energies
Article
High-Frequency LLC Resonant Converter with GaN
Devices and Integrated Magnetics
Yu-Chen Liu 1, * , Chen Chen 2 , Kai-De Chen 2 , Yong-Long Syu 2
1
2
*
and Meng-Chi Tsai 1
Department of Electrical Engineering, National Ilan University, No. 1 Section 1 Shennong Road,
Yilan 260, Taiwan; kid3181910@gmail.com
Department of Electronic Engineering, National Taiwan University of Science, and Technology, No. 43
Section 4 Keelung Rd Da’an District, Taipei 10607, Taiwan; D10502204@mail.ntust.edu.tw (C.C.);
d10502203@mail.ntust.edu.tw (K.-D.C.); x452800@gmail.com (Y.-L.S.)
Correspondence: ycliu@niu.edu.tw
Received: 15 April 2019; Accepted: 5 May 2019; Published: 10 May 2019
Abstract: In this study, a light emitting diode (LED) driver containing an integrated transformer with
adjustable leakage inductance in a high-frequency isolated LLC resonant converter was proposed as an
LED lighting power converter. The primary- and secondary-side topological structures were analyzed
from the perspectives of component loss and component stress, and a full-bridge structure was
selected for both the primary- and secondary-side circuit architecture of the LLC resonant converter.
Additionally, to achieve high power density and high efficiency, adjustable leakage inductance was
achieved through an additional reluctance length, and the added resonant inductor was replaced with
the transformer leakage inductance without increasing the amount of loss caused by the proximity
effect. To optimize the transformer, the number of primary- and secondary-side windings that
resulted in the lowest core loss and copper loss was selected, and the feasibility of the new core
design was verified using ANSYS Maxwell software. Finally, this paper proposes an integrated
transformer without any additional resonant inductor in the LLC resonant converter. Transformer loss
is optimized by adjusting parameters of the core structure and the winding arrangement. An LLC
resonant converter with a 400 V input voltage, 300 V output voltage, 1 kW output power, and 500 kHz
switching frequency was created, and a maximum efficiency of 97.03% was achieved. The component
with the highest temperature was the transformer winding, which reached 78.6 ◦ C at full load.
Keywords: LLC resonant converter; integrated transformer; adjustable leakage inductance;
LED driver
1. Introduction
Light emitting diode (LED) lighting has become more popular in recent years, particularly as
product energy efficiency has become more important to consumers [1–3]. Compared with conventional
lighting equipment, LEDs are brighter and have a longer service life. LEDs have thus been used in
various lighting scenarios, such as street lighting, indoor lighting, and backlighting. They have also
been used for lighting equipment with high power requirements, like baseball field or basketball court
lights. Most of these LED driver circuits have a two-stage architecture consisting of a power factor
correction converter in the first stage and an isolated buck converter in the second stage, with an LLC
resonant converter usually employed as the second-stage circuit [4,5].
Unlike other common isolated buck converters, an LLC resonant converter is characterized by
power components with zero voltage switching (ZVS) and zero current switching at the high—and
low—voltage ends, respectively, in a full load range. Additionally, unlike phase-shifted full-bridge
converters, an LLC converter has no output inductance at the low-voltage end and thus has higher
Energies 2019, 12, 1781; doi:10.3390/en12091781
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Energies 2019, 12, 1781
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conversion efficiency [6]. Moreover, to achieve high power density, increasing the switching frequency
of the power switch reduces the volume of the magnetic component; however, this is accompanied by
a considerable increase in switching loss. Therefore, in addition to the ZVS feature of the LLC resonant
converter, wide-band-gap switch components should also be employed to reduce the switching loss
under high-frequency operation [7,8]. Additionally, selecting an appropriate LLC resonant converter
architecture can further optimize the efficiency and reduce component stress [9–11]. The topologies
commonly used in the high-voltage end of the LLC resonant converter are the half bridge and full
bridge, whereas those used in the low-voltage end are the full bridge or center tap.
To achieve high power density, the leakage inductance of the transformer in this study was used as
the resonant inductor of the circuit [12–14], which reduces the number of magnetic components required.
Previous research replaced the resonant inductor with the leakage inductance of the transformers,
mostly through winding the transformer using litz wire and setting the operating frequency between
50 and 200 kHz. However, when the operating frequency is between 500 kHz and 1 MHz, the litz
wire is usually replaced by printed circuit board (PCB) windings to reduce the alternating-current
(AC) resistance of the copper traces under high-frequency operation. Additionally, the primary- and
secondary-side windings are interleaved to weaken the proximity effect. This approach reduces
proximity-effect-induced loss and minimizes the leakage inductance of the transformer [15–17], which
is a disadvantage in LLC resonant converters that require leakage inductance to design resonant tanks.
A conventional method for increasing the leakage inductance is to increase the spacing between the
primary and secondary sides [18–20], which is mostly achieved using a non-interleaved winding that
leads to a sharp rise in the proximity-effect-induced AC loss. Therefore, the concept of adjustable
leakage inductance [21,22] was adopted in this study, with an additional reluctance length added
between the primary-side and secondary-side windings of the transformer. This enabled the magnetic
flux generated by the primary-side winding to flow into the added reluctance length, thereby increasing
the primary-side leakage inductance. The proposed approach weakens the proximity effect in the
interleaved winding and attains the objective of increasing the leakage inductance. Compared to
existing LED power converter designs [23–25], this work reduces the switching loss via wide bandgap
devices and soft switching techniques under 500 kHz switching frequency conditions and utilizes
an integrated transformer without an additional resonant inductor to achieve high power density.
Ultimately, an LLC resonant converter with an output power of 1 kW, switching frequency of 500 kHz,
input voltage of 400 V, and output voltage of 300 V was achieved in this study.
In this study, a second-stage LLC resonant converter was proposed for the LED driver circuit,
and the LLC resonant circuit was used as a direct-current transformer (DCX) to operate the driver circuit
at high efficiency. In addition, this study also designed and optimized the primary- and secondary-side
topologies and magnetic components in the LLC resonant converter. In Section 2, under the conditions
of 1 kW output power, 400 V input voltage, and 300 V output voltage, the loss and component stress at
the primary—and secondary—side structures of the converter are analyzed and a topology suitable for
the specification in this study is selected. Section 3 details the mathematical induction of adjustable
leakage inductance and the appropriate number of primary- and secondary-side windings for the
new core based on the optimal point of core loss and copper loss. The feasibility of the designed core
structure was verified using ANSYS Maxwell software (ANSYS, Canonsburg, PA, USA). Section 4
presents the experimental results, including temperature distribution maps.
2. LLC Topology Comparison
The primary and secondary sides of different architectures are discussed in this section.
Because different circuit specifications have their appropriate architecture, the architecture is chosen
based on power level and component stress, as shown in Figure 1. The primary side may consist
of a half bridge or full bridge, whereas the secondary side comprises a center-tap and full-bridge
rectification. The choice of different architectures for the primary side results in different transformer
designs; hence, the primary side is mainly selected based on the corresponding architecture for the
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the primary side is mainly selected based on the corresponding architecture for the appropriate
the
primary
is mainly
selected
based on on
thethe
corresponding
architecture
the appropriate
power
level.side
As for
the different
architectures
secondary side,
there are for
different
component
appropriate
power
level.
As
for
the
different
architectures
on
the
secondary
side,
there
are
different
power
level.
for the of
different
architectures
secondaryarchitecture
side, there are
component
stresses
andAs
numbers
switches.
Therefore, on
thethe
appropriate
for different
the secondary
side is
component
stresses
and
numbers
of
switches.
Therefore,
the
appropriate
architecture
for
the
secondary
stresses
numbers
of switches.
Therefore,
the appropriate
architecture
mainly and
selected
according
to the level
of the output
voltage and
current. for the secondary side is
side
is mainly
selected
according
to theoflevel
of the output
and current.
mainly
selected
according
to the level
the output
voltagevoltage
and current.
Figure 1. Architecture selection diagram.
Figure 1. Architecture selection diagram.
The common structures for the primary side are the half bridge and full bridge (Figure 2). For
The common
structures
for
primary
side
areare
the
half
bridge
andand
fullfull
bridge
(Figure
2). For
the
common
structures
forthe
thethe
primary
side
half
bridge
(Figure
2).
For
the half
bridge,
the
voltage across
resonant
tank
isthe
+V
in
to
0bridge
V; however,
the
actual
voltage
across
half
bridge,
the the
voltage
across
thethe
resonant
isbetween
+V
00V;
however,
the
actual
across
the
bridge,
voltage
across
resonant
tank
is +V
tothe
V;
however,
the
actual voltage
voltage
thehalf
transformer
is ±V
in/2.
Therefore,
the
turnstank
ratio
primary
and
secondary
sides must
be
in into
the
transformer
is
±V
/2.
Therefore,
the
turns
ratio
between
the
primary
and
secondary
sides
must
±Vinin
/2. Therefore,
turns ratioThe
between
thetransfer
primaryformula
and secondary
sides(1)
must
accounted for when
designing
the the
transformer.
energy
in Equation
canbe
be
be
accounted
when
designing
the
transformer.
The
energy
formula
in Equation
(1)
accounted
for
designing
thethat
transformer.
The
energy
transfer
formula
in Equation
cancan
bein
rewritten
as for
awhen
general
formula
establishes
ZVS
under
atransfer
half-bridge
structure,
as(1)
shown
be
rewritten
a general
formulathat
thatestablishes
establishesZVS
ZVSunder
underaahalf-bridge
half-bridge structure,
structure, as
as shown in
rewritten
as
a general
formula
Equation
(2).as
Equation (2).
2 11 2 2
1 1 LI
(1)
CV
LI2 ≥ ≥1CV
(1)
1
2
2 2LI ≥ 2 2CV 2
(1)
2
2
ininwhich
whichthe
theunit
unitofofLLisisHenry
Henry(H),
(H),I IisisAmpere
Ampere(A),
(A),CCisisFarad
Farad(F),
(F),and
andVVisisVolt
Volt(V).
(V).
in which the unit of L is Henry (H), I is Ampere (A), C is Farad (F), and V is Volt (V).
tdead
tdead
LmL≤
(2)
(2)
m ≤
16C
fsw
t
oss
C
f
16
dead
oss
sw
Lm ≤
(2)
16Coss f sw
ininwhich
isFarad
Farad(F),
(F),and
andffswswisisHertz
Hertz(Hz).
(Hz).
mmis
isHenry
Henry(H),
(H),tdead
tdead is
is seconds
seconds (s),
(s), C
Coss
whichthe
theunit
unitofofLL
oss is
in which the unit of Lm is Henry (H), tdead is seconds (s), Coss is Farad (F), and fsw is Hertz (Hz).
Vin
Vin
Lr
Lr Lm
Cr Lm
Cr
(a)
(a)
N1 : N2
N1 : N2
Vin
Vin
Lr
Lr Lm
Cr Lm
Cr
N1 : N2
N1 : N2
(b)
(b)
Figure2.2.Primary
Primarystructure
structure(a)
(a)half
halfbridge
bridgeand
and(b)
(b)Full
Fullbridge
bridgetopology.
topology.
Figure
Figure 2. Primary structure (a) half bridge and (b) Full bridge topology.
Fora afull-bridge
full-bridge
structure,
voltage
across
the transformer
is approximately
±Vinthe
, and
the
For
structure,
the the
voltage
across
the transformer
is approximately
±Vin , and
input
For
a full-bridge
structure,
thethe
voltage
the
isthe
approximately
±Vin,designing
and the
input
voltage
be directly
divided
by
the across
output
voltage
to obtain
turns
voltage
can
be can
directly
divided
by
output
voltage
totransformer
obtain
the turns
ratio ratio
whenwhen
designing
input
voltageFor
canprimary-side
be
divided
by to
theachieve
output
voltage
obtain
thestructure,
turns ratio
designing
the transformer.
Fordirectly
primary-side
switching
to achieve
in a full-bridge
structure,
the
energy
transformer.
switching
ZVS
in ZVS
a to
full-bridge
thewhen
energy
transfer
the
transformer.
primary-side
switching
toasachieve
ZVS in
a full-bridge
structure, the energy
transfer
formulaFor
Equation
can be
rewritten
the following
general
formula:
formula
Equation
(1) can
be(1)
rewritten
as the following
general
formula:
transfer formula Equation (1) can be rewritten as the following general formula:
tdead
tdead
(3)
LmLm≤ ≤ 8tC
f sw
dead
Lm ≤ 8Cossossfsw
(3)
8Coss f sw
Energies 2019, 12, 1781
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Under the conditions of 400 V input voltage, 300 V output voltage, and a half-bridge structure
of the primary side, the equivalent turns ratio of the primary and secondary sides is indicated by
Equation (4), whereas Equation (5) obtains the equivalent turns ratio of the two sides when a full-bridge
structure is adopted on the primary side. In choosing the primary-side architecture, the conditions of
primary-side ZVS are influenced by the stray capacitance [26]. In particular, the stray capacitance of
the secondary side mapped back to the primary side is affected by the turns ratio. Thus, if a half-bridge
structure was adopted under this specification, the stray capacitance mapped from the secondary to
the primary side would be magnified. Therefore, a full-bridge structure was employed in this study to
reduce the effect on ZVS condition. Table 1 [27] shows a comparison of the various ratings of the two
primary-side architectures.
Vin/2
N1
2
=
=
(4)
N2
Vo
3
V
4
N1
= in =
N2
Vo
3
(5)
Table 1. Comparison of primary-side architectures.
Primary Structure
Half-Bridge
Full-Bridge
Primary device voltage stress
Vin
(400 V)
Vin
(400 V)
r
4π2 +
Vo
Primary device current stress
N1
N2
4
r
RL 2 ( LTm )
2
4π2 +
Vo
N
N1
N2
4
2
r
RL 2 ( LTm )
2
4π2 +
Vo
N
N1
N2
4
RL 2 ( LTm )
(4.08 A)
(2.36 A)
4
2
N
4π2 + N1 RL 2 ( LTm )
2
√ N
4 2· N1 ·RL
2
Lm ≤
tdead
16Coss fsw
2
r
Vo
4
2
N
4π2 + N1 RL 2 ( LTm )
2
√ N
4 2· N1 ·RL
2
(3.38 A)
Lm ≤
tdead
8Coss fsw
Turns ratio
N1 :N2
(12:18)
N1 :N2
(24:18)
Primary device
GS66508B, 650 V
GS66508B, 650 V
Number of primary device
2
2
2
N
8· N1 ·RL
2
ZVS condition
8· N1 ·RL
(5.8 A)
2
N
(4.81 A)
Primary device rms current
Resonant inductor rms current
RL 2 ( LTm )
(8.25 A)
4π2 +
r
4
4· N1 ·RL
r
Vo
N1
N2
4· N1 ·RL
2
Vo
4
2
Total SR conduction loss
Irms · Rds(on) · 2
(1.665 W)
Irms · Rds(on) · 4
(1.114 W)
Winding loss of primary side
7.24 W
5.51 W
Proper specification
Low power
High power
In Table 1, T is the switching period, and its unit is seconds (s), and RL is the output load. Its unit is Ohm (Ω). ZVS,
zero voltage switching. SR, synchronous rectifier.
Common structures for the secondary side are center-tap and full-bridge rectification (Figure 3).
For center-tap rectification, the voltage over the secondary side of the transformer was 1 × Vo ;
however, the voltage over the synchronous rectifiers (SRs) was 2 × Vo , and overall, the conduction loss
amounted to that of two SRs. Based on this analysis, the center-tap structure was more suitable for
low-output-voltage and high-current specifications.
Compared with those in the center-tap structure, the voltage over the secondary side and the
SRs of the transformer in the full-bridge rectification structure were 1 × Vo ; however, the conduction
loss amounted to that of four SRs. Based on this analysis, full-bridge rectification was suitable for
however, the voltage over the synchronous rectifiers (SRs) was 2 × Vo, and overall, the conduction
loss amounted to that of two SRs. Based on this analysis, the center-tap structure was more suitable
for low-output-voltage and high-current specifications.
Compared with those in the center-tap structure, the voltage over the secondary side and the
Energies
2019,transformer
12, 1781
19
SRs of the
in the full-bridge rectification structure were 1 × Vo; however, the5 of
conduction
loss amounted to that of four SRs. Based on this analysis, full-bridge rectification was suitable for
high-output-voltage
andlow-current
low-current
specifications.
the high-output-voltage
specification
and
high-output-voltage and
specifications.
For For
the high-output-voltage
specification
and
considering
thetradeoff
tradeoff
between
the
SR voltage
rating,
SR conduction
loss, and secondary-side
considering the
between
the SR
voltage
rating, SR
conduction
loss, and secondary-side
copper
copper
loss,
full
wave rectification
was
for the secondary-side
structure,
and the switch
loss, full
wave
rectification
was selected
for selected
the secondary-side
structure, and the
switch employed
was the GS66508B.
2 showsTable
a comparison
SR rated voltage,
turns ratio,
and SR turns
employed
was theTable
GS66508B.
2 showsofathe
comparison
of the transformer
SR rated voltage,
transformer
number
of
the
two
secondary-side
architectures.
ratio, and SR number of the two secondary-side architectures.
N1 : N2 : N2
N1 : N2
RL
Lm
RL
Lm
Vo
(a)
Vo
(b)
Figure3.3.Secondary-side
Secondary-side
architecture:
(a) center
tap(b)
and
full bridge.
Figure
architecture:
(a) center
tap and
full(b)
bridge.
Table 2. Comparison of secondary-side architectures.
Table 2. Comparison of secondary-side architectures.
Secondary Structure
Center-Tap
Secondary Structure
Center-Tap
2 V0
2V0 V)
(600
r(600 V) N
2
SR voltage stress
SR voltage stress
SR current stress
SR current stress
SR rms current
Turns ratio
SR rms current
SR device
Number of SR device
Turns ratio
Total SR conduction loss
SR device
Number of SR device
Winding loss of secondary side
Proper specification
Total SR conduction loss
12
Full-Bridge
4
5π −48
1
2 T2
√ Vo 12π4 +
N2 R
4L
Lm 2
12 4 5π 2 −24πR
48 L N1 
2 2
Vo 12π +

 RL T
(5.5
Lm 2A)  N 2 
r
√
3
Vo
4
24 π2R
L N1
−48
12π4 + 5π
Lm 2
(5.5 24πR
A) L
N2
RL 2 T 2
(2.67 A)
4
5π 2 − 48  N1 
4
2 2
Vo 12π + N1:N2:N2

 RL T
2
Lm
N2 

(24:18:18)
3
24π RL
GS66508B, 650 V
(2.67 A)
2
N1:N2:N2
2
Irms · Rds(on) · 2
(24:18:18)
(0.713 W)
GS66508B, 650 V
2.41 W
2
Low output voltage
High
Irms2output
⋅ Rds(on)current
⋅2
(0.713 W)
Full-Bridge
V0
(300
4 V)
N
2
V0
(300 V)
r
−48
1
N2
Lm 2
2
4
24πR
L
12π4 + 5π
√ Vo
12
RL 2 T 2
4
5π − 48  N1 
2 2
Vo 12π +

 RL T
(5.5 A)
Lm 2  N 2 
12
r
24
4 π R
L
5π2 −48 N1
12π4 +
√ Vo
3
Lm 2
N2
24πRL(5.5
(2.67 A)
A)
4
5π − 48  N1 
2 2

 RL T
Lm 2  N 2 
(24:18)
24π RL
Vo N1:N2
12π 4 +
3
RL 2 T2
2
GS66508B, 650 V
(2.67 A)
N1:N2
Irms 2 · Rds(on) · 4
(24:18)
(1.426 W)
GS66508B, 650 V
2.41 W
4
4
High output voltage
2
Low output
Irmscurrent
⋅ Rds(on) ⋅ 4
(1.426 W)
Next,
the differences
Winding
loss ofbetween the four architectures (primary and secondary side) are compared.
2.41 W
2.41 Wresult in a
In terms of the primary-side switch voltage stress,
both the half bridge and full bridge
secondary side
voltage stress of 1 × Vin , whereas the secondary-side switch voltage stress is 2 Vo and Vo for center-tap
Low output voltage
High output voltage
and full-bridge
rectification, respectively. The voltage over the transformer was ±0.5 Vin when a
Proper specification
High
output
current
Low output
current
half-bridge structure was employed for the
primary
side,
whereas using a full-bridge
structure
yielded
a voltage of ±Vin . Therefore, when transmitting the same power, the transformer current was Ir when
Next, thestructure
differences
theprimary
four architectures
secondarystructure
side) arewas
compared.
a full-bridge
was between
used on the
side but had(primary
to be 2 Ir and
if a half-bridge
Inused.
terms
of thethe
primary-side
switch
voltagewas
stress,
both
thevoltage,
half bridge
and full
bridge
result in a
Because
voltage over the
transformer
half the
input
the current
on the
primary
side was greater when a half-bridge structure was employed than when the primary side comprised
a full-bridge structure. Therefore, the primary-side half-bridge architecture is suitable for circuits
Energies 2019, 12, 1781
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with low power applications to prevent excessive current flow through the transformer, which would
result in saturation. Regarding the secondary side, the component voltage stress when the center-tap
structure was used was twice that when full-bridge rectification was employed, whereas the number
of components was half; the center-tap structure is thus appropriate for low-voltage-output and
high-current applications. Table 3 shows a comparison of the characteristics for the four architectures.
Table 3. Comparison of the four architectures.
Component
Primary Side:
Half-Bridge
Secondary Side:
Center-Tap
Primary Side:
Half-Bridge
Secondary Side:
Full-Bridge
Primary Side:
Full-bridge
Secondary side:
Center-Tap
Primary side:
Full-Bridge
Secondary side:
Full-Bridge
Primary device
voltage stress
Vin
Vin
Vin
Vin
SR voltage stress
2 V0
V0
2V0
V0
Primary-side
transformer
voltage stress
±0.5 Vin
±0.5 Vin
±Vin
±Vin
Secondary-side
transformer
voltage stress
±V0
±V0
±V0
±V0
Primary-side
transformer
current
2 Ir
2 Ir
Ir
Ir
Proper
specification
Low power
Low output voltage
High output
current
Low power
High output
voltage
Low output current
High power
Low output voltage
High output
current
High power
High output
voltage
Low output current
The loss distribution of the four architectures was calculated on the basis of the specifications
in this study (Figure 4). According to the loss distribution illustrated in Figure 4, the loss of each
architecture type was mostly copper loss of the transformers and other loss types, including the
equivalent series resistance of the capacitor and via loss. The overall efficiency of the architecture
comprising a primary-side full-bridge structure and secondary-side center-tap structure was the highest
of all architectures. However, because the specification of this study was high output voltage, the SR
voltage rating of the secondary-side center-tap structure had to be 2 Vo ; additionally, the actual test
circuit was not ideal. Therefore, the architecture with primary-side full-bridge and secondary-side full
bridge structures, which had the second highest efficiency, was selected to prevent the SR from being
damaged by the high voltage.
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Figure 4. Comparison of loss types in different architectures.
Figure 4. Comparison of loss types in different architectures.
4. Comparison of
types in different
architectures.
3. Design Concept andFigure
Loss Optimization
ofloss
Adjustable
Leakage
Inductance
3.
Design
Concept and
andintegrated
Loss Optimization
Optimization
of
Leakage
Inductance
The conventional
leakage inductance
is formed
by leakage
flux that is lost to the air
3. Design
Concept
Loss
of Adjustable
Adjustable
Leakage
Inductance
and does
not pass through
the secondary
side.
Accurate
control of
the
amount
leakage
inductance
The
conventional
integrated
leakage
inductance
is
formed
by
leakage
fluxofthat
that
is lost
lost
to
The conventional integrated leakage inductance is formed by leakage flux
is
to the
the air
air
is
practically
difficult.
The
concept
of
adjustable
leakage
inductance
that
was
adopted
in
this
study
and
ofof
leakage
inductance
is
and does
does not
not pass
passthrough
throughthe
thesecondary
secondaryside.
side.Accurate
Accuratecontrol
controlofofthe
theamount
amount
leakage
inductance
was to adddifficult.
an additional
reluctance
length that
prevents
somethat
fluxwas
generated
on
the
primary
side
practically
The
concept
of
adjustable
leakage
inductance
adopted
in
this
study
was
to
is practically difficult. The concept of adjustable leakage inductance that was adopted in this study
from flowing
intoreluctance
the secondary-side
winding,
in turn
generating
leakage
inductance.
The flowing
leakage
add
length that
prevents
flux
generated
the primary
from
was an
to additional
add an additional
reluctance
length
thatsome
prevents
some fluxon
generated
on side
the primary
side
inductance
used
in
this
study
was
designed
using
the
concept
of
split
flow
of
the
transformer
into
secondary-side
winding, in turn
generating
leakage
inductance.
The inductance.
leakage inductance
used
fromthe
flowing
into the secondary-side
winding,
in turn
generating
leakage
The leakage
reluctance.
in
this studyused
was designed
usingwas
the concept
of using
split flow
the transformer
reluctance.
inductance
in this study
designed
the of
concept
of split flow
of the transformer
Figure
5
presents
the
concept
of
adjustable
leakage
inductance,
where
the
voltage of
of the
the primary
primary
Figure 5 presents the concept of adjustable leakage inductance, where the voltage
reluctance.
side
and
secondary
side
are
denoted
by
Vp
and
Vs,
respectively.
The
winding
in
the
primary
side
was
side and
secondary
side
areconcept
denoted
Vp and Vs,
respectively.
The where
winding
the primary
was
Figure
5 presents
the
of by
adjustable
leakage
inductance,
theinvoltage
of theside
primary
divided into two
two parts,
parts, of
of which
which one
one part wound
counterclockwise
with 18
18 turns
turns around
around the
the left
left outer
outer
divided
wound
counterclockwise
with
side andinto
secondary
side are
denoted part
by Vp
and Vs,
respectively. The
winding
in the primary
side was
leg,
and
the
other
wound
clockwise
with
6
turns
around
the
right
outer
leg.
Similarly,
the
winding
leg,
and into
the other
wound
turns around
the right outer
Similarly,
thethe
winding
on
divided
two parts,
of clockwise
which onewith
part 6wound
counterclockwise
withleg.
18 turns
around
left outer
on the
secondary
side
was
also
divided
into
two parts,
in which
onewound
part wound
clockwise
with
6
the
secondary
side
was
also
divided
into
two
parts,
in
which
one
part
clockwise
with
6
turns
leg, and the other wound clockwise with 6 turns around the right outer leg. Similarly, the winding
turns
around
the
left
outer
leg,
and
the
other
wound
counterclockwise
with
12
turns
around
the
right
around
the left outer
leg,
and
thedivided
other wound
counterclockwise
turns
around
the rightwith
outer6
on the secondary
side
was
also
into two
parts, in whichwith
one12
part
wound
clockwise
outer
leg. Moreover,
according
to Equation
(6), the magnetomotive
forceof(MMF)
of these windings
leg.
Moreover,
according
to
Equation
(6),
the
magnetomotive
force
(MMF)
these
windings
could
be
turns around the left outer leg, and the other wound counterclockwise with 12 turns around the right
could be represented
as
18
I
p, 6and
Is,
6
Ip,
and
12
I
s, and
their
voltage
as
V
pw
,
V
px,, and
V
sy, and
V
sz, respectively.
represented
as
18
I
,
6
Is,
6
Ip,
12
I
,
and
their
voltage
as
V
,
V
,
V
V
,
respectively.
R
p according to Equation
s
pw
px
outer leg. Moreover,
(6), the magnetomotive
forcesy (MMF) szof these windingso
Ro represents
the
reluctance
of the
outer
leg,
and
Rc represents
the
reluctance
of the
center
represents
the
reluctance
of
the
outer
leg,
and
R
represents
the
reluctance
center
leg.leg.
c
could be represented as 18 Ip, 6 Is, 6 Ip, and 12 Is, and their voltage as Vpw, Vpxof
, Vthe
sy, and Vsz, respectively.
Ro represents the reluctance of the outer leg, and Rc represents the reluctance of the center leg.
ϕ1
ϕ2
ϕ3
Ip
Is
ϕ1
ϕ2
ϕ3
+
Ro
Rc
Ro
Ip +
Is
Vpw
Vsy
+
+
Ro V Rc
18I
VRpxo 6Ip
−
−
p
pw
V+pw
V+sy
18Ip Vpw
Vpx 6Ip
V−px
V−sz
+
+
6Is
Vsy
Vsz 12Is
−
−
Vpx
Vsz
6Is
Vsy
Vsz 12Is
−
−
Figure 5.
5. Reluctance model for adjustable leakage inductance.
Figure
Figure 5. Reluctance model for adjustable leakage inductance.
mmf mm f
(6) (6)
R
R
mmf
(6) in the
φ = reluctance
= NI generated by the passing flux produced
Figure
Figure 66displays
displaysthe
theequivalence
equivalenceofofthe
the
R reluctance generated by the passing flux produced in
φ = φ = = NI = NI
left
by using
superposition
theorem.
Regarding
the corethe
structure,
because
the leg
leftthat
leg was
that achieved
was achieved
by the
using
the superposition
theorem.
Regarding
core structure,
Figure
6
displays
the
equivalence
of
the
reluctance
generated
by
the
passing
flux
produced
in
the
reluctances
of both outer
legsouter
are the
same,
reluctance reluctance
passing through
φ1 through
and φ3 are
because
the reluctances
of both
legs
are the
the equivalent
same, the equivalent
passing
ϕ1
the same,
left leg that
was achieved
by(7).
using
thethesuperposition
theorem.
Regarding
the
structure,
the
indicated
in indicated
Equation
After
reluctance
passing
through
the flux
hascore
been
and ϕ3 areasthe
same, as
in Equation
(7).
After the
reluctance
passing
through
theobtained,
flux has
because the reluctances of both outer legs are the same, the equivalent reluctance passing through ϕ1
and ϕ3 are the same, as indicated in Equation (7). After the reluctance passing through the flux has
Energies 2019, 12, x FOR PEER REVIEW
Energies 2019, 12, 1781
8 of 19
8 of 19
been obtained, ϕ1 could be presented as Equation (8); although the equivalent reluctance of ϕ1 and ϕ3
are
the same,
ϕ3 couldasbeEquation
presented
in Equation
(9) because
the MMFof is
for the
eachsame,
leg.
φ1 could
be presented
(8);asalthough
the equivalent
reluctance
φ1different
and φ3¬ are
Because
center legas
had
no windings,
only the
flux on the
outerthe
legs
are
φ3 couldthe
be presented
in Equation
(9) because
thevalues
MMF of
is different
forleft
eachand
leg.right
Because
center
listed.
leg had no windings, only the values of flux on the left and right outer legs are listed.
ϕ1
Ro
Rc
ϕ1
Ro
Rc
Ro
18Ip
Ro
18Ip
6Is
6Is
Figure
Figure 6.
6. Equivalent
Equivalent reluctance
reluctance model
model for
for flux
flux split
split flow.
flow.
Ro (Ro + 2Rc )
Rφ1 = Rφ3 = Ro ( Ro + 2 Rc )
(7)
Ro + Rc
Rφ = Rφ 3 =
(7)
c
Ro +RoR+
Rc
φ1 = 18Ip − 6Is ·
(8)
(Ro o++
Ro R
Rc2Rc )
φ1 = 18I p − 6 I s ⋅
(8)
Ro (RRoo +
+ 2RRcc )
(9)
φ3 = 6Ip − 12Is ·
Ro (Ro + 2Rc )
Ro + Rc
I p − 12
I s windings
⋅
φ3 = 6from
(9)
As mentioned, the MMF generated
the
Ro ( Ro + 2on
Rc ) each leg was determined using the
superposition theorem. Subsequently, Equations (10)–(12) represent the total flux of each leg in
consideration
of fluxthe
split
flow.generated from the windings on each leg was determined using the
As mentioned,
MMF
superposition theorem. Subsequently, Equations (10)–(12) represent the total flux of each leg in
18Ro + 24Rc
6Ro + 18Rc
consideration of flux split flow.
φ1_total =
· Ip −
· Is
(10)
Ro (Ro + 2Rc )
Ro (Ro + 2Rc )
18Ro + 24Rc
6 Ro + 18Rc
φ1_ total =
⋅ Ip −
12
6 ⋅I
(10)
φ2_total = Ro ( Ro + 2Rc ) · Ip −Ro ( Ro + 2Rc ) s · Is
(11)
Ro (Ro + 2Rc )
Ro (Ro + 2Rc )
1
(
)
(
)
1224Rc
6Ro +
12R6o + 18Rc
φ2 _ total
φ3_total
= = R R + 2 R ⋅ ·I Ipp−−R R + 2 R ⋅ I s · Is
( oo+ 2Rcc))
) c)
o (o (oRo + c2R
Ro (o R
R
(11)
(12)
According to Figure 7, the primary-side
of12the
Vp is the sum of Vpw and
6Ro + 24voltage
Rc
Ro +transformer
18Rc
φ3 _ total =
⋅ Ip −
⋅ Is
(12)
Vpx ; the secondary-side voltage of
the transformer
sum
of
V
and
Vsz . As demonstrated
by
sy
2
Ro ( Ro + 2 Rc ) Vs isRthe
R
R
+
o( o
c)
Equation (13), Faraday’s law of induction was employed to ascertain the relationship between the
According
thevariation
primary-side
of the
transformer
Vp is the sum voltage
of Vpw and
Vpx;
voltage,
numbertoofFigure
turns, 7,
and
in fluxvoltage
over time.
Moreover,
the primary-side
Vp and
the
secondary-side
voltage
of
the
transformer
V
s
is
the
sum
of
V
sy
and
V
sz
.
As
demonstrated
by
secondary-side voltage Vs of the transformer are represented using Equations (14) and (15).
Equation (13), Faraday’s law of induction was employed to ascertain the relationship between the
dφ Moreover, the primary-side voltage Vp and
voltage, number of turns, and variation in flux over time.
V=n
(13)
dt
secondary-side voltage Vs of the transformer are represented
using Equations (14) and (15).
360Ro + 576Rc dIp dφ 180Ro + 432Rc dIs
V· = n −
·
Ro (Ro + 2Rc ) dt dt Ro (Ro + 2Rc ) dt
(14)
(13)
180R
180R
324R
o o++432R
360 R
576 Rcc · dIpp −180
432
Ro o++
Rc cdI· sdIs
VsV=
=
⋅
−
⋅
p
dt
(
)
(
RR
R
+
2R
R
R
+
2R
o o (R
o o + 2 Rcc )
dt
Ro o( Ro o+ 2 Rc )c ) dt dt
(15)
(14)
Vp =
Vs =
180 Ro + 432 Rc dI p
180Ro + 324Rc dI s
⋅
−
⋅
Ro ( Ro + 2 Rc ) dt
Ro ( Ro + 2 Rc ) dt
(15)
Energies 2019, 12, 1781
Energies 2019, 12, x FOR PEER REVIEW
9 of 19
9 of 19
n2Llks
Llkp
+
Ip
Vp
+
Is /n
Lm
nV s
−
−
Figure
Figure7.7.TTmodel
modelofofthe
thetransformer.
transformer.
Byusing
usingFaraday’s
Faraday’slaw
lawof
ofinduction
inductionto
toassess
assessthe
therelationship
relationshipbetween
betweenthe
thevoltage,
voltage,reluctance,
reluctance,
By
andnumber
numberof
ofturns
turnsof
ofthe
thetransformer,
transformer,the
theTTmodel
modelof
ofthe
thetransformer
transformer(Figure
(Figure7)7)could
couldbe
beapplied.
applied.
and
In
Figure
7,
V
refers
to
the
primary-side
voltage
of
the
transformer,
and
V
refers
to
the
secondary-side
In Figure Vpp refers the primary-side voltage of the transformer, ands Vs refers to the secondaryvoltage
of the
transformer;
furthermore,
LlkpLlkprepresents
side
voltage
of the
transformer;
furthermore,
representsthe
theprimary-side
primary-sideleakage
leakage inductance,
inductance, LLlks
lks
representsthe
thesecondary-side
secondary-sideleakage
leakageinductance,
inductance, and
and LLmmrepresents
representsthe
theexcitation
excitationinductance
inductanceof
ofthe
the
represents
transformer.The
TheTTmodel
modelenabled
enabledthe
theequivalence
equivalenceof
ofthe
thevoltage,
voltage,current,
current,and
andleakage
leakageinductance
inductanceof
of
transformer.
thesecondary
secondaryside
sidewith
withthat
thatof
ofthe
theprimary
primaryside.
side.Equations
Equations(16)
(16)and
and(17)
(17)present
presentthe
theresults.
results.
the
dI
dI
dI
 dI
Lm
p p  Lm
s s
Vpp =
= LLmm++Llkp
−−
V
Llkp
(16)
(16)
dtdt  n n dtdt
dI
p
dI
Lm
Lm
 dI s s
Vs = − Lm  dI p + Lm2 + Llks
(17)
Vs = −  n  dt +  n2 + Llks  dt
(17)
n
dt
n
dt
 


Subsequently, Equations (14) and (16) could be compared with Equations (15) and (17).
Subsequently,
Equationsthe
(14)
and (16) among
could the
be leakage
compared
with Equations
(15) inductance
and (17).
Equations
(18)–(20) represent
relationship
inductance
and excitation
Equations
(18)–(20)
representsides
the of
relationship
among
leakage ofinductance
excitation
of the primary
and secondary
the transformer
andthe
the number
turns of theand
windings.
inductance of the primary and secondary sides of the transformer and the number of turns of the
360Ro + 576Rc
windings.
(18)
Lm + Llkp =
Ro (Ro + 2Rc )
360 Ro + 576 Rc
432Rc
LmL+mLlkp =180Ro +
(18)
= Ro ( Ro + 2 Rc )
(19)
n
Ro (Ro + 2Rc )
(
)
Lm Lm 180R180R
o +R324R
c
o + 432
c
+ L=
lks =
2
)
2R
n n
Ro ( Roo (+R2oR+
c
)
c
(20)
(19)
The comparison could be used to establish models of equivalent leakage inductance of the primary
Lm
180Ro + 324Rc
+L
and secondary sides of the transformer and
the
excitation
inductance. Such models could be presented
(20)
lks =
n2
Ro ( Ro + 2 Rc )
using Equations (21)–(23).
The comparison could be used to establish
of equivalent leakage inductance of the
240Rmodels
o + 576Rc
Lm = and the excitation inductance. Such models could(21)
primary and secondary sides of the transformer
be
Ro (Ro + 2Rc )
presented using Equations (21)–(23).
120Ro
(22)
Llkp =240 R + 576 R
o
(
Lm = Ro Ro + 2Rcc )
(21)
Ro ( Ro + 2 Rc )
45Ro
Llks =
(23)
Ro (120
Ro R+o 2Rc )
Llkp =
(22)
Ro ( Ro +core
2 Rc could
)
According to the obtained results, a three-legged
achieve adjustable leakage inductance
if the shape of the outer legs easily enables winding. Applying the winding coil is difficult when the
45Ro
Llks = because
commonly used PQ and RM cores are employed
of their outer leg shape; thus, EI or EE(23)
cores
Ro ( Ro + 2 Rc )
were used for adjustable leakage inductance [21]. The simulation results of the current distribution
of the
PCB tracetowindings
based on
the shapes
of the PQ and
cores were
obtained
with Maxwell
According
the obtained
results,
a three-legged
coreEIcould
achieve
adjustable
leakage
magnetic simulation
software.
The simulation
results presented
Figure 8the
yielded
the winding
for the
inductance
if the shape
of the outer
legs easily enables
winding. in
Applying
winding
coil is difficult
squarethe
core,
and the current
distribution
obtained
using the square
core
was considerably
morethus,
uneven
when
commonly
used PQ
and RM cores
are employed
because
of their
outer leg shape;
EI
than
using
round core,
leading
to excessively
current
at theofcorner
of the
or
EE that
coresobtained
were used
for the
adjustable
leakage
inductance
[21]. Thedense
simulation
results
the current
distribution of the PCB trace windings based on the shapes of the PQ and EI cores were obtained
with Maxwell magnetic simulation software. The simulation results presented in Figure 8 yielded the
winding for the square core, and the current distribution obtained using the square core was
Energies 2019, 12, x FOR PEER REVIEW
2019, 12,
12, x1781
x FOR
FOR PEER
PEER REVIEW
REVIEW
Energies 2019,
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10 of 19
1010of
of
19
of 19
10
considerably more uneven than that obtained using the round core, leading to excessively dense
considerably
more
uneven
than that
thathot
obtained
using
the round
round
core,
leading
to
excessively
dense
considerably
than
obtained
using
the
leading
excessively
dense
current
at themore
corneruneven
of the winding,
spots, and
higher
losses. core,
Therefore,
theto
cylindrical
core
was
winding,
hot
spots,
and
higher
losses.
Therefore,
the
cylindrical
core
was
selected
as
the
transformer
current at
at
the
corner
of the
the winding,
winding,
hot
spots, and
and higher
higher losses.
losses. Therefore,
Therefore, the
the cylindrical
cylindrical core
core was
was
current
of
hot
spots,
selected
asthe
thecorner
transformer
core in this
study.
core in this
study.
selected
as the
the
transformer core
core in
in this
this study.
study.
selected
as
transformer
(a)
(a)
(a)
(b)
(b)
(b)
Figure 8. Relationship between the winding shapes of effective core cross sections and current
Figure 8.
8. Relationship
Relationship
between
the
winding
shapes
of
effective
core
cross sections
sections and
and current
current
Figure
between
the
winding
Relationship
between
thesection;
winding
shapes
of effective
effective
core cross
distribution:
(a) square-shaped
cross
(b)shapes
round of
cross
section.core
distribution: (a)
(a) square-shaped
square-shaped cross
cross section;
round cross
cross section.
section.
distribution:
section; (b)
(b) round
The design presented in Figure 9 was proposed to achieve adjustable inductance through
presented
in in
Figure
9 was
proposed
to achieve
adjustable
inductance
through through
winding
The design
design
presented
Figure
was
proposed
to achieve
achieve
adjustable
inductance
The
design
Figure
99 was
proposed
to
adjustable
inductance
winding
on the presented
two outerin
legs
of the
three-legged
core
and the
obtainment
of even through
current
on
the
two
outer
legs
of
the
three-legged
core
and
the
obtainment
of
even
current
distributions
on PCB
winding
on
the
two
outer
legs
of
the
three-legged
core
and
the
obtainment
of
even
current
winding
on
the
two
outer
legs
of
the
three-legged
core
and
the
obtainment
of
even
current
distributions on PCB windings. Producing adjustable leakage inductance required that windings
be
windings.
Producing
adjustableProducing
leakage inductance
required
that
windings
be set only
on the outer
distributions
onouter
PCB windings.
windings.
Producing
adjustable
leakage
inductance
required
that windings
windings
be
distributions
on
PCB
adjustable
leakage
inductance
that
set
only on the
legs
and not
on the center
leg. This
method
enabled required
the cross-sectional
area be
of
legsonly
andon
notthe
onouter
the center
leg.not
This
method
enabled
themethod
cross-sectional
area
of the center leg
to be
set
only
on
the
outer
legs
and
not
on
the
center
leg.
This
method
enabled
the
cross-sectional
area
of
set
legs
and
on
the
center
leg.
This
enabled
the
cross-sectional
area
of
the center leg to be altered to a shape suitable for PCB winding, increasing the effectiveness of the
altered
to
a
shape
suitable
for
PCB
winding,
increasing
the
effectiveness
of
the
winding
space
the
the
center
leg
to
be
altered
to
a
shape
suitable
for
PCB
winding,
increasing
the
effectiveness
of
the
centerspace
leg toofbe
to a shape
suitable
forstudy
PCB proposed
winding, increasing
thePQ
effectiveness
of 9a),
the
winding
thealtered
transformer.
Therefore,
this
aligning two
cores (Figure
transformer.
Therefore,
this study Therefore,
proposed aligning
two
PQ coresaligning
(Figuretwo
9a), PQ
where
the(Figure
connected
winding
space
of
the
transformer.
Therefore,
this
study
proposed
aligning
two
PQ
cores
(Figure
9a),
winding
space
of
the
transformer.
this
study
proposed
cores
9a),
where the connected part serves as the center leg of the core, and removal of one outer leg of the
part
serves
as the center
legserves
of theas
core,
and
removal
ofthe
onecore,
outer
legremoval
of the original
forms
a new
where
the
connected
part
serves
as
thestructure
center
leg
of
the
core,
and
removal
of
onecore
outer
leg of
of
the
where
the
connected
part
the
center
leg
and
one
outer
leg
the
original
core
forms a new
three-legged
forof
the
core.
The
design
is as of
presented
in Figure
9b.
three-legged
structure
for
the
core.
The
design
is
as
presented
in
Figure
9b.
original core
core forms
forms aa new
new three-legged
three-legged structure
structure for
for the
the core.
core. The
The design
design is
is as
as presented
presented in
in Figure
Figure 9b.
9b.
original
Winding
Winding
Winding
Winding
Winding
Winding
PQ Core 1
PQ Core
Core 11
PQ
(a)
(a)
(a)
PQ Core 2
PQ Core
Core 22
PQ
New Core Structure
New Core
Core Structure
New
(b)Structure
(b)
(b)
Figure 9. Diagram of the innovative core structure: (a) PQ core structure; (b) the innovative core
Figure
9. Diagram
Diagramofof
ofthe
the
innovative
core
structure:
(a)core
PQstructure;
core structure;
structure;
(b) the
the innovative
innovative
core
Figure
Diagram
the
innovative
structure:
(a)
PQ
core
(b)
core
Figure 9.
innovative
corecore
structure:
(a) PQ
(b) the innovative
core structure.
structure.
structure.
structure.
Figure 10
Figure
10 shows
shows aa diagram
diagram of
of the
the core
coresize
sizedesign
designin
inthis
thisstudy.
study.Figure
Figure10a
10aisisthe
thetop
topview,
view,and
andr
Figure
10
shows
a
diagram
of
the
core
size
design
in
this
study.
Figure
10a
is
the
top
view,
Figure
10
shows
a
diagram
of
the
core
size
design
in
this
study.
Figure
10a
is
the
top
view,
and
represents
the
radius
of
the
effective
cross-sectional
area,
R
denotes
the
radius
of
the
core
that
can
be
r represents the radius of the effective cross-sectional area, R denotes the radius of the core that and
can
rberepresents
represents
the
radius
of
the
effective
cross-sectional
area,
R
denotes
the
radius
of
the
core
that
can
rwound,
the
radius
of
the
effective
cross-sectional
area,
R
denotes
the
radius
of
the
core
that
can
l
is
twice
the
horizontal
distance
from
the
core
cylinder
to
the
highest
point
of
the
center
leg,
m
wound, l is twice the horizontal distance from the core cylinder to the highest point of the center
be
wound,
l
is
twice
the
horizontal
distance
from
the
core
cylinder
to
the
highest
point
of
the
center
be
wound,
is twice
thewidth
horizontal
the
pointofofthe
the
center
is the
width
of
the of
center
leg, n leg,
isfrom
the
length
ofcylinder
theofcore,
d the
is the
and
leg,
m maximum
is thel maximum
thedistance
center
n is
thecore
length
theto
core,
dhighest
isthickness
the thickness
oftop
the
top
leg,
m
is
the
maximum
width
of
the
center
leg,
n
is
the
length
of
the
core,
d
is
the
thickness
of
the
top
leg,
m
is
the
maximum
width
of
the
center
leg,
n
is
the
length
of
the
core,
d
is
the
thickness
of
the
top
bottom
pieces,
and
t
represents
the
leg
height
of
the
core.
and bottom pieces, and t represents the leg height of the core.
and bottom
bottom pieces,
pieces, and
and tt represents
represents the
the leg
leg height
height of
of the
the core.
core.
and
l
l
r
r
R
R
m
m
n
n
(a)
(a)
(a)
d
dt
t
d
d
(b)
(b)
(b)
Figure
Figure 10.
10. Diagram
Diagram of
of the
the core
core size
size marking:
marking: (a)
(a) top
top and
and (b)
(b) side
side view.
view.
Figure 10.
10. Diagram
Diagram of
of the
the core
core size
size marking:
marking: (a)
(a) top
top and
and (b)
(b) side
side view.
view.
Figure
Energies 2019, 12, 1781
11 of 19
The overall loss of the transformer can be divided into core loss and copper loss. Core loss is the
product of core loss per unit volume and core volume, as shown in Equation (24). In Equation (25),
Pv denotes the unit volume loss, and Cm, x, and y can be acquired from the core manufacturer’s
manual. Combining Equations (24) and (25) reveals that the core loss and volume Vel are related to the
switching frequency fs and peak flux density Bmax , with core loss being linearly proportional to Vel and
exponentially proportional to fs and Bmax . Next, Bmax was expressed as Equation (26), where Vin denotes
the input voltage, Ae represents the effective cross-sectional area of the core, and Np is the number of
turns of the primary winding. In this study, the input voltage Vin , switching frequency fs, and effective
cross-sectional area of the core are 400 V, 500 kHz, and 194 mm2 , respectively. The relationship between
core loss and the number of primary-side turns is revealed through Equation (26), with a higher
number of turns leading to a drop in peak flux density, reducing the core loss. However, from the
perspective of copper loss, more turns resulted in greater loss. Thus, the optimal number of turns in
this study was acquired by quantifying the core loss and copper loss.
Coreloss = Pcv · Vel
y
Pv = Cm · f sx · Bmax
Bmax =
Vin
4 · Ae · Np · f s
(24)
(25)
(26)
In this study, a full-bridge LLC resonant conversion topology was employed for the primary-side
circuit architecture, whereas the secondary-side rectification architecture consisted of a full-bridge
topology. The turns ratio of the transformer was calculated using Equation (27), and substituting
the circuit specifications of this study (400 V input voltage and 300 V output voltage) yielded a
transformer turns ratio of 4:3. However, the minimal number of turns on the primary side cannot
be 1 because of the winding method of the adjustable leakage inductance, because the primary-side
should be wound to the two outer legs, and because the primary side on both legs cannot be the same.
Additionally, the winding ratio of the primary and secondary sides has to be an integer to prevent the
need for a non-integer number of turns on the secondary side. Table 4 shows that the winding width
of the core could be obtained by subtracting r from R, and the actual winding width was 5.5 mm.
n=
Vin
Vo
(27)
Table 4. Parameter design of the asymmetric resonant tank.
Core Size
Value
Ae
R
r
l
m
n
d
t
194 mm2
13.3 mm
7.8 mm
18.8 mm
7.29 mm
18.8 mm
6 mm
10.3 mm
The transformer turns ratio in this study was 4:3; thus, the number of turns at the primary and
secondary sides could be 4:3, 8:6, 12:9, and so on. The core loss per unit volume (Pv) increased
substantially when the peak flux density of the transformer exceeded 1000 G. Therefore, the peak flux
density was designed to be less than 1000 G in the core turns design. Next, Equation (26) was rewritten
as Equation (28), and Bmax was set to 1000 G. According to Equation (28), the minimum number of
winds on the primary side was 14.6. Practically, more windings mean more layers and greater costs.
Energies 2019, 12, x FOR PEER REVIEW
12 of 19
Energies 2019, 12, 1781
Energies 2019, 12, x FOR PEER REVIEW
12 of 19
12 of 19
number of winds on the primary side was 14.6. Practically, more windings mean more layers
and
greater costs. Therefore, only the following five windings on the primary and secondary sides were
number of
winds on
the primary
side was 14.6.
Practically,
windings mean
and
Therefore,
only
following
five windings
on the
primarymore
and secondary
sidesmore
werelayers
considered:
considered:
16:12,the
20:15,
24:18, 28:21,
and 32:24.
greater
costs.
Therefore,
only
the
following
five
windings
on
the
primary
and
secondary
sides
were
16:12, 20:15, 24:18, 28:21, and 32:24.
considered: 16:12, 20:15, 24:18, 28:21, and 32:24. Vin
Np >
= 14.6
(28)
Vin
Bmax ⋅ fs = 14.6
Np > 4 ⋅ Ae ⋅Vin
(28)
Np 4> · Ae · Bmax · f s= 14.6
(28)
4 ⋅ Ae ⋅ Bmax ⋅ fs
The peak flux density and core loss for different
numbers of turns were obtained using Equations
The peak flux density and core loss for different numbers of turns were obtained using
(24) andThe
(26),
and
the
results
are
plotted
in
Figure
11.
The relationship
between
coreusing
loss and
number
peak flux density and core loss for different numbers
of turns were
obtained
Equations
Equations (24) and (26), and the results are plotted in Figure 11. The relationship between core
of turns
was
nonlinear.
The difference
loss
16 andbetween
20 turnscore
on loss
the and
primary-side
(24) and
(26),
and the results
are plottedin
in core
Figure
11. between
The relationship
number
loss and number of turns was nonlinear. The difference in core loss between 16 and 20 turns on the
winding
was
4.8nonlinear.
W, whereas
and 32 in
turns
thebetween
primary-side
a core loss of
of turns
was
The 28
difference
coreon
loss
16 andwinding
20 turns yielded
on the primary-side
primary-side winding was 4.8 W, whereas 28 and 32 turns on the primary-side winding yielded a core
winding was0.8
4.8W.
W,This
whereas
28 and
turns for
on the
primary-side
yielded
core loss of
approximately
was the
main32reason
designing
Bmax to winding
be less than
1000aG.
loss of approximately 0.8 W. This was the main reason for designing Bmax to be less than 1000 G.
approximately 0.8 W. This was the main reason for designing Bmax to be less than 1000 G.
Figure
core
loss.
Figure11.
11.Peak
Peakflux
density
and
Figure
11.
Peak
fluxdensity
densityand
andcore
coreloss.
loss.
The
high-frequency
copper
loss
was
analyzed
Conventional
transformers
aremostly
mostly
The
high-frequency
copper
loss
was
analyzed
next.next.
Conventional
transformers
are mostly
wound
The
high-frequency
copper
loss
was
analyzed
next.
Conventional
transformers
are
wound
litz
wire;
however,
planar
isismore
toutilize
utilizethe
the
window
area
wound
with
litz
wire;
however,
planar
routing
more advantageous
advantageous
to
window
area
ofof
a a
with
litzwith
wire;
however,
planar
routing
isrouting
more
advantageous
to utilize the
window
area
of a transformer.
transformer.
Figure
compares
theuse
useand
of planar
planar
routing
and
Under
the
same
transformer.
Figure
1212
compares
of
routing
and four
four
litz wires.
wires.
Under
the
same
Figure
12 compares
the
use
of planarthe
routing
four litz
wires. Under
the litz
same
condition
of an
occupied
2, 2
2 ,an
2 ,litz
condition
areaofof4area
4mm
mm2of
the cross-sectional
cross-sectional
the
wires
condition
of of
an
occupied
area
,2,the
area
of
the
litz
wireswas
was3.142
mm
,
area
of 4 mm
theoccupied
cross-sectional
litz
wires was area
3.142of
mm
whereas
that
of3.142
themm
planar
2
2
2
whereas
that
planar
routing
was 44 mm
mm
(Figure
12a,b,
both
yielded
a a27%
whereas
that
of of
thethe
planar
routing
was
respectively);
both
yielded
27%
routing
was
4 mm
(Figure
12a,b,
respectively);
both(Figure
yielded 12a,b,
a 27% respectively);
difference
in DC
resistance
under
the
difference
in
resistance
underwas
theused
same
length.
Therefore,
PCB
was
used
asasthe
difference
in Therefore,
DCDCresistance
under
the
same
Therefore,
PCB routing
routing
wasto
used
the
same
length.
PCB routing
aslength.
the
transformer
winding
in
this study
achieve
high
transformer
winding
in
this
study
to
achieve
high
power
density.
transformer
winding in this study to achieve high power density.
power density.
4mm
4mm
1mm
1mm
4mm
4mm
1mm
1mm
Area: 3.142mm2
Area: 3.142mm2
(a)
(a)
Area: 4mm22
Area: 4mm
(b)
(b)
Figure 12. Winding usage in different transformers: (a) litz wire and (b) planar trace.
Figure
Figure12.
12.Winding
Windingusage
usagein
indifferent
different transformers:
transformers: (a)
(a)litz
litzwire
wireand
and(b)
(b)planar
planartrace.
trace.
PCB routing was selected over litz wire under the same transformer window area because it
PCB routing
routing
was
selected
over
litz wire
wire under
under
the same
same
transformer
window
area loss
because
PCB
was
over
the
transformer
window
area
because
resulted
in lower
DCselected
resistance
of litz
the
winding.
However,
a sharp
rise in AC
resistance
was itit
resulted
in
lower
DC
resistance
of
the
winding.
However,
a
sharp
rise
in
AC
resistance
loss
was
resulted
in lower
DCswitching
resistance
of the winding.
However,
a sharp
rise in 50
ACkHz–200
resistance
was
observed
when the
frequency
was increased
from the
conventional
kHzloss
to 500
observed
whenTherefore,
theswitching
switching
frequency
was
increased
from
conventional
50 kHz–200
to
observed
the
frequency
was
increased
from
thethe
conventional
kHz–200
kHzkHz
to 500
kHz–1 when
MHz.
the AC
resistance
loss
of the transformer
winding
was50
analyzed.
500 kHz–1
MHz.
Therefore,
the
AC
resistance
loss
of
the
transformer
winding
was
analyzed.
kHz–1
MHz.
Therefore,
the
AC
resistance
loss
of
the
transformer
winding
was
analyzed.
According to Dowell’s equation, the skin effect and proximity effect can be expressed by
According
to
Dowell’s
equation,where
the skin
skin
effect
and
proximity
effect can
can
be expressed
expressed
by
According
Dowell’s
equation,
the
effect
proximity
effect
Equations
(29)to
and
(30), respectively,
ξ = h/δ,
withand
h denoting
the thickness
of be
the
copper
wireby
Equations
respectively,
ξ=
the copper
copper
wire
in the transformer
and where
δwhere
representing
the hskin
depth the
of thickness
the transformer
winding.
Equations
(29) and
and (30),
(30),winding
respectively,
ξ = h/δ,
h/δ, with
with
denoting
of the
wire
in the
and and
δrepresenting
the skin(31),
depth
of the
winding.
m
Additionally,
m winding
can
be expressed
using
Equation
where
e transformer
represents
numberAdditionally,
of winding
in
thetransformer
transformer
winding
δ representing
the
skin
depth
of thethe
transformer
winding.
layers.
The
five
numbers
of
windings
that
were
employed
and
the
corresponding
distributions
of
can
be
expressed
using
Equation
(31),
where
e
represents
the
number
of
winding
layers.
The
five
numbers
Additionally, m can be expressed using Equation (31), where e represents the number of winding
of windings
that numbers
were employed
and thethat
corresponding
distributions
MMF are displayed
in Figure of
13.
layers.
The five
of windings
were employed
and theofcorresponding
distributions
Energies 2019, 12, 1781
13 of 19
Energies 2019, 12, x FOR PEER REVIEW
13 of 19
Because
thedisplayed
circuit architecture
study the
wascircuit
an LLC
rather thanin
bidirectional
CLLC,
leakage
MMF are
in Figure in
13.this
Because
architecture
this study was
an only
LLC the
rather
than
inductance
on
the
primary
side
was
adjusted.
Therefore,
the
secondary
side
was
wound
around
the
bidirectional CLLC, only the leakage inductance on the primary side was adjusted. Therefore,two
the
outer
legs with
same
or almost
the the
same
number
turns,
primary
and secondary
were
secondary
sidethe
was
wound
around
two
outer of
legs
withand
thethe
same
or almost
the same sides
number
of
wound
on
an
eight-layer
PCB
in
an
interleaved
manner.
A
total
of
seven
layers
of
PCB
winding
were
used,
turns, and the primary and secondary sides were wound on an eight-layer PCB in an interleaved
and
one layer
wasofreserved
as theofrouting
that connected
the two
manner.
A total
seven layers
PCB winding
were used,
andleg
onewindings.
layer was reserved as the routing
that connected the two leg windings.
ξ sinh(ξ) + sin(ξ)
Rac_skin = · sinh ξ + sin ξ · Rdc
( )
( )
2ξ
R ac _ skin = ⋅ cosh(ξ) − cos(ξ) ⋅ R dc
2 cosh(ξ ) − cos (ξ )
sinh(ξ) − sin(ξ)
ξ
· Rdc
Rac_proximity = ξ· (2m − 1)22 · sinh (ξ ) − sin (ξ )
Rac _ proximity =2 ⋅ ( 2m − 1) ⋅ cosh(ξ) + cos(⋅ξR)dc
2
cosh(ξ ) + cos (ξ )
MMF(e)
m=
MMF ( e )
m =MMF(e) − MMF(e − 1)
(29)
(29)
(30)
(30)
(31)
(31)
MMF ( e ) - MMF ( e -1)
Core
P=1
MMF
P=3
Right
Leg
gap
gap
gap
gap
S=2
S=2
S=3
gap
gap
gap
gap
P=3
P=1
P=3
P=2
gap
gap
gap
gap
S=2
S=2
S=3
S=2
gap
gap
gap
gap
P=3
P=1
P=3
P=2
gap
gap
gap
gap
S=2
S=2
S=2
S=3
gap
gap
gap
gap
P=3
P=1
P=3
P=2
(a)
(b)
Core
Left
Leg
P=5
MMF
Right
Leg
P=2
gap
gap
gap
gap
S=3
S=3
S=3
S=4
gap
gap
gap
gap
P=4
P=2
P=5
P=2
gap
gap
gap
gap
S=3
S=3
S=4
S=3
gap
gap
gap
gap
P=4
P=2
P=5
P=2
gap
gap
S=3
S=3
gap
gap
P=4
P=2
gap
gap
S=3
S=4
gap
gap
P=5
P=2
(c)
2NI
NI
0
-NI
-2NI
-3NI
-4NI
-5NI
-6NI
-7NI
-8NI
-9NI
P=2
MMF
7NI
6NI
5NI
4NI
3NI
2NI
NI
0
Right
Leg
Core
2NI
NI
0
-NI
-2NI
-3NI
-4NI
-5NI
-6NI
6NI
5NI
4NI
3NI
2NI
NI
0
P=4
MMF
MMF
P=2
S=2
Left
Leg
2NI
NI
0
-NI
-2NI
-3NI
-4NI
-5NI
P=3
Left
Leg
MMF
5NI
4NI
3NI
2NI
NI
0
-NI
Right
Leg
MMF
NI
0
-NI
-2NI
-3NI
-4NI
-5NI
6NI
5NI
4NI
3NI
2NI
NI
0
Left
Leg
Core
(d)
Figure 13. Cont.
MMF
Energies 2019, 12, 1781
14 of 19
Energies2019,
2019,12,
12,xxFOR
FORPEER
PEERREVIEW
REVIEW
Energies
14 of
of 19
19
14
Core
Core
gap
gap
S=4
S=4
2NI
2NI
NI
NI
00
-NI
-NI
-2NI
-2NI
-3NI
-3NI
-4NI
-4NI
-5NI
-5NI
-6NI
-6NI
-7NI
-7NI
-8NI
-8NI
-9NI
-9NI
-10NI
-10NI
P=6
P=6
Right
Right
MMF Leg
MMF Leg
P=2
P=2
gap
gap
8NI
8NI
7NI
7NI
6NI
6NI
5NI
5NI
4NI
4NI
3NI
3NI
2NI
2NI
NI
NI
00
Left
Left
Leg
Leg
MMF
MMF
S=4
S=4
gap
gap
gap
gap
P=6
P=6
P=2
P=2
gap
gap
gap
gap
S=4
S=4
S=4
S=4
gap
gap
gap
gap
P=6
P=6
P=2
P=2
gap
gap
gap
gap
S=4
S=4
S=4
S=4
gap
gap
gap
gap
P=6
P=6
P=2
P=2
(e)
(e)
Figure 13.
13. MMF
distribution map
map of
of different
differentnumbers
numbersof
ofwindings:
windings:(a)
(a)Np
Np=
16, Ns
Ns =
Np ==
= 20,
20,
Figure
MMF distribution
distribution
12; (b)
(b) Np
numbers
of
windings:
(a)
Np
== 16,
== 12;
Ns
=
15;
(c)
Np
=
24,
Ns
=
18;
(d)
Np
=
28,
Ns
=
21;
and
(e)
Np
=
32,
Ns
=
24.
Ns
=
=
24,
Ns
=
18;
(d)
Np
=
28,
Ns
=
21;
and
(e)
Np
=
32,
Ns
=
24.
Ns = 15; (c) Np = 24, Ns = 18; (d) Np = 28, Ns = 21; and (e) Np = 32, Ns = 24.
Figure 14
14 illustrates
illustrates
the copper
copper loss
loss and
and total
total loss
loss
of
the
transformer
for different
different
numbers
of
illustrates the
loss of
of the
the transformer
transformer for
different numbers
numbers of
of
Figure
turns.
The core
core loss
loss could
could be
be obtained
obtained from
from Figure
Figure
11. More
in lower
lower peak
peak flux
flux density
density
turns. The
Figure 11.
More turns
turns resulted
resulted in
turns.
of
the
core
and
thus
lower
core
loss.
However,
more
windings
also
led
to
greater
copper
loss,
which
the
core
and
thus
lower
core
loss.
more
windings
to
greater
copper
loss,
which
of the core and thus lower core loss. However, more windings also led to greater copper loss, which
could
be
divided
into
that
associated
with
DC
resistance
and
AC
resistance.
was
greater
could
be
divided
into
associated
with
resistance
and
AC
resistance.
DC
resistance
could be divided into that associated with DC resistance and AC resistance. DC resistance was greater
for
more
windings; however,
however,
the
resistance
that
actually
affects
the
high-frequency
copper
loss
is
AC
for more
more windings;
however, the
the resistance
resistance that
that actually
actually affects
affects the
the high-frequency
high-frequency copper
copper loss
loss is
is AC
AC
for
resistance
loss.
Because
an
eight-layer
board
was
used
for
transformer
routing,
more
turns
meant
that
resistance
loss.
eight-layer
board
routing,
more
turns
meant
that
resistance loss. Because an eight-layer board was used for transformer routing, more turns meant that
each
layer
of the
the PCB
PCB board
board
had to
to accommodate
accommodate more
more
windings,
which
narrowed
the
width
of
each
each layer
layer of
board had
more windings,
windings, which
which narrowed
narrowed the
the width
width of
of each
each
each
winding.
according
to
Figure
13,
more
windings
winding.
Moreover,
in
each
layer
resulted
in
a
higher
MMF,
winding. Moreover, according to Figure 13, more windings in each layer resulted in a higher MMF,
causing substantially
substantially greater
greater AC
AC resistance
resistance under
under high
high frequency,
frequency, which
which in
in turn
turn
resulted
in greater
greater
turn resulted
resulted in
greater
causing
copper
loss.
The various
amounts of
of core
core loss
loss and
and copper
in Table
Table
5,
and the
the results
results
copperloss.
loss.The
variousamounts
copperloss
lossare
arepresented
presentedin
Table5,
5,and
results
copper
are
plotted
in
Figure
14.
Ultimately,
the
number
of
turns
with
the
lowest
total
loss
(24:18)
was
selected
are
plotted
in
Figure
14.
Ultimately,
the
number
of
turns
with
the
lowest
total
(24:18)
selected
are plotted in Figure 14. Ultimately, the number of turns with the lowest total loss (24:18) was selected
as
the suitable
suitable
number
of
turns
of the
the transformer
transformer
in this
this study.
study.
Figure
15 shows
shows the
the peak
peak flux
flux density
density
asthe
suitablenumber
numberof
ofturns
turnsof
transformerin
study.Figure
Figure15
as
of
the
core,
as
simulated
by
ANSYS
of the
the core,
core, as
as simulated
simulated by
by ANSYS
ANSYS Maxwell
Maxwell software,
software,to
toverify
verifythat
thatthe
thecore
coreoperated
operatednormally.
normally.
of
Maxwell
software,
to
verify
that
the
core
operated
normally.
Figure 14. Copper
Copper loss and
and total loss.
loss.
Figure
Figure 14.
14. Copper loss
loss and total
total loss.
Energies 2019, 12, x FOR PEER REVIEW
15 of 19
Energies 2019, 12, 1781
Energies 2019, 12, x FOR PEER REVIEW
15 of 19
15 of 19
Figure 15. Flux density distribution by FEA 3D simulation.
Figure 15. Flux density distribution by FEA 3D simulation.
Figure 15. Flux density distribution by FEA 3D simulation.
Table 5. Parameter design of the asymmetric resonant tank.
Table 5. Parameter design of the asymmetric resonant tank.
Table
5. Parameter design
of the20:15
asymmetric
Condition\Np:Ns
16:12
24:18resonant
28:21 tank.
32:24
Condition\Np:Ns
16:12
20:15
24:18
28:21
32:24
Bmax (Gauss)
913
730
608 28:21
521 32:24
456
521
456
2.77
1.99
521 2.77 456 1.99
479
689 689
479 1.99
2.77
530
796 796
530
479
689
10.50
10.50 796
15.5715.57
530
13.27
13.27 15.57
17.5517.55
5.74 10.50
9.81 13.27 17.55
20:15 24:18
BmaxCondition\Np:Ns
(Gauss)
91316:12 730
608
Core
Loss
(W)
11.23
6.43 608
4.07
Bmax
(Gauss) 11.23913 6.43
730
Core Loss
(W)
4.07
(mΩ)
157 223
223 4.07
260
Rdc Core
(mΩ)Rdc
260
Loss
(W) 15711.23
6.43
Rac
(mΩ)
167
232
270
Rac (mΩ)
167
232
270
Rdc (mΩ)
157
223
260
Copper Loss
(W)
3.33
4.50
5.74
Copper
Loss (W) 167
3.33 232
4.50 270
5.74
Rac (mΩ)
Total Loss
(W) Loss (W)
14.56 14.5610.93
Total
10.93 9.81
9.81
4. 4.
Results
Results
Copper Loss (W)
Total Loss (W)
3.33
14.56
4.50
10.93
4. Results
AnAn
LLC
resonant
converter
with
1 kW
output
power
and
500
kHz
switching
frequency
was
LLC
resonant
converter
with
1 kW
output
power
and
500
kHz
switching
frequency
was
proposed
in this
study.
Figure
16a,bwith
shows
the actual
core
size
and
circuit
diagram,
respectively.
Table
6
proposed
inresonant
this
study.
Figure
16a,b
the actual
core
size
circuit
diagram,
respectively.
An LLC
converter
1shows
kW
output
power
and
500and
kHz
switching
frequency
was
details
the
components
and
design
parameters
used
in
this
study.
Table
6
details
the
components
and
design
parameters
used
in
this
study.
proposed in this study. Figure 16a,b shows the actual core size and circuit diagram, respectively.
Table 6 details the components and design parameters used in this study.
(a)
(b)
(a)
(b)
Figure
Experimental
prototype
core
structure
and
circuit.
Figure
16.16.
Experimental
prototype
of of
thethe
(a)(a)
core
structure
and
(b)(b)
circuit.
Figure Table
16. Experimental
prototype
theasymmetric
(a) core structure
and
(b) circuit.
6. 6.
Parameter
design
ofofof
the
resonant
tank.
Table
Parameter
design
the asymmetric
resonant
tank.
Component
Value
Table 6. Parameter
design of the asymmetric resonant
tank.
Component
Value
Resonant
and
Operating
Frequency
kHz
Resonant
and
Operating
Frequency 500
500
kHz
Component
Value
Transformer
Turns
Ratio
24:18
Transformer
Turns
Ratio
24:18
Resonant
and Operating
Frequency 500
kHz
Transformer
Material
3F36
Transformer
Material
3F36
Transformer
Turns
Ratio
24:18
Primary-Side Switch Device
GS66508B
Primary-Side
Switch
Device
GS66508B
Secondary-Side
Switch
Device
GS66508B
Transformer
Material
3F36
Secondary-Side
Switch
Device
GS66508B
Primary-Side
Driver
Si8271GB
Primary-Side Switch Device
GS66508B
Secondary-Side
Driver
Si8271GB
Primary-Side
Driver
Si8271GB
Secondary-Side
Switch
Device
GS66508B
Resonant
Capacitor
22.4
nF
Secondary-Side
Driver
Si8271GB
Primary-Side
Driver
Si8271GB
Leakage Inductance
4.7 µH
Resonant Capacitor
22.4 nF
Secondary-Side
Driver
Si8271GB
Magnetizing
Inductance
80.5 µH
LeakageCapacitor
Inductance
Resonant
Magnetizing
Inductance
Leakage Inductance
Magnetizing Inductance
4.7nF
μH
22.4
80.5
4.7 μHμH
80.5 μH
Energies 2019,
2019, 12,
12, 1781
x FOR PEER REVIEW
Energies
16
19
16 of
of 19
Figure 17 plots the measured conversion efficiency of the converter. The highest efficiency of
Figure
plots theat
measured
conversion
efficiency
thecircuit
converter.
highest at
efficiency
of 97.03%
97.03%
was17achieved
80% load.
Figure 18
displaysofthe
test The
waveform
full load,
which
was
achieved
at
80%
load.
Figure
18
displays
the
circuit
test
waveform
at
full
load,
which
includes
the
includes the waveforms of Vds, Vgs, and the resonant current ILr
Lr of the primary-side power switch
waveforms
of Vds, Vgs,Figure
and the19a–c
resonant
current
ILr of the primary-side
power
switch
operating properly.
operating properly.
shows
temperature
distribution
of the
primary-side
power
Figure
19a–c
shows
temperature
distribution
of
the
primary-side
power
components
at
full
load,
with
components at full load, with maximum temperatures of 38.1 °C, 40.4 °C, and 78.6 °C, respectively.
◦ C, 40.4 ◦ C, and 78.6 ◦ C, respectively. Because the specifications of
maximum
temperatures
of
38.1
Because the specifications of this paper are high-voltage to high-voltage, according to the loss analysis
this
paper 4,
arethe
high-voltage
to mainly
high-voltage,
according
the loss analysis
in Figure
thetransformer
loss can be
in Figure
loss can be
attributed
to thetotransformer,
especially,
on 4,the
mainly
attributed
to
the
transformer,
especially,
on
the
transformer
windings.
Because
the
primary
or
windings. Because the primary or secondary switching elements have zero-voltage-switch
turn-on,
secondary
switching
elementsof
have
turn-on,
the temperature
distribution
the temperature
distribution
the zero-voltage-switch
overall converter will
be concentrated
on the
windings of the
the
overall
converter will be concentrated on the windings of the transformer.
transformer.
Figure
17. Measured
Figure 17.
Measured power
power efficiency.
efficiency.
Figure 18.
18. Experimental
for the
the converter
converter at
at full
full load.
load.
Figure
Experimental waveforms
waveforms for
Energies 2019, 12, 1781
x FOR PEER REVIEW
of 19
1717of
(a)
(b)
(c)
19.Temperature
Temperature
of LLC
the converter
LLC converter
at full
load; (a) primary-side
devices, (b)
Figure 19.
of the
at full load;
(a) primary-side
GaN devices,GaN
(b) secondary-side
secondary-side
GaN
devices,
and
(c)
core
and
winding
of
transformer.
GaN devices, and (c) core and winding of transformer.
5.
Conclusions
5. Conclusions
This
This study
study determined
determined the
the primary-side
primary-side topology
topology and
and secondary-side
secondary-side rectification
rectification topology
topology
suitable
for
an
LLC
resonant
converter
under
a
switching
frequency,
input
voltage,
and
output
suitable for an LLC resonant converter under a switching frequency, input voltage, and voltage
output
of
500 kHz,
400kHz,
V, and
300V,V,and
respectively.
After loss analysis
andanalysis
determining
the rated voltage
and
voltage
of 500
400
300 V, respectively.
After loss
and determining
the rated
current
thecurrent
components,
the full-bridgethe
topology
was topology
selected for
both
the primary
and
secondary
voltage of
and
of the components,
full-bridge
was
selected
for both
the
primary
sides.
This
study
also
investigated
the
small
transformer
leakage
inductance
caused
by
an
interleaved
and secondary sides. This study also investigated the small transformer leakage inductance caused
winding
structure, winding
which was
employed
to reduce
the winding
MMF the
of the
transformer
under
by an interleaved
structure,
which
was employed
to reduce
winding
MMF of
the
high-frequency
switching.
The
adjustable
leakage
inductance
structure
was
thus
adopted
in
this
study,
transformer under high-frequency switching. The adjustable leakage inductance structure was thus
and
the influence
of coreand
shape
current distribution
wason
explored.
the feasibility
adopted
in this study,
theoninfluence
of core shape
current Subsequently,
distribution was
explored.
of
the core wasthe
verified
through
simulation
ANSYS
Maxwell
software.
Ultimately,
an LLC
Subsequently,
feasibility
of the
core wasusing
verified
through
simulation
using
ANSYS Maxwell
resonant
converter
with
1
kW
output
power
and
500
kHz
switching
frequency
was
designed
and
software. Ultimately, an LLC resonant converter with 1 kW output power and 500 kHz switching
tested.
The
results
verified
a
maximum
conversion
efficiency
of
97.03%.
frequency was designed and tested. The results verified a maximum conversion efficiency of 97.03%.
Author Contributions: Y.-C.L., C.C., K.-D.C. and Y.-L.S. conceived and designed the prototype and experiments;
Author Contributions: Y.-C.L., C.C., K.-D.C. and Y.-L.S. conceived and designed the prototype and
C.C., K.-D.C., Y.-L.S. and M.-C. Tsai performed the experiments; Y.-C.L., C.C., K.-D.C. analyzed the data; Y.-C.L.
experiments;equipment/materials/analysis
C.C., K.-D.C., Y.-L.S. and M.-C.
Tsai
performed
the experiments;
Y.-C.L., C. C., K.-D.C. analyzed
contributed
tools;
Y.-C.L.,
C.C., K.-D.C.
wrote the paper.
the data; Y.-C.L. contributed equipment/materials/analysis tools; Y.-C.L., C.C., K.-D.C. wrote the paper.
Funding: This work was supported in part by the Ministry of Science and Technology, Taiwan under Grant
107-2218-E-008 -012- and 107-2221-E-197 -030 -.
Funding: This work was supported in part by the Ministry of Science and Technology, Taiwan under Grant 107Conflicts
Interest:
The authors declare
2218-E-008of-012and 107-2221-E-197
-030 -.no conflict of interest. The funders had no role in the design of the
study; in the collection, analyses, or interpretation of the data; in the writing of the manuscript, or in the decision
to
publish of
theInterest:
results. The authors declare no conflict of interest. The funders had no role in the design of the
Conflicts
study; in the collection, analyses, or interpretation of the data; in the writing of the manuscript, or in the decision
to publish the results.
Energies 2019, 12, 1781
18 of 19
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© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).