Four-Channel Buck-Type LED Driver with Automatic Current Sharing and Soft Switching

Abstract

A buck-type LED driver together with automatic current sharing and high step-down voltage conversion ratio but without complex control is proposed. The proposed LED driver can not only achieve zero voltage switching (ZVS) turn-on by adding only one resonant coupled inductor, which resonates with parasitic capacitors of active switches, but also can obtain lower voltage gain and better conversion efficiency. In this paper, the operating principles and design considerations of the proposed converter are discussed in detail. In addition, the number of LED strings can be extended to more than four channels. Finally, the theoretical analysis and performance of the proposed LED driver are verified by simulations and experiments using a field-programmable logic gate array (FPGA) named EP3C5E144C8N as a circuit control kernel.

1. Introduction

With technological progress and economic development, traditional incandescent lamps and energy-saving bulbs are gradually being replaced by light-emitting diodes (LEDs), because LEDs are small, long-life, high in power efficiency, low-pollution and fast responding.

Usually, LEDs are connected in series and then in parallel, because if only the series connection is used, the voltage across the LED string will be high, and hence the output capacitor needs to have a large withstand voltage. In addition, if one of the LEDs of the LED string burns out, the entire LED string will not work. When LEDs are connected in parallel only, the function of current sharing is required, because each LED has its characteristics. For example, if the LED current sharing method is not implemented, the current deviation of the LED strings will gradually become large, and this will shorten the life of the LED or even burn it out. Therefore, LED current sharing methods have been proposed to ensure that the currents between multiple LED strings will not deviate too far.

Figure 1 shows the generalized classification of LED current sharing methods. LED current sharing methods are mainly divided into active and passive methods. Active current sharing methods [1,2,3] should use current regulators or current sensing devices. The disadvantage is that the circuit is complicated, and hence the cost is high. Therefore, the passive current sharing methods use the basic characteristics of circuit components, and this can greatly reduce the circuit size and cost. Passive current sharing methods can be divided into two types: (1) differential-mode transformer [4,5,6]; (2) capacitor [7,8,9]. The advantages of the first current sharing method: (1) simple structure and low cost, (2) applicable to a variety of different circuit structures, (3) easy to expand and (4) without complicated control circuits.

As for the first current sharing method, the operational behavior is such that when the LED current is unbalanced, the voltage across the two ends of the differential-mode transformer is not zero. At this moment, the differential-mode transformer will be activated to force the currents on both sides to be as identical as possible. The literature [4] proposes that in order to ensure that the magnetic element meets the volt-second balance in the steady state, a diode will be added to the demagnetization path to complete the demagnetization and reduce the current error. This will reduce the overall efficiency.

As for the second current sharing method, the ampere-second balance characteristic of the capacitor is used. In the steady state, the average current of the capacitor over one cycle is zero to achieve current balance. Compared with the first method, it has the advantages of (1) smaller size, (2) lower cost, (3) simpler structure, etc. However, every two LED strings must have a diode to control the direction of current flow, which also causes an increase in power loss.

Generally, the switching power supplies can be divided into hard switching and soft switching according to their switching methods. For hard switching to be considered [10,11], when the switch is on and off, there will be additional switching losses from the switch.

In order to reduce the switching loss, the related soft switching technology is proposed to avoid voltage and current overlap. Among them, soft switching includes zero voltage switching (ZVS) [12,13,14] and zero current switching (ZCS) [15,16,17,18].

Based on the aforementioned, resonant circuits have been proposed [19,20,21,22], in which inductors and capacitors are added to form resonance. Since the voltage across both ends of the switch is a capacitive voltage, the capacitive energy must be transferred to the inductor in the form of resonance before the switch is turned on, so that the voltage across the switch is zero, and then the switch is turned on to achieve zero voltage conduction. A novel type of LED driver was proposed which is based on the LED driver [23], as shown in Figure 2, where four switches can achieve ZVS turn-on by using the parasitic capacitors of the MOSFETs and only one coupled inductor. Moreover, to make sure each LED string has the same current, the differential-mode transformers are used.

In this paper, a four-channel buck-type LED driver with automatic current sharing and soft switching is presented, and its working principle is explained in detail. In Section 2, the operational principle is described. The specification considerations, together with how to control the LED proposed driver topology, are introduced in Section 3. Simulated and experimental results and discussions are presented in Section 4 as verification. Finally, some conclusions are given in the Section 5.

2. Proposed LED Driver

Figure 3 shows the proposed LED driver with soft switching. This LED driver was derived from [23] by adding one resonant coupled inductor to create two resonant inductors; by coupling odd output inductors together and even output inductor together to reduce the core size; and by adding differential-mode transformers to achieve current sharing. The proposed LED driver consists of four switches S₁, S₂, S₃ and S₄; four diodes D₁, D₂, D₃ and D₄; three energy-transferring capacitors C₁, C₂ and C₃; three mutual inductances M_r, M₁ and M₂; six self-inductances L₁₁, L₂₂, L₁, L₂, L₃ and L₄; and three differential-mode transformers T₁, T₂ and T₃. The load is composed of four LED strings, LS₁, LS₂, LS₃ and LS₄.

In the proposed LED driver, the four switches have the same duty cycle D. The driving signal phases of four switches S₁, S₂, S₃, and S₄, are 0°, 180°, 0°, and 180°, respectively. The value of D is limited to less than 0.5. The duty cycles for switches S₁ and S₃ are the same, equal to D, whereas the duty cycles for switches S₂ and S₄ are the same, equal to 1-D. Two blanking times per cycle are added between the two switches S₁ and S₂, and between the two switches S₃ and S₄, and their values are the same, called T_d. In order to ensure that the four switches can reach ZVS turn-on, the parasitic capacitor across the switch must be discharged within the time of T_d, and this switch must be turned on before this capacitor is charged again.

2.1. Symbol Definitions and Preliminary Assumptions

Before proceeding with the circuit analysis, some assumptions are made:

(1)

V_in is the input voltage.

(2)

The currents flowing through LS₁, LS₂, LS₃ and LS₄ are I_o1, I_o2, I_o3 and I_o4, respectively. Under ideal conditions, I_o1 = I_o2 = I_o3 = I_o4 = I_o.

(3)

The values of the energy-transferring capacitors C₁, C₂, and C₃ and the output capacitors C_o1, C_o2, C_o3 and C_o4 are large enough to make the voltages across them constant, which will be regarded as voltage sources in the analysis.

(4)

Assume that the values of the four self-inductors in M₁ and M₂ are equal—that is, L₁ = L₂ = L₃ = L₄; assume that the values of the two self-inductors in M_r are equal—that is, L₁₁ = L₂₂.

(5)

Assume that the values of the two mutual inductors M₁ and M₂ are equal—that is, M₁ = M₂ = k₁L₁, where k₁ is one coupling coefficient; assume that the mutual inductance M_r= k₂L₁₁, where k₂ is the other coupling coefficient.

(6)

i_S1, i_S2, i_S3 and i_S4 are the currents flowing through S₁, S₂, S₃ and S₄, respectively; i_L1, i_L2, i_L3 and i_L4 are the currents flowing through L₁, L₂, L₃ and L₄, respectively; i_C1, i_C2, i_C3 and i_C4 are the currents flowing through C₁, C₂, C₃ and C₄, respectively; i_D1, i_D2, i_D3 and i_D4 are the currents flowing through D₁, D₂, D₃ and D₄, respectively.

(7)

v_Lr1 and v_Lr2 are the voltages across L₁₁ and L₂₂, respectively; v_L1, v_L2, v_L3 and v_L4 are the voltages across L₁, L₂, L₃ and L₄, respectively; v_S1, v_S2, v_S3 and v_S4 are the voltages across S₁, S₂, S₃ and S₄, respectively; v_D1, v_D2, v_D3 and v_D4 are the voltages across D₁, D₂, D₃ and D₄, respectively; V_C1, V_C2 and V_C3 are the voltages across C₁, C₂ and C₃, respectively.

(8)

T_s is the switching period; f_s is the switching frequency.

(9)

The turn-on times of S₁, S₂, S₃ and S₄ are D₁T_s, D₂T_s, D₃T_s and D₄T_s, respectively. This circuit adopts a complementary gate driving method, so the duty cycle D₁ = D₃ = D, D₂ = D₄ = 1 − D. In addition, there are two blanking times between S₁ and S₂ over one switching cycle.

(10)

All the diodes, inductors and capacitors are regarded as ideal components.

(11)

v_gs1, v_gs2, v_gs3 and v_gs4 are gate driving signals for the four switches S₁, S₂, S₃ and S₄, respectively.

(12)

C_S1, C_S2, C_S3 and C_S4 are the parasitic capacitances on the four switches S₁, S₂, S₃ and S₄, respectively, where C_S1 = C_S2 = C_S3 = C_S4 = C_oss, ideally.

(13)

T₁, T₂, and T₃ are differential-mode transformers, and under ideal conditions, their permeability coefficients are regarded as infinite. Since the four output currents are the same, the sum of the magneto-motive force on each differential-mode transformer will be zero, so the effects of these transformers are ignored in the analysis.

(14)

The circuit operates in the continuous conduction mode (CCM), and there are ten operating states over one switching cycle, as shown in Figure 4.

(15)

Assume k₁ = k₂ = 1; then, L_eq1 = L_eq2 = L_eq3 = L_eq4 = 2L₁ and L_r1 = L_r2 = 2L₁₁ are as shown in Figure 5.

(16)

In order to simplify the analysis, based on Figure 5, the equivalent output inductors, output capacitors and LED strings are combined and regarded as stable current sources, as shown in Figure 6.

2.2. Operating Principle Analysis

State 1 (t₀ < t < t₁): As shown in Figure 7, the switches S₁ and S₃ are turned on with zero voltage switching (ZVS) but S₂ and S₄ are turned off, whereas all the four diodes are forward biased. The input voltage V_in, the diode D₁, the resonant inductor L_r1, the energy-transferring capacitor C₁ and the switch S₁ form a loop; the energy-transferring capacitor C₂, the output current I_o2, the diode D₃, the resonant inductor L_r2, the energy-transferring capacitor C₃ and the switch S₃ form a loop. Additionally, the corresponding equivalent circuit is shown in Figure 8. At the same time, L_r1 and L_r2 are demagnetized in opposite directions via S₁ and S₃, respectively.

In this state, the current i_C1(t) and i_C3(t) can be obtained according to the voltages across the resonant inductors L_r1 and L_r2:

$$v_{Lr1}(t)=L_{r1}\frac{d{i}_{C1}(t)}{dt}=V_{in}-V_{C1}\Rightarrow i_{C1}(t)=\frac{V_{in}-V_{C1}}{L_{r1}}\times (t-t_0)+i_{C1}(t_0)$$

(1)

$$v_{Lr2}(t)=L_{r2}\frac{d{i}_{C3}(t)}{dt}=V_{C2}-V_{C3}\Rightarrow i_{C3}(t)=\frac{V_{C2}-V_{C3}}{L_{r1}}\times (t-t_0)+i_{C3}(t_0)$$

(2)

where i_C1(t₀) and i_C3(t₀) are the currents in the energy-transferring capacitors C₁ and C₃ at t₀, respectively. Since the energy-transferring capacitors C₂ and C₃ are connected in series in this state,

$$i_{C2}(t)=-i_{C3}(t)$$

(3)

As the current in C₁ rises to zero, the state ends, as shown in (4) and (5). Substituting (4) and (5) into (1) and (2) can provide the time elapsed in state 1:

$$i_{C1}(t_1)=0$$

(4)

$$i_{C3}(t_1)=-i_{C2}(t_1)=0$$

(5)

$$t_1-t_0=-\frac{i_{C1}(t_0)\times L_{r1}}{V_{in}-V_{C1}}=-\frac{i_{C3}(t_0)\times L_{r2}}{V_{C2}-V_{C3}}$$

(6)

State 2 (t₁ < t < t₂): As shown in Figure 9, the switches S₁ and S₃ are turned on but S₂ and S₄ are turned off, whereas all the four diodes are forward biased. The input voltage V_in, the switch S₁, the energy-transferring capacitor C₁, the resonant inductor L_r1 and the output current I_o1 form one loop; the energy-transferring capacitor C₂, the switch S₃, the energy-transferring capacitor C₃, the resonant inductor L_r2, the output current I_o3 and the diode D₂ form the other loop. Additionally, the corresponding equivalent circuit is shown in Figure 8. At the same time, the resonant inductors L_r1 and L_r2 are magnetized in the forward direction. Once the currents in the resonant inductors are equal to the output currents, the diodes D₁ and D₃ are turned off with zero current switching (ZCS) and the operation enters state 3 immediately.

The currents in the resonant inductors L_r1 and L_r2 are positive, and their expressions are the same as in state 1; that is,

$$i_{C1}(t)=\frac{V_{in}-V_{C1}}{L_{r1}}\times (t-t_1)$$

(7)

$$i_{C3}(t)=\frac{V_{C2}-V_{C3}}{L_{r2}}\times (t-t_1)$$

(8)

$$i_{C2}(t)=-i_{C3}(t)$$

(9)

As the currents in the resonant inductors are the same as the output currents, the state ends, as shown in (10) and (11). Substituting (10) and (11) into (7) and (8) can provide the time elapsed in state 2:

$$i_{C1}(t_2)=I_{o1}$$

(10)

$$i_{C3}(t_2)=-i_{C2}(t_2)=I_{o3}$$

(11)

$$t_2-t_1=\frac{I_{o1}\times L_{r1}}{V_{in}-V_{C1}}=\frac{I_{o3}\times L_{r2}}{V_{C2}-V_{C3}}$$

(12)

State 3 (t₂ < t < t₃): As shown in Figure 10, the switches S₁ and S₃ are turned on but S₂ and S₄ are turned off, whereas the diodes D₂ and D₄ are forward biased but D₁ and D₃ are reverse biased. The input voltage V_in, the switch S₁, the energy-transferring capacitor C₁, the resonant inductor L_r1 and the output current I_o1 form one loop; the energy-transferring capacitor C₂, the switch S₃, the energy-transferring capacitor C₃, the resonant inductor L_r2, the output current I_o3 and the diode D₂ form the other loop. Additionally, the corresponding equivalent circuit is shown in Figure 11. As the switches S₁ and S₃ are turned off, the operation enters state 4.

During this state, the currents in the resonant inductors L_r1 and L_r2 are the same as the output currents I_o1 and I_o3, respectively, so

$$i_{C1}(t)=I_{o1}$$

(13)

$$i_{C3}(t)=-i_{C2}(t)=I_{o3}$$

(14)

As the switches S₁ and S₃ are turned off, the operation enters state 4. Accordingly, the time elapsed in state 3 can be obtained to be

$$t_3-t_2=D{T}_s-(t_2-t_1)-(t_1-t_0)$$

(15)

State 4 (t₃ < t < t₄): As shown in Figure 12, all the switches are off, whereas the diodes D₂ and D₄ are forward biased but D₁ and D₃ are reverse biased. This state belongs to the blanking time interval. During this state, the parasitic capacitors on switches S₁ and S₃, called C_S1 and C_S3, respectively, are charged, and the parasitic capacitors on the switches S₂ and S₄, called C_S2 and C_S4, respectively, are discharged. Additionally, the corresponding equivalent circuit is shown in Figure 13. As the voltages across the switches S₂ and S₄ drop to zero, the operation enters state 5.

During this state, the currents in the resonant inductors L_r1 and L_r2 are the same as the output currents I_o1 and I_o3, respectively, so

$$i_{C1}(t)=I_{o1}$$

(16)

$$i_{C3}(t)=I_{o3}$$

(17)

In order to analyze the voltage across and current in each switch, let the potential between the switches S₁ and S₂ be v_a(t), and the potential between the switches S₃ and S₄ be v_b(t). In addition, because in the previous state, the switches S₁ and S₃ are in the on state, the values of v_a(t) and v_b(t) at the instant t₃ are V_in and V_C2 such that v_a(t) and v_b(t) can be obtained as follows:

$$v_a(t)=V_{in}-\frac{I_{o1}}{C_{S1}+C_{S2}}\times (t-t_3)$$

(18)

$$v_b(t)=V_{C2}-\frac{I_{o3}}{C_{S3}+C_{S4}}\times (t-t_3)$$

(19)

After obtaining v_a(t) and v_b(t), the voltages on the four switches can be derived, and the resulting equations are

$$v_{S1}(t)=V_{in}-v_a(t)$$

(20)

$$v_{S2}(t)=v_a(t)-V_{C2}$$

(21)

$$v_{S3}(t)=V_{C2}-v_b(t)$$

(22)

$$v_{S4}(t)=v_b(t)$$

(23)

As the switches S₂ and S₄ have zero voltage across them, the operation state enters state 5, as shown in (24). Substituting (24) into (21) and (23) can provide the time elapsed in state 4, namely,

$$v_{S2}(t_4)=v_{S4}(t_4)=0$$

(24)

$$t_4-t_3=\frac{V_{in}\times (C_{S1}+C_{S2})}{2\times I_{o1}}$$

(25)

State 5 (t₄ < t < t₅): As shown in Figure 14, the four switches are all off, whereas the four diodes are all forward biased. The energy-transferring capacitor C₁, the resonant inductor L_r1, the output current I_o1, the diode D₂, the energy-transferring capacitor C₂ and the body diode of the switch S₂ form one loop; the energy-transferring capacitor C₃, the resonant inductor L_r2, the output current I_o3, the diode D₄ and the body diode of S₄ form the other loop. Additionally, the corresponding equivalent circuit is shown in Figure 15. At the same time, the resonant inductors L_r1 and L_r2 are demagnetized in the forward direction via the switches S₂ and S₄, respectively.

For this state, according to the voltages on the resonant inductors L_r1 and L_r2, the currents i_C1(t) and i_C3(t) can be obtained as

$$\begin{array}{l}{v}_{Lr1}(t)=L_{r1}\frac{d{i}_{C1}(t)}{dt}=V_{C2}-V_{C1}\\ \Rightarrow i_{C1}(t)=\frac{V_{C2}-V_{C1}}{L_{r1}}\times (t-t_4)+I_{o1}\end{array}$$

(26)

$$\begin{array}{l}{v}_{Lr2}(t)=L_{r2}\frac{d{i}_{C3}(t)}{dt}=-V_{C3}\\ \Rightarrow i_{C3}(t)=\frac{-V_{C3}}{L_{r2}}\times (t-t_4)+I_{o3}\end{array}$$

(27)

During this state, the energy-transferring capacitors C₁ and C₂ are in series, so

$$i_{C1}(t)=-i_{C2}(t)$$

(28)

At the same time, this state ends when switches S₂ and S₄ are on, and the time elapsed can be inferred, along with the current values of the energy-transferring capacitors C₁ and C₃ at the end of this state:

$$t_5-t_4=T_d-(t_4-t_3)$$

(29)

$$i_{C1}(t_5)=\frac{V_{C2}-V_{C1}}{L_{r1}}\times \left[T_d-(t_4-t_3)\right]+I_{o1}$$

(30)

$$i_{C3}(t_5)=\frac{-V_{C3}}{L_{r2}}\times \left[T_d-(t_4-t_3)\right]+I_{o3}$$

(31)

State 6 (t₅ < t < t₆): As shown in Figure 16, the switches S₂ and S₄ are turned on with ZVS but S₁ and S₃ are off, whereas all four diodes are forward biased. The switch S₂, the energy-transferring capacitor C₁, the resonant inductor L_r1, the output current I_o1, the diode D₂ and the energy-transferring capacitor C₂ form one loop; the switch S₄, the energy-transferring capacitor C₃, the resonant inductor L_r2, the output current I_o3 and the diode D₄ form the other loop. Additionally, the corresponding equivalent circuit is shown in Figure 15. At the same time, the resonant inductors L_r1 and L_r2 are still demagnetized in the forward direction through the switches S₂ and S₄, respectively.

During this state, the currents i_C1(t) and i_C3(t), flowing through the resonant inductors L_r1 and L_r2, respectively, are similar to those in state 5:

$$\begin{array}{ll}{i}_{C1}(t)& =\frac{V_{C2}-V_{C1}}{L_{r1}}\underset{t_0}{\overset{t}{\int }}d\tau \\ & =\frac{V_{C2}-V_{C1}}{L_{r1}}\times (t-t_5)+i_{C1}(t_5)\end{array}$$

(32)

$$\begin{array}{ll}{i}_{C3}(t)& =\frac{-V_{C3}}{L_{r2}}\underset{t_5}{\overset{t}{\int }}d\tau \\ & =\frac{-V_{C3}}{L_{r2}}\times (t-t_5)+i_{C3}(t_5)\end{array}$$

(33)

where i_C1(t₅) and i_C3(t₅) are the currents in capacitors C₁ and C₃ at the instant t₅, respectively, as shown in (32) and (33).

The energy transferring-capacitors C₁ and C₂ are in series in this state, so

$$i_{C1}(t)=-i_{C2}(t)$$

(34)

As the current in the energy-transferring capacitor C₂ rises to zero, state 6 ends, as shown in (35) and (36):

$$i_{C1}(t_6)=-i_{C2}(t_6)=0$$

(35)

$$i_{C3}(t_6)=0$$

(36)

Substituting (35) and (36) into (32) and (33), respectively, can provide the time elapsed in state 6, namely,

$$t_6-t_5=\frac{i_{C1}(t_5)\times L_{r1}}{V_{C1}-V_{C2}}=\frac{i_{C3}(t_5)\times L_{r2}}{V_{C3}}$$

(37)

State 7 (t₆ < t < t₇): As shown in Figure 17, the switches S₂ and S₄ are still on but S₁ and S₃ are still off, whereas all four diodes are still forward biased. The switch S₂, the energy-transferring capacitor C₂, the output current I_o2, the diode D₁, the resonant inductor L_r1 and the energy-transferring capacitor C₁ form one loop; the switch S₄, the output current I_o4, the diode D₃, the resonant inductor L_r2 and the energy-transferring capacitor C₃ form the other loop. Additionally, the corresponding equivalent circuit is shown in Figure 18. The resonant inductors L_r1 and L_r2 are magnetized in opposite directions through the switches S₂ and S₄, respectively. As soon as the currents in the resonant inductors are equal to the negative output currents, the diodes D₂ and D₄ are turned off with ZCS, and the operation enters state 8.

During this state, the current expressions of the energy-transferring capacitors C₁, C₂ and C₃ are similar to those in the previous state:

$$i_{C1}(t)=\frac{V_{C2}-V_{C1}}{L_{r1}}\times (t-t_6)$$

(38)

$$i_{C3}(t)=\frac{-V_{C3}}{L_{r2}}\times (t-t_6)$$

(39)

$$i_{C1}(t)=-i_{C2}(t)$$

(40)

At the instant t₇, the currents in the energy-transferring capacitors are the same as the negative output currents:

$$i_{C1}(t_7)=-i_{C2}(t_7)=-I_{o2}$$

(41)

$$i_{C3}(t_7)=-I_{o4}$$

(42)

Substituting (41) and (42) into (38) and (39), respectively, can provide the time elapsed in state 7, namely

$$t_7-t_6=\frac{I_{o2}\times L_{r1}}{V_{C1}-V_{C2}}=\frac{I_{o4}\times L_{r2}}{V_{C3}}$$

(43)

State 8 (t₇ < t < t₈): As shown in Figure 19, the switches S₂ and S₄ are still on but S₁ and S₃ are still off, whereas the diodes D₁ and D₃ are still forward biased but the diodes D₂ and D₄ are reverse biased. The switch S₂, the energy-transferring capacitor C₂, the output current I_o2, the diode D₁, the resonant inductor L_r1 and the energy-transferring capacitor C₁ form one loop; the switch S₄, the output current I_o4, the diode D₃, the resonant inductor L_r2 and the energy-transferring capacitor C₃ form the other loop. The corresponding equivalent circuit is shown in Figure 18. As the switches S₂ and S₄ are turned off, the operation goes to state 9.

During this state, the currents in the two energy-transferring capacitors are the same as the negative output currents:

$$i_{C2}(t)=-i_{C1}(t)=I_{o2}$$

(44)

$$i_{C3}(t)=-I_{o4}$$

(45)

As the switches S₂ and S₄ are turned off, the operation goes to state 9. The corresponding elapsed time can be obtained to be

$$t_8-t_7=(1-D)T_s-(t_6-t_5)-(t_7-t_6)$$

(46)

State 9 (t₈ < t < t₉): As shown in Figure 20, all four switches are off, whereas the diodes D₁, D₃ and D₄ on but D₂ off. This state belongs to the blanking time interval. During this state, the parasitic capacitors on switches S₁ and S_3, called C_S1 and C_S3, respectively, are discharged, and the parasitic capacitors on the switches S₂ and S₄ called C_S2 and C_S4, respectively, are charged. Additionally, the corresponding equivalent circuit is shown in Figure 21. As the voltages across the switches S₁ and S₃ drop to zero, the operation enters state 10.

During this state, the energy-transferring capacitor C₂ and the current I_o2 are connected in series, so

$$i_{C2}(t)=I_{o2}$$

(47)

According to the current in C_S4, the voltage on C_S4 can be obtained to be

$$v_{S4}(t)=\frac{I_{o4}}{2C_{S4}}\times (t-t_8)$$

(48)

Since during this state the diode D₄ is on, the sum of the voltages on four switches is V_in. In the case of voltage even distribution, the sum of the voltages on the switches S₁ and S₂ is half of the input voltage, whereas the voltages on the switches S₃ and S₄ is 0.5V_in, so it can be deduced that the voltage on the switch S₃, the current in the energy-transferring capacitor C₃ and the current in the switch S₃ are

$$\begin{array}{ll}{v}_{S3}(t)& =V_{C2}-v_{S4}(t)\\ & =V_{C2}-\frac{I_{o4}}{2C_{S4}}\times (t-t_8)\end{array}$$

(49)

$$i_{S3}(t)=\frac{I_{o4}}{2}+i_{C3}(t)=C_{S3}\frac{d{v}_{S3}(t)}{dt}$$

(50)

$$\begin{array}{ll}{i}_{C3}(t)& =C_{S3}\frac{d{v}_{S3}(t)}{dt}-\frac{I_{o4}}{2}\\ & =-I_{o4}\end{array}$$

(51)

$$i_{S3}(t)=-\frac{I_{o4}}{2}$$

(52)

According to Kirchhoff’s current law (KCL), the current in the switch S₂, called i_S2(t), can be shown as (53), in which I_o2 and i_S3(t) are known. i_S3(t) is shown in (52). Thus, the voltage on the switch S₂, called v_S2(t), can be obtained by

$$i_{S2}(t)=I_{o2}+i_{S3}(t)=C_{S2}\frac{d{v}_{S2}(t)}{dt}$$

(53)

$$\begin{array}{l}{v}_{S2}(t)=\frac{1}{C_{S2}}\underset{t_8}{\overset{t}{\int }}(I_{o2}-\frac{I_{o4}}{2})d\tau \\ =\frac{I_{o2}}{2C_{S2}}\times (t-t_8)+0\end{array}$$

(54)

Finally, the current relationship between the switch S₁, the energy-transferring capacitor C₁ and the switch S₂ is

$$i_{S1}(t)=i_{C1}(t)+i_{S2}(t)=C_{S1}\frac{d{v}_{S1}(t)}{dt}$$

(55)

Since the sum of the voltages on the switches S₁ and S₂ is half of the input voltage, the voltage on the switch S₁ can be obtained by

$$\begin{array}{ll}{v}_{S1}(t)& =\frac{V_{in}}{2}-v_{S2}(t)\\ & =\frac{V_{in}}{2}-\frac{I_{o2}}{2C_{S2}}\times (t-t_8)\end{array}$$

(56)

By substituting (56) into (55), the currents in the energy-transferring capacitor C₁ and the switch S₁ can be obtained by

$$\begin{array}{ll}{i}_{C1}(t)& =C_{S1}\frac{d{v}_{S1}(t)}{dt}-\frac{I_{o2}}{2}\\ & =-I_{o2}\end{array}$$

(57)

$$\begin{array}{ll}{i}_{S1}(t)& =i_{C1}(t)+i_{S2}(t)\\ & =-I_{o2}+\frac{I_{o2}}{2}\\ & =\frac{-I_{o2}}{2}\end{array}$$

(58)

As soon as the voltages on the switches S₁ and S₃ are zero, the operation proceeds to state 9. The corresponding time elapsed is

$$t_9-t_8=\frac{2\times V_{C2}\times C_{S4}}{I_{o4}}=\frac{V_{in}\times C_{S2}}{I_{o2}}$$

(59)

State 10 (t₉ < t < t₀ + T_s): As shown in Figure 22, all the four switches S₁ and S₃ are still off, whereas all the four diodes are still forward biased. The input voltage V_in, the diode D₁, the resonant inductor L_r1, the energy-transferring capacitor C₁ and the body diode of the switch S₁ form a loop; the energy-transferring capacitor C₂, the output current I_o2, the diode D₃, the resonant inductor L_r2, the energy-transferring capacitor C₃ and the body diode of the switch S₃ form a loop. Additionally, the corresponding equivalent circuit is shown in Figure 8. At the same time, L_r1 and L_r2 are demagnetized in opposite directions via S₁ and S₃, respectively, to achieve ZVS turn-on of S₁ and S₃.

At this point, the currents i_C1(t) and i_C3(t) are similar to those in state 1:

$$i_{C1}(t)=\frac{V_{in}-V_{C1}}{L_{r1}}\times (t-t_9)-I_{o2}$$

(60)

$$i_{C3}(t)=\frac{V_{C2}-V_{C3}}{L_{r2}}-I_{o4}$$

(61)

$$i_{C3}(t)=-i_{C2}(t)$$

(62)

This state ends when the switches S₁ and S₃ are turned on. The corresponding time elapsed and the current values of the energy-transferring capacitors C₁ and C₃ at the end of this state can be obtained by

$$t_0+T_s-t_9=T_d-(t_9-t_8)$$

(63)

$$\begin{array}{ll}{i}_{C1}(t_0+T_s)& =i_{C1}(t_0)\\ & =\frac{V_{in}-V_{C1}}{L_{r1}}\times \left[T_d-(t_9-t_8)\right]-I_{o2}\end{array}$$

(64)

$$\begin{array}{ll}{i}_{C3}(t_0+T_s)& =i_{C3}(t_0)\\ & =\frac{V_{C2}-V_{C3}}{L_{r2}}\times \left[T_d-(t_9-t_8)\right]-I_{o4}\end{array}$$

(65)

From the above analysis, one can see that in the proposed LED driver, four switches can achieve ZVS turn-on by using the parasitic capacitors of the MOSFETs and only one coupled inductor. Moreover, to make sure each LED string has the same current, differential-mode transformers are used.

2.3. Output Voltage Derivation

Before the output voltage is derived, the voltages on the three energy-transferring capacitors in the circuit should be obtained first, which can be acquired by using the potential mean value of each point in the circuit:

$$V_{C1}=\frac{1+D}{2}\times V_{in}$$

(66)

$$V_{C2}=\frac{V_{in}}{2}$$

(67)

$$V_{C3}=\frac{D}{2}\times V_{in}$$

(68)

Afterwards, the output voltage of the proposed circuit is derived. First, in each state, the voltage is multiplied by the current, and the input power P_in is the average of the sum of all the corresponding calculated values shown in (79):

$$\begin{array}{ll}{P}_{in}& =\frac{1}{T_s}\underset{t_0}{\overset{t_0+T_s}{\int }}{V}_{in}\times i_{in}(t)dt\\ & =V_{in}{f}_s\times \left[\begin{array}{l}\underset{t_0}{\overset{t_1}{\int }}{i}_{C1}(t)dt+\underset{t_1}{\overset{t_2}{\int }}{i}_{C1}(t)dt+\underset{t_2}{\overset{t_3}{\int }}{i}_{C1}(t)dt+\underset{t_3}{\overset{t_4}{\int }}{i}_{S1}(t)dt\\ +\underset{t_4}{\overset{t_8}{\int }}0dt+\underset{t_8}{\overset{t_9}{\int }}{i}_{S1}(t)dt+\underset{t_9}{\overset{t_0+T_s}{\int }}{i}_{C1}(t)dt\end{array}\right]\end{array}$$

(69)

Since the current in the energy-transferring capacitor C₁ rises from −I_o in state 10 and to I_o at the end of state 2, the sum of the corresponding average values is zero, as shown in (70):

$$\underset{t_0}{\overset{t_1}{\int }}{i}_{C1}(t)dt+\underset{t_1}{\overset{t_2}{\int }}{i}_{C1}(t)dt+\underset{t_9}{\overset{t_0+T_s}{\int }}{i}_{C1}(t)dt=0$$

(70)

Moreover, the currents in the switch S₁ in states 4 and 9 are 0.5I_o1 and −0.5I_o1, respectively, and the elapsed times of states 4 and 9 are the same, so the sum of the corresponding average values is zero, as shown in (81):

$$\underset{t_3}{\overset{t_4}{\int }}{i}_{S1}(t)dt+\underset{t_8}{\overset{t_9}{\int }}{i}_{S1}(t)dt=0$$

(71)

Therefore, (69) can be rewritten as

$$P_{in}=V_{in}{f}_s\times \underset{t_2}{\overset{t_3}{\int }}{i}_{C1}(t)dt$$

(72)

According to (15), (72) can be rewritten as

$$P_{in}=V_{in}{f}_s\times I_o\times (t_3-t_2)$$

(73)

By assuming that the input power P_in is equal to the output power P_o, the output voltage can be obtained as follows:

$$P_{in}=V_{in}{f}_s\times I_o\times (t_3-t_2)$$

(74)

$$P_o=4\times V_o\times I_o$$

(75)

$$V_o=\frac{t_3-t_2}{4\times T_s}\times V_{in}$$

(76)

The elapsed time experienced by state 3 is

$$\begin{array}{ll}{t}_3-t_2& =D{T}_s-(t_2-t_0)\\ & =D{T}_s-\frac{I_o\times L_{r1}}{V_{in}-V_{C1}}+\frac{i_{C1}(t_0)\times L_{r1}}{V_{in}-V_{C1}}\\ & =D{T}_s-\frac{I_o\times L_{r1}}{V_{in}-V_{C1}}-\frac{I_o\times L_{r1}}{V_{in}-V_{C1}}+\left(T_d-\frac{V_{in}\times C_{S2}}{I_o}\right)\\ & =D{T}_s-\frac{2\times I_o\times L_{r1}}{V_{in}-V_{C1}}+\left(T_d-\frac{V_{in}\times C_{S2}}{I_o}\right)\end{array}$$

(77)

By ignoring the blanking time T_d, the output voltage representation or the output current representation can be obtained to be

$$\begin{array}{l}{V}_o=\frac{D}{4}\times V_{in}-\frac{f_s\times I_o\times L_{r1}}{1-D}\\ \Rightarrow I_o=\frac{1-D}{L_{r1}\times f_s}\times (\frac{D}{4}\times V_{in}-V_o)\end{array}$$

(78)

According to (78), the output voltage V_o is determined by the duty cycle D, the resonant inductor L_r1, the output current I_o and the switching frequency f_s. In this paper, the change in D is used to adjust I_o to achieve LED dimming.

2.4. Soft Switching Analysis

In state 1, the current in the switch is negative when the switch is turned on, and hence the switch is turned on with ZVS. The proposed circuit utilizes the characteristics of inductance demagnetization to achieve ZVS. In state 10, the currents in the switches S₁ and S₃ flow through individual body diodes, and then the switches can be turned on with ZVS. The corresponding expression can be written as

$$i_{S1}(t_0)\le 0$$

(79)

In state 10, the switch S₁ and the energy-transferring capacitor C₁ are connected in series, and (79) can be rewritten as

$$i_{S1}(t_0)=i_{C1}(t_0)=\frac{V_{in}-V_{C1}}{L_{r1}}\times \left[T_d-(t_9-t_8)\right]-I_{o1}$$

(80)

By substituting (64) and (79) into (80), the minimum value of the resonant inductor L_r1 can be obtained by

$$\begin{array}{l}\frac{V_{in}-V_{C1}}{L_{r1}}\times (T_d-\frac{V_{in}\times C_{oss}}{I_o})-I_o\le 0\\ \Rightarrow (V_{in}-V_{C1})\times (T_d-\frac{V_{in}\times C_{oss}}{I_o})\le I_o\times L_{r1}\\ \Rightarrow L_{r1}\ge \frac{V_{in}\times (1-D)}{2\times I_o}\times (T_d-\frac{V_{in}\times C_{oss}}{I_o})\end{array}$$

(81)

3. Specification Considerations

Figure 23 shows the LED driver with automatic current sharing proposed in this paper. The system includes the main circuit and the feedback circuit. The main circuit is derived from an interleaved buck converter with low voltage stress and high step-down ratio [23]. As for the feedback control circuit, it adopts a current-detecting integral circuit (IC) named ACS712 to obtain the analog signal of the total output current. After sampling without analog-to-digital converter (ADC), this signal is sent to the FPGA, named EP3C5E144C8N, as a circuit control kernel, for calculation, to obtain suitable duty cycles to drive the four switches after individual isolated gate drivers, named TLP250H.

Table 1. System specifications.

Name	Specifications
System Operating Mode	Rated Load: CCM Half Load: BCM Light Load: DCM
Rated Input Voltage (Vin)	400 V
Rated Output Current per LED String (Io,rated)	0.35 A
Minimum Output Current per LED String in CCM (Io,min,BCM)	0.175 A
Minimum Output Current per LED String in DCM (Io,min,DCM)	0.0875 A
Rated Output Power (Po,rated)	38.64 W (4 Strings with 8 LEDs per String)
Minimum Output Power in CCM (Po,min,BCM)	17.36 W
Minimum Output Power in DCM (Po,min,DCM)	8.12 W
Switching Frequency (fs)/Period (Ts)	$100 \mathrm{kHz}/10 \mathsf{\mu }\mathrm{s}$

shows the specifications of the overall LED driver system. The specifications of LED and the specifications of components are shown in

Table 2. LED Specifications.

Name	Specifications
Forward Voltage (VF)	2.95~3.85 V
DC Operating Current (IF,max)	400 mA
Pulse Forward Current	500 mA
Junction Temperature	125 °C
Operating Temperature	−40~+85 °C
Typical Light Flux Output	100 lm@350 mA

and

Table 3. Component specifications.

Component	Specifications
S1, S2, S3, S4	IPA50R140CP
D1, D2, D3, D4	DSEP8-02A
C1, C2, C3	$47 \mathsf{\mu }\mathrm{F}$/400 V LTEC Electrolytic Capacitor
Co1, Co2, Co3, Co4	$220 \mathsf{\mu }\mathrm{F}$/50 V Electrolytic Capacitor
Mr	Core: ACME PQ20/20 Lr1 = Lr2 = 200 μF
M1, M2	Core: ACME PQ20/16 Leq1 = Leq2 = Leq3 = Leq4 = 600 μF
Gate Driver	TLP250H
Current Sensor	ACS712
LED	EHP-AX08EL/GT01H-P01/5670/Y/K42

, respectively.

4. Results and Discussion

4.1. Experimental Results

In the following, the waveforms were measured at rated load. From Figure 24, it can be seen that the voltages across the energy-transferring capacitors C₁, C₂ and C₃, called V_C1, V_C2 and V_C3, are all stabilized at different certain voltage values. Figure 25 shows the gate driving signals for S₁ and S₂, named v_gs1 (=v_gs3) and v_gs2 (=v_gs4), respectively. In addition, two blanking times of 700 us were inserted between v_gs1 and v_gs2. The corresponding oscillation in the negative half of i_Lr1 (=i_C1) and i_Lr2 (=i_C2) was caused by the resonance of the parasitic capacitance of the switch and the inductance in the circuit. In Figure 26, it can be seen that the DC values of the inductor currents i_Leq1 (=i_L1), i_Leq2 (=i_L2), i_Leq3 (=i_L3) and i_Leq4 (=i_L4) are approximately the same, and this is consistent with the current sharing among the four phases, so the load current can be evenly distributed. Figure 27 shows the currents flowing through the LED strings LS₁, LS₂, LS₃ and LS₄, named I_o1, I_o2, I_o3 and I_o4; and it can be seen that they are almost identical. Figure 28, Figure 29, Figure 30 and Figure 31 display the soft-switching waveforms for the switches S₁ to S₄. In these figures, it can be seen that all the switches experience ZVS turn-on. Additionally, in these figures it can be seen that the resonant waveforms of the switches S₁ and S₃ during the turn-off period are due to the parasitic capacitances of S₁ and S₃ resonating with inductances. Figure 32 shows the curve of efficiency versus load current. In this figure, for the proposed circuit the maximum efficiency occurring at 50% load is 91.78% and the efficiency at 50% load is 87%. In addition, the proposed circuit has better efficiency performance than the circuit shown in [23] does. This is because the proposed circuit has ZVS soft switching only above 50% load. Note that Figure 33 shows a photo of the experimental setup.

4.2. Current Sharing Error Percentage

The current sharing error percentage is defined as

$$e_y=\frac{\left(I_{oy}-\frac{1}{n}{\displaystyle \sum _{x=1}^n{I}_{ox}}\right)}{\frac{1}{n}{\displaystyle \sum _{x=1}^n{I}_{ox}}}\times 100\%$$

(82)

where e_y is the current sharing error percentage of the y-th LED string, n is the number of LED strings, I_oy is the current flowing through the y-th LED string and ${\displaystyle \sum _{x=1}^n{I}_{ox}}$, which is the sum of all the LED string currents.

The current sharing error percentages of LED strings under different loads were calculated as shown in

Table 4. Current sharing error percentages of LED strings under different loads.

		LS1	LS2	LS3	LS4
100%	Ion (mA)	348	351	352	351
	en (%)	0.71	−0.14	−0.43	−0.14
75%	Ion (mA)	259	258	262	261
	en (%)	0.38	0.77	−0.77	−0.38
50%	Ion (mA)	176	171	172	176
	en (%)	−1.29	1.58	1.01	−1.29
25%	Ion (mA)	84.8	88.3	86.4	90.6
	en (%)	3.11	−0.89	1.29	−3.51

, where n is 1 to 4. In this table, the absolute error percentage above 50% load is within 2%. The higher the current load is, the less the absolute error percentage. As for 25% load, the absolute error percentage is within 4% due to the load current being low.

4.3. Extension of Number of LED Strings

In Figure 34, the circuit diagram of the proposed LED driver with six channels is presented (constructed with PSIM software). From the simulation results shown in Figure 35, it can be seen that the current balance between six LED strings is well maintained.

4.4. Cost Comparison

The cost comparison between the proposed circuit and the compared circuit [23] is shown in

Table 5. Cost comparison between the proposed circuit and the compared circuit [23].

Component	Proposed		[23]
	Specifications	Price (in USD)	Specifications	Price (in USD)
MOSFETs	IPA50R140CP × 4	(2.74/item) × 4 = 10.96	SPA07N60C3 × 4	(2.25/item) × 4 = 9.00
Diodes	DSEP8-02A × 4	(1.68/item) × 4 = 6.72	DSEP8-02A × 4	(1.68/item) × 4 = 6.72
Electrolytic Capacitors	47 μF/400 V × 3 220 μF/50 V × 4	(2.68/item) × 3 = 8.04 (0.65/item) × 4 = 2.60	47 μF/400 V × 3 220 μF/50 V × 4	(2.68/item) × 3 = 8.04 (0.65/item) × 4 = 2.60
Cores	ACME PQ20/20 × 1 ACME PQ20/16 × 2 MA100 × 3	(1.15/item) × 2 = 2.30 (1.03/item) × 2 = 2.06 (0.45/item) × 3 = 1.35	ACME PQ20/16 × 4	(1.03/item) × 4 = 4.12
	Total Price	54.03	Total Price	30.48

. Although in this table the cost of the first is higher than that of the second, in Figure 32 the efficiency performance of the first is better than that of the second.

5. Conclusions

In this paper, we presented a high step-down LED driver combining a resonant coupled inductor with the parasitic capacitors on the switches, differential-mode transformers, odd output inductors coupled together and even output inductors coupled together, to achieve ZVS turn-on, current sharing and core size reduction. The proposed LED driver can not only achieve automatic current sharing and a high step-down voltage conversion ratio without complex control, but also the number of LED strings can be extended easily. From the experimental results, the ZVS turn-on of all the four switches and the current balance between the four LED strings can be realized above the minimum load of 50% load. The absolute error percentage for current sharing is within 2% at above 50% load. The efficiency is 87% at 50% load and can be up to 91.78% at 100% load. As for efficiency comparison, the proposed circuit has better efficiency above 50% load than the compared circuit does, whereas the latter has better efficiency below 50% load than the former does. This is because the proposed circuit has ZVS soft switching only above 50% load. As for cost comparison, the cost difference between the two is about USD 24. That is, the proposed circuit is more expensive.