IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 6, NOVEMBER 2004 1653

Use of Saturable Inductor to Improve the DimmingCharacteristics of Frequency-Controlled

Dimmable Electronic BallastsStephen T. S. Lee, Student Member, IEEE, Henry Shu-Hung Chung, Senior Member, IEEE, and

S. Y. (Ron) Hui, Fellow, IEEE

Abstract—This paper presents an investigation into the use ofsaturable inductor to improve the dimming characteristics of fre-quency-controlled dimmable electronic ballasts with a half-bridgeseries-resonant parallel-loaded inverter. The concept is based onthe fact that the effective resonant frequency increases as the in-ductor current increases, if the unsaturable inductor in the reso-nant tank circuit is replaced with a saturable one. Susceptibilityof the lamp power to the switching frequency variation at low lu-minous level can be reduced. This can lessen the problem of lampflickers at dimmed level and result in a wider dimming range andimproved controllability. The method gives a simple solution of im-proving the dimming characteristics without changing the circuitstructure. A fundamental frequency model that includes the char-acteristics of the nonlinear lamp resistance and filament resistanceis applied in the analysis. A PSIM simulation model for the sat-urable inductor is developed. Theoretical predictions are verifiedwith the experimental results of a 36-W T8 prototype.

Index Terms—Dimmable electronic ballasts, fluorescent lamps,illumination, illumination control.

NOMENCLATURE

Input dc voltage of the half-bridge series-resonant parallel-loaded inverter (HBSRI) inFig. 1(a).Inductance of the series inductor of the resonanttank circuit in Fig. 1(a) at the inductor current .Parallel capacitor of the resonant tank circuit inFig. 1(a).

characteristic impedance of theresonant tank circuit.

angular natural frequency of theresonant tank circuit.Switching frequency of and in the HBSRI

Angular switching frequency of andin the HBSRI.

normalized switching frequency.Filament resistance of the lamp at rated current.Equivalent resistance including the ac resistanceof and the on-resistance of and .rms lamp voltage at the lamp power .

Manuscript received March 31, 2003; revised January 21, 2004. This workwas supported by a grant from the Research Grants Council, Hong Kong Spe-cial Administrative Region under Project CityU 1233/02E. Recommended byAssociate Editor J. M. Alonso.

The authors are with the Department of Electronic Engineering, City Univer-sity of Hong Kong, Kowloon, Hong Kong (e-mail: eeshc@cityu.edu.hk).

Digital Object Identifier 10.1109/TPEL.2004.836627

Lamp resistance at the lamp power .Average input current of the HBSRI.

normalized lamp power, where isthe maximum lamp power.Number of turns of the winding of the saturableinductor .Saturation flux density of the magnetic core of

.Effective area of the magnetic core of .

I. INTRODUCTION

H IGH-FREQUENCY electronic ballasts for fluorescentlamps are popular these days. Their major advantages are

the high ballast efficiency and lamp lumen efficacy, as comparedto the magnetic ballasts [1]. Important design considerations ofballasts include high power factor, low total harmonic distor-tion, low electromagnetic interference (EMI), low lamp currentcrest factor, and a low level of reduced flickering [2], [3]. Inorder to comply with some international standards, such as IEC61 000-3-2 Class C appliances [4], many existing electronicballasts consist of a front stage input power factor corrector(PFC) and a second stage of high-frequency ballast inverter[5]. The two stages are interlinked by a dc link of fixed voltage(e.g., 400 V). In practice, a voltage-fed or current-fed inverteris usually chosen for the second stage. Among various topolo-gies, the voltage-fed half-bridge series-resonant parallel-loadedinverter (HBSRI) shown in Fig. 1(a) is the most popular one[5]–[12].

The common dimming method is to adjust the switchingfrequency of the second stage [11], so that the reactances ofand are varied with the switching frequency of andand the lamp power is controlled. Many commercially availableintegrated circuits have been developed for this particularapplication. Although this technique is direct and simple, ithas been shown in [11] that the dimming characteristics (i.e.,lamp-power-to-switching-frequency characteristics) are non-linear in nature. The lamp power is susceptible to the switchingfrequency at low luminous level that lowers the controllabilityof the ballast. Thus, sophisticated control scheme is need tostabilize the operating point.

Recently, a phase-locking technique was introduced in [10]that can dim the luminous level down to 1%. Based on the factthat the lamp power can be derived from the phase shift betweenthe resonant inductor current and the switched voltage [i.e., The

0885-8993/04$20.00 © 2004 IEEE

1654 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 6, NOVEMBER 2004

Fig. 1. Half-bridge series resonant parallel loaded inverter (HBSRI).(a) Schematic diagram. (b) Waveforms of i and i . (c) Schematic diagramwith saturable inductor.

voltage across nodes “X” and “Y” in Fig. 1(a)], the switchingfrequency is controlled by a phase lock loop.

This paper addresses a simple solution of improving the dim-ming characteristics of ballast using frequency control withoutsignificant modification of both power and control circuits. Asaturable inductor is used to replace . The effective resonantfrequency increases as the inductor current increases. Suscepti-bility of the lamp power to the switching frequency variation atlow luminous level can be reduced. This can lessen the problemof lamp flickers at dimmed level, resulting in a wider dimmingrange and improved controllability. A fundamental frequencymodel that includes the characteristics of the nonlinear lamp re-sistance and filament resistance is applied in the analysis [6],

Fig. 2. Approximated fundamental-frequency model of the HBSRI.

[11]. Theoretical predictions are verified with the experimentalresults of a 36-W T8 prototype.

II. DIMMING CHARACTERISTICS OF BALLASTS

In Fig. 1(a), the capacitor is used to provide a stable dcvoltage of at node “Y.” The duty cycle of and isslightly less than 0.5. and are used to facilitate thezero-voltage-switching of and . A near-square ac voltagewaveform, as shown in Fig. 1(b), of amplitude appearsacross nodes “X” and “Y.” Since the resonant tank circuit is usu-ally designed to operate at a high quality factor, the fundamentalfrequency component of the square wave is the dominant onein the circuit [6], [11]. An equivalent circuit model is shownin Fig. 2(a), in which the fluorescent lamp is modeled by a re-sistance network consisting of the lamp resistor and fourfilament resistances of value [9]. For the sake of simplicityin the analysis, the lamp voltage is assumed to be equal to thevoltage across . This is valid because the lamp voltage ispractically much higher than the voltage drop of the filaments.Typical waveforms of the inductor current and inverter inputcurrent are shown in Fig. 1(b).

and are expressed by the following equations[11]:

(1)

(2)

where and are constants related to the physical dimensionsof the lamp. Experimental results show that the above mathe-matical model is valid for varying from 10% to 100% of thefull power.

can be expressed as

(3)

where you have the first equation shown at the bottom of thepage.

LEE et al.: USE OF SATURABLE INDUCTOR 1655

is determined by averaging in Fig. 1(b). Thus

(4)

As and are much larger than and , (4) can besimplified into

(5)

Based on Fig. 2, can also be expressed as

(6)

By substituting (6) into (5) and assuming that the conversionefficiency of the HBSRI is 100%, it can be shown that

(7)

(8)

As is regulated at a designed value, the lamp power is di-rectly proportional to . Thus, is the control parameter thatdetermines the magnitude of and the lamp power. By solving(7), the required value of that gives the lamp power is (9),shown at the bottom of the page. Fig. 3(a) shows the relation-ships of - with different , where . equals400 V and (2) is used for , where VW and

V for a T8 36-W lamp. In order to study the controlla-bility, control sensitivity is defined as

(10)

Fig. 3(b) shows the variations of against with different. It can be observed that varies widely over the dimming

range. Of particular importance, increases significantly atlow luminous level and the susceptibility to switching frequency

Fig. 3. Dimming characteristics. (a) F - ^P with different Z . (b) � - ^P withdifferent Z .

variation also increases. Although the controllability can be im-proved with a larger value of , the maximum attainable lamppower is reduced [Fig. 3(a)].

III. MODIFYING THE DIMMING CHARACTERISTICS

WITH SATURABLE INDUCTOR

A linear dimming characteristics is considered in the fol-lowing. is constant throughout the dimming range. Thus, adimming characteristics is defined as

(11)

where is the expected value of and is the angularswitching frequency at .

For a given value of , the expected can be obtained by(11). Thus, the required value of at a lamp power is ob-tained by solving the transcendental equation of (8). Fig. 4(a)shows the required – characteristics. should increaseand then decrease as the lamp power reduces. The calculationsare based on the component values in Table I.

With the determined values of , and , the rms valueof can be obtained by (3). Fig. 4(b) shows three possible

– characteristics with different , which is normalized bya formula of . and , are almost in one-to-one

(9)

1656 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 6, NOVEMBER 2004

Fig. 4. Characteristics of L for achieving the power relationship in (11).(a) L – ^P . (b) L –i with different values of �.

TABLE ICOMPONENT VALUES AND PARAMETERS USED IN THE PROTOTYPE

mapping with . This gives the design constraint for. The - characteristics can be realized by connecting an

unsaturated inductor in series with a saturable inductor ,as shown in Fig. 1(c). Since is small at large gives aminimum inductance for . Thus

(12)

If is a sloped air-gap inductor [13], its inductance is

(13)

Fig. 5. Theoretical L –i characteristics.

where is the value of for below the saturation current. and are the maximum and minimum gap sizes along

the sloped air gap, respectively.Fig. 5 shows the theoretical – characteristics.

A. Simulation Model for

The time-domain responses of the ballast with the saturableinductor are studied by using the software PSIM Ver. 4.1 [14].A simulation model for is derived as

(14)

where and are the voltage across and the currentthrough , respectively.

By integrating both sides of (14), it can be shown that

(15)

Since PSIM is based on stepwise simulation, (15) is approxi-mated as

(16)

where is the simulation time step and in (14) equals ..

After rearranging (16), it can be shown that

(17)

As and varies slightly in one simulation step,and are

assumed. Equation (17) can be rewritten into

(18)

LEE et al.: USE OF SATURABLE INDUCTOR 1657

Fig. 6. Simulation model for L on PSIM.

Thus, a voltage-controlled current source can be used to model. Its current magnitude depends on the current and the past

values of the inductor voltage and current. Based on (18),Fig. 6 shows the simulation model used. is across thenodes “ ” and “ ” in Fig. 6. The mappings between

and are tabulated in the lookup table file—“Ls.tbl.”

B. Design Guidelines for and

Design of and is based on the conditions at points “A”and “B” in Fig. 5. has not started saturation at point “A,”while it is fully saturated at point “B.” At point “A”

(19)

At point “B”

(20)

Although Fig. 5 shows the theoretical value of at a givenlamp power, the calculations assume that is unsaturatedand is purely sinusoidal. However, in the actual operation,

sweeps over the saturated and unsaturated regions ofthat cause nonsinusoidal. Thus, determination of the slopefactor [i.e., in (13)] should be based on the actualcircuit responses. By applying the Secant method [15] andthe model in Fig. 6, is iterated at the full-load lamp power

and the expected switching frequency. The iteration stepsare as follows.

Step 1) The value of at point “B” in Fig. 5 is takenfor .

Step 2) With two assumed values of ( and ), thecorresponding - characteristics are then de-rived [i.e., by using (13)]. The lamp powers (i.e.,

and ] in the two cases aresimulated with PSIM.

Step 3) A new value of is iterated by using the iterativeformula of

(21)

where and.

Again, and are obtained bythe simulation results of PSIM.

Fig. 7. Comparisons of the P –! characteristics with and without thesaturable inductor. (a) f –P . (b) Enlargement of f –P . (c) � –P .

Step 4) The above step is repeated until isless than a tolerance and will be acceptedas the required slope factor.

Step 5) As shown in [13], the number of turns of thewinding for is

(22)

and the gap sizes and are

(23)

where is the effective area of the core foris the saturation flux density in the core

of , and is the current that starts tosaturate.

1658 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 6, NOVEMBER 2004

Fig. 8. Experimental inductor current waveforms at different lamp power: (a) 100%, (b) 50%, and (c) 10%. (Current: 500 mA/div and Timebase: 10 �s/div.)

IV. EXPERIMENTAL VERIFICATIONS

A T8 36-W prototype was built and tested with two sets of. is regulated at 380 V. The value of the first set of is

2.234 mH, while the second set consists of a saturable inductorof 1.59 mH connecting in series with an unsaturable inductorof 644 H in Fig. 1(c). The component values and the pa-

rameters are tabulated in Table I. Fig. 7 shows a comparison ofthe dimming characteristics with the two sets of inductors. Thecomparison is started from the same power of 32 W to the lamp,which is about 90% of the rated power shown on the tube. Effi-cacy under high-frequency operation is increased by about 10%thereby enabling the lamp to be operated at a lower input powerthan at 50-Hz mains power frequency. increases drasticallyat about 30% of the full power with the first set of . The lampstarts to flicker and extinguishes easily. With the second set of

, the lamp can be dimmed down to 10% without flickering.is relatively constant over the dimming range [Fig. 7(c)].

Dimming is smooth and stable. The controllability is thus im-proved with the saturable inductor, particularly at the low lumi-nous level. Fig. 7(b) shows an enlargement of the dimming char-acteristics from 16 to 3.2 W. It can be seen that the sensitivity

of to from 14 to 5 W is high with the unsaturable inductor.Compared Fig. 7 with the expected dimming characteristics inFig. 3, the actual relationships between and are not linearthroughout the dimming range. The reason is that the induc-tance of is instantaneously varying with the inductor current.There are discrepancies between the assumed one in Section III.Nevertheless, the proposed design and analysis method gives asimple and feasible means to design the required value ofand for replacing .

As the inductance decreases with the increase in the inductorcurrent, the lamp current waveform will then be distorted.Figs. 8 and 9 show the experimental inductor current and thelamp current waveforms when the lamp power is at 100%, 50%,and 10% of the rated power. It can be seen from Fig. 8 thatstarts to saturate at about 0.29 A, introducing a high-frequencycomponent in the inductor current. Nevertheless, providesa low-impedance path for this high-frequency component. Thelamp current crest factor, which can significantly affect thelamp life, varies with the lamp power. Fig. 10 shows the lampcurrent crest factor (CF) at different lamp power. It was foundthat CF is less than 1.7 throughout the dimming range thatprovides rated lamp life performance [3].

LEE et al.: USE OF SATURABLE INDUCTOR 1659

Fig. 9. Experimental lamp current waveforms at different lamp power: (a) 100% (Current 500 mA/div), (b) 50% (Current: 200 mA/div), and (c) 10% (Current:50 mA/div). (Timebase: 10 �s/div).

Fig. 10. Lamp current crest factor (CF) at different lamp power.

V. CONCLUSION

A simple method of using saturable inductor to improvethe dimming characteristics of frequency-controlled dimmableelectronic ballasts with HBSRI is presented. Susceptibility ofthe lamp power to the switching frequency variation at lowluminous level is reduced. This can lessen the problem of lampflickers at dimmed level, resulting in wide dimming range andimproved controllability.

REFERENCES

[1] M. Bairanzade, “The electronic control of fluorescent tubes, state of theart,” in Power Electronics—30. Toulouse, France: Motorola Toulouse,pp. 30–49.

[2] W. R. Alling, “Important design parameters for solid state ballasts,”IEEE Trans. Ind. Applicat., vol. 25, pp. 203–207, Mar. 1989.

[3] A.C. Supplied electronic ballasts for tubular fluorescent lamps—perfor-mance requirements, Std. IEC 60 929, 1996.

[4] Electromagnetic compatibility-Part 3-2: Limits—limits for harmoniccurrent emissions (equipment input current <= 16 A per phase), Std.IEC 61 000-3-2, Oct. 2001.

[5] I. D. Santo and U. Moriconi, “Electronic ballast with PFC using L6574and L6561,” STMicroelectronics, AN993 Application Note, May 1998.

[6] M. Kazimierczuk and W. Szaraniek, “Electronic ballast for fluorescentlamps,” IEEE Trans. Power Electron., vol. 8, pp. 386–395, Oct. 1993.

[7] L. Nerone, “A mathematical model of the class D converter for compactfluorescent ballasts,” IEEE Trans. Power Electron., vol. 10, pp. 708–715,Nov. 1995.

[8] T. F. Wu, T. Yu, and M. Chiang, “Single-stage electronic ballast withdimming feature and unity power factor,” IEEE Trans. Power Electron.,vol. 13, pp. 586–597, May 1998.

[9] T. F. Wu and Y. Wu, “Improved start-up scenario for single-stage elec-tronic ballast,” IEEE Trans. Power Electron., vol. 15, pp. 471–478, May2000.

[10] S. Hui, Y. Ho, and H. Chung, “An electronic ballast with wide dimmingrange, high power factor, and low EMI,” IEEE Trans. Power Electron.,vol. 16, pp. 465–472, July 2001.

1660 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 6, NOVEMBER 2004

[11] Y. Ho, S. Lee, H. Chung, and S. Hui, “A comparative study on dimmingcontrol methods for electronic ballasts,” IEEE Trans. Power Electron.,vol. 16, pp. 828–836, Nov. 2001.

[12] P. Wood, “Fluorescent ballast design using passive PFC and crest factorcontrol,” International Rectifier, AN-998 Applicat. Note, 2003.

[13] W. Wolfle, W. Hurley, and S. Arnold, “Power factor correction for ac-dcconverters with cost effective inductive filtering,” in Proc. Power Elec-tronic Specialists Conf., Galway, Ireland, 2000, pp. 332–227.

[14] “User’s Manual of SIM 4.1,” Powersim Technologies, Inc., 2000.[15] A. Jeffrey, Mathematics for Engineers and Scientists, 2nd ed. Camden,

NJ: Nelson, 1981.

Stephen T. S. Lee (S’00) received the B.Eng. degree(with honors) in electronic engineering from the CityUniversity of Hong Kong in 1999, where he is cur-rently pursuing the Ph.D. degree.

His research interest is the design of dimmableelectronic ballast for various types of fluorescentlamps.

Henry Shu-Hung Chung (M’95–SM’03) receivedthe B.Eng. (with first class honors) and Ph.D. degreesin electrical engineering from The Hong Kong Poly-technic University, in 1991 and 1994, respectively.

Since 1995, he has been with the City Universityof Hong Kong, where he is currently an Asso-ciate Professor in the Department of ElectronicEngineering. His research interests include time-and frequency-domain analysis of power elec-tronic circuits, switched-capacitor-based converters,random-switching techniques, digital audio ampli-

fiers, soft-switching converters, and electronic ballast design. He has authoredfour research book chapters, and over 162 technical papers including 80refereed journal papers in the current research area, and holds four U.S. patents.

Dr. Chung received the Grand Applied Research Excellence Award fromthe City University of Hong Kong in 2001. He was Associate Editor andGuest Editor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—PART

I: FUNDAMENTAL THEORY AND APPLICATIONS. He is currently IEEE StudentBranch Counselor and was Track Chair of the Technical Committee on PowerElectronics Circuits and Power Systems, IEEE Circuits and Systems Society,from 1997 to 1998.

S. Y. (Ron) Hui (F’03) was born in Hong Kong in1961. He received the B.Sc. degree (with honors)from the University of Birmingham, Birmingham,U.K., in 1984, and the D.I.C. and Ph.D. degree fromthe Imperial College of Science and Technology,University of London, London, U.K., in 1987.

He was a Lecturer in power electronics at the Uni-versity of Nottingham, Nottingham, U.K., from 1987to 1990. In 1990, he took up a lectureship at the Uni-versity of Technology, Sydney, Australia, where hebecame a Senior Lecturer in 1991. He joined the Uni-

versity of Sydney in 1993 and was promoted to Reader of Electrical Engineeringin 1996. Presently, he is a Chair Professor of Electronic Engineering, City Uni-versity of Hong Kong. He has published over 150 technical papers, includingover 85 refereed journal publications.

Dr. Hui received the Teaching Excellence Award in 1999 and the GrandApplied Research Excellence Award in 2001 from the City University of HongKong. He has been appointed an Honorary Professor by the University ofSydney, Australia in 2000.