energies
Article
Optimal Design of a High Efficiency LLC Resonant
Converter with a Narrow Frequency Range for
Voltage Regulation
Junhao Luo 1 , Junhua Wang 1
1
2
*
ID
, Zhijian Fang 1, *
ID
, Jianwei Shao 1 and Jiangui Li 2, *
School of Electrical Engineering, Wuhan University, Wuhan 430072, China; junhao_l@foxmail.com (J.L.);
junhuawang@whu.edu.cn (J.W.); hitwhshao@whu.edu.cn (J.S.)
School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China
Correspondence: fzj@whu.edu.cn (Z.F.); jianguili@whut.edu.cn (J.L.); Tel.: +86-159-2727-9055 (Z.F.)
Received: 24 March 2018; Accepted: 24 April 2018; Published: 2 May 2018
Abstract: As a key factor in the design of a voltage-adjustable LLC resonant converter, frequency
regulation range is very important to the optimization of magnetic components and efficiency
improvement. This paper presents a novel optimal design method for LLC resonant converters,
which can narrow the frequency variation range and ensure high efficiency under the premise of
a required gain achievement. A simplified gain model was utilized to simplify the calculation and
the expected efficiency was initially set as 96.5%. The restricted area of parameter optimization
design can be obtained by taking the intersection of the gain requirement, the efficiency requirement,
and three restrictions of ZVS (Zero Voltage Switch). The proposed method was verified by simulation
and experiments of a 150 W prototype. The results show that the proposed method can achieve
ZVS from full-load to no-load conditions and can reach 1.6 times the normalized voltage gain
in the frequency variation range of 18 kHz with a peak efficiency of up to 96.3%. Moreover,
the expected efficiency is adjustable, which means a converter with a higher efficiency can be designed.
The proposed method can also be used for the design of large-power LLC resonant converters to
obtain a wide output voltage range and higher efficiency.
Keywords: LLC resonant converter; frequency range; optimal design; gain; efficiency
1. Introduction
LLC resonant converters are widely used for their advantages of high efficiency, high power
density, easy implementation of magnetic integration, no need for a filter inductor for the output side,
and low EMI [1–5]. An LLC resonant converter is required to work efficiently in a certain range of
output voltages in many applications, such as charging for electric vehicles or other batteries. However,
there is a problem of a wide frequency regulating range [6] for the design of a voltage-adjustable
converter, which will lead to increased transformer size and conduction losses [7,8] and is not conducive
to the optimization of magnetic components and efficiency improvement [9]. The problems above
limit the application of LLC resonant converters in the charging field. Therefore, in the optimal design
of an LLC resonant converter, the frequency variation range should be reduced and high efficiency
needs to be ensured under the premise of satisfying the required gain.
The frequency-domain analysis method fundamental harmonic approximation (FHA) is a
commonly used method to obtain the voltage gain for the design of LLC resonant converters based
on the equivalent alternating current (AC) circuit of the resonant tank. However, the accuracy is
unsatisfying. Other approaches, such as state-plane [10,11] or time-domain analysis [12,13] rely on the
exact model of the converter to provide a precise description of a circuit’s behavior. Compared with
Energies 2018, 11, 1124; doi:10.3390/en11051124
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Energies 2018, 11, 1124
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the FHA-based method, time-domain analysis can obtain a higher accuracy. Thus, the parameters of
the system can be comprehensively considered for the optimization of its design.
Based on the analysis of six different operating modes of an LLC resonant converter in
the time-domain model, the frequency-voltage gain distribution and the frequency-output power
distribution of each operating mode are obtained by listing the boundary equations between the
operating modes [14]. In Reference [15], high efficiency is set as the objective function, and the optimal
values of the resonance parameters are solved by computer programming based on time-domain state
equations and optimization methods for numerical nonlinear systems. However, due to the multiple
combinations of the time-domain modes of an LLC resonant converter and the difficulty involved
in obtaining an analytical solution of the boundary conditions under different operating modes,
a simplified time-domain analysis model is established in this paper to simplify the design complexity.
In order to optimize the operation frequency range of LLC resonant converters, Reference [16]
proposed a design method which limits the maximum working frequency under the condition
of meeting the variation range of the output voltage. Nevertheless, it is not fully considered.
A method [17] based on full mode time-domain analysis was proposed to achieve different output
voltage ranges by combinations of different modes with high accuracy. However, it works in various
combinations of modes, which is not conducive to performance optimization of the converter, with an
increased complexity of the design process. In Reference [18], a modified LLC converter with two
transformers is proposed that can reduce the excitation current while maintaining a high gain range
by changing the equivalent magnetizing inductance and turns ratio. Nevertheless, the increased
number of transformers lowers the power density. In Reference [9], an LLC resonant converter with
a dual resonant frequency is proposed to achieve narrow switching frequency variation. However,
the converter added a new pair of small-rated power switches and an auxiliary inductor with an
increased volume and cost. Reference [19] presented an optimization method based on operation mode
analysis and peak gain placement. Following the approach, the conduction loss can be minimized
while maintaining the required gain range. The method can reach 1.455 times the normalized voltage
gain in the frequency variation range of about 56 kHz. Reference [20] presented a design method for a
high efficiency LLC resonant converter with a wide output voltage. The magnetic components of the
converter are optimized based on precise time-domain analysis. The method can reach 1.41 times the
normalized voltage gain in the frequency variation range of about 38 kHz.
This paper proposes an optimal design method for LLC resonant converters that can narrow
the frequency range and ensure high efficiency under the premise of obtaining the required gain.
The paper is organized as follows:
•
•
•
•
•
In Section 2, different operating modes of an LLC resonant converter are analyzed and the optimal
working mode is selected. Based on the state equations, a simplified time-domain analysis model
is established to obtain the gain curve;
In Section 3, conditions to achieve ZVS on the primary side from full-load to no-load conditions
are studied, through which three restrictions on converter parameters can be obtained;
In Section 4, to achieve high efficiency LLC resonant converters, the loss and efficiency are
calculated. Taking the intersection of the gain requirement, the efficiency requirement, and three
restrictions of ZVS, the restricted area of parameter optimization design can be obtained;
In Section 5, the proposed method is verified by simulation and experiment; and
The conclusions are given in Section 6.
2. Simplified Gain Model
A full-bridge LLC resonant converter considering the parasitic capacitance is shown in Figure 1,
which is composed of a resonant inductor, a resonant capacitor, and a magnetic inductor. Cp and
Cs are the equal self-capacitances of the primary and secondary windings, respectively; and Cps is
the equal mutual capacitances between the primary and secondary windings. The converter has the
Energies 2018, 11, 1124
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Energies
2018, 11, x FOR
PEER REVIEW
advantages
of achieving
ZVS on the primary side and ZCS (Zero Current Switch) on the secondary3 of 17
side. Meanwhile, the SRs (Synchronous Rectifier) are used to reduce the conduction losses. Due to
3 of 17
advantages,
LLC
resonant
convertershave
have been
been widely
high
efficiency
andand
highhigh
power
thesethese
advantages,
LLC
resonant
converters
widelyused
usedinin
high
efficiency
power
density
applications.
density
applications.
these advantages,
LLC resonant converters have been widely used in high efficiency and high power
Energies 2018, 11, x FOR PEER REVIEW
density applications.
S3
S1
ir
a
vi
S3
S1
a
Cr
vab ir
vi
vab
Lm
im
b
S2
b
c
Lm
Cr
im
Cp
Cp
vcd
Cs
vcd
Cs
S6
S6
Cps
C
vo
R
vo
R
b
b
S4
Cd
d
is
is
S4
S2
S7
cS5
ip
Lr
S7
S5
ip
Lr
S8
S8
Cps
LLC resonant
converter
circuit
considering
parasitic
capacitance.
Figure
1.1.LLC
converter
circuit
considering
the
parasitic
capacitance.
FigureFigure
LLC1.resonant
resonant
converter
circuit
considering
thethe
parasitic
capacitance.
There
arefour
four kinds
kinds
modes
(P, (P,
PO,
PON,
and
PN)
f when
≤ f rwhen
(resonant
There
are
four
kinds ofof
operating
modes
PON,
and when
PN) PN)
f ≤ frf ≤ fr
There
are
ofoperating
operating
modes
(P,PO,
PO,
PON,
and
frequency)
[19,20]
as
is
displayed
in
Figure
2.
When
the
switching
frequency
of
the
LLC
(resonant
frequency)
[19,20]
as
is
displayed
in
Figure
2.
When
the
switching
frequency
of
the
LLC
(resonant frequency) [19,20] as is displayed in Figure 2. When the switching frequencyresonant
of
the LLC
converter
equals
the
resonant
frequency,
it
is
called
P
mode
as
is
shown
in
Figure
2a.
At
this
mode,
resonant
converter
equals
the
resonant
frequency,
it
is
called
P
mode
as
is
shown
in
Figure
2a.
At
this
resonant converter equals the resonant frequency, it is called P mode as is shown in Figure 2a. At this
only only
Lr and
in the
the resonant
inductor
current
ir is air standard
sinesine
wave,
mode,
r C
and
participate
in
the
thethe
resonant
inductor
current
is a istandard
r participate
mode,
only
LrLand
CCr rparticipate
inresonance,
theresonance,
resonance,
resonant
inductor
current
r is a standard sine
and and
the magnetizing
current
im is iam triangular
wave.
wave,
the magnetizing
current
is a triangular
wave.
wave, and the magnetizing current im is a triangular wave.
S1
S2
S1
S1
S2
vab
v
θ
vab
vLm
vabLm
vLm
ir
θ
θ
irim
0
im
isec
0
Ts/2
θ
Ts
Ts/2
0
Ts t
ir
vab
vLm
im
ir
isec
iTmr/2 Ts/2
0
isec
isec
t
(a)
S1
(a)
θ <0
O
imisec
P
0
N
Ts/2
N
Ts/2
isec
0
Ts
(c)
Tr/2 Ts/2
Ts
t
t
S2
S1
S2
ZVS loss
ir vab
im vLm
θ <P0
isec
t
O
Ts
vab
vLm
θ = 0 ir
vab
vLmim
P
Imp
(b)
ZVS loss
θ=
0 0 ir
Imp
S1
S2
S2
vab
vLm
S2
(b)
ZVS loss
S1
ZVS loss
S2
S1
ir
im
N
Ts/2
P
0
Ts
t
Ts
N
isec
t
Ts/2
(d)
Ts
t
Figure
2. Operating
mode
division
of LLC
(f ≤ (f1):≤(a)
mode(f
= 1); (b)
PO(b)
mode;
(c) PON
(d)
Figure
2. Operating
mode
division
of LLC
1):P (a)
P mode(f
= 1);
PO mode;
(c) mode;
PON mode;
PN(d)
mode.
(c)
(d)
PN mode.
Figure
Operating
LLC (f ≤works
1): (a) at
P mode(f
1); (b)asPO
mode; (c)The
PON
mode; (d)
As is2.displayed
inmode
Figuredivision
2b, the of
converter
the PO =mode
f decreases.
converter
As is displayed in Figure 2b, the converter works at the PO mode as f decreases. The converter
enters
the O mode at the end of the P mode when ir = im, and the switches on the secondary side cut
PN mode.
enters the O mode at the end of the P mode when i = i , and the switches on the secondary side cut
off. At the O mode, Lm, Lr, and Cr resonate together. rThementire PO mode circuit works in the ZVS
off. At the O mode, Lm , Lr , and Cr resonate together. The entire PO mode circuit works in the ZVS
region.
secondary
achieve works
ZCS. The
is considered
the best working
As isMeanwhile,
displayed the
in Figure
2b,side
the can
converter
at PO
themode
PO mode
as f decreases.
The converter
mode
[19,20].
enters the O mode at the end of the P mode when ir = im, and the switches on the secondary side cut
continues
the converter
enters The
the PON
mode
the PN
mode.
As can
off. At When
the Of mode,
Lm,toLrdecrease,
, and Cr resonate
together.
entire
PO or
mode
circuit
works
in be
the ZVS
seen
from
Figure
2c,d,
the
two
modes
have
lost
their
ZVS
characteristics
and
their
resonant
current
region. Meanwhile, the secondary side can achieve ZCS. The PO mode is considered the best working
lag angle is less than or equal to zero. The PON and PN modes lie in capacitive impedance states. In
mode [19,20].
addition, the relationship between the voltage gain and the switching frequency is no longer
Energies 2018, 11, 1124
4 of 17
region. Meanwhile, the secondary side can achieve ZCS. The PO mode is considered the best working
mode [19,20].
When f continues to decrease, the converter enters the PON mode or the PN mode. As can be seen
from Figure 2c,d, the two modes have lost their ZVS characteristics and their resonant current lag angle
is less than or equal to zero. The PON and PN modes lie in capacitive impedance states. In addition,
the relationship between the voltage gain and the switching frequency is no longer monotonous,
and closed-loop instability may occur at these modes. According to the above analysis, the designed
LLC resonant converter in this paper works at the PO mode.
1.
P mode
When the converter works at P mode, Equation (1) can be obtained as follows for the magnetic
inductance:
dim
nvo = Lm
.
(1)
dt
It can be obtained from the KCL equation of the LLC resonant converter in half a cycle:


ir = Ir sin(2π f r t − θ P )




im = im (0) + nvo · t/Lm





 i s = n (ir − i m )
.
Io f f = ir (0.5T )



ir (0) = i m (0)




ir (0.5T ) = im (0.5T )



 i (0) = −i (0.5T )
r
r
(2)
Ioff represents the off-current of the MOSFET, Im represents the peak value of the magnetizing
current, and θ P represents the angle that the resonant current lags with voltage vab .
At P mode, fs = fr . It can be derived as follows:
Ir sin(θ P ) = Im =
2.
nvo
.
4Lm f r
(3)
PO mode
As for the PO mode, when the switching frequency fs is close to the resonant frequency fr and the
Lm is large, the time of O mode is relatively short and the current change is very small. To simplify
the calculation, ir and im can be considered unchanged at O mode. The peak value of the magnetizing
current is indicated in Formula (3). The resonance current and magnetizing current can be expressed
respectively as:
(
ir1 (t) = Ir sin(2π f r t − θ PO ), 0 ≤ t ≤ Tr /2
ir =
o
ir2 (t) = 4 nv
f r Lm , Tr /2 < t < Ts /2
(
.
(4)
o
im1 (t) = nvo · t/Lm − 4 nv
f r Lm , 0 ≤ t ≤ Tr /2
im =
o
im2 (t) = 4 nv
f r Lm , Tr /2 < t < Ts /2
Ts represents the switching cycle at this time. When t = 0:
ir (0) = Ir sin(−θ PO ) = −
nvo
.
4 f r Lm
(5)
During a half-switching period, the average value of the primary current of the transformer and
the average value of the secondary current satisfy the relation:
2
Ts
Z Ts /2
0
|n(ir − im )|dt = Io .
(6)
Energies 2018, 11, 1124
5 of 17
According to Formulas (3)–(6):
Ir cos(θ PO ) =
πIo f r
2n f s
(7)

2
2
f
f

 θ PO = arctan( 2πnf r IvooLm · f rs ) = arctan( 2πnf rRLm · f rs )
r
r
.
πIo f r 2
πvo f r 2
2
2

o
o
 Ir = ( 4 nv
( 4 nv
f L ) + ( 2n f ) =
f L ) + ( 2nR f )
r m
s
r m
(8)
s
When fs = fr , the effective value of the original and secondary resonant currents of the converter is
shown in Formula (9).
r
Ir, fr =
Ir, f r ,RMS
Is, f r ,RMS
q
2
2
π Io 2
πvo 2
o
o
( 4 nv
)
+
(
)
=
( 4 nv
2n
f r Lm
f r Lm ) + ( 2nR )
√
= Ir, fr / 2
r
q R
√
2
2
2
2
T /2
= T2r 0 r (n(ir − im ))2 dt = 24π3 (5π 2 − 48)( 4nfr vLom ) + 12( π Rvo )
(9)
At P mode, the magnetizing inductance is clamped at the output voltage. The corresponding
state equation is:
(
d
ir1 (t) = nvo
vi − vCr1 (t) − Lr dt
.
(10)
d
Cr dt vCr1 (t) = ir1 (t)
At O mode, the secondary diode turns off naturally, and it can be considered approximately
that the inductor current is unchanged and the voltage of the resonant capacitor increases linearly.
The corresponding state equation is:
Cr
d
v (t) = ir2 (t) = im2 (t).
dt Cr2
(11)
According to the continuity of the signal at the P and O modes and the symmetry of the voltage
of the resonant capacitor, it can be derived that:
v o = vi +
nvo
( Ts − Tr ).
4Lm Cr
(12)
The normalized gain expression is given after simplifying Formula (12):
M=
nv0
=
vi
1−
1
π2 fr
4k ( f s
− 1)
.
(13)
3. MOSFET ZVS Condition
The essence of ZVS in the power switch is to release the voltage Vds on junction capacitances
of the MOSFET to zero in the dead time of the circuit, then the drive signal Vgs of the MOSFET
arrives, and ZVS is thereby achieved. The ZVS implementation of MOSFET includes the following
three conditions:
•
ZVS condition 1: The input impedance of the resonant network is inductive, which can ensure
that the junction capacitor is discharged rather than charged. Additionally, the direction of the
resonant current should not change during the dead time.
An LLC equivalent circuit considering the parasitic capacitance is shown in Figure 3.
Energies 2018, 11, 1124
Energies 2018, 11, x FOR PEER REVIEW
6 of 17
6 of 17
Cr
Lr
ir
vab
im
Lm
Ceq
Rac
Figure 3. Equivalent circuit of an LLC resonant converter.
Figure 3. Equivalent circuit of an LLC resonant converter.
The
tank are:
are:
The impedance
impedance characteristics
characteristics of
of the
the resonant
resonant tank
1
1
/ / m // / 1/ Ra//R
ZZinin= =
sLrsL+r + +1 sL
+m sL
ac
sCeq c
r
sCr sC
sC
eq
(14)
f − k2 C f 3
k2 f 2 Q
1
(14)
= Z0 { 2 2 k2 2 f 2Q 2 2 + j[ f − f1+ 2 2 k 2kf
2
3 2 ]}
k f Q +(kC f −1)
k f Q +(−kCk f 2Cf
−1)
]}
= Z0{ 2 2 2
+ j[ f − + 2 2 2
k f Q + ( kCf 2 − 1) 2
f k f Q + ( kCf 2 − 1) 2
q
√
where Z0 = Lr /Cr ; k = Lm /Lr represents the inductance coefficient; Q = ωRracLr = R1ac CLrr represents
ω r Lr
Lr
1
= Lm √
/ 1Lr represents
where
coefficient;f Q
represents
Z0 = factor;
Lr / Cr ; f k=
=
the quality
representsthe
theinductance
resonant frequency;
= =ffrs R
represents
the
normalized
r
R
C
2π Lr Cr
ac
ac
r
C
frequency; C = Ceqr represents the normalized equivalent capacitance; and Ceq represents
the parasitic
fs
1
f =the
= the primary
represents
thethe
resonant
frequency;
representspoint
the
the
quality equivalent
factor; f r to
capacitance
side. When
imaginary
part is zero,
boundary
fr
2π Lr Cr
where the impedance characteristic
lies between the inductive and capacitive states can be obtained.
Ceq
normalized frequency; C =
represents the normalized
equivalent capacitance; and Ceq represents
k f − k2 C f 3
1
Cr
f− +
=0
(15)
k2 f 2primary
Q2 + (kCside.
f 2 − 1When
)2
the parasitic capacitance equivalent f to the
the imaginary part is zero, the
boundary point where the impedance characteristic lies between the inductive and capacitive states
The following can be derived:
can be obtained.
s
1
− k12Cf 3(kC f 2 − 1)2
kC kf
f2 −
=0 .
(15)
(16)
Qmax ( ff, k−) =+ 2 2 2 2
−
f k kf( fQ −+1()kCf 2 − 1)k22 f 2
The
The following
following can
can be
be derived:
obtained:
kCf 2 − 1 ( s
kCf 2 − 1) 2
(
,
)
f
k
=
−
2π f r Lr
2π fQ
L
kC f 2 − .1
(kC f 2 − 1)2
max
2
r m
k ( f( f −, k1)) = k 2 f 2
Q=
=
< 0.95Qmax
−
R ac
kR ac
k ( f 2 − 1)
k2 f 2
The following can be obtained:
s
(16)
(17)
2
kR
kC f 2 − 1
(kC f 2 2− 1)
π f r Lm ac
2π fLr Lmr < 20.95
kCf2 2− 1 .( kCf 2 − 1) 2
−
(18)
2−
=
−
Q=
( f1, )k ) =
(17)
2π <f r 0.95kQ
( fmax
k f
Rac
kRac
k ( f 2 − 1)
k2 f 2
Qmax represents the maximum Q that satisfies the inductive nature of the impedance. Usually,
the design Q should have a margin of aboutkR5%. Equation
is a2 −necessary
condition of ZVS, but this
( kCf
1) 2
kCf 2 − 1 (18)
ac
.
<
0.95
−
L
(18)
m
condition alone does not guarantee ZVS of2πthe
f switch.
k ( f 2 − 1)
k2 f 2
r
•
ZVS
During
the dead
time,
the resonant
current nature
must beoflarge
enough to discharge
Q
max condition
represents2:the
maximum
Q that
satisfies
the inductive
the impedance.
Usually,
the junction
capacitor
the
MOSFET
to zero. During
entire dead
time, the
the design
Q should
have avoltage
marginofof
about
5%. Equation
(18) is athe
necessary
condition
of discharge
ZVS, but
current cannot
changed
in direction.
the junction capacitance of the MOSFET will
this condition
alone be
does
not guarantee
ZVS Otherwise,
of the switch.
be recharged after being discharged.
•
ZVS condition 2: During the dead time, the resonant current must be large enough to discharge
the
junction
capacitor
voltage
ofthe
thecurrent
MOSFET
Duringside
the entire
time,
the discharge
As can
be seen
from Figure
2a,
of to
thezero.
secondary
is zerodead
when
MOSFETs
on the
current
cannot
be
changed
in
direction.
Otherwise,
the
junction
capacitance
of
the
MOSFET
will
primary side turn off, i.e., ir = im . Additionally, the magnetizing current reaches a peak, which
is
be recharged
after being
discharged.
the discharging
current
of MOSFET
junction capacitance as illustrated in Equation (3). During dead
time,As
thecan
resonant
current
not only
junction
capacitance
ofside
the MOSFETs,
butMOSFETs
also changes
the
be seen
from Figure
2a,fills
thethe
current
of the
secondary
is zero when
on the
primary side turn off, i.e. ir = im. Additionally, the magnetizing current reaches a peak, which is the
discharging current of MOSFET junction capacitance as illustrated in Equation (3). During dead time,
the resonant current not only fills the junction capacitance of the MOSFETs, but also changes the
Energies 2018, 11, 1124
7 of 17
voltage across the parasitic capacitance from nvo to −nvo . The minimum resonant current that satisfies
the conditions is:
nvo
v
(19)
Imin = 4Coss i + 2Ceq
Td
Td
where Coss represents the output capacitance of the MOSFET and Td represents the dead time. Another
necessary condition for achieving ZVS is:
nvo
,
4 f r Lm
(20)
nvo
.
4 f r Imin
(21)
Imin <
i.e.,
Lm <
•
ZVS condition 3: Impedance angle
Even if the above two necessary conditions are satisfied, it is also necessary to determine whether
ZVS is achieved by checking the value θ of Equation (8). If the impedance angle is too small, it means
that the resonant circuit operates near the critical area of the inductive and capacitive state, which is
dangerous for the converter.
As can be seen from Equation (8), θ gets the minimal value when fs = f min and Io is the largest.
At this operating point, it is the hardest to achieve soft switching. Under the condition that the parasitic
capacitance is fully discharged in the dead time, ZVS can be achieved over the entire output voltage
range as long as the operating point is guaranteed to be soft-switched. To ensure ZVS when the output
is fully loaded at the minimum operating frequency, the resonant current should not reverse during
the dead time, i.e.θ ≥ 2π f r Td . The body diode of the switch should be conducted before the drive
signal arrives. It can be derived from θ ≥ 2π f r Td and Equation (8):
Lm ≤
n2 v o
fs
· .
2π f r Io tan(2π f r Td ) f r
(22)
When the converter is operating at the minimum frequency with full load (fs = f min , Io = Io,max ),
the critical value of the magnetizing inductance is:
Lm ≤
n2 R
f
· min
2π f r tan(2π f r Td )
fr
(23)
where R represents the direct current (DC) equivalent resistance under a full-load condition; and f min
represents the minimum operating frequency. An LLC resonant converter’s design should meet the
highest gain at a minimum-frequency, full-load condition, i.e.,
M | fmin ≥ Mmax .
(24)
The three conditions for achieving ZVS from full-load to no-load conditions are Equations (18),
(21) and (23).
4. Optimal Design of LLC Resonant Converter Parameters
The goal of the LLC resonant converter’s design is to select a set of parameters that can achieve
high efficiency while meeting the output voltage and power requirements. This paper presents an
optimal design method for LLC resonant converter parameters that can meet the gain requirement
and ensure high efficiency at the same time. The converter parameters required are shown as follows:
•
•
(1) Rated output power Po = 150 W; and
(2) Input voltage vi = 100 V; rated output voltage vo = 30 V; Output voltage range vomin –vomax =
24–48 V.
Energies 2018, 11, 1124
Mmax =
nvo max
vi
Mmin =
nvo min
.
vi
(25)
8 of 17
(26)
The maximum and minimum normalized gains of the LLC resonant converter are:
4.1. Loss and Efficiency Analysis
Mmax =
nvomax
vi
(25)
When the LLC resonant converter is in operation, its power losses mainly include primary
nv Ps on the secondary side; resonant inductance
power switch losses Pp; synchronous rectifier
Mmin losses
= omin
.
(26)
vi efficiency of the converter can be obtained as
losses PLr; and transformer losses PT. The total loss and
[20–23]
4.1. Loss and Efficiency Analysis
Ploss = Pp + Ps + PLr + PT
When
the LLC resonant converter is in operation, its power losses mainly include primary power
2 2
f the secondary
Np Ilosses
NL I rresonant
switch losses
Pp ; synchronous rectifier lossesI mPtsf on
side;
inductance
PLr ;(27)
β
m βT
= I r2,RMS (2Rds + RLr + RT , p ) + I s2,RMS RT ,s +
+ Ps + k Lr f α Lr ( μLr r ) Lr VLr + kT f αT ( μT
) VT
and transformer losses PT . The total loss and
of the converter
can be obtained aslT [20–23]
Coss
lL
24efficiency
r
Ploss = Pp + Ps + PLr + PT
2
2
R T,s +
= Ir,RMS
(2Rds + R Lr + R T,p ) + Is,RMS
2 t2 f
Im
f
24Coss
P
Po + Ploss
η+=Ps + k Lor f αLr (µ Lr
NLr Ir β Lr
VLr
l Lr )
+ k T f αT (µ T
Np Im β T
lT ) VT
(27)
Po
(28)
(28)
η=
of the
tf represents drop time of the switching
where Coss represents the output capacitance
Po +MOSFET;
Ploss
off current; the subscripts Lr and T represent the resonant inductance and transformer, respectively;
where Coss represents the output capacitance of the MOSFET; tf represents drop time of the switching
N off
represents
thesubscripts
number Lof and
turns
of the inductor
coil;inductance
μ represents
the magnetic
permeability;
current; the
T represent
the resonant
and transformer,
respectively;
r
l represents
the
magnetic
circuit
length;
f
represents
the
operating
frequency;
V
represents
the core
N represents the number of turns of the inductor coil; µ represents the magnetic permeability;
volume;
k represents
the circuit
core loss
coefficient;
α =the1.5–1.7
represents
theV frequency
losscore
index;
l represents
the magnetic
length;
f represents
operating
frequency;
represents the
β =volume;
2–2.7 represents
thethe
magnetic
index; and
k, α, and
β can bethe
obtained
by consulting
relevant
k represents
core lossloss
coefficient;
α = 1.5–1.7
represents
frequency
loss index; βthe
= 2–2.7
core
manual the
to get
its specific
value. and k, α, and β can be obtained by consulting the relevant core
represents
magnetic
loss index;
WhentoPget
o = 150
W, vo =value.
30 V, and vi = 100 V, the relationship of Ploss, η versus f, and Lm is indicated
manual
its specific
When
Po respectively.
= 150 W, vo = 30
andbe
vi =
100 from
V, the Figure
relationship
Ploss , η versus
f, and
Lm is indicated
in Figure
4a,b,
AsV,can
seen
4, theofefficiency
of the
converter
gradually
in Figure
As can the
be seen
from Figure
the efficiency
of the converter
increases
as4a,b,
f andrespectively.
Lm rise. However,
efficiency
upper4,limit
of the converter
tends to gradually
be a constant
increases
as
f
and
L
rise.
However,
the
efficiency
upper
limit
of
the
converter
tends
to
be
a
constant
m
after f and Lm reach a certain degree. The theoretical value of the efficiency has an upper
limit.
after
f
and
L
reach
a
certain
degree.
The
theoretical
value
of
the
efficiency
has
an
upper
limit.
m
Therefore, the values
of f and Lm need to be reasonably selected.
Therefore, the values of f and Lm need to be reasonably selected.
(a)
(b)
Figure
relationofofPPloss,,ηηversus
versusf fand
andLLm: :(a)
(a)P Ploss
; (b)
Figure 4.
4. The
The relation
; (b)
η. η.
loss
m
loss
4.2. Optimization Process
The overall design idea of this paper is illustrated in Figure 5, and the rated operating point
is designed at the resonant frequency. At first, give the initial value of f min , and then calculate k
Energies 2018, 11, x FOR PEER REVIEW
9 of 17
4.2. Optimization Process
Energies 2018, 11, 1124
9 of 17
The overall design idea of this paper is illustrated in Figure 5, and the rated operating point is
designed at the resonant frequency. At first, give the initial value of fmin, and then calculate k satisfying
satisfying
the gain
required to
according
to (13)
Equations
(13)
and (25). to
According
Equation
(18),
k can be
the
gain required
according
Equations
and (25).
According
Equationto(18),
k can be
converted
converted
to
the
constraint
of
ZVS.
Based
on
the
three
ZVS
constraints
and
the
efficiency
requirements,
to the constraint of ZVS. Based on the three ZVS constraints and the efficiency requirements, the
the intersection
of optimal
the optimal
design
be obtained
to select
an appropriate
fr and
Lm that
so that
Lr and
intersection
of the
design
can can
be obtained
to select
an appropriate
fr and
Lm so
Lr and
Cr
C
can
also
be
determined.
If
the
intersection
does
not
exist,
the
efficiency
or
f
can
be
appropriately
r
mincan be appropriately
can also be determined. If the intersection does not exist, the efficiency or fmin
reducedto
toobtain
obtainthe
theparameters.
parameters.
reduced
Give the initial
value of fmin
Reduce
Normalized gain
required at f=fmin
Calculate
k
Simplified
gain model
Constraint 3
Formula(29)
Efficiency
requirement
Constraint1、2
Formula(21)(23)
N
Intersection
Y
Determine
fr and Lm
Figure 5. Flow chart for the optimal design of the parameters.
Figure 5. Flow chart for the optimal design of the parameters.
To limit the frequency to a small range, fmin = 0.8fr is initially taken. When f = fmin, the gain curve
Toobtained
limit thefrom
frequency
to a(13)
small
f min in
= 0.8f
When f the
= f min
, the gain
r is initially
can
be
Equation
as range,
displayed
Figure
6, wheretaken.
M represents
normalized
Article
curve
can
be
obtained
from
Equation
(13)
as
displayed
in
Figure
6,
where
M
represents
the
normalized
voltage gain and it can be obtained from Equations (24) and (25) that k ≤ 1.6454. The critical point is
voltageingain
and6.it can be obtained from Equations (24) and (25) that k ≤ 1.6454. The critical point is
shown
Figure
shown in Figure 6.
Optimal
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
1
2
3
4
5
6
7
8
9
k
Figure
6.6.6.
Simplified
time-domain
gain
curves
of
different
kkvalues
in
PO
mode.
Figure
Simplified
time-domain
gain
curves
different
kvalues
values
PO
mode.
Figure
Simplified
time-domain
gain
curves
ofof
different
inin
PO
mode.
When
f =f f=minfmin
= 0.8
fr, the
function
curve
inin
Equation
(18)
is is
shown
inin
Figure
7.7.
AsAs
can
bebe
seen
from
When
= 0.8f
r, the
function
curve
Equation
(18)
shown
Figure
can
seen
from
When f = fmin = 0.8fr , the function curve in Equation (18) is shown in Figure 7. As can be seen
the
figure,
the
value
gradually
increases
asas
k increases.
the
figure,
the
value
gradually
increases
k increases.
from the figure, the value gradually increases as k increases.
Figure 6. Simplified time-domain gain curves of different k values in PO mode.
When f = fmin = 0.8fr, the function curve in Equation (18) is shown in Figure 7. As can be seen from
10 of 17
10 of 17
as k increases.
Energies 2018, 11, 1124
Energies
2018, 11,
FOR PEER
REVIEWincreases
the figure,
thex value
gradually
5
4.5
4
Function
3.5
3
2.5
2
1.5
1
1
2
3
4
5
6
7
8
9
k
r
2
kC f 222−1
f 2 −212 )
kCf
− 1− (kC
( kCf
−.1)22
Figure7.7.Function
Functioncurve
curveofof k kCf
2
k2 f 2 − 1) ..
Figure
Figure
7. Function curve
of kk k( f 22−−1)1 −−( kCf
2 2
1)
kk((ff −−1)
kk2 ff2
The required maximum normalized voltage gain Mmax ≥ 1.6 (k ≤ 1.6454), where Equation (18) is
in requiredFigure
9.
As
can
be
seen
from
The
maximum
equivalent
to Equation
(29). normalized voltage gain Mmax ≥ 1.6 (k ≤ 1.6454), where Equation (18) is
Figure
9,
the
limited
area
will
be
very
severe
when
the
efficiency
demand
is
relatively
large.
equivalent to Equation (29).
s frequency in the restricted area s
Moreover, the resonance
is too 2small, which2 is detrimental
to the
2
2
2−1
2 f 2 − 1) 2
2
2− 1
2 f 2− 1)
2π f r Lm
kC
f
kC
f
(
kC
(
kC
2
π
f
L
kCf
−
1
(
kCf
−
1)
kCf
−
1
(
kCf
−
1)
volume reduction
and
density of
< 0.95max
(r km high
(29)
= 0.95k
< 0.952power
max( k −
− the )LLC
)resonant
= 0.95 k converter.
−− 2 2 2 2
(29)
R ac
k( f − 1) k ( f 2 −k1)2 f 2 k 2 f 2
k(kf( 2f 2−− 1)
1)
R ac
k fk f
k =1.6454
k =1.6454
The three constraints for achieving ZVS from full-load to no-load conditions are Equations (21),
The three constraints for achieving ZVS from full-load to no-load conditions are Equations (21),
(23) and (29). The optimal design of the parameters is actually the selection of parameters in
(23) and (29). The optimal design of the parameters is actually the selection of parameters in intersecting
intersecting regions of Equations (21), (23), (28) and (29). The intersection is shown in Figure 8 when
regions of Equations (21), (23), (28) and (29). The intersection is shown in Figure 8 when the demand
the demand efficiency is set to be greater than 96.5%.
efficiency is set to be greater than 96.5%.
η=0.965
Hz
Energies 2018, 11, x; doi: FOR PEER REVIEW
www.mdpi.com/journal/energies
η
Restricted
Region
H
Figure 8. Intersection of ZVS constraints and efficiency requirement (η > 96.5%).
Figure 8. Intersection of ZVS constraints and efficiency requirement (η > 96.5%).
When the expected efficiency increases, the efficiency curve shifts to the right. At the time, the
When
expected
efficiency
increases,
curve shifts
to the right.
At the time,
intersectionthe
narrows
or even
disappears.
Whenthe
theefficiency
expected efficiency
decreases,
the efficiency
curve
the
intersection
narrows
or
even
disappears.
When
the
expected
efficiency
decreases,
the
shifts to the left, and the intersection becomes larger as shown in Figure 9. As can be efficiency
seen from
curve
shifts
to the
left, and
intersection
largerthe
as shown
in Figure
9. Asiscan
be seen from
Figure
9, the
limited
areathewill
be very becomes
severe when
efficiency
demand
relatively
large.
Figure
9,
the
limited
area
will
be
very
severe
when
the
efficiency
demand
is
relatively
large.
Moreover,
Moreover, the resonance frequency in the restricted area is too small, which is detrimental to the
volume reduction and high power density of the LLC resonant converter.
Energies 2018, 11, 1124
11 of 17
11 of 17
the resonance frequency in the restricted area is too small, which is detrimental to the volume reduction
Energies
2018,
11, x FOR
PEER REVIEW
2 of 2
and high
power
density
of the LLC resonant converter.
f(Hz)
f(Hz)
Energies 2018, 11, x FOR PEER REVIEW
(a)
(b)
(b)
Figure 9. Influence of(a)
expected efficiency on the restricted design area of the converter:
(a) Increased
efficiency;
(b) Decreased
efficiency.
Figure
9. Influence
of expected
efficiency on the restricted design area of the converter: (a) Increased
Figure 9. Influence of expected efficiency on the restricted design area of the converter: (a) Increased
efficiency;
(b)
Decreased
efficiency.
efficiency; (b) Decreased efficiency.
Based on the above analysis, the parameters of the converter selected in the intersecting area in
Figure
8 are
shown
in analysis,
Table 1.the
The
loss composition
analysisselected
is performed
according area
to the
Based
on the
above
parameters
of the converter
in the intersecting
in
Based on
theindicated
above analysis,
the
parameters
ofshow
the converter
selected inloss
the and
intersecting
area
in
parameters
as
is
in
Figure
10.
The
results
that
the
conduction
turn-off
loss
of
Figure 8 are shown in Table 1. The loss composition analysis is performed according to the
Figure
8
are
shown
in
Table
1.
The
loss
composition
analysis
is
performed
according
to
the
parameters
as
MOSFETs on
parameters
as the
is primary side and the on-state switching loss on the secondary side account for the
is indicated
in Figure
10. TheThe
results
showswitching
that the conduction
and turn-off
loss of MOSFETs
the
majority
of the
total losses.
on-state
loss on theloss
secondary
side accounts
for 58% on
of the
primary
side
and
the
on-state
switching
loss
on
the
secondary
side
account
for
the
majority
of
the
total
total losses. The iron loss of the transformer and the inductor accounts for less than 1%; thus, they are
losses.
The in
on-state
switching loss on the secondary side accounts for 58% of the total losses. The iron
not
shown
the figure.
loss of the transformer and the inductor accounts for less than 1%; thus, they are not shown in the figure.
Table 1. Optimal parameters of the LLC resonant converter.
Table 1. Optimal parameters of the LLC resonant converter.
Parameter
Input
voltage
Parameter
Rated
Output
voltage
Input voltage
Rated
power
Rated
Output
voltage
Rated power
Transformer
ratio
Transformer
ratio
Resonant
inductor
Resonant inductor
Resonant
capacitor
Resonant capacitor
Magnetic
inductor
Magnetic inductor
Output capacitor
Output
capacitor
Value
100 V
Value
30 V
V
100
150
30 VW
150
W
10:3
10:3μH
85.1
85.1 µH
36.7 nF
36.7 nF
140
μH
140 µH
1000
1000uF
uF
Figure 16. Gain curve comparison. FHA = fundamental harmonic approximation.
The measured efficiency curve is presented in the Figure 17. Under the medium and full-load
conditions, the converter can maintain a high efficiency. The peak efficiency of the LLC resonant
Figure
Figure 10.
10. Loss
Loss composition
composition analysis of the LLC resonant converter.
Energies 2018, 11, 1124
12 of 17
Energies 2018, 11, x FOR PEER REVIEW
Energies 2018, 11, x FOR PEER REVIEW
12 of 17
12 of 17
5. Simulation and Experiments
5. Simulation
andand
Experiments
5. Simulation
Experiments
•
•
(1) Simulation
• Simulation
(1) Simulation
(1)
The parameters in Table 1 are verified by simulation, and the results are shown in
The parameters
in Table
1 are verified
by simulation,
and the
results
are shown
in Figures
in Table
1 are verified
by simulation,
and
the results
are shown
in 11
The parameters
Figures 11 and 12. The waveforms under different load conditions at the resonant frequency are
and 12.
The11
waveforms
different
load
conditions
at the resonant
frequency
are shown
at the resonant
frequency
are in
Figures
and 12. Theunder
waveforms
under
different
load conditions
shown in Figure 11. As can be seen from Figure 11, ZVS on the primary side can be achieved from a
Figureshown
11. As
be seen
Figure
11, ZVS
on 11,
theZVS
primary
can be
achieved
from a full-load
incan
Figure
11. Asfrom
can be
seen from
Figure
on theside
primary
side
can be achieved
from a to
full-load to a no-load condition when f = fr, which proves the effectiveness of the proposed method.
when
f = fr, which
proves the effectiveness
of themethod.
proposed method.
full-load
to a no-load condition
a no-load
condition
= frgain
, which
proves
the
of the
thesimulation
proposed
next step
= 0.8 fr = 72 kHz;
results areThe
shown
The next
step is towhen
verifyf the
requirement
at f effectiveness
f
=
0.8
f
r =simulation
72
kHz;
the
simulation
results
are
shown
The next
step
is requirement
to verify the gain
requirement
at
is toinverify
the
gain
at
f
=
0.8
f
=
72
kHz;
the
results
are
shown
in
Figure
12.
r
Figure 12.
in Figure 12.
S1
100
0 100
-100
0
S2
S1
S2
S1
vab
vLmvab
vLm
-2
ir
im ir
im
40
vo
2
0
2
0
-2
40
30
20
30
0 100
-100 0
-100
2
0
-2
vo
0
0 100
-100
0
-100
2
0
-2
2
0
-2
t
(a)
(a)
S1
S1
100
ir
im ir
im
2
0
-2
t
20
0
S2
vab
vLmvab
vLm
100
-100
S2
S1
t
t
(b)
(b)
S2
S2
vab
vab
vLm
vLm
ir
im ir
im
t
t
(c)
(c)
Figure 11. Simulation waveforms under different loads (f = fr): (a) full load; (b) 1% rated load; (c)
Figure
11. Simulation
waveforms
underdifferent
different
loads
): (a)
full(b)
load;
1%load;
rated
Figure
11. Simulation
waveforms under
loads
(f = (f
fr): =
(a)frfull
load;
1% (b)
rated
(c)load;
no load.
(c) nono
load.
load.
4
3
2
1
0
-1
-2
-3
200
0 200
-200 0
5 -200
0
5
-5 0
100 -5
50 100
0 50
0
S1
S1
vLm
vabvLm
vab
ir
i
im r
im
vo
vo
-4
4
3
2
1
0
-1
-2
-3
-4
S2
S2
200
0 200
-200 0
20-200
0
20
0
-20
60 -20
50
40
60
50
40
t
S1
S1
vLm
vabvLm
vab
S2
S2
ir
im ir
im
vo
vo
t
t
t
(a)
(b)
(a)
(b)
Figure 12. Simulation waveforms under different loads (f = 0.8fr): (a) full load (P = 150 W); (b) heavy
Figure 12. Simulation waveforms under different loads (f = 0.8fr): (a) full load (P = 150 W); (b) heavy
load12.
(R =Simulation
6, P = 384 W).
Figure
waveforms under different loads (f = 0.8fr ): (a) full load (P = 150 W); (b) heavy
load (R = 6, P = 384 W).
load (R = 6, P = 384 W).
As is displayed Figure 12a, the waveform under a full-load condition is nearly consistent with
As is displayed Figure 12a, the waveform under a full-load condition is nearly consistent with
the simplified gain analysis model described above. Although the waveforms of the resonant current
theis
simplified
gain
analysis
model
described above.
Although
the waveforms
resonant
currentwith
As
displayed
Figure
12a,
the waveform
under
a full-load
condition of
is the
nearly
consistent
the simplified gain analysis model described above. Although the waveforms of the resonant current
and the magnetizing current in Figure 12b have a small deviation from the simplified gain model,
it has little effect on the gain calculation. As can be seen from Figure 12b, soft switching can still be
Energies 2018, 11, x FOR PEER REVIEW
Energies 2018, 11, 1124
Energies 2018, 11, x FOR PEER REVIEW
13 of 17
13 of 17
13 of 17
and the magnetizing current in Figure 12b have a small deviation from the simplified gain model, it
and
magnetizing
current
Figure 12bAs
small
the simplified
gain can
model,
itbe
hasthe
little
effectaon
the
gain
calculation.
be
seendeviation
from Figure
softWswitching
still
achieved
under
heavy
loadin
condition
(Rhave
=can
6, aoutput
power
is from
Pmax12b,
= 384
> rated
power
150
W)
has
little effect
onathe
gainload
calculation.
As(Rcan
be
seen from
Figure
12b,
softWswitching
can still
be
achieved
under
heavy
condition
=
6,
output
power
is
P
max
=
384
>
rated
power
150
W)
while satisfying the required voltage gain. Additionally, the minimum voltage of 24 V can be obtained
achieved
under a heavy
load condition
= 6, Additionally,
output power the
is Pmax
= 384 Wvoltage
> rated of
power
W)be
while satisfying
the required
voltage(R
gain.
minimum
24 V150
can
at about 106 kHz.
while
satisfying
the
required
voltage
gain.
Additionally,
the
minimum
voltage
of
24
V
can
be
obtained at about 106 kHz.
at about 106 kHz.
•obtained
(2) Experiments
•
(2) Experiments
• The
(2) Experiments
practicability and effectiveness of the proposed method are further verified through
The practicability and effectiveness of the proposed method are further verified through
experiments.
The
prototype
of the experimental
setup
is method
shown
in
13.verified
The experimental
The practicability
and effectiveness
of thesetup
proposed
areFigure
further
through
experiments.
The prototype
of the experimental
is shown
in Figure
13.
The experimental
results
results
are
shown
in
Figures
14–17,
where
Figure
14
is
the
experimental
waveform
under
different
load
experiments.
The
prototype
of the
experimental
shown in Figure
13. The experimental
results
are shown in
Figures
14–17,
where
Figure 14setup
is theis experimental
waveform
under different
load
conditions
the
resonant
frequency.
are
shownatinat
Figures
14–17,
where Figure 14 is the experimental waveform under different load
conditions
the
resonant
frequency.
conditions at the resonant frequency.
Output
Lr
Output
Transformer
Lr C r
Transformer Controller
Controller
Cr
Input
Input
Figure 13. The prototype of the experimental setup.
Figure 13. The prototype of the experimental setup.
Figure 13. The prototype of the experimental setup.
v
vab
ab
100V/div
100V/div
ir
5A/div
ir
5A/div
v
vgs
S2
S2
S1
S1
10V/div
gs
10V/div
Time: 4μ s / div
Time: 4μ s / div
(a)
(a)
vab
v
ab
100V/div
100V/div
ir
5A/div
ir
5A/div
v
vgs
S2
S2
S1
S1
10V/div
gs
10V/div
Time: 4μ s / div
Time: 4μ s / div
(b)
(b)
Figure 14. Cont.
ir
5A/div
S1
S2
Energies 2018, 11, 1124
vgs
Energies 2018, 11, x FOR PEER REVIEW
14 of 17
14 of 17
10V/div
Time: 4μ s / div
vab
100V/div
(c)
Figure 14. Experimental waveforms under different loads (f = fr): (a) full load; (b) 1% rated load;
ir
(c) no load. 5A/div
S2
S1
As is displayed
vgsin Figure 14, ZVS of the MOSFETs can be effectively achieved under all load
conditions at the10V/div
resonant frequency, which is consistent with the theoretical and simulation results.
The fluctuation of the resonant current at a no-load condition in Figure 14c is caused by the charge
Time: 4μ s / div
and discharge effects of the parasitic capacitance.
Figure 15 shows the experimental waveforms under different load conditions when f = 71.72
kHz. As can be seen from Figure 15, the LLC resonant
converter can effectively achieve ZVS under a
(c)
rated load condition at fmin; the converter lies in a critical state under a heavy load condition, but ZVS
fr): (a)
(b) 1%
ratedrated
load;load;
Figure 14. Experimental
waveforms
under
different
loads
(f = (f
Experimental
waveforms
under
different
loads
fr ):full
(a)load;
fullFigure
load;
(b)
The fluctuation
of
resonant
current
at O= mode
in
15a1%
is also caused
by
can Figure
still be14.
achieved.
(c)no
noload.
load.
(c)
the parasitic capacitance.
As is displayed in Figure 14, ZVS of the MOSFETs can be effectively achieved under all load
conditions at the resonant frequency, which is consistent with the theoretical and simulation results.
The fluctuation v
of the resonant current at a no-load condition in Figure 14c is caused by the charge
ab
and discharge effects of the parasitic capacitance.
100V/div
Figure 15 shows the experimental waveforms under different load conditions when f = 71.72
kHz. As can be seen from Figure 15, the LLC resonant converter can effectively achieve ZVS under a
ir at fmin; the converter lies in a critical state under a heavy load condition, but ZVS
rated load condition
5A/div
can still be achieved. The fluctuation of resonant current at O mode in Figure 15a is also caused by
S1
S2
the parasitic capacitance.
vgs
10V/div
Time: 4μ s / div
vab
100V/div
Energies 2018, 11, x FOR PEER REVIEW
15 of 17
(a)
ir
5A/div
vvgsab
S1
S2
100V/div
10V/div
Time: 4μ s / div
ir
5A/div
(a)
vgs
S2
S1
10V/div
Time: 4μ s / div
(b)
71.72
kHz
(a) load;
full load;
(b) heavy
Figure15.
15.Experimental
Experimentalwaveforms
waveformsunder
underdifferent
different
loads
Figure
loads
(f (=f =
71.72
kHz):
(a)): full
(b) heavy
load.
load.
Gain curves of the designed LLC resonant converter obtained by FHA analysis, the simplified
gain model, simulation, and experiment are compared in Figure 16, where f represents the
normalized frequency. Figure 16 indicates that the gain curve obtained by FHA analysis has a
relatively large discrepancy with the simulation and the experiment. The gain is smaller than the
actual, and the gain obtained by the simplified gain model is very similar that obtained by the
simulation and the experiment. It is relatively accurate to design the gain requirement of the
Energies 2018, 11, x FOR PEER REVIEW
2 of 2
Energies 2018, 11, 1124
15 of 17
As is displayed in Figure 14, ZVS of the MOSFETs can be effectively achieved under all load
conditions at the resonant frequency, which is consistent with the theoretical and simulation results.
The fluctuation of the resonant current at a no-load condition in Figure 14c is caused by the charge and
discharge effects of the parasitic capacitance.
Figure 15 shows the experimental waveforms under different load conditions when f = 71.72 kHz.
As can be seen from Figure 15, the LLC resonant converter can effectively achieve ZVS under a rated
load condition at f min ; the converter lies in a critical state under a heavy load condition, but ZVS can
still be achieved. The fluctuation of resonant current at O mode in Figure 15a is also caused by the
parasitic capacitance.
(a)
(b) analysis, the simplified
Gain curves of the designed
LLC resonant converter obtained by FHA
gain model,
simulation,
and
experiment
are compared
in Figure
16, where
f represents
the normalized
Figure
9. Influence
of expected
efficiency
on the restricted
design area
of the converter:
(a) Increased
frequency.efficiency;
Figure 16
the gain curve obtained by FHA analysis has a relatively large
(b)indicates
Decreasedthat
efficiency.
discrepancy with the simulation and the experiment. The gain is smaller than the actual, and the
Basedby
onthe
thesimplified
above analysis,
parameters
the converter
selected inby
the
intersecting
area
in the
gain obtained
gainthe
model
is veryofsimilar
that obtained
the
simulation
and
Figure
8
are
shown
in
Table
1.
The
loss
composition
analysis
is
performed
according
to
the
experiment. It is relatively accurate to design the gain requirement of the converter by the simplified
parameters as is
gain model in PO mode when the frequency variation range is very small.
Figure 16. Gain curve comparison. FHA = fundamental harmonic approximation.
Figure 16. Gain curve comparison. FHA = fundamental harmonic approximation.
The measured efficiency curve is presented in the Figure 17. Under the medium and full-load
The
measured
efficiencycan
curve
is presented
in the Figure
17.efficiency
Under the
medium
and full-load
conditions,
the converter
maintain
a high efficiency.
The peak
of the
LLC resonant
conditions, the converter can maintain a high efficiency. The peak efficiency of the LLC resonant
converter can reach about 96.3% when the output power is about 120 W. There is a small difference
between the measured efficiency and the theory since the loss of the capacitor ESR and the layout
resistance are not considered in the theoretical analysis. The efficiency varies with the input voltage,
LLC power level, selection of MOSFET, and so on. It is not convenient to compare the efficiency with
other methods under different conditions. Compared with the prototypes in studies [3,5,19,20] as
shown in Table 2, the maximum normalized voltage gain and efficiency of the prototype in this paper
are improved under a small power level. Moreover, the expected efficiency is adjustable, which means
a converter with a higher efficiency can be designed as illustrated in Figure 9.
Table 2. Fair comparison to the other published methods.
Prototype
Efficiency
Power
Maximum Normalized
Voltage Gain
Frequency Range
[3]
[5]
[19]
[20]
In this paper
96.4%
95.5%
98%
97.6%
96.3%
350 W
1.5 kW
400 W
3.3 kW
150 W
1.2
1.67
1.455
1.41
1.6
45 kHz
30 kHz
56 kHz
38 kHz
18 kHz
Energies 2018, 11, 1124
Energies 2018, 11, x FOR PEER REVIEW
16 of 17
16 of 17
Figure
efficiency curves.
curves.
Figure17.
17.Measured
Measured efficiency
6. Conclusions
Table 2. Fair comparison to the other published methods.
Maximum Normalized
This paper
focused Efficiency
on the problem
of the wide frequency regulating
range in
the design of
Prototype
Power
Frequency
Range
Voltage Gain
voltage-adjustable LLC resonant converters and proposed an optimal design method, which can
[3]
Wefficiency of the
1.2converter under the45premise
kHz of satisfying
narrow the frequency
range96.4%
and ensure350
high
[5]
95.5%
1.5
kW
1.67
30
kHz
the required gain.
[19] method 98%
56akHz
The proposed
is verified400
byW
simulation of1.455
and experiment using
150 W prototype.
[20]that the simplified
97.6% gain
3.3model
kW utilized has
1.41
38 kHz
The results show
a relatively high degree
of accuracy when
In this
paper range
96.3%
150 Wand ZVS can 1.6
18 from
kHz a no-load to a
the frequency
variation
is very small,
be effectively achieved
full-load and even a heavy-load condition. The method proposed in this paper can achieve 1.6 times
6. Conclusions
the normalized voltage gain in the frequency variation range of 18 kHz with a peak efficiency of up
to 96.3%.
The maximum
normalized
voltage
gain
andfrequency
efficiency regulating
of the prototype
maintain
focused on
the problem
of the
wide
range can
in the
design an
of
This paper
excellent
performance
a small
power level.
Moreover,
expected
efficiency
is adjustable,
voltage-adjustable
LLCunder
resonant
converters
and proposed
anthe
optimal
design
method,
which can
which
a converterrange
with aand
higher
efficiency
be designed.
method under
proposed
this paper
narrowmeans
the frequency
ensure
high can
efficiency
of theThe
converter
theinpremise
of
can
also bethe
used
for the design
satisfying
required
gain. of large-power LLC resonant converters to obtain a wide output voltage
rangeThe
andproposed
higher efficiency.
method is verified by simulation of and experiment using a 150 W prototype. The
results show that the simplified gain model utilized has a relatively high degree of accuracy when
Author Contributions: J.L. and J.W. conceived and designed the simulation and experiments; J.L. and Z.F.
ZVS
be the
effectively
the frequency
variation range
very
small,the
and
performed
the experiments;
J.S. andisJ.L.
analyzed
data;
J.L.can
wrote
paper. achieved from a no-load to
a full-load and even a heavy-load condition. The method proposed in this paper can achieve 1.6 times
Acknowledgments: This work was supported in part by the National Natural Science Foundation of China under
theProject
normalized
voltage
in the
frequency
range
of 18 kHz
with
a peak efficiency
of the
up
the
of 51707138
andgain
51507114
and
in part by variation
the National
Key Research
and
Development
Plan under
Project
of 2017YFB1201002.
to 96.3%.
The maximum normalized voltage gain and efficiency of the prototype can maintain an
excellentofperformance
under adeclare
smallno
power
level.
Moreover, the expected efficiency is adjustable,
Conflicts
Interest: The authors
conflict
of interest.
which means a converter with a higher efficiency can be designed. The method proposed in this paper
can also be used for the design of large-power LLC resonant converters to obtain a wide output
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© 2018 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
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