A High Power Factor LED Driver with Intrinsic Current Balancing Capability

Abstract

The research proposed a novel LED driver with the functions of power-factor correction (PFC) and current balancing. A flyback converter and a Class-D series resonant converter were integrated by sharing an active switch to form a single-stage circuit topology. The flyback converter played the role of a PFC circuit. The component parameters were designed to make the flyback converter to operate at discontinuous-conduction mode (DCM). In this way, the input line current can be sinusoidal, resulting in near unity power factor and low total harmonic distortion in current (THDi). The resonant converter was connected in series with a differential-mode transformer with a turns ratio of 1 to drive four LED strings. The current of the four LED strings will be automatically and evenly balanced by using the 1:1 transformer. This article analyzed the different modes of operation in detail, derived the mathematical equations and designed the parameters of the circuit components. Finally, a 72-W prototype LED driver was implemented and tested. A satisfactory performance has verified the feasibility of the proposed LED driver.

1. Introduction

Light-emitting diodes (LED) have a much longer lifespan than traditional light sources, due to continuous innovation and advancement in manufacturing techniques and materials. Generally, the service life of LEDs can reach about 100,000 h, whereas fluorescent lamps and incandescent bulbs typically last only a few thousand hours. In addition, LED has many benefits, including compact size, high energy efficiency, good color rendering, fast response speed, and so on. These advantages mean that LEDs are widely used in many light applications [1,2,3]. Nowadays, the power level of a high-brightness LED is approximately hundreds of milliwatts to several watts. For large luminous lighting systems, a large number of LEDs are required to meet high power requirements. These LEDs are connected in combinations of series and/or parallel connections [4,5].

Even for the same type of LED, the voltage–current characteristic curve of each LED will inevitably have slight differences. Moreover, connecting multiple LEDs in series will amplify the difference between each LED string, resulting in unbalanced LED current in each string. What is more serious is that LED has a negative temperature coefficient characteristic, that is, its forward voltage decreases with the increase of temperature. This negative temperature coefficient characteristic will aggravate the current imbalance between the strings and even cause the LED to burn out due to thermal runaway. Therefore, the study of current balancing techniques for parallel-connected LEDs is an important topic for LED lighting apparatuses. This helps to extend the life of the LEDs and ensures that they all operate at their maximum efficiency. For lower power lighting equipment, current-mirror technology is usually used to achieve current balancing [6,7,8]. Current-mirror technology uses transistors in series with each LED string. These transistors are controlled to have the same current, i.e., the same current in the LED strings. Since these transistors are not operated as switches and their conducting voltages are high, resulting in large conduction losses.

The active current-balancing techniques use logic circuits to regulate the current of each string of LEDs [9,10,11,12]. This method requires a more complex circuit and is more expensive because all LED strings require separate current control loops and drive circuits. Passive current-balancing techniques use passive components such as diodes, inductors, capacitors or transformers [13,14,15,16,17,18]. Compared to active techniques, passive techniques are simpler because no additional active switches and complex control circuitry are required. Among them, some techniques use multiple transformers with primary windings connected in series so that the secondary windings can have the same current [13,14]. Other methods place each LED string in series with a capacitor and/or inductor with high impedance. Using high-impedance inductors or capacitors can effectively alleviate the influence of current imbalance caused by differences in LED equivalent resistance [15,16]. Nevertheless, these approaches require the use of bulky transformers, inductors, or capacitors. References [17,18] used the ampere-second balance principle of capacitance to automatically balance the current between LED strings. The disadvantage is that, when expanding the number of LED strings, it is necessary to add resonant inductors and capacitors, resulting in a large increase in the number of components. A series resonant converter has the advantage of low switching losses due to zero-voltage switching on (ZVS) when it is designed to operate with an inductive load. In addition, its resonant capacitor can block the DC component of the input voltage so that the resonant current flowing through it is a pure AC component. In other words, the forward average value of the resonant current is the same as the reverse average value. When the load is two anti-parallel LED strings, the currents flowing through the LED strings are automatically equal without adding any components for current balancing [19,20].

Another research topic related to LED drivers is PFC; the power factor and THDi of lighting equipment must comply with standards such as IEC 61000-3-2 Class D and IEEE 519. Therefore, LED drivers must use an additional ac/dc, which serves as a power-factor correction (PFC) circuit to satisfy these standards. It results in a two-stage circuit topology. The first stage is a PFC circuit to shape the input current into a sine wave and the second stage is a dc/dc converter to regulate the LED voltage. Although performing well, the two-stage approach requires more circuit components. Aiming to reduce the number of components and to improve energy conversion efficiency, many single-stage LED drivers which integrate the PFC circuit and the dc/dc converter have been proposed [21,22,23,24,25]. In references [21,22], the PFC circuits are boost converters, which are operated at either boundary-conduction mode (BCM) or discontinuous-current mode (DCM). Operating the boost converter at BCM or DCM can achieve a high power factor with easier control. However, when a boost converter operates at BCM or DCM, the dc-bus voltage should be at least twice the peak of the ac input to achieve a nearly unity power factor. In contrast, buck-boost or flyback converters are also commonly used as PFC circuits. However, they have no such limitation on the dc-link voltage. A high power factor can be achieved by operating them at a fixed switching frequency and a fixed duty cycle over the line frequency cycle [23,24,25]. In reference [23,24], a buck-boost converter was used as the PFC circuit, while in reference [25] a flyback converter was used. Typically, the LED voltage is much lower than the magnitude of the input voltage. The flyback converter uses a coupled inductor as an energy storage component and the winding turns ratio can be selected according to the output voltage specification. When the primary-to-secondary turns ratio is high, the voltage rating of the dc/dc converter can be effectively reduced.

In this paper, a new single-stage LED driver derived by integrating a flyback-typed PFC circuit and a Class-D series resonant converter was proposed. One of the two active switches of the resonant converter was shared with the flyback converter. The flyback converter served as the PFC circuit while the Class-D series resonant converter served as the dc/dc converter. A differential-mode transformer was added to the resonant converter [26]. With this 1:1 turns ratio transformer, the automatic current balancing capability can be extended to four LED strings without resorting to any complex control circuitry. This paper is organized as follows. Section 2 describes the circuit topology of the LED driver and the circuit operation in different operating modes. Detailed circuit analyses, an illustrative prototype, and the experimental results of LED driver are provided in Section 3 and Section 4, respectively. Finally, some conclusions are given in Section 5.

2. Analysis of the Proposed LED Driver Circuit

By integrating a flyback converter and a Class-D series resonant converter, the novel single-stage LED driver was proposed, as shown in Figure 1. The load was composed of four strings of LEDs. There were two MOSFETs, S₁ and S₂, with intrinsic body diodes D_S1 and D_S2, respectively. The flyback converter consists of a coupled inductor T₁, a MOSFET S₂, a diode D₁, and a dc-link capacitor C_dc. It is operated at a discontinuous-conduction mode (DCM). In this way, in each high-frequency cycle, the primary current of T₁ is triangular-shaped, and its peak value in each high-frequency cycle forms a sinusoidal envelope. A low-pass filter (L_f and C_f) can remove the high frequency components of the primary current and the input line source only needs to provide the average value. The series resonant converter consists of S₁, S₂, a resonant tank (L_r and C_r), a diode D₃, and a differential-mode transformer T₂. The turn ratio of T₂ is equal to one. Therefore, the primary and secondary currents of T₂ are equal.

The input voltage is sinusoidal.

$$v_{in}\left(t\right)=V_m\sin \left(2\pi f_{L}t\right),$$

(1)

where f_L and V_m are the frequency and amplitude of the input voltage, respectively.

S₁ and S₂ are alternatively turned on and off by two high-frequency gate voltages, v_GS1 and v_GS2. They are a pair of symmetrical and complementary and square wave voltages. There is a short deadtime between them to avoid simultaneous conduction of S₁ and S₂.

To simplify the circuit analysis, the following assumptions were made:

• All components are considered ideal;
• The leakage inductance of T₁ and T₂ is negligible in comparison to the magnetizing inductance;
• The switching frequency (f_s) of S₁ and S₂ is far higher than f_L, thus, V_in is considered constant in a high-frequency period;
• The capacitances C_dc and C_o1–C_o4 are large enough so that the voltages across them (V_dc, V_o1–V_o4) are constant at steady-state operation;
• The current of each LED string is equal. (I_LED1 = I_LED2 = I_LED3 = I_LED4 = I_LED).

Based on these assumptions, there will be six modes of operation in a high frequency cycle at a steady state. Figure 2 shows the current loops for each mode, where v_rec is the rectified line voltage and R₁–R₄ represent the equivalent resistance of these four LED strings. Figure 3 illustrates the key waveforms of the proposed circuit in high-switching cycles. The circuit operation of each mode was analyzed as follows.

2.1. Mode I ($t_0<t<t_1$)

Mode I begins at time t₀ as soon as the gate signal v_GS2 goes from a low to a high level to turn on S₂. Figure 2a shows the equivalent circuit of Mode I. The primary inductance voltage of T₁ is equal to the rectified input voltage. Owing to DCM operation, the primary current i_L1 rises from zero linearly.

$$v_{L1}\left(t\right)=V_m\left|\sin \left(2\pi f_{L}t\right)\right|,$$

(2)

$$i_{L1}\left(t\right)=\frac{V_m\left|\sin \left(2\pi f_{L}t\right)\right|}{L_1}\left(t-t_0\right),$$

(3)

where L₁ is the primary inductance of T₁. As shown in the equivalent circuit, the input voltage of the series resonant converter is zero volts.

$$v_{AB}\left(t\right)=0.$$

(4)

The resonant current i_r is positive and flows through both windings of T₂, D_o1, D_o3, and D₃. The turn ratio of T₂ is equal to 1, so the winding currents are equal to half of i_r.

$$i_{Do1}\left(t\right)=i_{pri}\left(t\right)=\frac{i_r\left(t\right)}{2},$$

(5)

$$i_{Do3}\left(t\right)=i_{sec}\left(t\right)=\frac{i_r\left(t\right)}{2}.$$

(6)

Applying Kirchhoff’s voltage law to the resonant current loop yields the following equations.

$$v_{CB}\left(t\right)=v_{pri}\left(t\right)+V_{o1}=-v_{sec}\left(t\right)+V_{o3}.$$

(7)

With a turn ration of 1, the primary winding voltage v_pri and the secondary winding voltage v_sec are equal. From Equation (7), v_CB, v_pri, and v_sec, can be obtained.

$$v_{pri}\left(t\right)=v_{sec}\left(t\right)=\frac{V_{o3}-V_{o1}}{2},$$

(8)

$$v_{CB}\left(t\right)=\frac{V_{o1}+V_{o3}}{2}.$$

(9)

When i_r resonates to zero and changes its polarity, the circuit enters mode II.

2.2. Mode II ($t_1<t<t_2$)

S₂ remains on, and v_L1 and i_L1 equations are the same as Equations (2) and (3). The current i_L1 increases continuously and linearly. In this mode, i_r becomes negative and flows through both windings of T₂, D_o2, D_o4, D₂, and S₂.

$$i_{Do2}\left(t\right)=-i_{pri}\left(t\right)=\frac{-i_r\left(t\right)}{2},$$

(10)

$$i_{Do4}\left(t\right)=-i_{sec}\left(t\right)=\frac{-i_r\left(t\right)}{2}.$$

(11)

Applying Kirchhoff’s voltage law to the resonant current loop yields

$$v_{CB}\left(t\right)=v_{pri}\left(t\right)-V_{o2}=-v_{sec}\left(t\right)-V_{o4}.$$

(12)

From Equation (12), v_CB, v_pri and v_sec, can be obtained.

$$v_{pri}\left(t\right)=v_{sec}\left(t\right)=\frac{-V_{o4}+V_{o2}}{2},$$

(13)

$$v_{CB}\left(t\right)=\frac{-\left(V_{o2}+V_{o4}\right)}{2}.$$

(14)

When v_GS2 becomes zero volts, S₂ is switched off and the circuit goes to Mode III.

2.3. Mode III ($t_2<t<t_3$)

Prior to this mode, both currents i_L1 and i_r flow through S₂, and i_L1 reaches a peak value expressed as

$$i_{L1,peak}\left(t\right)=\frac{V_m\left|\sin \left(2\pi f_{L}t\right)\right|}{L_1}\left(t_2-t_0\right)=\frac{V_m\left|\sin \left(2\pi f_{L}t\right)\right|}{L_1}D{T}_s,$$

(15)

where T_s and D represent the switching cycle and duty ratio of S₂. An induced current in the secondary winding of T₁ will be generated to make the magnetic flux through the core of T₁ be consistent. The induced current i_L2 flows through D₁ to charge the dc-link capacitor C_dc. The voltage across L₂ is equal to −V_dc, so i_L2 declines.

$$i_{L2}\left(t\right)=n{i}_{L1, peak}\left(t\right)-\frac{V_{dc}}{L_2}\left(t-t_2\right),$$

(16)

where L₂ represents the secondary inductance of T₁ and n denotes the ratio of the number of turns of the primary winding to that of the secondary winding (n = N₁/N₂).

At the beginning of this mode, i_r diverts from S₂ to flow through the intrinsic diode D_S1. As shown in Figure 3, i_r is in the negative half cycle of its sinusoidal waveform and gradually rises. After a short deadtime after S₂ is turned off, v_GS1 changes from zero volts to a high-level voltage. Since i_r is still negative, it will keep flowing through D_S1. The input voltage of the resonant converter is equal to the dc-link voltage. The voltage and current equations for i_Do2, i_Do4, v_pri, v_sec, and v_CB are the same as Equations (10)–(14). When i_r rises to pass the zero-crossing point, it changes polarity and starts to flow through S₁, and the circuit enters operation Mode IV.

2.4. Mode IV ($t_3<t<t_4$)

Current i_r is positive and flows through both windings of T₂, D_o1, D_o3, and S₁. The voltage and current equations for i_Do1, i_Do3, v_pri, v_sec, and v_CB are the same as Equations (5)–(9). For the flyback PFC circuit, i_L2 keeps declining. When i_L2 declines to zero, the circuit enters Mode V.

2.5. Mode V ($t_4<t<t_5$)

In this mode, there is no current in the flyback converter. Only the dc-link capacitor continuously supplies current to the load resonant circuit. S₁ is turned off as soon as v_GS1 becomes zero volts and the circuit enters Mode VI.

2.6. Mode VI ($t_5<t<t_6$)

Mode VI has the same resonant current loop as Mode I; therefore, the voltage and current equations for i_Do1, i_Do3, v_pri, v_sec, and v_CB are the same as in Equations (5)–(9). When v_GS2 changes from zero volts to a high level, S₂ is turned on and the circuit operation goes into Mode I of the next high frequency cycle.

3. Mathematical Equations for Parameters Design

3.1. Flyback-Typed Power-Factor Correction Circuit

Based on analysis of the operation modes, i_L1 rises linearly from zero at the beginning of Mode I and reaches a peak value at the end of Mode II. From (3), the peak value of i_L1 is equal to

$$i_{L1, peak}(t)=\frac{D{T}_s{V}_m\sin (2\pi f_{L}t)}{L_1}=\frac{D{V}_m\sin (2\pi f_{L}t)}{L_1{f}_s},$$

(17)

where D represents the duty ratio of S₂. Figure 4 shows the conceptual waveform of T₁ primary current and the input current. The cutoff frequency of L_f and C_f will be designed to be less than one-eighth of f_s so that most of the high-frequency components of i_L1 can be removed and the line input voltage only provides the average of i_L1 over one high frequency cycle.

$$i_{in}(t)=\overline{i_{L1}(t)}=\frac{1}{T_S}{\displaystyle {\int }_0^{T_s}{i}_{L1}}(t)\cdot dt=\frac{D^2{V}_m}{2L_1{f}_s}\sin \left(2\pi f_{L}t\right).$$

(18)

It can be seen from Equation (18) that the line current is not only sinusoidal but also in phase with the input voltage. Therefore, high power factor and low THDi ca be obtained. The input power can be derived and expressed as

$$P_{in}=\frac{1}{\pi }{\displaystyle {\int }_0^{\pi }{V}_m\sin (2\pi f_{L}t)\cdot i_{in}(t)d(2\pi f_{L}t)=\frac{D^2{V}_m^2}{4L_1{f}_s}}.$$

(19)

The LED power can be expressed as

$$P_{LED}=\frac{\eta D^2{V}_m^2}{4L_1{f}_s},$$

(20)

where η represents the energy-conversion efficiency. Equation (20) indicates that the output power can be controlled by regulating either the switching frequency or the duty ratio.

To ensure DCM operation, the drop time of the T₁ secondary current from peak to zero must be less than (1 − D)T_s.

$$T_{off}(t)=\frac{V_m\left|\sin (2\pi f_{L}t)\right|}{n{V}_{dc}}D{T}_s<(1-D)T_s.$$

(21)

From Equation (21), when V_dc is high enough, it is guaranteed that the flyback converter can operate at DCM during the entire period of the input voltage.

$$V_{dc}>\frac{D{V}_m}{n\left(1-D\right)},$$

(22)

3.2. Class-D Series Resonant Converter

The equivalent circuit of the series resonant converter is shown in Figure 5a. According to the analysis of operation modes, the input voltage of the resonant converter is expressed as

$$v_{AB}\left(t\right)=\{\begin{array}{l}{V}_{dc}, \mathrm{for} 0<\mathsf{\omega }t\le \pi \\ 0, \mathrm{for} \pi <\mathsf{\omega }t\le 2\pi \end{array}.$$

(23)

This voltage can be expanded into Fourier series,

$$v_{AB}\left(t\right)=\frac{V_{dc}}{2}+{\displaystyle \sum _{n=1, 3, 5, \dots }\frac{2V_{dc}}{n\pi }\sin \left(n\mathsf{\omega }t\right)}.$$

(24)

The root-mean-square value of the fundamental voltage of v_AB is given by

$$V_{1, rms}=\frac{\sqrt{2}{V}_{dc}}{\pi }.$$

(25)

It can be known from Equations (9) and (14) that v_CB is also a square wave expressed as

$$v_{CB}\left(t\right)=\{\begin{array}{l}0.5\left(V_{o1}+V_{o3}\right), \mathrm{for} \theta <\mathsf{\omega }t\le \theta +\pi \\ -0.5\left(V_{o2}+V_{o4}\right), \mathrm{for} \theta +\pi <\mathsf{\omega }t\le \theta +2\pi \end{array}.$$

(26)

In the practical circuit, the number of LEDs in each string is equal, and LEDs of the same type have almost the same voltage, so

$$V_{o1}\approx V_{o2}\approx V_{o3}\approx V_{o4}\approx V_{LED},$$

(27)

where V_LED represents the total voltage of each LED sting. Combining Equations (26) and (27), the Fourier expansion for v_CB is

$$v_{CB}\left(t\right) = {\displaystyle \sum _{n=1, 3, 5, \dots }\frac{4V_{LED}}{n\pi }\sin \left(2n\pi f_{s}t\right)}\hspace{1em}\hspace{1em}n = 1, 3, 5\dots$$

(28)

The root-mean-square value of the fundamental voltage of v_CB is given by

$$V_{o1, rms}=\frac{2\sqrt{2}{V}_{LED}}{\pi }.$$

(29)

When a series resonant circuit has a high loaded quality factor, the current in the resonant tank would be approximately sinusoidal, and the series resonant converter can be approximately analyzed by using the fundamental wave method (FWM). The equivalent circuit for FWM analysis is shown in Figure 5b, where R_o,equ is the equivalent load resistance [21,22].

$$R_{o,equ} = \frac{V_{o1,rms}}{I_{r,rms}}.$$

(30)

The load quality factor of a series resonant circuit is defined as

$$Q_L = \frac{\sqrt{L_r/{\mathrm{C}}_r}}{R_{o,equ}}.$$

(31)

The LED current is supplied from the resonant current. At steady-state operation, the following equation must be satisfied.

$$\frac{2}{T_s}{\displaystyle \underset{0}{\overset{\frac{T_s}{2}}{\int }}\sqrt{2}}{I}_{r,rms}\sin \left(2\pi f_{s}t\right)dt=4I_{LED}.$$

(32)

The following equation is obtained by solving Equation (32),

$$I_{r,rms}=\sqrt{2}\pi I_{LED},$$

(33)

where I_LED represents the current in each LED string. The phasor relationship between V_o1 and V₁ can be expressed as follows:

$$\overrightarrow{V_1}=V_{o1}\angle 0^{°}+j{X}_s{I}_r\angle 0^{°},$$

(34)

where the impedance of the resonant tank is

$$X_s = 2\pi f_s{L}_r-\frac{1}{2\pi f_s{C}_r}.$$

(35)

Using Equation (34), the following equation is derived:

$${\left(V_{1,rms}\right)}^2={\left(I_{r,rms}{X}_s\right)}^2+{\left(V_{o1,rms}\right)}^2.$$

(36)

Referring to Figure 2a,b, the following equations can be obtained.

$$v_{CB}\left(t\right)=\{\begin{array}{l}{V}_{pri}+0.7+V_{o1}=-V_{sec}+0.7+V_{o3} \mathrm{when} D_{o1}\mathrm{and} D_{o3} \mathrm{are} \mathrm{on}. \\ V_{pri}-0.7-V_{o2}=-V_{sec}-0.7-V_{o4} \mathrm{when} D_{o2} \mathrm{and} D_{o4}\mathrm{are} \mathrm{on}. \end{array}$$

(37)

From Equation (37), the primary voltage of T₂ can be expressed as

$$V_{pri}\left(t\right)=V_{sec}\left(t\right)=\{\begin{array}{l}0.5\left(V_{o3}-V_{o1}\right) \mathrm{when} D_{o1}\mathrm{and} D_{o3} \mathrm{are} \mathrm{on}. \\ 0.5\left(V_{o2}-V_{o4}\right) \mathrm{when} D_{o2} \mathrm{and} D_{o4}\mathrm{are} \mathrm{on}. \end{array}$$

(38)

4. Circuit Design and Experimental Results

A 72-W LED driver was used as an illustrative example. The circuit specification is listed in

Table 1. Circuit specification.

Vin	110 V ± 10% (rms), 60 Hz
PLED	72 W (24 × 3 W)
VLED	23.1 V (6 × 3.85 V)
ILED	0.78 A
fs	50 kHz
D	0.45

. The load was four LED strings. Each string was composed of six 3-W LEDs. The rated current and rated voltage of each LED were 0.78A and 3.85 V, respectively. The duty ratio and switching frequency of S₁ are 0.45 and 50 kHz, respectively.

4.1. Parameters Design

4.1.1. Parameters of the Flyback Converter

According to Inequality (22), the dc-link voltage is inverse proportion to the turns ratio of T₁. The higher the turns ratio, the lower the dc-link voltage. In this illustrative example, the turns ratio is chosen as 2:1 and, as a result of the calculation of Inequality (22), V_dc must be higher than 70 V.

$$V_{dc}>\frac{0.45\times 110\times \sqrt{2}\times 1.1}{2\left(1-0.45\right)}=70 \mathrm{V}.$$

Here, the value of V_dc is designed to be 100 V. By using Equation (20), the primary inductance of T₁ is calculated based on an assumption of 90% circuit efficiency.

$$L_1=\frac{0.9\times {\left(110\times \sqrt{2}\right)}^2\times 0.45^2}{4\times 72\times 50\times {10}^3}=0.306 \mathrm{mH}.$$

4.1.2. Parameters of the Resonant Converter

The component parameters are calculated from the following steps.

• Step 1 Calculate I_r,rms.

The root-mean-square value of i_r is calculated by using Equation (33).

$$I_{r,rms}=\sqrt{2}\pi \times 0.78=3.46 \mathrm{A}.$$

• Step 2 Calculate V_1,rms and V_o1,rms.

The root-mean-square value of V₁ is calculated by using Equation (25).

$$V_{1, rms}=\frac{\sqrt{2}\times 100}{\pi }=45 \mathrm{V}.$$

As shown in Figure 1, each LED string is connected in series with a diode, and the conduction voltage of the diode is considered when designing the parameters. Referring to Figure 5b, the root-mean-square value of V_o1 can be calculated from Equation (29).

$$V_{o1, rms}=\frac{2\sqrt{2}\left(0.7+23.1\right)}{\pi }=21.4 \mathrm{V}.$$

• Step 3 Calculate R_o,equ and X_s.

By using Equations (30) and (36), the equivalent load resistance and impedance of the series resonant circuit are calculated, respectively.

$$R_{o,equ} = \frac{V_{o1,rms}}{I_{r,rms}}=\frac{21.4}{3.46}=6.18 \Omega$$

$$X_s=\frac{\sqrt{{\left(V_{1,rms}\right)}^2-{\left(V_{o1,rms}\right)}^2}}{I_{r,rms}}=\frac{\sqrt{{\left(45\right)}^2-{\left(21.4\right)}^2}}{3.46}=11.44 \Omega .$$

• Step 4 Determine Q_L and Calculate L_r and C_r.

Typically, when Q_L is higher than 2, i_r will approach a sinusoid [27]. Here, Q_L is chosen to be 3. Substituting Q_L = 3 and X_s = 11.44 Ω into Equations (31) and (35), respectively, the values of L_r and C_r are calculated.

$$C_r = 232 \mathrm{nF}, L_r = 0.08 \mathrm{mH}.$$

In order to use standard capacitance value close to 232 nF, C_r is chosen to be 220 nF, and then L_r is recalculated.

$$C_r = 220 \mathrm{nF}, L_r = 0.0825 \mathrm{mH}.$$

4.2. Experimental Results

The control circuitry was composed of a microcontroller (dsPIC33FJ16GS504) and two power MOSFET drivers (TLP250). From Equation (20), the LED power can be controlled by regulating the switching frequency of the active switches. A current sensor (ACS712) was used to sense the current in one of the LED strings and send its output to the microcontroller. Then, the frequency was adjusted to achieve stable LED current. A prototype circuit with the component parameters, as shown in

Table 2. Component parameters.

T1 turns ratio n	2
DC-link Voltage Vdc	100 V
Inductor Lf	0.5 mH
Capacitor Cf	2 μF
T1 primary inductance L1	0.306 mH
Capacitances Cdc, Co1–Co4	100 μF
Resonant Inductance Lr	0.083 mH
Resonant Capacitance Cr	220 nF
Active switches S1, S2,	SPW47N60C3
Diodes Dr1~Dr4, D1~D3, Do1~Do4	MUR460

, was built and tested.

The experimental results at rated power are shown in Figure 6a–g. Figure 6a shows the primary current (the lower waveform) and the secondary current (the upper waveform) in T₁ measured near the peak input voltage. Since the turn ratio of T₁ is 2, it can be seen that the peak value of the secondary current is twice that of the primary current. In addition, the current waveforms indicate that the flyback converter is operated at DCM, as expected. Figure 6b shows the voltage and current of the input line. Both of them are sinusoidal waveforms. As shown, the input current can follow the waveform of the line voltage and in phase with each other. It ensures a high power factor and low THDi. The measured power factor of 0.989 and THDi of 5.27% validate the excellent functionality of the flyback-typed PFC circuit. The drain-to-source voltage and current of S₁ are shown in Figure 6c. By designing the series resonant converter to present inductive characteristics, the resonant current will lag the input voltage of the resonant converter. Therefore, as soon as S₂ is turned off, the resonant current is converted to flow through the parasitic capacitor of S₁. When the parasitic capacitor is discharged to near zero volts (0.7 V), the resonant current will flow through D_s1 and then the voltage across S₁ is clamped to almost zero volts and the ZVS operation of S₁ is achieved, resulting in low switching losses. However, the shared active switch S₂ cannot fulfill ZVS operation. The drain-to-source voltage and current of S₂ are shown in Figure 6d. Since D₂ prevents the parasitic capacitance of S₂ from discharging to the resonant circuit, a spike current happens due to the short-circuit discharge of the parasitic capacitance as soon as turning on S₂, leading to higher switching-on losses.

Moreover, both currents of the flyback and Class-D converters flow through the shared active switch (S₂). In practice, there is unavoidable leakage inductance in the coupled inductor of the flyback converter. When S₂ is turned off, the current of the leakage inductance cannot be transferred to the resonant circuit. It will flow to and charge the parasitic capacitor of S₂. Since the parasitic capacitor is usually very small, it will not only be charged to high spike voltage (as shown) but also cause high switching losses. Some lossless and passive snubber circuits have been reported to reduce the spike voltage. The resonant current in the series resonant current is shown in Figure 6e. Since the loaded quality factor is high enough, the resonant current is approximately a sine wave with a zero DC component. Figure 6f,g show the voltages and currents of the four LED strings, respectively. The measure voltages are 22.86 V, 23.18 V, 22.53 V, and 23.08 V while the measured currents are 0.75 A, 0.77 A, 0.76 A, and 0.76 A, respectively. The maximum difference of each string current is about 0.02 A, which should be the value of the magnetizing current of T₂. The measured circuit efficiency is 88.2%. As predicted, the LED currents are almost the same; this proves the current balancing capability.

5. Conclusions

The study presented a novel LED driver. The circuit topology of a single stage was derived by integrating a flyback converter and a Class-D series resonant converter. Both converters share an active switch and the control circuit. A near unity power factor is obtained when the flyback converter is operated at DCM. The series resonant converter combines a differential-mode transformer with a turn ratio of 1. With the function of series resonant circuit and 1:1 transformer, the current of four LED strings can be automatically equalized, without any additional control circuit for current balancing. The measured power factor is as high as 0.99 and the THDi is 5.27% at the rated power operation. In addition, the experimental results verified that the proposed circuit can indeed achieve the LED current balancing function, and the measured circuit efficiency is 88.2%.