309
IEEE TRANSACTIONS ON POWER ELEmONICS, VOL. 8,N0.3 , JULY 1993
Phase-Controlled Series-Parallel Resonant Converter
Dariusz Czarkowski and Marian K. Kazimierczuk, Senior Member, IEEE
Abstract-A constant-frequency phase-controlled series-parallel
resonant dc-dc converter is introduced, analyzed in the frequency domain, and experimentally verified. To obtain the dc-dc
converter, two identical series-parallel resonant inverters are
paralleled and the resulting phase-controlled resonant inverter is
loaded by a voltage-driven rectifier. The converter can regulate
the output voltage at a constant switching frequency in the
range of load resistance from full-load resistance to infinity while
maintaining good part-load 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 phase-controlled series-parallel resonant converter with
a center-tapped 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 reverse-recovery
losses in diodes because of low d i l d t at turn-off. However,
most frequency-controlled 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 phase-controlled 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 phase-controlled converters is that as one
leg of MOSFET switches is loaded inductively, the other is
loaded capacitively [8]. For inductive loads, there is no tum-on
loss, but there is tum-off loss. In contrast, for capacitive loads,
there is no tum-off loss, but there is tum-on 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 tumed-off and have very little penalty
on conduction losses.
This paper presents a new phase-controlled ceries-parallel
resonant converter ( P C SPRC), its steady-state analysis in the
Manuscript received July 5 , 1992: revised February 19, 1993. This work was
supported by the National Science Foundation by Grant ECS-8922695.
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 voltage-switching phase-controlled series-parallel inverter.
frequency domain, design equations, and experimental results.
In the proposed circuit, two identical series-resonant 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 phase-controlled series-parallel
resonant inverter (PC SPRI). It consists of two conventional
Class D voltage-switching series-parallel inverters [ 11-[4]:
inverter 1 and inverter 2. Each inverter is composed of two
switches with their antiparallel diodes, a series-resonant circuit
L-Cl, 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 voltage-driven
rectifiers analyzed in [ 161 and shown in Fig. 2, a phasecontrolled series-parallel 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, zero-voltage
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 [ 161-1 181. The converter
is suitable for medium-to-high power applications with the
upper switching frequency limit of 150 kHz, as recommended
in 1141.
11. ANALYSIS
OF CLASSD PHASE-CONTROLLED
SERIES-PARALLEL
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.
0885-8993/93$0! 1.00 @ 1993 IEEE
IEEE TRANSACTIONS ON POWER El.JXlXONICS.
310
VOL. 8. N0.3 ,JULY 1993
Fig. 3. Equivalent circuit for the fundamental components of the Class D
phase-controlled 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 voltage-driven rectifiers. (a) Half-wave rectifier. (b)
Transformer center-tappedrectifier. (c) Bridge rectifer.
2) The power MOSFET's are modeled by switches with
ON-resistances
+
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
Phase-Controlled Series-Parallel Inverter
Each switching leg and the dc input voltage source VI of the
inverter shown in Fig. 1 form a square-wave 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 square-wave 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 dc-to-ac voltage transfer function of the Class
D phase-controlled 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: PHASE-CONTROLLED SERIES-PARALLEL 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 Phase-Controlled
Series-Parallel 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 part-load efficiency.
Close examination shows that the peak transistor currents
are twice as high as those in a full-bridge 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. Three-dimensional representation of the magnitude of the dc-to-ac
transfer function of the phase-controlled Class D series-parallel 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. Three-dimensional 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 . Three-dimensional 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. Three-dimensional 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 phase-controlled
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: PHASE-CONTROLLED SERIES-PARALLEL 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 phase-controlled 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 phase-controlled 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 series-resonant circuit is
r = TDS
rL
rcl, where T D S = ( T D S 1 T D S ~ ) is
/ ~
the average resistance of the on-resistances 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 series-resonant 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 phase-controlled
314
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 8, N0.3 , JULY 1993
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 ac-to-dc voltage transfer function of the rectifier is
Fig. 8. Three-dimensional 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 dc-to-ac voltage transfer function of the actual inverter
is
111. CLASSD VOLTAGE-DRIVEN
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 Center-Tapped 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 half-wave 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 ac-to-dc
voltage transfer function of the rectifier is
315
CZARKOWSKI AND KAZIMIERCZUK PHASE-CONTROLLED SERIES-PARALLEL 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
M-Sl
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 phase-controlled series-parallel resonant converter
that consists of an inverter of Fig. 1 and a center-tapped
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
IEEE TRAMACTIONS ON POWER ELELTKONICS, VOL. 8. N 0 . 3 , JULY 1993
-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 ON-resistaric.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 center-rapped
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. Vci-tical : 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 drain-to-source 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 drain-to-\ource voltages I ' / ) . ~ and ( . / I .
bottom transistor\ of the imerters at I = 28 V and I ? , = IS <!.
t h ) I ; = XI0 V. Vertical: S O V/di\: horimntal: 2 / I \ / div.
o f rhe
150 \'.
I o = 2.3 A. The phase shift (,!I was measured observing the
drain-to-source voltage waveforms of the switches. Fig. 17
shows the drain-to-source voltage waveforms of the bottom
transistors at \ j =1SO V and R L = 15. 75. and 3500 ( 2 , The
drain-to-source 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 11-A. Fig. 19 shows that the imhalance of the
currents through serie\ resonant circuits is about 1.3: I .
VI. CONCLUSlOh
A new phase-controlled series-parallel 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 part-load efficiency of the converter is high (Fig. 1 1 ).
4 ) The full-load 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: PHASE-CONTROLLED SERIES-PARALLEL 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’91-SM’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
1984-1985, 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 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 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