In this paper, a revolutionary buck converter is proposed with softswitching technology, which is realized by a coupled inductor. Both zerovoltage switching (ZVS) of main switch and zerocurrent switching (ZCS) of freewheeling diode are achieved at turn on and turn off without using any auxiliary circuits by the resonance between the parasitic capacitor and the coupled inductor. Furthermore, the peak voltages of the main switch and the peak current of the freewheeling diode are significantly reduced by the coupled inductor. As a result, the proposed converter has the advantages of simple circuit, convenient control, low consumption and so on. The detailed operation principles and steadystate analysis of the proposed ZVSZCS buck converter are presented, and detailed power loss analysis and some simulation results are also included. Finally, experimental results based on a 200W prototype are provided to verify the theory and design of the proposed converter.
I. INTRODUCTION
Buck converters have been widely used in the industry, especially in lowvoltage and highcurrent applications. With the development of power electronics technology, it is imperative to demand smallsized, lightweight, and highreliability qualities and power density for the converters. To achieve these, highswitching frequency is used to the converters. However, the increase of switching losses results in an increase of switching frequency, if converters operate under hardswitching conditions, and consequently, adversely affects the efficiency of the overall circuits. Then, softswitching techniques are applied to the converters, which will considerably decrease switching losses, improve efficiency, and enhance stability. In addition, soft switching can reduce electromagnetic interference and the size of heat sinks.
In recent years, to achieve soft switching, many researchers have proposed a great amount of methods. Zerovoltage switching (ZVS) and zerocurrent switching (ZCS) are the most popular methods of soft switching, which can be realized by quasiresonant circuits
[1]

[11]
. While some auxiliary components are normally added to the converter to obtain quasiresonant circuits, such as switches, diodes, inductors, capacitors and so on. In
[4]
,
[5]
, the loss of main switch is decreased by the quasiresonant circuits, but some additional elements work under hardswitching conditions, which generate a large amount of power losses. Therefore, it is not obvious that the total efficiency of the converters has improved. Highpeak voltage or current of the main power switches and the diodes also happened
[6]

[8]
. Consequently, higher ranks of devices must be adopted for the converters, and additional power losses will also be generated. In any case, the control algorithm is more complicated than that of conventional pulse width modulation converters because of the auxiliary switches being added to the converters.
Coupled inductor also has been applied to the conventional converters in the early researches to realize soft switching that can obtain high efficiency
[12]

[18]
. In
[13]
, even though the efficiency of the proposed converter can be improved under heavyload conditions, it is worse than that of the conventional ones under lightload conditions because the auxiliary circuits generate a large number of additional conduction losses at light load. To make the main switch achieve ZCS condition, it is demanding the converter to operate under discontinuous conduction mode in
[15]
. When the current of the main small inductor is discontinuous, the coupled inductor can supply power to the loads. However, the additional diode and the copper losses of the coupled inductor itself have an adverse effect on the total efficiency. Although the topology of the buck converter in
[17]
is very simple, the switching frequency is variable, which makes the control method much more complex.
In this paper, a revolutionary control method is proposed to achieve soft switching, based on the extended topology in
[17]
. The topology of proposed ZVSZCS buck converter is shown in
Fig. 1
. As is evident from the figure, the filter inductor of the conventional converter is replaced by a coupled inductor. The main power switch can work under ZVS conditions at turn on and turn off. The freewheeling diode can also operate under ZCS conditions at turn on and turn off, i.e., soft switching of the proposed converter can be achieved. Moreover, there are not any auxiliary components or quasiresonant circuit branches, which often generate additional power dissipations. Hence, the control method is very facile, similar to that of the conventional converter. A 200W prototype is also built to verify the theory of the proposed converter.
The topology of proposed ZVSZCS buck converter.
The rest of this paper is organized as follows: Section II takes a brief description of the proposed converter, then the key waveforms and the equivalent circuits of each mode are presented. In Section III, the requirements of achieving soft switching and the specific parameter design of proposed converter are given. Section IV presents some simulation results and the detailed power dissipations. In Section V, the experimental results are obtained to illustrate the proposed converter. Finally, some conclusions are included in Section VI.
II. CONVERTER DESCRIPTION AND OPERATING PRINCIPLES
 A. Description of the Converters
The topology of proposed ZVSZCS buck converter is shown in
Fig. 1
.
S
_{1}
is the power MOSFET, and
D
_{S}
is an antiparallel diode that integrates in the power MOSFET.
D
_{1}
is the freewheeling diode,
C
_{1}
is the filter capacitor, and
C
_{r}
is the parasitic capacitor.
L
_{1}
and
L
_{2}
are tightly coupled on the same ferrite core that constitutes a coupled inductor. The coupled inductor
L
_{1}
is so small that its current can be bidirectional. Because of the resonance between the parasitic capacitor
C
_{r}
and the coupled inductor
L
_{1}
, switch
S
_{1}
can be turned on and off under ZVS conditions. The coupled inductor
L
_{2}
creates ZCS conditions for the freewheeling diode
D
_{1}
that is turned on and off.
 B. Operation Principles and Analysis
The operation processes of switching circuits are repeated by the switching period, and any particular time during the switching period can be chosen as a starting point to analyze them. The analysis processes can be simplified by selecting the appropriate starting point. This paper chose a starting point at switch S1 turnedoff moment. The key ideal waveforms of the proposed ZVSZCS buck converter are shown in
Fig. 2
. The operation of the proposed converter in one switching period can be divided into six, and the equivalent circuits of each stage are presented in
Fig. 3
. The detailed analyses of each mode are described as follows:
Key ideal waveforms of the proposed ZVSZCS buck converter.
Proposed ZVSZCS buck equivalent circuits of each operation mode. (a) Mode 1, t_{0}t_{1}. (b) Mode 2, t_{1}t_{2}. (c) Mode 3, t_{2}t_{4}. (d) Mode 4, t_{4}t_{5}. (e) Mode 5, t_{5}t_{6}. (f) Mode 6, t_{6}t_{0}.
1) Mode 1 [t_{0}t_{1}, Fig. 3(a)]:
The freewheeling diode
D
_{1}
turns on in this interval. Before
t
_{0}
, the switch
S
_{1}
is turned on, and
u
_{Cr}
is equal to zero. The freewheeling diode
D
_{1}
is turned off, and
i
_{2}
is also equal to zero. At
t
_{0}
, switch
S
_{1}
turns off under a ZVS condition, and the current of the coupled inductor
L
_{1}
reaches maximum value, i.e.,
i
_{S}
=
i
_{1}
=
I
_{1max}
. At the same time, the freewheeling diode
D
_{1}
turns on automatically under a ZCS condition. After
t
_{0}
, the coupled inductor
L
_{1}
discharges, and
i
_{1}
starts decreasing from
I
_{1max}
, while the coupled inductor
L
_{2}
, parasitic capacitor
C
_{r}
charge,
i
_{2}
, and
u
_{Cr}
increase from zero. At
t
_{1}
,
i
_{S}
drops to zero, and
i
_{1}
and
i
_{2}
are equal to
I
_{t1}
.The voltage across
C
_{r}
reaches steady value, and the charging is completed.
According to Magnetism Chain Conservation Theorem, this process can have
According to Magnetism Chain Conservation Theorem, this process can have
Simplifying (1),
i
_{1}
and
i
_{2}
at
t
_{1}
can be obtained as follows:
2) Mode 2 [t_{1}t_{2}, Fig. 3(b)]:
The coupled inductor
L
_{1}
and
L
_{2}
discharge in this interval. After
t
_{1}
,
i
_{1}
and
i
_{2}
are equal, and decrease linearly. The voltage across
C
_{r}
remains steady value, and
i
_{S}
is equal to zero.
The conduction voltage drop
u
_{D1}
of the freewheeling diode
D
_{1}
is ignored, and based on KCL and KVL, we can obtain
The voltage equations of the coupled inductor
L
_{1}
and
L
_{2}
can be described as follows:
By substituting (4) into (3), the slopes of
i
_{1}
and
i
_{2}
are derived as follows:
The slope of the filter inductor current of the conventional buck converter in this interval is equal to
Obviously, we can obtain
Consequently, it demonstrates that the discharging of the proposed buck converter is slower than that of conventional buck converter in this mode, and it contributes to decrease the ripple of output voltage
V
_{o}
.
Combining (3) and (4), the voltage across coupled inductor
L
_{1}
,
L
_{2}
, and parasitic capacitor
C
_{r}
can be written as follows:
3) Mode 3 [t_{2}t_{4}, Fig. 3(c)]:
The resonance between the parasitic capacitor
C
_{r}
and coupled inductor
L
_{1}
occurs in this interval. At
t
_{2}
,
i
_{1}
and
i
_{2}
are equal to zero. It provides a necessary condition for the freewheeling diode
D
_{1}
turned off under a ZCS condition. After
t
_{2}
, the parasitic capacitor
C
_{r}
discharges through coupled inductor
L
_{1}
, and
i
_{1}
changes its direction and is equal to
i
_{S}
. At
t
_{3}
,
i
_{1}
reaches negative maximum value. Then,
i
_{1}
starts to decline negatively until the voltage
u
_{Cr}
drops to zero at
t
_{4}
.
Let us make an assumption that the output capacitor
C
_{1}
is large enough, or the output voltage
V
_{o}
is constant. Based on KCL and KVL, we can obtain
The current equation of coupled inductor
L
_{1}
and the voltage equation of parasitic capacitor
C
_{r}
can be expressed as follows:
Combining (9) and (10), the following resonant equation can be written as follows:
The initial conditions of the resonant circuit at
t
_{2}
are
i
_{1}
= 0, and
. Some assumptions are made in this interval as follows:
According to the abovementioned equations in this mode,
i
_{1}
,
i
_{S}
, and
u
_{Cr}
are derived as follows:
where the constraint condition is
t
_{2}
≤
t
≤
t_{4}
.
4) Mode 4 [t_{4}t_{5}, Fig. 3(d)]:
The antiparallel diode
D
_{S}
is turned on in this interval. At
t
_{4}
, the discharging of parasitic capacitor
C
_{r}
is completed, and
u
_{Cr}
is equal to zero. After
t
_{4}
, the antiparallel diode
D
_{S}
turns on. As a result, it makes
u
_{Cr}
stay at zero. Meanwhile,
i
_{1}
is negative and is equal to
i
_{S}
, which declines linearly. The conduction voltage drop of the antiparallel diode
D
_{S}
can be neglected, and based on KVL equation, the voltage
u
_{L1}
across coupled inductor
L
_{1}
is given by
Then, the slope of
i
_{1}
can be obtained as follows:
At the same time, the voltage
u
_{L2}
across coupled inductor
L
_{2}
can be derived as follows:
According to KVL, the voltage
u
_{D1}
of the freewheeling diode can be written as follows:
5) Mode 5 [t_{5}t_{6}, Fig. 3(e)]:
The switch
S
_{1}
is turned on, and the current
i
_{1}
is negative in this interval. Before
t
_{5}
, the current
i
_{1}
flows through antiparallel diode
D
_{S}
, and the voltage
u
_{Cr}
of the parasitic capacitor
C
_{r}
is equal to zero. Therefore, a ZVS condition of the switch
S
_{1}
turned on can be obtained at
t
_{5}
. After
t
_{5}
, it is the same as Mode 4, except that
i
_{1}
flows through switch
S
_{1}
. The current
i
_{1}
decreases negatively with the slope(
V
_{in}

V
_{o}
)/
L
_{1}
until it reaches zero at
t
_{6}
.
6) Mode 6 [t_{6}t_{0}, Fig. 3(f)]:
The switch
S
_{1}
is turned on, and the current
i
_{1}
is positive in this interval. At
t
_{6}
, the current
i
_{1}
changes its direction. After
t
_{6}
, this mode is the same as Mode 4 and Mode 5, except that the current
i
_{1}
is positive. Then,
i
_{1}
increases linearly with the slope(
V
_{in}

V
_{o}
)/
L
_{1}
until switch
S
_{1}
turns off at
t
_{0}
. At the end of this mode, the next operating cycle begins.
III. SOFT SWITCHING ANALYSIS AND DESIGN PARAMETERS
 A. Analysis of the Soft Switching
The proposed buck converter can easily achieve ZCS conditions of the freewheeling diode
D
_{1}
, as long as the coupled inductor
L
_{1}
is so small that it can reduce the current
i
_{1}
to zero and become negative, i.e., the coupled inductor
L
_{1}
works under a discontinuous conduction mode (DCM). Then, some assumptions are made as follows:
where
R
is load resistor,
T
_{S}
is switching period,
N
is turn ratio, and the dimensionless parameter
K
is a measure of the tendency of a converter to operate in the DCM.
Therefore, the following formula must be satisfied to make the proposed converter operate under DCM
where
D
is the duty cycle.
However, to obtain ZVS conditions of the switch
S
_{1}
, the switch
S
_{1}
must be turned on between
t
_{4}
and
t
_{6}
, as shown in
Fig. 4
.
ZVS condition analyses particularly.
According to the voltage across parasitic capacitor
C
_{r}
in equation (15),
t
_{4}
can be obtained as follows:
Then, we can obtain
where
I
_{t4}
is the current
i
_{S}
at
t
_{4}
.
Consequently, Δ
T
that is between
t
_{4}
and
t
_{6}
can be derived as follows:
 B. Design of the Proposed Circuits
As presented in formula (22), the coupled inductor
L
_{1}
must be chosen a small one to satisfy it. However, to achieve ZVS better, it demands Δ
T
as long as possible.
The voltage conversion ratio
M
_{D}
is the ratio of the output to the input voltage of the converter, and can be obtained under DCM as follows:
Thus, the equation (25) can be simplified as follows:
As we can see in equation (27), the Δ
T
is closely related to
ω
_{0}
, i.e., the coupled inductor
L
_{1}
and resonant capacitor
C
_{r}
. Therefore, when the design of the coupled inductor
L
_{1}
is completed, and the voltage conversion ratio
M
_{D}
and turn ratio
N
are constant, it can be chosen a large resonant capacitor
C
_{r}
to increase Δ
T
. But at the same time, the current
i
_{1}
at
t
_{3}
is 
U
_{0}
/
Z
_{0}
, which also increases. As a matter of fact, we expect to decrease the value of
i
_{1}
at
t
_{3}
. Hence, the volume of
C
_{r}
must be appropriate. The specific values and others parameter values are shown in
Table I
.
RELATED SPECIFICATIONS OF THE PROPOSED CONVERTER
RELATED SPECIFICATIONS OF THE PROPOSED CONVERTER
IV. SIMULATION ANALYSIS
 A. Soft Switching Waveforms of Simulation
To illustrate the operation of the proposed ZVSZCS buck converter, it has been accomplished through a simulation with Multisim software. Using the parameters in
Table I
, the softswitching waveforms are obtained, in which the turn ratio
N
is equal to 1, as shown in
Fig. 5
.
The soft switching waveforms of simulation. (a) ZVS conditions of switch S_{1} (magnification: voltage is 0.5 and current is 1). (b) ZCS conditions of freewheeling diode D_{1} (magnification: voltage is 0.2 and current is 1). (c) The voltage and current of coupled inductor L_{1} (magnification: voltage is 0.833 and current is 1).
The resonant circuit, which consists of the coupled inductor
L
_{1}
and parasitic capacitor
C
_{r}
, provides a necessary condition for switch
S
_{1}
turned on under a ZVS condition. Furthermore, the ZVS condition of switch
S
_{1}
turned off is obtained by the parasitic capacitor
C
_{r}
, as shown in
Fig. 5
(a). Since the proposed converter works under DCM, the current
i
_{2}
is equal to zero at the freewheeling diode
D
_{1}
both turned on and turned off. Therefore, the ZCS conditions of the freewheeling diode
D
_{1}
that is turned on and turned off are achieved, as shown in
Fig. 5
(b). The voltage
u
_{L1}
and current
i
_{1}
of coupled inductor
L
_{1}
are supplied in
Fig. 5
(c).
 B. Analysis of Power Losses
The power losses of the proposed ZVSZCS buck converter can be divided into three segments, i.e., switch losses, diode losses, and others. When the turn ratio
N
is equal to 1, power losses at different output power are shown in
Fig. 6
. As we can see in the figure, the main factors that affect the total efficiency of the proposed converter are the switch and diode losses.
Power losses of the proposed converter.
As shown in
Fig. 5
(a), the switch losses are closely related to the voltage
u
_{Cr}
, i.e., the switch losses will decrease as the voltage
u
_{Cr}
declines and when the switch
S
_{1}
turns off. The voltage of parasitic capacitor
C
_{r}
in equation (8) can be simplified as follows:
The normalized parameter
u
_{Cr_N}
is
Similarly,
Fig. 5
(b) shows that the diode losses will reduce as the current
i
_{2}
declines at freewheeling diode
D
_{1}
turned on moment. The maximum value
I
_{1max}
of the current
i
_{1}
at
t
_{0}
can be derived under hardswitching conditions as follows:
Therefore, the current
i
_{2}
of coupled inductor
L
_{2}
at
t
_{1}
in equation (2) can be simplified as follows:
Normalized Current
I
_{t1_N}
is defined as
The contours of
u
_{Cr_N}
and
I
_{t1_N}
are shown in
Fig. 7
(a) and (b), respectively, in which
K
is constant value. The
x
axis represents the duty cycle
D
, and the
y
axis represents the turn ratio
N
. As shown in
Fig. 7
, the increase of duty cycle
D
results in a decrease of
u
_{Cr_N}
. However,
I
_{t1_N}
increases first, then decreases, while
u
_{Cr_N}
and
I
_{t1_N}
will both decrease as the turn ratio
N
increases. In
Fig. 8
, the switch losses and freewheeling diode losses are presented with different turn ratio
N
at diverse output power, respectively. Both the switch losses and freewheeling diode losses can be decreased by increasing the turn ratio
N
. Hence, the total power losses can be decreased by increasing the turn ratio
N
, i.e., the overall efficiency of the proposed converter can be improved this way.
Contour graphs of the proposed converter. (a) u_{Cr_N} contour graph. (b) I_{t1_N} contour graph.
Switch and freewheeling diode losses of the proposed converter. (a) Switch losses. (b) Freewheeling diode losses.
 C. Evaluation of Output Voltage
The ripple of output voltage
V
_{o}
, an important index to evaluate the performance of proposed buck converter, is affected by the slopes of
i
_{1}
and
i
_{2}
when the freewheeling diode
D
_{1}
turns on. The equation (5) can be simplified as follows:
In any case, the value of coupled inductor
L
_{1}
is so small that the current
i
_{1}
can be negative. Hence, the ripple of output voltage also closely associates with the current
i
_{1}
. At
t
_{3}
, the negative maximum of the current
i
_{1}
is
According to the couple of equations above, when the coupled inductor
L
_{1}
, parasitic capacitor
C
_{r}
, and output voltage
V
_{o}
are constant, 
k
 and 
I
_{t3}
 will both decrease as turn ratio
N
increases. That is to say, the ripple of
V
_{o}
can be decreased by increasing turn ratio
N
. In
Table II
, the ripples of
V
_{o}
are presented at different turn ratio
N
by simulation.
RIPPLE OF OUTPUT VOLTAGE AT DIFFERENT TURN RATIO
RIPPLE OF OUTPUT VOLTAGE AT DIFFERENT TURN RATIO
V. EXPERIMENTAL RESULTS
To verify the theoretical and simulated results of the proposed ZVSZCS buck converter, a 200W and 50kHz prototype has been built in the laboratory. The photograph of the proposed converter prototype is shown in
Fig. 9
. The used parameter values are the same as those specified in the simulation, and the semiconductors used are
The prototype of the proposed converter.
 Switch
S
_{1}
: MOSFET IRL2910S
 Freewheeling diode
D
_{1}
: MBR30200PT.
 A. Soft Switching Waveforms of Experiment
The experimental softswitching waveforms of the proposed ZVSZCS buck converter at medium load, light load and full load are shown in
Fig. 10
,
11
, and
12
, respectively. It is presented that the ZVS operations of the switch
S
_{1}
at turned on and off moment are achieved in
Fig. 10
(a). The coupled inductor
L
_{1}
and parasitic capacitor
C
_{r}
constitute a resonant circuit that provides a ZVSturned on condition for the switch
S
_{1}
. The parasitic capacitor
C
_{r}
is parallel with the switch
S
_{1}
, and makes a necessary condition for the switch
S
_{1}
turned off under a ZVS condition. In
Fig. 10
(b), the ZCS conditions of the freewheeling diode
D
_{1}
turned on and off also happen. Because of the proposed converter working under DCM, the current
i
_{2}
dropped to zero before the freewheeling diode
D
_{1}
turned off. Furthermore, the current
i
_{2}
keeps at zero until the freewheeling diode
D
_{1}
turns on. The experimental voltage
u
_{L1}
and current
i
_{1}
of coupled inductor
L
_{1}
are shown in
Fig. 10
(c). In comparison to
Fig. 11
and
12
, the proposed buck converter can successfully achieve ZVS and ZCS conditions, as well.
Experimental waveforms at medium load. (a) ZVS conditions of switch S_{1} (current i_{S}: 5A/div. and voltage u_{Cr}: 10V/div.). (b) ZCS conditions of freewheeling diode D_{1} (current i_{2}: 5A/div. and voltage u_{D1}: 20V/div.). (c) The voltage and current of coupled inductor L_{1} (current i_{1}: 5A/div. and voltage u_{L1} : 10V/div.).
Experimental waveforms at light load. (a) ZVS conditions of switch S_{1} (current i_{S}: 5A/div. and voltage u_{Cr}: 20V/div.). (b) ZCS conditions of freewheeling diode D_{1} (current i_{2}: 2A/div. and voltage u_{D1}: 20V/div.). (c) The voltage and current of coupled inductor L_{1} (current i_{1}: 5A/div. and voltage u_{L1} : 20V/div.).
The experimental waveforms at full load. (a) ZVS conditions of switch S_{1} (current i_{S}: 10A/div. and voltage u_{Cr}: 20V/div.). (b) ZCS conditions of freewheeling diode D_{1} (current i_{2}: 10A/div. and voltage u_{D1}: 20V/div.). (c) The voltage and current of coupled inductor L_{1} (current i_{1}: 10A/div. and voltage u_{L1} : 10V/div.).
 B. Efficiency
The efficiency curves of the buck converters are shown in
Fig. 13
. As we can observe in the figure, the overall efficiency values of the proposed buck converter are relatively high with respect to those of the rest buck converters. Moreover, the efficiency reaches 97.3% at full load. The figure also shows that even at light load (about 10% of the full power) the measured efficiency is as high as 91%.
Measured efficiency.
VI. CONCLUSION
In this paper, a simple structure of ZVSZCS buck converter with coupled inductor has been proposed. Both the switch working under ZVS conditions and freewheeling diode working under ZCS conditions at turned on and off are achieved. The detailed theoretical analyses of the operating principle at steady state have also been provided. The main factors of power losses are discussed. The prototype of the proposed buck converter was built, and the simulation and experimental results confirm the related theoretical analyses. Since no additional component is added in this topology, the proposed converter presents a simple structure and also enjoys a very simple control method, as well as that of the conventional buck converter.
BIO
Xinxin Wei was born in Henan, China. He received his B.S. degree in Electronics Engineering from Zhongyuan University of Technology, Zhengzhou, China in 2013. He is currently a postgraduate student in the School of Electronics Engineering, Chongqing University. His research interest area is power electronics in general, especially the analysis and design of switching power converters, highfrequency power conversion and softswitching converters.
Ciyong Luo was born in Anhui in 1973. He received his B.S and M.S degrees in Automatic Control and Ph.D. degree in Electronics Engineering from Chongqing University, Chongqing, China, in 1995, 1998, and 2005, respectively. From January 2011 to January 2012, he was with the Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK, as a Visiting Scholar. He is currently an Associate Professor in the School of Electrical Engineering, Chongqing University. His research interests include the modeling, design, and control of power converters, softswitching power converters, the modeling and analysis of the dynamical behavior of switching DCDC converters, and powerfactor correction circuits.
Hang Nan was born in Hubei in 1989. He received his B.S. degree in electrical engineering from Hubei University of Technology, Wuhan, China in 2013. He is currently a postgraduate student in the School of Electronics Engineering Chongqing University. His research interests include the modulation methods of switching power converters, power electronics, and especially, DCDC converters.
Yinghao Wang was born in Hebei in 1989. He received his B.S. degree in electrical engineering from Chongqing University, Chongqing, China in 2013. He is currently a postgraduate student in the School of Electronics Engineering Chongqing University. His research interests include the modulation methods of switching power converters, and the modeling and analysis of the dynamical behavior of switching DCDC converters.
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