Optimal Design of Multi-Output LLC Resonant Converter with Independently Regulated Synchronous Single-Switched Power-Regulator

: This paper presents a tightly regulated multi-output isolated converter that employs only an independently regulated synchronous Single-Switched Post-Regulator (SSPR). The proposed converter is a highly accurate single-ended secondary side post-regulator based on a Series Resonant Converter (SRC); furthermore, it has a voltage-doubler characteristic. The proposed post-regulator requires only one auxiliary switch, in contrast with a bulky and expensive non-isolated DC–DC converter. Moreover, the added voltage-doubler can tightly regulate the slave output current. In addition, the voltage-doubler can improve electromagnetic interference characteristics and reduce switching losses arising from the Zero Current Switching (ZCS) operation of all power switches. The validity of the proposed converter is veriﬁed using experimental results obtained via a prototype converter applicable to an LED 3D TV power supply.


Introduction
Liquid crystal display (LCD) TVs are witnessing a rapid change in backlighting technology, from cold cathode fluorescent lamps (CCFLs) to LEDs. There are several attributes of LEDs that justify this change: improved contrast ratios, mercury-free operation, and relatively low power consumption.
As internal power supply units are used in most LCD TVs, designing slim systems with high-efficiency power supplies at appropriate costs for the LCD TV consumer market continues to present a formidable challenge for the power electronics industry. LCDs are, by far, the most widely produced and sold television display type. LCD screens, which are energy efficient, are available in a wider range of screen sizes than cathode-ray tube and plasma displays. Each of the functional blocks in an LCD TV, such as the audio technology, backlighting, and video and audio signal processors, requires a particular power solution. Therefore, several voltage lines are required to power each of the functional blocks. The backlight is the most power consuming sub-system within a flat TV. Although there are several backlighting technologies, ranging from plasma technology to CCFL, the current trend is towards an LED backlight solution for LCD TVs that allows for slim cabinets. It is challenging for TV manufacturers to select an architecture that allows for design optimization without also increasing cost and circuit complexity. Generally, manufacturers employ a universal power supply that supports a voltage range of AC90-264 V. This allows one power supply design for a specific TV size to be used for a series of models, leading to reduced development costs.  With LCD TVs trending towards slimmer designs, a high end-to-end efficiency is paramount. Adding additional power processing stages limits the overall performance and adds overhead to the drive architecture. Accordingly, efficient and cost-effective LED driver circuits that eliminate intermediate stages have gained increased attention from the industry [1][2][3]. Additionally, with the continuous advancements in LED technology and performance, TV architectures (e.g., LED string With LCD TVs trending towards slimmer designs, a high end-to-end efficiency is paramount. Adding additional power processing stages limits the overall performance and adds overhead to the drive architecture. Accordingly, efficient and cost-effective LED driver circuits that eliminate intermediate stages have gained increased attention from the industry [1][2][3]. Additionally, with the continuous advancements in LED technology and performance, TV architectures (e.g., LED string Energies 2020, 13, 4341 3 of 15 voltages and current tolerances) are continuously changing; hence, a modular power supply solution that is easily adaptable to such changes can significantly reduce the design cycle time. Figure 1 shows a schematic of a conventional multi-output LED driving circuit [4]. The resonant converter controls only one master output, and the slave output is not controllable. To manage this issue, a conventional LED application requires an additional power regulator, e.g., a buck converter or boost converter. However, adding the post-regulator results in increased power dissipation and cost. Figure 2 shows the primary side of the proposed converter, which is the same as a conventional inductor-inductor-capacitor (LLC) resonator converter. However, the secondary side of the proposed converter consists of a rectifier diode, one output capacitor, and one auxiliary switch, instead of an expensive secondary post-regulator, i.e., boost converter, as shown in Figure 1 [5][6][7][8][9][10][11].
Energies 2020, 13, x FOR PEER REVIEW 3 of 16 voltages and current tolerances) are continuously changing; hence, a modular power supply solution that is easily adaptable to such changes can significantly reduce the design cycle time. Figure 1 shows a schematic of a conventional multi-output LED driving circuit [4]. The resonant converter controls only one master output, and the slave output is not controllable. To manage this issue, a conventional LED application requires an additional power regulator, e.g., a buck converter or boost converter. However, adding the post-regulator results in increased power dissipation and cost. Figure 2 shows the primary side of the proposed converter, which is the same as a conventional inductor-inductor-capacitor (LLC) resonator converter. However, the secondary side of the proposed converter consists of a rectifier diode, one output capacitor, and one auxiliary switch, instead of an expensive secondary post-regulator, i.e., boost converter, as shown in Figure 1 [5][6][7][8][9][10][11]. The secondary side of the proposed converter also comprises a single-switched post-regulator with voltage-doubler characteristics as shown in Figure 2, and the proposed voltage doubling method improves the stable cross-regulation performance under the high load conditions of LED Back Light Unit (BLU) power and low load conditions of image power. Thus, one simple control loop can be used to control the LED string currents to further simplify the design. An additional benefit of the proposed scheme is that it can be readily modified for a different number of LED strings/combinations.
In this paper, to overcome the aforementioned drawbacks, high efficiency and cost-effective current balance LED drivers are proposed, as shown in Figure 2. In addition, experimental results are presented to verify the theoretical analysis and effectiveness of the proposed converter.

Control Method for Proposed Converter
The basic concept described in the paper is to supply the rectified secondary current directly driving the LED string and the regulated current to a single series transformer. As shown in Figure  2, the proposed post-regulator should be synchronized with the switching voltage of the secondary winding. Figure 3 shows the manner in which the proposed initial current control regulation is performed for one LED channel. The gating signal of the auxiliary switch is synchronized with the primary side switch to ensure zero voltage switching [12][13][14]. The secondary side of the proposed converter also comprises a single-switched post-regulator with voltage-doubler characteristics as shown in Figure 2, and the proposed voltage doubling method improves the stable cross-regulation performance under the high load conditions of LED Back Light Unit (BLU) power and low load conditions of image power. Thus, one simple control loop can be used to control the LED string currents to further simplify the design. An additional benefit of the proposed scheme is that it can be readily modified for a different number of LED strings/combinations.
In this paper, to overcome the aforementioned drawbacks, high efficiency and cost-effective current balance LED drivers are proposed, as shown in Figure 2. In addition, experimental results are presented to verify the theoretical analysis and effectiveness of the proposed converter.

Control Method for Proposed Converter
The basic concept described in the paper is to supply the rectified secondary current directly driving the LED string and the regulated current to a single series transformer. As shown in Figure 2, the proposed post-regulator should be synchronized with the switching voltage of the secondary winding. Figure 3 shows the manner in which the proposed initial current control regulation is performed for one LED channel. The gating signal of the auxiliary switch is synchronized with the primary side switch to ensure zero voltage switching [12][13][14].
The output voltage V o1 can be controlled by determining the switching frequencies of M 1 and M 2 , as in a conventional LLC resonant converter [15][16][17][18]. However, i o2 is controlled by the turn-on point of M 3 when M 2 is turned on. That is, although M 2 is conducting and −v CR is applied to the primary side of the transformer, M 3 , which is turned off, prevents the input power from being transferred to the output side. At this time, D 4 and D 5 are turned on and charged to C 1 and C 2 , respectively. Therefore, resonance does not occur between C R and L R , i sec2 is maintained at zero, and the initial current I ini decreases with the slope of −v CR /(L R + L M ). When M 3 is turned on with M 1 conducting, the secondary-side diode D 3 is turned on, and simultaneously, the resonant current between C R and L R is transferred to the output side of the converter. At this point, in the case that M 3 is turned on earlier, the resonant current i pri(t) is increased further, owing to the larger initial value I ini , which causes the output current i o2 to increase. In contrast, the resonant current i pri(t) decreases more when M 3 is turned on later.
Energies 2020, 13  The output voltage Vo1 can be controlled by determining the switching frequencies of M1 and M2, as in a conventional LLC resonant converter [15][16][17][18]. However, io2 is controlled by the turn-on point of M3 when M2 is turned on. That is, although M2 is conducting and −vCR is applied to the primary side of the transformer, M3, which is turned off, prevents the input power from being transferred to the output side. At this time, D4 and D5 are turned on and charged to C1 and C2, respectively. Therefore, resonance does not occur between CR and LR, isec2 is maintained at zero, and the initial current Iini decreases with the slope of −vCR/(LR + LM). When M3 is turned on with M1 conducting, the secondary-side diode D3 is turned on, and simultaneously, the resonant current between CR and LR is transferred to the output side of the converter. At this point, in the case that M3 is turned on earlier, the resonant current ipri(t) is increased further, owing to the larger initial value Iini, which causes the output current io2 to increase. In contrast, the resonant current ipri(t) decreases more when M3 is turned on later.

Analysis of Operational Modes
The main waveforms are shown in Figure 4. The proposed converter operates in five modes [19] according to the conduction state of each switch (M1, M2, and M3), as shown in Figure 5.

Analysis of Operational Modes
The main waveforms are shown in Figure 4. The proposed converter operates in five modes [19] according to the conduction state of each switch (M 1 , M 2 , and M 3 ), as shown in Figure 5.  For the expediency of mode analysis in a steady state, several assumptions are made, as follows.
(1) The switch is ideal, except for the internal diode.
(2) The transformer is ideal, except for the magnetizing inductance L m and leakage inductance L R .
(3) The output capacitors C o1 and C o2 are large enough to be considered as constant DC voltage sources V o1 and V o2 , respectively. (4) The switching transition interval between M 1 and M 2 is small enough to be ignored.
It is assumed that the switch M 1 is conducting before t 0 and that a transformer magnetizing current i Lm flows through M 1 , as shown in Figure 4. Figure 4. Key waveforms of proposed converter. For the expediency of mode analysis in a steady state, several assumptions are made, as follows. When the current of the resonant inductor L R flows through the body diode of M 2 , I pri starts to rise. As the voltage V IN -v CR across the primary side of the transformer is higher than the reflected output voltage (N P /N S1 )V o1 , D 1 is turned on. Concurrently, the transformer primary current i pri starts to increase, based on the resonance between C R and L R . The magnetic current i Lm increases linearly as the reflected output voltage (N P /N S1 )V o1 is applied to L m . Therefore, it does not participate in the resonance during this period. In this mode, the circuit operates as a series resonant converter (SRC), with a resonant inductor L R and resonant capacitor C R . This mode is terminated when the L R current is the same as the L m current. Mode 2 [t 1 -t 2 ]: When the transformer primary current i pri becomes equal to i LM and i sec1 reaches zero at t 1 , Mode 2 begins. At this moment, D 1 is blocked, and V IN -v CR is applied to L M + L R . The value of i pri is still increasing owing to the resonance between C R and L M + L R , as shown in Figure 5c, and the primary current i pri is still increasing, based on the resonance between C R and L m + L R .
Mode 3 [t 2 -t 3 ]: When M 2 is turned off and M 1 is turned on at t 2 , Mode 3 begins. Although M 1 is conducting and −v CR is applied to the primary side of the transformer, the turned off M 3 prevents the input power from being transferred to the output side. Therefore, resonance does not occur between C R and L R , i sec2 is maintained at zero, and the initial current I ini decreases with the slope of −v CR /(L R + L m ).
The primary current i pri decreases in the same manner as the resonance between C R and L M + L R .

Mode 4 [t 3 -t 4 ]:
When M 3 is turned on at t 3 , Mode 4 starts, as shown in Figure 4. D 3 is turned on because the voltage v CR is higher than the reflected output voltage (N P /N S2 )V o2 . Concurrently, the primary current begins to decrease owing to the resonance between C R and L R . In addition, the reflected output voltage −(N P /N S2 )V o2 is applied to L M , causing the magnetizing current i LM to decrease linearly.

Output Voltage Analysis
For convenience of analysis, it is assumed that the dead time between M 1 and M 2 is zero, and that i LM linearly increases or decreases with the slope of V o1 /n 1 L M or −V o2 /n 2 L M , respectively.
As shown in Figure 6, the steady-state offset current i LM through L M can be obtained as:  Figure 6. Waveforms of resonant current ipri(t) and voltage vCR(t) for steady state.
Here n1 = Ns1/Np and n2 = Ns2/Np, respectively. From Equation (1), the values of Ip and Iv can be expressed as follows: Here, Ts is the switching period. Moreover, iLM1 and iLM2 can be obtained from Equations (4) and (5), as follows: Here n 1 = N s1 /N p and n 2 = N s2 /N p , respectively. From Equation (1), the values of I p and I v can be expressed as follows: Here, T s is the switching period. Moreover, i LM1 and i LM2 can be obtained from Equations (4) and (5), as follows: Furthermore, when M 2 is conducting, the difference between i pri and i LM1 is transferred to the output side as i sec1 . Similarly, when M 1 is conducting, the difference between i pri and i LM2 is transferred to the output side as i sec2 . From Equations (2), (6), and (7), i sec1 during t 0 -t 1 and i sec2 during t 3 -t 4 can be obtained as follows: In the equations above, ω is the angular frequency. Therefore, the output load currents I o1 and I o2 can be calculated from the mean values of i sec1 and i sec2 , respectively, as follows: Here, D' is the turn-off duty ratio of the switch M 3 . From Equations (10) and (11), where t rs = t r − D'T s , the output voltages V o1 and V o2 can be obtained, as follows: Here, the variables α, β, γ are defined:

Simplified Design Guidelines
The design of resonant components such as L R , L M , and C R always involves a compromise between the maximum load variation, maximum allowable operating frequency deviation, maximum input voltage range, circulating energy in the resonant circuit, and short-circuit characteristics. The optimal operating point of the converter can be reached for a given input voltage and load resistance. Therefore, in practice, a converter is typically designed using operating conditions such as a high resonant frequency and maximum DC-link voltage. In the design of an LLC topology, it is crucial that the manufacturing tolerances of the inductors and capacitors are higher than those in standard productions.
(1) Switching frequency (f s ) The switching frequency of the converter is determined based on the total losses of the switches and transformer. Generally, a higher switching frequency selection results in a lower magnetic flux; thus, the core size, as well as the core loss, can be reduced. However, a higher switching frequency also results in a higher AC loss on the winding of the transformer and a turn-off loss on the switches, reducing the converter efficiency. As a result, the selection of the switching frequency is a trade-off between these two effects. The trade-off depends on the power rating, type of semiconductor, and operating range of the converter.
(2) Resonant tank frequency (f n ) One goal is to minimize the resistive losses in the duration of the circulating stages of Mode 2 and Mode 5, as shown in Figure 4. This can be achieved by setting the frequency ratio f n of the switching frequency (f s ) to the resonant frequency of the resonant tank (f r ) smaller than (but close to) unity.
This frequency ratio is designed such that the converter can be operated at a switching frequency between f r2 and f r1 , where f r2 and f r1 are determined by {(L M + L R ) and C R } and {L R and C R }, respectively. This operating point is located in Region 2, as shown in Figure 7 [19].  In Figure 7, Region 1 is the SRC operation region. The converter operates in this region when the switching frequency is higher than fr1. The magnetizing inductance does not participate in the resonance, and a ZVS condition is naturally assured. Region 2 is the multi-resonant converter region. The load condition between fr1 and fr2 determines the operation of the converter under ZVS and zero current switching (ZCS) conditions.
In this region, the energy stored in the magnetic components triggers ZVS for the opposite Metal Oxide Semiconductor Field Effect Transistor (MOSFET). Region 3 is an overloaded region. In this area, the converter enters the ZCS mode. In general, the LLC resonant converter is designed to operate in Regions 1 and 2, owing to output regulation and ZVS operation. To ensure ZVS operation, the operating range of the converter should be above fr2. Therefore, LR and CR are chosen to be guaranteed under a heavy load. The selection of LM determines the switching frequency range and In Figure 7, Region 1 is the SRC operation region. The converter operates in this region when the switching frequency is higher than f r1. The magnetizing inductance does not participate in the resonance, and a ZVS condition is naturally assured. Region 2 is the multi-resonant converter region. The load condition between f r1 and f r2 determines the operation of the converter under ZVS and zero current switching (ZCS) conditions.
In this region, the energy stored in the magnetic components triggers ZVS for the opposite Metal Oxide Semiconductor Field Effect Transistor (MOSFET). Region 3 is an overloaded region. In this area, Energies 2020, 13, 4341 9 of 15 the converter enters the ZCS mode. In general, the LLC resonant converter is designed to operate in Regions 1 and 2, owing to output regulation and ZVS operation. To ensure ZVS operation, the operating range of the converter should be above f r2 . Therefore, L R and C R are chosen to be guaranteed under a heavy load. The selection of L M determines the switching frequency range and the MOSFET turn-off current. The smaller the value of L M , the narrower the operating range. However, the MOSFET turn-off current will be higher, increasing the switching loss. The ZVS operation of the MOSFETs and the ZCS operation of the output auxiliary switches are particularly important for the efficiency and optimal design of the LLC resonant converter. In Figure 6, the primary current is always negative at t 0 , ensuring that M 2 operates under a ZVS condition. In addition, M 1 always operates under the ZVS condition, owing to the positive I p . Therefore, the ZVS condition of the two power switches depends on the magnetizing inductance L M and dead time duration t dt , as follows: From Equation (6), the limitation of the magnetizing inductance can be derived as follows: Here, t dt is the dead time and C ds is the equivalent capacitance of the MOSFETs. The magnetizing inductor needs to be small enough to achieve the ZVS condition, and large enough to reduce the turn-off losses. Therefore, in an optimal design, L M should have the maximum value that meets the ZVS requirement. Figure 8 shows a flow chart for the optimal design of inductor-inductor-capacitor (LLC) resonance tank. The following is the step-by-step design guide line.

Optimal Design of the LLC Resonant Converter
Step 1. Refer to the above "(1) Switching frequency (f s ) (2) Resonant tank frequency (f n )" and select the switching frequency range. The converter is designed to operate in Region 2 at high and low input voltages to minimize switching loss due to hard-switching. For ZCS operation of the secondary-side output rectifier, switching frequency f s shall be lower than resonant frequency f r1 . The limit of f r is defined as follows.
Step 2. When Q decreases (load decrease) higher peak gains are obtained. In addition, the important factor determining peak gain is the ratio between L M /L R . The ratio between L M /L R and quality factor is defined as follows.
Step 3. The turn ratio n should be calculated from the relationship between the input and output voltages.
Step 4. The magnetizing inductance needs to be small enough to achieve the ZVS condition, and large enough to reduce the turn-off losses. From Equation (14), the limitation of the magnetizing inductance can be derived as: Energies 2020, 13, 4341 10 of 15 Step 5. The leakage inductance can be calculated from Equation (15) and as follows: Here, n is transformer turns ratio and R ac is AC equivalent load resistance, R ac = 8n 2 π 2 R o , n = N P N s .
Step 7. The resonant capacitor can be calculated from Equation (15) and as follows: Energies 2020, 13, x FOR PEER REVIEW 11 of 16 Figure 8. Flowchart for optimal design of inductor-inductor-capacitor (LLC) resonance tank.

Experimental Results
To verify the feasibility of the proposed converter, a prototype of a 120 W output power converter for LED 3D TVs is implemented. The prototype of the proposed LED driver is shown in Figure 9.  Table 1 shows the design specifications and circuit parameters for the prototype. Table 2 shows a comparison between the conventional and proposed circuits, in terms of the number of components.

Experimental Results
To verify the feasibility of the proposed converter, a prototype of a 120 W output power converter for LED 3D TVs is implemented. The prototype of the proposed LED driver is shown in Figure 9.

Experimental Results
To verify the feasibility of the proposed converter, a prototype of a 120 W output power converter for LED 3D TVs is implemented. The prototype of the proposed LED driver is shown in Figure 9.  Table 1 shows the design specifications and circuit parameters for the prototype. Table 2 shows a comparison between the conventional and proposed circuits, in terms of the number of components. As shown in Table 2, the proposed converter has fewer components than the number of components in the conventional converter owing to the absence of the additional non-isolated DC-DC converter.  Table 1 shows the design specifications and circuit parameters for the prototype. Table 2 shows a comparison between the conventional and proposed circuits, in terms of the number of components. As shown in Table 2, the proposed converter has fewer components than the number of components in the conventional converter owing to the absence of the additional non-isolated DC-DC converter. Figure 10 shows the ZCS operating waveforms of the proposed converter; when M 3 is turned on, the resonant current of the primary side starts flowing. It is clear that ZCS is ensured, based on the zero current at the end of the ICR switching.

Item
Conventional     Figure 11 shows the experimental waveforms at 2D (99%, 10%, 1%, and 0.2%) and 3D (10% and 1%) dimming ratios. As shown in Figure 11, the LED current becomes zero for the low dimming signal, and it is exactly controlled to be 2D_210 mA and 3D_630 mA for the high dimming signal. Moreover, although the proposed LED driver comprises only a few components, the current through the LED array is well-controlled and balanced according to all of the dimming ratios.  Figure 11 shows the experimental waveforms at 2D (99%, 10%, 1%, and 0.2%) and 3D (10% and 1%) dimming ratios. As shown in Figure 11, the LED current becomes zero for the low dimming signal, and it is exactly controlled to be 2D_210 mA and 3D_630 mA for the high dimming signal. Moreover, although the proposed LED driver comprises only a few components, the current through the LED array is well-controlled and balanced according to all of the dimming ratios. Based on Table 1, Figure 12 shows the total efficiency of the power system from AC to the final LED backlight (AC EMI + PFC + DC/DC + LED backlight driver) and the efficiency of each stage is also compared. Efficiency measurements are efficiency data according to LED dimming conditions as shown in Figure 11. This is a measure of operating from dark to full brightness on a TV screen.   Figure 12 shows the total efficiency of the power system from AC to the final LED backlight (AC EMI + PFC + DC/DC + LED backlight driver) and the efficiency of each stage is also compared. Efficiency measurements are efficiency data according to LED dimming conditions as shown in Figure 11. This is a measure of operating from dark to full brightness on a TV screen. Assuming that the components not specified in Figure 12 have similar power consumptions, the proposed driver shows a lower consumption by approximately 1.74 W power loss than the conventional driver. Probably of the most importance is the high efficiency with this LLC topology that allows slim power supply designs. LED string current control is achieved using the LLC resonant half bridge topology in current mode control. Typical efficiency for the proposed converter in TV application is shown in Figure 12; the total efficiency from AC to backlight can be achieved by more than 90% with this architecture.

Conclusions
In this paper, optimal design of a multi-output LLC resonant converter with an independently regulated synchronous single-switched power-regulator is proposed. As an isolated DC-DC converter and LED drivers are integrated into one power stage in the proposed LED driver system, it consists of two cascaded power stages. The proposed post-regulator requires only one auxiliary switch, in contrast with a bulky and expensive non-isolated DC-DC converter Through the analysis of the control method for the proposed converter, the simplified design guidelines and magnetizing inductance are designed to obtain soft switching capability. The proposed driver system features a relatively low cost, simple structure, high efficiency, and high power density. In addition, it can ensure the ZVS operation of power switches and the ZCS operation of output auxiliary switches along the entire load range. It has highly desirable advantages, such as reduced switching losses and heat generation.
Finally, through the experimental results it can be seen that very fast LED rise and fall currents can be achieved with this control scheme that allow excellent linearity performance under any dimming conditions. The proposed converter is simple and achieves excellent dimming current control between multiple outputs, and the highest AC to backlight efficiency. The PSIM simulation and experimental results using the prototype converter verified the validity of the proposed architecture.  Probably of the most importance is the high efficiency with this LLC topology that allows slim power supply designs. LED string current control is achieved using the LLC resonant half bridge topology in current mode control. Typical efficiency for the proposed converter in TV application is shown in Figure 12; the total efficiency from AC to backlight can be achieved by more than 90% with this architecture.

Conclusions
In this paper, optimal design of a multi-output LLC resonant converter with an independently regulated synchronous single-switched power-regulator is proposed. As an isolated DC-DC converter and LED drivers are integrated into one power stage in the proposed LED driver system, it consists of two cascaded power stages. The proposed post-regulator requires only one auxiliary switch, in contrast with a bulky and expensive non-isolated DC-DC converter Through the analysis of the control method for the proposed converter, the simplified design guidelines and magnetizing inductance are designed to obtain soft switching capability. The proposed driver system features a relatively low cost, simple structure, high efficiency, and high power density. In addition, it can ensure the ZVS operation of power switches and the ZCS operation of output auxiliary switches along the entire load range. It has highly desirable advantages, such as reduced switching losses and heat generation.
Finally, through the experimental results it can be seen that very fast LED rise and fall currents can be achieved with this control scheme that allow excellent linearity performance under any dimming conditions. The proposed converter is simple and achieves excellent dimming current control between multiple outputs, and the highest AC to backlight efficiency. The PSIM simulation and experimental results using the prototype converter verified the validity of the proposed architecture.