A TRIAC-Dimmable LED Lamp Driver With Wide

1434 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 3, MARCH 2014

A TRIAC-Dimmable LED Lamp Driver With WideDimming Range

Ruihong Zhang, Student Member, IEEE, and Henry Shu-hung Chung, Senior Member, IEEE

AbstractLED light bulbs are becoming increasingly popularas they consume much less power than traditional incandescentlamps. To enable full compatibility with incandescent lamps, apartfrom delivering the same light output and quality, they are expectedto be operable with standard TRIAC-based light dimmers. How-ever, the input current of the LED light bulbs at dimming couldfall below the holding current of the TRIAC, resulting in limiteddimming range and lamp flickering. This paper presents a TRIAC-dimmable LED lamp driver allowing wide dimming range. Theconcept is based on controlling the input reactive power, so thatthe input current is increased to a level higher than the holdingcurrent of the TRIAC, while the LED array power is regulated.The driver consists of two power conversion stages, including afour-quadrant acdc converter for shaping the input current anda resonant converter for regulating the output power to the LEDarray. The two converters share the same switching network. Mod-eling, analysis, and design of the driver will be presented. An LEDprototype has been built and evaluated. Experimental results re-veal that the true firing angle of the TRIAC can be adjusted downto 172, and the lamp power can be dimmed from 7.2 to 0.3 Wlinearly.

Index TermsFull bridge, LED driver, resonant converter,TRIAC dimmer.

I. INTRODUCTION

W ITH recent development in solid-state lighting technol-ogy, LED replacement light bulbs are quickly becomingavailable for general illumination as they have higher luminousefficacy and longer life expectancy than traditional incandescentlamp bulbs [1]. To enable full compatibility, the operational fea-tures of LED lamps are always expected to exhibit similar to orbetter than that of the incandescent lamps. Among them, com-patibility of the LED lamps with TRIAC-based light dimmershas attracted much research interest, since many TRIAC-basedlight dimmers had been installed in various places, originallyfor controlling incandescent lamps. However, the evolvementof a technology that allows LED lamps to perform wide rangedimming is still less impressive. The main difficulty arises fromthe low LED lamp input current, and the high and diversified

Manuscript received October 6, 2012; revised February 5, 2013 and March 29,2013; accepted May 14, 2013. Date of current version September 18, 2013. Thiswork was supported by e.Energy Lighting Limited through Project 9231038.Recommended for publication by Associate Editor C. A. Canesin.

The authors are with the Centre for Smart Energy Conversion and Uti-lization, City University of Hong Kong, Kowloon, Hong Kong (e-mail:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2013.2263935

Fig. 1. Typical circuit of the TRIAC-based light dimmer.

magnitude of the TRIAC holding current. Practically, the hold-ing current of TRIAC ranges from 20 to 80 mA while the inputcurrent of LED lamps can be less than 60 mA, hindering thecompatibility of LED lamps with different TRIAC-based lightdimmers. For the same lamp brightness, the input current of LEDlamps is only one-tenth of the incandescent lamps, and its mag-nitude is too small to hold the TRIAC in the conduction stateafter the TRIAC is latched. Thus, existing TRIAC-dimmableLED lamp drivers cannot provide a very wide dimming range.For example, a 15-W LED lamp driver using a flyback converterwith primary-side regulation to control the LED current is pro-posed in [2] and [3]. The adjustable dimming range reported isfrom 35 to 150. In [4], an active damper circuit together withthe primary-side regulation method is proposed. It provides suf-ficient turn-on input current with smaller power consumption, ascompared with the passive damper circuit, in order to latch theconduction state of the TRIAC. However, the effect of the hold-ing current of the TRIAC on the dimming range has not beenaddressed. The maximum dimming range reported is around130. Thus, challenges will appear if the dimmed power level isfurther reduced.

Fig. 1 shows the typical circuit of the TRIAC-based lightdimmer. The resistors R1 and R2 and capacitor C form an RCnetwork. R1 is used to adjust the phase and the voltage across C.When the voltage across the capacitor C reaches the breakdownvoltage of DIAC, a gate signal will be applied to the TRIAC.The control knob of R1 can thus control the firing angle (turn-ontime) of the TRIAC and lamp power. Fig. 2 shows the typicalwaveforms of the line voltage vin and the input current iin ofthe lamp controlled by a TRIAC. The angles and ( ) arethe firing angle and extinction angle of the TRIAC, respectively.The TRIAC is turned OFF naturally at ( ) when iin is lessthan the holding current Ih .

Fig. 3 shows the minimum lamp power Pmin against the firingangle with holding current ranging from 20 to 80 mA underthe condition that the conduction time of the TRIAC is not lessthan 30 and the load is purely resistive. Generally, the higher

0885-8993 2013 IEEE

ZHANG AND CHUNG: TRIAC-DIMMABLE LED LAMP DRIVER WITH WIDE DIMMING RANGE 1435

Fig. 2. Typical waveforms with resistive load [Case IIiin is in phase withvin ( = 0)].

Fig. 3. Minimum lamp power against the firing angle.

the holding current, the higher the minimum lamp power. Forexample, at = 10, Pmin = 10 W when Ih = 20 mA, and Pmin= 40 W when Ih = 80 mA. Detailed derivations of the curveswill be given in Section II. Thus, the curves can explain whylow-power LED lamps have limited dimming range. Moreover,at large firing angle, lamps could flicker easily at the frequencyof 100 or 120 Hz, namely invisible flicker. Although the invis-ible flicker cannot be easily seen by human eyes, it will causepossible health problems, like brain damaging, headaches, eyestrain, and so on [5].

The previous problem can be lessened by adding a resistor,namely bleeding circuit [6], [7], in the lamp driver in order toconsume minimum power. However, this will introduce extrapower loss in the whole driver. In [8], a TRIAC-dimmable LEDdriver that does not require any bleeding circuit is proposed. Theconcept is based on reducing the conduction time of the TRIACwhen the firing angle is large. It allows the dimmer to turn offif the input current is lower than the holding current. Thus, theinput current is pulsating. In [9], the circuit is extended from theballast for compact fluorescent lamps. It consists of a capacitornetwork for increasing the input current and thus maintainingthe TRIAC conduction. However, the LED current is pulsatingand the reported maximum dimming is about 10%.

A TRIAC-dimmable LED lamp driver allowing wide dim-ming range is presented. It consists of two power conversionstages. The first stage controls the active and reactive power

drawn from the line, so that the input current is programmedto satisfy the minimum holding current requirement. The lampcan thus exhibit a wide dimming range. The second stage is anisolated resonant converter for regulating the LED array current.The lamp power is controlled to be in linear relationship withthe firing angle. The two converters share the same switchingnetwork, which is in variable frequency and variable duty cy-cle control [10], [11]. The function of the variable frequencycontrol is used to remove the line frequency ripple in the LEDcurrent and regulate the output LED lamp power. The functionof the variable duty cycle control is used to shape the inputcurrent. An LED driver prototype has been built and evaluated.The lamp power can be adjusted from full power of 7.2 to 0.3 Wwith the true firing angle down to 172. Section II describes theoperating principles of the proposed driver. Section III gives aset of design procedure. Section IV will show the experimentalverification. The conclusions follow in the last section.

II. OPERATING PRINCIPLES OF THE PROPOSED LED DRIVERFig. 4 shows the circuit schematic of the proposed driver,

which consists of two power conversion stages. The first stageis a four-quadrant acdc converter and the second stage is anLLC resonant converter. The two converters share the switchesS1 S4 . Fig. 5 shows the equivalent circuit model of the powerstage. The ac side of the switching network is represented bya voltage source vAB , which is composed of a low-frequencycomponent vAB ,L and a high-frequency component vAB ,H . Thesecondary side of the transformer Tr is referred to the primaryside and is modeled by an equivalent resistor Req .

A. First StageFour-Quadrant ACDC ConverterThe four-quadrant acdc converter which adopts the full-

bridge topology can be capable of operating in all four quad-rants of the iin vin plane and regenerate the energy back tothe grid [12], [13]. It can also be considered as a bidirectionalconverter that can perform bidirectional power flow [14]. Thefour-quadrant acdc converter is composed of an input filterformed by the inductor Lin and the capacitor Cin , inductorsLs1 and Ls2 , switches S1 S4 , and dc-link capacitor Cdc . It isconnected to the output stage through the nodes A and B.The input current iin is programmed to be lagging, in-phase,or leading the input voltage vin , so that the active and reactivepower drawn from vin are controlled and iin is kept higher thanthe holding current of the TRIAC on dimming.

As the voltage waveform across the capacitor Cin is nearly thesame as the dimmer output voltage vin , the input filter formedby the inductor Lin and the capacitor Cin is excluded in Fig. 5,for the sake of simplicity in the analysis.

Let the lamp power PLED vary linearly with the firing angle. PLED is expressed as

PLED() =

{Pr , < 0

Pr

(1

), 0 < (1)

where Pr is the rated lamp power.


Fig. 4. Circuit schematic of the proposed TRIAC-dimmable LED driver.

Fig. 5. Equivalent circuit model of the power stage.

The voltages vin , vin , and the current iin are expressed as

vin(t) = Vm sint (2)

vin(t) ={

0, t < Vm sint, t < +

(3)

iin (t) ={

0, t < Im sin(t ), t < +

(4)

where Vm and Im are the amplitude of the input voltage vin andinput current iin , respectively, is the angular line frequency,and is the phase difference between vin and iin .

There are three possible operational cases. They are Case Iiin leads vin (i.e., < 0), Case IIiin is in phase with vin(i.e., = 0) , and Case IIIiin lags vin (i.e., > 0). Thethree cases are illustrated in Figs. 6, 2, and 7, respectively. CaseI is operated when is small. can be negative, zero, or pos-itive with different TRIAC holding currents. Their waveformsare shown in Fig. 6(a)(c). Case III is operated when is large.Since is operating-point dependent, there will have three pos-sible scenarios in Case III, including < , = , and > .Their waveforms are shown in Fig. 7(a)(c), respectively.

The average input active power Pavg in all three cases isexpressed as

Pavg(, , ) =12

[ +

VmIm sin sin( )d

+ 2+

+VmIm sin sin( )d

]

=VmIm

2[( + ) cos

+ sin( + ) cos( )]. (5)Consider the critical condition that the input current at the

extinction angle equals Ih :

Ih = Im sin. (6)To ensure stable operation, iin should not be less than Ih over

the TRIAC conduction time. Thus, when TRIAC is turned ONat t = , based on (4)

Im sin( ) Ih . (7)By substituting (6) into (7)

. (8)The curves shown in Fig. 3 are obtained by using (5) and (6),

and putting = 0, = for /36 5/12, and putting = 0, = + / 6 for 5/12 < .

Then, assume that the system efficiency is 100%, Pavg =PLED . By putting (1) and (6) into (5)

Pr

(1

)=

VmIh2 sin

[( + ) cos

+ sin( + ) cos( )]. (9)


Fig. 6. Case Iiin leads vin ( < 0). (a) < 0. (b) = 0. (c) > 0.

The rms value of the input voltage vin , Vrms , is

Vrms =Vm

2. (10)

The rms value of the input current iin , Irms , is as shown (11)at the bottom of the page.

The apparent input power S is

S(, , ) = VrmsIrms =VmIm

21

[( + ) + sin( + ) cos( )].(12)

Fig. 7. Case IIIiin lags vin ( > 0). (a) < . (b) = . (c) > .

By using (5) and (12), the input power factor PF is

PF (, , ) =PavgS

=( + ) cos + sin( + ) cos( )[( + ) + sin( + ) cos( )] .

(13)Equation (13) gives the input power factor with different val-

ues of , , and that can satisfy the required power level givenin (9). Thus, PF can be maximized by changing . Fig. 8 illus-trates the maximum achievable power factor with different val-ues of and Ih ranging from 20 to 80 mA, and the required val-ues of for giving the maximum power factor. The parameters

Irms(, , ) =

12

{ +

[Im sin( )]2d + 2+

+[Im sin( )]2d

}

= Im

12

[( + ) + sin( + ) cos( )] (11)


Fig. 8. Maximum achievable power factor against firing angle with the re-quired phase shift.

TABLE ISPECIFICATIONS OF THE PROTOTYPE

Fig. 9. Actual power factor against firing angle with the simplified phase shiftcontrol.

used in the analysis are given in Table I, in which the ratedpower is 7.2 W. However, according to Fig. 8, the phase shift has to be varied with and Ih . This is impractical as theholding current of a TRIAC is difficult to be determined. Thus,a fixed relationship between and is designed by linearizingthe curve when the holding current is 80 mA in Fig. 8.It is given in Fig. 9. This is the worst case of all the situationsin Fig. 8. In other words, the LED driver will operate normally

Fig. 10. Waveform of vAB .

with TRIAC having holding current below 80 mA. When

2+

(19)

dmin = 1 dmax . (20)Figs. 11(a)(d) show the variations of d(t) over a line cycle

at = 0, 45, 90, and 145, respectively.

B. Second StageLLC Resonant ConverterThe LLC resonant converter is composed of the switches

S1 S4 , inductor Lr , capacitor Cr , transformer Tr , output fil-ter, and LED array. The resonant path is formed by Lr , magne-tizing inductance Lm of the transformer Tr , and Cr . The LLCresonant converter has many advantages over conventional res-onant converters, as it can regulate the output over wide inputand load ranges with zero-voltage switching and a relativelysmall variation of the switching frequency [15], [16]. As de-scribed in (18), the duty cycles of the switches vary with theline frequency. vAB ,L in Fig. 5 will have small effect on the

output, as the impedance of Cr is very high. Thus, only thehigh-frequency component of vAB , vAB ,H is considered in thefollowing discussion. Let Kv be the ratio between the rms val-ues of the voltage across Req , vR , (|vR |), and vAB ,H (|vAB ,H |).Referring to Fig. 5

Kv

(sr

)=

|vR ||vAB ,H | =

|Req//jsLm |Req//jsLm + jsLr + 1js Cr

=m

(sr

)2{

mQsr

[1

(sr

)2]}2+

[(m + 1)

(sr

)2 1

]2(21)

where Q = ZrR e q is the quality factor, Zr =

LrCr

is thecharacteristic impedance, m = LmLr , s = 2fs , and fs is theswitching frequency, and r = 1Lr Cr is the angular resonantfrequency.

Fig. 12 shows the relationships between Kv and s/r withdifferent combinations of the values of Q and m. Kv is sensitiveto Q and is less sensitive to m for m > 1.

The waveform of vAB shown in Fig. 10 is even symmetrical.For the sake of simplicity in the analysis, only the fundamen-tal frequency component is considered in the following analy-sis. Based on Fourier analysis, the fundamental component ofvAB ,H , v

FAB ,H is

vFAB ,H (t) = VFAB,H (vdc , d) cos(st)

=4vdc

sin[d(t)] cos(st) (22)

where V FAB,H (vdc,d) = 2Ts T s

2

T s2vAB (t) cosstdt = 4vd c sin

[d(t)].Thus, the lamp power can be expressed as

PLED() =K2v

(sr

) vFAB ,H (t)2Req()

=8v2dcK

2v

(sr

)sin2[d(t)]

2Req()(23)

where |vFAB ,H | =V FA B ,H

2is the rms value of vFAB ,H .

The equivalent load resistance Req at different LED currentcan be expressed in terms of the LED array voltage as

Req() =2n2vLEDiLED()

. (24)

Detailed proof of (24) is given in the Appendix.By putting (24) into (23)

vdc =nvLED

2Kv(

sr

)sin[d(t)]

. (25)

According to Fig. 12, in order to ensure that the resonant cir-cuit operates in the inductive mode, sr > 1. Kv will then be lessthan unity. Since the minimum value of the term sin[d(t)] in


Fig. 12. Relationships between Kv and s /r . (a) m = 0.5. (b) m = 1. (c) m = 2. (d) m = 2.5. (e) m = 3.

the denominator of (25) is sin[ dmax] or sin[ dmin ], the min-imum value of vdc required, vdc,min , is determined by puttingKv

(sr

)= 1 into (25). Thus

vdc,min =nvLED

2 sin[dmax]=

nvLED2 sin[dmin ]

. (26)

By putting (26) into (19) with vdc = vdc,min , the followingimplicit function for dmax can be obtained:

dmax =

12+

sin[dmax]

V 2m2VmImLs sin + 2L2s I2mnvLED

,

2

+

max{[

1 d(

+

)], d

(

)},

>

2+

(27)where d

(+

)and d

(

)are obtained by (18).

For a given firing angle , all parameters, except dmax , in(27) are known. dmax is determined by an iterative method.

vdc,min is then obtained by putting the determined dmax into(26). Hence, the relationships between vdc,min and shown inFig. 13 are obtained by repeating the previous analysis methodwith different values of .

By substituting (18) into (25) with vdc=vdc,min , Fig. 14 showsthe variation of Kv over one line cycle at different firing angle ofthe TRIAC, in which the minimum value of Kv ,Kv,min occurswhen sin[d(t)] = 1. Thus

Kv,min =nvLED2vdc,min

. (28)

Fig. 15 shows the variation of Kv,min against .

C. Control MethodThe controller shown in Fig. 4 regulates the lamp power at

different firing angles by sensing the voltage vin , input cur-rent iin , dc-link voltage vdc , and LED array current iLED , andcontrolling both the duty cycle and switching frequency of theswitches. The purpose of adjusting the duty cycle is to performthe input current shaping while the purpose of adjusting the


Fig. 13. vdc ,min against .

switching frequency is to regulate the lamp power so that theline-frequency harmonics are removed. The control method isdescribed as follows.

The firing angle is first detected by the sensed vin . It will beused to derive the reference dc-link voltage Vdc,ref , based on thecurve vdc,min depicted in Fig. 13. The actual dc-link voltagevdc will be compared with the reference dc-link voltage Vdc,ref ,and their error vdc will be passed to a PI controller, namelyPI-1, to derive the reference input current iin,ref , which will bein the form of

iin,ref ={

0, t < Im,ref sin(t ), t < +

(29)

where Im,ref is the amplitude of the reference input currentiin,ref .

The actual input current iin will be compared with the ref-erence input current iin,ref , and their error iin will be passedto a PI controller, namely PI-2, to derive the modulating signalvm for the PWM modulator. The gate signals for S1 S4 arederived by comparing vm with the carrier signal vtri . In (29), is determined by considering the firing angle, as depicted inFig. 9. The amplitude Im,ref is determined by the output of PI-1.Thus, the duty cycles of the switches are controlled through thiscontrol mechanism.

The switching frequency is controlled as follows. After deter-mining the firing angle, a reference LED array current, iLED ,ref ,is derived as follows:

iLED ,ref =PLED()

vLED. (30)

The actual LED array current iLED will be compared with thereference LED array current iLED ,ref and their error iLEDwillbe passed to a PI controller, namely PI-3, to vary the frequencyof the carrier signal vtri . It should be noted that the previouscontrols are all performed on a microcontroller.

III. DESIGN PROCEDURE

The values of Ls1 = Ls2 = Ls/2, Lin , Cin , n, Lr , Cr , Lm ,Cdc , Lo , and Co are determined by considering the followingparameters:

1) Pr : Rated lamp power;2) Vm : Amplitude of the voltages vin and vin expressed in

(2) and (3);3) fs,min : Minimum switching frequency of the switches;4) is : The ripple current through the inductors Ls1 and Ls2

when the switching frequency is the minimum;5) Ih,max : Maximum designed holding current of the

TRIAC;6) 0 : Introduced phase shift when = 5 shown in Fig. 9;7) vdc,r : vdc at the rated lamp power;8) vdc,r : peak-to-peak ripple voltage on vdc at the rated

lamp power;9) iLo : The ripple current through the inductor Lo when

the switching frequency is the minimum.Step 1: The amplitude of iin , Im , is determined by using (6).

That is

Im =Ih,max

sin(0 0) . (31)

Ls is then determined by considering that the switching fre-quency is the lowest. The duty cycle of S1 and S4 , d, shouldbe maximum. Based on (16) and (17), vin should be maximumwhen d is maximum, so vLs is neglected for the sake of sim-plicity in calculation. By substituting (16) into (17)

dmax =vin + vdc

2vdc(32)

Lsis

dmax(1/fs,min)= vdc vin . (33)

By substituting (32) into (33)

Ls =dmax(vdc vin)

fs,minis

=(v2dc,r v2m )2vdcfs,minis

(34)

where is is taken to be 40% of Im when the switching fre-quency is the lowest.

Therefore

Ls1 = Ls2 =Ls2

. (35)

Step 2: Lin and Cin are determined by considering thatthe high-frequency ripple current through Ls1 and Ls2 flowsthrough Cin at fs,min . Assume that the impedance of Lin islarger than three times the impedance of Cin at fs,min . Thus

2fs,minLin > 31

2fs,minCin

LinCin > 342f 2s,min. (36)


Fig. 14. Variation of Kv over one line cycle at different firing angle. (a) = 0. (b) = 45. (c) = 90. (d) = 145.

Fig. 15. Variation of Kv ,min against .

Step 3: The value of n is determined by (26)

n =2vdc,rvLED

sin(dmax) =2vdc,rvLED

sin(dmin). (37)

Step 4: With = 0, based on (24), Req(0) equals

Req(0) =2n2v2LED

Pr. (38)

If the quality factor Q at the rated power is Qr , the character-istic impedance Zr is equal to

Zr = QrReq(0). (39)

Fig. 16. Trajectories of Kv ,min against s r for different lamp power andm = 2.5.

Thus, based on Fig. 12, Fig. 16 shows the trajectories ofKv,min against sr for different lamp power and m = 2.5. It canbe observed from the trajectories that:

1) if Qr is small, for example, Qr = 2, there is considerablevariation of the switching frequency from the rated powerto the dimmed power;

2) if Qr is large, for example, Qr = 20, the lamp power istoo sensitive to the variation to the switching frequency.


Thus, it can be observed that Qr = 5 gives the compromisebetween the previous two considerations. Thus, based on (38)and (39)

Zr =

LrCr

= 5Req(0)

Lr = 100n4v4LEDP 2r

Cr . (40)

Based on (21), the resonant frequency is designed at fs,min .Thus

fs,min =1

2

LrCr. (41)

Thus, by solving (40) and (41) for Lr and Cr , it can be shownthat

Lr =5n2v2LEDPrfs,min

(42)

Cr =Pr

20n2v2LEDfs,min. (43)

The value of Lm is chosen by taking m = 2.5. Thus, basedon (21)

Lm = mLr

=12.5n2v2LEDPrfs,min

. (44)

Step 5: For the sake of simplicity in the design, the value ofCdc is designed by assuming that the input current is in phasewith the supply voltage at the rated power condition

Pr =12

20

VmIm sin2 tdt

=VmIm

2. (45)

Cdc absorbs the difference between the input power and theaverage lamp power. Thus, the maximum variation of the energyEC stored in the capacitor is

EC =Pr

. (46)

Assume that vdcvaries between vdc,r and vdc,r + vdc,r , andvdc,r


Fig. 17. Experimental results of the prototype (vin : 250 V/div, iin : 500 mA/div, iLED : 200 mA/div, Timebase: 4 ms/div). (a) Without TRIAC and PLED =7.2 W. (b) = 25 and PLED = 7.2 W. (c) = 45 and PLED = 5.4 W. (d) = 90 and PLED = 3.6 W. (e) = 145 and PLED = 1.4 W. (f) = 172and PLED = 0.3 W.

Fig. 18. Switching frequency fS versus the lamp power PLED .Fig. 19. Measured lamp power PLED and efficiency versus firing angle .


Fig. 20. Photographs of the prototype driver. (a) Top view. (b) Side view.

to the flyback-type structure given in [7]. The lowest efficiencyis found to be 52% when the firing angle is 172. Fig. 13 showsthe experimental results of vdc versus the firing angle. Its profileis similar to the theoretical prediction.

Fig. 20 shows the prototype driver for a 7-W LED lamp.In terms of physical size, the present design can be optimizedfurther. For example, the circuitry can be further reduced as thefour switches and their corresponding drivers can be integratedwith current semiconductor packaging technologies.

V. CONCLUSIONA TRIAC-dimmable LED lamp driver that can provide wide

dimming range for extremely low-power operation without dis-sipative bleeding circuit has been presented. By introducing thereactive power control, the input current can be increased whilethe active power is regulated. The concept has been demon-strated on a 7.2 W prototype, which can be dimmed down to0.3 W. Experiments reveal that the current ripple of the LEDis small. The output power of LED can be controlled in linearrelationship with the firing angle of the TRIAC. The theoret-ical predictions and experimental measurements are in closeagreement.

APPENDIXPROOF OF (24)

The high-frequency component of vAB , vAB ,H , is only con-sidered here as the low-frequency component is blocked by the

capacitor Cr . In Fig. 5, the magnetizing inductance of the trans-former Lm is much larger than the equivalent resistance Req athigh-frequency switching. Thus, Lm is neglected in the analysis.The phasor for representing vFAB ,H in (22) vFAB ,H is

vFAB ,H =4vdc

2sin[d(t)]0. (A.1)

The current ip flowing through Lr and Cr is

ip =iLED()

2n (A.2)

where is the phase difference between vFAB ,H and ip .So, the output power transferred to the secondary side of

transformer is

P = vAB ,H ip cos()

=2vdciLED()

nsin[d(t)] cos . (A.3)

Thus,

cos =nP

2vdciLED() sin[d(t)]. (A.4)

The voltages across Lr , vLr , and Cr , vC r , are

vLr = ipsLr 90 =iLED()sLr

n(90 ) (A.5)

vCr =ip

sCr 90 =iLED()nsCr

(90 ). (A.6)

Based on KVL, the voltage across Req , vR , is

vR = vFAB ,H vLr vCr . (A.7)

Req is approximated by assuming that the imaginary part ofvR in (A.7) is negligible. Thus, by considering the real part of(A.7) and substituting (A.1), (A.5), and (A.6) into (A.7)

Req = Re[vR

ip] =

2n2vLEDiLED()

(A.8)

|vR | = |ip |Req =

2nvLED . (A.9)

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Ruihong Zhang (S12) received the B.Eng. degreein computer science and the M.Eng. degree in elec-trical engineering, both from the Harbin Institute ofTechnology, Harbin, China, in 2005 and 2008, re-spectively. She is currently working toward the Ph.D.degree in electrical engineering from the City Uni-versity of Hong Kong, Kowloon, Hong Kong.

Her current research interests include the light-ing system, power-factor-correction, resonant con-verters, ac/dc, dc/dc converters, and energy-recyclingtechniques.

Henry Shu-hung Chung (M95SM03) receivedthe B.Eng. degree, in 1991, and the Ph.D. degree inelectrical engineering, in 1994, both from Hong KongPolytechnic University, Kowloon, Hong Kong.

Since 1995, he has been with the City Universityof Hong Kong, Kowloon. He is currently a Profes-sor in the Department of Electronic Engineering, andthe Director of the Centre for Smart Energy Conver-sion and Utilization Research. He has authored sixresearch book chapters, and more than 300 technicalpapers including 140 refereed journal papers in his

research areas, and holds 26 patents. His research interests include time- andfrequency-domain analysis of power electronic circuits, switched-capacitor-based converters, random-switching techniques, control methods, digital audioamplifiers, soft-switching converters, and electronic ballast design.

Dr. Chung is currently the Chairman of Technical Committee on High-Performance and Emerging Technologies of the IEEE Power Electronics Soci-ety, and an Associate Editor of the IEEE TRANSACTIONS ON POWER ELECTRON-ICS, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, PART I: FUNDAMENTALTHEORY AND APPLICATIONS, and the IEEE JOURNAL OF EMERGING AND SE-LECTED TOPICS IN POWER ELECTRONICS.

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A TRIAC-Dimmable LED Lamp Driver With Wide

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