Analysis and spectral characteristics of a spread …hcso/tpe_3_00.pdf · IEEE TRANSACTIONS ON...

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 2, MARCH 2000 399

Analysis and Spectral Characteristics of aSpread-Spectrum Technique for Conducted EMI

SuppressionK. K. Tse, Member, IEEE,, Henry Shu-Hung Chung, Member, IEEE,, S. Y. (Ron) Hui, Senior Member, IEEE,, and

H. C. So, Member, IEEE

Abstract—Frequency modulation (FM) and random switchingmethods have been used for reducing conducted electromagneticinterference (EMI) in power converters. Limited theoreticalstudies and comparisons of these schemes, however, are available.In this paper, a detailed analysis and the spectral characteristicsof a random carrier-frequency (RCF) technique for suppressingconducted EMI in an offline switched-mode power supply are pre-sented. The analysis provides a theoretical platform for studyingthe characteristics of this random switching scheme. The levelof randomness is defined for the RCF scheme and varied in theconverter example so that its effects on the power spectra can bedemonstrated. Theoretical predictions of the spectral characteris-tics of this scheme are confirmed with measurements. The RCFscheme has been compared with the standard constant-frequencypulsewidth modulation (PWM) scheme and the FM scheme.Comparisons of their spectral performance show that the RCFscheme has better conducted EMI suppression than the FM andstandard PWM schemes.

Index Terms—AC-DC power conversion, pulsewidth modula-tion, random switching technique, switching circuit.

I. INTRODUCTION

NOWADAYS, switched-mode power supplies have to bedesigned not only to provide the required electrical func-

tions, but also to meet international electromagnetic compati-bility (EMC) standards. Inherently, switched-mode power sup-plies are electrically noisy. A typical configuration with the con-ducted electromagnetic interference (EMI) test setup is shownin Fig. 1 [1]. Two conflicting filter design constraints have tobe considered. Firstly, in order to comply with the internationalEMI regulations, a differential and common-mode EMI filteris generally put in series with the line input. Secondly, for sat-isfying the safety requirements, the maximum values of the de-coupling capacitors and (which are usually less than 0.01µF and are connected between the supply lines and ground) arelimited. These conflicting requirements make proper design ofthe noise filter not straightforward.

The switching device in a switched-mode power supply isthe principle source of EMI. Decoupling capacitors andthe parasitic capacitors – form a closed loop. Part of the

Manuscript received August 25, 1998; revised July 7, 1999. This work wassupported by the Hong Kong Research Council. Recommended by AssociateEditor, J. Van Wyk.

The authors are with the Department of Electronic Engineering, City Univer-sity of Hong Kong, Hong Kong (e-mail: [email protected]).

Publisher Item Identifier S 0885-8993(00)02335-8.

switch voltage will appear on and . As the device's voltageconsists of the fast switching edges, harmonics up to severalmegahertz may appear on and , and hence on the supplynetwork. The input current is generally pulsating and thus is richin harmonic components. Most of the differential-mode noisecan in principle be bypassed by the filter capacitorsand .Their capacitance values are dependent on the maximum peakof the harmonic components. However, the practical filteringeffects of capacitors are not perfect. It is necessary to considerother alternatives so that the conducted EMI can be minimized.

The most effective way of suppressing conducted EMI is toact on the noise source. One obvious approach is to deal with theswitching methods of the power device. Frequency modulation(FM) has been incorporated into the pulse-width-modulation(PWM) of the power converter [2] in order to reduce the inputdiscrete harmonics. This approach is an important step forwardin dealing with the conducted EMI issue because it offers asimple and yet effective method for modifying a standard PWMscheme to meet EMC standards. Recently, random switchingtechnique has been recognized as an emerging technologyfor power converters [3]. Various random switching schemes,which are originated from statistical communication theory[11], have been reported for dc/ac and dc/dc power conversion[3]–[10]. The basic principle of introducing randomness intostandard PWM scheme is to spread out the harmonic power sothat no harmonic of significant magnitude exists. As a result,discrete harmonics are significantly reduced and the harmonicpower is spread over the spectrum as ‘noise’ (continuous spec-trum). Although some papers such as [12] have comparisonson PWM inverters, there is no reported comparison on thesetwo approaches for offline switched-mode power supplies.

It has been pointed out in [10] that the continuous noise spec-trum within the pass band of the converter's output low-passfilter could lead to noise-induced low-frequency voltage ripplein the converter's output. This undesirable feature may prohibitthe use of random modulation in dc/dc converters, which re-quire tight voltage regulation. In [10], this problem has beenhighlighted in the random pulse width modulation (RPWM) andrandom pulse position modulation (RPPM) schemes. For theRPWM method, the duty cycle of the switch is continuouslychanging in every switching cycle although the average dutycycle is theoretically equal to the nominal duty cycle. This dutycycle variation worsens the voltage ripple problem. In the RPPMscheme, there is also some possibility that two adjacent pulsesof fixed duty cycle may appear together. Rigorous analyses of

0885–8993/00$10.00 © 2000 IEEE

400 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 2, MARCH 2000

Fig. 1. Typical configuration of an offline switched-mode power supply with conducted EMI test setup.

Fig. 2. Waveforms of flyback converter operating in discontinuous conductionmode with RCF scheme. (a) Sawtooth and reference voltage waveforms. (b)Gate signal. (c) Input currenti . (d) Switch voltagev .

these two random schemes for dc–dc converters have been pre-sented in [13], [14].

In this paper, the random carrier frequency (RCF) schemefor dc–dc converter is examined and compared with the stan-dard PWM scheme and the FM scheme. One attractive fea-ture of the RCF scheme is that it inherently ensures constant

TABLE ICOMPONENT VALUES OF A PRACTICAL

OFFLINE FLYBACK CONVERTER

duty cycle operation in the dc–dc converter. The variation of theoutput voltage is not as significant as the RPWM and RPPMschemes and therefore allows simple feedback control design.At the same time, the power spectra of the converter input cur-rent and the switch voltage will spread over a wide frequencyrange so that no harmonic of significant magnitude exists. Ef-fectively, the envelopes of the power spectra of the differen-tial-mode and common-mode conducted EMI can in principlebe reduced. These EMI aspects have been verified experimen-tally in [7]–[9]. However, the lack of theory of such schememakes it difficult to decide how much randomness should beintroduced. In this paper, a mathematical analysis of the abovephenomena of the RCF method is given. The scope of this paperis not to answer all questions about the RCF scheme. Instead, itaims at providing a platform for understanding the spectral per-formance and the effect of the variation of the level of random-ness. The model of an offline switched-mode power supply andmathematical derivations of the frequency spectra of the inputcurrent and the switch voltage waveform with and without RCFscheme are presented in Section II. Practical measurements ofthe conducted EMI of a 58-W, 220-V/24-V, 50-Hz offline fly-back converter are given in Section III, together with analyticalpredictions. The results are compared with the standard constantswitching frequency scheme and the FM [2] scheme. The con-clusion follows in Section IV.

TSEet al.: ANALYSIS AND SPECTRAL CHARACTERISTICS OF A SPREAD-SPECTRUM TECHNIQUE FOR CONDUCTED EMI SUPPRESSION 401

(a)

(b)

Fig. 3. Synthesis of RCF switching signal. (a) Feedback circuit. (b) Noise generator.

II. M ODELS AND MATHEMATICAL DERIVATIONS

A. Source of EMI

As shown in Fig. 1, a standard line-impedance stabilizationnetwork (LISN) is connected between the power supply andthe supply lines. As the supply source impedance is high,a common-mode harmonic current will flow through theground plane, parasitic capacitance – , and .If denotes the effective parasitic capacitance between thedrain voltage of the switch (i.e., ) and the ground plane,the spectral magnitude of at frequency , can beobtained by

(1)

where is the spectral magnitude of . Thus, the spectralmagnitude of the voltage across and , can beapproximated by

(2)

if .

For the input side, since , and form a potential di-vider with the simulated 50- supply line resistance in theLISN, part of appears on . Thus, in order to reduce thevoltage across , and can be increased. However,this will substantially decrease the voltage supplying to the con-verter circuit, due to the increase in the voltage drop across

, and .In practice, the value of and hence are slightly difficult

to be determined. The above derivations are mainly for illus-trating the major EMI source. In order to simplify the analysis, itis assumed that the switch voltage is not affected by the parasiticcomponents. The validity of this assumption is ensured by theclose agreement between the experimental measurements andthe theoretical predictions.

In this study, the RCF scheme is applied to the PWMswitching of the main switch . Fig. 2(a) shows the randomizedsawtooth waveform that is compared with a reference signalto generate the gate signal [Fig. 2(b)]. The duty cycleofis fixed in the respective cycle, although the switching period(stochastic variable) is varied. Thus, the differential-modenoise (due to the input current) and the common-mode noise(due to the switch voltage) can be spread over a certainfrequency range. Spreading the harmonic power of the inputcurrent and the switch voltage signal is discussed separatelyin the following sub-sections. The mathematical derivations


(a)

(b)

Fig. 4. Experimental waveforms of the converter. (a)< = 0. (b)< = 0:2. [Channel 1: Output voltage (1 V/div, with ac coupling). Channel 2: Gate signal (10V/div). Channel 3: Input current (1 A/div). Channel 4: Switch voltage (200 V/div). Timebase: 10µs/div.]

are based on a flyback converter operating in discontinuousconduction mode (DCM), which is a commonly used config-uration in many low-power applications. The attraction of theflyback converter is its single power conversion step, wherethe ‘flyback’ transformer provides the features of electricalisolation and as an energy storage medium.

B. Spectral Characteristics of the Input Current Waveform

Fig. 2(c) shows the waveform of the input currentof theconverter. For a generic switching cycle equals

can be expressed as

for

elsewhere(3)

where is the input voltage and is the inductance of the fly-back transformer. is a randomized switching period resultingfrom the RCF. The general expression of is

(4)

The auto-correlation of is defined as

(5)

where is the expected value of the quantity inside thebracket. is the observation interval, containing expectedvalue of . That is

(6)


(a) (b)

(c) (d)

Fig. 5. Experimental power spectra. (a) Input current with< = 0. (b) Input current with< = 0:2. (c) Switch voltage with< = 0. (d) Switch voltage with< = 0:2.

By substituting (4) and (6) into (5)

(7)

If denotes the Fourier transform of and de-notes the time integral in (7)

(8)

Referring to [11]

(9)

Equation (8) can be expressed as

(10)

Hence, the autocorrelation of can be expressed as

(11)

Based on the Wiener-Khinchin theorem [11], the power spec-trum of a signal is the Fourier transform of its autocorrela-tion function . Conversely, the autocorrelation can be givenby the inverse Fourier transform of the power spectrum. That is

(12)


(a) (b)

(c) (d)

Fig. 6. Theoretical predictions of the power spectra. (a) Input current with< = 0. (b) Input current with< = 0:2. (c) Switch voltage with< = 0. (d) Switchvoltage with< = 0:2.

and

(13)

By this relationship, the power spectrum ofover the range ofpositive frequency, , is easily observed from (11), i.e.,

(14)

The expected value of the summation in (14) forms a geometricseries. Thus

for (15)

Detailed proofs are shown in the appendix.

For

(16)

It should be noted that (15) is a general expression for RCFswitching schemes under consideration if is substitutedby the Fourier transform of a cycle of the considered signal. InSection II-C, the derivation of power spectrum of switch voltageis based on (15).

1) Standard Constant Switching Frequency (Standard)Scheme:If the converter operates with standard scheme, (14)is modified with

(17)

and

(18)

where is a constant. The power spectrum can be shown to be

(19)


Using the Poisson identity, the sum of exponential terms in (19)is defined as the sum of delta functions over the spectrum. Thatis

(20)

where .Thus, the power spectrum of in the standard scheme is

(21)

By (3), the Fourier transform of a cycle of is

(22)

Thus, the squared absolute value is

(23)

For the standard scheme, is determined by substituting(23) into (21).

2) RCF Scheme:Assume that the randomness ofis sub-ject to a probability density function , which has the uni-form distribution with upper limit and lower limit (i.e.,

). Let denote the period deviation andde-note the level of randomness on

(24a)

(24b)

Hence, the probability density function of is of the form

otherwise(25)

For a non-zero , the expected values of the terms in (15) arefound as follows:

(26)

(27)

(28)

(29)

By substituting (26)–(29) into (15), in the RCF schemecan be found. As will be shown in Section III, will be-come close to a continuous spectrum asincreases.

C. Spectral Characteristics of the Switch Voltage Waveform

The waveform of the drain-source voltage of inFig. 2(d) is expressed as

forforfor

(30)where is the turns ratio of the flyback transformer and isthe output voltage, which is equal to

(31)

where is the output load resistance. is the expected valueof the duty cycle in RCF scheme. It is the nominal value of theduty cycle in standard scheme.

(32)

(33)

Following the similar approach for , the power spectrumcan be expressed as

for (34)


For

(35)

1) Standard Constant Switching Frequency (Standard)Scheme:For the standard scheme, is a constant and

(36)

The Fourier transform of a cycle of is

(37)

and hence, its squared absolute value is given as

(38)

2) RCF Scheme:In order to calculate , (34) is used.With the same assumptions of randomness ofin (25), theexpected values of the terms in (34) can be expressed as follows,

(39)

(40)

(41)

Similar to the characteristics of the input current will bechanged from a discrete harmonic spectrum to a continuousspectrum as the level of randomness inincreases.

III. EXPERIMENTAL VERIFICATIONS

Fig. 3(a) shows the synthesis of RCF switching signal in thefeedback network for the offline flyback converter shown inFig. 1. The noise generator circuit is shown in Fig. 3(b). Thetransistor is used as a noise diode that gives constant noise signalstrength over wide frequency band. The ripple of noise output

and its DC value are adjustable by changing VR1and VR2, respectively. The component values of the converterare tabulated in Table I. The output power of the converter is58 W. The output of the error amplifier is compared to a ran-domized sawtooth signal. A composite random signal, whichcontains a fixed dc signal and a noise with maximum am-plitude , generates the randomized sawtooth signal. Thelevel of randomness in the RCF scheme can also be definedas

(42)

At the end of every switching cycle, the composite randomsignal is sampled and then fed to a voltage controlled oscillator(VCO) to generate the next sawtooth cycle. The nominalswitching frequency is set at 50 kHz. corresponds tothe standard PWM scheme and the switching frequency is 50kHz. When , the switching frequency is uniformlyrandomized within the frequency range from 45 kHz to 55 kHz.Fig. 4 shows the experimental voltage and current waveformsof the converter's main switch when and ,respectively. The gate signal is measured before the driver inFig. 3(a). The output voltage under two cases is maintainedat 24 V with ripple voltage of about 400 mV. In Fig. 4(a),the period of the input current pulses is fixed at 20µs whilethe one in Fig. 4(b) is changed in every cycle. Although RCFcan generate low-frequency noise within the pass band of theoutput filter, the output can be regulated to an acceptable levelsince the dynamics of the voltage output will be much slowerthan the crossover frequency of the feedback path. Hence theoutput voltage can be effectively stabilized as shown in Fig. 4.

Experimental measurements of the power spectra of[i.e.,] and [i.e., ] are shown in Fig. 5. The

results were taken from a signal analyzer HP89410A with theuse of the Hanning window, 4096 time samples, and a samplingrate of 2.5 MHz.


(a)

(b)

Fig. 7. Variation of power spectrum with<. (a) Input current. (b) Switchvoltage.

It is important to note that the true power spectrum derived inSection II is based on infinite time-records of the RCF switchingsignal. However, as pointed out in [15], power spectra obtainedfrom digital signal processing technique are strictly approxima-tions because of the finite number of time records involved in thecalculation. In order to make a better comparison of the theoret-ical power spectrum and the experimental ones , amathematical compensation for the analytical power spectrum

is performed by convoluting with the window func-tion . That is

(43)

where is one of discrete frequency points given by FFT anal-ysis, and the characteristic of the window functionis subjectto the following factor in FFT-based processing.

1) Type of windowing function.2) Number of sampled time-record.3) Sampling rate.

By considering the above factors, the modified analytical solu-tion is compared to the experimental from theFFT-based spectrum analyzer, using the same parameters asHP89410A.

The analytical prediction of and are shownin Fig. 6. All results are determined by taking the convolution

(a)

(b)

Fig. 8. Measured conducted emission. (a)< = 0. (b)< = 0:2.

(43) associated with the solutions of (15), (21), (34) and (36), re-spectively. Both analytical and experimental results are in closeagreement. It can be observed that the RCF technique substan-tially reduces the discrete switching frequency harmonics. Thepeak harmonic power of the RCF scheme is much lower thanthat of the standard scheme. Using the theory developed, a three-dimensional representation of the variations of the power spec-trum with respect to the value of are generated and shown inFig. 7. When equals zero, the operation is same as the standardPWM scheme. Discrete harmonics at multiples of the switchingfrequency can be observed. It is important to note that the powerspectrum changes gradually from discrete harmonics spectrumto continuous noise spectrum with an increasing. The overallenvelope of the power spectrum also decreases asincreases.

For the measurement of the conducted EMI of the converter,a LISN Farnell LSN30 and an EMC analyzer HP8591EM areused. Quasi-peak detector is used for all the testing. Fig. 8 showsthe measured conducted emission under the above two casesand the limits of CISPR Publication 22 Class A devices. When

, some discrete harmonics exist and exceed the limit. With, the harmonics are spread over. The spectrum is within

the limit. Moreover, there is an approximately 10 dB reductionin the envelope of the spectrum with RCF. This can demonstratethe effectiveness of using RCF in suppression of EMI of theoffline switched-mode power supply.

The RCF scheme is also compared with the FM scheme. Likethe RCF scheme, the switching frequency of the FM scheme isallowed to vary within the frequency range from 45 kHz to 55


(a) (b)

(c)

Fig. 9. Power spectra of the conducted emissions. (a) Standard PWM. (b) FM of 2 kHz on standard PWM. (c) RCF scheme.

kHz. The FM scheme is modulated at 2 kHz. Fig. 9 shows acomparison of the conducted EMI when the converter is oper-ated with

1) standard PWM [Fig. 9(a)];2) FM of 2 kHz on standard PWM [2] [Fig. 9(b)];3) RCF scheme [Fig. 9(c)].

In order to investigate the details of the spectral characteristics,a frequency span of 1 MHz–1.1 MHz is studied for improvingthe frequency resolution. It can be seen that the FM schememanages to reduce the discrete harmonic components to someextent when compared with the standard PWM scheme. Thediscrete harmonics are formed by the modulating frequencyand the switching frequency [2]. Compared to the standardPWM, some discrete harmonics that do not exist in the standardPWM scheme are generated with the FM. However, the RCFscheme offers the best conducted EMI suppression among thethree schemes under consideration.

IV. CONCLUSION

An analysis on the random carrier frequency PWM methodhas been presented. The theory provides a mathematicalplatform for studying the spectral characteristic of this randomPWM scheme. Spread spectrum switching technique dispersesthe discrete switching harmonics in standard PWM dc/dc

converter as a wide-spectrum noise. It has the effect of reducingconducted EMI emissions as demonstrated in an experimentalprototype. The RCF technique involves the randomization ofthe carrier frequency, but has the inherent feature of keepingduty cycle constant. The effects of the level of randomnesson the degree of spectrum spreading are studied. Analyticalprediction is verified with the practical measurements. Theimplementation here is simple and only involves a slight modi-fication on existing circuits using standard PWM technique. Inconclusion, the RCF scheme offers a simple solution to reduceconducted EMI in power converters. In terms of conductedEMI suppression, this study demonstrates that the RCF schemeis better than the FM scheme which has been incorporated intothe PWM scheme of many commercial power converters.

APPENDIX

denotes the double-summation of the expected term in(14); thus, (14) becomes

(A.1)

(A.2)


(A.3)

It should be noted that is dependent on if

(A.4)

and is dependent on if

(A.5)

Hence, (A.3) can be shown to be

(A.6)

where

(A.7)

Consider

(A.8)

and

forfor

(A.9)

Thus, (A.7) becomes a real number as follow:

(A.10)

Since , (A.10) is simplified as

(A.11)

By substituting (A.11) into (A.6):

(A.12)

Finally, (A.1) becomes

(A.13)

REFERENCES

[1] K. H. Billings, Ed.,Switchmode Power Supply Handbook. New York:McGraw Hill, 1989.

[2] F. Lin and D. Y. Chen, “Reduction of power supply EMI emission byswitching frequency modulation,” inProc. IEEE Power Electron. Spec.Conf., 1993, pp. 127–133.

[3] M. P. Kazmierkowski and F. Blaabjerg, “Impact of emerging technolo-gies on PWM control of power electronic converters,”IEEE Ind. Elec-tron. Soc. Newsletter, pp. 9–13, Dec. 1995.

[4] A. M. Stankovic, G. C. Verghese, and D. J. Perreault, “Analysis and syn-thesis of randomised modulation schemes for power converters,”IEEETrans. Power Electron., vol. 10, no. 6, pp. 680–693, Nov. 1995.

[5] S. Y. R. Hui, I. Oppermann, and S. Sathiakumar, “Microprocessor basedrandom PWM schemes for DC-AC power conversion,”IEEE Trans.Power Electron., vol. 12, no. 2, pp. 253–260, Mar. 1997.

[6] T. Tanaka, T. Ninomiya, and K. Harada, “Random switching control indc–dc converters,” inProc. IEEE Power Electron. Spec. Conf., 1989, pp.500–507.

[7] D. S. Stone and B. Chambers, “The effect of carrier frequency modula-tion of PWM waveforms on conducted EMC problems in switched modepower supplies,”EPE J., vol. 5, no. 3, pp. 32–37, Jan. 1996.

[8] , “Effect of spread-spectrum modulation of switched mode powerconverter PWM carrier frequencies on conducted EMI,”Electron. Lett.,vol. 31, no. 10, pp. 769–770, May 1995.

[9] , “Easing problems in switched mode power converters by randommodulation of the PWM carrier frequency,” inProc. Appl. Power Elec-tron. Spec. Conf., 1996, pp. 327–332.

[10] Y. Shrivastava, S. Y. R. Hui, S. Sathiakumar, H. Chung, and K. K. Tse,“Effects of continuous noise in randomised switching dc–dc converters,”Electron. Lett., vol. 33, no. 11, pp. 919–921, May 1997.

[11] D. Middleton, An Introduction to Statistical CommunicationTheory. New York: McGraw-Hill, 1988.

[12] J. T. Boys, “Theoretical spectra for narrow-band random PWM wave-forms,” Proc. Inst. Elect. Eng. B, vol. 140, no. 6, Nov. 1993.

[13] Y. Shrivastava, S. Y. R. Hui, S. Sathiakumar, H. Chung, and K. K. Tse,“Harmonic analysis of non-deterministic switching methods for dc–dcpower converters,” IEEE Trans. Circuits Syst.—Part I. , to be published.

[14] Y. Shrivastava, S. Y. R. Hui, S. Sathiakumar, K. K. Tse, and H. Chung,“A comparison of deterministic and non-deterministic switchingmethods for dc–dc converters,”IEEE Trans. Power Electron., vol. 13,pp. 1046–1055, Nov. 1998.

[15] M. M. Bech, J. K. Pedersen, F. Blaabjerg, and A. M. Trzynadlowski, “Amethodology for true comparison of analytical and measured frequencydomain spectra in random PWM converters,” inProc. IEEE Power Elec-tron. Spec. Conf., 1998, pp. 36–43.


K. K. Tse (S'95) received the B.Eng. degree inelectrical engineering (with honors) from the HongKong Polytechnic University, Hong Kong, in 1995and the Ph.D. degree from the Department ofElectronic Engineering, City University of HongKong, Hong Kong, in 2000.

He is a Research Fellow with the Department ofElectronic Engineering, City University of HongKong. He has authored over eighteen technicalpapers in his research interests, which includecomputer-aided simulation technique, numerical

modeling methods, EMI reduction, and random switching scheme for dc–dcconverters.

Dr. Tse received First Prize in the 1998 IEEE Postgraduate Student PaperContest, IEEE Hong Kong Section, and third prize in 1998 IEEE Region 10Postgraduate student paper contest.

Henry Shu-Hung Chung (S'92–M'95) received theB.Eng. degree (with first class honors) in electricalengineering and the Ph.D. degree from The HongKong Polytechnic University, Hong Kong, in 1991and 1994, respectively.

Since 1995, he has been with the City Universityof Hong Kong, where he is currently an AssociateProfessor in the Department of Electronic Engi-neering. His research interests include time- andfrequency-domain analysis of power electroniccircuits, switched-capacitor-based converters,

random-switching techniques, digital audio amplifiers, fuzzy-logic control, andsoft-switching converters. He has authored over 105 technical papers includingover 47 journal papers.

Dr. Chung received the China Light and Power Prize and was awarded theScholarship and Fellowship of the Sir Edward Youde Memorial Fund, in 1991and 1993, respectively. He is currently Chairman of the Council of the SirEdward Youde Scholar's Association and IEEE student branch counselor. Hewas track chair of the technical committee on power electronics circuits andpower systems of IEEE Circuits and Systems Society in 1997–1998. He iscurrently an Associate Editor of the IEEETRANSACTIONS ONC IRCUITS AND

SYSTEMS—PART I. He has also been listed inMarquis Who's Who in the World.

S. Y. (Ron) Hui (SM'94) was born in Hong Kongin 1961. He received the B.Sc. degree (with honorsfrom the University of Birmingham, U.K. in 1984,and the D.I.C. and Ph.D. degrees from the ImperialCollege of Science, Technology, and Medicine,London, U.K., in 1987.

He was a Lecturer in power electronics at the Uni-versity of Nottingham, U.K. from 1987 to 1990. In1990, he went to Australia and took up a lectureshipat the University of Technology, Sydney, Australia,where he became a Senior Lecturer in 1991. Later,

he joined the University of Sydney and was promoted to Reader of ElectricalEngineering and Director of Power Electronics and the Drives Research Groupin 1996. He is now a Chair Professor of Electronic Engineering at the City Uni-versity of Hong Kong. He has published over 130 technical papers, includingover 70 refereed journal publications. His research interests include all aspectsof power electronics.

Dr. Hui is a Fellow of the IEE, the IEAust and the HKIE. He is an AssociateEditor of the IEEE TRANSACTIONS ONPOWER ELECTRONICS.

H. C. So(M'95) was born in Hong Kong in 1968. Hereceived the B.Eng. degree in electronic engineeringfrom the City Polytechnic of Hong Kong, HongKong, in 1990 and the Ph.D. degree in electronicengineering from the Chinese University of HongKong, Hong Kong.

From 1990 to 1991, he was an Electronic Engineerwith the Research and Development Division, EverexSystems Engineering, Ltd., Hong Kong. From 1995to 1996, he worked as a Post-Doctoral Fellow at theChinese University of Hong Kong. He is currently a

Research Assistant Professor in the Department of Electronic Engineering, CityUniversity of Hong Kong. His research interests include adaptive signal pro-cessing, detection and estimation, source localization, and wavelet transform.

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