetic interference (EMI) issues have been reported due to some high frequency oscillations.In order to eliminate such EMI issues, pulse frequency modulation (PFM) and phase shift (PS) control are combined in [19].But efficiency degrades due to high circulating currents when phase shift is utilized for a wide voltage range.In [20], asymmetric pulse width modulation (APWM) is adopted at the primary side in order to boost the conversion ratio, but voltage gain is still strongly dependent on load.
In [17,[21][22][23][24] various operation modes like synchronous rectification (SR), BM, PS, APWM, Pulse-width modulation (PWM) are studied for resonant converter to work with PFM control.Although proposed operational modes in the literature extend the gain requirements and narrow down the switching frequency range, they have their own limitations.BM presents a severe EMI problem, while the conversion ratio of SR, APWM and PWM are not independent of the load conditions.Promising techniques for wide voltage range DC applications have been discussed in [25], but topology structure and control is complicated.
In this paper, a LLC topology with PWM and PFM hybrid modulation have been proposed.PWM is introduced to the secondary side auxiliary switch to make the voltage regulation independent of the load.Therefore, the main LLC topology is designed to work at its resonant frequency under most of the load conditions and thus never lose ZVS under light load conditions.Furthermore, by making the auxiliary switch constantly on/off, the secondary sides switch networks can reconfigure between half and full bridges structures.This helps to further extend the voltage gain range.Last but not the least, in extreme voltage scenarios, frequency modulation can be activated to extend the voltage gain range even further.To summarize, the benefits of the proposed topology include: (1) an ultra-wide voltage gain range; (2) wide soft-switching range; and (3) load independent PWM based voltage regulation.

Topology Description
In this paper, a LLC topology is proposed, as shown in Figure 2.This DC-DC resonant converter topology has been derived from the full-bridge LLC topology with voltage doubler structure at the secondary side of the transformer.In comparison with the orthodox voltage doubler configuration, an active switch has been added controlled by PWM.The duty cycle of this additional switch determine the output voltage of the converter.Hence, under most of the load conditions, converter operates at resonant frequency.While PFM can also be used to meet the high voltage output conditions.

Operation Principle
The control strategies for the proposed converter are demonstrated in Table 1.In forward mode, the output voltage ranges of 200-440 has been met with a constant input voltage of 400 V with 2:1 transformer turns ratio (n:1).Detailed operational stages in PWM shown in Figure 3 have been briefly discussed here and the corresponding equivalent circuits are shown in Figure 4.The switching frequency of S5 is also equal to fr.On the secondary side, a minor phase shift (tdelay) is introduced between the switching on of S5 and tdead.This makes sure that the body diode of S5 conducts earlier in case of forward mode than the turnon of the S5.Generally, the duty cycle of Vgs5 (D) should be controlled within the range of (0.5, 1) Considering Figure 3 for PWM mode, Stage I starts at t0 when S1,4 are turned-off.Stage I is within the tdead of S1-4.The voltage vab decreases from VDC. ir charges the output capacitors (Cos) of S2,3 and discharges Cos of S1,4.Since Cos is comparatively smaller, ir can be realized as constant, and Vab decrease linearly.

( ) ( ) ( )
Stage II is further divided into two stages.In the first step of stage II, Vab and Vtx continue to decrease.When D2 conducts, its forward voltage drop is about zero.According to KVL, the negative Vtx now enables body diode D2 to be forward biased; and thus the output capacitor of S5 (Cs5) is discharged.At the second step, S2,3 are turned ON and the body diode D5 of S5 starts conducting.In this stage, S2,3 are turned ON with ZVS.
Stage III: [t2, t3).At t2, S5 is turned on.At t2, S5 is turned on.It is obvious that the conduction of S5 body diode in the former stage forms the ZVS state for the switching-on of S5.While, at the secondary side of the converters' transformer, D2 and S5 both conduct.Cr and Lr resonate at the resonant frequency and this resonance frequency is equivalent to fr.
Stage IV [t3, t4). is stays zero after t3.Thus, the transformer secondary side is open-circuited.Lm joins the resonance with Lr and Cr.ir equals to iLm and varies sinusoidal.Stage V [t4, t5). is within the deadband of S1-4 and thus, the circuit operation in this stage is similar to that in stage I.

Operation Principle
The control strategies for the proposed converter are demonstrated in Table 1.In forward mode, the output voltage ranges of 200-440 has been met with a constant input voltage of 400 V with 2:1 transformer turns ratio (n:1).Detailed operational stages in PWM shown in Figure 3 have been briefly discussed here and the corresponding equivalent circuits are shown in Figure 4.The switching frequency of S 5 is also equal to f r .On the secondary side, a minor phase shift (t delay ) is introduced between the switching on of S 5 and t dead .This makes sure that the body diode of S 5 conducts earlier in case of forward mode than the turn-on of the S 5 .Generally, the duty cycle of V gs5 (D) should be controlled within the range of (0.5, 1).
Considering Figure 3 for PWM mode, Stage I starts at t 0 when S 1,4 are turned-off.Stage I is within the t dead of S 1-4 .The voltage v ab decreases from V DC .i r charges the output capacitors (C os ) of S 2,3 and discharges C os of S 1,4 .Since C os is comparatively smaller, i r can be realized as constant, and V ab decrease linearly.
Stage II is further divided into two stages.In the first step of stage II, V ab and V tx continue to decrease.When D 2 conducts, its forward voltage drop is about zero.According to KVL, the negative V tx now enables body diode D 2 to be forward biased; and thus the output capacitor of S 5 (C s5 ) is discharged.At the second step, S 2,3 are turned ON and the body diode D 5 of S 5 starts conducting.In this stage, S 2,3 are turned ON with ZVS.
Stage III: [t 2 , t 3 ).At t 2 , S 5 is turned on.At t 2 , S 5 is turned on.It is obvious that the conduction of S 5 body diode in the former stage forms the ZVS state for the switching-on of S 5 .While, at the secondary side of the converters' transformer, D 2 and S 5 both conduct.C r and L r resonate at the resonant frequency and this resonance frequency is equivalent to f r .
Stage IV [t 3 , t 4 ).i s stays zero after t 3 .Thus, the transformer secondary side is open-circuited.L m joins the resonance with L r and C r .i r equals to i Lm and varies sinusoidal.Stage V [t 4 , t 5 ). is within the deadband of S 1-4 and thus, the circuit operation in this stage is similar to that in stage I.At t5, the deadband is over and vab increases to VDC.Before the channels are turned ON, the drain to source voltages of switches S1,4 are discharged to zero.Thus, the turning on of S1,4 is ZVS.At t5, S1,4 are turned ON and stage VI starts.In this stage, Vab is equivalent to VDC. is is positive and body diode D5 of S5 conducts as shown in Figure 4f.S5 is turned off at t6 and Stage VII begins.As the primary side inductor current is continuous, the current path is moved from S5 to D3.At t7, is becomes zero and the circuit enters into stage VIII.Since S1,4 are still ON, is remains zero.Therefore, the power devices on the secondary side are not ON.Stage VIII ends when S1,4 are turned off.
During PFM mode in forward mode, the converter operates at a frequency lower than its designed resonant frequency (fr) such that it operates in region 1 of PFM gain curve discussed below.In this way, converter MOSFETs will always operate in ZVS condition while power diodes will operate under ZCS condition.The secondary side will act as the voltage doubler as the D of S5 will have a value 1.At t 5 , the deadband is over and v ab increases to V DC .Before the channels are turned ON, the drain to source voltages of switches S 1,4 are discharged to zero.Thus, the turning on of S 1,4 is ZVS.At t 5 , S 1,4 are turned ON and stage VI starts.In this stage, V ab is equivalent to V DC .i s is positive and body diode D 5 of S 5 conducts as shown in Figure 4f.S 5 is turned off at t 6 and Stage VII begins.As the primary side inductor current is continuous, the current path is moved from S 5 to D 3 .At t 7 , i s becomes zero and the circuit enters into stage VIII.Since S 1,4 are still ON, i s remains zero.Therefore, the power devices on the secondary side are not ON.Stage VIII ends when S 1,4 are turned off.

Lr
During PFM mode in forward mode, the converter operates at a frequency lower than its designed resonant frequency (f r ) such that it operates in region 1 of PFM gain curve discussed below.In this way, converter MOSFETs will always operate in ZVS condition while power diodes will operate under ZCS condition.The secondary side will act as the voltage doubler as the D of S 5 will have a value 1.
Inventions 2018, 3, 77 4 of 10 At t5, the deadband is over and vab increases to VDC.Before the channels are turned ON, the drain to source voltages of switches S1,4 are discharged to zero.Thus, the turning on of S1,4 is ZVS.At t5, S1,4 are turned ON and stage VI starts.In this stage, Vab is equivalent to VDC. is is positive and body diode D5 of S5 conducts as shown in Figure 4f.S5 is turned off at t6 and Stage VII begins.As the primary side inductor current is continuous, the current path is moved from S5 to D3.At t7, is becomes zero and the circuit enters into stage VIII.Since S1,4 are still ON, is remains zero.Therefore, the power devices on the secondary side are not ON.Stage VIII ends when S1,4 are turned off.
During PFM mode in forward mode, the converter operates at a frequency lower than its designed resonant frequency (fr) such that it operates in region 1 of PFM gain curve discussed below.In this way, converter MOSFETs will always operate in ZVS condition while power diodes will operate under ZCS condition.The secondary side will act as the voltage doubler as the D of S5 will have a value 1.

Gain Analysis
In PWM mode, the voltage at the output of the rectifying stage is the loose function of the load.Only stages III, VI, VII are used to deliver the power.Figure 5 shows the curves of the normalized voltage gain G norm = nV o /V DC versus the duty cycle under diverse operative load resistances (R L ) for PWM mode.It is worth mentioning that capacitor voltage (V C2 ) is not strongly dependent on the effective load resistance of the rectifier.Also, the duty cycle of the auxiliary switch at the secondary side has no effect on V C4 .

Gain Analysis
In PWM mode, the voltage at the output of the rectifying stage is the loose function of the load.Only stages III, VI, VII are used to deliver the power.Figure 5 shows the curves of the normalized voltage gain Gnorm = nVo/VDC versus the duty cycle under diverse operative load resistances (RL) for PWM mode.It is worth mentioning that capacitor voltage (VC2) is not strongly dependent on the effective load resistance of the rectifier.Also, the duty cycle of the auxiliary switch at the secondary side has no effect on VC4.Gain curves in PFM mode for the proposed LLC resonant converter have been shown in Figure 6.These gain curves are based on the PFM_LLC gain expression for the voltage doubler configuration derived below using first harmonic analysis [26,27]:  Gain curves in PFM mode for the proposed LLC resonant converter have been shown in Figure 6.These gain curves are based on the PFM_LLC gain expression for the voltage doubler configuration derived below using first harmonic analysis [26,27]: Inventions 2018, 3, 77 5 of 10

Gain Analysis
In PWM mode, the voltage at the output of the rectifying stage is the loose function of the load.Only stages III, VI, VII are used to deliver the power.Figure 5 shows the curves of the normalized voltage gain Gnorm = nVo/VDC versus the duty cycle under diverse operative load resistances (RL) for PWM mode.It is worth mentioning that capacitor voltage (VC2) is not strongly dependent on the effective load resistance of the rectifier.Also, the duty cycle of the auxiliary switch at the secondary side has no effect on VC4.Gain curves in PFM mode for the proposed LLC resonant converter have been shown in Figure 6.These gain curves are based on the PFM_LLC gain expression for the voltage doubler configuration derived below using first harmonic analysis [26,27]:

MOSFETs ZVS
ZVS is ensured in the MOSFETs if the current flowing through these switches is negative at the instant they are turned ON.During the dead-time, the current flowing through the primary side should be able to charge and discharge the output capacitance of the primary side MOSFETs.The value of this current is dependent on Lm and the t dead .Thus, ZVS depends on f s , t dead , L m and C oss .So, the magnetizing inductance can be designed using the same expression as the full-bridge LLC resonant converter [19] to ensure ZVS condition.This relationship is: Therefore, t delay and t dead can be well designed to ensure the ZVS of S 1-5 over the full load range.

Design Example
Consider a design example of 1 kW prototype with a constant DC input of 400 V to meet the output voltage requirement of 200-440 Vdc.The resonant frequency is chosen to be 100 kHz for the proposed design.The transformer turns ratio is 2:1 provided that nominal battery voltage is 400 Vdc, and the converter can operate in voltage doubler configuration.Thus, to meet the voltage output of 200-400 Vdc, PWM mode is used as shown in Figure 5.While PFM is used to meet the output voltage requirement of 400-440 V provided that rectifier is in voltage doubler mode.For a resonant frequency of 100 kHz, the C oss of the MOSFET is 250 pF, and the dead-time is 200 ns, the converters' magnetizing inductance is calculated as L m ≤ = 500 µH.This indicates that the magnetizing inductance of 500 µH or less ensures ZVS turning-on of the primary-side MOSFETs.L m can't be too large and can't be too small.An optimal value of magnetizing inductance has to be designed such that required gain can be achieved while limiting circulating currents.Careful simulations and repeated experiments are done to calculate the magnetic components parameters and resonance capacitance value.
The input voltage is 400 V while PFM is utilized for the output voltage of 400-440 V.The required gain is 1-1.10 in the forward PFM mode as shown in Figure 6.In order to make the gain curve monotonically decrease and also to encounter with the voltage gain requirements L m , L r , C r are calculated as following:

Experimental Results
A 1-kW prototype of PWM-LLC DC-DC converter is constructed with 400 V input voltage and 200-440 V output voltage.The experimental prototype has been shown in Figure 7.This power level is selected mainly to verify the proof of concept.Resistive load (RL) is used to as the output load in this experiment.The circuit parameters are shown in Table 2. Figure 8 shows the waveform for the converter at D = 1 whereas rectification stage acts as the voltage doubler.Figure 9 shows the ZVS condition of auxillary secondary side switch while Figure 10 describes the waveform for duty cycle less than 1. Figure 11 shows the converter operating at PFM mode where D = 1, but operating frequency is less than the designed resonant frequency.The calculated efficiency has been shown in Figure 12 for various output voltages calculated by open loop experiments.

Conclusions
In the proposed work, a novel idea to regulate output voltage has been introduced by utilizing an additional auxiliary switch at the secondary side and controlling its PWM.The proposed resonant LLC converter maximizes the converter efficiency by ensuring the ZVS and ZCS condition of MOSFETs and power diodes.A 1 kW prototype has been constructed to verify the concept that matches the power ratings of a typical Level 1 EV charger.The measured peak efficiency of the constructed prototype is 96.8% for the output voltage of 400 V at 100 kHz.The experimental results verify the load independent voltage regulation of the proposed topology.The proposed work doesn't explain the control of the prototype as per the charging profile of EV batteries, as the application of the proposed LLC converter is not limited to EV charging requirements, but also feasible for any application that require wide voltage range.In future work, the detailed operation and control of the proposed topology according to the charging profile of the EV battery will be discussed and analyzed.
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.

Conclusions
In the proposed work, a novel idea to regulate output voltage has been introduced by utilizing an additional auxiliary switch at the secondary side and controlling its PWM.The proposed resonant LLC converter maximizes the converter efficiency by ensuring the ZVS and ZCS condition of MOSFETs and power diodes.A 1 kW prototype has been constructed to verify the concept that matches the power ratings of a typical Level 1 EV charger.The measured peak efficiency of the constructed prototype is 96.8% for the output voltage of 400 V at 100 kHz.The experimental results verify the load independent voltage regulation of the proposed topology.The proposed work doesn't explain the control of the prototype as per the charging profile of EV batteries, as the application of the proposed LLC converter is not limited to EV charging requirements, but also feasible for any application that require wide voltage range.In future work, the detailed operation and control of the proposed topology according to the charging profile of the EV battery will be discussed and analyzed.
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.

Conclusions
In the proposed work, a novel idea to regulate output voltage has been introduced by utilizing an additional auxiliary switch at the secondary side and controlling its PWM.The proposed resonant LLC converter maximizes the converter efficiency by ensuring the ZVS and ZCS condition of MOSFETs and power diodes.A 1 kW prototype has been constructed to verify the concept that matches the power ratings of a typical Level 1 EV charger.The measured peak efficiency of the constructed prototype is 96.8% for the output voltage of 400 V at 100 kHz.The experimental results verify the load independent voltage regulation of the proposed topology.The proposed work doesn't explain the control of the prototype as per the charging profile of EV batteries, as the application of the proposed LLC converter is not limited to EV charging requirements, but also feasible for any application that require wide voltage range.In future work, the detailed operation and control of the proposed topology according to the charging profile of the EV battery will be discussed and analyzed.
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.

Conclusions
In the proposed work, a novel idea to regulate output voltage has been introduced by utilizing an additional auxiliary switch at the secondary side and controlling its PWM.The proposed resonant LLC converter maximizes the converter efficiency by ensuring the ZVS and ZCS condition of MOSFETs and power diodes.A 1 kW prototype has been constructed to verify the concept that matches the power ratings of a typical Level 1 EV charger.The measured peak efficiency of the constructed prototype is 96.8% for the output voltage of 400 V at 100 kHz.The experimental results verify the load independent voltage regulation of the proposed topology.The proposed work doesn't explain the control of the prototype as per the charging profile of EV batteries, as the application of the proposed LLC converter is not limited to EV charging requirements, but also feasible for any application that require wide voltage range.In future work, the detailed operation and control of the proposed topology according to the charging profile of the EV battery will be discussed and analyzed.

Figure 1 .
Figure 1.Gain analysis of a typical LLC resonant converter.

Figure 1 .
Figure 1.Gain analysis of a typical LLC resonant converter.

Figure 5 .
Figure 5. Voltage gain in PWM mode versus equivalent RL and D.

Figure 6 .
Figure 6.Gain curves of the proposed converter under pulse frequency modulation (PFM) in FM.

Figure 5 .
Figure 5. Voltage gain in PWM mode versus equivalent R L and D.

Figure 5 .
Figure 5. Voltage gain in PWM mode versus equivalent RL and D.

Figure 6 .
Figure 6.Gain curves of the proposed converter under pulse frequency modulation (PFM) in FM.Figure 6. Gain curves of the proposed converter under pulse frequency modulation (PFM) in FM.

Figure 6 .
Figure 6.Gain curves of the proposed converter under pulse frequency modulation (PFM) in FM.Figure 6. Gain curves of the proposed converter under pulse frequency modulation (PFM) in FM.

r C r L m D 1 D 2 C o1 S 4 S 3 V bat D 3 n:1 S 2 S 1 v ab V DC v tx i r i s i Lm v Cr C o2 S 5 v cd i D3 i s5 Figure 2. Proposed
Pulse-width modulation (PWM)-LLC Topology with reconfigurable structure. L

Table 1 .
Forward mode Control and Configuration Characteristics.

Table 1 .
Forward mode Control and Configuration Characteristics.

v gs v gs v ab v ds5 i s i r i D2 v cd i Lm i D3 i s5 v gs2 ,v gs3 v gs1 ,v gs4 tdelay v gs5 0.5tdelay dT s Figure 3.
Operational Principle in PWM mode.

t 0 t 1 t 2 t3 t5 t6 t7 t8 t4 v gs v gs v ab v ds5 i s i r i D2 v cd i Lm i D3 i s5 v gs2 ,v gs3 v gs1 ,v gs4 tdelay v gs5 0.5t delay dT s Figure 3.
Operational Principle in PWM mode.

Table 2 .
Design Parameters of the Prototypes.

Table 2 .
Design Parameters of the Prototypes.

Table 2 .
Design Parameters of the Prototypes.

Table 2 .
Design Parameters of the Prototypes.