LLC LED Driver with Current-Sharing Capacitor Having Low Voltage Stress

In this paper, an LLC light-emitting diode (LLC LED) driver based on the current-sharing capacitor is presented. In the proposed LED driver, the LLC resonant converter is used to step down the high input voltage, to provide galvanic isolation, to offer a constant current for LEDs. Moreover, the current-sharing capacitor connected to the central-tapped point of the secondary-side winding is used to balance the currents in two LED strings. By doing so, the voltage stress on this capacitor is quite low. Above all, the equivalent forward voltages of the two LED strings are generally influenced by the temperature and the LED current, and this does not affect the current-sharing performance, as will be demonstrated by experiment on the difference in number of LEDs between the two LED strings. In addition, only the current in one LED string is sensed and controlled by negative feedback control, while the current in the other LED string is determined by the current-sharing capacitor. Moreover, this makes the current control so easy. Afterwards, the basic operating principles and analyses are given, particularly for how to derive the effective resistive load from the LED string. Eventually, some experimental results are provided to validate the effectiveness of the proposed LED driver.


Introduction
As compared with the traditional lighting sources, like the incandescent lights, fluorescent lights, and halogen lights, etc., the high-brightness lighting-emitting diodes (LEDs) have become promising due to their long life, compact size, and eco-friendly characteristics [1]. The LED lights are widely used in the indoor lighting, outdoor lighting, and display backlighting. In these applications, multiple LEDs are connected to increase the luminous flux. The LEDs can be connected in series and parallel, depending on the output voltage and current of the LED driver. In general, multiple LEDs are connected in series to form an LED string, and then the LED strings are connected in parallel with each other. Since each LED has different voltage and current characteristics, the constant current control is required to equalize each LED string current. Therefore, LED current sharing technique is necessary. The LED current sharing can be classified into two methods. One is the active method [2][3][4][5][6][7][8][9], and the other is the passive method [10][11][12][13][14][15].
Generally, the active method uses semiconductor devices and integrated circuits to achieve LED current sharing. The active method has some disadvantages, such as complexity and high cost. The passive method, which features low cost and simplicity, is developed as another LED current sharing method. The passive method can be subdivided into inductive and capacitive methods. The inductive method usually uses the current-sharing transformers. For the current-sharing transformer method, the differential transformer sharing transformers. For the current-sharing transformer method, the differential transformer with a 1:1 turns ratio is used to balance the LED current. On the other hand, the capacitive method uses the capacitors to achieve LED current balance. The current sharing is achieved based on the capacitor ampere-second balance. In Figure 1, the literatures [14] and [15] display the low-power two-channel LED drivers using the capacitor to achieve LED current balance. They are suitable for low-input voltage and low-power applications. These two LED drivers are based on step-up converters. The output voltage of the twochannel LED driver is the sum of the voltages across two LED strings, and this is different from the parallel connection. Thus, these kinds of LED drivers are called pseudo multistring LED drivers. However, if the resonance behavior is taken into account, then the soft switching of the switch and diode will happen, causing the overall efficiency can be upgraded. Consequently, the non-isolated boost resonant LED driver shown in [16] is presented. In this circuit, only the diode in the resonant path can have zero-current-switching (ZCS) turn-off. In addition, if the resonance behavior as well as galvanic isolation taking into consideration, then the isolated voltage-bucking resonant LED driver as displayed in [17] is proposed. In this circuit, only all the diodes on the secondary side have ZCS. Prior work: (a) non-isolated two channel LED driver with automatic current balance and zero voltage switching [14]; (b) non-isolated single-switch two-channel LED driver with passive regenerative snubber [15]. Therefore, an isolated LED driver based on the LLC resonant converter is proposed herein. Both switches have zero-voltage-switching (ZVS) turn-on and both the diodes on the secondary side have ZCS turn-off except at light load. The proposed LED driver is based on the current-sharing capacitor with a quite low voltage stress. In this paper, the basic operating principles, steady-state analyses, and experimental results will be given in the following sections. Figure 2 shows the proposed two-channel LED driver. For analysis convenience, there are some assumptions to be made as follows.

Basic Analysis of the Proposed LED Driver
(1) The switches and components are ideal except for the metal-oxide-semiconductor field-effect transistor (MOSFET) switches and the transformer. Prior work: (a) non-isolated two channel LED driver with automatic current balance and zero voltage switching [14]; (b) non-isolated single-switch two-channel LED driver with passive regenerative snubber [15].
Therefore, an isolated LED driver based on the LLC resonant converter is proposed herein. Both switches have zero-voltage-switching (ZVS) turn-on and both the diodes on the secondary side have ZCS turn-off except at light load. The proposed LED driver is based on the current-sharing capacitor with a quite low voltage stress. In this paper, the basic operating principles, steady-state analyses, and experimental results will be given in the following sections. Figure 2 shows the proposed two-channel LED driver. For analysis convenience, there are some assumptions to be made as follows.

Basic Analysis of the Proposed LED Driver
(1) The switches and components are ideal except for the metal-oxide-semiconductor field-effect transistor (MOSFET) switches and the transformer.  (2) The values of all the capacitors are large enough. Thus, the voltages across them are regarded as constant. (3) The two output voltages are identical, namely, Vo1 = Vo2.
The following analyses contain the (a) operating principles; (b) LED modeling; (c) LED load characteristics; (d) voltage gain characteristics; and (e) extension of the proposed LED driver.

Operating Principles
There are 8 operating states in the proposed LED driver. Figure 3 shows the key waveforms over one switching period. As shown in Figure 4a, S1 is ON, but S2 is OFF. Thus, Lr and Cr resonate with each other and iLr increases from zero. During this state, iLr is larger than iLm. Therefore, the The following analyses contain the (a) operating principles; (b) LED modeling; (c) LED load characteristics; (d) voltage gain characteristics; and (e) extension of the proposed LED driver.

Operating Principles
There are 8 operating states in the proposed LED driver. Figure 3 shows the key waveforms over one switching period. The following analyses contain the (a) operating principles; (b) LED modeling; (c) LED load characteristics; (d) voltage gain characteristics; and (e) extension of the proposed LED driver.

Operating Principles
There are 8 operating states in the proposed LED driver. Figure 3 shows the key waveforms over one switching period. As shown in Figure 4a, S1 is ON, but S2 is OFF. Thus, Lr and Cr resonate with each other and iLr increases from zero. During this state, iLr is larger than iLm. Therefore, the As shown in Figure 4a, S 1 is ON, but S 2 is OFF. Thus, L r and C r resonate with each other and i Lr increases from zero. During this state, i Lr is larger than i Lm . Therefore, the current i p is transferred from the primary side to the secondary side, thus making D 1

LED Modeling
The LED string can be modeled as a piecewise linear model as shown in Figure 5. The equivalent LED string model contains one ideal diode Dideal, one equivalent on-resistance RLED and one equivalent forward voltage VF, with all the three connected in series. Also, the LED string current is defined as ILED. Hence, the LED string voltage VLED can be expressed as As shown in Figure 4b, S 1 is still ON, but S 2 is still OFF. During this state, since i Lr is equal to i Lm , there is no current flowing through the secondary side, thereby causing the Energies 2021, 14, 112 5 of 18 energy required by LS1 and LS2 to be provided by C o1 and C o2 , respectively. At the same time, C r , L r , and L m resonate together, thus causing i Lr to be increased quite slowly. This state ends when S 1 turns off at t 2 .
2.1.3. State 3 (t 2 , t 3 ) As shown in Figure 4c, S 1 is turned OFF and S 2 still keeps OFF. During this state, C oss1 is charged and C oss2 is discharged, thus causing the energy required by LS1 and LS2 to be still provided by C o1 and C o2 , respectively. This state ends when C oss1 is charged to V in , and C oss2 is discharged to zero at t 3 .

State 4 (t 3 , t 4 )
As shown in Figure 4d, S 1 keeps OFF, but S 2 is turned ON with zero voltage switching (ZVS) due to i Lr flowing through D b2 . During this state, i Lr is smaller than i Lm . Therefore, the current -i p is reflected from the secondary side to the primary side, thereby making D 2 forward biased and hence providing energy to C o2 and LS2. As for LS1, it is powered by C o1 . At the same time, the voltage −nV o2 is across L m , thereby causing i Lm to be decreased linearly. This state ends when i Lr reaches zero at t 4 .

State 5 (t 4 , t 5 )
As shown in Figure 4e, S 1 still keeps OFF, but S 2 keeps ON. During this state, i Lr changes the direction. The voltage -nV o2 is still across L m . Thus, i Lm is still decreased linearly. This state ends when i Lr equals i Lm at t 5 .
2.1.6. State 6 (t 5 , t 6 ) As shown in Figure 4f, S 1 still keeps OFF, but S 2 still keeps ON. Since i Lr is equal to i Lm , there is no current flowing through the secondary side, thereby causing the energy required by LS1 and LS2 to be provided by C o1 and C o2 , respectively. At the same time, C r , L r and L m resonate together, thus causing i Lr to be decreased quite slowly. This state ends when S 2 turns off at t 6 .
2.1.7. State 7 (t 6 , t 7 ) As shown in Figure 4g, S 1 still keeps OFF, and S 2 is turned OFF. During this state, C oss1 is charged and C oss2 is discharged, thus causing the energy required by LS1 and LS2 to be still provided by C o1 and C o2 , respectively. This state ends when C oss1 is discharged to zero, and C oss2 is charged to V in at t 7 .
2.1.8. State 8 (t 7 , t 0 + T s ) As shown in Figure 4h, S 2 keeps OFF, but S 1 is turned ON with ZVS due to i Lr flowing through D b1 . During this state, −i Lr is smaller than −i Lm . Therefore, the current i p is transferred from the primary side to the secondary side, thus making D 1 forward biased and hence providing energy to C o1 and LS1. As for LS2 it is powered by C o2 . At the same time, the voltage nV o1 is across L m , thus causing i Lm to be increased linearly. This state ends when i Lr reaches zero at t = t 0 + T s .

LED Modeling
The LED string can be modeled as a piecewise linear model as shown in Figure 5. The equivalent LED string model contains one ideal diode D ideal , one equivalent on-resistance R LED and one equivalent forward voltage V F , with all the three connected in series. Also, the LED string current is defined as I LED . Hence, the LED string voltage V LED can be expressed as

LED Load Characteristics
The AC equivalent load can be modeled by using the fundamental harmonic approximation (FHA). The AC equivalent circuit of the proposed LLC resonant LED driver is shown in Figure 6. The derivation is shown as follows.
The current iac(fund) is defined as a fundamental sinusoidal wave on the secondary side. That is, where Ip is the maximum value of iac(fund)(t).
The expression of VLED can be changed to is the average current of iD1 and equal to ILED.
By substituting (4) into (3), VLED can be rewritten to be In addition, the voltage on the secondary side, vac(t), can be expressed to be Also, the voltage vac(t) can be represented by a Fourier series as follows: Since vac(t) is an odd function waveform, an is zero. Thus, The fundamental waveform of vac(t), called vac(fund)(t), is Based (4) and Vo1 = VLED, the effective resistive load Ro,ac can be signified by

LED Load Characteristics
The AC equivalent load can be modeled by using the fundamental harmonic approximation (FHA). The AC equivalent circuit of the proposed LLC resonant LED driver is shown in Figure 6. The derivation is shown as follows. Figure 6. AC equivalent circuit of the proposed LED driver. Figure 7 shows the two-port model of the FHA resonant circuit. The output load resistor Rout can be regarded as the equivalent static resistance of the LED string at a given forward current, that is, VLED divided by ILED. In addition, the voltage gain is

Voltage Gain Characteristics
From (12), it can be seen that the fundamental component of the input voltage is As derived in (9), the output voltage fundamental component is Based on (11), (13), and (14), the DC-DC input-to-output voltage conversion ratio can be derived as follows: From (15), the DC-DC input-to-output voltage conversion ratio is The current i ac(fund) is defined as a fundamental sinusoidal wave on the secondary side. That is, i ac( f und) (t) = I p sin(ω s t) where I p is the maximum value of i ac(fund) (t).
The expression of V LED can be changed to where i D1 (t) T s is the average current of i D1 and equal to I LED. Therefore, i D1 (t) T s can be expressed to be By substituting (4) into (3), V LED can be rewritten to be In addition, the voltage on the secondary side, v ac (t), can be expressed to be Also, the voltage v ac (t) can be represented by a Fourier series as follows: Energies 2021, 14, 112 Since v ac (t) is an odd function waveform, a n is zero. Thus, Based (4) and V o1 = V LED , the effective resistive load R o,ac can be signified by Figure 7 shows the two-port model of the FHA resonant circuit. The output load resistor R out can be regarded as the equivalent static resistance of the LED string at a given forward current, that is, V LED divided by I LED . In addition, the voltage gain is x FOR PEER REVIEW 8 of 19

Voltage Gain Characteristics
From (17), it can be seen that Q and K will affect the voltage gain. The output resistance in Figure 7 is replaced with the LED equivalent model as shown in Figure 8. Based on (1), Based on (16), Equation (19) can be rewritten as The input voltage waveform of the AC resonant tank is From (12), it can be seen that the fundamental component of the input voltage is As derived in (9), the output voltage fundamental component is Energies 2021, 14, 112 8 of 18 Based on (11), (13), and (14), the DC-DC input-to-output voltage conversion ratio can be derived as follows: From (15), the DC-DC input-to-output voltage conversion ratio is |M(j2π f s )| (16) In Figure 6, by transferring the time domain to the s domain and let s = j2π f s , the magnitude of the voltage gain M(j2π f s ), called M, can be derived as follows: where , and Z o = L r C r . From (17), it can be seen that Q and K will affect the voltage gain. The output resistance in Figure 7 is replaced with the LED equivalent model as shown in Figure 8. Based on (1), (  From (17), it can be seen that Q and K will affect the voltage gain. The output resistance in Figure 7 is replaced with the LED equivalent model as shown in Figure 8. Based on (1), Based on (16), Equation (19) can be rewritten as From (19), it can be seen that the LED current can be regulated by changing the switching frequency fs, and this means that the gain adjustment is made by frequency modulation. As seen in Figure 9, by giving an LED current command ILED_command, the frequency modulator will change the switching frequency fs, and vo,FHA will be varied to a corresponding value according to the designed voltage gain M.
From (19), it can be seen that the LED current can be regulated by changing the switching frequency f s , and this means that the gain adjustment is made by frequency modulation. As seen in Figure 9, by giving an LED current command I LED_command , the frequency modulator will change the switching frequency f s , and v o,FHA will be varied to a corresponding value according to the designed voltage gain M.  Figure 10 shows the control strategy of the proposed LED driver. From Figure 10a, it can be seen that one of the LED strings is sensed and the current signal is transformed to the voltage signal and then sent to UCD3138, which contains an error ADC, a filter, and a digital PWM as shown in Figure 10b. The sensed current signal will be sent to the error ADC and compared with the prescribed reference value. After this, the error signal will be sent to the filter, called the PID controller. Eventually, the calculated duty cycle and frequency will control the MOSFETs to regulate the LED string currents.  Figure 10 shows the control strategy of the proposed LED driver. From Figure 10a, it can be seen that one of the LED strings is sensed and the current signal is transformed to the voltage signal and then sent to UCD3138, which contains an error ADC, a filter, and a digital PWM as shown in Figure 10b. The sensed current signal will be sent to the error ADC and compared with the prescribed reference value. After this, the error signal will be sent to the filter, called the PID controller. Eventually, the calculated duty cycle and frequency will control the MOSFETs to regulate the LED string currents.  Figure 10 shows the control strategy of the proposed LED driver. From Figure 10a, it can be seen that one of the LED strings is sensed and the current signal is transformed to the voltage signal and then sent to UCD3138, which contains an error ADC, a filter, and a digital PWM as shown in Figure 10b. The sensed current signal will be sent to the error ADC and compared with the prescribed reference value. After this, the error signal will be sent to the filter, called the PID controller. Eventually, the calculated duty cycle and frequency will control the MOSFETs to regulate the LED string currents.

Effect of Variations in Equivalent forward Voltage on Current Sharing
As shown in Figure 10a, since the voltages across the two central-ta are the same, this means that

Effect of Variations in Equivalent forward Voltage on Current Sharing
As shown in Figure 10a, since the voltages across the two central-tapped windings are the same, this means that Assuming that the diodes D 1 and D 2 are two-in-one, V D1 can be regarded as almost equal to V D2 . Therefore, (20) can be simplified to (21): Based on (21), if the two LED strings are identical, then V C1 is zero; otherwise, V C1 is not zero. This means that the difference in equivalent forward voltage between the two LED strings can be absorbed by the current-sharing capacitor C 1 . Figure 11 shows the four-channel LED driver, which can be derived from the proposed two-channel LED driver. However, in practice, the effective resistive load R o,ac will be changed. Consequently, the design of the associated parameters will be repeated if necessary.

Effect of Variations in Equivalent forward Voltage on Current Sharing
As shown in Figure 10a, since the voltages across the two central-tapped windings are the same, this means that Assuming that the diodes D1 and D2 are two-in-one, VD1 can be regarded as almos equal to VD2. Therefore, (20) can be simplified to (21): Based on (21), if the two LED strings are identical, then VC1 is zero; otherwise, VC1 is not zero. This means that the difference in equivalent forward voltage between the two LED strings can be absorbed by the current-sharing capacitor C1. Figure 11 shows the four-channel LED driver, which can be derived from the pro posed two-channel LED driver. However, in practice, the effective resistive load Ro,ac wil be changed. Consequently, the design of the associated parameters will be repeated if nec essary.  Figure 11. Four-channel LED driver derived from the proposed LED driver.

Design Considerations
To verify the effectiveness of the proposed LED driver, a prototype is built up and tested. Table 1 shows the system specifications of the proposed converter, whereas Table  2 shows the component specifications used in the proposed converter. Moreover, the de sign procedures of (a) LED selection; (b) transformer turns ratio (n); (c) maximum voltage conversion ratio (Mmax) and minimum voltage conversion ratio (Mmin); (d) effective resis tive load reflected to the primary side of the transformer (n 2 Ro,ac); (e) ratio of magnetizing inductance to resonant inductance ratio (K) and quality factor (Q); and (f) resonant capac itance (Cr), resonant inductance (Lr), and magnetizing inductance (Lm).

Design Considerations
To verify the effectiveness of the proposed LED driver, a prototype is built up and tested. Table 1 shows the system specifications of the proposed converter, whereas Table  2 shows the component specifications used in the proposed converter. Moreover, the design procedures of (a) LED selection; (b) transformer turns ratio (n); (c) maximum voltage conversion ratio (M max ) and minimum voltage conversion ratio (M min ); (d) effective resistive load reflected to the primary side of the transformer (n 2 R o,ac ); (e) ratio of magnetizing inductance to resonant inductance ratio (K) and quality factor (Q); and (f) resonant capacitance (C r ), resonant inductance (L r ), and magnetizing inductance (L m ). Table 1. System specifications of the proposed LED driver.

System Parameters Specifications
350 mA Nominal LED power value (P LED ) 30 W Resonant frequency (f r ) 100 kHz Ratio of magnetizing inductance to resonant inductance (K) 5 Quality factor (Q) 0.48 Table 2. Components used in the proposed LED driver.

Determination of Transformer Turns Ratio
The turns ratio of the transformer can be figured out under normal input voltage and unity voltage gain, namely, M nor = 1: Based on the above calculation, the turns ratio n is selected to be 5. Via recalculation, the new voltage gain is 1.04.

Maximum and Minimum Voltage Gains
The maximum voltage gain and the minimum voltage gain are calculated as follows: To prevent the operating point from going into the capacitive region, the maximum voltage gain should have a margin. The corresponding margin is 0.15 times M max . Therefore, the value of M max is changed to

Effective Resistive Load on the Primary Side
Based on (10), the effective resistive load on the primary side, R ac , is calculated as follows:

Selection of K and Q and Determination of Switching Frequency Range
In the proposed LED driver, the value of K is selected to be 5. From Figure 12, it can be seen that the values of M change with different values of Q. In this paper, Q is selected to be 0.48. The minimum switching frequency f s_min and the maximum switching frequency f s_max are shown below: To prevent the operating point from going into the capacitive region, the maximum voltage gain should have a margin. The corresponding margin is 0.15 times Mmax. Therefore, the value of Mmax is changed to

Effective Resistive Load on the Primary Side
Based on (10), the effective resistive load on the primary side, Rac, is calculated as follows:

Selection of K and Q and Determination of Switching Frequency Range
In the proposed LED driver, the value of K is selected to be 5. From Figure 12, it can be seen that the values of M change with different values of Q. In this paper, Q is selected to be 0.48. The minimum switching frequency fs_min and the maximum switching frequency fs_max are shown below:

Resonant Capacitance, Resonant Inductance and Magnetizing Inductance
Based on the effective resistive load calculated in (26), the selected resonant frequency fr = 100 kHz, and the selected quality factor Q = 0.48, the resonant capacitance Cr can be worked out from (29). Moreover, based on (29), the resonant inductance Lr can be figured out from (30). Finally, based on the selected K = 5, the magnetizing inductance can be found from (31):

Resonant Capacitance, Resonant Inductance and Magnetizing Inductance
Based on the effective resistive load calculated in (26), the selected resonant frequency f r = 100 kHz, and the selected quality factor Q = 0.48, the resonant capacitance C r can be worked out from (29). Moreover, based on (29), the resonant inductance L r can be figured out from (30). Finally, based on the selected K = 5, the magnetizing inductance can be found from (31):

Experimental Results
Figures 13-18 show the measured waveforms at rated loads. Figure 13 shows the gate driving signals for the switches Q 1 and Q 2 , and the voltage stresses v ds1 and v ds2 . From this figure, it can be seen that the voltage stresses on Q 1 and Q 2 are around 400 V.

Experimental Results
Figures 13-18 show the measured waveforms at rated loads. Figure 13 shows the gate driving signals for the switches Q1 and Q2, and the voltage stresses vds1 and vds2. From this figure, it can be seen that the voltage stresses on Q1 and Q2 are around 400 V.  Figure 14 displays the resonant inductor current iLr, and the resonant capacitor voltage vCr. From this figure, it can be seen that the switching frequency fs is smaller than the resonant frequency fr. Also, when the resonant inductance current equals the magnetizing inductance current, there is no current transferring to the secondary side. During this period, Cr, Lr and Lm resonate together, resulting in a slow increase of the resonant current.  Figure 15 shows the diode currents. From this figure, it can be seen that the diode currents reach zero before the MOSFET switches are turned on, and this means that the diodes are turned off with zero-current switching (ZCS).  Figure 16 shows the voltages on the two LED strings, named Vo1 and Vo2, and the currents in the two LED strings, named ILS1 and ILS2. From this figure, it can be seen that Vo1 and Vo2 are both about 41 V, and ISL1 and ISL2 are regulated to be 350 mA.  Figure 15 shows the diode currents. From this figure, it can be seen that the diode currents reach zero before the MOSFET switches are turned on, and this means that the diodes are turned off with zero-current switching (ZCS).   Figure 16 shows the voltages on the two LED strings, named Vo1 and Vo2, and the currents in the two LED strings, named ILS1 and ILS2. From this figure, it can be seen that Vo1 and Vo2 are both about 41 V, and ISL1 and ISL2 are regulated to be 350 mA.     Furthermore, in order to verify the current-sharing performance of variations in forward voltage due to the temperature and the LED current, the number of LEDs for LS1 is 12 LEDs and the number of LEDs for LS2 is 9 LEDs. From Figure 19, it can be seen that two currents in LS1 and LS2 are almost the same, about 350 mA, but the difference in voltage between LS1 and LS2 is 10 V (= Vo1 -Vo2 = 40 V-30 V = 10 V). From this result, it is obvious that if the forward voltage is varied due to the temperature and the LED current, the current sharing is still performed well.   Furthermore, in order to verify the current-sharing performance of variations in forward voltage due to the temperature and the LED current, the number of LEDs for LS1 is 12 LEDs and the number of LEDs for LS2 is 9 LEDs. From Figure 19, it can be seen that two currents in LS1 and LS2 are almost the same, about 350 mA, but the difference in voltage between LS1 and LS2 is 10 V (= Vo1 -Vo2 = 40 V-30 V = 10 V). From this result, it is obvious that if the forward voltage is varied due to the temperature and the LED current, the current sharing is still performed well.  Figure 14 displays the resonant inductor current i Lr , and the resonant capacitor voltage v Cr . From this figure, it can be seen that the switching frequency f s is smaller than the resonant frequency f r . Also, when the resonant inductance current equals the magnetizing inductance current, there is no current transferring to the secondary side. During this period, C r , L r and L m resonate together, resulting in a slow increase of the resonant current. Figure 15 shows the diode currents. From this figure, it can be seen that the diode currents reach zero before the MOSFET switches are turned on, and this means that the diodes are turned off with zero-current switching (ZCS). Figure 16 shows the voltages on the two LED strings, named V o1 and V o2 , and the currents in the two LED strings, named I LS1 and I LS2 . From this figure, it can be seen that V o1 and V o2 are both about 41 V, and I SL1 and I SL2 are regulated to be 350 mA. Figure 17 displays the voltage across C 1 , named V C1 , and current flowing through C 1 , named i C1 . From this figure, it can be seen that V C1 is zero due to V o1 almost equal to V o2 . Figure 18 displays the efficiency. From this figure, it can be seen that the rated-load efficiency is around 94.8%, and the highest efficiency is around 96.6%.
Furthermore, in order to verify the current-sharing performance of variations in forward voltage due to the temperature and the LED current, the number of LEDs for LS 1 is 12 LEDs and the number of LEDs for LS 2 is 9 LEDs. From Figure 19, it can be seen that two currents in LS1 and LS2 are almost the same, about 350 mA, but the difference in voltage between LS1 and LS2 is 10 V (= V o1 − V o2 = 40 V − 30 V = 10 V). From this result, it is obvious that if the forward voltage is varied due to the temperature and the LED current, the current sharing is still performed well. Furthermore, in order to verify the current-sharing performance of variations in forward voltage due to the temperature and the LED current, the number of LEDs for LS1 is 12 LEDs and the number of LEDs for LS2 is 9 LEDs. From Figure 19, it can be seen that two currents in LS1 and LS2 are almost the same, about 350 mA, but the difference in voltage between LS1 and LS2 is 10 V (= Vo1 -Vo2 = 40 V-30 V = 10 V). From this result, it is obvious that if the forward voltage is varied due to the temperature and the LED current, the current sharing is still performed well. In Figure 20, it can be seen that the voltage across C1 is not zero, equal to about 5 V, which can be obtained based on (21). In Figure 20, it can be seen that the voltage across C 1 is not zero, equal to about 5 V, which can be obtained based on (21). In addition, as shown in Figure 18, the current consumed by the system can be calculated based on output power divided by efficiency and input voltage. Accordingly, the current consumed at 25% load current with 91.6% efficiency is 0.02047 A, the current consumed at 70% load current with 96.6% efficiency is 0.05435 A, and the current consumed at 100% load current with 94.8% efficiency is 0.07911 A.

Comparison of Waveforms and Efficiencies
In the following, Figure 17 is compared with Figures 21 and 22, whereas Figure 18 is compared with Figures 23 and 24. From Figures 17, 21 and 22, it can be seen that the currents in two LED strings for each figure are almost the same. Since the input voltages in [14] and [15] are of 3.3 V 10% ± , the number of efficiency curves for each of these two literatures is three. The highest efficiency among Figures 18, 23 and 24 is 96.6% from Figure 18, whereas the lowest efficiency among them is 86.5% from Figure 24. In addition, as shown in Figure 18, the current consumed by the system can be calculated based on output power divided by efficiency and input voltage. Accordingly, the current consumed at 25% load current with 91.6% efficiency is 0.02047 A, the current consumed at 70% load current with 96.6% efficiency is 0.05435 A, and the current consumed at 100% load current with 94.8% efficiency is 0.07911 A.

Comparison of Waveforms and Efficiencies
In the following, Figure 17 is compared with Figures 21 and 22, whereas Figure 18 is compared with Figures 23 and 24. From Figures 17, 21 and 22, it can be seen that the currents in two LED strings for each figure are almost the same. Since the input voltages in [14] and [15] are of 3.3 V ± 10%, the number of efficiency curves for each of these two literatures is three. The highest efficiency among Figures 18, 23 and 24 is 96.6% from Figure 18, whereas the lowest efficiency among them is 86.5% from Figure 24. sumed at 70% load current with 96.6% efficiency is 0.05435 A, and the current consumed at 100% load current with 94.8% efficiency is 0.07911 A.

Comparison of Waveforms and Efficiencies
In the following, Figure 17 is compared with Figures 21 and 22, whereas Figure 18 is compared with Figures 23 and 24. From Figures 17, 21 and 22, it can be seen that the currents in two LED strings for each figure are almost the same. Since the input voltages in [14] and [15] are of 3.3 V 10% ± , the number of efficiency curves for each of these two literatures is three. The highest efficiency among Figures 18, 23 and 24 is 96.6% from Figure 18, whereas the lowest efficiency among them is 86.5% from Figure 24.

Conclusions
An isolated LED driver based on the LLC resonant converter is presented herein. In the proposed LED driver, the current-sharing capacitor is used to balance the LED currents. Therefore, the active current sharing circuits are not required. From the experimental results, it can be seen that the currents in the two LED strings are identical without considering the difference in equivalent forward voltage between the two LED strings.

Conclusions
An isolated LED driver based on the LLC resonant converter is presented herein. In the proposed LED driver, the current-sharing capacitor is used to balance the LED currents. Therefore, the active current sharing circuits are not required. From the experimental results, it can be seen that the currents in the two LED strings are identical without considering the difference in equivalent forward voltage between the two LED strings. Furthermore, the number of the LED channels can be increased. A detailed design of the proposed LED driver is shown in this paper, particularly for how to obtain the effective resistive load from the LED string. As for current control, only the current in one LED string is sensed and controlled by negative feedback control, and the current in the other LED string is determined by the current-sharing capacitor. By doing so, this makes the current control quite easy. Moreover, the measured efficiency shows that the efficiency at rated load is around 94.8%, and the efficiency can be up to 96.6%.

Data Availability Statement:
No new data were created or analyzed in this study. Data sharing is not applicable to this article.