Phase-locked-loop-control-based electronic ballastfor fluorescent lamps

R.-L. Lin and Y.-T. Chen

Abstract: The paper proposes an electronic ballast in which the resonant frequency of the circuit iscontinuously tracked by the phase-locked loop (PLL). This electronic ballast, which employs PLLcontrol, has a high tolerance for the variations that exist in the equivalent resistance of a lamp. Atpresent, the PLL control is used to drive cold-cathode fluorescent lamps (CCFLs), in whichvariations in equivalent resistance between ignition and the steady state are small, so that phasedifferences at the resonant frequency are almost fixed; thus the resonant frequency can be trackedcontinuously by the operating frequency. However, if variations in equivalent resistance are large,the phase difference at the resonant frequency may be not fixed, and thus the resonant frequencymay be not continuously tracked by the operating frequency. The paper proposes the electronicballast for fluorescent lamps with large variations in equivalent resistance between ignition and thesteady state. According to the phase characteristics of various resonant tanks and an optimumdesign of the resonant tank, the circuit’s resonant frequency is continuously tracked by the PLL.Since the current regulator circuit limits the value of the lamp current as the operating frequencyincreases from the resonant frequency, the lamp current is accurately controlled, regardless ofvariations in the load. The paper discusses the implementation of the proposed ballast with PLLcontrol, which offers high tolerance for the variations of the equivalent resistance in the lamp.

1 Introduction of control schemes for electronicballasts

The electronic ballast is composed of an AC/DC rectifierunit and a DC/AC inverter unit. The AC/DC rectifiersupplies a DC voltage to the DC/AC inverter, and the DC/AC inverter uses a high-frequency voltage to drive the lamp.Conventionally, the configuration of this electronic ballastincludes a full-bridge rectifier and a class D inverter [1], asshown in Fig. 1.

Figure 2 shows the categories of control schemes for DC/AC inverters, which can be either fixed-frequency [2] orvariable-frequency controls. The variable-frequency controlis further compartmentalised into voltage feedback control,current-feedback control [3–5] and PLL control [6–8]. Thesecontrol schemes will be discussed in Section 2.

Generally speaking, due to the aging characteristic oflamps, their steady-state equivalent resistances are notalways constant. Also, different types of lamp utilise thesame specifications. Therefore, lamps have different levels ofequivalent resistance, which leads to different voltage gainsfor their resonant tanks, especially in the steady state. Basedon variations in lamps’ levels of equivalent resistance, lampvoltage cannot be accurately supported with fixed-frequencycontrol; however, voltage or current feedback control hasovercome this defect.

Figure 3 shows the effects caused by variations in theequivalent resistances of the lamps. Lamps 1 and 2 in Fig. 3have different equivalent resistances, which lead to differentvoltage gains for their resonant tanks, especially in thesteady state.

In the steady state, by the voltage-feedback control, lamp1 can be operated with the desired voltage gain when theoperating frequency is fstable1. Unfortunately, due to thefluctuating equivalent resistance in lamp 2, its operatingfrequency cannot be adjusted to provide the desired voltage.During the operation of lamp 2, the circuit operating

R Lamp

Vacresonant tank

DC/AC inverterAC/DC rectifier

Fig. 1 Configuration of the electronic ballast

frequency control

fixed-frequency control

voltage or current-feedback control phase-locked-loop control

variable-frequency control

Fig. 2 Control schemes for DC/AC inverters

The authors are with the Department of Electrical Engineering, National ChengKung University, Tainan City, Taiwan, ROC

E-mail: rayleelin@ee.ncku.edu.tw

r IEE, 2005

IEE Proceedings online no. 20045199

doi:10.1049/ip-epa:20045199

Paper first received 26th October 2004 and in revised form 13th January 2005.Originally published online: 8th April 2005

IEE Proc.-Electr. Power Appl., Vol. 152, No. 3, May 2005 669

frequency may be lower than the circuit resonant frequencyfr2, thus causing an increase in switching losses [1]. For thesame reason, the current-feedback control scheme also hasthis defect. The PLL control scheme has been proposed toovercome this drawback.

In Fig. 3, due to the PLL control, lamp2 is controlled atthe resonant frequency fr2, and so the switching losses arenot a concern. Consequently, the PLL control is better thanboth voltage feedback and current feedback controlmethods.

With the PLL control, the operating frequency is able tocontinuously track the resonant frequency, but the voltagemay be higher than the requested gain at the resonantfrequency. To resolve this issue, an external circuit is used toincrease the operating frequency, and thus the voltage gaincan be reduced sufficiently.

At present, the PLL control is used to drive cold-cathodefluorescent lamps (CCFLs), in which variations in equiva-lent resistance between ignition and the steady state aresmall, so that phase differences at the resonant frequencyare almost fixed; thus, the resonant frequency can becontinuously tracked by the operating frequency. However,if variations in equivalent resistance are large, the phasedifference at the resonant frequency may be not fixed, andthus the resonant frequency may not be tracked continu-ously by the operating frequency.

This paper proposes our electronic ballast for fluorescentlamps with large variations in equivalent resistance betweenignition and the steady state. Because of the phasecharacteristics of various resonant tanks and an optimumdesign of the resonant tank, the circuit’s resonant frequencyis continuously tracked by the PLL. And thus, thanksto the current regulator circuit, which limits the valueof the lamp’s current as the operating frequency in-creases from the resonant frequency, the lamp currentis accurately controlled, regardless of variations in theload.

2 Analysis of PLL control for electronic ballast

The block diagram of the proposed PLL-control electronicballast, shown in Fig. 4, is composed of a AC input, a full-bridge rectifier, half-bridge switches, a resonant tank, a PLLcontrol circuit, a current regulator circuit and a half-bridgedriver circuit. In this block diagram, the square wave,produced by the half-bridge switches, which are bothswitched at 50% duty cycle, supports the resonant tank.And thus, according to a phase difference detected in theresonant tank, the PLL control circuit regulates theoperating frequency of the half-bridge driver. The functionof the current regulator circuit is to maintain a fixed currentin the lamp.

The phase characteristics of the series–parallel resonanttank (SPRT) will be analysed and discussed to determine asuitable resonant tank for tracking the resonant frequencywith PLL control. Phase detection of voltages is preferableto phase detections of currents, because the latter involvesmany disadvantages, such as I2R losses with a serialresistance, noise interferences in the current-feedback signal,and the expense of Hall sensors. Therefore, the phases ofvoltages in the SPRT at the resonant frequency will beobserved and analysed in Section 3.

As shown in Fig. 4, an SPRT is composed of an inductorL, two capacitors (Cs and Cp), and a resistance RLamp.Based on variations in the equivalent resistance during thelamp’s ignition and at the steady state, with different valuesof the resistance RLamp, the phases and gains of the inputvoltage Vi in relation to the output voltage Vo in the SPRTat the resonant frequency will be obtained.

The relationship of the input voltage Vi to the outputvoltage Vo is shown in (1); then the gain and phase of Vo/Vi

amplitude (Vo/Vi)

ignition gain

operating gain

fstartfr1

fr2

fstable1

before ignitionafter ignitionlamp 1

lamp 2

frequency

Fig. 3 Relationship between amplitude of Vo/Vi and operatingfrequency

current-regulator

circuit

half-bridgedriver circuit

phase detection

phase comparator

low pass filter

vco

PLL IC

full-bridgerectifier

Vac VDCVi Vc Cp

CsL

R lampVo−− − −

+

+ + +

Fig. 4 Block diagram of the proposed electronic ballast with PLL control

670 IEE Proc.-Electr. Power Appl., Vol. 152, No. 3, May 2005

are derived, as shown in (2) and (3):

Vo

Viðf Þ ¼

R1

j2pfCp1

j2pfCpþ R

j2pfLþ 1

j2pfCsþ

R1

j2pfCp1

j2pfCp þ R

ð1Þ

VoViðf Þ

¼ 2p

Cs2R2Lampf 2

64p6L2Cs2Cp2R2Lampf 6 32p4LCsCpR2

Lampf 4ðCsþ CpÞþ16p4L2Cs2f 4 þ 4p2R2

Lampf 2ðCs2 þ Cp2Þþ8p2CsR2

Lampf 2ðCp LÞ þ 1

8>>>>>>>>><>>>>>>>>>:

9>>>>>>>>>=>>>>>>>>>;ð2Þ

ff Vo

Viðf Þ ¼ arctan

4p2LCsf 2 1

2pRLampf ð4p2LCsCpf 2 Cs CpÞ

ð3ÞTo simulate the ignition and the steady state of the lamp inthe SPRT, the inductor L, the capacitor Cs, the capacitor Cp

and the three different values of the resistance RLamp are,respectively, 1mH, 100nF, 10nF, 100O, 1kO and 1MO;the result of this setup is shown in Fig. 5. By observing thephases, the phase difference between Vi and Vo at theresonant frequency is always 901 when RLamp is largerthan 1kO. However, in RLamp, the value of the phase at theresonant frequency, 100O, rises to151. Therefore, becauseof variation of RLamp, the phase difference at the resonantfrequency is not fixed.

The relationship of the input voltage Vi to the voltage Vc

is shown in (4); then the gain and phase of Vc/Vi are

derived, as shown in (5) and (6):

Vc

Viðf Þ ¼

R1

j2pfCp1

j2pfCpþ Rþ 1

j2pfCs

j2pfLþ 1

j2pfCsþ

R1

j2pfCp1

j2pfCp þ R

ð4Þ

Vc

Viðf Þ

¼ 2p4p2R2

Lampf 2ðCsþ CpÞ2 þ 1

8p2LCsCpR2Lampf 2ð8p4f 2LCsCp 4Cs 3Cp LÞ

þ16p4L2Cs2f 4 þ 4p2R2Lampf 2ðCs2 þ Cp2Þ þ 1

8>>>><>>>>:

9>>>>=>>>>;

ð5Þ

ff Vc

Viðf Þ

¼ arctan8p2LCs2RLampf 3

16p4LCsCpR2Lampf 4ðCsþ CpÞ 4p2R2

Lampf 2ðCsþ CpÞ2

þ4p2LCsR2Lampf 2 1

8>>>><>>>>:

9>>>>=>>>>;ð6Þ

To simulate the ignition and the steady state of the lamp inthe SPRT, inductor L, capacitor Cs, capacitor Cp and thethree different parameters of the resistance RLamp are,respectively, 1mH, 100nF, 10nF, 100O, 1 kO and 1mO;the result of this setup is shown in Fig. 6. By observing thephases, the phase difference between Vi and Vc at theresonant frequency is always 901 when RLamp is largerthan 1kO. However, in RLamp, the value of the phase at theresonant frequency, 100O, rises to 301. Therefore, owingto the variation of RLamp, the phase difference at theresonant frequency is not fixed. However, the variation of

Rlamp=1k Ω

Rlamp=100 Ω

Rlamp=1M Ω

10 100

frequency, kHz

1000

100

10

1

0.1

|Vo

/ Vi |

Rlamp=1k Ω

Rlamp=100 Ω

Rlamp=1M Ω

10 100

frequency, kHz

degr

ee (

Vo

/ Vi)

0−15

−90

−180

Fig. 5 Gains and phases of Vo/Vi

L¼ 103H, Cs¼ 107F, Cp¼ 108F

1000

1

100

10

0.110 100

frequency, kHz

R lamp= 1M Ω

R lamp= 1k Ω

R lamp= 100 Ω

R lamp= 1M Ω

R lamp= 1K Ω

R lamp= 100Ω

−90

−180

−30

0

10 100

frequency, kHz

degr

ee (

Vc

/ Vi )

|Vc / V

i |

Fig. 6 Gains and phases of Vc/Vi

L¼ 103H, Cs¼ 107F, Cp¼ 108F

IEE Proc.-Electr. Power Appl., Vol. 152, No. 3, May 2005 671

the phase in Vc/Vi at the resonant frequency is lower thanthe variation of the phase in Vo/Vi at the resonantfrequency.

Section 3 will show further analysis of the SPRT with anoptimal design, in order to observe the relationship betweenthe phases of Vc/Vi at the resonant frequency and thevariations in the load resistance.

Equation (4) is modified to obtain the following:

Vc

Viðf Þ ¼

4p2f 2R2LampðCsþ CpÞð4p2f 2LCsCp Cs CpÞ

ð4p2f 2LCs 1Þð8p3f 3LCpCsRLamp 2pfCsRLamp 2pfCpRLampÞ2

þð1 4p2f 2LCsÞ2

j

ð8p3f 3LCpCsRLamp 2pfCsRLamp 2pfCpRLampÞ2pfRLampðCsþ CpÞð4p2f 2LCs 1Þ

ð8p3f 3LCpCsRLamp 2pfCsRLamp 2pfCpRLampÞ2

þð1 4p2f 2LCsÞ2

ð7Þ

When the phase of Vc/Vi is 901, the imaginary part of (7)is zero; then, (8) is solved to obtain (9), which shows theparameters of inductance L.

4p2f 2R2LampðCsþ CpÞð4p2f 2LCsCp Cs CpÞ

ð4p2f 2LCs 1Þð8p3f 3LCpCsRLamp 2pfCsRLamp 2pfCpRLampÞ2

þð1 4p2f 2LCsÞ2

¼ 0 ð8Þ

L ¼4p2f 2R2

LampðCsþ CpÞ2 þ 1

4p2f 2Csð4p2f 2CpCsR2Lamp þ 4p2f 2Cp2R2

Lamp þ 1Þð9Þ

Assuming that the required gain of Vo/Vi for the lampin the steady state is A, as shown in (10), then (9) and (10)can be used to derive the parameters of capacitor Cs, asfollows:

A ¼ Vc

Viðf Þ

¼

2pfCsRLamp

8p2LCsCpR2Lampf 2ð8p4f 2LCsCp 4Cs 3Cp LÞÞ

þ16p4L2Cs2f 4 þ 4p2R2Lampf 2ðCs2 þ Cp2Þ þ 1

( )

ð10Þ

Cs ¼

8p3f 3Cp3R3Lamp þ 2pfCpRLampð1 A2Þ

þA ðp

4p2f 2Cp2R2Lamp þ 1 A2Þ

2pfRLampðA2 4p2f 2R2LampCp2Þ ð11Þ

Based on (11), (9) becomes

L ¼

8p3f 3Cp4R5Lamp þ 2pfCp2R3

Lampð1 A2ÞþA2 þ 2CpR2

LampAð4p2f 2Cp2R2Lamp þ 1 A2Þ

ð2pfCpRLampAð4p2f 2Cp2R2Lamp þ 1 A2Þ þ A2

n oðð8p3f 3Cp3R3

Lamp þ 2pfCpRLampð1 A2ÞþAð4p2f 2Cp2R2

Lamp þ 1 A2Þð12Þ

Based on the equation of the input impedance in the SPRT,the value of the resonant frequency can be derived, asshown in (13) and (14).

Ziðf Þ ¼ j2pfLþ 1

j2pfCsþ

R1

j2pfCp1

j2pfCp þ Rð13Þ

At the resonant frequency, the imaginary part is zero, so

fr ¼

CpR2LampðCp þ CsÞ LCs

þ L2Cs2 þ 2LCsCpR2LampðCp CsÞ

n

þCp2R4LampðCsþ CpÞ2

o12

8p2LCsCp2R2Lamp

26666666666664

37777777777775

ð14Þ

where fr is the resonant frequency.Using (6), (11), (12) and (14), Fig. 7 shows the relation-

ship between the phases of Vc/Vi at the resonant frequencyand the capacitance Cp in the steady state, where RLamp,three gains and four operating frequencies are, respectively,225O, 0.5, 1, 2, 3, 50kHz, 75kHz and 100kHz. In Fig. 7, atthe resonant frequency, the phase of Vc/Vi is only slightlyaffected by the design of the operating frequency, but isgreatly impacted by the gain of the ratio Vo/Vi. Therefore,with a larger gain requirement, the phases of Vc/Vi at theresonant tend to 901. Additionally, with smaller values ofCs, the phases of Vo/Vi at the resonant also tend to 901.

3 Design of resonant tank

The proposed electronic ballast for use with fluorescentlamps will be designed with a suitable resonant tank. Thespecifications for this ballast are given in Table 1. Thecircuit input voltage is a 110V, 60Hz AC, and an Fl36dfluorescent lamp [9], whose equivalent resistance is 225O atsteady state. As shown in Fig. 3, the AC/DC rectifier iscomposed of a full-bridge rectifier without power-factorcorrection (PFC) [10]. The DC/AC inverter is composed ofa half-bridge inverter, where the gate signals of the switchesare symmetrically square waveforms with a duty cycle of0.5.

0

−20

− 40

− 60

− 80

− 90

phas

e of

Vi t

o V

c at

res

onan

t fre

quen

cy, d

eg

1 10 100 1

Cp, nF

Vo

Vi= 0.5

VoVi

= 1

Vo

Vi= 2

Vo

Vi= 3

Fig. 7 Relationships between the phases of Vc/Vi at the resonantfrequency and Cp in the steady state with different levels of voltagegainRLamp¼ 225O

672 IEE Proc.-Electr. Power Appl., Vol. 152, No. 3, May 2005

Referring to Fig. 3, the 110V, 60Hz AC input voltage isrectified to a 156V DC for driving the DC/AV inverter.Thus, the square waveform, whose duty cycle is 0.5, isgenerated by switching the 156V direct current in the half-bridge switches. To simplify the analysis of resonant tanks,the fundamental waveform of the input voltage in theresonant tank is a 70V sine wave. Based on thespecifications, as shown in Table 1, the output voltage inthe lamp is calculated to be 90V. To provide sufficientoutput voltage, the voltage gain must be at least 1.3.Additionally, owing to the existence of parasitic resistancesand thermal losses in the circuit, there has to be enough of again margin to avoid an insufficient level of output voltage.Therefore, the voltage gain at the resonant frequency of50kHz is 3. Thus the gain margin is 1.7.

Referring to Fig. 7, the bold curve of the voltage gain 3shows that the phase at the resonant frequency (of between701 and 851 with an RLamp of 225O and with differentvalues of Cp) is able to achieve approximately 901. Thus,locking the phase difference to be 901 in the Vc/Vi of theSPRT is adequate for the electronic ballast proposed in thispaper.

In the SPRT, the phase of Vc/Vi at the resonantfrequency changes with different values of Cp, as shownin Fig. 8, where A is 3, and Cs and L are determined by (11)and (12), respectively. As shown in Fig. 8, smaller values ofCp are necessary in order for the resonant frequency to betracked. Unfortunately, the value of inductance L is largerfor a smaller Cp, as shown in Fig. 9, which shows therelationship between L and Cp, where A is 3, and Cs and Lare determined by (11) and (12), respectively. Additionally,a smaller Cs is necessary with a small Cp, as shown inFig. 10, which shows the relationship between Cs and Cp,where A is 3, and Cs and L are determined by (11) and (12),respectively.

The parameters of the SPRT can be designed accordingto the preceding analysis, as shown in Table 2. The phase ofVi to Vc at the resonant frequency is nearly 801 in thesteady state. Although, the phase 801 is close to 901, thebias voltage in the VCO of the PLL is smaller than others.Additionally, from the standpoint of input impedance, thePF of cos(101) is higher than for other cases. Besides, theresonant frequency at the steady state is very close to50kHz. Using the parameters shown in Table 2, thefollowing paragraphs will analyse all components in termsof voltage and current stresses.

The relationships between the gain of Vo/Vi and thephase of Vc/Vi are shown in Fig. 11. The gain of Vo/Vi is 3at the resonant frequency with an RLamp of 225O.Therefore, the current-regulator circuit limits to 0.4A thecurrent that flows through RLamp; so the gain of Vo/Vi willbe adjusted to 1.3, which means that the switchingfrequency will be about 57.7kHz, as shown in Fig. 11.Therefore, the phase of Vc/Vi is about 1481.

Table 1: Specification for the proposed electronic ballast

Specification Values

Circuit input voltage 110VRMS 60Hz AC

Lamp power 36W

Lamp voltage 90V AC

Lamp current 400mA

Lamp equivalent resistance 225O

Input voltage of the resonant tank 70VRMS AC

Required voltage gain 1.3

Resonant frequency 50kHz

Voltage gain at resonant frequency 3

−90

−70

−80

Vc Vi

(fr )

, deg

ree

∠

40n 40.5n 41.5n 42.5n41n 42nCp, F

Fig. 8 Relationships between the phases of Vc/Vi at the resonantfrequency and Cp in the steady state

100m

10m

1m

0.1m

L (H

)

40n 41n 42n40.5n 41.5n 42.5n

Cp, F

Fig. 9 Relationship between Cp and L

1m

100u

100n

10u

10n

0.1n

1u

1n

40n 41n 42n40.5n 41.5n 42.5n

Cp, FC

s, F

Fig. 10 Relationship between Cp and Cs

Table 2: Parameters of the SPRT

SPRT

Phase of Vo/Vi at resonant frequency 80.71

L 0.491mH

Cs 39.5nF

Cp 40.6nF

Resonant frequency (RLamp¼225O) 49kHz

Resonant frequency (Rlamp¼1MO) 50.7kHz

IEE Proc.-Electr. Power Appl., Vol. 152, No. 3, May 2005 673

The voltage and current stresses on all components canbe calculated using Kichhoff’s voltage law and Kichhoff’scurrent law. The results are shown in Table 3. Based on thisresult, all components will be implemented.

4 Experimental results

In this work, by use of a PLL IC (CD4046) [11], theswitching frequency of the SPRT is limited within a certainrange in order to achieve accurate 901-phase locking.Although the phase at the resonant frequency is onlyapproximately 801, the error of 101 can be offset by a biasvoltage in the input of the VCO.

Referring to Table 2, in the SPRT, the resonantfrequencies at the ignition and in the steady state are50.7kHz and 49kHz, respectively. Additionally, fromFig. 11 and Table 3, the switching frequency in the steadystate is adjusted to be 57.7kHz with the current-regulatorcircuit. Therefore, the frequency range of the VCO is limitedto between 40kHz and 70kHz.

When the lamp is driven in the steady state, as shown inFig. 12, in which the switching frequency is about 56.8kHz,the phase difference between Vc and Vi in the steady state,as shown in Fig. 13, is about1461. This result is consistentwith the previous analysis given in Fig. 11.

Different levels of input AC voltage (110V720%) areapplied in order to determine the effects in the lamp. Asshown in Figs. 14–17, the values of lamp voltage andcurrent approach the same values, regardless of the valuesof the input AC voltage. However, the efficiency, includingthe power losses in the linear power supply used in the logic

10.0

7.5

5.0

2.5

0

Rlamp= 1Mohm

Rlamp= 225 ohm

Vc

Vi

Vo

Vi

Rlamp= 1Mohm

Rlamp= 225 ohm

40 k 50 k 57.7 k 60 k4.5 104 5.5 104

frequency, HZ

frequency, HZ

40 k 50 k 57.7 k 60 k

0°

−90°

−180°

−148°

Fig. 11 Gain of Vo/Vi and the phase of Vc/Vi

Table 3: Voltage and current stresses on all components ofthe SPRT

fSW 57.7kHz

VR Lamp 90.8VRMS

IR Lamp 0.403ARMS

VL 250VRMS

IL 1.4ARMS

VCS 97.8VRMS

ICS 1.4ARMS

VCP 90.8VRMS

ICP 1.34ARMS

lam

p vo

ltage

, Vla

mp

curr

ent,

A

93.5 V(RMS)

time

0.4 A(RMS)

Fig. 12 Lamp voltage and current in the steady stateInput AC voltage¼ 110VRMSSwitching frequency¼ 56.8kHzLamp voltage: 100V/divisionLamp current: 0.5A/divisionTime base: 10ms/division

Vi

VC

146°phase difference

Vin(50V/div); Vc(200V/div); time base(10 µs);switching frequency = 56.8 kHz

time

Fig. 13 Waveforms of Vc and Vi in the steady stateVin: 50V/divisionVc: 200V/divisionTime base: 10ms/divisionSwitching frequency: 56.8kHz

100

95

9090 100 110 120 130

lam

p vo

ltage

, V

input AC voltage, V

Fig. 14 Lamp-voltage variation with different input AC voltages(110 V720%)

674 IEE Proc.-Electr. Power Appl., Vol. 152, No. 3, May 2005

and driver circuitry, decreases with increase in input powerbecause of the losses in the circuit.

As for the crest factor [13], the waveforms of VDC bus andthe lamp’s current in the steady state are shown in Fig. 18,in which the crest factor is 1.46. Additionally, with differentlevels of input AC voltage (110V720%), variation of crestfactor is as shown in Fig. 19. This result shows that the crestfactors are lower than the maximum limit of 1.7.

As illustrated in Fig. 20, which shows the process of lampignition, the lamp is ignited instantaneously.

By using variable resistances instead of the lamp load atthe steady state, the results for the same input voltage of110VMS are shown in Figs. 21–24. With the current-regulator circuit, the output currents approach the samemagnitude, regardless of the values of Rload. However, theoutput voltage and power increase with incrementalincreases in Rload. Additionally, with different values ofRload, the efficiency is approximately 80%, which includes

400

395

39090 100 110 120 130

input AC voltage, V

lam

p cu

rren

t, m

A

Fig. 15 Lamp-current variation with different input AC voltages(110 V720%)

input AC voltage, V

50

40

45

3590 100 110 120 130

pow

er, W

lamp power input power

Fig. 16 Variations of lamp power and input power with differentinput AC voltages (110 V720%)

90

80.0

77.5

75.0100 110 120 130

effic

ienc

y, %

input AC voltage, V

Fig. 17 Efficiency variation with different input AC voltages(110 V720%)

0.4 A (RMS)1.17 A (peak-peak)crest factor = 1.46

lampcurrent

VDC bus

Fig. 18 Relationship between VDC bus and lamp currentInput AC voltage: 110V RMSSample rate: 20M sample/sVDC bus: 50V/divisionLamp current: 0.4A/divisionTime base: 10ms

2.0

1.0

1.5

90 100 110 120 130

input AC voltage, V

cres

t fac

tor

Fig. 19 Crest-factor variation with different input AC voltages(110 V720%)

Vlamp

Ilamp

Vlamp(500 V/div) ; Ilamp(1 A/div) ; time base (5 ms)

Fig. 20 Lamp ignition

120

100

80

60

40137 152 190 201 237 262 283

Rload, Ω

lam

p vo

ltage

, V

Fig. 21 Output-voltage variation with Rload (around225O730%)

400

395

390

Rload, Ω

lam

p cu

rren

t, m

A

137 152 190 201 237 262 283

Fig. 22 Output-current variation with Rload (around225O730%)

IEE Proc.-Electr. Power Appl., Vol. 152, No. 3, May 2005 675

the power losses in the linear power supply used in the logicand driver circuitry.

These experimental results have verified the analysis anddesigns discussed in Section 3. With sufficient gain margins,the lamp voltage and current can be supported withdifferent levels of input AC voltage, regardless of variationsof Rload or other components in the circuits. In addition,based on the PLL control, the lamp can be startedinstantaneously. Therefore, with the procedure describedin Section 3, the different specifications of the ballast, inwhich the resonant frequency of the circuit is continuouslytracked by the PLL, can easily be designed. Additionally,for the Vc/Vi in the SPRT, locking the phase difference at901 has the best effect in terms of tracking the resonantfrequency. Since the prototype circuit does not have thefront-end power-factor-correction converter, its measuredinput power factor is 0.53. Fig. 25 shows the measuredinput-current harmonics of the prototype circuit, comparedwith the IEC 61000 Class-C Standard.

5 Conclusions

This paper has proposed an electronic ballast for use withthe SPRT in which the resonant frequency is continuouslytracked by the PLL. According to the phase characteristicsof the SPRT, by using the SPRT, the PLL is adjusted withthe least bias voltage for locking to 901, the phasedifference of Vc/Vi in the resonant tank. The power-factorof the input impendence is close to unity when the phase ofVc/Vi is locked close to 901.

The voltage gain of the resonant tank at the resonantfrequency must be carefully designed. Because of variationsin the input AC voltage and the load, if the gain margin inthe circuit is relatively large, sufficient voltage gains canmaintain the lamp current. However, because of the highgain margin, the PF of the resonant tank will be relativelylow. If the gain margin in the resonant tank is small, thevoltage gain will be insufficient to ignite the lamp andmaintain the lamp current. Besides, based on the smallergain margin, the load tolerance and the input AC voltagewill be lower.

This paper has used PLL control to implement theballast; this offers high levels of load tolerance and inputAC voltage. Even though the input AC voltage hasvariations of 20%, the lamp current is still accuratelycontrolled by the regulator circuit. Additionally, theproposed ballast not only endures 30% variations in Rload,but also maintains the rated currents in Rload. In addition,whatever the input AC voltage, the crest factor is alwayslower than 1.7, which is necessary for extending the lifetimeof the lamp. As for the ignition, by tracking the resonantfrequency, an adequate voltage gain can be provided duringthis period; thus the lamp can be started instantaneously.During operation of the proposed ballast, the efficiency isaround 80%.

6 Acknowledgments

This work was partially sponsored by the National ScienceCouncil, Taiwan, ROC, under awards NSC 92-2213-E-006-087 and NSC 93-2213-E-006-138.

7 References

1 Kazimierczuk, M., and Czarkowski, D.: ‘Resonant power converters’(John Wiley & Sons, Inc, 1995)

2 Sun, Y.: ‘Improved simulation accuracy and reduced design time forelectronic ballast designs which incorporate fixed frequency controllerICs’. Proc. IAS’96, 6–10 October 1996, Vol. 4, pp. 2183–2188

3 Zaitsu, T.: ‘Converter comprising a piezoelectric transformer and aswitching stage of a resonant frequency different from that of thetransformer’, US Patent 5 768 111, 26 February 1996

4 Moo, C.S., Cheng, H.L., Lin, T.F., and Yen, H.C.: ‘Designing adimmable electronic ballast with voltage control for fluorescent lamp’.Proc. ISIE’99, 12–16 July 1999, Vol. 2, pp. 786–791

5 Rodriguez, F., Ribas, J., and Alonso, J.M.: ‘Analysis and design of theLCC-parallel series inverter with resonant current control as HPSlamp ballast’. Proc. Power Electronics Specialists Conf., 17–21 June2001, Vol. 2, pp. 980–985

6 Baker, E.: ‘Design of radial mode piezoelectric transformers for lampballast applications’. MS Thesis, Virginia Tech, May 2002

7 Harold, W.: ‘Single-input phase locking piezoelectric transformerdriving circuit’, US Patent 5 866 968, 7 May 1997

8 Hiroyuki, S.: ‘Inverter circuit for lighting a cold cathode tube by theuse of a piezoelectric transformer’, US Patent 5 854 543, 29 Dec. 1998

9 http://www.tfc.com.tw/english/english.htm10 Moo, C.S., Lin, T.F., and Hsieh, Y.C.: ‘A single-stage high power

factor electronic ballast for fluorescent lamps with constant poweroperation’. Proc. EPE-PEMC, Kosice, Slovak Republic, Sept. 2000

11 CD4046BC data sheet, Fairchild Semiconductor Corporation, 200212 Cayless, M.A., and Marsden, A.M.: ‘Lamps and lighting’ (Edward

Arnold, 1983)13 Lin, R.-L.: ‘Phase-locked loop control based electronic. ballast’,

Taiwan Patent application 093118006, 21 June 2004

Rload, Ω

output power input power

pow

er, W

60

40

20137 152 190 201 237 262 283

Fig. 23 Variations in input power and output power with Rload

(around 225O730%)

85.0

75.0

80.0

137 152 190 201 237 262 283

effic

ienc

y, %

Rload, Ω

Fig. 24 Efficiency variation with Rload (around 225O730%)

100

90

80

70

60

50

40

30

20

10

0

inpu

t-cu

rren

t har

mon

ics,

%

1 2 3 4 5 6 7 8 9 10 11 12 13

harmonicsIEC 61000 class-C

Fig. 25 Measured input-current harmonics of the prototype circuit

676 IEE Proc.-Electr. Power Appl., Vol. 152, No. 3, May 2005