IEEETRANSACTIONS
ON INDUSTRYAPPLICATIONS.VOL 34. NO. 3. MAY/JUNE1998
597
White-Noise Modulation of High-Frequency
High-Intensity Discharge Lamp Ballasts
Laszlo Laskai, Senior Member, IEEE, Prasad N. Enjeti, Senior Member, IEEE, and Ira J. Pitel, Senior Member, IEEE
Abstract-In
this paper, a new method is proposed to avoid
acoustic-resonance-related
instabilities
in metal halide lamps
when operated with a high-frequency
electronic ballast. Angle
modulation of the inverter switching pattern has been used as a
vehicle to randomize lamp driving frequency and to limit lamp
power spectrum below the instability
threshold. The optimal
modulating pattern is obtained by studying the angle-modulated
spectra by periodic and random signals. Analysis is supported
by simulations and verified experimentally
with the ballasting
of 250-W lamps.
zones, resonant frequencies must be known and repeatable
between different lamps and manufacturers. Considering all
factors involved, it is not practical to operate HID lamps
without some form of ameliorative measure.
Lamp power spectrum spreading is one way to prevent
acoustic resonances, since generation of acoustic waves occurs
only if the sound-wave source is sufficiently high in the sensitive frequency region. A nonsinusoidal lamp voltage [9]-[ 111,
for instance, a square-wave voltage or an angle-modulated
Index Terms-Acoustic
resonance, ballast, high-intensity
dis- lamp voltage [lo], [12]-[15],
has such a distributed power
charge lamp, metal halide lamp, white-noise modulation.
spectrum. Square-wave operation distributes lamp spectra in a
theoretically infinite number of harmonics. Still, disadvantages
to this approach are limited power specwal term reduction
I. INTK~DUCTI~N
in lower order harmonics and aggravated electromagnetic
0 FLICKER, improved lumen maintenance, control over
interference problems.
lamp power and light color, longer lifetime, and smaller
Angle modulation, an alternative, is well contained [IS],
and lighter ballasts are some of the advantages for driving
[
191.
Wide-band frequency modulation [ 13]-[ 151 and phasemetal halide and other high-intensity discharge (HID) lamps
shift
keying
[ 121, with predetermined modulating patterns,
from a high-frequency source [l], [2], [13]. Nevertheless,
have been utilized to prevent lamp instabilities of a given
due to the occurrence of acoustic resonances, high-frequency
type. However, these modulations are not adequate to prevent
ballasting of HID lamps has been a major challenge.
instabilities for all lamps of a given power rating made by
The acoustic-resonance-related instabilities are rather well
various manufacturers.
described theoretically [2]-[8]. The periodic input power and
In response to these concerns, this paper proposes a new
the subsequent energy exchange by elastic collisions bemethod
of stabilizing high-frequency operation of metal halide
tween charged particles and neutral gas are the source of
lamps.
The
proposed method limits lamp power spectrum
pressure perturbations. As the input frequency is increased.
below an instability threshold by randomizing the inverter
and an eigenfrequency is approached, a pressure-wave mode
frequency. Randomization of the switching pattern, by way
becomes propagational, which, in turn, perturbs the discharge
of
angle modulation or by randomization of the pulse position
path. Lamp properties that determine the eigenfrequencies
or the pulsewidth, has been used to reduce acoustic noise in
are known to vary with manufacturing tolerances (different
motors and EM1 in switching power supplies [21]-[24].
geometry or filling) and by lamp age.
Angle-modulation process with random noise produces a
Apart from lamp-related factors, which can be optimized
power
density spectrum that is proportional to the first-order
to reduce resonances [2], [ 141, innovative ballasting methods
probability density of the modulating noise. When lamp voltare needed to make high-frequency operation possible with
age (or current) frequency is modulated by random noise, lamp
existing lamps. Tuned high-frequency operation requires the
power
spectral density is continuous with low amplitude and
knowledge of resonance-free zones and, to operate in these
narrow bandwidth. This allows the use of high (2 resonant
Paper MSDAD 97-I, presented at the 1994 Industry Applications Society
Annual Meeting, Denver CO, October 2-7, and approved for publication in inverters, preferred in electronic ballasting.
The proposed method retains all the advantages of conventhe IEEE TRANSACTIONS
ONINDUSTRYAPPLICATIONS
by the Production and
Application of Light Committee of the IEEE Industry Applications Society. tional pulsewidth modulation (PWM), that is, real-time control,
Manuscript releasedfor publication May 19, 1997.
linear operation, good transient response, and it contributes to
L. Laskai was with the Department of Electrical Engineering, Texas A&M
University, College Station, TX 77843-3148 USA. He is now with Corporate reduced EM1 in the ballast.
Research and Development, General Electric Company, Schenectady,NY
In Section II of this paper, spectral behavior of angle12301 USA (e-mail: laskai@crd.ge.com).
modulated
waves with periodical modulation is investigated.
P. N. Enjeti is with the Department of Electrical Engineering, Texas
A&M University, College Station. TX 77843-3148 USA (e-mail: en- In Section Ill, the proposed random modulations are discussed
Jeti@ee.tamu.edu).
and compared to periodical modulations. Experimental results
I. J Pitel is wth Magna-Power Electronics, Inc., Boonton. NJ 07005 USA
of
the prototype ballast [ 151 and practical implemenration
(e-mail: i.pitel@ieee.org).
Pubhsher Item Identifier S 0093-9994(98)03878-X.
issues in Section IV conclude the paper.
N
0093-9994/98$10.00 0 1998 IEEE
IEEE TRANSACTIONSON INDUSTRYAPPLICATIONS,VOL. 34. NO. 3. MAY/JUNE1998
YHI
1caPa
Frequency
lXl*
rn".4
(a)
(b)
Frquency
Cc)
Fig. 1. Nornuked amplitude spectra of (a) an unmodulated wave (/I = 0) and two angle-modulated waves (b) I, > 10 and (c) 1, = 50
II.
ANGLE MODULATION
WITH PERIODIC SIGNALS
We shall first consider the spectral characteristics of anglemodulated waves by periodic signals. Several periodic modulating patterns shall be examined, with the objective of
finding the optimal periodic modulating pattern. The desired
pattern is determined by the spectra1 behavior of the modulated
wave, that is, spectral density distribution, maximum spectral
components, and required bandwidth.
The spectra1 behavior of the modulated wave by standard
modulating patterns, such as sine wave, square wave, triangular, and saw tooth, have been investigated in prior research
[12]-[15].
The commonly used description of a sinusoidal anglemodulated wave is
v(t) = A0 cos Q(t)
where Q(t) = w,t - @(t)
(1)
where the instantaneous phase Q(t) or Q(t) contains the
modulating signal A0 is a constant, t represents time, and
LJ, is the angular frequency of the carrier, in this case, lamp
voltage (or lamp current) [16]-[19].
Phase and frequency modulations are two closely related
angle-modulation methods. In the case of phase modulation,
the modulating signal is directly proportional to the instantaneous phase Q(t) or Q(t), and for frequency modulation, the
modulating signal is directly proportional to the first derivative
of Q(t) or CD(t).
To study spectra1 behavior of the modulated wave v(t) in
steady state, we shall define its amplitude spectra1 density
V(f) and its average power spectral density S,(f), assuming
that, in mathematical terms, v(t) is a real function, defined over
(-x’ < t < x)), and its integrable as (v(t)/ in (--30, xj) [16],
[ 171. Hence, the amplitude spectral density V(f) is defined as
a Fourier transform of the modulated wave v(t):
32
v(t)e-+tdt
(2)
V(f) =
s -z-a
where w(= 2~,f) is the modulated wave angular frequency.
Further, in the interval (O,T), the average power spectral
density S,(f), across unit resistance load, is
where IV(f)1
denotes the modulus of the amplitude spectrum
vu 1.
A. Angle Modulation
by Sine Wave
The power spectrum density S,,(f) of an angle-modulated
wave modulated by a sinusoidal modulating signal v,,,(t) =
Z30cos w,t, for sufficiently small frequency deviations and
slow sweeps about the carrier frequency, is
where
&nl = 1
for m = 1
E77L- 2
for m # I
CL= PsAl
or
CL= CLF~I.
LASKAI rr ul.: WHITE-NOISEMODULATIONOF HIGH-FREQUENCY
HID LAMP BALLASTS
599
/
/
1
(a)
(b)
Cc)
Fig. 1. Limiting spectra for (a) sine wave, (b) square wave, and (c) sym
metrical sweepor saw tooth.
modulation
index, p
Fig. 2. Normalized maximum term versusmodulatingindex
For phase and frequency modulations
modulation index p is defined as
LL~A~ and PFhI, the
where D+ and DF represent constants. Typical spectra for
several modulation indices are shown in Fig. I. Observe the
relationship between amplitude of the power spectrum to the
modulation index.
The average power of the modulated wave
is independent with angle modulation; however, carrier and
sidebands, spaced at fc i mf,, can vary. According to (4),
the magnitude of the spectral terms is determined by &(p),
denoting Bessel functions of the first kind. Fig. 2 illustrates
the impact of the modulation index increase on the maximum
spectral term 1S, (f ) 1,l,aX.
The maximum spectral term, which can excite an acoustic
resonance, can be minimized by making p > 10. For the
theoretical limit case [17], or CL+ co, the power spectra is
(8)
decrease in bandwidth. This is an obvious conclusion from
(9) for phase modulations. In a similar manner, the same
principle applies to a frequency-modulated spectrum, since
the modulating index, (6), is inversely proportional to the
modulating frequency.
Fig. 4 shows the experimental current waveforms for periodic modulations. Sine-wave modulated lamp current and
its amplitude spectrum are shown in Fig. 4(a) and (b). It has
been experimentally determined that a tenfold reduction in the
maximum current spectral term is necessary to stabilize all
trial lamps. To obtain this reduction, the required bandwidth
for sine-wave modulating signal was BWFI\,~ = 35 kHz
@FhI z 170 and fa = 100 Hz).
The choice of center frequency had no bearing on the
results; it was varied in the range of 2040 kHz, a range
limited by our setup. For the depicted spectrum, the center
frequency was tuned to keep the power spectrum just above
the audio range. Note that the pressure driving frequency is
twice the supply frequency, since the average rate of energy
absorbed by electrons is proportional to the square of the input
voltage [4]. For sine-wave modulations, this means that, by
distributing energy in the 1742-kHz frequency range, we are
preventing pressure perturbances in the 34-84-kHz range.
One disadvantage of such a wide bandwidth, noticeable
in Fig. 4(b), is undesirable amplitude modulation. Resonant
networks, which are frequently used in high-frequency ballast
for impedance matching, attenuate spectral components unevenly. This can cause high-current crest factors in the lamp
and shorten lamp life.
B. Angle Modulation
as illustrated in Fig. 3(a). In summary, wideband sine-wave
modulations lead to uneven spectral distributions.
According to (4), angle-modulated spectra require an infinite
bandwidth. In practice, according to Carson’s estimate, 98%
of the total power is contained in a bandwidth determined by
the maximum frequency deviation and maximum frequency
of the modulating signal [ 161. For wide-band modulations, the
required bandwidth is
by a Square Wuve
As previously discussed, we wish to estimate the spectral
behavior for high-modulation indices. Due to similarities in
phase- and frequency-modulated spectra, as highlighted in
the previous section, we shall consider only the frequencymodulated spectrum. Fig. 5 shows a typical amplitude spectrum obtained by simulations for CLFhI = 20. As ,+fil i w,
the FM wave spectral density becomes
So(f)FlvI
= ${6[f
+ s[f
for phase and frequency modulations, respectively.
If the maximum frequency deviation is held constant, a
decrease in modulating frequency fa carries a proportional
- (fc - bFhIfa)]
- (fc + ~Fhlfa)j)
(11)
where To( = 27r/wa) is the square-wave signal period. The limiting form spectrum is illustrated in Fig. 3(b). Theoretically, all
energy is in two delta pulses at the boundaries of the required
IEEETRANSACTIONSON INDUSTRYAPPLICATIONS,VOL. 34. NO. 3. MAY/JUNE1998
nun: 2S.Okws
~.,.I...,S,‘.‘I....I.“‘!
m
20.0mVlu
w
/h(f) :
I--..A.r-_
(b)
(a)
Run: 25.okw8
hk
2.oomV S.OOkHr
sample
TrnkRun: sook.s/s
t _. +
~-__---..
=“. !. . ,. --.
.,
.,
.! V’
Sampk
-._ .(
!, --j
I
1 . . ..I.....
. ...1.....
u
20.0mVC
. . . . I.,,.
mc
m
2.00mV 5.OOkHz
Cd)
(cl
Tok
Run: 21.01(5/s
.___..__r -.--
Sample
,++
____
*
“?‘.‘.!.“‘!.““““(
1.L.. i . . . . L. . . . 8. . . . I . . . . i..&&g&y.J
. Ins
m i?o.omv%
(e)
-----j
Tlk Run: SOOkS/r
m
sampk
2.OOmV5.00kHz
(0
Fig. 4 Experimental lamp current waveforms: (a) and (b) for sine-wave modulating signal; (c) and (d) for square-wave modulating signal; and (e) and
(f) for symmetrical sweep. (For all time-domain waveforms horizontal scale: 2 ms/div and vertical scale: I A/div; for all frequency-domain waveforms
horizontal scale: 5 kHz/div and vertical scale: 0.1 Aldiv.)
LASKAI ~‘1u/ WHITE-NOISEMODULATIONOF HIGH-FREQUENCY
HID LAMP BALLASTS
601
V(f)
IV(f)
04
Fig. 7. Spectrum of band-limited white noise and correlated FM wave
spectrum.
5K
6K
IOK
12K
14K 15K
Frequency
III. PROPOSEDBAND-LIMITED WHITE-NOISE MODULATIONS
Fig. 5. Typical square-wave-modulatedamplitude spectrum (/tt.~~ = 20)
5&
6K
8K
1OK
12K
14K
15K
Frequency
Angle-modulated spectrum, produced through intermodulation by carrier and periodic modulating signal, as described
in (4) for sine-wave modulations (Fig. l), has a discrete
spectral density. When random noise is the modulating signal,
which has a continuous spectrum, in addition to carrierrelated discrete term, the principal part of the angle-modulated
spectrum is continuous.
Strictly speaking, amplitude and power spectral densities
V(f) and S,(f), as defined in (2) and (3) do not exist for
random processes, since integral in (2) does not converge as
t + LIZ,. However, this can be circumvented in mathematical
terms by utilizing the Wiener-Khintchine relationship between
autocorrelation function R\.(t) of a random process V(t),
defined as
R\-(T)
Fig. 6. Amplitude spectrum for symmetrical sweep (/(I.RI = 20)
bandwidth. Somewhat better distribution can be achieved with
a more complex or random sequence [ 121, [ 161, [20].
Experimental waveforms are shown in Fig. 4(c) and (d).
For a tenfold maximum current spectral term reduction, the
required bandwidth is BWF~~ = 30 kHz (fa = 100 Hz). This
shows little benefit over sine-wave angle modulations.
C. Modulation by Saw Tooth or Symmetrical Sweep
Frequency modulations by a saw tooth or a symmetrical
sweep produce a similar spectrum. A typical amplitude spectrum for symmetrical sweep, shown in Fig. 6, suggests an
even power distribution and a well-utilized bandwidth. As
PFhr + w, the spectral density for both modulating signals,
shown in Fig. 3(c), becomes
where pyhrfa represents the maximum frequency deviation,
and w~(= 27r/To) is the modulating signal frequency. According to (12), the modulation index increase is proportional to the
maximum amplitude decrease; unlike for sine-wave-modulated
spectra, this relationship is linear.
Experimental results, illustrated in Fig. 4(e) and (f), show
a 50% reduction in bandwidth over that of sine-wave modulation.
= E{V(t)V(t
+ 7))
(13)
where E(e) denotes the expected value operator and power
spectral density function S,(f). According to this relationship,
S,(f)
= F{&,(T)}
= 11
RL+),-jdT
dr.
(14)
Power spectral density function S,(f) is defined as the Fourier
transform of the autocorrelation function RL, (t).
While the mathematical tools for analysis of the angle
modulations by random processes change from before, as
noise is described in terms of statistical properties, essential
properties, such as one estimated by Carson’s rule, remain the
same.
According to the principle of adiabatic frequency sweeps
[ 171, for large modulation indices, the power density of the
angle-modulated wave is proportional to the first-order probability density of the frequency-modulating process. Hence, for
phase modulation by a random noise VA,(t), the modulated
wave spectral density is
where
and IJ~(LG) represents the density distributions
of the modulating noise.
of the derivate
IEEETRANSACTIONSON INDUSTRYAPPLICATIONS.VOL. 34. NO. 3. MAY/JUNE199X
602
. i,.(r)..i....:...i.
:,. .:...
j .1
.
. . .._ ..:...:.........:.
,.:...,...
1l...., f .-.,,.: :. . . ..I.:. ,.i ;.
m
‘.“’
:
i
2O.UmV-b
103.0 HZ
102.0 hz
. . . . . . . . ..I
-.
I
.:
:
:
.._...
,:
...:.,
,:
Fig. 8. (a) Experimental modulating noise time-domain waveform (horizontal scale: 20 ms/div, vertical scale: 100 mV/div), and (b) its spectrum
(horizontal scale: 25 Hz/div, vertical scale: 50 mV/div).
Frequency-modulated
wave spectral density by noise
process yv(r?), with a bandwidth Ow,v, is similar to the
phase-modulated one, ( 15), since phase modulation by a noise
process Vnr(t) is equivalent to frequency modulation by noise
process I&(t). Hence,
where
In this instance, spectral density is proportional to the firstorder density distribution WI(Y) of the modulating noise
h(t).
When noise is the modulating signal, the presence or
absence of a discrete carrier term emerges as a difference
between angle-modulated wave spectra. The exact calculation
of the carrier contribution is relatively complicated and is
beyond the scope of this paper. For phase modulations, the
noise contribution around f = 0 vanishes rapidly, and there
Fig. 9. (a) Experimental band-limited white-noise-modulated lamp current
(horizontal scale: 2 ms/div, vertical scale: 1 Aldiv) and (b) its fast Fourier
transform (FIT) (horizontal scale: 5 kHz/div, vertical scale: 0.1 A/div).
is always a residual carrier term. The existence of a carrier
term in a frequency-modulated spectrum is a function of
noise spectral characteristics at and around f = 0. When the
modulating noise spectrum contains terms in this range, all
energy is in the continuum and no carrier appears [ 171.
White noise, as do most tractable noise signals, has a normal
or Gaussian distribution. Hence, according to the principle
of adiabatic sweep, the main contribution of the frequencymodulated spectrum, (16), is a term proportional to Gaussian
distribution. Spectral densities of the band-limited white noise
and the correlated frequency-modulated wave are illustrated
in Fig. 7.
According to (16), spectral reduction is achieved by increasing the modulating index PF. Like before, this will increase
modulated-wave spectral bandwidth. As for periodic signals,
this can be counterbalanced by reducing the modulating noise
bandwidth awnr.
Relevant experimental waveforms are shown in Figs. 8
and 9. Fig. S(b) shows the FFT of the band-limited white
noise, where bandwidth ilwnr = fa = 100 Hz has been
selected to equal the modulating frequency used in periodical
modulations. For illustration. the corresoondina
time-domain
I
LASKAI er ol WHITE-NOISEMODULATIONOF HIGH-FREQUENCY
HID LAMP BALLASTS
603
b
b
Fig. 10. A unity power factor electronic ballast.
(4
(b)
(cl
Fig. 11. Arc appearancewith (a) 60.Hz magnetic ballast, (b) high-frequency electronic ballast with acoustic resonances,and (c) high-frequency electronic
ballast without acoustic resonances.
waveform is also shown in Fig. 8(a). The time-domain lamp
current waveform, Fig. 9(a), shows virtually no sign of amplitude modulations, and according to its FFT, Fig. 9(b),
the modulated wave bandwidth is BWN = 2.5 kHz. This
represents a bandwidth reduction of around 14 times over
comparable sinusoidal modulations.
IV. EXPERIMENTAL SETUP
Experimental waveforms, discussed during the analysis,
were obtained with an electronic ballast, shown in Fig. 10.
The ballast, developed at the Power Electronics Laboratory,
Texas A&M University, consists of a unity power factor input
rectifier section and a half-bridge series resonant inverter,
interfacing the lamp with the dc bus, as discussed in [15].
A digital pseudorandom sequence generator has been used
to generate white noise [2.5]. Uneven attenuation, shown
in Fig. 8(b), results from the second-order low-pass filter,
however, it carries no significance as lamp power spectrum
is determined by probability density of the modulating noise
and its bandwidth.
Two different lamps, MVR250AJ and M250/U, made by GE
and Osram, were used in the experiments. Arc appearances
with a conventional 60-Hz ballast, with a high-frequency ballast with acoustic resonances and with a high-frequency ballast
without acoustic resonances, are shown in Fig. 11. There were
604
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS. VOL. 34. NO. 3. MAY/JUNE 1998
no observable differences between important lamp properties
for 60.Hz or stable high-frequency operation. Observe that
arc bowing in horizontally operated 60-Hz arc is not present
at high frequencies. However, this change had no effect on
luminous flux or light quality.
V. CONCLUSION
In this paper, a new modulation method has been proposed to avoid acoustic-resonance-related problems in metal
halide lamps when operated with high-frequency electronic
ballasts. Angle modulation has been utilized to randomize the
inverter switching frequency and to limit lamp power spectrum
below the instability threshold. Along with the proposed
band-limited white-noise modulations, three different anglemodulation strategies were described, sine wave, square wave,
and symmetrical sweep.
To obtain stable operation with 250-W metal halide lamps,
which were used for experimental verification, the dominant
spectral terms were reduced by tenfold. To achieve this reduction, required modulated-wave bandwidth for the periodical
modulating signals was 15-35 kHz and the proposed random
signal approach required only 2.5 kHz. The center or carrier
frequency was selected to be just above the audio frequency
range, hence, reducing EMI-related concerns.
The proposed stabilizing method allowed the use of high Q
resonant inverters for HID lamp ballasting. Experiments with
250-W lamps, made by different manufacturers, showed good
results.
REFERENCES
111 1. J. Pitel, “Emerging lighting control technologies: The alternativesand
trade-offs,” .I. Illurn. Eng. Sot., vol. 12, no. 4, pp. 624-632, Apr. 1985.
The High-Pressure Lamp. Deventer, The
Netherlands: Kluwer TechnischeBoeken, 1986.
[31 M. Schulz and K. U. Ingard, “Acoustic kink instability in an argon
discharge,” Phys. Fluids, vol. 10, no. 5, pp. 1031-1036, May 1967.
New York:
L41 P. M. Morse and K. U. lngard, Theoretical Acoustics.
McGraw-Hill, 1968.
151 H. L. Wetting, “Acoustic resonancesin cylindrical high-pressure arc
dischar-ges,”J. Appl. Phys., vol. 49, no. 5, pp. 2680-2683, May 1978.
161J. W. Denneman, “Acoustic resonancesin high-frequency operated low
wattage metal halide lamps,” Philips J. Res.. vol. 38, nos. 4/5, pp.
263-272, 1983.
171 J. M. Davenport and R. J. Petti, “Acoustic resonancephenomenain low
wattage metal halide lamps,” J. Illurn. Eng. Sot., vol. 12, no. 4, pp.
6333642, Apr. 1985.
181 R. Schafer and H.-P. Stormberg, “Investigations of the fundamental
longitudinal acoustic resonanceof high pressuredischarge lamps,” J.
Appl. Phw., vol. 53, no. 5, pp. 3476-3481, May 1982.
191 H. P. Stormberg and R. Schafer, “Excitation of acoustic instabilities in
discharge lamps with pulsed supply voltage,” Lighfing Res. Techrrol.,
vol. 15, no. 3, pp. 127-132, 1983.
1101 Y. Koshimura er al., “Stable high-frequency operation of high intensity
discharee lamos and their ballast desian.” in Proc. CIE 20th Session.
1983, pp. E3&E36/2.
1111J. Park ef al., ‘Solid state chopper ballast for gaseousdischargelamps,”
U.S. Patent 3 890537, 1975..L121Gamer et al., “Method of operating a high-pressure metal vapor dischargelamp and circuit arrangementfor carrying out this method,” U.S.
Patent 4705991, 1987.
1131 H. I. Faehnrich and E. Rausch, “Electronic ballasts for metal-halide
lamps,” J. Illurn. Eng. Sot., pp. 131-141, Summer 1988.
1141 S. Wada et al., “Study of HID lamps with reducedacousticresonances,”
.I. Illurn. Eng. Sot., pp. 1622175, Winter 1987.
1151 L. Laskai, P. Enjeti, and 1. J. Pitel, “A unity power factor electronic
ballast for metal halide lamps,” in Proc. IEEE Applied Power Elrctmnics
corlj:, 1994, pp. 31-37.
I2J J. de Groat and J. van Vhet,
1161J. D. Gibson, Principles qf Digitcrl
and Analog Communications.
New
York: Macmdlan, 1993.
1171 D. Middleton, Introduction fo Statistical Communication Theory. New
York: McGraw-Hill, 1960.
Ll81J. R. Carson and T. C. Fry, “Variable frequency electric circuit theory
with aoolication to the theorv of freouencv modulation.” Bell Svst.Tech.
J., voi.‘l6, pp. 513-540, 1937. I
.
LJ9J El. Van der Pal, “Frequency modulation,” Proc. IRE, vol. 18, no. 7, pp.
1194-1205, July 1930.
1201R. R. Anderson and J. Salz, “Spectra of digital FM,” Llrll Syst. Tech. J..
vol. 44, pp. 1165-I 189, JulyyAug. 1965.
L2lJ T. G. Habetler and D. M. Divan, “Acoustic noise reduction in sinusoidal
PWM drives using randomly modulated carrier,” IEEE Trans. Power
Electron., vol. 6, pp. 356-363, July 1991.
T. Tanaka er a/., “Random switching control in dc-dc converters,” in
17-21
Proc. IEEE Power Electronics Specialist Co@, 1989, pp. 500-507.
L231A. M. Stankovic et al.. “Monte-Carlo verification of power spectrum
formulas for random modulation schemes,”presented at the 3rd IEEE
Workshop Computers in Power Electronics, Berkley, CA, 1992.
~241 A. M. Trzynadlowski et al., “Random pulse modulation technique for
voltage controlled drive systems,”ht. J. Electron., vol. 68, no. 6, pp.
1027-1037, 1990.
Cambridge, U.K.: Cam125~ P. Horowitz and W. Hill, Art of Elrctronics.
bridge Univ. Press, 1980.
Laszlo Laskai (M’87-SM’96) received the Dip].lug. degree from the University of Novi Sad, Novi
Sad, Yugoslavia, in 1982 and the Ph.D. degreefrom
Texas A&M University, College Station, in 1994,
both in electrical engineering.
From 1983 to 1986, he was with Investproject, Novi Sad, Yugoslavia, working on standby
power generation and power distribution for large
industrial consumers.From 1986 to 1990, he was
with Chronar Corporation, Princeton, NJ where he
was involved in the development of power conversion equipment for photovoltaic applications and high-frequency ballasts for
gaseousdischarge lamps. Since 1994, he has been with Corporate Research
and Development, General Electric Company, Schenectady,NY. His curreut
researchinterests are in lighting and medical electromcs.
Dr. Laskar currently serves as Chairman and Transactions Editor for
the Production and Application of Light Committee of the IEEE lndustr-y
Applications Society (IAS). He is also an active member of the IAS Industrial
Power Conversion Committee.
Prasad N. Enjeti (S’86-M’EE-SM’95) receivedthe
B.E. degree from Osmania University, Hyderabad,
India, in 1980, the M.Tech. degree from the Indian
Institute of Technology, Kanpur, India, in 1982,
and the Ph.D. degree from Concordia University,
Montreal, Que., Canada, in 1987, all in electrrcal
engineering.
Following receipt of the Ph.D. degree, he joined
the Department of Electrical Engineering, Texas
A&M University, College Station, where he is currently an AssociateProfessor.His primary research
interests are advance convertersfor power supplies and motor drives, power
quality issuesand active power filter development, utility interface issuesand
“clean” power converter designs. and electronic ballasts for HuorescentHID
lamps. He is the Lead Developer of the Power Quality Laboratory, Texas
A&M University, and is actively involved in many projects with industries
and is engaged in teaching, research, and consulting in the area of power
electronics,power quality, and clean power utility interface issues.
Prof. Enjeti is a RegisteredProfessional Engineer in the State of Texas.He
is TransactionsEditor for the Industrial Power Converter Committee (IPCC)
of the IEEE Industry Applications Society (IAS) and an AssociateEditor of
the IEEE TRANSACTIONSONPOWER ELECTRONICS.He was the recipient of the
IAS Second and Third Best Paper Awards in 1993 and 1996, respectively,
the award for the second best transactionspaper published in midyear 1994
to midyear 1995 in the IEEE TRANSACTIONSONINDUSTRYAPPLICATIONS,and
the IAS Magazine Prize Article Award m 1996.
LASKAI
~‘f ol.. WHITE-NOISE
MODULATION
OF HIGH-FREQUENCY
HID LAMP
BALLASTS
Ira J. Pitel (M’73-SM’82) receivedthe B.S. degree
from Rutgers-The State University of New Jersey,
New Brunswick, the M.S. degree from Bucknell
, University, Lewisburg, PA, and the Ph.D. degree
from Carnegie-Mellon University, Pittsburgh, PA,
in 1972, 1975, and 1978, respectively.
From 1973 to 1976, he was with GTE Sylvania,
researchinghigh-frequencyballasting techniquesfor
gaseousdischargelighting. He joined Bell Laboratories in 1978 and Exxon Enterprisesin 1979. At
Exxon, he was involved in high-power converter
structuresfor ac motor drives, power processingfor advancedbattery systems,
and controlled lighting. He was eventually transferred to one of Exxon’s
subsidiaries,Cornell-Dubilier Electronics,where he was Managerof Research
and Development. In 1981, he founded Magna-Power Electronics, Boonton,
NJ, a company specializing in custom and standard power conditioning
products.As President,he is responsiblefor contract researchand development
and manufacturingof its line of IO-500.kW dc power supplies. In 1986. he
joined TexasA&M University as an Adjunct AssociateProfessor.HISresearch
interestsare high-power ac-to-dc converters,static inverters, spacecraftpower
supplies. and specialty lightmg controls. He holds 21 patents in the field of
power electronics.
Dr. Pitel is the co-recipient of the 1995 Society Prize Paper Award of the
IEEE Industry Applications Society (IAS). He servedas Committee Chairman
of the IAS Industrial Power Converter Committee in 1988-1989, Department
Chairman of the IAS Industrial Power Conversion Systems Department in
1994-l 995, and IAS Society Secretaryand Vice Presidentin 1997 and 1998,
respectively.He is a member of Eta Kappa Nu and Tau Beta Pi.
605