Single-capacitor phase-controlled series resonant converter - Circuits

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I.

FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 40, NO. 6, JUNE 1993

383

Single-Capacitor Phase-Controlled Series Resonant Converter Dariusz Czarkowski and Marian K. Kazimierczuk, Senior Member, IEEE

Abstract- A new phase-controlled series resonant dddc converter is described, analyzed, and experimentally verified. The circuit comprises a phase-controlled inverter and a Class D current-driven rectifier. The phase-controlled inverter consists of two switching legs, two resonant inductors, and a single resonant capacitor connected in series with an ac load. The phase shift between the voltages that drive the MOSFET’s is varied to control the ac current of the inverter and thereby regulate the dc output voltage of the converter. A frequency-domain analysis is used to derive basic equations which govern the circuit operation. An important advantage of the converter is that the operating frequency can be maintained constant. For operation at a switching frequency greater than 1.15 resonant frequency, the load of each switching leg is inductive. The proposed converter has an excellent full-load and part-load efficiency. An experimental prototype of the converter with a center-tapped rectifier was built and extensively tested at an output power of 78 W and a switching frequency of 200 kHz. The theoretical and experimental results were in good agreement.

I. INTRODUCTION

P

HASE-CONTROLLED series resonant inverters [ I]-[3] and converters [4]-[7] can be operated at a fixed frequency, while conventional resonant converters [8]-[ 121 are controlled by varying the operating frequency, usually over a wide range. A variable operating frequency is a very undesirable feature because it is difficult to handle electromagnetic interference (EMI) and filtering problems and to effectively utilize magnetic components. In the phase-controlled inverters described in [3], [4], two switching legs are used to drive one resonant circuit. A phase shift between the pairs of the drive voltages of power switches is varied to regulate the dc output voltage. However, the resonant circuit represents an inductive load for one switching leg and a capacitive load for the other. For power MOSFET’s and IGBT’s, operation with inductive loads is preferred [ 111. For capacitive loads, current spikes are generated by reverse recovery of antiparallel diodes. Snubbers can alleviate this problem, but the converter circuit becomes complex. On the other hand, thyristors do not turn off naturally with inductive loads and therefore cannot be used as power switches in such converters. The singlecapacitor phase-controlled series resonant converter analyzed in this paper eliminates the aforementioned drawback by using two identical resonant inductors. This arrangement results in inductive loads for both switching legs when the operating Manuscript received November 4, 1992; revised February 24, 1993. This work was supported by the National Science Foundation under Grant ECS8922695. This paper was recommended by Associate Editor John Choma, Jr. The authors are with the Department of Electrical Engineering, Wright State University, Dayton, OH 45435. IEEE Log Number 9209003.

Fig. I .

Single-capacitor phase-controlled Class D series resonant inverter.

frequency is higher than the resonant frequency by a factor of 1.15. Therefore, power MOSFET’s without snubbers can be used as power switches. The objective of this paper is to present a new phasecontrolled series resonant converter along with the frequencydomain analysis for steady-state operation, and experimental results. The significance of this work is that it introduces a new efficient constant-frequency resonant converter along with tools for its analysis and design. The phase-controlled Class D inverter shown in Fig. I consists of a dc input voltage source V I ,two switching legs, two resonant inductors L, one resonant capacitor C , an ac load R,, and a coupling capacitor Cc. Each switching leg comprises two switches with antiparallel diodes. If the load resistance Ri in the inverter of Fig. 1 is replaced by one of the Class D current driven rectifiers [13] shown in Fig. 2, a single-capacitor phase-controlled series resonant converter (SC PC SRC) is obtained. Its dc output voltage Vo can be regulated against load and line variations by varying the phase shift between the voltages which drive switching legs while the operating frequency is maintained constant.

11. ANALYSIS OF CLASS D

PHASE-CONTROLLED INVERTER

A. Assumptions The analysis of the phase-controlled Class D inverter of Fig. 1 is performed under the following simplifying assumptions:

The loaded quality factor Q L of the resonant circuit is high enough that the currents i l and i 2 through the resonant inductors are sinusoidal. The power MOSFET’s are modeled by switches with ON-resistance rDs. The reactive components of the resonant circuit are linear, time invariant, and do not have parasitic resonances. Both resonant inductors are identical.

B. Voltage Transfer Function of Phase-Controlled Class D Inverter In Fig. 1, the switching legs and the dc input VI form square-wave voltage sources. Since the currents i l and 22

1057-7122/93$03.00 0 1993 IEEE

~

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FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 40, NO. 6 , JUNE 1993

and

respectively. Using the principle of superposition, one obtains the voltage across the branch C-R;

(b) n:l

and the output voltage of the inverter

v, cos ($)

v o = VCRRi 1 -

U-

~ i + mi + . j ~ L ( z - % )

(C) Fig. 2. Class D current-driven rectifiers. (a) Half-wave rectifier. (b) Transformer center-tapped rectifier. (c) Bridge rectifier.

2v, cos

-

(2)

n [ l + j Q r . ( Zthrough the resonant inductors are sinusoidal, only the power of the fundamental component of each input voltage source is transferred to the output. Therefore, the square-wave voltage sources can be replaced by sinusoidal voltage sources representing the fundamental components as shown in Fig. 3. These fundamental components are

(wt

+ ;)

711

= V,COS

v2

= v, cos ( w t -

and

;)

%)]

(9)

J2/Lc

where w, = is the resonant frequency, Q L w,L/(2&) = 2,/(2R’) is the loaded quality factor, and 2, = is the characteristic impedance of the resonant circuit. The factor “2” in this definition arises from the fact that the series connection C-R, can be divided into two identical branches C/2-2Ri at 4 = 0. Thus, one can imagine the SC PC SRC as two identical conventional series resonant inverters: inverter 1 and inverter 2, in which the resonant capacitors and the ac loads are connected in parallel. Rearrangement of (9) gives the dc-to-ac voltage transfer function of the phasecontrolled Class D inverter

d m

where 2 v, = -v, 7T

(3)

and 4 is the phase shift between 211 and w ~ The . voltages at the inputs of the resonant circuits are expressed in the complex domain by

v1 = Vmed4/2)

Hence, the magnitude of M I is

(4)

and

v2 = vme-W2).

(5)

The voltages across the branch C-Ri caused by voltage sources V1 and V2 separately, i.e., with the other voltage source shorted, are expressed as

v1[ (Ri + &)l l j w L]

VCRi = . JWL

+ [(R’ + &)IljwL]

-VCR =

I1 =

jwL

avI

(6)

{ % sin (a) +

Fig. 4 illustrates M I as a function of loaded quality factor Q L and phase shift 4 at f / f o = 1.33. The currents through the resonant inductors L of inverter 1 and inverter 2 are given by (12), and by (13), next page. Hence, one arrives at the amplitude of the current through the resonant inductor of inverter 1 (see (14) next page) and the amplitude of the current through the resonant inductor of inverter 2 (see (15)

QL

cos

($)

-

~ Q sin L

sZo[l + ~ Q L ( :

-

($)[(2)’-l)] }

%)]

CZARKOWSKl AND KAZIMIERCZUK: PHASE-CONTROLLED SERIES-PARALLEL RESONANT CONVERTER

385

1.1 1

9

V1

5

.a

51

.7 6

5 A

0

30

60

90

120

150

180

120

150

180

@I Fig. 3. Equivalent circuit of the phase-controlled Class D inverter of Fig. 1 for the fundamental component.

(a)

0

30

90

60

4 w

(b) Fig. 4. Three-dimensional representation of the magnitude of the dc-to-actransfer function of the phase-controlled Class D inverter M I as a function of Q1, and $ at f/fo = 1.33.

Fig. 5. Normalized amplitudes of the currents through the resonant circuits as functions of q5 at f / f o = 1.33 and Q L = 1. 3, and 5. (a)ImlZo/Vr versus 4. (b) Im2Z,/Vr versus$.

below). Fig. 5 shows normalized amplitudes I m l Z o / V ~and ImZZo/VI as functions of (b at f / f o = 1.33 and Q L = 1, 3, and 5. The output current is

are examined. From (4) and (12), the impedance seen by the voltage source YI is given in (17), next page, and, from (5) and (13), the impedance seen by the voltage source v2 is given in (1 8), next page. Fig. 6 depicts principal arguments 41and $9 as functions of q5 at f / f o = 1.33 and Q L = 1, 3, and 5. Numerical calculations and experimental evidence show that $1 and $2 are positive for f / f o > 1.15 at any load and any phase shift. This indicates that both the inverter 1 and the inverter 2 are loaded by inductive loads for f / f o > 1.15. In the converter design given in Section IV, the normalized operating frequency is f /fo = 1.33. Therefore, the figures in this section are drawn for f / f o = 1.33.

To determine whether the switches are loaded capacitively or inductively, the impedances seen by the switching legs at the fundamental frequency are calculated and their angles

v2 I2

=

-

VCR -

*

VI { ,"" sin ( 2 )

-

jwL

2vI iml= nzo

+ Q L COS ($)+ ~ Q sinL (g) [ (3)' -l)] } ~ z o [ 1+ ~ Q L ( E 3)] -

[%sin($)

+ Q L c o s ( $ ) ] ~ + Q ~ ~ ~ ~ ~ ( $ ) [ ( ~ ) ~ - ~ ] ~ 2

1+Q;(:-3)

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FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 40, NO. 6, JUNE 1993

D inverter is obtained as

120 100

2v; cos2

V;“) PRa = -

(g )

Ri

.

(21)

40

0

30

90

60

120

150

The parasitic resistance of each switching leg with resonant inductor can be estimated as T = T D S T L rc,/2, where rDs = (rDS1 T D S 2 ) / 2 is the average resistance of the onresistances of the MOSFET’s, T L is the ESR of the resonant inductor, and TC, is the ESR of the coupling capacitor C1. Hence, one obtains the conduction power loss in the switching legs and the inductors of inverter 1 and inverter 2 as PT1 = 7-1$,/2 and PT2 = r I k 2 / 2 ,respectively. Substituting (14) and (15) into these equations, one obtains the conduction loss in four MOSFET’s, two inductors L, and coupling capacitor C,

180

100

80

_. -,

; .

+ +

+

4r)

60

40 20

0

30

60

90

120

150

180

(b)

Fig. 6. Phases of the input impedances 2 1 and 2 2 versus 6 atf/fo = 1.33 and Q L = 1. 3 and 5. (a) ~1 versus 0.(b)ci2 versus 4.

(22) The maximum value of the amplitude of the current through the resonant inductor I,(,,,, can be found from (14) because I,1 is always greater than Im2. Hence, one obtains the maximum amplitude of the voltage across the resonant inductor L as

The maximum value of the voltage across the resonant capacitor C occurs at a full load and is

where Io,(m,,, is the maximum value of the amplitude of the output current of the inverter. C. EfJiciency of Phase-Controlled Class D Inverter

From (1 l), the output power of the phase-controlled Class

V1

21 E - = I1

2 -x WO

COS($)QL(E 2 ) +sin($) -

sin($)QL(z

-

%)

The conduction loss in the resonant capacitor C is found as

where Io(,,s) is the rms value of the output current given by (16) and r c is the ESR of the resonant capacitor C . The total conduction loss in the inverter is given in (24), next page. Neglecting switching losses, drive power, and second-order effects (such as nonlinear interactions) and using (21) and (24), one arrives at the efficiency of the phase-controlled inverter by using the calculation shown in (25), next page. Fig. 7 shows the efficiency of the inverter as a function of phase shift 4 and loaded quality factor Q L for f / f o = 1.33, r = 2 R,r c = 0.2 R,and 2, = 226 R.It can be seen that the inverter has an excellent efficiency at both full and part loads. The dc-to-ac voltage transfer function of the actual inverter is shown in (26), next page.

+j[sin($)QL(E +:j[sin($)

-

3)- c o s ( $ ) ]

+QL$cos($)]

- Zl@1

(17)

387

CZARKOWSKI AND KAZIMIERCZUK: PHASE-CONTROLLED SERIES-PARALLEL RESONANT CONVERTER

100

95

75 7n I -

o

30

60

90

120

150

iao RL(Q)

W) Fig. 7. Inverter efficiency '11 as a function of 0 atf / f o = 1.33, 2, = 226 R,r = 2 R,r r = 0.2 R,and Q L = 1, 3, and 5.

Fig. 8. Phase shift @ versus load resistance RL at VI = 270 V and Vo = 28 V.

90

111. CLASSD CURRENT-DRIVEN RECTIFIERS

80

A comprehensive analysis of the Class D current-driven rectifiers of Fig. 2 is given in [13]. The final design equations are given below.

70

$

60 50

40

A. Class D Half-Wave Recti'er A circuit of a Class D half-wave rectifier is depicted in Fig. 2(a). Its input resistance is shown in (27) at the bottom of this page, where V R is~ the amplitude of the fundamental component U R of the rectifier input voltage, n is the transformer turns ratio, 71tr is the transformer efficiency, VF is the diode forward voltage, R F is the diode forward resistance of the "battery-resistance'' large-signal model of the diode for the on-state, and TESR is the ESR of the filter capacitor Cf. The efficiency of the rectifier is

30 270

275

285

280

295

290

300

WV)

Fig. 9. Phase shift

Q

versus VI at full load RL

= 10 R andVo = 28 V

100

95

-

90

P

85

80 10

where P; is the input power of the rectifier. The ac-to-dc voltage transfer function of the rectifier is

MR

vo VR"

*

+ *($

20

25

30

35

40

45

50

RL(R)

Fig. 10. Efficiency

V t r

,Jz[l+ % +

15

of the converter versus load resistance R L atV1 = 270 V and \ b = 28 V

- l)]

(29)

where

T/Rrms is the rms value of the rectifier input voltage.

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388

(c) S ~ and drain currents 2~~ and zo2 of bottom transistors of inverter 1 and inverter 2 at Fig. 11. Waveforms of drain-to-source voltages ~ D andrDs4 1) = 270 V and 10 = 28 V.(a) R L = 10 0. (b) RL = 50 0. (c) R L = x.Vertical: 200 V and 1 Ndiv.; horizontal: 1 ps/div.

and

The peak value of the diode forward current is (30) IDhrI

= TI0

vo MR E VRrms

TVtr

2

4

1

+ $+

+ F ( G - l)]. (34)

and the peak value of the diode reverse voltage is

The peak value of the diode forward current is

VDRM= Vo.

IDM=

B. Class D Transformer Center-Tapped Recti$er

TI0

-

2

(35)

and the peak value of the diode reverse voltage is

The parameters of the transformer center-tapped rectifier depicted in Fig. 2(b) are

(g

+ V R = - PO =

P;

Vtr

1+%+*+cLsE(Tz-1) Vo

~ R L

RL

8

-

')]

C. Class D Bridge Rect$er

(32)

The parameters of the bridge rectifier shown in Fig. 2(c) are

389

CZARKOWSKI AND KAZIMIERCZUK PHASE-CONTROLLED SERIES-PARALLEL RESONANT CONVERTER

(b)

Fig. 13. Waveforms of drain-to-source voltages U D S ~andaDs4 of bottom transistors at VO = 28 V and R L = 10 R. (a)VI = 270 V. (b) VI = 300 V. Vertical: 200 V/div.; horizontal: 1 pddiv.

Let us assume

fo

= 150

kHz and

f/fo

= 1.33. Hence,

f = 200 kHz. Consider the case for full power for which

Fig. 12. Waveforms of drain-to-source voltages 1 ' ~ asn~d t ' ~ s 4of bottom transistors at \> = 270 V and 10 = 28 V. (a)RL = 10 R. (b) R L = 50 R. (c) R L = ca. Vertical: 200 Vldiv.; horizontal: 1 pddiv.

P o m a x = 78.4 W and Iomax= 2.8 A. Assume the rectifier efficiency VR = 95% and the transformer tums ratio n = 2.5. From (32) and (33), the input resistance of the rectifier is found to be Ri = 53.3 R. Using (34), one can calculate MR = 0.422. Assuming the inverter efficiency 71 = 94%, the voltage transfer function of the inverter is calculated as M I = V O / ( ' f ) I V I m i n h f R ) = 0.261. Assume COS($/^) = 0.9. From ( I I ) , one obtains Q L = 2.03. Hence, L = ( 2 R ; Q t ) / w o = 229.6 pH and C = 2/(w?L) = 9.8 nF.

V. EXPERIMENTAL RESULTS

To verify the equations derived above, the circuit designed in Section IV was breadboarded, using IRF740 MOSFET's (Intemational Rectifier) as switches, IR3 1DQ06 Schottky diodes, L = 240 pH, C = 9.4 nF, an isolation transformer The peak value of the diode forward current is with n = 2.5, and Cf = 47 pF. An ML4818 (Microlinear) TI0 IC was used to drive the MOSFET's and shift the phase IDM = 2 4. The measured value of the resonant frequency fo was 150 kHz and the measured value of the switching frequency and the peak value of the diode reverse voltage is fa was 200 kHz. The on-resistance of each MOSFET was r D s = 0.5 R and the value of ESR of each resonant inductor L was T L = 1.5 R. Hence, the parasitic resistance of each inverter T was estimated to be 2 Q. The value of ESR of IV. DESIGNEXAMPLE the resonant capacitor C was TC = 0.2 R. The parameters A transformer single-capacitor phase-controlled series res- of the rectifier were: VF = 0.4 V, RF = 0.075 R , and onant converter consisting of the inverter of Fig. 1 and the rESR = 0.05 0. The characteristics of the converter were measured as funccenter-tapped rectifier of Fig. 2(b) is designed. The specifica~ R.~ tions ~ of the load resistance RL and the dc input voltage VI tions are: VI = 270 to 300 V, VO= 28 V, and R L = 10

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Fig. 15. Voltage and current waveforms of converter with center-tapped rectifier at \'I = 270 V, 4 = O o , and short circuit at the output. (a) Waveforms of voltage 7 : ~across the resonant capacitor and currentszl and 22 through the resonant inductor. Vertical: 200 V/div. and1 Ndiv.; horizontal: 1 ps/div. (b) Waveforms of voltage U D and current io of rectifier diode. Vertical: 10 V and ,5 Ndiv.; horizonta1:l psldiv.

depicts the drain-to-source voltage waveforms of the bottom transistors of the inverters at VI = 270 V and RL = 10, 50 0, and CO. The drain-to-source voltage waveforms of the bottom transistors for RL = 10 R and VI = 270 and 300 V are displayed in Fig. 13. Fig. 14 shows the waveforms of the voltage across the resonant capacitor and the currents through Fig. 14. Waveforms of voltage Z'C across the resonant capacitor (upper trace) the resonant inductors of the inverters for RL = 10, 50 R, and and currents 21 and 22 through resonant inductor of inverter 1 (middle trace) and inverter 2 (lower trace), respectively, atl/l = 270 V and Vo = 28 V. 00. It can be seen that as load was decreased these waveforms (a) R L = 10 CL. (b) R L = 50 R.(c) R L = W . Vertical: 200 Vldiv. and 1 became more distorted from initial sinusoids. At no load, the Ndiv.; horizontal: 1 ps/div. currents became triangular and the voltage constant (with small ripples due to an unavoidable circuit asymmetry). The behavior of the converter with a short circuit at the output was tested and at the fixed dc output voltage VO= 28 V. The measured and it was found that the operation is safe for any value of 4. Fig. calculated characteristics of the phase 4 as a function of load 15(a) depicts the waveforms of the voltage across the resonant resistance RL at VI = 270 V and VO = 28 V are shown in capacitor and the currents through the resonant inductors and Fig. 8. Fig. 9 depicts plots of measured and calculated 4 as a Fig. 15(b) depicts the voltage and current waveforms of a function of VI at full load resistance RL = 10 R and Vo = 28 diode in the rectifier at VI = 270 V and 4 = 0". The output V. Plots of the measured and calculated converter efficiency current with a short circuit at the output and 4 = 0" was (excluding the drive power) versus RL are shown in Fig. 10 10 = 7.6 A. For the open circuit at the output, the converter for VI = 270 V and VO = 28 V. The part load efficiency of operation was safe at high values of the control angle 4 . A the converter is very good. It can be seen that the measured decrease of 4 may lead to a voltage breakdown of the rectifier and calculated characteristics of the converter were in good diodes. agreement. Fig. 11 depicts the waveforms of the drain-to-source voltVI. CONCLUSIONS ages and drain currents of the bottom transistors in inverter 1 A frequency-domain analysis and experimental results for a and inverter 2 for the load resistances RL = 10, 50 0, and single-capacitor phase-controlled series resonant converter was 00, which corresponds to full load, 20% of full load, and no load, respectively. The figure shows that the switching legs given. Basic features of the converter are summarized below: were loaded inductively. The phase shift 4 was measured ob1) The converter can regulate the output voltage VO from serving drain-to-source voltage waveforms of switches. Fig. 12 a full load to infinity by varying the phase shift between

CZARKOWSKI AND KAZIMIERCZUK: PHASE-CONTROLLED SERIES-PARALLEL RESONANT CONVERTER

2)

3) 4)

5) 6)

7)

the drive voltages of the two inverters while maintaining a fixed operating frequency. Both inverters are loaded by inductive loads for f / f o > 1.15. The efficiency of the converter is high at light loads. The converter is inherently short-circuit and open-circuit protected by the impedances of the resonant circuits. The converter with the transformer turns ratio TI = 1 is a step-down converter. Unlike in most other converters, very low values of the dc-to-dc voltage transfer function are achievable in a single stage. The operation at a constant frequency and inductive loads for both switching legs is achieved at the expense of a second resonant inductor.

REFERENCES H. Chireix, “High power out phasing modulation,” Proc. IRE, vol. 23, pp. 1370-1392, NOV. 1935. F. H. Raab, “Efficiency of out phasing RF power-amplifier systems,” IEEE Trans. Commun., vol. COM-33, pp. 1094-1099, Oct. 1985. I. J. Pitel, “Phase-modulated resonant power conversion techniques for high-frequency link inverters,” IEEE Trans. Ind. Appl., vol. IA-22, pp. 1044-1051, Nov./Dec. 1986. F. S . Tsai and F. C. Y. Lee, “A complete dc characterization of a constant-frequency, clamped-mode, series-resonant converter,” in IEEE Power Elecrronics Specialisrs Conf Rec. (Kyoto, Japan, April 11-14, 1988), pp. 987-996. M. K. Kazimierczuk, “Synthesis of phase-modulated resonant dc/ac inverters and dc/dc convertors,” IEE Proc., Pr. B, Electric Power Appl.. vol. 139, pp, 387-394, July 1992. D. Czarkowski and M. K . Kazimierczuk, “Phase-controlled CLL resonant converter,” presented at the IEEE Applied Power Electronics Conference (APEC’93), San Diego, Calif., Mar. 7-1 I , 1993, pp. 488-493. M. K. Kazimierczuk and D. Czarkowski, “Phase-controlled series resonant converter,” presented at the IEEE Power Electronics Specialists Conf. (PESC’93), Seattle, Wash., June 20-24, 1993, pp. 1002-1008. R. J. King, and T. A. Stuart, “A normalized model for the half-bridge series resonant converter,” IEEE Trans. Aerosp. Elecrron. Syst.. vol. AES-17, pp. 190-198, Mar. 1981. V. Vorpirian and S. Cuk, “A complete dc analysis of the series resonant converter,” in IEEE Power Electronics Specialists Conf: Rec. (Cambridge, Mass., June 14-17, 1982), pp. 85-100. A. F. Witulski and R. W. Erickson, “Design of the series resonant converter for minimum stress,” IEEE Trans Aerosp. Electron. Syst.. vol. AES-22, pp. 356363, July 1986.

39 1

[ l 11 R. L. Steigerwald, “A comparison of half-bridge resonant converter topologies,” IEEE Trans. Power Electron., vol. PE-3, pp. 174-182, Apr. 1988. [ 121 T. Sloane, “Design of high-efficiency series-resonant converters above resonance,” IEEE Trans. Aerosp. Electron. Syst., vol. 26, pp. 393402, Mar. 1990. [13] M. K. Kazimierczuk, “Class D current-driven rectifiers for dc/dc converter applications,” IEEE Trans. Ind. Electron., vol. 38, pp, 1165-1 172, Nov. 1991.

Dariusz Czarkowski received the M.S. degree in electronics engineering and the M.S. degree in electrical engineering from University of Mining and Metallurgy, Cracow, Poland, in 1988 and 1989, respectively. In 1989, he joined the Moszczenica Coal Mining Company and from 1990 he worked as an Instructor at University of Mining and Metallurgy. He is presently a Research Assistant at the Department of Electrical Engineering, Wright State University, Dayton, OH. His research interests are in the areas of the modeling and control of power converters, electric drives, and modem power devices.

Marian K. Kazimierczuk received the M S., and Ph.D , and D Sci degrees in electronics engineering from the Department of Electronlcs, Technical University of Warsaw, Warsaw, Poland, in 1971, and 1978, and 1984, respectively He was a Teaching and Research Assistant from 1972 to 1978 and Assistant Professor from 1978 to 1984 with the Department of Electronics, Institute of Radio Electronics, Technical University of Warsaw, Poland In 1984, he was a Project Engineer for Design Automation, Inc., Lexington, MA In 198485, he was a Visiting Professor with the Department of Electncal Engineering, Virginia Polytechnic Institute and State University, VA Since 1985, he has been with the Department of Electrical Engineering, Wright State University, Dayton, OH, where he is currently an Associate Professor His research interests are in high-frequency high-efficiency power tuned amplifiers, resonant dc/dc power converters, dc/ac inverters, high-frequency rectifiers, and lighting systems He has published over 120 technical papers, more that 50 of which have appeared in IEEE Transactions and Joumals Dr Kazirmerczuk received the IEEE Harrell V. Noble Award in 1991 for his contributions to the fields of aerospace, industnal, and power electronics He is also a recipient of the 1991 Presidential Award for Faculty Excellence in Research and the 1993 Teaching Award from Wright State University.