variation of the instantaneous luminous flux of fluorescent lamps fed by dimmable electronic...

Variation of the instantaneous luminous flux offluorescent lamps fed by dimmable electronic ballastswith frequency control

I.D. Kateri, C.A. Bouroussis and F.V. Topalis

Abstract: Effects of hysteresis and inertial processes on the instantaneous luminous flux of fluor-escent lamps (FLs) are experimentally investigated, which are fed by frequency controlled, dim-mable, electronic ballasts. Other phenomena are also examined, such as the time displacementbetween the light ripple and the waveform of the electrical power of the lamp, the ‘modulation’of the instantaneous luminous flux waveform and generally, the behaviour of the lamp atvarying high frequency (HF) levels. For a typical FL, fed by dimmable electronic ballast with fre-quency control, inertial processes are reduced, as the operating frequency of the lamp decreases.The time displacement between the instantaneous luminous flux and the lamp power hasmaximal and minimal as frequency varies. As frequency of the FL increases, the diffusion ofthe metastable states of the Hg atoms is enhanced and the ‘modulation’ of the instantaneous lumi-nous flux decreases. The hysteresis and the looping of lamp’s voltage–current and luminous flux–current characteristics at various frequency levels indicate that it is necessary to add an inductanceand a capacitance to the equivalent electrical circuit of a FL at HFs.

1 Introduction

The non-stable emission of light sources causes the effect oflight flicker on human visual perception. The main sourcesof light flicker are the flicker of supply voltage waveformand the fluctuations caused by non-integer harmonics[1–3]. Recent studies on lighting indicate that light flickermay induce discomfort in humans [4, 5].The current standards for voltage flicker are based on the

observation of the threshold of annoyance caused by 60 Wincandescent lamps [6, 7]. Similar data for fluorescentlamps (FLs) are rare. There is a major difference betweenthe response of incandescent and FLs to voltage fluctuations,because the physical mechanism of electrical energy conver-sion to light differs between these lamp types. So, there isdefinitive need for more research to understand properlythe luminous behaviour of FLs.The FLs fed by magnetic ballast from the 50 to 60 Hz line

produce a noticeable flicker. In contrast to 50–60 Hz fre-quency, the produced luminous intensity from a FL fed bya high frequency (HF) electronic ballast causes less butnot negligible flicker [8]. There is a recent research that isfocused on the relation between the instantaneous powerconsumption and the instantaneous light intensity of a FL,fed by magnetic ballast, at 50–60 Hz [9].Many FL models have been proposed in the literature to

describe the electrical characteristics of the lamp at HFoperation. Moo et al. [10, 11] propose a power-dependentresistance to represent the equivalent circuit. Cervi et al.

# The Institution of Engineering and Technology 2007

doi:10.1049/iet-epa:20070034

Paper first received 4th November 2006 and in revised form 29th March 2007

The authors are with the School of Electrical and Computer Engineering,Photometry Laboratory, National Technical University of Athens, 9 IroonPolitechniou Str., Zografou, Athens 157 80, Greece

E-mail: [email protected]

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[12] presents a mathematical model based on a regressivemethod employing an exponential function. This functionrepresents the FL resistance as function of electricalpower consumed by the lamp.Others propose a model [13–15] with a two-parameter

linear equation to describe the electrical characteristics ofa FL. This linear equation is derived from the observationthat the measured steady-state rms values of lamp voltageand lamp current at various power levels lay across a lineon the v– i plane approximately. Further models [16, 17]represent the lamp voltage as a cubic function of the lampcurrent when the FL operates at different power levelsand at constant HF. It is apparent that the behaviour ofthe lamp at HF needs in deep investigation.The objective of this research is the theoretical analysis

and experimental study of the instantaneous luminous fluxwaveform and lamp’s behaviour at HF excitation for awide frequency range 43.03–88.97 kHz. This will givethe possibility to develop a model that will include twomajor electrical features of the FL operated at HF: the vari-ation of lamp’s impedance on the respective dimming leveland its dynamic response to changes in electrical excitation.

2 Measurement of lamp characteristics

2.1 Experimental apparatus

The experimental apparatus was developed for the measure-ment of the instantaneous values of the emitted light and ofthe electrical characteristics (current, voltage and power) ofthe tested FL. The lamp is a T8 18 W fluorescent tube oper-ating at HF, in the range of 43.03–88.97 kHz. Table 1 liststhe lamp specifications from the manufacturer in which onlyparameters at the rated power are specified. The waveformsof the luminous intensity, lamp current and lamp voltageare recorded using the experimental set-up of Fig. 1a. The

IET Electr. Power Appl., 2007, 1, (6), pp. 890–896

instantaneous electrical power waveform is calculated fromthe respective current and voltage waveforms.The voltage, current and luminous intensity waveforms

are recorded simultaneously with a Tektronix TDS 20144-channel digital oscilloscope with 100 MHz bandwidthand 1 GS/s sampling rate. The current of the tested FL atHF excitation is measured by a Tektronix P6021 currentprobe with sensitivity 2 mA/mV and bandwidth 450 Hzto 60 MHz. The voltage of the lamp is measured with aTektronix P5200 differential probe, with 1/50 range andbandwidth up to 25 MHz.The waveform of the luminous flux of the tested FL is

recorded with a photodiode in a linear photometer circuitwith operational amplifier. The photodiode is placed at afixed distance from the lamp, in a closed photometerchamber to avoid stray light. The analogue output of thecircuit is connected to one channel of the oscilloscope.The output of the photometer circuit is transformed to

luminous flux units (lumens) using an International Lightresearch radiometer IL1715. The sensor head is placed inthe photometer chamber, close to the photodiode. Thus,

Table 1: Specifications of the fluorescent lamp

Rated lamp power 18 W

Rated filament power 1 W

Filament resistance 9.6 V

Starting voltage � 230 Vrms

IET Electr. Power Appl., Vol. 1, No. 6, November 2007

the output of the photometer circuit is scaled to thereading of the research radiometer and finally to the lumi-nous flux of the lamp.

2.2 Measurement of instantaneous luminousintensity waveform

The linear photometer circuit (Fig. 1b) consists of a TL082JFET-input operational amplifier and a discrete PIN photo-diode IPL 10020BW with 4 ns response time and 1.4 nAdark current. An optional CIE V(l) filter ensures that theresponse of the photodiode is similar to the human’s eyeresponse.The potential of the non-inverting input of the operational

amplifier is equal to the potential of the inverting input thatis grounded because the differential input voltage of theoperational amplifier is nearly zero (Ed ’ 0 V). Thus, thephotodiode is reverse biased because the anode is alwaysat negative potential, that is lower than the potential ofthe cathode (VA ¼ 2VCC, VC ’ 0 V).The complex impedance of the non-inverting input of the

operational amplifier is very high (theoretically infinite).Therefore there is not current flow through the terminal ofthe non-inverting input and the photocurrent of the photo-diode flows through the feedback resistor RF.The output voltage of the circuit is equal to the voltage of

the feedback resistor (Vo ¼ VRF¼ ID � RF) due to the

common terminal of the feedback resistor and the outputresistor, whereas the non-common terminals are at thesame (zero) potential. Therefore the output voltage of the

Fig. 1 Calculation of instantaneous electrical power waveform

a Schematic experimental set-upb Photometer circuitc Power feeder circuitd Resonant curve of the resonant tank circuit of the ballast

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circuit is proportional to the photocurrent of the reversedbiased photodiode that is proportional to the quantity ofthe incident light.The fast response of the selected photodiode and the con-

stant transfer function of the photometer circuit enablereliable measurement of the instantaneous luminous fluxwaveform. The time constant of the circuit is muchsmaller than the period of the excitation of the lamp.Thus, the amplification of the light signal is independentof the frequency of the incident light.The reliability and the frequency response of the photo-

meter circuit are checked using a specially designed powerfeeder circuit (Fig. 1c). This circuit produces light pulses ofknown amplitude and frequency. These pulses are the inputof the linear photometer circuit. In this way, the responseof the photometer circuit is checked against a known input.The circuit is fed by a programmable arbitrary waveformgenerator (TTi-TGA 1240). The photodiode and the LED,that is actually the output of the above circuit, are placed ina black collimating tube for the coupling between the two cir-cuits. The input signal of the power feeder circuit is a squarewave with constant amplitude and a frequency in the range of50 Hz to 300 kHz. In all cases, the experimental results showthat the output signal of the photometer circuit has constantamplitude and represents accurately the form and the fre-quency of the input signal of the power feeder circuit.

3 Hysteresis at HFs

Experimental tests were carried out in order to study theinstantaneous luminous flux waveform of a FL T8 18 Wat various HF levels. The supply voltage of the lampsystem is 230 V AC, 50 Hz. The lamp itself is fed by a dim-mable electronic ballast with frequency control that consiststhe ballast and a controller fed by 1–10 V DC controlvoltage. The load circuit of the ballast consists of a seriesresonant tank, a capacitor and the FL. The resonant tankis formed by an inductor and a capacitor in series with theFL. The change in the control voltage results frequencychange of the half bridge series resonant inverter of theused electronic ballast. This causes change in the impedance(Z ) of the series resonant tank. Thus, the electrical power ofthe lamp can be regulated varying the switching frequencyof the inverter [18, 19]. The resonant frequency ( fr) of theresonant tank is 36.63 kHz and the corresponding impe-dance has the minimum value of 52 V, as is shown in theresonant curve (Fig. 1d). The used ballast can only be oper-ated above the resonant frequency and is designed to drivethe FL to the full power at an inverter frequency of43.03 kHz. At the frequency of 43.03 kHz the load circuitis inductive. Thus, the increase in the frequency causesless electrical power consumed by the lamp. When the oper-ating frequency of the lamp is low, the lamp power is highand the resistance of the lamp discharge column is low asresult of the highly ionised lamp’s gas and vice versa.The selected range of the control voltage for the exper-

imental measurements extends from 6.59 to 10 V DC andthe operating frequencies of the tested FL extend from43.03 to 88.97 kHz.Fig. 2 shows the simultaneously recorded waveforms w(t)

of luminous flux, i(t) of the lamp current and v(t) of the lampvoltage at three HF levels: 43.03 kHz, 68.31 kHz and88.97 kHz, that is at the minimum, medium and maximumoperating frequency of the lamp, respectively. Fig. 3 showsw(t) against the waveform p(t) of power of the lamp at thesame frequency levels. The p(t) is obtained by multiplicationof v(t) and i(t), in real time, taking the voltage and the current

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directly on the lamp. It is obvious that the waveform w(t)follows the variation of the waveform p(t).It is observed from Fig. 3 that the luminous flux w(t) does

not take zero value at the instants where the waveform p(t)of the power passes from zero. On the other hand, Fig. 3shows a slight delay (time displacement) of the luminousflux waveform, regarding the waveform p(t) of the power.This hysteresis of the luminous flux may be attributed to akind of inertia in the generation of light due to the delayin the ionisation of the mercury atoms (on the order of milli-seconds) and the delay in the excitation of the fluorescentpowder by the ultraviolet radiation (on the order of nanose-conds). It seems that during the ionisation processes, theelectrons diffuse to the walls faster than the positive ionsdue to their lighter mass and their higher random thermalvelocities. This leaves an excess of positive ions in theplasma. The resulting positive charge tends to attract the

Fig. 2 Lamp current i(t) (grey line) 0.2 A/div, lamp voltage v(t)(wavy line) 50 V/div and luminous flux w(t) (normal line)281.6 lm/div of a T8 18 W FL with electronic ballast at threeHF levels

Time base: 2 ms/diva 43.03 kHzb 68.31 kHzc 88.97 kHz


electrons and slows down their diffusion rate. The samepositive charge produces a radial electric field of significanteffect. The field exerts forces in such a way as to augmentthe drift velocity of the ions and retard that of the electrons,and the charge separation reaches a state of balance inwhich ions and electrons diffuse with the same velocity.This process is well known as ‘ambipolar diffusion’ in thelamp’s gas. Additionally, the positive column frequentlyshows along its length distinct and regular bands of lumin-osity, moving or stationary, called ‘striations’ or ‘striae’.These are related to fluctuations in the electron and ion con-centration. The ‘striation’ phenomenon is generallyoccurred when FL is dimmed under frequency control,because any disturbance in the plasma can set up periodicityof space charge and electric field along the column, dueessentially to the different diffusion rates of electrons andions. The ‘ambipolar diffusion’ and ‘striations’ in thelamp’s gas cause phenomena of hysteresis [20]. Such

Fig. 3 Luminous flux w(t) (normal line, 281.6 lm/div) againstlamp power p(t) (grey line, 10 W/div) with electronic ballast atthree HF levels

Time base: 2 ms/diva 43.03 kHzb 68.31 kHzc 88.97 kHz


inertial processes have been well investigated in [21] andmore thoroughly in [22] where the lamp is described asan HF-inertial current-controllable element.In Table 2 is shown the time displacement Dt between

w(t) and p(t) at various operating frequencies of the lamp,as calculated by the experimental data. The minimumvalue 0.45 ms of Dt appears at 68.31 kHz whereas themaximum value 1.35 ms at 83.61 kHz. This could be associ-ated with a possible inductance and capacitance in thelamp’s equivalent circuit, as a result of a specific physicalprocess within the lamp.It can be observed from Fig. 3 that the ripple of the

instantaneous luminous flux changes as the frequencyvaries. The ‘modulation’ of the w(t), that is the peak-to-peakvalue of the ‘relative ripple’ of this waveform, at each fre-quency, quantitatively is described by the parameter M [9]

M ¼wmax � wmin

F(1)

where F is the average luminous flux produced by the lampoperating at this frequency. In Table 2 are shown the calcu-lated M values from the experimental data at various fre-quencies. As the operating frequency of the FL increases,the depth of ‘modulation’ of the w(t) waveform decreases.This happens because the inertial processes are strong andthe lamp gas cannot follow the changes of the HF excitation.The minimum value of ‘modulation’ is 0.11 at themaximum operating frequency (88.97 kHz) because the dif-fusion of the metastable states of the Hg atoms is noticeableand leads to smoothing of the w(t) waveform. Themaximum value of the ‘modulation’ is 0.64 at the ratedpower where the frequency is 43.03 kHz.The change of ‘modulation’ of w(t) waveform at various

HF levels shows a similarity with the output waveform of acapacitor filter connected to a full-wave rectifier. In moredetails, when the frequency fi of the AC input voltage ofthe full-wave rectifier is high enough ( fi � 1/T, where Tis the discharge time constant of the filter capacitor), the‘ripple’ of filter output (DV ) is very low, according to theequation [23]

DV ¼Iload

4� fi � C(2)

The AC input voltage frequency of the full-wave rectifiercorresponds to the excitation frequency of the FL. Also, the‘ripple’ of the filter output corresponds to the ‘modulation’of the w(t) waveform. The discharge time constant of thefilter capacitor corresponds to a time constant of the FL

Table 2: Time displacement and modulation of theluminous flux at tested frequencies

Frequency, kHz Time

displacement, ms

Modulation

f1 43.03 1.03 0.64

f2 46.90 0.99 0.58

f3 54.70 0.77 0.46

f4 63.78 0.65 0.39

f5 68.31 0.45 0.29

f6 78.13 0.76 0.26

f7 83.61 1.35 0.20

f8 86.81 0.45 0.18

f9 88.97 0.40 0.11

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that depends on the equivalent lamp’s capacitance andcould be linked to a specific process in the lamp.The latter aspect has many theoretical and practical impli-

cations since the equivalent circuit of the lamp is of primeimportance when considering stability and response oflamp/ballast systems in open–closed loop configurations.

4 Reactive behaviour of the FL at highfrequencies

4.1 Saturation of luminous flux

The measurements of the luminous flux, lamp current, lampvoltage and lamp power indicate some reactive features ofthe lamp at HF operation. Fig. 4a and b shows thedynamic lamp’s v– i and w– i characteristics at various HFlevels, as derived from the experiments.Under dimming conditions, the lamp current decreases

whereas the lamp voltage increases, as the operation fre-quency of the FL increases (Fig. 4a). The negative resistivecharacteristic of FL is well known and can be explained bythe ionisation processes inside the fluorescent tube. Insidethe tube, the arc is a low-pressure mercury-rare-gas dis-charge where the ionisation processes are dominated by col-lision ionisation, especially a ‘two-stage ionisation’. Duringthese collisions, either an electron with more than 10.4 eVof energy can collide with a mercury atom in the groundstate, ionising it; or an electron with kinetic energygreater than the difference between ionisation potential

Fig. 4 v–i and w–i characteristics of dynamic lamp of variousHF levels

a Dynamic v– i characteristics of a T8 18 W FL with dimmable elec-tronic ballast with frequency control (lamp current 0.1 A/div, lampvoltage 25 V/div)b Dynamic w– i characteristics of a T8 18 W FL with dimmable elec-tronic ballast with frequency control (lamp current 0.1 A/div, lumi-nous flux 140.8 lm/div). f1, . . . , f9: Operating frequency at thespecific dimming level (see Table 2 for the frequency values)

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and excitation potential can ionise an atom in a givenexcited state. Since the density of excited atoms in the dis-charge increases with increasing electron density andcurrent, the rate of ionisation per average electron at agiven temperature also must increase with current. On theother hand, in a diffusion-controlled discharge, the lossrate per electron is a constant, independent of electrondensity and hence of current. Consequently, a system inwhich the loss rate per electron is unchanged with currentbut the ionisation rate per electron increases with currentcannot be in a steady state. As a result, the electron tempera-ture required to maintain the ionisation rate per electronequal to the loss rate per electron decreases with increasingcurrent. Therefore the electric field (and hence lampvoltage) required to maintain the discharge at a steadystate decreases as the lamp current increases [20, 24].The dependence of the luminous flux upon the lamp

current, at various HF levels, can be determined byfitting a curve to the peaks of the family of w– i character-istics of Fig. 4b. The result of this curve fitting is shown inFig. 5.Under frequency control, the luminous output decreases

with decreasing the lamp current, as is shown in curveA–B of Fig. 5. Since the frequency of collision of electronswith gas atoms (ve) increases with increasing the frequency,the electron mobility will be decreased, according to the fol-lowing equation [20]

me ¼e

m� ne(3)

where e is the charge on the electron and m the electronmass.The axial electric field is determined by the requirement

that electrical energy input per unit volume to the electrongas equals energy loss per unit volume by electron gas[20]. Thus

je � E ¼ ne �We(Te) (4)

where je is the electron current density, E the rms value ofthe axial electric field, ne the number of electrons per unitvolume and We(Te) the average total energy loss per elec-tron at electron temperature Te. The electron currentdensity is given by [20]

je ¼ e� ne � me � E (5)

By (4) and (5), E is calculated as [20]

E ¼We(Te)

e� me

� �1=2

(6)

According to (6), the electric field (and hence the electrontemperature and lamp voltage) must be increased to

Fig. 5 Luminous flux against lamp current of a T8 18 W underfrequency control


maintain the balance between the ionisation rate and lossrate. The total excitation rate of an atom that has onlythree states (ground state, states E1 and E2) can be expressedapproximately as [20]

R ’ C1 � e(�e�E1)=(K�Te) þ C2 � e(�e�E2)=(K�Te) (7)

where C1 and C2 are constants and K is the Boltzmannconstant.If the desired 254 nm ultraviolet radiation is assumed to

come from the lower of the two excited states, the fractionof the total energy input that contributes to excitation to thedesired state (ultimately emitted as radiation) is [20]

F ¼R1

R¼

C1 � e(�e�E1)=(K�Te)

C1 � e(�e�E1)=(K�Te) þ C2 � e(�e�E2)=(K�Te)

¼1

1þ (C2=C1)� e(�e�(E2�E1)=(K�Te)

(8)

Consequently, according to (8), luminous outputdecreases with increasing electron temperature (and hencevoltage) and decreasing lamp.It can also be observed that the luminous output increases

to a saturation level beyond which it does not increasefurther (curve B–C of Fig. 5). The saturation appears atthe higher values of the lamp current and eventually tothe lower operation frequencies, as analysed in the previoussection. The threshold of the curve of Fig. 5 was found to beat 46.9 kHz, which is approximately equal to the rated fre-quency of the tested lamp.The saturation level of the luminous flux is a result of the

‘local thermal equilibrium’ in the discharge tube. In the FL,there is no real thermodynamic equilibrium because radi-ation exits from the system. However, ‘local thermal equili-brium’ exists when the rate of exciting and quenchingcollisions becomes very much larger than the rate of radiat-ing transitions [20]. The luminous flux of the lamp is pro-portional to n�/t 0, where t 0 is the average ‘imprisonment’time for the 254 nm ultraviolet photons, whereas n� is thedensity of the excited mercury atoms. As the operation fre-quency of the FL decreases sufficiently, the electron densityin the plasma gets sufficiently high, and n�/t 0 approaches aconstant value, which corresponds to the luminous flux sat-uration level.

4.2 Capacitive and inductive features of FL

Fig. 6a–c is dynamic v– i, w– i, p– i characteristics of thelamp waveforms at the rated frequency. These plotspresent hysteresis due to inherent properties of the lampas described in the previous section. Arrows are placed onthe curves of these figures to show the directions in whichthe characteristics v– i, w– i and p– i are traced. Thelooping is the same at the dynamic lamp’s v– i, w– i, p– icharacteristics of all the tested frequencies.The counter-clockwise passing direction of the loop of the

v– i characteristic, as is shown in Fig. 6a, would mean that thelamp has some capacitive features. Indeed, the maximum ofthe voltage function v(t) is obtained after the maximum ofthe current function i(t). It should bementioned that the rever-sal of the v– i hysteresis curve has been experimentallyobserved in a recent research [25] where the hysteresiseffect in the discharge process at HF was also predicted forcertain discharge lamps using a computer model.The hysteresis right half plane loop of the w– i character-

istic follows a counter-clockwise direction, as is plotted inFig. 6b, that is the luminous flux waveform is reduced onthe leading side. On the other hand, the hysteresis left half


plane loop of the same characteristic follows a clockwisepath, that is the luminous flux waveform is reduced on thetrailing side.In the process of the electrical to light energy conversion,

the luminous flux is strongly dependent on the lamp power.Thus, the looping of the w– i characteristic meets thelooping of the p– i, as is shown in Fig. 6b and c,respectively.The clockwise passing direction of the left half plane

loop of the w– i characteristic indicates some inductivefeatures of the lamp. On the other hand, the counter-clockwise direction of the right half plane loop of thesame characteristic indicates some capacitive features ofthe lamp at HF operation. The above considerationimplies a situation that it is different from conventionalinductive or capacitive looping of the magnetic or the fer-roelectric material, in which energy is stored and released

Fig. 6 v–i, w–i, p–i characteristics of the lamp waveforms atthe rated frequency

a v– i characteristic at 43.03 kHz (lamp current 0.1 A/div, lampvoltage 25 V/div)b w– i characteristic at 43.03 kHz (lamp current 0.1 A/div, luminousflux 140.8 lm/div)c p– i characteristic at 43.03 kHz (lamp current 0.1 A/div, lamppower 5 W/div)

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during alternating portions of the cycle. However, bothinductive and capacitive looping shows that during someportions of the cycle, the luminous flux and the lampvoltage have different polarities in reference with thelamp current.So, in the case of a FL, which is basically a resistive

element, the hysteresis loops of the v– i and w– i character-istics at varying HF levels indicate some reactive features ofthe element.The role of the FL as a circuit element as well as many

intricate phenomena inside the discharge tube is significantfor the analysis and design of electronic ballasts [26, 27].Behaviour of FL at varying HF levels, where the lamp pre-sents some inductive and capacitive features, show that it isneeded to be an inductance and a capacitance to the equiv-alent electrical circuit.

5 Conclusions

The common practice for the evaluation of lighting systemsis generally based on the reliability, the cost, the energy effi-ciency and the quality. However, the evaluation of the light-ing quality is limited to few criteria, such as the illuminancelevel, the brightness and the uniformity. Factors that influ-ence the nervous system and the human behaviour arerarely investigated due to their complexity and the highcost. The variation of the instantaneous luminous flux of flu-orescent tubes that causes light flicker is important not onlyfor these reasons but also for the investigation of thephenomena which take place in the fluorescent tube. Theexisting knowledge on the magnetic ballasts is proved tobe limited for the explanation of the behaviour of thelamp at HF and, more important, for the determination ofthe light producing mechanism quantitatively andqualitatively.This paper investigated the inertial processes and the

phenomena of hysteresis in the lamp tube and how they influ-ence the luminous flux that is produced by the lamp. Thebehaviour of the lamp at HFwas also investigated. The exper-iments showed that the waveform of the instantaneous lumi-nous flux has no zeros at the instants of zeroing of theinstantaneous lamp power due to inertial processes in the tube.The time displacement between the waveforms of the

luminous flux and the electrical power at various HFlevels of excitation exhibits maximal and minimal points.It was also observed that the frequency of the dimmableelectronic ballast, which feeds the FL, affects the depth of‘modulation’ of the instantaneous luminous flux waveform.The depth of ‘modulation’ decreases with the increase of thefrequency due to the stronger inertia of the processes in thefluorescent tube. On the other hand, as the HF excitationdecreases, the relative ripple of the instantaneous luminousflux increases and exhibits the maximum peak-to-peakvalue at the rated HF of the lamp.The hysteresis loops of the v– i and w– i characteristics at

varying HF levels indicate some inductive and capacitivefeatures of the FL. Consequently, more research is neededin this area because the lamp characteristics could greatlyaffect the design of the ballast and the choice of thecircuit components, in cases where the power is notstable.

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variation of the instantaneous luminous flux of fluorescent lamps fed by dimmable electronic...

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