Engineering, 2009, 1, 201-210
doi:10.4236/eng.2009.13024 Published Online November 2009 (http://www.scirp.org/journal/eng).
Quasi-Square Wave Mode Phase-Shifted PWM LCC
Resonant Converter for Regulated Power Supply
S. PADMANABHAN, Y. SUKHI, Y. JEYASHREE
R M K Engineering College, Anna University, Chennai, India
Received January 10, 2009; revised February 21, 2009; accepted February 23, 2009
Abstract
This paper presents an improved self sustained oscillating controller circuit using LCC components for im-
proving the overall efficiency of the system. It has a micro controller based active controller, which controls
the performance from no-load up to full-load. The steady state characteristics are developed and a design
example is given in detail. The proposed controller allows zero current switching at any loading condition
which results in a reasonable reduction of power loss during switching with a promising efficiency. Analyti-
cal and experimental results verify the achievement the design specifications.
Keywords: Zero Voltage Switching, Zero Current Switching, DC-DC Converter, Resonant Converter, Soft
Switching
1. Introduction
With ever increasing concerns about electromagnetic
compatibility (EMC) issues, more attention is being paid
to resonant converters as they provide better sinusoidal
waveforms. Furthermore, resonant converters can make
use of natural oscillation to achieve zero voltage switch-
ing (ZVS) and/or zero current switching (ZCS) thus
eliminating switching losses [1]. As such both higher
power-packing densities and conversion efficiencies can
be achieved at high switching frequencies without snub-
bers. The full-bridge converter is widely used in power
dc–dc conversions because it can achieve soft-switching
with the help of LCC components added in the circuit [2].
The soft-switching techniques for PWM full bridge con-
verter can be classified into two kinds: one is zero-volt-
age-switching (ZVS) and the other is zero-current-
switching (ZCS). For dc-dc power conversion applica-
tions, the conventional phase-shift full-bridge dc/dc
converter has drawn more attention in recent decades due
to its advantages: high conversion efficiency, high power
density, and low electro magnetic interference [3–8]. In
order to obtain high conversion efficiency for dc-dc
power conversion applications, a soft-switched dc/dc
converter with a LCC primary-side energy storage ele-
ments based on [9–12] is studied and implemented in this
paper.
Section II presents the principle of operation of the
LCC resonant converter. Successively, the Section III
deal with the mathematical analysis of converter. The
performance characteristics of the converter are obtained
from the mathematical analysis in section IV. An optimum
design procedure of this converter is proposed in section
V paper only after having a study on the performance
characteristics of the LCC resonant converter and it can
be considered as a design reference for other engineers.
Finally, a 100-kHz, 48W (40V/1.2A) laboratory-made
prototype is built up to verify all the theoretical analysis
and evaluation. The highest full-load conversion effi-
ciency of this converter reaches about 95.56%. Com-
pared with the traditional dc/dc converter, its advantage
in high conversion efficiency shows good potential for
various dc-dc power converter applications. Finally,
some conclusions of the work are provided in Section
IX.
2. Principle of Operation
Like switch mode dc-to-dc converter, resonant convert-
ers are used to convert dc-to-dc through an additional
conversion stage: the resonant stage in which dc signal
is converted to high frequency ac signal. The potential

S. PADMANABHAN ET AL.
202
Figure 1. Block diagram.
advantage of resonant converter include the natural com-
mutation of power switches, resulting in low switching
power dissipation and reduced component stresses, which
in terns results in increased power efficiency and in-
creased switching frequency; higher operating frequen-
cies results in reduced size and weight of equipment and
results in faster responses; possible reduction in EMI
problems. Since the size and weight of the magnetic
components (inductors and transformers) and capacitors
in a converter are inversely proportional to the converter
switching frequency, many power converters have been
designed at progressively higher frequencies in order to
reduce excessive size and weight and obtain fast con-
verter transients. In recent years, the market demand for
wide applications that need variable speed drives, highly
regulated power supplies, uninterruptible power supplies,
and the desire to have smaller size and lighter weight
power electronics systems has been increased. There are
many soft witching techniques available in the literature
to improve the switching behavior of dc-to-dc resonant
converters. At the time of writing these words, intensive
research in soft switching is under way to further improve
efficiency with increased switching frequency of power
electronic circuits.
A dc-to-dc resonant converter can be described by the
major circuit blocks as shown in Figure 1. The dc-to-ac
input inversion circuit, the resonant energy buffer tank
circuit, and the ac-to-dc output rectifying circuit. Typically,
the dc to ac inversion is achieved by using a various types
of switching network topologies. The resonant tank which
serves as an energy buffer between the input and output is
normally synthesized by using lossless frequency selective
network. The purpose of that network is to regulate the
energy flow from the source to the load. Finally, the
ac-to-dc conversion is achieved by incorporating rectifier
circuits at the output section of the converter.
3. Mathematical Analysis of Converter
Figure 2 shows the A.C. equivalent circuit of LCC
Figure 2. A.C equivalent circuit of LCC resonant converter.
Figure 3. Output circuit of bridge rectifier and filter
component to resonant converter.
resonant converter. The following assumptions are used in
the mathematical analysis of the series parallel resonant
converter.
1) The switches, diodes, inductors, capacitors and snu-
bber components used are ideal.
2) The effects of snubber are neglected.
3) The filter inductance is large enough to keep the
load current constant.
4) The high frequency transformer is ideal and has
unity turns ratio.
Where N - is the resonant network, Rac - AC equiva-
lent load resistance, VAB - RMS fundamental component
of VAB.
From the output circuit of bridge rectifier and filter
component to resonant converter fig.3, Vcp and Ib represent
the rms fundamental component of Vcp (t) and Ib (t)
respectively. The output circuit consists of the diode bridge
rectifier and inductive filter present in the output circuit.
The D. C. output voltage is obtained as the average of
A.C. input voltage, Vcp

0
0
12sin
cp
EVtd

t



 (1)
0
22
cp
E

V (2)
 = 2f and f is the switching frequency. The rms value of
the fundamental component of Diode Bridge current is
calculated using Fourier analysis as
 
2
0
1sin
2
bb
I
ittd t




 (3)
Figure 4. Quasi-square voltage waveform of LCC resonant
converter.

S. PADMANABHAN ET AL.203
0
22
b
I
I

 (4)
Using Equation (2) & (4) the equivalent A. C. resistance as
seen at the input of the rectifier bridge is given by
2
8
cp
ac L
b
V
R
I

R
(5)
 and D are related by:
=D (6)
The duty ratio D is defined as the ratio of the time duration
for which the switch S1 & S2 or S3 & S4 are switched on
simultaneously i.e. ton to the half of the switching period
(T/2) i.e., D = ton/ (T/2).When the switches S1 and S2 (S3 or
S4) are switched on simultaneously, the voltage across A
and B is the input voltage Ein.
The R.M.S. fundamental Voltage across A and B is
given by:

2
0
1sin
2
AB AB
VVttd

t



 (7)
 




/23 /2
/23 /2
1sin sin
2
AB inin
VEtdtEt
 
 
 




 



dt




(8)
22sin /2
in
AB
E
V


 (9)
The equivalent circuit of the converter across the terminal
A and B shown in Figure 2 is replaced by its equivalent
circuit shown in Figure 5. In order to simplify the
presentation, all the equations are normalized using the
following base quantities.
Base voltage = Ein
Base impedance = 0L
Base current = Ein / 0L
Base frequency 0 = 1/√LC
The RMS fundamental voltage across the parallel
Figure 5. AC equivalent circuit of resonant converter.
capacitor Cp is given by:

1
[](
11
11
AB
cp
Lcs
ac cp
ac cp
V
V
jX XRjX
RjX

 

)
1
(10)
here
XL = L, Xcs = 1/Cs , Xcp = 1/Cp (11)
Substituting the Equation (11) in Equation (10), the
equation becomes
LSL
P
S
P
AB
cp RCR
L
jLC
C
C
V
V




1
8
12
2


 (12)
Substituting the Equation (9) in Equation (12) and after
simplification, the equation becomes
























ym
yjQy
m
m
E
Vin
cp
)1(
18
1
1
2/sin22
2
2



(13)
where
m = Cs / Cp, Q = oL/ RL =1/oC RL ,y = /o (14)
Substituting Equation (13) in Equation (2) and after
normalization, the equation becomes


0
2
2
sin/ 2
11
1
81
i
E
EmyjQy
mm





 

 

 
y
(15)
The equivalent impedance across the terminals A and B
is given by

1
11
eqL CS
ac CP
ZjXX
RjX


(16)
Substituting Equation (5), Equation (11) in Equation (14),
the equation becomes
2
11
8
eq
LSL PL
L
Zj
RCR
j
CR








 

 






(17)
Using Equation (11) in Equation (17) and after simplifi-
cation, the equation becomes
 
2
11
[]
1 18
eq L
ZjRQy ym
my jQm


 

 



(18)
After simplification and rearranging the terms we get
1
0
3
eq
BjB
ZL
B


2 (19)

S. PADMANABHAN ET AL.
204
where

2
12
8
1
Qm
Bym







(20)

23
1
1(
m
By B
ym ym

 




1)
(21)
32
8
1(1)
Qm
Bym







(22)
Normalizing Equation (19), the equation becomes
12
3
j
eqpu eqpu
BjB
Z
Ze
B


 (23)
22
12
2
3
eqpu
BB
ZB

 (24)
Impedance angle
11
2
tan B
B

 (25)
The resonant link current I
AB
equ
V
I
Z
 (26)
II

 (27)
where
AB
equ
V
IZ  (28)
Substituting Equation (9) in Equation (4) and after nor-
malization, the equation becomes
22sin
2
pu
equ
IZ


 (29)
Peak Inductor is given by
4sin 2
2
ppu ppu
equ
II
Z


 (30)
0
cs
cs ppu
X
VI
L

 (31)
Using (30) Peak Voltage across Cs is calculated as
(1
ppu
cs ppu
I
Vym )

(32)
The peak Voltage across CP is obtained using Equation (1)
and rearranging the terms.
2
O
cp ppu
in
E
VE

 (33)
The load ripple voltage is given by,
1/2
22
accrms c
VVV

 

 (34)
Vcrms is the total rms load voltage.Vo is the average load
voltage.
The Voltage ripple factor, which is a measure of the rip-
ple content, is given by the equation
ac
c
V
RF V  (35)
Similarly the Voltage ripple factor using the filter ele-
ments is given by the equation
2rms
c
V
RipplleFactor V  (36)
where V2rms represents the rms value of the second har-
monic component.
22
32
m
rms
V
VLC

 (37)
where Vm represents the maximum value of voltage after
rectification.
The efficiency of the converter is calculated using the
expression
%
out
in
P
P
 100 (38)
4. Performance Characteristics
4.1. Variation of Input Impedance Magnitude and
Phase Angle vs. Normalized Switching
Frequency
The effect of impendence on circuit performance has been
studied using Equation (19) to Equation (22) and have been
used to draw the curves of the variation of the normalized
input impedance magnitude and impedance phase angle,
with change in normalized switching yield stress for
various values of Q are shown in Figure 6 and Figure 7
respectively.
It can be seen that for a particular value of quality factor
Q the impedance magnitude decreases as the frequency
increases up to a certain value, after which it increases with
frequency, but with less effect. The effect of quality factor
variation can also be observed. As Q decreases the input
impedance magnitude verses normalized switching fre-
quency curve shifts towards higher frequency. It is
observed that at about 0.9pu frequency, all the input

S. PADMANABHAN ET AL.205
impedance magnitude curve converges and diverges as the
frequency increases.
From impedance phase angle curves the boundary
between operation below and above resonance can be
identified. The frequency at which the impedance phase
Figure 6. Variation of impedance magnitude versus
normalized switching frequency for various values of Q with
m = 1.
Figure 7. Variation of impedance angle in degrees versus
normalized switching frequency for various values of Q with
m = 1.
Figure 8. Variation of peak inductor current versus norma-
lized switching frequency for various values of Q with m = 1.
angle  is equal to zero is defined as fr. This frequency
forms boundary between leading power factor and lagging
power factor operation. For f<fr, <0, the resonant circuit
represents a capacitive load (below resonance operation),
for f>fr, >0 the resonant circuit represents an inductive
load (above resonance operation). It is seen from Figure 7
that fr depends on Q.
4.2. Variation of Peak Inductor Current vs.
Normalized Switching Frequency
Equation 30 shows that peak inductor current is a function
of Q and y. Figure 8 shows that peak inductor current
increases with increase in Q, since the output voltage
decreases for the same output power. But for a given value
of y, it can be seen peak current decreases as load current
increases with increase in value of Q.
4.3. Variation of Duty Ratio vs. Q for M=1
The qualitative analysis of the relationship between duty
ratio and quality factor Q is made. Figure 9 to Figure 16
show how the duty ratio D varies as Q changes, to keep
output load voltage constant at particular value. These
curves are obtained by solving Equation 15 numerically for
duty ratio as a function of Q for various values of converter
gain Eo/Ein (for 0.7 to 1.0) and various switching
frequency (yield stress = 0.7 to 0.9).
It is observed that as the Eo/Ein decreases, the duty ratio
versus Q curves shifts downwards. The increase in value of
yield stress results in shrinkage of D vs. Q Curve ranges.
However when Cs/Cp ratio is observed that the above two
characteristics are intensified. The detailed analysis offers
each figure is given in the following paragraphs.
If the normalized frequency is further increased, the
graphs show similar pattern as described above. Figure 10,
Figure 11 and Figure 12 are shown for yield stress y= 0.8,
Figure 9. Variation of duty ratio versus quality factor with m
= 1, y = 0.75.

S. PADMANABHAN ET AL.
206
Figure 10. Variation of duty ratio versus quality factor with m
= 1, y = 0.80.
Figure 11. Variation of duty ratio versus quality factor with m
= 1, y = 0.85.
0.85 and 0.9 respectively. Figure 13,14,15,16 show the
effect of increased capacitance ratio of 2. From these graph,
it is observed that as the value of yield stress changes from
0.85 to 0.9, the range of Q becomes narrower with
increasing of Eo/Ein, (0.7 to 1.0). Also, at light load (Q is
small), when Eo/Ein increases, the duty ratio increases
while the spread of duty ratio decreases. Similarly, it
becomes narrower and shifts to smaller values of duty ratio
D as yield stress increases.
4.4. Variation of Duty Ratio vs. Q for m=2
Figure 13 to Figure 16 show how the duty ratio D varies as
Q changes, to keep output load voltage constant at particul-
ar value. These curves are obtained by solving Equation 15
numerically for duty ratio as a function of Q for various
values of converter gain Eo/Ein (for 0.7 to 1.0) and various
switching frequency (yield stress = 0.7 to 0.9).
It is observed that as the Eo/Ein decreases, the duty ratio
versus Q curves shifts downwards. The increase in value of
yield stress results in shrinkage of D vs. Q Curve ranges.
However when Cs/Cp ratio is observed that the above two
characteristics are intensified. The detailed analysis offers
each figure is given in the following paragraphs.
Figure 12. Variation of duty ratio versus quality factor with m
= 1, y = 0.9.
Figure 13. Variation of duty ratio versus quality factor with m
= 2, y = 0.75.
If the normalized frequency is further increased, the
graphs show similar pattern as described above. Figure 13,
Figure 14, 15 and 16 show the effect of increased
capacitance ratio of 2. From these graph, it is observed that
as the value of yield stress changes from 0.85 to 0.9, the
range of Q becomes narrower with increasing of Eo/Ein,
(0.7 to 1.0). Also, at light load (Q is small), when Eo/Ein
increases, the duty ratio increases while the spread of duty
ratio decreases. Similarly, it becomes narrower and shifts to
smaller values of duty ratio D as yield stress increases.
5. Design of Series Parallel Resonant
Converter
Following criteria has been taken into account in order to
obtain optimum design of series - parallel resonant con-
verters.
1) Normalized switching frequency `y', such that main-
tains the lagging power factor conditions.
2) Minimum inverter output peak current for small rating
and losses.
3) Minimum stress in series & parallel capacitor.
4) Minimum variation of Duty ratio from full load to no
load i.e. good voltage regulation.

S. PADMANABHAN ET AL.207
Figure 14. Variation of duty ratio versus quality factor with m
= 2, y = 0.80.
Figure 15. Variation of duty ratio versus quality factor with m
= 2,y = 0.85.5.Design of series parallel resonant converter.
5.1. Selection of Cs/Cp (m)
It is observed from Figure 10 and Figure 14 that as m
increases, the variation in the duty ratio required to keep
the output constant decreases. For regulation of output
voltage, the duty ratio has to be varied over larger range
for m = 1.compared to m = 2. The effect of m on
equivalent input impedance of the resonant network
should be considered
while taking the values of m. From Equation (19)
which is used to plot the variation of equivalent input
impedance Zeqpu with the variation on normalized
switching frequency and is shown in Figure 6. From the
equation it is observed that as m increases from 1 to 2 the
equivalent input impedances Zeqpu of resonant network
decrease. This result in increased peak current through
various components and consequently increased power
loss. So from these considerations, the value of m = 1
should be taken.
Figure 16. Variation of duty ratio versus quality factor with
m = 2, y = 0.90.
5.2. Selection of Normalized Switching Frequency
The output voltage is regulated at all load by proper
selection of y. In Figure 10 for y = 0.75 the output voltage
can be regulated at Eo/Ein = 0.8 for the variation in Q up to
6. But at y =0. 8, the output voltage can be maintained at
this value of only up to Q = 5 (Figure 11). As y increases
further, the range of Q up to which the converter can be
regulated decreases. This implies that too high value of y
cannot be chosen especially when wide load variations are
expected. Besides, y should not be of low value. Otherwise
operation above resonance may not possible. Keeping these
two factors in mind, y = 0.8 have been chosen. It can be
seen from figure 10 that for variation in Q up to 5, Eo/Ein
=0.8 can be maintained. As shown in Figure 7, for y =0.8,
the input impedance angle changes from positive to nega-
tive as the values of Q is changed from 5 corresponding to
full load to 1 for light load. This means that near full load,
the converter operates above resonance and at partial loads
the converter operates below resonance.
5.3. Selection of Tank Circuit Q at Full Load
Size of tank depends upon the value of quality factor Q and
it should not be large. Equation (19), Equation (20),
Equation (21), Equation (22) and Equation (30) show that
peak inductor current is a function of Q and y. Figure 8
shows that peak inductor current increases with increase in
Q, since the output voltage decreases for the same output
power. But for a given value of y, it can be seen that the
peak inductor current decreases as load current increases
with increase in value of Q. However this decrease is not
drastic for values of Q greater than 5. A compromised
value of Q = 5 is chosen in this design.
5.4. Selection of Normalized Converter Gain
It is clear from the circuit topology that output current is

S. PADMANABHAN ET AL.
208
rectified and averaged tank current reflected to the
secondary side of the transformer. Since the tank current is
directly related to the output current, therefore we should
choose a large conversion ratio, so that the turns ratio is
minimized, resulting in the smallest possible tank current
on the primary for a specified output current on the
secondary. Hence the conversion ratio should be chosen
close to one. Based on above consideration, the following
optimum values are selected in the design of the converter.
Normalized frequency y = 0.8.
Cs/Cp ratio m = 1
Q of tank circuit at full load = 5
6. Design
Input voltage Ein = 50 volts. Output voltage Eo =40 volts.
Output Current = 1.2 Amps. Switching frequency = 100
kHz
From the performance characteristics, the following
values are considered for design.m=Cs/Cp = 1, Q=5, y=1.1
Load resistance R=V0/I0=32
01
LL
RQQC


5 32160
LQR
C 
Resonant frequency fo is given by fo = f/y = 100,000/1.1 =
90.9 kHz
But
0
1
2
fLC


3
1290.910
LC
  
The values of L & C are L = 280H and C = 0.01  F.
7. Experimental Results
This section aims to validate the concepts developed in the
previous sections. This section is intended to highlight the
compliance of the proposed converter with the desired
design specifications. Some testing results are presented in
this section to verify the theoretical predictions of previous
sections. An experimental proto type has been implement-
ed for a resistive load as shown in Figure 17. The load
rating is 40V, 50W, 1.2A. The resonant inductor is
0.28mH and the inductor is wound around ferrite core and
the series resonant capacitor is 0.01F and the capacitor
used is of polypropylene film type.
The switching frequency is 100 KHz. All the four
switches used is of IRF450 with an external fast recovery
diode BYE26E connected across each switching device.
In the secondary side, the diodes used for rectification
are FR306. The filter inductor is 40H and is wound
around ferrite core. The filter capacitance is 100F, 63V
and the capacitor used is of electrolytic type. Figure 16 to
Figure 18 shows the experimental output obtained. In
each Figure, (a) shows the voltage across the series in-
ductor and (b) shows the output voltage across the load
after connecting the filter elements.
Table 3 efficiency obtained with conventional method
(without LC) for variable I/P D-C supply voltage and
switching frequency = 100 kHz
Table 4 efficiency obtained for series parallel resonant
converter (proposed method) for I/P D-C supply voltage =
30 V and switching frequency = 100 kHz.
Table 1&2 give the Comparison of Results between
Calculated and experimental results respectively of Series
parallel resonant converter for an input DC supply voltage
of 50V and switching frequency of 100 kHz.
Table 1. Calculated results.
Table 2. Experimental results.
Table 3. Experimental results.

S. PADMANABHAN ET AL. 209
Figure 17. Experimental circuit.
Figure 18. Experimental results for series parallel resonant converter at 60% load with m=1: (a) VLS, (b) V0 with filter.

S. PADMANABHAN ET AL.
210
Table 4. Experimental results.
8. Conclusions
This paper presents a new front-end dc–dc power supply
based on the series parallel resonant converter. A
detailed design procedure has been given to select the
values of the resonant components for a design case.
Experimental results show that the proposed converter
enjoys a high efficiency. It can be concluded from the
experimental output that the variation of the working
efficiency with output load power for different duty ratio
is in direct proportion with the load.
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