Circuit Topology Analysis for LED Lighting and Its Formulation Development

energies

Article Circuit Topology Analysis for LED Lighting and its Formulation Development

William Chen, Ka Wai Eric Cheng * and Jianwei Shao

Power Electronics Research Centre, Department of Electrical Engineering, The Hong Kong Polytechnic University, Kowloon 999077, Hong Kong, China; [email protected] (W.C.); [email protected] (J.S.) * Correspondence: [email protected]

Received: 30 July 2019; Accepted: 24 October 2019; Published: 4 November 2019

Abstract: Light emitted diode (LED) is becoming more popular in the illumination field, and the design of LED lighting is generally made to provide illumination at lower power usage, helping save energy. A power electronic converter is needed to provide the power conversion for these LEDs to meet high efficiency, reduce components, and have low voltage ripple magnitude. The power supply for LED is revisited in this paper. The LEDs connected in series with diode, transistor, or inductor paths are examined. The formulation for each of the cases is described, including the classical converters of buck, boost, buck–boost, and Cuk.´ The circuit reductions of the classic circuit, circuit without the capacitor, and without a freewheeling diode are studied. Using LED to replace freewheeling diodes is proposed for circuit component reduction. General equations for different connection paths have been developed. The efficiency and output ripple amplitude of the proposed power converters are investigated. Analytical study shows that the efficiency of proposed circuits can be high and voltage ripple magnitude of proposed circuits can be low. The results show that the proposed circuit topologies can be easily adapted to design LED lighting, which can meet the criteria of high efficiency, minimum components, and low-voltage ripple magnitude at the same time.

Keywords: LED driving circuit; diode path; transistor path; inductor path; theoretical analysis; ripple amplitude; eﬃciency; component count

1. Introduction LED is now an emerging product to replace conventional lighting and has gained acceptance in the lighting market, which started from a light source to now being used in decorative, display, and public lighting applications, such as display lighting, spotlight, streetlight, and general lighting [1–4]. The power levels of 1 W, 3 W, and 5 W are very common. Power level to 50 W is also available. Based on the commercial data collected, the power range of the LED drivers can be broadly divided into three groups, namely, low power (<25 W), medium power (25–100 W), and high power (>100 W) [1]. The fluorescent lamp requires voltage in the hundreds [5], and the HID lamps require tens of thousands of volts for the initial startup [6,7]. Therefore, LED is best used for low-voltage applications, which is safer and much more energy efficient [1,8]. Other advantages of LED lamps include the colour control, longer lifespan, and high efficiency [9]. Common available LED of lower power and higher power is still very expensive for consumers and is generally used for industrial applications. Therefore, the design of LED low-power devices is usually limited to lower power such as 5 W or less.

Energies 2019, 12, 4203; doi:10.3390/en12214203 www.mdpi.com/journal/energies Energies 2019, 12, 4203 2 of 27

LEDs must be driven by DC sources, and mixing multicolored LEDs can provide a large chromatic variation [10]. LED is a semiconductor device with no gaseous discharge or striking electrodes. Its lifetime is much higher than other lighting sources and it can be turned on and off under very high frequency, compared to other lamps. The long lifetime (e.g., 50,000 h) of modern LED devices is a factor that puts LED technology ahead of other light sources [1]. LED has even been applied to special effect designs [11]. According to [1], circuit topologies suitable for LED drivers can be categorized into passive LED drivers and switched-mode LED drivers based on whether high-frequency switching operation is performed. This passive LED driver consists of passive components and diodes only, without using any power electronic switches, auxiliary power supply, and control boards [12]. Passive drivers do not perform high-frequency switching operations and are thus simpler and more reliable, having long product lifetime, but they suffer from excessive power losses, so these drivers are not suitable for LED. Switched-mode drivers operate at high frequency and can involve compact size, low power loss, and precise output regulation. These properties allow them to have a broader range of applications. One merit of a switched-mode driver is that its output can be designed to exhibit small voltage and/or current ripples. Therefore, switched mode drivers are suitable to drive LED lighting. Classical topologies including the buck [13], boost [14,15], buck–boost [16], Cuk´ [17,18], and phase-shifted [19] can all be used as switched-mode drivers. LED drivers should be properly designed in order to fully utilize their potential benefits, such as the lifetime, efficiency, luminous efficacy, forward voltage drop, and spectral power distribution of the device [20,21]. Considering the special application of LED lighting, LED drivers should meet at least two criteria: (1) High efficiency without a complicated control circuit; (2) reduced components. The energy factor for LED circuit should be low in order to maximize the efficiency [22]. Recently, many driver topologies that have been modified to achieve high-efficiency operation require a complicated control circuit [13,23,24]. Reference [13] proposed a single-stage LED driver based on buck topology, which adopts current path control switches to improve efficiency and power factor. The proposed driver was configured as a hybrid combination of buck topology and multiple switches. Reference [23] introduced a bridgeless buck power factor correction rectifier that substantially improves efficiency at the low end of the universal line range. Reference [24] proposed a LED driver consisting of a buck–boost converter and a buck converter. Each converter adopts a power MOSFET as the active switch. Both active switches can operate at zero-voltage switching-on (ZVS) to effectively reduce the switching losses. However, almost all driving topologies designed to improve efficiency have complicated control circuits and many components. Thus, they are unsuitable for low-power lighting applications [25,26]. In addition, diode-like v–i characteristic implies that a slight variation of the applied voltage across an LED can cause a large fluctuation in its current and subsequently its luminous outputs [1]. In the case of LED embedded lighting, the output ripple amplitude is also a key factor when we design an LED driving circuit. Moreover, to reduce the conducted electromagnetic interference (EMI), a small ripple is required [27,28]. The output ripple amplitude also affects the lifetime of LEDs [29]. Reference [30] presented a design of a zero-voltage-ripple (ZVR) buck dc–dc converter. The circuit uses an autotransformer for ripple cancellation in the output voltage. Reference [31] proposed an electrolytic capacitor, with less power factor correction, and LED driver with reduced current ripple. The proposed LED driver is composed of a non-inverting buck–boost power-factor correction (PFC) converter and bidirectional converter (BDC) for ripple current cancellation. Reference [32] proposed a simple capacitors clamped current sharing circuit for multi-string LEDs to solve the current imbalance problem caused by the voltage drop tolerance of LED. In [33], an input-current, ripple-free, two-channel LED driver is presented. In the proposed LED driver, a current-sharing capacitor is integrated into the boost converter to achieve the current-sharing among the LEDs and to upgrade the output voltage gain. However, the presented methods in [30–33] need many switches, control drivers, or other extra components, which leads to complexity and high cost. In [34,35], with the charge balance principle of Energies 2019, 12, 4203 3 of 27 the capacitor, the LED currents can be automatically balanced. However, the structures used in [34,35] are more suitable for high-input-voltage applications. There is still a need to develop output ripple amplitude drivers with less components and no complexity for LEDs limited to a lower power. To overcome the aforementioned drawbacks and figure out an appropriate circuit topology that has high efficiency without a complicated control circuit, low component count, and low output ripple amplitude, this paper proposes a new family of power converters for the LED lighting field. They are modified versions of the buck, boost, buck–boost, and Cuk´ converter to provide the LED power excitation. Unlike previous works, the circuit proposed in this paper is used for the driver of LEDs at the diode path and transistor, based on the classical switched-mode power converters, which can simplify the circuit topology. Thus, the modified version can reduce the cost and component count, while also having a high efficiency. The previously mentioned circuit has a large shortcoming, the loss in resistor R, so this paper further simplifies the circuit in the inductor path. Theoretical electrical efficiency of these simplified converters in the inductor path is close to 100%. In addition, ripple analysis shows that output ripple amplitude can be low in this family of power converters. The experiment confirms the operation of the simplified converter with a reduced number of components. This paper is organized as follows: Section2 reviews the classical switched-mode power converters and proposes new topologies that put LEDs in a different path. Structures and theoretical analysis of the proposed circuit are explained in Section2. The voltage conversion, output power, and the e fficiency are presented. Section3 compares the e fficiency and output ripple amplitudes of the proposed new topologies. The experimental results are given in Section4. In Section5, the novelty of the work is presented. The conclusion is given in Section6.

2. LED Driving Circuit Topologies

2.1. Basic Topology Switched-mode power converters can be used directly for excitation of the LED lamps. The output of the converters is connected directly to the LED. The output voltage can be regulated by transistor duty ratio to control the LED output. Figure1 shows the connection of the converter for the LED. The LEDs shown are an LED array with LEDs connected in series. There are a number of LEDs connected in parallel that depend on the application. Only one row is drawn for clarity. To simplify theoretical analysis, the following assumption is made: All the circuit components are ideal in this paper. The voltage conversion ratio from input to output is the same as the conversion ratio for classical power converters. Energies 2019, 12, 4203 4 of 27 Energies 2019, 12, x FOR PEER REVIEW 4 of 28

T L

D LED C

GND

(a)

L D

T LED C

GND

(b)

T D

LED L C

GND

(c)

L2 T C1 D L1 LED C2

GND

(d)

FigureFigure 1. 1.Conventional Conventional method method for for LED LED connection. connection. ((aa)) BasicBasic LEDLED buckbuck converter; (b) Basic LED LED boost boost converter;converter; (c ()c Basic) Basic LED LED buck–boost buck–boost converter; converter; ( d(d)) Basic Basic LED LEDCuk ´Ćuk converter.converter.

Energies 2019, 12, x FOR PEER REVIEW 5 of 28

EnergiesThe2019 voltage, 12, 4203 conversion ratio from input to output is the same as the conversion ratio for classical5 of 27 power converters.

2.2. LEDs LEDs in Diode Path Switched-mode power converters converters are are used used for for the the design design of of power conditioning conditioning for for the the LED. LED. The power supply voltage and the LED voltage are low; therefore, an isolated version is used. It is designed to reduce the cost and component count. The following power version that was used is a modifiedmodiﬁed form of the classical switched mode power converters.

2.2.1. LED Buck Converter 2.2.1. LED Buck Converter Figure2 shows the conversion from the classical buck converter into an LED converter. The diode Figure 2 shows the conversion from the classical buck converter into an LED converter. The is replaced by the LED as shown. The original conversion ratio of the buck converter Vo/Vin is D, diode is replaced by the LED as shown. The original conversion ratio of the buck converter Vo/Vin is in which D is the duty ratio of the transistor T. D, in which D is the duty ratio of the transistor T.

T L

Vin LED Vo C R

GND

Figure 2. LED buck converter. Figure 2. LED buck converter. In the present circuit, the on-state voltage of LED cannot be ignored, so the revised voltage conversionIn the is:present circuit, the on-state voltage of LED cannot be ignored, so the revised voltage Vo = V D nV (1 D) (1) conversion is: in − LED − where n, is the number of LEDs in the series connected. VLED is assumed to be the on-state voltage of VVDnVDo in LED (1  ) (1) the LED, and although the VLED may vary with current and duty ratio, for simplicity, it is assumed wherethat all n, losses is the are number lumped of LEDs together in the as VseriesLED. connected. The connection VLED is of assumed the LED to can be also the beon-state in parallel. voltage The of peakthe LED, voltage andacross although allthe the LEDs VLED may is: vary with current and duty ratio, for simplicity, it is assumed that all losses are lumped together as VLED. VTheD_p connection= Vin of the LED can also be in parallel. The(2) peak voltage across all the LEDs is: The average current of LED is:

VVD_p in (2) ZTs The average current of LED is: I = i dt =Io(1 D) (3) D D −

(1 DT)sTs − IidtID(1 ) DDo (3) The power level of LED is: (1DT ) s The power level of LED is: T Z s 2 2 2 T nV V D(1 D) n V (1 D) s nV VLED D(1 Din ) n22 V (1 D ) 2 LED P = i v dt = nV I (1 D) = LED in− LED − (4) LED LEDPivdtnVIDLEDLED LED LEDLED LEDo o (1 )  − RRR − R (4) (1DT ) s (1 D)Ts − where VLED is the on-state voltage of LED. whereTheVLED poweris the loss on-state lies on voltageR and is of equal LED. to: The power loss lies on R and is equal to: 2 2 V VDin nV LED (1 D ) 2o 2 (5) PR V (V D nV (1 D)) P = oRR= in − LED − (5) R R R

Energies 2019, 12, x FOR PEER REVIEW 6 of 28 Energies 2019, 12, 4203 6 of 27 The efficiency of the LED circuit is:

The eﬃciency of the LED circuitPnVVDDnVD is: (1 )22 (1  ) 2  LED LED in LED (6) PP VD22 nVVD(1 D ) LED R in LED in 2 2 2 P nVLEDVinD(1 D) n V (1 D) η = LED = − − LED − (6) The operation is feasible when PLED is valid:2 2 PLED + PR V D nV V D(1 D) in − LED in − nV V D(1 D ) n22 V (1  D ) 2 (7) The operation is feasible when PLED inis valid: LED i.e., nV V D(1 D) > n2V2 (1 D)2 (7) LED in − LED − VDin nV LED (1 D ) (8) i.e., The above inequality is the same asV derivedinD > nV fromLED( 1(1). D) (8) Another condition for the circuit is that the total power− as shown in (6) is valid or greater than zero.The above inequality is the same as derived from (1). Another condition for the circuit is that the total power as shown in (6) is valid or greater than zero. 22 VDin nVVD LED in (1 D ) (9) 2 2 Vin D > nVLEDVinD(1 D) (9) i.e., − i.e., VD nV(1 D ) V inD > nV LED(1 D) in LED − Efficiency Equation (6) can be reduced to: Eﬃciency Equation (6) can be reduced to:

nVLED (1 D )  nVLED(1 D) (10) η = VDin − (10) VinD

2.2.2. LED Boost Converter Figure3 3 shows shows thethe LEDLED BoostBoost converter.converter. TheThe diode diode is is replaced replaced by by the the LED LED as as shown. shown.

L LED

T R C

GND

Figure 3. LED Boost converter. Figure 3. LED Boost converter. Using a similar derivation, the voltage conversion is: Using a similar derivation, the voltage conversion is: Vin Vo = nV (11) 1 VD − LED VnV− in (11) oLED1 D The power loss is: 2 2 The power loss is: Vo (Vin nVLED(1 D)) PR = = − − (12) R 2 2 2 R(1 D) V VnVDin LED−(1 ) P o (12) R R RD(1 )2

The output power of LED is:

Energies 2019, 12, 4203 7 of 27

EnergiesThe 2019 output, 12, x FOR power PEER of REVIEW LED is: 7 of 28

ZTs Ts V nV IVnVIo o LED PLED PivdtnVD= iLEDvLEDdt =nV ooLED(1(1 )D) = (13) LED LED LED LEDLED 1 D − R ) (13) (1DT ) 1 DR (1 D)Ts s − − TheThe eefficiencyﬃciency cancan bebe derivedderived as:as: PDnV(1 )  P LED(1 D)nV LED (14) = LED = LED η PPLED R− V in (14) PLED + PR Vin

2.2.3.2.2.3. LEDLED Buck–BoostBuck–Boost ConverterConverter FigureFigure4 4shows shows the the LED LED buck–boost buck–boost converter. converter. The The original original diode diode is is replaced replaced by by LED. LED.

T LED

R L C

GND

Figure 4. LED buck–boost converter. Figure 4. LED buck–boost converter. Using a similar derivation, the voltage conversion is the same as the buck counterpart: Using a similar derivation, the voltage conversion is the same as the buck counterpart: DVin Vo = DV nV (15) VnV1 Din − LED (15) oLED1− D The power loss can be obtained as: The power loss can be obtained as:

2 2 2 Vo 2 (VinD nVLED(1 D)) P = V = VDin− nV LED (1− D ) (16) R P o 2 (16) R R R(1 D)2 R RD(1− ) TheThe outputoutput powerpower ofof LEDLED is:is:

T ZTs s IVnV PivdtnVDooLEDIo (1 ) VonVLED (17) PLED =LEDiLED LEDvLED LEDdt =nV LEDLED1 DR(1 D) = (17) (1DT ) s 1 D − R (1 D)Ts − The efficiency can be derived− and is the same expression as the buck converter: The eﬃciency can be derived and is the same expression as the buck converter: PDnV(1 )  LED LED (18) PPP (1 VDD)nVLED η = LED R= − in (18) PLED + PR VinD 2.2.4. LED Ćuk Converter The other power converter can also be converted by this concept. Figure 5 shows the LED Ćuk converter. The Ćuk converter requires a number of components, and the cost is a concern. The use of two inductors does not benefit the LED.

Energies 2019, 12, 4203 8 of 27

2.2.4. LED Cuk´ Converter The other power converter can also be converted by this concept. Figure5 shows the LED Cuk´ converter. The Cuk´ converter requires a number of components, and the cost is a concern. The use of twoEnergies inductors 2019, 12, doesx FOR notPEER beneﬁt REVIEW the LED. 8 of 28

L1 L2 C1

LED T C2 R

GND

´ FigureFigure 5.5. LEDLED CukĆuk converter.converter.

The voltage conversion is the same as the buck–boost counterpart: The voltage conversion is the same as the buck–boost counterpart:

DVDVin VoVnV= in nVLED (19)(19) oLED1 D − 1− D TheThe powerpower lossloss cancan bebe obtainedobtained as:as:

2 2 2 2 VoV (VVDinD nV LED(1(1 DD ) )) P = o= in− LED − (20) R P  2 (20) R R R RRD((11 D ))2 − TheThe outputoutput powerpower ofof LEDLED is:is:

Ts Ts VnV PivdtnViIDZ ( )(1 ) o LED LED LED LED LED in o VonV LED (21) PLED = (1DTi )LEDvLEDdt =nVLED(iin + Io)(1 D) = R (21) s − R (1 D)Ts The efficiency can be derived− and is the same expression as the buck converter: The eﬃciency can be derived and is thePDnV same expression(1 ) as the buck converter:  LED LED (22) PP VD PLED R(1 D in)nVLED η = LED = − (22) PLED + PR VinD 2.3. LEDs in Transistor Path 2.3. LEDs in Transistor Path There are other topologies for LED connection. The LED array can be put in series with the There are other topologies for LED connection. The LED array can be put in series with the transistor. Figure 6 shows the connection of the LED in the transistor path. When the transistor is transistor. Figure6 shows the connection of the LED in the transistor path. When the transistor is turned on, the LED is turned on as well. turned on, the LED is turned on as well.

Energies 2019, 12, 4203 9 of 27

Energies 2019, 12, x FOR PEER REVIEW 9 of 28

L T LED Io L D

Vin D Vo LED C R C R

T GND GND

(a) (b)

L1 L2 C1 TLED D LED C2 L D R C R T

GND GND

Figure 6. TransistorFigure 6. Transistor path path LED LED converter. converter. ( aa) )Buck; Buck; (b) (Boost;b) Boost; (c) Buck–Boost; (c) Buck–Boost; (d) Ćuk. (d) Cuk.´

2.3.1. LED Buck2.3.1. LED Converter Buck Converter In Figure 6a, the on-state voltage of LED cannot be ignored, so the revised voltage conversion is: In Figure6a, the on-state voltage of LED cannot be ignored, so the revised voltage conversion is:

VVDnVDoinLED (23)

Vo = V D nV D (23) The power loss can be obtained as: in − LED 2 2 V VDin nVD LED The power loss can be obtained as:P o (24) R RR The power level of LED is: 2 2 Vo (VinD nVLEDD) PDTRs = = − 2 (24) R nVRLED D() V in nV LED PivdtnVID (25) LED LED LED LED o R 0s The power level of LED is: The efficiency of the LED buck circuit is reduced to:

DTs PnV Z  LED LED 2 (26) PPV nVLEDD (Vin nVLED) P = i v dt =nVLED RI D = in − (25) LED LED LED LED o R 0s 2.3.2. LED Boost Converter The eﬃciencyFor LED of the boost LED converters buck in circuit Figure 6a, is reducedthe output voltage to: of R is:

P nV η = LED = LED (26) PLED + PR Vin

2.3.2. LED Boost Converter For LED boost converters in Figure6a, the output voltage of R is:

V nV D V = in − LED (27) o 1 D − The power loss is: 2 2 Vo (VinD nVLEDD) PR = = − (28) R R(1 D)2 − Energies 2019, 12, 4203 10 of 27

The power level of LED is:

DT Z s ( ) nVLEDD Vin nVLEDD PLED = iLEDvLEDdt = − (29) (1 D)2R 0s −

The eﬃciency of the LED circuit is reduced to:

P nV D η = LED = LED (30) PLED + PR Vin

2.3.3. LED Buck–Boost Converter In Figure6c, the output voltage of R is:

(V nV )D V = in − LED (31) o 1 D − The power loss can be obtained as:

2 2 2 Vo (Vin nVLED) D PR = = − (32) R R(1 D)2 − The power level of LED is:

DTs Z 2 nVLEDD (Vin nVLED) PLED = iLEDvLEDdt = − (33) (1 D)2R 0s −

The eﬃciency of the LED buck–boost converter is:

P nV η = LED = LED (34) PLED + PR Vin

2.3.4. LED Cuk´ Converter For LED Cuk´ converters, the output voltage of R is:

(V nV )D V = in − LED (35) o 1 D − The power loss can be deduced as:

2 2 2 Vo (Vin nVLED) D PR = = − (36) R R(1 D)2 − The power level of LED is:

DTs Z 2 nVLEDD (Vin nVLED) PLED = iLEDvLEDdt = − (37) (1 D)2R 0s −

The eﬃciency of the LED Cuk´ converter can be obtained as:

P nV η = LED = LED (38) PLED + PR Vin Energies 2019, 12, x FOR PEER REVIEW 11 of 28

PnV  LED LED (38) PPV Energies 2019, 12, 4203 LED R in 11 of 27

2.4. LEDs in Inductor Path 2.4. LEDs in Inductor Path The above circuit in Sections 2.2 and 2.3 has a large problem due to the loss in resistor R. The above circuit in Sections 2.2 and 2.3 has a large problem due to the loss in resistor R. Therefore, Therefore, efficiency of the converter cannot be very high. Under high-frequency operation, it is not eﬃciency of the converter cannot be very high. Under high-frequency operation, it is not necessary for necessary for the DC voltage to be filtered as that of a power supply; hence, the circuit can be further the DC voltage to be ﬁltered as that of a power supply; hence, the circuit can be further reduced. reduced. 2.4.1. Buck Converter 2.4.1. Buck Converter Figure7 shows a chopper circuit for LED and is based on the “buck” converter. The circuit is similarFigure to the 7 shows classical a chopper chopper. circuit for LED and is based on the “buck” converter. The circuit is similar to the classical chopper.

Vin LED L

GND

FigureFigure 7. 7. SimplifiedSimpliﬁed LED LED chopper chopper like like a a “buck” “buck” converter. converter.

TheThe output output voltage voltage of of buck buck converter converter path path can can be be expressed expressed as: as:

VVVDnVo =V D nV (39)(39) oin − LEDLED TheThe voltage voltage conversion conversion is is now: now: V nV = V in (40) nVLED  1 in D (40) LED 1−D The output power is: The output power is: ZTs P = i v dt =nI V LED Ts LED LED o LED (41)

PivdtnIVLED(1 D)Ts LED LED o LED (41) −  (1DT ) s The eﬃciency is: The efficiency is: P nV D η = LED = LED (42) VinIin V D nV (1 D) PnVDin − LED − ==LED LED (42) 2.4.2. Boost Converter VIinin VD in nV LED (1 D )

EnergiesFigure 2019,8 12 shows, x FOR thePEER Simpliﬁed REVIEW LED Boost converter. 12 of 28 2.4.2. Boost Converter Figure 8 shows the Simplified LED Boost converter.

FigureFigure 8.8. SimpliﬁedSimplified LEDLED BoostBoost converter.converter.

The output of the boost converter can be written as: VnV V  in LED (43) o 1 D V I  o (44) in 1 D The voltage conversion ratio is: V nV  in (45) LED 1 D The output power is:

T s nI V PivdtoLED (46) LED LED LED 1 D (1DT ) s

The efficiency of the LED circuit is:

P 1 ==LED (47) VIin in 1- D 1  1 Since 1-D , which is not possible, it can be concluded that η is equal to 1 in the consideration of concerned circuits with ideal elements. In the whole paper, when it comes to η being equal to 1, it refers to the concerned circuits. The efficiency is close to 1 but not equal to 1 in the real system.

2.4.3. Buck–Boost Converter Figure 9 shows the Simplified LED buck–boost converter.

LED L

GND

Figure 9. Simplified LED buck–boost converter.

The output voltage of the buck–boost converter can be expressed as:

Energies 2019, 12, x FOR PEER REVIEW 12 of 28

Figure 8. Simplified LED Boost converter.

EnergiesThe2019 output, 12, 4203 of the boost converter can be written as: 12 of 27 VnV V  in LED (43) The output of the boost converter can beo written1 as:D

Vin VnVo LED Vo = I − (44)(43) in 1 D 1− D The voltage conversion ratio is: Vo I = (44) in 1 D − Vin The voltage conversion ratio is: nVLED  (45) 1V D nV = in (45) LED 1 D The output power is: − The output power is: T T s nI V PivdtZ s oLED LED LED LED nIoVLED (46) P = (1DT ) i v dt = 1 D (46) LED sLED LED 1 D (1 D)Ts − The efficiency of the LED circuit is:− The eﬃciency of the LED circuit is: P 1 ==LED (47) P VI1- D1 η = LEDin in= (47) VinIin 1 D 1 − 1 Since 1  , which is not possible, it can be concluded that η is equal to 1 in the consideration Since 1 1-D D> 1, which is not possible, it can be concluded that η is equal to 1 in the consideration of concernedof concerned circuits− circuits with with ideal ideal elements. elements In. In the the whole whole paper, paper, when when it it comes comes to toη ηbeing being equal equal to to 1, 1, it it refersrefers to to the the concerned concerned circuits. circuits. The The e efficiencyﬃciency is is close close to to 1 1 but but not not equal equal to to 1 1 in in the the real real system. system.

2.4.3.2.4.3. Buck–Boost Buck–Boost Converter Converter FigureFigure9 9shows shows the the Simpliﬁed Simplified LED LED buck–boost buck–boost converter. converter.

LED L

GND

FigureFigure 9. 9.Simpliﬁed Simplified LED LED buck–boost buck–boost converter. converter. The output voltage of the buck–boost converter can be expressed as: The output voltage of the buck–boost converter can be expressed as: DV nV V = in − LED (48) o 1 D − The voltage conversion ratio is: V nV = in (49) LED 1 D − The output power is: ZTs nI V P = i v dt = o LED (50) LED LED LED 1 D (1 D)Ts − − Energies 2019, 12, x FOR PEER REVIEW 13 of 28

DV nV V  in LED (48) o 1 D The voltage conversion ratio is:

V nV  in (49) LED 1 D The output power is:

T Energies 2019, 12, 4203 s nI V 13 of 27 PivdtoLED (50) LED LED LED 1 D (1DT ) s The eﬃciency of the LED circuit is: The efficiency of the LED circuit is:

nVnVLED 1 1 η ===LED = (51)(51) VinVDD (1-(1 DD ) D)D in − Since 1 1 > 1, which is not possible, it can be concluded that η is close to 1. Since(1 D)D  1 , which is not possible, it can be concluded that η is close to 1. −(1-DD ) 2.4.4. Cuk´ Converter 2.4.4. Ćuk Converter Figure 10 shows the Simpliﬁed Cuk´ converter. Figure 10 shows the Simplified Ćuk converter.

L1 C1

T LED L2

GND

FigureFigure 10.10. SimpliﬁedSimplified LED ĆCuk´uk converter. converter.

TheThe output output voltage voltage can can be be derived derived as:as:

DVDVinin nVnV LEDLED VoV=o  − (52)(52) 1 DD − TheThe voltage voltage conversion conversion for for the theCuk ´Ćuk converterconverter is:

Vin nVLED  Vin 2 D (53) nVLED = (1 D ) D (53) (1 D)2 The output power is: − The output power is: T s nDIV(1 ) Pivdto LED LEDTs  LED LED (54) Z(1DT ) 1 D s n(1 D)IoVLED PLED = iLEDvLEDdt = − (54) The efficiency of the LED circuit is: 1 D (1 D)Ts − − nDV(1 ) 1 ==LED The eﬃciency of the LED circuit is: 2 (55) VDin (1-D )

1 n(1 D)VLED 1  1 η = − = (55) Since 2 , which is not possible, it can be concluded that2 η is close to 1. (1-D ) VinD (1 D) − Since 1 > 1, which is not possible, it can be concluded that η is close to 1. (1 D)2 − 2.5. LED Path in General

We deﬁned nT, nD, and nL as the number of series LEDs in the transistor, diode, and inductor paths, respectively. The LED path described in Sections 2.2–2.4 can be summarized as a general equation.

2.5.1. Buck Converter Using the voltage second balance techniques, the output voltage of the buck converter path can be expressed as: Vo = V D n V D (1 D)n V n V (56) in − T LED − − D LED − L LED Energies 2019, 12, 4203 14 of 27

where nT, nD, and nL are the number of LEDs in-series in the transistor, diode, and inductor paths. The output power is: P = (n D + (1 D)n + n )IoV (57) LED T − D L LED The eﬃciency is: (nTD nD(1 D) + nLD)VLED η = − − (58) V D n V (1 D) in − L LED − 2.5.2. Boost Converter The output voltage of the boost converter path can be expressed, using the voltage second balance techniques in a similar method, as:

Vin nTDVLED nLVLED Vo = n V (59) 1 D − D LED − 1 D − 1 D − − − The output power is: (n D + (1 D)n + n )Io P = T − D L V (60) LED 1 D LED − The eﬃciency is: (nTD + nD(1 D) + nL)VLED η = − (61) Vin

2.5.3. Buck–Boost Converter In a similar method, the output voltage of the buck–boost converter can be expressed as:

DVin nTDVLED nLVLED Vo = nDV (62) 1 D − LED − 1 D − 1 D − − − The output power is: (n D + (1 D)n + n )Io P = T − D L V (63) LED 1 D LED − The eﬃciency is: (nTD + nD(1 D) + nL)VLED η = − (64) VinD

2.5.4. Cuk´ Converter As before, the output voltage can be derived in a similar method. There are two inductors in the converter, and the derivation has to consider the expressed as:

DVin nTDVLED nL1VLEDD Vo = n V n V (65) 1 D − D LED − 1 D − L2 LED − 1 D − − − The output power is:

(n D + (1 D)n + n D + n (1 D))Io P = T − D L1 L2 − V (66) LED 1 D LED − The eﬃciency is:

(nTD + nD(1 D) + nL1D + nL2(1 D))VLED η = − − (67) VinD Energies 2019, 12, 4203 15 of 27

3. Comparison of Circuit Topology

3.1. Efficiency Analysis The efficiency of different LEDs’ driving circuit topologies is listed in Table1.

Table 1. Output eﬃciency of diﬀerent LEDs’ driving circuit topologies.

Topology LED in the Diode Path LED in the Transistor Path LED in the Inductor Path

(1 D)nV nV nVLEDD Buck − LED LED Vin Vin VinD nVLED(1 D) (1 D)nV nV D − − Boost − LED LED close to 1 Vin Vin (1 D)nV nV Buck–Boost − LED LED close to 1 VinD Vin (1 D)nV nV Cuk´ − LED LED close to 1 VinD Vin

The efficiency of the LED in diode converters is plotted in Figure 11. The parameters used are n = 3 and Vin = 12 V, VLED = 3.3 V. It can be seen from Figure 11 that buck, buck–boost, and Cuk´ converters have the same efficiency under the same parameters. When D < 0.45, the efficiency of buck, buck–boost, and Cuk´ converters is close to 100%; when 0.45 D, the efficiency reduces rapidly. The ≤ reason is that when the duty ratio is small, according to Equations (1), (15), and (19), the voltage across theEnergies resistance 2019, 12 becomes, x FOR PEER very REVIEW small. 16 of 28

FigureFigure 11. 11.Relationship Relationship between efficiency eﬃciency and and DD ofof the the LED LED in in the the diode diode converter. converter.

TheThe e ffiefficiencyciency of of the the boost LED converterin transistor decreases converters linearly is plotted with inD .Figure The e ffi12.ciency The parameters of the LED used driven ´ byare buck, n = 3 buck–boost, and Vin = 12 andV, VCukLED = converters3.3 V. It can isbe larger seen from than Figure that driven 12 that by the the efficiency boost converter of buck, buck– at any D value.boost, The and e ffiĆukciency converters of the converteris constant, is and relatively the constant high foris relatively the low dutyhigh. ratio. The efficiency The efficiency increases of the converterslinearly with is extremely D for the lowboost for converter, the high and duty the ratio, efficiency especially is relatively whenthe high duty for the ratio high is close duty toratio. 1. The efficiency of the LED in transistor converters is plotted in Figure 12. The parameters used are n = 3 and Vin = 12 V, VLED = 3.3 V. It can be seen from Figure 12 that the efficiency of buck, buck–boost, and Cuk´ converters is constant, and the constant is relatively high. The efficiency increases linearly with D for the boost converter, and the efficiency is relatively high for the high duty ratio.

Figure 12. Relationship between efficiency and D of the LED in transistor converter.

Energies 2019, 12, x FOR PEER REVIEW 16 of 28

Figure 11. Relationship between efficiency and D of the LED in the diode converter.

The efficiency of the LED in transistor converters is plotted in Figure 12. The parameters used are n = 3 and Vin = 12 V, VLED = 3.3 V. It can be seen from Figure 12 that the efficiency of buck, buck– Energiesboost,2019, 12and, 4203 Ćuk converters is constant, and the constant is relatively high. The efficiency increases16 of 27 linearly with D for the boost converter, and the efficiency is relatively high for the high duty ratio.

FigureFigure 12. 12.Relationship Relationship between between e efficiencyfficiency and DD ofof the the LED LED in intransistor transistor converter. converter. Energies 2019, 12, x FOR PEER REVIEW 17 of 28 The efficiency of the LED in the inductor converters is plotted in Figure 13. The parameters used The efficiency of the LED in the inductor converters is plotted in Figure 13. The parameters used are n = 3, VLED = 3.3 V. Vin can be obtained using Equations (25), (27), and (29). It can be seen from are n = 3, VLED = 3.3 V. Vin can be obtained using Equations (25), (27), and (29). It can be seen from Figure 13 that the efficiency of boost, buck–boost, and Cuk´ converters is close to 100%, which means Figure 13 that the efficiency of boost, buck–boost, and Ćuk converters is close to 100%, which means that lossthat loss is zero is zero in anin an ideal ideal case. case. For For thethe buck converter, converter, the the efficiency efficiency increases increases rapidly rapidly as D asincreases,D increases, and the speed of increasing increases when DD< 0.490.49. When0.490.49 D D, the efficiency is 1 too. The and the speed of increasing increases when  . When  ≤ , the efficiency is 1 too. The theoreticaltheoretical electrical electrical effi efficiencyciency to to the the LED LED is is closeclose to 100% 100% as as the the R Ris iseliminated eliminated from from the circuit. the circuit.

FigureFigure 13. 13.Relationship Relationship between between eefficiencyﬃciency and and DD ofof the the LED LED in inductor in inductor converter. converter.

3.2. The Output Ripple Amplitude An LED can be modelled as a series connection of a voltage source, an ideal diode and a resistor [29], hence assuming it is represented by a fixed voltage VLED and a resistive component Rd as a simplified LED model, it is then to analyze the output ripple amplitude, which affects the color drift characteristic and lifetime of LEDs. In the case of the LED buck converter (Figure 2), the current ripple of the inductor can be expressed as: VnV iDToLED(1  ) (68) L L The output voltage ripple is equal to: VnV VinRoLED nDTR(1  ) (69) LEDLd L d

It should be pointed out that ΔVLED in this paper refers to the ripple voltage of the series LED. In the case of the LED Boost converter (Figure 3), the current ripple of the inductor can be deduced as: nV+- V V VDT iDTLED o in (1  ) = in (70) L LL The output voltage ripple is:

Energies 2019, 12, 4203 17 of 27

3.2. The Output Ripple Amplitude An LED can be modelled as a series connection of a voltage source, an ideal diode and a resistor [29], hence assuming it is represented by a fixed voltage VLED and a resistive component Rd as a simplified LED model, it is then to analyze the output ripple amplitude, which affects the color drift characteristic and lifetime of LEDs. In the case of the LED buck converter (Figure2), the current ripple of the inductor can be expressed as: Vo + nVLED ∆iL = (1 D)T (68) L − The output voltage ripple is equal to:

V + nV ∆V = ∆i nR = o LED n(1 D)TR (69) LED L d L − d

It should be pointed out that ∆VLED in this paper refers to the ripple voltage of the series LED. In the case of the LED Boost converter (Figure3), the current ripple of the inductor can be deduced as: nV + Vo V V DT ∆i = LED − in (1 D)T = in (70) L L − L The output voltage ripple is:

nV DTR ∆V = ∆i nR = in d (71) LED L d L In the case of the LED buck–boost converter (Figure4), the current ripple of the inductor can be obtained as: V + nV V DT ∆i = o LED (1 D)T = in (72) L L − L The output voltage ripple can be calculated as:

nV DTR ∆V = ∆i nR = in d (73) LED L d L

In the case of the LED Cuk´ converter (Figure5), the current ripple of the inductor can be deduced as:

V = in ∆iL1 DT (74) L1

Vo + nVLED Vin ∆iL2 = (1 D)T = DT (75) L2 − L2 The output voltage ripple is equal to:

1 1 = ( + ) = ( + ) ∆VLED ∆iL1 ∆iL2 nRd nVinDTRd (76) L1 L2

In the case of the transistor path LED buck converter (Figure6a), the current ripple of the inductor can be expressed as: V nV Vo ∆i = in − LED − DT (77) L L The output voltage ripple is:

V nV Vo ∆V = ∆i nR = in − LED − nDTR (78) LED L d L d Energies 2019, 12, 4203 18 of 27

In the case of the transistor path LED Boost converter (Figure6b), the current ripple of the inductor can be equal to: nV V V DT ∆i = LED − in (1 D)T = in (79) L L − L The output voltage ripple can be deduced as:

nV DTR ∆V = ∆i nR = in d (80) LED L d L In the case of the transistor path LED buck–boost converter (Figure6c), the current ripple of the inductor can be obtained as: V nV ∆i = in − LED DT (81) L L The output voltage ripple is equal to:

V nV ∆V = ∆i nR = in − LED nDTR (82) LED L d L d

In the case of the transistor path LED Cuk´ converter (Figure6d), the current ripple of the inductor can be deduced as: V nV = in LED ∆iL1 − DT (83) L1

Vp Vo nV − − LED ∆iL2 = DT (84) L2 where VP is the capacitor charging voltage when T is oﬀ. The output voltage ripple is:

V nV Vp Vo nVLED = ( + ) = ( in LED + − − ) ∆VLED ∆iL1 ∆iL2 nRd − nDTRd (85) L1 L2

In the case of the simpliﬁed LED buck converter (Figure7), the current ripple of the inductor is equal to: V + nV ∆i = o LED (1 D)T (86) L L − The output voltage ripple can be expressed as:

V + nV ∆V = ∆i nR = o LED n(1 D)TR (87) LED L d L − d In the case of the simpliﬁed LED Boost converter (Figure8), the current ripple of the inductor is:

nV V V DT ∆i = LED − in (1 D)T = in (88) L L − L The output voltage ripple can be calculated as

nV DTR ∆V = ∆i nR = in d (89) LED L d L In the case of the simpliﬁed LED buck–boost converter (Figure9), the current ripple of the inductor is: nV V T ∆i = LED (1 D)T = in (90) L L − L The output voltage ripple is equal to:

nV TR ∆V = ∆i nR = in d (91) LED L d L Energies 2019, 12, 4203 19 of 27

In the case of the simpliﬁed LED Cuk´ converter (Figure9), the current ripple of the inductor can be deduced as: V = in ∆iL1 DT (92) L1

nVLED VinDT ∆iL2 = (1 D)T = (93) L2 − L (1 D) 2 − TheEnergies output 2019, 12 voltage, x FOR PEER ripple REVIEW can be calculated as: 20 of 28 " # The output voltage ripples of different LEDs’ dr1iving circuit1 topologies are list in Table 2. = ( + ) = + ∆VLED ∆iL1 ∆iL2 nRd nVinDTRd (94) L1 L (1 D) Table 2. Output voltage ripples of different LEDs’2 driving− circuit topologies. TopologyThe output LED voltage in the ripplesdiode path of di ﬀerent LEDLEDs’ in drivingthe transistor circuit path topologies are LED list in inthe Table inductor2. path nV DTR VnVV nV DTR Buck Table 2.inOutput d voltage ripples ofin diﬀerent LED LEDs’ o nDTR driving circuit topologies. in d L L d L Topology LED in the Diode Path LED in the Transistor Path LED In The Inductor Path nVin DTR d nVin DTR d nVin DTR d Boost Buck nV inDTRd Vin nVLED Vo nVinDTRd L L − L L− nDTRd L L nVinDTRd nVinDTRd nVinDTRd Boost L L L Buck– nV DTRnVinDTRd VnVV-in nVLED nVinTRnVd TR Buck–Boost in d L in−L LED nDTRd L in d V nVnDTRd Boost ( in− LED + L1 1 L L1 1 1 L Cuk´ ( + )nVinDTRd + nVinDTRd L1 L2 Vp Vo nVLED L1 L2(1 D) − − )nDTRd − VVnVL2  -  11 VnVin- LED poLED 11 Ćuk () nVin DTR d () nDTR  nV DTR LL d in d 12 LL12 LL12(1 D ) Taking n = 3 and Vin = 12 V, VLED = 3.3 V, Rd = 2.5 Ω, T = 20 µs, L = 2000 µH as an example, accordingTaking to Table n =2 ,3 theand voltageVin =12 V, ripple VLED= 3.3 magnitude V, Rd = 2.5 Ω of, T the = 20 LEDs μs, L = for 2000 the μH LED as an in example, diode converters according is plottedto in Table Figure 2, the14. voltage It can be ripple seen magnitude from Figure of 15the that LEDs buck, for the boost, LED and in diode buck–boost converters converters is plotted have in the same voltageFigure 14. ripple It can amplitudes be seen from under Figure the 15 samethat bu parameters.ck, boost, and The buck–boost voltage rippleconverters magnitude have the increasessame linearlyvoltage with Dripplefor all amplitudes the four converters. under the Thesame voltage parameters. ripple The magnitude voltage ofripple the LEDmagnitude driven increases by the buck, linearly with D for all the four converters. The voltage ripple magnitude of the LED driven by the boost, and buck–boost converters is smaller than that driven by the Cuk´ converter at any D values. buck, boost, and buck–boost converters is smaller than that driven by the Ćuk converter at any D The voltage ripple magnitude of the converters is relatively low for the low duty ratio. For the Cuk´ values. The voltage ripple magnitude of the converters is relatively low for the low duty ratio. For converter, ∆V /nV < 18.0%; for buck, boost, and buck–boost converters, ∆V /nV < 9.0%. the Ćuk LEDconverter,LED ΔVLED/nVLED < 18.0%; for buck, boost, and buck–boost converters,LED ΔVLEDLED/nVLED < 9.0%.

FigureFigure 14. Relationship 14. Relationship between between voltage voltage ripple ripple magnitude magnitude and DD ofof the the LED LED in indiode diode converters. converters.

Using the same parameters, according to Table 2, the voltage ripple magnitude of the LEDs in transistor converters is plotted in Figure 15. It can be seen from Figure 15 that the voltage ripple magnitude increases linearly with D for boost and buck–boost converters and the curves of buck and Ćuk converters are just like a parabola structure. The voltage ripple magnitude of the LED driven by

Energies 2019, 12, x FOR PEER REVIEW 21 of 28

the buck and buck–boost converters is very small. For the buck converter, ΔVLED/nVLED < 0.4%, and for the buck–boost converter, ΔVLED/nVLED < 1.6%. For the Ćuk converter, the voltage ripple magnitude increases as D increases (D < 0.66); the voltage ripple magnitude reduces rapidly as D Energies 2019, 12, 4203 20 of 27 increases ( 0.66D 0.89 ); and the voltage ripple magnitude reduces to zero when 0.89  D , which means the ripple is completely eliminated. For the Ćuk converter, ΔVLED/nVLED < 6.5%.

FigureFigure 15. Relationship 15. Relationship between between voltage voltage ripple ripple magnitude magnitude and D andof the D LEDof the in LED transistor in transistor converters. converters. Using the same parameters, according to Table2, the voltage ripple magnitude of the LEDs in transistorUsing converters the same parameters is plotted in and Figure taking 15 .VP It = can 25 V, be L seen1 = L2 from = 2000 Figure μH as 15 an that example, the voltage according ripple to magnitudeTable 2, the increases voltage ripple linearly magnitude with D for of boost the LEDs and buck–boost in transistor converters converters and is theplotted curves in ofFigure buck 16. and It ´ Cukcan be converters seen from are Figure just like 17 that a parabola buck and structure. boost converters The voltage have ripple the same magnitude voltage of ripple the LED amplitudes driven byunder the buckthe same and parameters, buck–boost and converters the voltage is very ripple small. amplitude For the of buck the buck–boost converter, ∆ converterVLED/nVLED is constant.< 0.4%, ´ andThe forvoltage the buck–boost ripple magnitude converter, increases∆VLED linearly/nVLED 0.4,/nV voltageLED < 6.5%. ripple magnitude µ of ĆUsinguk converter the same is parameters more than and 1V, taking whichV Pmeans= 25 V, thatL1 = ΔLV2 LED= 2000/nVLEDH > as10.0%. an example, The voltage according ripple to Tablemagnitude2, the voltage of the buck, ripple boost, magnitude and Ć ofuk the converters LEDs in transistoris relatively converters low for isthe plotted low duty in Figure ratio. 16For. It buck, can beboost, seen and from Ćuk Figure converters, 17 that buckΔVLED and/nV boostLED < 9.1%. converters have the same voltage ripple amplitudes under the same parameters, and the voltage ripple amplitude of the buck–boost converter is constant. The voltage ripple magnitude increases linearly with D for buck, boost, and Cuk´ converters. The voltage ripple magnitude of the LED driven by the buck and boost converters is smaller than that driven by the buck–boost converter at any D value. For Cuk´ converters, voltage ripple magnitude increases rapidly as D increases, and the speed also increases. When D > 0.4, voltage ripple magnitude of Cuk´ converter is more than 1V, which means that ∆VLED/nVLED > 10.0%. The voltage ripple magnitude of the buck, boost, and Cuk´ converters is relatively low for the low duty ratio. For buck, boost, and Cuk´ converters, ∆VLED/nVLED < 9.1%.

Energies 2019, 12, 4203 21 of 27 Energies 2019, 12, x FOR PEER REVIEW 22 of 28

Energies 2019, 12, x FOR PEER REVIEW 23 of 28 by the duty ratio control, as shown in Appendix A. Figure 17 shows experimental waveforms of the boost converter at switching frequency fs = 50 kHz and 80% duty ratio. Figure 18 shows the output waveforms, with the output voltage impressed onto the LED. The measured efficiency was 69%. From Section 2.4.2, we know that the efficiency of circuits with ideal elements was close to 1. The error was 31%. The reason was the switching losses of the LEDs and the transistor. Figures 19 and 20 show the results at 100 kHz with 80% duty ratio. The dimming could be regulated successfully. The LED FigureilluminationFigure 16. 16. RelationshipRelationship output was between between confirmed voltage voltage to ripple ripplebe regula magnitude magnitudeted successfully and and DD ofof the the by LED LED the in inhigh-frequency inductor converters. switching signal. It can be seen from Figures 14–16 that voltage ripple magnitude of boost converters is the same. Referencing the values, we could get a conclusion that voltage ripple magnitude of LED in transistor converters is minimal and that voltage ripple magnitude of the LED in inductor converters is maximal under the same parameters.

For LEDs in diode path circuits, it can be found from Figures 11 and 14 thatGND buck and boost converters have very high efficiency (almost no loss) and relatively low voltage ripple magnitude for the low duty ratio. For LEDs in transistor path circuits, we can conclude from Figures 12 and 15 that buck, buck– boost, and Ćuk converters have relatively high efficiency and low voltage ripple magnitudeGND for any duty ratio. For buck and buck–boost converters, voltage ripple magnitude is low (ΔVLED/nVLED < 0.4% for buck; ΔVLED/nVLED < 1.6% for buck–boost). For the Ćuk converter, the ripple is completely GND eliminated for the high duty ratio. For LEDs in transistor inductor circuits, we can conclude from Figures 13 and 16 that all converters have very high efficiency (almost no loss), except buck converters, at a low duty ratio. Boost and Ćuk converters have relatively low voltage ripple magnitude for a low duty ratio at the sameFigure time. 17. Input characteristics of thethe proposedproposed boostboost converterconverter withwith ffs == 5050 kHz. kHz. ( (TopTop Trace Trace) Input ToVoltage sum (5 (5up, VV/div);/ div);the appropriate ((MiddleMiddle TraceTrace circuit)) Input Input topology, Current Current (2 (2 which A A/div);/div); can ( Bottom(Bottom meet Trace criteriaTrace)) Input Input of LED Power Power lighting (2 (2 W W/div)./div). for special effect designs, can be selected from the proposed circuit topology. According to different special It can be seen from Figures 14–16 that voltage ripple magnitude of boost converters is the same. effect application requirements, different circuits will be chosen. Boost and Ćuk LEDs in transistor Referencing the values, we could get a conclusion that voltage ripple magnitude of LED in transistor inductor circuits can be selected if we need extremely high efficiency and minimal components. Buck, converters is minimal and that voltage ripple magnitude of the LED in inductor converters is maximal buck–boost, and Ćuk LEDs in transistor path circuits can meet requirements if extremely low voltage under the same parameters. ripple magnitude is needed. Extremely high efficiency and relatively less components can also be For LEDs in diode path circuits, it can be found from Figures 11 and 14 that buck and boost achieved by buck and boost LEDs in diode path circuits for a low duty ratio. converters have very high eﬃciency (almost no loss) and relatively low voltage rippleGND magnitude for 4.the Experimental low duty ratio. Results For LEDs in transistor path circuits, we can conclude from Figures 12 and 15 that buck, buck–boost, and CukExperimental´ converters results have are relatively presented high in e ﬃFiguresciency 17–2 and0. low To voltageconfirm ripplethe operation magnitude of the for simplified any duty boost converter with a reduced number of components, a simplified booster converterGND was used. The ratio. For buck and buck–boost converters, voltage ripple magnitude is low (∆VLED/nVLED < 0.4% for components used are: L = 70µH, transistor = IRF540, LED = 3W LED with 6 in series. The circuit as shown in Figure 8 was used for the test. The brightness of the LEDs could be regulated successfully GND

Figure 18. Output characteristics of proposed boost converter with fs = 50 kHz. (Top Trace) Output Voltage (10 V); (Middle Trace) Output Current (2 A/div); (Bottom Trace) Output Power (20 W/div).

Energies 2019, 12, 4203 22 of 27 Energies 2019, 12, x FOR PEER REVIEW 23 of 28

´ bybuck; the∆ dutyVLED ratio/nVLED control,< 1.6% as for shown buck–boost). in Appendix For the A. CukFigure converter, 17 shows the experimental ripple is completely waveforms eliminated of the boostfor the converter high duty at ratio. switching frequency fs = 50 kHz and 80% duty ratio. Figure 18 shows the output waveforms,For LEDs with in transistor the output inductor voltage circuits, impressed we can on concludeto the LED. from The Figures measured 13 and efficiency16 that all converterswas 69%. ´ Fromhave verySection high 2.4.2, efficiency we know (almost that no the loss), efficiency except of buck circuits converters, with ideal at a lowelements duty ratio.was close Boost to and 1. CukThe errorconverters was 31%. have The relatively reason lowwas voltagethe switching ripple magnitudelosses of the for LEDs a low and duty the ratiotransistor. at the Figures same time. 19 and 20 showTo the sum results up, theat 100 appropriate kHz with circuit80% duty topology, ratio. The which dimming can meet could criteria be regulated of LED lighting successfully. for special The LEDeffect illumination designs, can output be selected was confirmed from the to proposed be regula circuitted successfully topology. by According the high-frequency to different switching special ´ signal.effect application requirements, different circuits will be chosen. Boost and Cuk LEDs in transistor inductor circuits can be selected if we need extremely high efficiency and minimal components. Buck, buck–boost, and Cuk´ LEDs in transistor path circuits can meet requirements if extremely low voltage ripple magnitude is needed. Extremely high efficiency and relatively less components can also be achieved by buck and boost LEDs in diode path circuits for a low duty ratio.

4. Experimental Results GND Experimental results are presented in Figures 17–20. To confirm the operation of the simplified boost converter with a reduced number of components, a simplified booster converter was used. The components used are: L = 70 µH, transistor = IRF540, LED = 3 W LED with 6 in series.GND The circuit as shown in Figure8 was used for the test. The brightness of the LEDs could be regulated successfully by the duty ratio control, as shown in AppendixA. Figure 17 shows experimental waveforms of the GND boost converter at switching frequency f s = 50 kHz and 80% duty ratio. Figure 18 shows the output waveforms, with the output voltage impressed onto the LED. The measured efficiency was 69%. From Section 2.4.2, we know that the efficiency of circuits with ideal elements was close to 1. The error was 31%. The reason was the switching losses of the LEDs and the transistor. Figures 19 and 20 show the resultsFigure at17. 100 Input kHz characteristics with 80% duty of the ratio. proposed The dimmingboost converter could with be regulatedfs = 50 kHz. successfully. (Top Trace) Input The LED illuminationVoltage (5 output V/div); was (Middle confirmed Trace) to Input be regulated Current (2 successfully A/div); (Bottom by the Trace high-frequency) Input Power (2 switching W/div). signal.

GND

Figure 18. f Top Trace Figure 18. Output characteristics of proposed boost converter with fs == 5050 kHz. kHz. (Top ( Trace)) Output Voltage (10 V); (Middle TraceTrace)) OutputOutput CurrentCurrent (2(2 AA/div);/div);( Bottom(Bottom TraceTrace)) Output Output Power Power (20 (20 W W/div)./div).

Energies 2019, 12, 4203 23 of 27 EnergiesEnergies 20192019,, 1212,, xx FORFOR PEERPEER REVIEWREVIEW 2424 ofof 2828

GNDGND

FigureFigure 19.19. InputInput characteristics characteristics ofof thethe proposedproposed boostboostboost converterconverterconverter withwithwith f ffss == 100100100 kHz.kHz. (( (TopTop Trace Trace)) Input Input Voltage;Voltage; ((MiddleMiddle TraceTrace))) Input InputInput Current; Current;Current; ( Bottom((Bottom Trace Trace))) Input InputInput Power. Power.Power.

GNDGND

FigureFigure 20.20. Output characteristics ofof proposedproposed boostboost converterconverter withwith fffss == 100100100 kHz.kHz. (( (TopTop Trace Trace)) OutputOutput Voltage;Voltage; ((MiddleMiddle TraceTrace))) Output OutputOutput Current; Current;Current; ( Bottom((Bottom Trace Trace)) Output) OutputOutput Power. Power.Power.

5.5. Discussion Discussion WhenWhen comparedcompared with with the the classical classical LED LED driving driving topologies topologiestopologies presented presentedpresented in [ 13inin– [13–18],[13–18],18], the proposedthethe proposedproposed new familynew family of power of power converters converters have the have following the following advantages: advantages:advantages: First, the First,First, design thethe can designdesign be used cancan to bebe reduce usedused the toto costreducereduce and thethe components. costcost andand components.components. Since the LEDs SinceSince are thethe put LEDsLEDs in the areare diode, put in transistor, the diode, and transistor, inducer and paths, inducer the drivers paths, canthethe driversdrivers have less cancan components. havehave lessless components.components. Thus, if a small Thus,Thus, size ifif aa smallsmall is required, sizesize isis required, therequired, corresponding thethe correspondingcorresponding size canbe sizesize reduced. cancan bebe Second,reduced.reduced. the Second,Second, proposed thethe proposedproposed converters convertersconverters can work cancan at low workwork voltage. atat lowlow Third,voltage.voltage. high Third,Third, effi ciency highhigh efficiencyefficiency is achieved isis achievedachieved without awithout complicated a complicated control circuit.control circuit. In Figures In Figures 11–13, 11 the–13, proposed the proposed power power converters converters could could achieve achieve high ehighfficiency efficiency at specific at specific duty duty ratios. ratios. However, However, current currentrrent high high ehighfficiency efficiencyefficiency research researchresearch often oftenoften focuses focusesfocuses on high onon high LEDhigh powerLED power applications applications [36]. [36]. These These new new power power converters converterserters can becancan used bebe usedused in special inin specialspecial occasions occasionsoccasions where wherewhere low voltage,lowlow voltage,voltage, low size,lowlow size,size, and and highand highhigh efficiency efficiencyefficiency is needed. isis needneed Moreover,ed.ed. Moreover,Moreover, the output thethe outputoutput ripple riripple amplitude amplitude is low is low in this in familythisthis familyfamily of power ofof powerpower converters. converters.converters. From FromFrom theoretical theoreticaltheoretical analyses, ananalyses, the output the output voltage voltage ripple ripple of the of proposed the proposed LED driversLED drivers can be can reduced be reduced significantly significantly at specific at specific duty ratios.duty ratios.

Energies 2019, 12, 4203 24 of 27

However, this paper pays more attention to the topology and theoretical derivation. All the circuit components are ideal in this paper. Therefore, in some cases, the eﬃciency can be close to 100%. But for real circuits, there are switching losses and conduction losses of LEDs and the transistor. The switching losses of MOSFET PSW in this paper can be expressed as [37]:

Psw = VinIdmaxtcross f (95) where Idmax is the maximum current through MOSFET, and tcross is overlap time. The conduction losses of MOSFET PCOND in this paper can be expressed as [37]:

2 PCOND = IRMS Rds (96) where IRMS is the root–mean–square value of the current, and Rds is resistance. When the eﬃciency is being calculated, PSW and PCOND should be taken into account. LED is the freewheeling diode in Sections 2.2 and 2.4. The conduction losses of the freewheeling diode cannot be neglected. The conduction losses of freewheeling diode PCOND-D are:

2 PCOND-D = ID_AVG Rd (97) where ID_AVG is the diode average current. The way to reduce the conduction losses is to reduce the forward voltage drop of the diode and the transistor. The switching losses of the freewheeling diode or LED include turn-on losses and turn-oﬀ losses. Turn-on losses can be derived as:

Z t f p PD, turn-on = f VF(t)iF(t)dt 0.5VfpIfptfp f (98) 0 ≈ where tfp is the forward recovery time, Vfp is the peak forward voltage, and Ifp is the peak forward current. Turn-on losses are:

Z t2 PD, turn-off = f VF(t)iF(t)dt 0.5VrpIrptrp f (99) to ≈ where trp is the reverse current descent time, Vrp is the peak back voltage, and Irp is the peak back current. When the efficiency is calculated, PSW, PCOND, PCOND-D, PD,turn-off, and PD,turn-on should be taken into account. In the next research, we will build circuits to verify these topologies, and the ideal elements will be replaced by real ones. There is another issue that should be taken into account. Because uneven voltage is inevitable among the LEDs, this factor can affect the life of LEDs, which leads to potential safety problems for the circuits. As the LED lifespan increases, the driver controls the overall lifetime of the LED system. However, the driver consists of a number of components, and the components’ lifespan is usually less than that of LED chips; therefore, the safety issue is still unknown. The authors will explore these issues in our next research.

6. Conclusions In this paper, we propose a new family of power converters to the low-power LED lighting for lighting and special eﬀect design. It was found that the LED could replace the freewheel diode in the converters. It can also be placed in the transistor and inducer paths. The proposed circuits reduce both the cost and component count through simplifying the classic driving for LEDs, especially for Energies 2019, 12, 4203 25 of 27

LEDs in inductor path circuits. The formulation of an output conversion ratio, power of the LED, and the efficiency was derived. Efficiency and output ripple amplitude of the proposed circuit topologies are discussed in this paper. Analytical study shows that efficiency of proposed circuits can be high. Buck,Energies buck–boost, 2019, 12, x FOR and PEERCuk´ REVIEW LEDs in transistor path circuits have relatively high efficiency. It should26 of be28 emphasized that buck and boost LEDs in diode path circuits and all LEDs in inductor path circuits have almostalmost no no loss. loss. It wasIt was found found that that low outputlow output ripple ripple amplitude amplitude could becould obtained be obtained for the proposed for the circuits.proposed For circuits. buck andFor buck–boostbuck and LEDsbuck–boost in transistor LEDs pathin transistor circuits, voltagepath circuits, ripple magnitudevoltage ripple was verymagnitude low (∆ wasVLED very/nVLED low< (Δ0.4%VLED for/nVLED buck, < 0.4%∆VLED for/nV buck,LED <ΔV1.6%LED/nV forLED buck–boost). < 1.6% for buck–boost). The results alsoThe showresults that also the show proposed that the circuit proposed topologies circuit topologi could bees easily could adoptedbe easily toadopted design to LED design lighting LED becauselighting highbecause effi ciency,high efficiency, less components, less components, and low and voltage low voltage ripple magnituderipple magnitude criteria criteria can be can met be at met the at same the time.same time. Finally, Finally, the experimental the experimental waveforms waveforms of the of laboratory the laboratory prototype prototype confirmed confirmed the operation the operation of the simplifiedof the simplified converter. converter. An LED integrated in the inductor winding has been demonstrated that is another method of integration of inductor and LEDsLEDs byby combiningcombining thethe LEDLED leadsleads andand inductorinductor winding.winding. It is It shownis shown in Appendixin the appendix.A. Author Contributions: Conceptualization, W.C., K.W.E.C., and J.S.; investigation, W.C. and K.W.E.C..; Author Contributions: Conceptualization, W.C., K.W.E.C., and J.S.; investigation, W.C. and K.W.E.C.; writing—review andand editing,editing, W.C.W.C. andand K.W.E.C.;K.W.E.C.; supervision,supervision, K.W.E.C. K.W.E.C. Funding: This research was funded by the Research Committe Committeee of the Hong Kong Polytechnic University under the project code: 845G and ZDBL. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Appendix A

FigureFigure A1.A. TheThe LED LED connected connected in in inductor inductor path. path.

References

1. Li, S.; Tan, S.;S.; Lee,Lee, C.K.;C.K.; WaWaffenschmiffenschmidt,dt, E.; E.; Hui, Hui, S.Y.; S.Y.; Tse, Tse, C.K. C.K. A A survey, survey classification,, classification, and an criticald critical review review of oflight-emitting light-emitting diode diode drivers. drivers.IEEE IEEE Trans. Trans. Power Power Electron. Electron.2016 2016, 31, ,31 1503–1516., 1503–1516. [CrossRef ] 2. Lin, H.; Hu, J.; Zhou, X.; Lu, Z.; Wang, L. New DC Grid Power Line CommunicationCommunication Technology Used in Networked LED Driver. Energies 2018, 11,, 3531.3531. [CrossRef] 3. Arias, M.;M.; Lamar, Lamar, D.G.; D.G.; Sebastian, Sebastian, J.; Balocco, J.; Balocco, D.; Diallo, D.; Diallo, A.A. High-E A.A.ffi High-Efficiencyciency LED Driver LED Without Driver Electrolytic Without ElectrolyticCapacitor for Capacitor Street Lighting. for StreetIEEE Lighting. Trans. IEEE Ind. Electron. Trans. Ind.2013 Electron., 49, 127–137. 2013, 49 [CrossRef, 127–137.] 4. Liu, Y.-C.;Y.-C.; Chen,Chen, C.; C.; Chen, Chen, K.-D.; K.-D.; Syu, Syu, Y.-L.; Y.-L.; Tsai, Tsai, M.-C. M.-C. High-Frequency High-Frequen LLCcy LLC Resonant Resonant Converter Converter with GaNwith GaNDevices Devices and Integrated and Integrated Magnetics. Magnetics.Energies Energies2019, 201912, 1781., 12, 1781. [CrossRef ] 5. Cheng, K.W.E.; Wang, H.; Cheng,Cheng, D.K.W. Derivation of an Electronic Ballast with a Secondary DC DC Output. Output. Int. J. J. Circ. Circ. Theor. Theor. Appl. Appl. 20072007, ,1414, ,466. 466. 6. Yan, W.; Hui,Hui, S.Y.S.Y. AnAn analysisanalysis intointo thethe dimmingdimming control and characteristic of discharge lamps. IEEEIEEE Trans. Trans. Power Electron. 2005, 20, 1432–1440. [CrossRef] 7. Dong, P.; Cheng, K.W.E.; Wang, D.H.; Divakar, B.P. Investigation on the Modeling and Ageing Characteristics of the HID Car Headlight Automotive System. J. Key Eng. Mater 2008, 364, 1280–1284. 8. European Commission. Low Voltage Directive 2006/95/EC; The European Parliament and of The Council, Official Journal of the European Union, 12 Dec 2006. 9. Choi, W.Y.; Kwon, J.M.; Kwon, B.H. Efficient LED back-light power supply for liquid-crystal-display. IET Electr. Power Appl. 2007, 1, 133–142. 10. Lo, Y.; Wu, K.; Pai, K.; Chiu, H. Design and Implementation of RGB LED Drivers for LCD Backlight Modules. IEEE Trans. Ind. Electron. 2009, 56, 4862–4871.

Energies 2019, 12, 4203 26 of 27

7. Dong, P.; Cheng, K.W.E.; Wang, D.H.; Divakar, B.P. Investigation on the Modeling and Ageing Characteristics of the HID Car Headlight Automotive System. J. Key Eng. Mater 2008, 364, 1280–1284. 8. European Commission. Low Voltage Directive 2006/95/EC; The European Parliament and of The Council, Official Journal of the European Union: Brussels, Belgium, 2006. 9. Choi, W.Y.; Kwon, J.M.; Kwon, B.H. Efficient LED back-light power supply for liquid-crystal-display. IET Electr. Power Appl. 2007, 1, 133–142. [CrossRef] 10. Lo, Y.; Wu, K.; Pai, K.; Chiu, H. Design and Implementation of RGB LED Drivers for LCD Backlight Modules. IEEE Trans. Ind. Electron. 2009, 56, 4862–4871. 11. Cheng, K.W.E. Classical Switched Mode and Resonant Power Converter; The Hong Kong Polytechnic University: Hong Kong, China, 2002; Chapter 2; pp. 15–64. ISBN 962-367-364-7. 12. Hui, S.Y.; Li, S.N.; Tao, X.H.; Chen, W.; Ng, W.M. A Novel Passive Offline LED Driver with Long Lifetime. IEEE Trans. Power Electron. 2010, 25, 2665–2672. [CrossRef] 13. Baek, J.; Chae, S. Single-Stage Buck-Derived LED Driver with Improved Efficiency and Power Factor Using Current Path Control Switches. IEEE Trans. Ind. Electron. 2017, 64, 7852–7861. [CrossRef] 14. Lu, Y.; Czarkowski, D.; Bury, W.E. High efficiency adaptive boost converter for LED drivers. In Proceedings of the 2011 7th International Conference-Workshop Compatibility and Power Electronics (CPE), Tallinn, Estonia, 1–3 June 2011; pp. 315–318. 15. Mannam, R.; Vangala, N. Soft switching boost converter for DC input LED drivers. In Proceedings of the 2016 7th India International Conference on Power Electronics (IICPE), Patiala, India, 17–19 November 2016; pp. 1–5. 16. Lin, R.; Chang, Y.; Lee, C. Optimal Design of LED Array for Single-Loop CCM Buck–Boost LED Driver. IEEE Trans. Ind. Electron. 2013, 49, 761–768. [CrossRef] 17. Mohamed, L.; Hamid, N.F.A.; Isa, Z.M.; Saudin, N.; Ramly, N.H.; Ahamad, N.B. Cuk converter as a LED lamp driver. In Proceedings of the 2012 IEEE International Conference on Power and Energy (PECon), Kota Kinabalu, Malaysia, 2–5 December 2012; pp. 262–267. 18. Lin, W.; Yuzhen, X.; Zheng, Q.L. A high efficiency integrated step-down Cuk and flyback converter for LED power driver. In Proceedings of the 2015 9th International Conference on Power Electronics and ECCE Asia (ICPE-ECCE Asia), Seoul, Korea, 1–5 June 2015; pp. 60–64. 19. Chan, H.L.; Cheng, K.W.E.; Sutanto, D. Phase-shift controlled DC-DC converter with bi-directional power flow. IEE Proc.-Electr. Power Appl. 2001, 148, 193–201. [CrossRef] 20. Lun, W.; Loo, K.H.; Tan, S.; Lai, Y.M.; Tse, C.K. Bilevel Current Driving Technique for LEDs. IEEE Trans. Power Electron 2009, 24, 2920–2932. 21. Chen, H.; Tan, S.; Hui, S.Y. Color Variation Reduction of GaN-Based White Light-Emitting Diodes Via Peak-Wavelength Stabilization. IEEE Trans. Power Electron. 2014, 29, 3709–3719. [CrossRef] 22. Cheng, K.W.E. Storage energy for classical switched mode power converters. IEE Proc.-Electr. Power Appl. 2003, 150, 439–446. [CrossRef] 23. Jang, Y.; Jovanović,M.M. Bridgeless high-power-factor buck converter. IEEE Trans. Power Electron. 2011, 26, 602–611. [CrossRef] 24. Cheng, H.; Lin, C. Design and Implementation of a High-Power-Factor LED Driver with Zero-Voltage Switching-On Characteristics. IEEE Trans. Power Electron. 2014, 29, 4949–4958. [CrossRef] 25. Wu, X.; Xie, X.; Chen, Z.; Qian, Z.; Zhao, R. Low voltage and current stress ZVZCS full bridge DC–DC converter using center tapped rectifier reset. IEEE Trans. Ind. Electron. 2008, 55, 1470–1477. [CrossRef] 26. Hsieh, H.I.; Li, J.S.; Chen, D. Effects of X capacitors on EMI filter effectiveness. IEEE Trans. Ind. Electron. 2008, 55, 949–955. [CrossRef] 27. Narendran, N.; Gu, Y. Life of LED-based white light sources. IEEE Disp. Technol. 2005, 1, 167. [CrossRef] 28. Hsieh, Y.Y.; Juang, Y.Z. Analysis and suppression of overcurrent in boost LED drivers. IEEE Disp. Technol. 2013, 9, 388–395. [CrossRef] 29. Dong, Z.; Tse, C.K.; Hui, S.Y.R. Circuit Theoretic Considerations of LED Driving: Voltage-Source Versus Current-Source Driving. IEEE Trans. Power Electron. 2019, 34, 4689–4702. [CrossRef] 30. Saini, D.K.; Ayachit, A.; Salvatierra, T.; Kazimierczuk, M.K. Design of zero-voltage-ripple buck dc-dc converter. In Proceedings of the 2017 IEEE 60th International Midwest Symposium on Circuits and Systems (MWSCAS), Boston, MA, USA, 6–9 August 2017; pp. 456–459. Energies 2019, 12, 4203 27 of 27

31. Reddy, U.R.; Narasimharaju, B.L. Single-stage electrolytic capacitor less non-inverting buck-boost PFC based AC–DC ripple free LED driver. IET Power Electron. 2017, 10, 38–46. [CrossRef] 32. Yu, Y.; Zhang, F.; Ni, J. Capacitor clamped current sharing circuit for multistring LEDs. In Proceedings of the 2012 IEEE Energy Conversion Congress and Exposition (ECCE), Raleigh, NC, USA, 15–20 September 2012; pp. 3568–3574. 33. Hwu, K.; Jiang, W. Input-Current-Ripple-Free Two-Channel LED Driver. IEEE Trans. Ind. Electron. 2017, 64, 5865–5874. [CrossRef] 34. Wu, X.K.; Zhang, J.M.; Zhao, M.Q. A simple two-channel LED driver with automatic precise current sharing. IEEE Trans. Ind. Electron. 2011, 58, 4783–4788. [CrossRef] 35. Zhao, C.; Xie, X.; Liu, S. Multioutput LED drivers with precise passive current balancing. IEEE Trans. Power Electron. 2013, 28, 1438–1448. [CrossRef] 36. Lee, E.S.; Choi, B.H.; Nguyen, D.T.; Choi, B.G.; Rim, C.T. Static regulated multistage semiactive LED drivers for high-eﬃciency applications. IEEE Trans. Power Electron. 2015, 31, 6543–6552. [CrossRef] 37. Maniktala, S. Switching Power Supplies A–Z; Elsevier: Amsterdam, The Netherlands, 2012.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).