Implementation of a Dimmable LED Driver with Extendable Parallel Structure and Capacitive Current Sharing

Abstract

A dimmable LED driver along with an extendable series structure and interleaved capacitive current sharing is presented herein, the LED connection of which is changed from the traditional series structure to the proposed parallel structure. The number of LED strings can be extended. As the number of LED strings is increased, the output voltage of this LED driver and the voltage stress on the main switch are ideally not influenced. Moreover, only one current sensor is needed to achieve current control and dimming. In this paper, the basic operating principle of the proposed LED driver is described and analyzed. Finally, the effectiveness of this LED driver is demonstrated by experiment based on the field-programmable gate array (FPGA).

1. Introduction

As generally recognized, LEDs are getting more attractive in the world due to their small size, light weight, and long life [1,2]. An LED is driven by the current due to its behavior like a diode [3]. The higher the current in the LED, the higher is the forward-biased voltage across the LED [4]. Furthermore, the higher the temperature in the LED, the lower is the forward-biased voltage across the LED. In general, the arrangement of LEDs is first in series and then in parallel, so as to avoid a high voltage across the output of the LED driver. And hence, the current balance among LED strings is very important so as to avoid uneven currents in the LED strings. These uneven currents will affect the LED luminance and cause the temperature in the LED to be increased and the life of the LED to be reduced. Therefore, many literatures have presented current-sharing methods for LED strings [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] so as to make currents distributed among LED strings as identically as possible. The LED current-sharing methods are classified into two types. One is active [5,6,7,8,9], and the other is passive [10,11,12,13,14,15,16,17,18,19,20,21]. As for the active current-sharing method, each LED string contains one current regulator and one current sensor to balance currents among LED strings. The main demerit of this method is the high complexity of the circuit. Hence, the passive current sharing method is presented to overcome this disadvantage. This method can be classified into two types. One is based on the differential-mode transformer, and the other is based on the energy-transferring capacitor. For the first type to be considered [10,11,12,13,14], as the currents in two LED strings are not identical, this transformer will be activated, and hence, the two currents will be forced to be regulated as identically as possible. In [10], an LED driver is constructed of one Zeta converter with several current-balancing transformers such that the magnetizing energy can be recycled. In [11], several daisy-chained transformers are applied to current-balance multiple LED strings. In [12], only for two LED strings to be considered, an LED driver is made of one traditional boost converter with one differential transformer used as a current-sharing device. In [13], the LED driver is the same as that shown in [11], except for isolation capacitors used in the former. In [14], an LED driver is established by one twin-bus converter along with several differential transformers such that the voltage stress on the switch is reduced. However, in practice, the current-sharing error comes from the magnetizing current of the transformer. For the second type to be considered [15,16,17,18,19,20,21], the current balance between the two LED strings is based on the ampere-second balance. In [15], an LED driver constructed of an isolated LCLC resonant circuit along with capacitive current balance. In [16], an LED driver is built from one traditional boost along with one coupled inductor and capacitive current balance such that the output voltage can be upgraded. In [17], an isolated CLL resonant converter with several balance capacitors is applied to driving multiple LED strings. In [18], isolated and non-isolated LED drivers are constructed by the traditional converters with switched capacitors used. In [19], an LED driver is constructed by one voltage-boosting converter with automatic current balance and zero-voltage switching such that the switching loss can be reduced. In [20], an LED driver is built from one traditional boost converter along with capacitive current balance, input ripple cancellation, and passive clamp such that the input current ripple is reduced and the voltage gain improved. In [21], a two-channel LED driver is established by one coupled-inductor converter along with capacitive current balance and one passive regenerative snubber such that the voltage gain is upgraded and the leakage energy can be recycled. However, in actuality, the current sharing error comes from the leakage current of the current-sharing capacitor.

Based on the aforementioned literatures, each circuit from [10,11,12,13,14,15,16,17,18,19,20,21] has the capability of extending the number of LED strings to two or more, if necessary, except for [12,20,21]. Since the current balance based on the differential transformer will occupy a relatively large space, the current balance of the proposed LED driver is based on the capacitor. The proposed LED driver is used to improve the LED driver in [18]. In [18], due to the LED strings connected in series, the voltage gain is the sum of all the voltages across the output capacitors as shown in (4) in [18] divided by the input voltage. Furthermore, the number of LED strings cannot be increased to more than four. To overcome this problem, by means of current-sharing interleaved capacitors, the voltage gain of the LED driver is not influenced at all as the number of LED strings is increased. Above all, the voltage stress on the main switch is always the same for any number of LED strings used.

2. Proposed LED Driver Circuit

Since the number of LED strings shown in [18] is four, in order to effectively describe the behavior of the current-sharing interleaved capacitors used in the proposed LED driver, the number of LED strings is set to six. The proposed LED driver circuit in Figure 1 is constructed of one switch, Q₁; one input inductor, L; five current-sharing interleaved capacitors, C₁, C₂, C₃, C₄, and C₅; six diodes, D₁, D₂, D₃, D₄, D₅, and D₆; and six output capacitors C_o1, C_o2, C_o3, C_o4, C_o5, and C_o6. In addition, six LED strings are used as load.

Prior to analysis of the basic operating principle of this circuit, some associated symbols and some assumptions are to be given in the following.

(1)

All the capacitors are large enough such that the voltages across them can be regarded as constant.

(2)

The input voltage is signified by V_in and the output voltages are represented by V_o1, V_o2, V_o3, V_o4, V_o5, and V_o6.

(3)

The currents in L and Q₁ are indicated by i_L and i_ds, respectively.

(4)

The currents in C₁, C₂, C₃, C₄, and C₅ are denoted by i_C1, i_C2, i_C3, i_C4, and i_C5, respectively.

(5)

The currents in C_o1, C_o2, C_o3, C_o4, C_o5, and C_o6 are signified by i_o1, i_o2, i_o3, i_o4, i_o5, and i_o6, respectively.

(6)

The voltages on L and Q₁ are represented by v_L and v_ds, respectively.

(7)

The voltages on C₁, C₂, C₃, C₄, and C₅ are expressed by V_C1, V_C2, V_C3, V_C4, and V_C5, respectively.

(8)

The switching period is denoted by T_s.

(9)

The turn-on time interval of Q₁ is DT_s, where D is the duty cycle.

(10)

The switch, the inductor and all diodes and capacitors are viewed as ideal, and all the LED strings are identical.

(11)

The gate driving signal for Q₁ is signified by v_gs.

(12)

The circuit is operated in the continuous conduction mode (CCM), that is, there are two operating states over one switching cycle, as shown in Figure 2.

2.1. Operating Principle Analysis

(1)

State 1: [$t_0\le t\le t_1$]: As shown in Figure 3, Q₁ is turned on. At the same time, D₁, D₃, and D₅ are turned off, whereas D₂, D₄, and D₆ are turned on. During this state, the voltage across L is V_in, L is magnetized, whereas C₁, C₂, C₃, C₄, and C₅ are discharged through Q₁ and provide energy to LS₂, LS₄, and LS₆ and C_o2, C_o4, and C_o6. In addition, the energy required by LS₁, LS₃, and LS₅ is provided by C_o1, C_o3, and C_o5, respectively.

(2)

State 2: [$t_1\le t\le t_2$]: As shown in Figure 4, Q₁ is turned off. At the same time, D₂, D₄, and D₆ are turned off, whereas D₁, D₃, and D₅ are turned on. During this state, the voltage across L is V_in – v_a, where v_a = V_C1 + V_o1. The inductor L, together with V_in, charges C₁, C₂, C₃, C₄, C₅, C_o1, C_o3, and C_o5, whereas the energy required by LS₂, LS₄, and LS₆ are provided by C_o2, C_o4, and C_o6, respectively.

2.2. Voltage Gain

As Q₁ is turned on, the voltage across L, v_L(on), can be expressed as

$$v_{L(on)}=V_{in}.$$

(1)

As Q₁ is turned off, the voltage across L, v_L(off), can be expressed as

$$v_{L(off)}=V_{in}-v_a.$$

(2)

According to the voltage-second balance over one switching cycle, the following equation can be obtained:

$$D{V}_{in}+(1-D)(V_{in}-v_a)=0.$$

(3)

By rearranging (3), the input voltage V_in can be obtained as

$$V_{in}=v_a(1-D).$$

(4)

During the turn-on period of Q₁, the following equations can be found:

$$\{\begin{array}{l}{V}_{C1}+V_{C4}-V_{o2}=0\\ V_{C2}+V_{C5}-V_{o4}=0\\ V_{C3}-V_{o6}=0\end{array}.$$

(5)

During the turn-off period of Q₁, the following equations can be found:

$$\{\begin{array}{l}{V}_{C1}+V_{o1}=v_a\\ V_{C2}+V_{o3}+V_{C4}=v_a\\ V_{C3}+V_{o5}+V_{C5}=v_a\end{array}.$$

(6)

By summing the equations shown in (5), the following equation can be obtained:

$$V_{C1}+V_{C2}+V_{C3}+V_{C4}+V_{C5}-V_{o2}-V_{o4}-V_{o6}=0.$$

(7)

By summing the equations shown in (6), the following equation can be obtained:

$$V_{C1}+V_{C2}+V_{C3}+V_{C4}+V_{C5}+V_{o1}+V_{o3}+V_{o5}=3v_a.$$

(8)

By subtracting (7) from (8), the voltage v_a can be obtained as

$$v_a=\frac{1}{3}(V_{o1}+V_{o2}+V_{o3}+V_{o4}+V_{o5}+V_{o6}).$$

(9)

Finally, by substituting (9) into (4), the corresponding voltage gain can be found to be

$$\frac{v_a}{V_{in}}=\frac{\frac{1}{3}{\displaystyle \sum _{m=1}^6{V}_{om}}}{V_{in}}=\frac{1}{1-D}.$$

(10)

From (10), it can be seen that the required duty cycle is determined by averaging all the voltages across LED strings and then multiplying this result by two. If all the LED strings are identical, then (10) can be simplified to be

$$\frac{v_a}{V_{in}}=\frac{2V_{o1}}{V_{in}}=\frac{1}{1-D}.$$

(11)

From (11), it can be seen that the duty cycle can be determined by the output voltage of one LED string. That is, the output voltage and duty cycle of the proposed LED driver are kept constant as the number of LED strings is increased, and Equation (11) still holds.

2.3. Boundary Condition of Input Inductor L

The boundary condition for L is described as

$$\{\begin{array}{l}2I_L\ge \Delta i_L\Rightarrow L\mathrm{works}\mathrm{in}\mathrm{the}\mathrm{CCM}\\ 2I_L\le \Delta i_L\Rightarrow L\mathrm{works}\mathrm{in}\mathrm{the}\mathrm{DCM}\end{array},$$

(12)

where I_L and Δi_L are DC and AC components of i_L.

For analysis convenience, it is assumed that the input power is equal to the output power, and hence, the input current I_in can be represented by

$$I_{in}=\frac{1}{1-D}\times \frac{V_o}{R_{eq}},$$

(13)

where R_eq is the equivalent output resistance.

The average current of i_L, I_L, can be expressed as

$$I_L=I_{in}$$

(14)

$$I_L=\frac{1}{1-D}\times \frac{V_o}{R_{eq}}.$$

(15)

Furthermore, the current ripple of i_L, Δi_L, can be represented by

$$\Delta i_L=\frac{V_L\Delta t}{L}=\frac{V_{in}D{T}_s}{L}.$$

(16)

Therefore, as 2I_L ≥ Δi_L, the input inductor L will operate in the CCM, and hence, the following equation can be obtained:

$$\begin{array}{l}2I_L\ge \Delta i_L\\ \Rightarrow 2\times \frac{1}{1-D}\times \frac{V_o}{R_{eq}}\ge \frac{V_{in}D{T}_s}{L}\\ \Rightarrow \frac{2L}{R_{eq}{T}_s}\ge \frac{V_{in}D(1-D)}{V_o}\\ \Rightarrow \frac{2L}{R_{eq}{T}_s}\ge {(1-D)}^{2}D\\ \Rightarrow K_L\ge K_{crit\_L}(D)\end{array},$$

(17)

where $K_L=\frac{2L}{R_{eq}{T}_s}$ and $K_{crit\_L}(D)={(1-D)}^{2}D$.

From (17), it can be seen that as K_L ≥ K_{crit_L}(D), the input inductor L operates in the CCM; otherwise, in the DCM. Therefore, the operation boundary curve of L can be drawn as shown in Figure 5.

2.4. Current Sharing Concept

For convenience of analysis, only the current-sharing interleaved capacitor C₁ is taken into account. According to the ampere-second balance, the absolute value of the electric charge during the turn-on period of Q₁, Q_{C1_on}, is equal to the electric charge during the turn-off period of Q₁, Q_{C1_off}; namely,

$$\left|Q_C{}_{1\_off}\right|=Q_{C1\_on}$$

(18)

$$\frac{1}{T_s}{\displaystyle {\int }_0^{D{T}_s}\left|i_{C1(on)}\right|}dt=\frac{1}{T_s}{\displaystyle {\int }_{D{T}_s}^{T_s}{i}_{C1(off)}}dt.$$

(19)

The current in the LED string LS₁ is equal to the absolute average value of the negative part of i_C1 during the turn-on period of Q₁, and the current in the LED string LS₂ is equal to the average value of the positive part of i_C1 during the turn-off period of Q₁; therefore:

$$\left|I_{C1(on)}\right|=I_{C1(off)}=I_{LS1}=I_{LS2}.$$

(20)

3. System Control Strategy

Figure 6 shows the systems configuration of the proposed LED driver. This system contains the main power stage and the feedback control loop. The main power stage is constructed by the proposed LED driver. As for the feedback control loop, the current in the last LED string is sensed by the current sensor and then sent to the analog-to-digital converter (ADC), which transfers the analog signal to the digital signal. Afterwards, this digital signal is transferred to the field-programmable gate array (FPGA) to get a suitable control force after some calculations, so as to control the switch such that the currents in all the LED strings can be controlled near a desired value.

4. Design Considerations

Prior to tackling this section, the system specifications are given in

Table 1. System specifications.

Circuit Operating Mode	CCM
Input voltage (Vin)	$12\pm 10\%$
Output voltage (Vo)	$27.6\mathrm{V}(=8\times 3.45\mathrm{V})$
LED Rated current (Io,rated)/Rated Power (Po,rated)	350 mA/29 W
LED Minimum current (Io,min)/ Min. Power (Po,min)	87.5 mA/7.25 W
Switching frequency (fs)/Period (Ts)	100 kHz/10 µs
LED forward voltage (VF) and current (IF) at rated condition	3.45 V/0.35 A
LED cut-in forward voltage (VF,LED) at zero current	2.7 V
LED strings	6 strings with 4 LEDs per string

as follows.

4.1. Determination of Duty Cycle

According to the LED V-I curve shown in [22], the forward voltage V_F and forward current I_F at rated condition are 3.45V and 0.35A, respectively, whereas the cut-in forward voltage V_F,LED at zero current is 2.7 V. Hence, the equivalent resistance R_F,LED is 2.143 Ω.

4.1.1. Duty Cycles at Rated Load

The maximum duty cycle at rated load, D_max,rated, is determined by the minimum input voltage V_in,min and is shown as follows:

$$D_{max,rated}=1-\frac{V_{in,min}}{I_{LED}\times \Sigma R_{F,LED}+\Sigma V_{F,LED}}=1-\frac{10.8}{0.35\times 17.14+21.6}=0.608$$

(21)

The minimum duty cycle at rated load, D_min,rated, is determined by the maximum input voltage V_in,max and is shown as follows:

$$D_{min,rated}=1-\frac{V_{in,max}}{I_{LED}\times \Sigma R_{F,LED}+\Sigma V_{F,LED}}=1-\frac{13.2}{0.35\times 17.14+21.6}=0.522$$

(22)

4.1.2. Duty Cycles at Minimum Load

The maximum duty cycle at minimum load, D_max,min, is determined by the minimum input voltage V_in,min and is shown as follows:

$$D_{max,min}=1-\frac{V_{in,min}}{25\%\times I_{LED}\times \Sigma R_{F,LED}+\Sigma V_{F,LED}}=1-\frac{10.8}{0.25\times 0.35\times 17.14+21.6}=0.532$$

(23)

Also, the minimum duty cycle at minimum load, D_min,min, is determined by the maximum input voltage V_in,max and is shown as follows:

$$D_{min,min}=1-\frac{V_{in,max}}{25\%\times I_{LED}\times \Sigma R_{F,LED}+\Sigma V_{F,LED}}=1-\frac{13.2}{0.25\times 0.35\times 17.14+21.6}=0.428$$

(24)

4.2. Design of L

In order to make sure that the input inductor L works in the CCM, the minimum average input inductor current I_L,min should satisfy the following inequality:

$$I_{L,min}\ge \frac{\Delta i_L}{2},$$

(25)

where $\Delta i_L$ is the input inductor current ripple.

Via setting the efficiency equal to one, the following equation can be obtained as

$$I_{L,min}=I_{in,min}=\frac{P_{o,min}}{V_{in,max}}.$$

(26)

Therefore, the inequality of L can be expressed as

$$L\ge \frac{V_{in,max}{D}_{min,min}{T}_s}{2\times I_{L,min}}=\frac{V_{in,max}^2{D}_{min,min}{T}_s}{2\times P_{o,min}}=\frac{{13.2}^2\times 0.428\times 10\mathsf{\mu }}{2\times 7.25}=51.36\mathsf{\mu }\mathrm{H}.$$

(27)

Eventually, the value of L is set at 60 µH.

4.3. Design of C_o1–C_o6

The values of C_o1–C_o6 are worked out at a rated condition. Since the voltages across the capacitors C_o1, C_o2, C_o3, C_o4, C_o5, and C_o6 are clamped by the identical LED strings, V_o1 = V_o2 = V_o3 = V_o4 = V_o5 = V_o6. Furthermore, the capacitors C_o1, C_o3, and C_o5 are used to provide the energy for L_S1, L_S3, and L_S5 during the turn-on period of Q₁, respectively, whereas the capacitors C_o2, C_o4, and C_o6 are used to provide the energy for L_S2, L_S4, and L_S6 during the turn-off period of Q₁, respectively. In addition, it is assumed that the voltage ripple for each output capacitor is set at 1% of its DC voltage. Therefore,

$$C_{o1}=C_{o3}=C_{o5}\ge I_{o,rated}\times \frac{D_{max,rated}\times T_s}{V_{o1}\times 1\%}=0.35\times \frac{0.608\times 10\mathsf{\mu }}{13.8\times 0.01}=15.4\mathsf{\mu }\mathrm{F}$$

(28)

$$C_{o2}=C_{o4}=C_{o6}\ge I_{o,rated}\times \frac{(1-D_{max,rated})\times T_s}{V_{o2}\times 1\%}=0.35\times \frac{(1-0.522)\times 10\mathsf{\mu }}{13.8\times 0.01}=12.1\mathsf{\mu }\mathrm{F}.$$

(29)

Finally, one 22 μF/25 V capacitor is for C_o1 and also for C_o2, C_o3, C_o4, C_o5, and C_o6.

4.4. Design of C₁–C₅

The values of C₁–C₅ are figured out at rated condition. In this LED driver, the capacitors C₁, C₂, and C₃ have the same operating behavior, namely, V_C1 = V_C2 = V_C3, whereas the capacitors C₄ and C₅ have the same operating behavior, namely, V_C4 = V_C5. From state 2 with the switch Q₁ being off and based on Kirchhoff’s law (KVL), the following equation can be obtained:

$$-V_{C4}-V_{o3}-V_{C2}+V_{C1}+V_{o1}=0$$

(30)

Hence, V_C4 = 0 since V_C1 = V_C2 and V_o1 = V_o3. In the same way, V_C5 = 0.

From state 1 with the switch Q₁ being on and based on KVL, the following equation can be obtained:

$$V_{C1}-V_{o2}+V_{C4}=0.$$

(31)

Hence, V_C1 = V_o2 since V_C4 = 0. In the same way, V_C2 = V_o4 and V_C3 = V_o6.

In addition, it is assumed that the voltage ripple for each capacitor is set at 1% of its DC voltage. Therefore,

$$C_1=C_2=C_3\ge \frac{P_{o,rated}}{3\times V_{in,min}}\times \frac{D_{max,rated}\times T_s}{V_{o1}\times 1\%}=\frac{29}{3\times 10.8}\times \frac{0.608\times 10\mathsf{\mu }}{13.8\times 0.01}=39.1\mathsf{\mu }\mathrm{F}$$

(32)

Eventually, one 47 μF/25 V capacitor is for C₁ and also for C₂ and C₃. As for C₄ and C₅, they have the same capacitances as that for C₁ for design convenience.

In the following, the component specifications are tabulated in

Table 2. Component specifications.

Components	Specifications
MOSFET: Q1	IRF3250Z
Diodes: D1, D2, D3, D4, D5, D6	STPS30L60C
Current Sharing Capacitors: C1, C2, C3, C4, C5	22 µF/25 V
Output Capacitors: Co1, Co2, Co3, Co4, Co5, Co6	47 µF/25 V
Inductor	Core: T106-18B, L = 60 µH
Gate Driver	TC4420

.

5. Experimental Results

Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 shows the waveforms related to the proposed LED driver at rated condition. Figure 7 shows the gate driving signal for Q₁, v_gs, the voltage on Q₁, v_ds, and the current in L. Figure 8 shows the gate driving signal for Q₁, v_gs, the voltages across C₁, C₂, and C₃, called V_C1, V_C2, and V_C3, respectively. Figure 9 shows the gate driving signal for Q₁, v_gs, and the voltages across C₄ and C₅, called V_C4 and V_C5, respectively. Figure 10 shows the gate driving signal for Q₁, v_gs, and the voltages across D₁, D₂, and D₃, called v_D1, v_D2, and v_D3, respectively. Figure 11 shows the gate driving signal for Q₁, v_gs, and the voltages across D₄, D₅, and D₆, called v_D4, v_D5, and v_D6, respectively. Figure 12 shows the gate driving signal for Q₁, v_gs, and the currents in C₁, C₂, and C₃, called i_C1, i_C2, and i_C3, respectively. Figure 13 shows the gate driving signal for Q₁, v_gs, and the currents in C₄ and C₅, called i_C4 and i_C5, respectively. Figure 14 shows the voltage across LS₁, V_o1, the current in LS₁, i_LS1, the voltage across LS₂, V_o2, and the current in LS₂, i_LS2. Figure 15 shows the voltage across LS₃, V_o3, the current in LS₃, i_LS3, the voltage across LS₄, V_o4, and the current in LS₄, i_LS4. Figure 16 shows the voltage across LS₅, V_o5, the current in LS₅, i_LS5, the voltage across LS₆, V_o6, and the current in LS₆, i_LS6.

From Figure 7, the input inductor L operates in the CCM. From Figure 7, Figure 10 and Figure 11, the voltages across Q₁, D₂, D₄, and D₆ have voltage rings during the turn-off transient of Q₁, due to resonance among the body capacitance of Q₁, the diode parasitic capacitances of D₂, D₄, and D₆, and the line parasitic inductances. From Figure 8, the voltages across C₁, C₂, and C₃ are fixed at some values, whereas from Figure 9, the voltages across C₄ and C₅ are kept close to zero. From Figure 10 and Figure 11, the voltages across D₁, D₃, and D₅ have voltage rings during the turn-on transient of Q₁, due to resonance among the diode parasitic capacitances of D₁, D₃, and D₅, and the line parasitic inductances. From Figure 12 and Figure 13, the currents flowing through C₁ to C₅ have negative current rings since the voltages across D₁, D₃, and D₅ have voltage rings during the turn-on transient of Q₁, whereas the current flowing through C₁ to C₅ have positive current rings since the voltages across D_2, D₄, and D₆ have voltage rings during the turn-off transient of Q₁. From Figure 14, Figure 15 and Figure 16, the current sharing between LEDs performs well, and the corresponding voltages across LS₁ to LS₆ are almost the same due to all LED strings being almost identical.

In addition,

Table 3. Associated current sharing error percentage (CSEP) measurements at minimum load.

	LS1	LS2	LS3	LS4	LS5	LS6
ILS (mA)	85.4	86	85.2	86.6	85.3	86.5
VLED (V)	10.7	11.4	10.6	11.5	10.6	11.5
Error (%)	−0.5	0.2	−0.73	0.9	−0.62	0.78

,

Table 4. Associated CSEP measurements at half load.

	LS1	LS2	LS3	LS4	LS5	LS6
ILS (mA)	172	175	172	175	172	175
VLED (V)	11.3	12.1	11.2	12.1	11.2	12.2
Error (%)	−0.86	0.86	−0.86	0.86	−0.86	0.86

and

Table 5. Associated CSEP measurements at rated load.

	LS1	LS2	LS3	LS4	LS5	LS6
ILS (mA)	348	352	348	347	349	351
VLED (V)	12.4	13	12.3	13.2	12.3	13
Error (%)	−0.33	0.81	−0.33	−0.62	−0.04	0.53

show the current sharing error percentage (CSEP) under an input voltage of 12 V and different current levels in LED strings. The definition of CSEP is shown as follows:

$${\mathrm{CSEP}}_y=\frac{I_{LSy}-({\displaystyle \sum _{x=1}^m{I}_{LSx}})÷m}{({\displaystyle \sum _{x=1}^m{I}_{LSx})}÷m}\times 100\%$$

(33)

where CSEP_y is the CSEP of the y-th LED string, m is the total number of LED strings, I_LSy is the current flowing through the y-th LED string, and ${\displaystyle \sum _{x=1}^m{I}_{LSx}}$ is the sum of all the currents flowing through the LED strings.

Based on the calculated measurements from Table 3, Table 4 and Table 5, the CSEP values for any load locate between −1% and 1%. Therefore, the proposed LED driver has a good capability of current sharing.

In the following, how to measure the efficiency of the proposed LED driver is described. As shown in Figure 17, one current sensing resistor is in series with the input current path. First, a digital meter, called Fluke 8050A, is used to measure the voltage across this resistor so as to obtain the value of the input current. Sequentially, another digital meter, also called Fluke 8050A, is used to measure the input voltage. Accordingly, the input power can be worked out. As for the output power, six LED strings with the same number of LEDs, manufactured by Everlight Lighting Co., are used as the load of this LED driver. At the same time, the voltages across these six LED strings are measured by the other digital meter, also called Fluke 8050A. After this, the currents in these six LED strings are measured by a current probe, named TCPA 300, manufactured by Tektronix Co. Accordingly, the output power can be worked out. Finally, the corresponding efficiency can be figured out based on the calculated input and output powers. Figure 18 shows the curve of efficiency versus load current percentage. From this figure, it can be seen that the efficiency is above 90% all over the load range and can be up to 97.6%.

6. Further Discussion on Current-Sharing Performance

In this section, to further demonstrate the current performance of the proposed LED driver, the number of LEDs for all the LED strings are not identical, e.g., three LEDs for LS₁, one LED for LS₂, three LEDs for LS₃, two LEDs for LS₄, four LEDs for LS₅, and three LEDs for LS₆. The waveforms shown in Figure 19, Figure 20, Figure 21 and Figure 22, based on the PSIM software, are obtained under the rated LED current of 350 mA. Figure 19 shows the gate driving signal for Q₁, v_gs, the voltage on Q₁, v_ds, and the current in L, i_L. Figure 20 shows the voltage across LS₁, V_o1, the current in LS₁, i_LS1, the voltage across LS₂, V_o2, and the current in LS₂, i_LS2. Figure 21 shows the voltage across LS₃, V_o3, the current in LS₃, i_LS3, the voltage across LS₄, V_o4, and the current in LS₄, i_LS4. Figure 22 shows the voltage across LS₅, V_o5, the current in LS₅, i_LS5, the voltage across LS₆, V_o6, and the current in LS₆, i_LS6, since the voltage across each LED is assumed to be 3.45 V at rated current. Accordingly, based on (10), the calculated duty cycle, close to the simulated value shown in Figure 19, is

$$D=\frac{\frac{1}{3}{\displaystyle \sum _{m=1}^6{V}_{om}}-V_{in}}{\frac{1}{3}{\displaystyle \sum _{m=1}^6{V}_{om}}}=\frac{18.4-12}{18.4}\approx 0.35$$

(34)

In addition, from Figure 19, Figure 20, Figure 21 and Figure 22, it can be seen that even though the LED counts for individual LED strings are not the same, the currents flowing through all the LED strings are almost identical due to current control and current-sharing interleaved capacitors.

7. Conclusions

For the circuits shown in the literature [10,11,12,13,14,15,16,17,18,19,20,21], each circuit has the capability of extending the number of LED strings to two or more if necessary, except for [12,20,21]. Since the current balance based on the differential transformer will occupy a relatively large space, the current balance of the proposed LED driver is based on the capacitor. In this paper, an LED driver with extendable parallel structure and automatic current balance is presented. This LED driver is modified from series-type LED strings in [18] to parallel-type LED strings. The output voltage of the proposed LED driver with parallel-type LED strings is determined by averaging all the voltages across LED strings and then multiplying this result by two, different from the LED driver with series-type LED strings shown in [18], the output voltage of which is the sum of all the voltages across LED strings shown in (4) in [18]. Therefore, in [18], the voltage rating of the main switch will be increased, causing the turn-on resistance of the main switch to be increased. In addition, the number of LED strings cannot be increased to more than four. For the proposed LED driver, if all the LED strings are identical, then the output voltage is kept constant as the number of LED strings is increased; if not, then the output voltage is changed slightly. Moreover, only one current sensor is required to realize current control and dimming.