This study examines the zerovoltage switching (ZVS) operation of an activeclamped forward converter (ACFC) with a currentdoubler rectifier (CDR). The ZVS condition can be obtained with a much smaller leakage inductance compared to that of a conventional ACFC. Due to the significantly reduced leakage inductance, the design is optimized and the circulating loss is reduced. The operation of the ACFC with a CDR is analyzed, and a detailed ZVS analysis is conducted on the basis of a steadystate analysis. From the results, a design consideration for ZVS improvement is presented. Loss analyses of the converters shows that enhanced softswitching contributes to an efficiency improvement under lightload condition. Experimental results from a 100W (5V/20A) prototype verify that the ACFC with a CDR can attain ZVS across an extended load range of loads and achieve a higher efficiency than conventional ACFCs.
I. INTRODUCTION
The forward converter has been one of the most extensively used topologies in low and mediumpower DCDC converter applications (e.g., computer and telecommunication systems) because of its simple circuitry, low cost, and high efficiency. However, several issues remain such as highvoltage spikes across the MOSFET and resetting of the transformer. To solve these problems, forward converters have used several reset schemes. An activeclamp circuit is the most widely used scheme because it does not require an additional reset winding or energy dissipative component to minimize the voltage stress across the MOSFET
[1]

[7]
. In addition, an activeclamp circuit enables zerovoltage switching (ZVS) in a MOSFET.
In a conventional activeclamped forward converter (ACFC), the main switch can achieve ZVS by harnessing either the magnetizing inductance
[8]

[10]
or the leakage inductance
[12]

[14]
. The method of magnetizing inductance requires a gap in the transformer that increases the magnetizing current, discharging the output capacitor of the MOSFET and resulting in ZVS. However, a hardswitching operation is employed rather than a softswitching one when a decreased switching loss cannot compensate for the increased conduction loss
[10]
. Consequently, this method is only suitable for converters with a small input current and a highinput voltage
[11]
. The method of the leakage inductance uses the resonance between the leakage inductance and the output capacitor of the MOSFET to discharge the stored energy. The ZVS condition is more easily met as the leakage inductance increases. However, large duty cycle losses result in an overall decrease in efficiency. Several methods have been proposed to improve the ZVS operation while using a relatively large magnetizing inductance and a small leakage inductance
[15]

[17]
. However, these methods either require additional components
[15]
,
[16]
or only apply to ACFCs with an externally driven synchronous rectifier on the secondary side
[17]
.
In order to overcome these limitations, this paper proposes an ACFC with a CDR to improve ZVS operation. CDR is widely used in applications with lowoutput voltage and highoutput current because the rootmeansquare (RMS) current on the transformer secondary is small and the output voltage ripple is reduced
[18]

[20]
. Many previous studies have reported on the general advantages of CDRbased topologies
[21]

[25]
. It has also been reported that CDR improves ZVS operation when used with a phaseshifted fullbridge converter
[26]
,
[27]
. However, for a phase shifted full bridge converter, the primary current should decay rapidly during the zero state
[27]
, and the output inductor current should become negative at the switching instant for ZVS improvement, which compromises the general advantages of CDR. While an ACFC with a CDR can inherently use the output inductor energy to improve ZVS operation, it has never been remarked before. Hence, an excessive resonant inductor has been used
[12]
or ZVS has been reported with only empirical results
[21]
,
[28]

[30]
.
Therefore, the present study rigorously analyzes an ACFC with a CDR to achieve enhanced ZVS operation. This paper demonstrates that an ACFC with a CDR improves the ZVS performance and presents a design consideration for further improvements. A quantitative comparison of the losses in an ACFC with a CDR and those in other ACFCs verifies that the enhanced ZVS performance is responsible for the improvement in lightload efficiency. The experimental results also show that enhanced softswitching contributes to improvement in efficiency under lightload. Therefore, an ACFC with a CDR exhibits a high efficiency across all load conditions.
Despite its advantages, the proposed converter needs an additional output inductor. If discrete magnetic components are used, three cores are required: one for the transformer and two for the output inductors. These can increase the cost and size of the converter. However, since previous studies
[31]

[34]
have reported that the three cores can be replaced by integrated magnetic structures, the present study focuses on the aspect of CDR efficiency.
The paper is structured as follows: Section II describes the circuit configuration of the ACFC with a CDR. Section III presents a ZVS analysis based on a steadystate analysis, and provides design considerations for ZVS improvement. Section IV presents a loss analysis to verify the role of the enhanced ZVS performance in improving efficiency. Section V experimentally verifies the assertions of Section IV using a 100W (5V/20A) prototype, and Section VI concludes the paper.
II. CIRCUIT CONFIGURATION
The circuit configurations of the conventional ACFC and an ACFC with a CDR are shown in
Figs. 1
(a) and
1
(b), respectively. Unlike the conventional ACFC,
R_{L}
_{1}
,
R_{L}
_{2}
, and
R_{t}
which are the equivalent series resistances (ESR) of
L
_{1}
,
L
_{2}
, and the transformer, are considered in
Fig. 1
(b) for the ZVS analysis as explained later. The auxiliary switch
S
_{2}
and the clamp capacitor
C_{c}
are components of the activeclamp circuit and recycle leakage energy. The transformer is modeled with a magnetizing inductance
L_{m}
and an equivalent leakage inductance reflected on the primary side
L_{lk}
. The main switch
S
_{1}
is operated with the duty cycle
D
, and the auxiliary switch
S
_{2}
is operated complementarily to the duty cycle of
S
_{1}
, with dead times preceding and following the auxiliary switch action. Both of the switches include body diodes
D_{s}
_{1}
and
D_{s}
_{2}
, and output capacitors
C_{s}
_{1}
and
C_{s}
_{2}
. The secondary side comprises two synchronous switches
SR
_{1}
and
SR
_{2}
, two output inductors
L
_{1}
and
L
_{2}
, and an output capacitor
C_{o}
.
Circuit configuration. (a) Conventional ACFC. (b) ACFC with CDR.
Activeclamp circuitry can be applied to either the high side or the low side. Highside clamps are applied across the primary side of the transformer and use an Nchannel auxiliary switch on the clamp network. Hence, they are appropriate for highinputvoltage applications. However, additional highside gate circuitry is needed to drive the auxiliary switch. A lowside clamp is applied across the draintosource of the main switch and a Pchannel auxiliary switch is used on the clamp network. The draintosource voltage rating of the Pchannel switch is lower than that of the Nchannel switch and it cannot be used for offline applications. However, it does not require any additional gate drive circuitry and improves the precision of the control over the delay timing for ZVS.
The level of the input voltage in most forward converter applications is lower than the line voltage. Therefore, the lowside clamp is adopted in this paper. The fundamental principles are exactly the same for both clamps. As a result, the following analyses can also be applied to highside clamps.
III. ZVSANALYSIS
ZVS operation of
S
_{2}
is guaranteed regardless of load variations
[15]
and does not need to be considered separately in the design consideration. Consequently, the ZVS analysis of
S
_{1}
is conducted in the following.
 A. Steadystate analysis
Steadystate waveforms of the ACFC with a CDR are shown in
Fig. 2
. The operation modes and analyses are complicated by the resonant operation. The circuit operation and ZVS analysis are simplified by the following assumptions:

1) The dead times are much shorter than the switch turnon times and are negligible.

2)Llkis much less thanLm.

3)Ccis large enough to make the clamp voltage constant.
Steadystate waveforms.
Since these assumptions make scarcely any changes in the minimum value of
i_{Llk}
(
t
), which is the most significant value for the ZVS analysis, they simplify the analysis without introducing any inaccuracies.
When the above conditions are applied, the total number of intervals in one switching cycle decreases from ten to two and
D
becomes equal to the effective duty
D_{eff}
. Equivalent circuits for these two states are depicted in
Fig. 3
. The steadystate waveforms of the converter are shown in
Fig. 4
.
The two operation states to calculate steadystate DC average values. (a) State 1: S_{1} is on. (b) State 2: S_{2} is on.
Approximated steadystate waveforms.
To ensure the ZVS of
S
_{1}
, the energy stored in
L_{lk}
must be larger than the energy stored in
C_{s}
_{1}
at the moment the switch is turned on,
t
_{1}
.
L_{lk}
and
i_{Llk}
(
t
_{1}
) are critical determinants of the ZVS of
S
_{1}
. ZVS is more easily achieved when both determinants increase. Large values of
L_{lk}
degrade the converter efficiency and affect the voltage conversion ratio of the forward converter. Therefore, it is more desirable to increase
i_{Llk}
(
t
_{1}
).
In the conventional ACFC, the leakage current
i_{Llk}
(
t
) is equal to the magnetizing current
i_{Lm}
(
t
), and it discharges
C_{s}
_{1}
at
t
_{1}
, as shown in
Fig. 5
(a). The ZVS operation of
S
_{1}
is not easily achieved with a small leakage inductance because the magnitude of
i_{Llk}
(
t
_{1}
) is not large enough to totally discharge
C_{s}
_{1}
.
Current flow of transformer and C_{s}_{l} at t_{1}. (a) Conventional ACFC. (b) ACFC with CDR.
Meanwhile, the transformersecondary current
i_{sec}
(
t
) can flow bidirectionally on the ACFC with a CDR. In this case,
i_{Llk}
(
t
) is not equal to
i_{Lm}
(
t
). It is determined from the sum of
i_{Lm}
(
t
) and the transformerprimary current
i_{pri}
(
t
) at
t
_{1}
, as shown in
Fig. 5
(b). The increment of
i_{pri}
(
t
_{1}
), reflected from
i_{L}
_{2}
(
t
_{1}
), can contribute to the ZVS of
S
_{1}
. The steadystate and ripple values of
i_{Lm}
(
t
) and
i_{pri}
(
t
) must be obtained to investigate how enhanced ZVS operation occurs in the proposed converter. The steadystate values of
i_{Lm}
(
t
),
i_{L}
_{1}
(
t
),
i_{L}
_{2}
(
t
), and
v_{Cc}
(
t
) can be obtained by solving the statespace equations (The detailed derivation is provided in the Appendix). The results are as follows
[22]
:
From Eqs. (1) and (3), it can be seen that
I_{Lm}
multiplied by the transformer turn ratio
N
is equal to
I_{L}
_{2}
This is due to the charge balance on
C_{c}
. Therefore,
i_{Llk}
(
t
_{1}
) is determined by the ripple current of
i_{Lm}
(
t
) and
i_{L}
_{2}
(
t
). The absolute value of
i_{Llk}
(
t
_{1}
) is given by:
where
V_{SR}
stands for the sum of the voltage drops across the ESRs and synchronous switches.
In the case of the conventional ACFC, 
i_{Llk}
(
t
_{1}
)*, which corresponds to 
i_{Llk}
(
t
_{1}
), can be written as follow
[3]
:
where
 B. ZVS advantageous area
For improved ZVS operation in the ACFC with a CDR relative to the conventional ACFC, 
i_{Llk}
(
t
_{1}
) has to be larger than 
i_{Llk}
(
t
_{1}
)*. If it is assumed that
E_{Cs}
= 0 for the worst case design and neglect
V_{SR}
in Eq. (5), the ZVS condition for the extended load range can be described as follow:
When the condition in Eq. (8) is met, the ACFC with a CDR shows enhanced ZVS characteristics when compared with the conventional ACFC. From the small values of
L_{lk}
, the duty cycle loss is reduced and the design of a forward converter becomes convenient. If the condition in Eq. (8) can be easily satisfied, the ACFC with a CDR represents an appropriate substitute for the conventional ACFC.
The advantageous ZVS conditions for the ACFC with a CDR and the conventional ACFC are investigated according to Eq. (8) using the converter system specifications given in
Table I
. The results for both converters are given in
Fig. 6
. The boundary condition line separates the region where the ACFC with a CDR most easily achieves ZVS from the corresponding region for the conventional ACFC. The ACFC with a CDR attains ZVS with a smaller leakage inductance than the conventional ACFC. Moreover, the difference between the minimum inductances for each converter increases as the load decreases.
SYSTEM SPECIFICATION
ZVS advantageous condition.
 C. ZVS condition for the ACFC with a CDR
The main switch ZVS condition for the ACFC with a CDR is given by the following:
where
V
_{g max}
max is maximum input voltage.
Using Eqs. (4) and (5) while assuming that
V_{SR}
is negligible, Eq. (9) can be arranged as:
where
D
_{min}
is the minimum duty ratio.
Unlike the conventional ACFC, the leakage inductor for ZVS is not load dependent for the ACFC with a CDR. A leakage inductor that meets the condition in Eq. (10) guarantees the ZVS condition across the entire range of loads. Furthermore, the ACFC with a CDR can achieve ZVS while keeping
L_{lk}
much lower than
L_{m}
if the output inductor is properly designed. The leakage inductance for ZVS is shown in
Fig. 7
under the following conditions:
L_{m}
varies from 0 to 400 μH,
L
_{2}
varies from 0.5 to 2 μH, and
V_{g}
is fixed at 48 V. The optimal design conditions can be easily identified from
Fig. 7
.
Leakage inductance for ZVS operating ACFC with CDR.
IV. LOSS ANALYSIS
To verify that the enhanced ZVS performance was responsible for the improved efficiency, a loss analysis was conducted. The ACFC with a CDR was designed according to the system specifications in
Table I
, and the results are shown in
Table II
. For the conventional ACFC, the design specifications are the same as those of the ACFC with a CDR, except that a 1μH output inductor was used in the conventional ACFC.
DESIGN RESULTS OF THE ACFC WITH CDR
DESIGN RESULTS OF THE ACFC WITH CDR
The loss factors considered in this analysis are as follows: 1) the conduction loss in the FETs and ESRs (
P_{cond}
); 2) the switching loss in the FETs (
P_{sw}
); and 3) the transformer core loss (
P_{core}
). Numerical expressions for each of the loss factors are derived below.
First, the conduction loss is calculated from the resistance and RMS current through each resistor. The conduction loss is expressed as:
Next, the switching loss is estimated from the output capacitor loss and power loss during the switching transition period. The switching loss can be expressed as:
where
V_{i}
and
I_{i}
are the switch voltage and current, and
t_{on}
and
t_{off}
are the turnon and turnoff switching periods of the corresponding power MOSFET, respectively. In the case of synchronous switches, only the turnoff losses are accounted for because they always attain ZVS by the load current and turnon losses are negligible.
Finally, the core loss is given by
where
ρ_{m}
,
V_{e}
, and
B_{m}
are the core material density, the core volume, and the maximum flux density, respectively.
K_{c}
,
α
, and
β
are constants that can be determined by fitting the core data provided by the manufacturer
[35]
.
The total efficiency and loss component are calculated for the four converters:

1) ACFC with a CDR (Lm= 200 μH &Llk= 3 μH).

2) Hard switching ACFC (Lm= 200 μH &Llk= 3 μH).

3)LlkZVS ACFC (Lm= 80 μH &Llk= 5 μH).

4)LmZVS ACFC (Lm= 40 μH &Llk= 3 μH).
All of the device parameters needed in the loss calculation are obtained from the datasheet provided by the manufacturer. The results of the loss analysis are shown in
Fig. 8
.
Comparison of estimated efficiency and loss components. (a) ACFC with CDR and hardswitching ACFC. (b) ACFC with CDR and softswitching ACFCs.
In
Fig. 8
(a), the estimated efficiency and loss components of the ACFC with a CDR and the hardswitching ACFC are presented. The ACFC with a CDR has the lowest switching loss due to its outstanding ZVS characteristics. It exhibits a higher efficiency than the hardswitching ACFC at lightload conditions, when switching losses dominate. Due to its small RMS current on the secondary, the ACFC with a CDR also exhibits a higher efficiency in the heavyload range. Therefore, the ACFC with a CDR achieves a high efficiency when compared to the hardswitching ACFC throughout the whole load.
In
Fig. 8
(b), a comparison of the ACFC with a CDR and two softswitching ACFCs is presented. The
L_{lk}
ZVS ACFC has the advantage of softswitching due to its large leakage inductance, thereby attains ZVS from mediumload conditions. However, the duty cycle loss and auxiliary switch turnoff loss increase with the load. Consequently, the
L_{lk}
ZVS ACFC exhibits the worst heavyload efficiency of all of the converters. The
L_{m}
ZVS ACFC achieves softswitching due to its reduced
L_{m}
and it shows a high efficiency at lightload conditions. However, the heavyload efficiency is worse than the ACFC with a CDR because of the increased conduction loss on the primary side.
The loss analysis shows that the ACFC with a CDR exhibits the most outstanding ZVS performance. The lightload efficiency is expected to improve with softswitching. At heavy loads, the advantages of a small RMS current on the secondary contribute to a high efficiency. The two softswitching ACFCs also show high efficiency at lightloads. However, heavyload efficiency get worse because of the duty cycle loss, switch turnoff loss and primary side conduction loss.
V. EXPERIMENTAL RESULTS
The improved efficiency of the ACFC with a CDR was experimentally verified. Prototypes of the ACFC with a CDR (
L_{m}
= 200 μH &
L_{lk}
= 3 μH), a hardswitching ACFC (
L_{m}
= 200 μH &
L_{lk}
= 3 μH), a
L_{lk}
ZVS ACFC (
L_{m}
= 80 μH &
L_{lk}
= 5 μH), and a
L_{m}
ZVS ACFC (
L_{m}
= 40 μH &
L_{lk}
= 3 μH) were built and tested.
The waveforms for the leakage inductor current (
i_{Llk}
), transformer secondary current (
i_{sec}
), magnetizing inductor current (
i_{Lm}
), and two output inductor currents (
i_{L}
_{1}
and
i_{L}
_{2}
) are shown in
Fig. 9
for the ACFC with a CDR at a 10% load. The function for
i_{Lm}
is calculated from
i_{Llk}
and
i_{sec}
divided by the transformer turn ratio. As seen in
Fig. 9
, the average <
i_{Lm}
> is 226 mA, whereas the average <
i_{L}
_{2}
> is 982 mA. This is nearly
N
times larger than <
i_{Lm}
>. Therefore,
i_{Llk}
(
t
_{1}
) is determined by the ripple current of
i_{Lm}
and
i_{L}
_{2}
, as shown in
Fig. 4
.
Current waveforms of the ACFC with CDR at 10% load condition.
Waveforms for the draintosource voltage of
S
_{1}
(
V_{ds}
_{1}
), the gatetosource voltage of
S
_{1}
(
V_{gs}
_{1}
), the gatetosource voltage of
S
_{2}
(
V_{gs}
_{2}
), and the leakage inductor current (
i_{Llk}
) are shown in
Fig. 10
for the ACFC with a CDR.
V_{ds}
_{1}
is zero before
S
_{1}
is turned on, which confirms the ZVS of
S
_{1}
with a low electromagnetic interference (EMI) despite a small leakage inductance under all load conditions. The primary conduction loss is greater than that of the conventional ACFC because of the increased
i_{pri}
(
t
_{1}
). Nevertheless, a decrease in the primaryswitching loss compensates for the increased primary conduction loss. As a result, the efficiency of the ACFC with a CDR is higher than that of the hardswitching converter at light load.
Waveforms of the ACFC with CDR (L_{m} = 200 μH & L_{lk} = 3 μH). (a) 10% load. (b) 50% load. (c) 100% load.
Waveforms for the hardswitching ACFC at a 10% load are shown in
Fig. 11
(a). When
S
_{1}
is turned on, a hardswitching operation is observed with EMI noise before
V_{ds}
_{1}
becomes zero. This diminishes the lightload efficiency of the hardswitching ACFC, as seen in
Fig. 14
(a). Waveforms of the hardswitching ACFC at 50% and 100% load are shown in
Fig. 11
(b) and
Fig. 11
(c), respectively. At the 100% load condition,
S
_{1}
almost achieves ZVS due to the increased load current. However, the ACFC with a CDR still shows a high efficiency.
Waveforms of conventional ACFC (L_{m} = 200 μH & L_{lk} = 3 μH). (a) 10% load. (b) 50% load. (c) 100% load.
Waveforms for the
L_{lk}
ZVS ACFC at a 10% load are shown in
Fig. 12
(a). Due to its large leakage inductance, hardswitching operation is observed with less EMI noise below 50% load condition. From a 50% load,
S
_{1}
almost achieves ZVS as seen in
Fig. 12
(b). However, an increased duty cycle loss is observed at the heavy load condition, which deteriorates the efficiency.
Waveforms of L_{lk}–ZVS ACFC (L_{m} = 80 μH & L_{lk} = 5 μH). (a) 10% load. (b) 50% load. (c) 100% load.
Waveforms for the
L_{m}
ZVS ACFC are shown in
Fig. 13
. Due to its reduced magnetizing inductance, softswitching operation is observed with less EMI noise under all load conditions. However, an enlarged primary current is observed relative to the other ACFCs. This decreases efficiency at heavyload.
Waveforms of L_{m}–ZVS ACFC (L_{m} = 40 μH & L_{lk} = 3 μH). (a) 10% load. (b) 50% load. (c) 100% load.
In conclusion, the ACFC with a CDR achieves ZVS of
S
_{1}
more easily than the conventional ACFC, even with a small leakage inductance. Improvements in efficiency are most evident in the lightload conditions, especially, when the switching loss is the dominant factor in the total loss. The conventional ACFC is also able to perform ZVS with an increased resonant inductance or a reduced magnetizing inductance. However, its heavyload efficiency is worsened by its large duty cycle loss, auxiliary switch turnoff loss and primary side conduction loss. Consequently, the ACFC with a CDR has a higher efficiency with less EMI noise than the other ACFCs for all load conditions (see
Fig. 14
).
Efficiency measurement. (a) ACFC with CDR and hardswitching ACFC. (b) ACFC with CDR and softswitching ACFCs
VI. CONCLUSIONS
In this paper, the ZVS operation of an ACFC with a CDR is studied. Placing the CDR in the transformer secondary, the ZVS condition can be obtained with a much smaller leakage inductance compared to the conventional ACFC. A detailed ZVS analysis is conducted on the basis of a steadystate analysis. The design consideration for ZVS improvement is presented. A loss analysis of the converter shows that the enhanced ZVS performance contributes to improved efficiency under lightload conditions. Experimental results with a 100W (5V/20A) prototype verified that the ACFC with a CDR can attain ZVS of the main switch more efficiently in spite of a small leakage inductance and that it can achieve a high efficiency compared to other ACFCs throughout the whole load range.
BIO
Paul Jang received his B.S. degree in Electrical Engineering from Seoul National University, Seoul, Korea, in 2010; where he is presently working towards his Ph.D. degree. His current research interests include converter parallel operation, modular converter systems, distributed power systems, and soft switching converters.
HyeJin Kim received his B.S. and M.S. degrees in Electrical Engineering from Seoul National University, Seoul, Korea, in 2010, and 2012, respectively; where he is presently working towards his Ph.D. degree. His current research interests include the design, analysis, and control of power factor correction converters and distributed power systems.
BoHyung Cho received his B.S. and M.S. degrees from the California Institute of Technology, Pasadena, CA, USA; and his Ph.D. degree from the Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, VA, USA, all in Electrical Engineering. Prior to his research at Virginia Tech, he was a member of the Technical Staff with the Department of Power Conversion Electronics, TRW Defense and Space System Group, USA. From 1982 to 1995, he was a Professor in the Department of Electrical Engineering, Virginia Tech. In 1995, he joined the School of Electrical Engineering, Seoul National University, Seoul, Korea, where he is presently working as a Professor. His current research interests include power electronics, distributed power systems, and the modeling, analysis and control of spacecraft power processing equipment. Dr. Cho is a member of Tau Beta Pi. He was a recipient of the 1989 Presidential Young Investigator Award from the National Science Foundation. He chaired the 2006 IEEE Power Electronics Specialists Conference.
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