for the phasecontrolled seriesparallel resonant converter with a centertapped rectifier at an output power of 52 W and a switching frequency of 127 kHz.
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PhaseControlled SeriesParallel Resonant Converter Dariusz Czarkowski and Marian K. Kazimierczuk, Senior Member, IEEE
AbstractA constantfrequency phasecontrolled seriesparallel resonant dcdc converter is introduced, analyzed in the frequency domain, and experimentally verified. To obtain the dcdc converter, two identical seriesparallel resonant inverters are paralleled and the resulting phasecontrolled resonant inverter is loaded by a voltagedriven rectifier. The converter can regulate the output voltage at a constant switching frequency in the range of load resistance from fullload resistance to infinity while maintaining good partload efficiency. The efficiency of the converter is almost independent of the input voltage. For switching frequencies slightly above the resonant frequency, power switches are always inductively loaded, which is very advantageous if MOSFET’s are used as switches. Experimental results are given for the phasecontrolled seriesparallel resonant converter with a centertapped rectifier at an output power of 52 W and a switching frequency of 127 kHz. The measured current imbalance between the two inverters was as low as 1.2:l.
I. INTRODUCTION
R
ESONANT power conversion technology offers many advantages in comparison with PWM one. Among them are low electromagnetic interference (EMI), low switching losses, small volume and weight of components due to high operating frequency, high efficiency, and low reverserecovery losses in diodes because of low d i l d t at turnoff. However, most frequencycontrolled resonant converters, e.g., [ 11[4], suffer from a wide range of frequencies which is required to regulate output voltage against load and line variations. This makes it difficult to filter EM1 and effectively utilize magnetic components. As a remedy for these problems, several fullbridge topologies of phasecontrolled resonant inverters and converters have been proposed and analyzed [SI[ 151. In these circuits, the operating frequency can be maintained constant. A drawback of some phasecontrolled converters is that as one leg of MOSFET switches is loaded inductively, the other is loaded capacitively [8]. For inductive loads, there is no tumon loss, but there is tumoff loss. In contrast, for capacitive loads, there is no tumoff loss, but there is tumon loss. However. for capacitive loads, the antiparallel diodes generate high current spikes and switching losses, considerably reducing efficiency. Therefore, for power MOSFET’s, the inductive load conditions are preferred [I], [ 14). References [ 131[ 151 describe phaseshift resonant converter topologies in which all four MOSFET switches are inductively tumedoff and have very little penalty on conduction losses. This paper presents a new phasecontrolled ceriesparallel resonant converter ( P C SPRC), its steadystate analysis in the Manuscript received July 5 , 1992: revised February 19, 1993. This work was supported by the National Science Foundation by Grant ECS8922695. The authors are with the Department of Electrical Engineering, Wright State University, Dayton, OH 45435. IEEE Log Number 92093 1 1.
I
1
1
1 b
J
Fig. 1. Class D voltageswitching phasecontrolled seriesparallel inverter.
frequency domain, design equations, and experimental results. In the proposed circuit, two identical seriesresonant circuits share the same ac load. At operating frequencies higher than the resonant frequency, power switches are loaded inductively. This allows an easy use of power MOSFET’s because snubbers are not required [I]. The proposed converter is efficient at part load because the amplitudes of the currents through the resonant circuits and switches decrease with increasing load resistance and are well balanced. Fig. 1 depicts a Class D phasecontrolled seriesparallel resonant inverter (PC SPRI). It consists of two conventional Class D voltageswitching seriesparallel inverters [ 11[4]: inverter 1 and inverter 2. Each inverter is composed of two switches with their antiparallel diodes, a seriesresonant circuit LCl, and an ac load resistance 2R, connected in parallel with the capacitor C2/2. The parallel combination of capacitors C2/2 and load resistances 2R, results in capacitor Cz and the load resistance R,. If the load resistance R, in the inverter of Fig. 1 is replaced by one of the Class D voltagedriven rectifiers analyzed in [ 161 and shown in Fig. 2, a phasecontrolled seriesparallel resonant converter is obtained. Its dc output voltage Vo can be regulated against load and line variations by varying the phase shift between the voltages that drive inverter 1 and inverter 2 while maintaining a fixed operating frequency and inductive loads for both pairs of switches. For inductively loaded switching legs, zerovoltage switching can be accomplished by adding a shunt capacitor in parallel with one of the switches in each leg and using a dead time in drive voltages of MOSFET’s [ 1611 181. The converter is suitable for mediumtohigh power applications with the upper switching frequency limit of 150 kHz, as recommended in 1141. 11. ANALYSIS OF CLASSD PHASECONTROLLED
SERIESPARALLEL RESONANTINVERTER
A . Assumptions The analysis of the PC SPRI of Fig. 1 begins with the following simplifying assumptions: 1) The loaded quality factor Q L of the inverter is high enough so that the currents il and i 2 are sinusoidal.
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VOL. 8. N0.3 ,JULY 1993
Fig. 3. Equivalent circuit for the fundamental components of the Class D phasecontrolled inverter of Fig. 1.
Using the principle of superposition, one obtains the output voltages due to the voltages V1 and V2,respectively,
+ 
where
"0 (c) Fig. 2. Class D voltagedriven rectifiers. (a) Halfwave rectifier. (b) Transformer centertappedrectifier. (c) Bridge rectifer.
2) The power MOSFET's are modeled by switches with ONresistances
+
A = G z / ( 2 c i ) ,C = ( C i C z / 2 ) / ( C i C z / 2 ) , =
WO
TDS.
3) The reactive components of the resonant circuits are
d m
is the corner frequency and QL
2 R i / ( ~ o L= ) 2Ri/Zo
is the normalized load resistance (or the loaded quality factor). The factor 2 arises from the configuration of a single inverter (1 or 2) in which the value of the parallel capacitor is C2/2 and the load is 2&. Using (3), (6), and (7), one arrives at the output voltage of the inverter
passive, linear, time invariant, and do not have parasitic resonances. 4) Components of both resonant circuits are identical.
B . Voltage Transfer Function of Class D PhaseControlled SeriesParallel Inverter Each switching leg and the dc input voltage source VI of the inverter shown in Fig. 1 form a squarewave voltage source. Since the input currents 21 and 22 of the resonant circuits are sinusoidal, only the power of the fundamental component of each input voltage source is transferred to the resonant circuit. Therefore, the squarewave voltage sources can be replaced by sinusoidal voltage sources that represent the fundamental components as shown in Fig. 3. These fundamental components are described by v1 = V,cos(wt v2
+ )42
that yields the dctoac voltage transfer function of the Class D phasecontrolled inverter
(1)
4 = V,cos(wt  ) 3
(2)
2 = VI
(3)
Let us denote
where
v,
lr
and 4 is the phase shift between v1 and v2. The phasors of the voltages at the input of the resonant circuits are expressed by
v1= Vmej(@/2)
(4)
and W w wo A b (  , A ) = (  ). WO wo wA+1
CZARKOWSKI AND KAZIMIERCZUK: PHASECONTROLLED SERIESPARALLEL RESONANT CONVERTER
311
Hence,
1 MI I
n
4.
2. I.
Fig. 4 shows ( M II as a function of different pairs of parameters selected from the set 4, QL, w / w o , and A, while the other two parameters are kept constant.
0. 6.
15
C. Currents and Powers of Class D PhaseControlled SeriesParallel Inverter The phasors and the amplitudes of the currents through the resonant inductors are given by (13)(16) below. Fig. 5 shows normalized amplitudes ImlZo/VI and I m 2 Z o / V ~as functions of Q L and 4 for f / f o = 1.1 and A = 1. It can be seen that the amplitudes decrease with 4 and the difference between them is low at any operating point in comparison with their absolute values. The maximum values of the normalized amplitudes ImlZo/VI and Im2Z0/V1occur at low values of 4. Equations (15) and (16) differ by terms containing szn($/2), which are close to zero at low values of 4.Therefore, the current imbalance between the two inverters is small. Since the amplitudes ImlZo/VI and Im2Zo/VI decrease with 4,the converter offers good partload efficiency. Close examination shows that the peak transistor currents are twice as high as those in a fullbridge PWM converter at the same output power. To determine whether the switches are loaded capacitively or inductively, complex powers at the fundamental frequency
0.5
I MI I 1.5 1 .o
0.5 0.0 0.
4. 6. 0. (C)
'
0.
ab (d)
Fig. 4. Threedimensional representation of the magnitude of the dctoac transfer function of the phasecontrolled Class D seriesparallel inverter. (a) 1 . l f I ) as a function of Q L and 0 at f / f o = 1.1 and 4= 1. (b) l~bfllas a function of Q L and 4at f / f o = 1.1 and d = 0. (c) l M ~ las a function of f / f o and A at Q L = 1 and d = 0. (d) IMII as a function of QLand f / f o at A = 1 and o = 0.
are calculated and their angles are examined. Another method for determining the type of the load for the switches is to calculate the impedances Z1 = V1/11 and 2 2 = V2/I2 seen by the voltage sources w1 and 212 at the fundamental frequency.
1993
IEEE TRANSACnONS ON POWER EIEClXONICS. VOL. 8, NO3 , 312
r . \
, 120.
90. 60. 30. 200.
4. I.

200. 0.
1.

0.
0.
Qb.
(b) Fig. 5. Threedimensional representation of the normalized amplitudes of the currents through the resonant circuits atf/ f o = 1.1 and A = 1. (a) I,,,~ZO/V1versus Q L and 4 (b) I,2Z0/1.j versus Q L and 0.
The complex power supplied by the voltage source
211
(b) Fig. 6 . Threedimensional representation of the power angles 4"i and ~2 at f / f o = 1.1 and A = 1. (a) ~ ' versus 1 Q L and 0.(b) $9 versus Q L and 0.
is
1 s1 = v11; 2 zvl' n2Z,b(
z .A )
d, z,A ) + szn(
b( X
$)COS(
$) +j[a(
2,A)  c o s 2 ( $ ) ]
4 E ' A ) Ji&b(EA
=) SI 1
e J W 1=
Pi
(17)
+jQi
where 1 5'1 1 is the apparent power, PI is the real power, Q1 is the reactive power, and $1 = Arg(S1) is the principal argument of SI.The power supplied by the voltage source v2 is
d
b( 2,A )  szn( $)cos( $ )
x
L
+ j [ a (E.4)  cos2( $ ) ]
a( L WO . 4)  j & b (
= 1S2(e31112 = P2 + j Q 2
E.4) (18)
where (5'2) is the apparent power, P2 is the real power, Q2 Fig. 7. Threedimensional representation of the power angles zi, as a function of Qr. and o at f / f o = 1 and .4 = 1. is the reactive power, and $12 = Arg(S2) is the principal argument of S z . Fig. 6 depicts principal arguments $1 and The replacement of resonant capacitors C1 in Fig. 1 by $2 as functions of 4 and QL, for f / f o = 1.1 and A = 1. Close examination shows that $1 and $2 are always positive coupling capacitors results in a topology of a phasecontrolled for f / fo > 1.03 at A = 1. This indicates that both inverter 1 parallel resonant inverter (PC PRI). Equations that govern the and inverter 2 are loaded by inductive loads for f/fo > 1.03 operation of PC PRI can be obtained from those given in this section by setting A = 0. It can be shown that, for the PC at A = 1.
CZARKOWSKI AND KAZIMIERCZUK: PHASECONTROLLED SERIESPARALLEL RESONANT CONVERTER
PRI, all switches are loaded inductively for f / f o > 1.07. The replacement of the capacitor Cp by an open circuit results in a topology of a phasecontrolled series resonant inverter (PC SRI). The condition of inductive loads for all switches in the case of PC SRI is f / f o > 1, i.e., operation above resonance. However, equations for PC SRI must be derived separately because w, requires a redefinition. For PC SPRI, the minimum operating frequency f m i n that ensures inductive loads for the switches is, therefore, in the range from f o to 1.07f0 and depends bn A. As was mentioned in the previous paragraph, the condition is f / f o > 1.03 for A = 1. The complex power of the fundamental component S supplied to the inverter is given by (19), (see (19) above) where (SI is the apparent power, P is the real power, and Q is the reactive power supplied to the inverter. The angle $ = Arg(S) is the power factor angle of S and is
+=
The power factor angle $ is depicted in Fig. 7 as a function of 4 and QL for f / f o = 1.1 and A = 1. Although the power of the higher harmonics is neglected, this figure gives useful information about the ratio of real to reactive power in the circuit. The output power of the Class D phasecontrolled inverter is obtained from (19) .
The maximum value of the amplitude of the current through the resonant circuit Im(max)can be found from (15) for operation above the resonant frequency f o . Thus, one obtains the maximum value of the amplitude of the voltage across
313
resonant capacitor C1 Im(ma,,
Vclm = ___
(22)
WC1
and across resonant inductor L VLm = W L 4 n ( 7 n a x ) .
(23)
D. Efficiency of Class D PC SPRI The parasitic resistance of each seriesresonant circuit is r = TDS rL rcl, where T D S = ( T D S 1 T D S ~ ) is / ~ the average resistance of the onresistances of the MOSFET’s, r L is the ESR of the resonant inductor L, and rc1 is the ESR of the resonant capacitor C1. Therefore, one can find the conduction power loss in the seriesresonant circuits of inverter 1 and inverter 2 as Prl = r&/2 and P r 2 = rIL2/2, respectively. Substituting (15) and (16) for Iml and Im2, one obtains the conduction loss in four MOSFET’s, two inductors L , and two capacitors C 1 (see (24) below). Using (9), the conduction loss in the capacitor C, is found as
+ +
+
where rc2 is the ESR of the capacitor C2. The total conduction loss in the inverter is
PT = P r s
f
PCZ

4v;
7r”2,2{[4$>A)l2
+ &[b(:,A)12)
W + 2rc2(1+ A)2()2cos WO
Neglecting switching losses and drive power and using (21) and (26), one arrives at the efficiency of the phasecontrolled
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where V R and ~ 1 ~ ~ are 1 the~ amplitudes of the fundamental components of the rectifier input voltage and current, n is the transformer turns ratio, RL is the load resistance, Titr is the transformer efficiency, VF is the diode threshold voltage, Vo is the dc output voltage, T L F is the dc ESR of the filter inductor, RF is the diode forward resistance, a h w = ( d w ) / 2 = 0.1808, TC is the ESR of the filter capacitor, T L f is the ac ESR of the filter inductor, and L f is the filter inductance. The efficiency of the rectifier is
0.
60
200.0.
'*
(at
where P2 and PO are the input and output powers of the rectifier, respectively. The actodc voltage transfer function of the rectifier is
Fig. 8. Threedimensional representation of the inverter efficiency r ) ~as a function of Q and Q L at f / f o = 1.1,and A = 1, 2, = 202.9 0 , r = 2 . 1 R, and r c 2 = 0.1 R.
inverter (see (27)below). Fig. 8 shows the efficiency of the inverter as a function of phase shift 4 and normalized load resistance Q L for f / f o = 1.1, T = 2.1 0 , T C Z = 0.1 0 , and 2, = 202.9 0. It can be seen that the inverter has an excellent efficiency at both full and part loads. The efficiency at no load is zero, since there are resonant currents, but no output current. The dctoac voltage transfer function of the actual inverter is
111. CLASSD VOLTAGEDRIVEN RECTIFTERS A comprehensive Of the 'lass rectifiers of Fig. 2 was performed in [ 161. The key expressions, from the designer's point of view, are given below.
where V R is ~ the rms value of the rectifier input voltage. The peak values of the diode forward current and the diode reverse voltage are
and
B . Class D Transformer CenterTapped Rectifier Fig. 2(b) depicts a circuit of a Class D transformer centertapped rectifier. The input resistance of the rectifier is
R = VRWI 2 
A . Class D HalfWave Rectifier Fig. 2(a) depicts a circuit of a Class D halfwave rectifier. The input resistance of the rectifier is

IRlin
VF [If+ VO
.ir2n2RL
871tr
RF + T L F RL
+ act
(rc
+r L f ) R LI f 2q
(34) where act = ( d w ) / 2 = 0.0377. The actodc voltage transfer function of the rectifier is
315
CZARKOWSKI AND KAZIMIERCZUK PHASECONTROLLED SERIESPARALLEL RESONANT CONVERTER
120
90 80
100

g !
80
3
U
70 60
60
50
40
40
20 15
45
75
30 150
105
160
170
180
190
200
WV)
R L ( V
Fig. 9. Phase shift 4 versus load resistance RL at VI=150 V and Vo=28 V.
5 and V,= 28 V. Fig. 10. Phase shift 4 versus input voltage V I at R ~ = 1 R
....
70
C. Class D Bridge Rectifier
MSl
84 81
VR E
78
'
15
I
I
I
45
75
105
R L W
and
(a) 95.5 
MR
,
95
F
94.5
e
where ab = act. The peak value of the diode current is given by (32) and the peak value of the diode voltage is R
VDRM= Vo. 2
94 93.5
(40)
i
15
45
75
105
R L P )
(b)
IV. DESIGNEXAMPLE The design procedure is illustrated by a design example of a transformer phasecontrolled seriesparallel resonant converter that consists of an inverter of Fig. 1 and a centertapped rectifier of Fig. 2(b). The specifications of the converter are: VI = 150 to 180 V, Vo = 28 V, and R L , ~ = 15 ~ R.
Fig. 12. Calculated effciencies of the inverter and the rectifier versus load resistance RL at V1=150 V and Vo=28 V. (a) Effciency of the inverter 91. (b) Effciency of the rectifier 1 ) ~ .
The maximum value of the output power is PO,,, = = 52.3 W. Assume that the rectifier efficiency at
V$/&,in
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tapped Voltage .ircuit\. current
inductor II ,,, = 27'4 L The peA \ d u e s ot the diode forward current dnd the diode ItLerse \olt'ige are In11 = 1 87 A and I1111\1
=
V V k \ i ~Rt I ~ IcI I 11 Kr W I rs
To \ didcite the aid>u s . J hie'idboarti of the convertei designed 111 the pic\ IOLI\ \cctioii b a s built, ucing IRF630 MOSFET's (International Kcctifier) as switches, MBR 10100 Schottky diodes ( AZotorola). I, = 2x0 / / H . = 13.6 nF. ( ' ? = 27.2 nF. an isolation transfurnrcr with / I = 2. I,, = 1.:1 mH. and (.',f = IO0 /'I. Ail R . I L A X 1 8 (Micro Linear) IC was uvxi to drile the MC)SFE'l"b ant1 shift the phase Q. The measured value of the resoiiaiit treclucncq' was 1 15.5 k H r was 127 full load is 94% and the transformer turn> ratio is 2:l. Llsing and the measured ~ a l u oc l the sv, itching frequency (34) and (36). one can calculate the minimum value of the AH[, The ONresistaric.r. ot' cacti MOSFET was I ' L ) , ~= 0.4 (2. input resistance of the rectifier R,,,,,,, 7S.80 0.Consider the value of ESK of each resonant inductor at 116 kHr. was operation at full power. From ( 3 s ) . .Ill( = 0.422).Assume r 1 = 1..) 0 . and ilie \ alue o f ESR of each resonant capacitor I ~: 0 . 2 f!, Hcnce. the parasitic resistance that r / I = 9G%, ( J L , , ? , , ) = 0.75.  / d o = I . 1. anti . I 1. From at 127 kH/ \vas was the relationship \ ; I / \ > = ~411,.1A11~ and (2X). 1.211( = O.L>!H i u a s found to be 2. I i!. 'fhc ESK of the capacitor was From (13). (.os(o / 2 ) = 0.94, which corresponds to ('1 = 40" I ( .2 = 0. i 5 1 . 'I'hc e\timatccl tiuiihtormer efficiency /it). and is a suitable value for full power. Assuming = 115 07%. The measured \slur of' the tic rehistance of the filter inductor was 1.1 = 0 . 2 !! iriid the iic resistance of the tilter kHz. one obtains L = % l Z , , , , , , , / ( ~ ~ , C ) ~ ~ and C' = l / ( ~ i : L ) = 6.59 nF. Using ( 1 5 ) and (23). one inductor at I O 0 LHr \ h a > I , / I = 2. I C ? . The ESR of the filter can calculate the maximum value of the \,(>Itageacros'r the capacitor ( ' / wa\ I.( = i 0 in!!. The parameters of the diode 7.) m(1. resonant capacitor I>,1,,1 = 22s V and aci.o\s the resonant iiiodel nerc 11. = ( 1 . 1 I'; t i i d li1 ,fq
1
1
1 :
Fig. 16. Voltage and current wavetomi\ of the converter with 'I centerrapped rectifier at Vi =I50 V. CFO. and a11 opcn circuit at the output. (a! Voltage I ' V J acre\\ capacitor C'l and ciirrt'nt\i~and 12 through the re~onant circuit\. Vertical : 20 V and 1 .4/div: Iiorimntal: 2 2 p r / div. th! Voltnge I , , ) and current (11 of rectitirr diode. Vcitical : 5 V and I .A/di\: honroni:il: 2 / I \ / div.
The characteristics of the converter were measured as functions of the load resistance RI, and the dc input voltage 11 at a fixed dc output voltage 1;) = 28 I. Measured and calculated characteristics of the phase i,, are plotted in Fig. 9 as functions of load resistance RL at 1; = IS0 V and 1;) = 3X V. Fig. 10 depicts plots of measured and calculated o as functions of I; at R L = 15 0 and 1;) = 28 V. Plots of the measured and calculated converter efficiency = r/r r/n (excluding the drive power) versus IZL are portraqed in Fig. 1 1 . The measured efficiency of the converter was 87% at full load and 75% at 20% of full load. The calculated efficiencies versus R L are shown separately for the invcrter and the rectifier i n Fig. 13. Fig. 13 displays plots of the measured and calculated converter efticiency I/ as a function of of 1; at R L = IS !! and I;,= 28 V. The efficiency was virtually independent of \ > . I t can be seen that the measured and calculated characteristics of the converter were in good agreement. Fig. 14 depict5 the uavefornis of the draintosource voltages and drain currents of the bottom transistor4 in inverter 1 and inverter 2 for the load resistances I?L = IS. 75. and 2500 ( 1 , which corresponds to full load. 30% of full load. and 0.6% of full load. respectively. Observe that the converter can regulate the output voltage from full load to no load. For an open circuit at the output, the waveforms of the currents through the remnant circuits iiIe displayd i n Fig. 15(a) and
the koltagc and current waveforms of a diode in the rectifier are shown in Fig. IS(b) at o= 180" and l i = IS0 V. The measured value of the output voltage for an open circuit at the output and at phase shift =180" was \;I =2 V. With an open circuit at the output. a decrease in c:, may lead to a voltage breakdown of the rectifier diodes. The behavior of the converter with a short circuit at the output was also tested and it was found that the operation is safe for any value of (1). Fig. 16(a) depicts the waveforms of the currents through the resonant circuits and Fig. 16(b)depicts the voltage and current waveforms of a diode in the rectifier u ith a short circuit at the 150 V and o= 0". Thc output current was output for I)= c j
IEEE 1'RANSACITIONS ON POWER ELECTRONICS, VOL. 8 , N0.3 , JULY 1993
(b) Fly. 18. Wa\efomi\of drainto\ource voltages I ' / ) . ~ and ( . / I . bottom transistor\ of the imerters at I = 28 V and I ? , = IS
o f rhe 150 \'.
I o = 2.3 A. The phase shift (,!I was measured observing the draintosource voltage waveforms of the switches. Fig. 17 shows the draintosource voltage waveforms of the bottom transistors at \ j =1SO V and R L = 15. 75. and 3500 ( 2 , The draintosource voltage waveforms of the bottom transistors for RL = I 5 Q and \ > = I S 0 and 300 V are displayed in Fig. 18. Fig. 19 shows the waveforms of the voltage across the capacitor ( ' 2 and the currents through the resonant circuits of the inverters for RL, = 15. 75. and 3500 5 1. I t can be seen that these waveforms were approximately 4inusoidal over a wide range of' the load resistance. which contimi5 the assumption 4)in Section 11A. Fig. 19 shows that the imhalance of the currents through serie\ resonant circuits is about 1.3: I . VI. CONCLUSlOh A new phasecontrolled seriesparallel resonant converter has been introduced. analyzed. and experimentally verified. Its basic properties are summarized belom : I ) The converter can regulate the output voltage 1;) from full load to no load by varying the phase shift between the drive voltages of the two inverters while maintaining a tixed operating frequency. 3) Both slvitching legs are loaded b! inductive loads for ' , J , .: 1,0:!1 at  1 = 1 (for ,j"f'. i l.ll7 at ai! . t i and ,f'
therefore powel MOSFET's mithout snubbers can be used as switches. 3) The partload efficiency of the converter is high (Fig. 1 1 ). 4 ) The fullload efficiency of the converter is almost independent of I > . 5 ) The imbalance of amplitude\ of currents flowing through the resonant inductor5 i \ \'er\ IOU (i.e.. 1.2:1 ) over a full range of the load resistance and the line voltage. 6) The converter is inherently short circuit and open circuit protected by the impcdances of the resonant circuits. 7 ) The foregoiny benefitz Lire achieved at the expense of hi gher number of re wiant coni ponen t s .
CZARKOWSKI AND KAZIMIERCZUK: PHASECONTROLLED SERIESPARALLEL RESONANT CONVERTER
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Dariusz Czarkowski was bom in Poland on April 1, 1965. He received the M.S. degree in electronics engineering and the M.S. degree in electrical engineering from the 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 Inshctor 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 (M’91SM’91) received the M.S., and Ph.D., and D.Sci. degrees in electronics engineering from the bepartment of Electronics, 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 19841985, he was a Visiting Professor with the Department of Electrical Engineering, Virginia Polytechnic Institute and State University, VA. Sihce 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 highfrequency highefficiency power tuned amplifiers, resonant dc/dc power converters, dc/ac inverters, highfrequency rectifiers, and lighting systems. He has published over 120 techrlical papers, more than SO of which appeared in IEEE Transactions and Journals. Dr. Kazimierczuk received the IEEE Harrell V. Noble Award for his contributions to the fields of aerospace, industrial, and power electronics in 1991. He is also a recipient of the 1991 Presidential Award for Faculty Excellence in Research and the 1993 Teaching Award from Wright State University