Control Design and Performance Analysis of a Double-Switched LLC Resonant Rectifier for Unity Power Factor and Soft-Switching

This paper presents and analyzes an AC-DC power converter structure, which is comprised of a Power Factor Correction (PFC) module and a LLC resonant DC-DC converter module. This converter only uses two switches, and requires three less diodes and one less switch compared to popular LLC resonant converter solutions. Compared to its conventional counterpart, the rectifier of interest has high energy efficiency while a smaller size, owing to the soft-switching in the LLC resonant converter. Detailed theoretical analyses are conducted in this study, followed by software simulation and hardware experimentation, which demonstrate that the single stage double-switched (DS)-LLC rectifier is able to realize unity power factor and a wide output range, indicating its effectiveness and applicability.


I. INTRODUCTION
Due to unique advantages, LED lighting has been recognized as the most promising fourth-generation lighting solution, which has seen rapid development in recent years [1]- [3].
However, low efficiency and high cost are deemed the biggest problems in current LED drivers, especially for highfrequency operations. LLC resonant converter can realizes Zero Voltage Switch (ZVS) turn-on of switching transistor, Zero Current Switch (ZCS) turn-off of rectifier diode for wide-range inputs and loads [4], [5], low voltage stress of switching transistors and rectifier diodes [6], [7] and low switching loss, which can eliminate the reverse recovery problem of the rectifier diode, reduce the diode loss and improve the efficiency of the converter [8]. With these favorable features, LLC resonant converters are often used as LED drivers in high-frequency conditions.
Usually, a rectifier is placed before the LLC resonant converter. The single-phase AC-DC converters with isolated The associate editor coordinating the review of this manuscript and approving it for publication was Tariq Masood . transformers have been widely applied to LED power supplies [9] as shown in Fig. 1(a). As a result, the diode rectifiers draw highly distorted current from the AC power source, leading to a poor input power factor (PF) [10], as shown in Fig. 1(b). Additionally, the traditional Switch Mode Power Supply (SMPS) with a rectifier bridge connected with the power grid suffers the distortion of the input current and generates a large number of harmonics, which deteriorates the input PF and can cause electromagnetic interferences (EMI) [11].
In order to reduce the harmonics and EMI pollution to the power grid, a pre-stage Boost PFC circuit can be introduced and connected with the diode bridge to shape the input AC current to be sinusoidal and in phase with the AC voltage [12]- [14].
Compared to other PFC solutions, the Boost PFC topology, as shown in Fig. 2 [15]- [17], has many advantages, such as simple structure, high PF and low EMI [18]- [20]. Thus it has had the widest adoption in the LED lighting industry [21]. As shown in Fig. 3, combined with a traditional LLC resonant converter, PFC function and a wide output range can be   achieved, and the voltage stress of the two power switches is proven to be reduced. Thus this topology has served as a prevailing LED lighting driver candidate [21], [22]. However, the above converter structure is normally composed of a diode bridge rectifier, a PFC stage and a DC-DC LLC resonant converter, which bears the disadvantages of needing too many switches, high component cost and energy waste. The same problem happens to the circuits such as [23] and [24], both of which use too many diodes, causing unnecessary energy loss due to forward voltage drop. It is therefore important to introduce a new converter topology that can solve these shortcomings whilst having a simple structure with fewer components.
Aware of the above issues, in this paper, we present and analyze a single-stage Double-Switched LLC AC-DC resonant converter that requires fewer components and has higher energy efficiency. This topology only requires two switches, which is realized through the pre-stage Boost topology and the LLC resonant converter sharing two common switches. The DS-LLC AC-DC resonant converter can realize both PFC and LLC functions with two fewer diodes compared with the converters in [23], [24]. Thus the original double-stage structure is reduced into a single-stage AC-DC topology. In addition, the number of diodes used in this converter is also smaller than that in the conventional topology. In order to verify the functionality and effectiveness of the DS-LLC resonant converter, simulation and experimentation are conducted in this study, which show great agreement with theoretical analyses, demonstrating the superiority of the presented converter over the conventional ones and also its wide applicability in energy conversion.
The remainder of the paper is organized as follows. In Section II, the working principle of the DS-LLC resonant converter is detailed, followed by the description of power factor correction function by this converter in Section III. Then, the matching design of switching frequency and the closed-loop design is elaborated in Section IV and Section V, respectively. Simulation and experimentation are presented in Section VI. Lastly, this paper concludes in Section VII.

II. WORKING PRINCIPLE OF OF THE DS-LLC CONVERTER
The DS-LLC resonant AC-DC converter is shown Fig. 4, and its working principle is analyzed as follows.

A. TOPOLOGY OF DS-LLC AC-DC RESONANT CONVERTER
As shown in Fig. 4, the converter is composed of a singlephase PFC circuit and a DC-DC LLC resonant converter, which collectively achieve unity PF correction, a wide output range and at the same time AC-DC conversion. Therein, the PFC circuit comprises an inductor L, two switches S 1 and S 2 (including their body diodes and capacitors), two diodes D 1 and D 2 , and a linking capacitor C d , whereas the isolated DC-DC LLC resonant converter is composed of two shared switches S 1 and S 2 , a resonant capacitor C r , a transformer T , two rectifier diodes D O1 , D O2 and an output capacitor filter C O . A transformer T contains the magnetizing inductor L m and leakage inductor L r . With two shared switches being ON and OFF, the introduced converter can realize both PFC and LLC functions.
Compared to the traditional topology which consists of a pre-stage Boost topology and the LLC resonant converter, this topology has the following advantages: • A simpler structure of bridgeless boost PFC to obtain high PF; • One less power switch since PFC circuit stage shares a pair of switches with the LLC resonant converter stage; • High energy efficiency achieved by soft-switching in the LLC resonant stage; 44512 VOLUME 8, 2020 • A wide output range achieved by pulse frequency modulation(PFM) control which can be applied to step-load change and stabilize the output voltage; • A very compact structure and artful design: a resonant capacitor is added to resonate with the resonant inductor which is integrated with the transformer on the magnetic core, so the magnetizing inductor and leakage inductor in the transformer are fully utilized.  TABLE 1 shows switches' ON-OFF statuses in the ten operation modes. Detailed analysis of each mode is described as follows. Mode 1 (t 0 < t < t 1 ): Positive half-cycle begins at t = t 0 , when the switches S 1 and S 2 are off. The diodes D 1 and D 2 are off, and the equivalent circuit is shown as Fig. 6(a). The current flowing into inductor L m , namely i Lm , is equal to the current of resonant inductor L r , namely i Lr . L m starts to resonate with L r and C r , and the primary current of the transformer T , namely i p = 0. Then, diodes D O1 and D O2 turn off due to the endured negative voltage. The output is insulated by transformer T . In loop C O − R O , capacitor C O produces energy, which is consumed by load R O . The resonant current i Lr charges the parasitic capacitor of switch S 2 , namely C S2 , and discharges the parasitic capacitor of S 1 , namely C S1 , creating ZVS conditions [25], [26]. Mode 2 (t 1 < t < t 2 ): At t = t 1 , when the voltage of C S1 , i.e., v CS1 , is smaller than the input voltage v a , diode D 1 turns on, and the inductor L starts absorbing energy and enduring voltage (v a − v CS1 ). The equivalent circuit is shown as Fig. 6(b). Then, v CS1 decreases to 0 at t = t 2 and Mode 2 completes.
The equivalent circuit of Mode 3 is shown in Fig. 6(c), when v CS1 decreases to 0 at t = t 2 . The free-wheel diode of S 1 , namely D S1 , is turned on, which results in Zero-Voltage-Switching (ZVS) turn-on of S 1 . The driving signal of S 1 is on but S 1 is still off because of the clamped diode D S1 . At the same time, the diode D O1 is turned on and primary voltage of T is clamped at nU O , i.e., n (voltage ratio of T ) times of output voltage. Then, the magnetizing inductor L m absorbs energy under the primary voltage nU O . L r and C r are in resonance, and one can obtain i p = i Lr − i Lm . Inductor L absorbs energy and endures voltage v a . When the resonant current i Lr changes from negative to 0, Mode 3 completes.
Mode 4 (t 3 < t < t 4 ): At t = t 3 , Mode 4 as shown in Fig. 6(d) starts. i Lr increases from 0 to positive and S 1 is turned on. Inductor L keeps absorbing energy and enduring voltage v a and L m keeps absorbing energy under the primary voltage nU O . L r and C r are in resonance; meanwhile, D 1 is on, Mode 5 (t 4 < t < t 5 ): At t = t 4 , i Lm = i Lr , then L m , L r and C r resonate. D O1 and D O2 endure negative voltage and then turn off. The output is insulated by transformer T . C O charges load R O , as shown in Fig. 6(e). Meanwhile, the inductor L absorbs energy from the input source.
Mode 6 (t 5 < t < t 6 ): At t = t 5 , S 1 and S 2 are turned off, D O1 and D O2 are also off. The current of inductor L m is equal to the current of resonant inductor L r , and L m starts to resonate with L r and C r . C O produces energy to load R O . Resonant current i Lr charges the parasitic capacitor C S1 , and C S2 discharges. At t = t 6 , v CS1 becomes larger than the VOLUME 8, 2020 input voltage v a , and inductor L releases energy and endures voltage (v CS1 − v a ). Then, when C S2 discharges and v CS2 decreases to 0, D S2 is turned on and Mode 6 ends.
Mode 7 (t 6 < t < t 7 ): In the time-domain operation curves in Fig. 5 at t = t 6 , D S2 turns on, which meets the operating condition for ZVS. The driving signal of S 2 is on but S 2 is still off because of the clamped diode D S2 . The corresponding equivalent circuit is shown in Fig. 6(g), wherein inductor L produces energy to C d under the voltage (v Cd −v a ). Meanwhile, D O2 is turned on, and the primary voltage of T is clamped at −nU O and L m rises linearly. L r and C r are in resonance and one can obtain i p = i Lr − i Lm . Then, when the resonant current i Lr decreased to 0, Mode 6 completes.
Mode 8 (t 7 < t < t 8 ): At t = t 7 as shown in Fig. 6(h), i Lr = 0 and begins to decrease to be negative. Then, S 2 is turned on, and D O2 is also on. Similar to Mode 7, the primary voltage of T is clamped at −nU O and releases energy to L m . L r and C r are in resonance. In the meantime, i Lr goes through L m and the primary side of T , and then transfers energy to R O . L releases energy to C d . When i L decreases to 0 and D 1 endures negative voltage and turns off, Mode 8 finishes.
Mode 9 (t 8 < t < t 9 ): As shown in Fig. 6(i) at t = t 8 , i L = 0 and L m and the primary side of T transfer energy to R O . When i Lm reaches i Lr , Mode 9 completes.
Mode 10 (t 9 < t < t 10 ): As shown in Fig. 6(j), at t = t 9 , i Lm = i Lr and L m begins to take part in resonance. D O1 and D O2 endure negative voltages and turn off. The output is insulated by transformer T , and C O charges load R O .

III. POWER FACTOR CORRECTION OF THE DS-LLC RESONANT CONVERTER
Since a large number of articles have elaborated how LLC resonant converter works in the secondary resonant region such as [27]- [29], this section mainly focuses on the realization of the PFC function. In order to ensure successful power factor correction, it is necessary to increase the inductor current from zero to the peak value and then decrease the inductor current from the peak value to zero within one cycle [30], [31]. Since the implementation of the LLC resonant function requires a constant duty cycle of 0.5, the inductor current needs to be reduced to zero in fixed duty cycle.  Since the LLC resonant converter is equivalent to a load connected to the pre-stage Boost PFC converter, the following LLC resonant converter is simplified as a resistive load in order to explain the realization of PFC, as shown in the Fig. 7. Because the dead zone is much smaller than one switching cycle, the dead zone is ignored. Taking the positive half cycle as an example, when the switch S 1 is turned on and the S 2 is turned off, the operation of the converter is shown in Fig. 8, and the relationship between inductor current and the input voltage can be expressed as: where i L is the inductor current, u L is the inductor voltage, T S is the switching period, v Cd is the voltage of the linking capacitor, and d 1 is the duty cycle during which the inductor current increases. We can obtain that the peak value of the inductor current i LP is where f S is the switching frequency. When switch S 2 is turned on and S 1 is turned off, the operation of the converter is as shown as Fig. 9, and the relationship between inductor current and output voltage of the pre-stage can be expressed as: where d 2 is the duty cycle during which inductor current decreases to zero and U Re is the voltage across R e .  The magnitude of the drop in the inductor current is thus: From (3) and (6), we can get where v a = U m sin ωt.
From the above equations, if PFC is implemented, we will have namely Simplifying formula (9), we can have v Cd > 2U m sin ωt.
Equation (10) indicates that to ensure the functionality of the PFC module, the voltage across the linking capacitor v Cd must be at least twice the peak value of the input voltage v a , i.e., v Cd > 2U m .
In other words, because the slope of the inductor current is proportional to the voltage across it, as shown in the Fig. 10, when the inductor current rises, the slope K 1 is calculated as, VOLUME 8, 2020 and when the inductor current drops, its slope K 2 is Since the duty cycle is constantly 0.5, to ensure the implementation of PFC, it should be ensured that K 1 <-K 2 , i.e., v Cd > 2U m .
Therefore, to ensure the PFC module is functional, the inductor current should be reduced by adjusting v Cd , that is, the energy stored in the inductor is transferred to the linking capacitor v Cd . The following relationship shows the v Cd and other factors, and the average input power of every switching cycle during the positive half-frequency cycle is: where N = T /2T S , T is the period of input voltage. Substituting (3) and (7) into (15), we can have: Since v Cd = U Re , and T S is small enough relative to T , (16) can be expressed as, Since the linking capacitor C d only supplies energy to the load when S 1 is turned on and S 2 is turned off, the output power is obtained as, Suppose the efficiency is 1, namely P in = P out ; one can have Simplifying (19) yields: It can be seen from (20) that when the load R e and frequency f S are constant, if the converter is able to realize the PFC function, the critical value of L is, When R e , f S ,v a are fixed, the relationship between L and v Cd is shown as Fig. 11. Therefore, in order to ensure the realization of PFC, it is necessary to employ inductor values below the critical value of L.
The LLC resonant converter module can be viewed an impedance. When the LLC resonant converter runs in  ZVS or ZCS conditions, it can be regarded as an inductive impedance Z = R + jX , so when applying the above theory, equation (18) can be converted to where ϕ z = arctan(X /R). The relation between v Cd and L can be analyzed with a similar procedure.

IV. FREQUENCY MATCHING
Since the LLC resonant converter works in a wide frequency range, the switching frequency f S may affect the realization of the PFC in pre-stage PFC module. Therefore, before carrying out the simulation and experiment, it is necessary to match the frequency range in which the two functions can be implemented simultaneously. From (21), the relationship between the switching frequency f S and v Cd is shown in Fig. 12: According to the working condition of the PFC in the Boost topology, the voltage of the linking capacitor v Cd should be at least twice as large as the peak value of the input voltage v a , namely U m . Therefore, in order to ensure the implementation of PFC and LLC resonant function, the range of frequency f S can be selected is , f 3 is the critical frequency of the Boost PFC module:  The frequency range that can be selected is shown in Fig. 13.

V. CLOSED-LOOP DESIGN OF THE DS-LLC RESONANT CONVERTER
Since the load often changes, it is necessary to design a control method to stabilize the output voltage in order to adapt to wide output range. According to [32], [33], based on FHA, we can obtain the gain of the LLC resonant converter as: where k = L r /L m , Q = (2πf 1 L r )/(n 2 R O ).
Here, Q = 0.195, and the relationship between G LLC and load R O is shown in the Fig. 14 with the relationship between G LLC and switching frequency f S shown in the same figure.
The voltage across the linking capacitor v Cd in the prestage PFC converter decreases as frequency f S increases. Therefore, when load R O changes, the switching frequency f S can be changed to ensure gain G LLC is constant, and consequently the output voltage U O is constant. The control based on pulse frequency modulation(PFM) is designed as shown in Fig. 15. Through small signal analysis, the open-loop transfer function of the output voltage G fV is obtained as: where Term r CO is the parasitic resistance of the output capacitor C O . The frequency−domain simulation results are shown in Fig. 16. The uncompensated loop gain described in blue lines indicates a poor system response. Therefore, a PI compensator is used to increase the dynamic response, and the preferred crossover frequency of the output voltage loop is chosen as 1/9 of the stable switching frequency, namely 8.9kHz. The transfer function of the PI compensator is where k p and k i are the proportional and integral gains. The parameters of the PI compensated loop gain are chosen as k p = 2.24 × 10 12 and k i = 1.44 × 10 17 . The compensated loop gain of the output voltage loop is shown in Fig. 16 in red lines. It can be seen that the compensated loop gain has a crossover frequency of 8.92kHz with a phase margin of 50.3 • , which indicates a better dynamic response. VOLUME 8, 2020

VI. SIMULATION AND EXPERIMENTATION
In order to verify the functionality of the DS-LLC resonant AC-DC converter, simulation is conducted using PSIM software. Simulation parameters of the LLC converter are shown in TABLE 2. According to (17), in order to ensure the realization of PFC, the expression of the critical Boost inductor L can be obtained as: Therefore, we set the Boost inductor L value as 47µH.

A. SIMULATION RESULTS
As shown in Fig. 17, the DS-LLC resonant converter can realize Boost PFC function, where the input AC current is sinusoidal and in phase with the AC voltage. In the magnified figure, the rising slope of the input current is smaller than the absolute value of the falling slope. Therefore, the inductor current can fall to zero in the second half of the switching cycle after rising in half a switching cycle,   meaning that the PFC is realized, which is consistent with the theory.
With the LLC resonant converter, the DS-LLC resonant converter realizes ZVS of MOS transistors S 1 and S 2 , as shown in Fig. 18. The source-drain voltages of the switches S 1 and S 2 drop to zero before the rising edge of the driving voltage V GS , indicating that the switches S 1 and S 2 achieve zero-voltage-switch turn-on. Besides, zero-currentswitch turn-off is realized in both rectifier diodes D O1 and D O2 on the secondary side of transformer, as shown in Fig. 19. The diodes D O1 and D O2 on the secondary side of the transformer are alternately turned on, and both of them are turned on after the current of the other one drops to zero, achieving zero-current-switch turn-off.
The above simulation results verify the function of the PFC and LLC resonant converter.

B. EXPERIMENTATION
With the same parameters used in the simulation, the corresponding experiments based on IC L6599 and STM32F103 are conducted in a prototype established in this study, which is shown in Fig. 20.
The experimental results of the PFC function are shown in Fig. 21, where it can be observed that the Boost PFC function is achieved. Refining the waveform, it can be seen that the rising slope of the input current is smaller than the absolute value of the falling slope, which is consistent with the theory and the simulation results, and is also key to the successful realization of the PFC.
Figs. 22 and 23 show the waveform of the realization of ZVS condition in switches S 2 (the ZVS condition in switches S 1 is the same as S 2 ) and the ZCS of rectifier diodes D O1 and D O2 on the secondary side of the transformer, which proves the soft switching functionality of these switches.
On the same parameters, we conducted a step-load-change experiment. The load changes from 60 to 100 (where the maximum voltage when the load is 60 and the frequency is minimum is equal to the minimum voltage when the load is 100 and the frequency is maximum). As shown in Fig. 24, when a sudden change occurs in the load, the output voltage can be adjusted quickly by the PFM control to stabilize the voltage. The result of this experiment well verifies the wide output range feature of this converter, because the output voltage is adjusted by the switching frequency f S and    then stabilized at the voltage levels before the load changes. In other words, we can get different voltage level by adjusting the switching frequency f S , hence a wide output range.
The efficiency of the LLC resonant converter is shown in Fig. 25. Therefore, the experiment results are consistent with the simulation and theory, and have shown the functionality and advantages of this converter.

VII. CONCLUSION
In this paper, we have presented and analyzed a single-stage double-switched AC-DC power converter, which has softswitching functions for power switches, nearly unity power factor and a wide output range. In particular, two switches are shared by the PFC converter and the LLC resonant converter for size reduction and cost saving. Detailed analyses, including operational modes, mathematical deduction of the Boost PFC, the frequency matching design and the closed-loop control design, have been presented in this paper. Finally, simulation and experimental results have well verified the feasibility and effectiveness of the introduced converter, which is envisioned to have wide applicability in the LED driver industry.