Optimal Design Methodology for
LLC Resonant Converter
Bing Lu, Wenduo Liu, Yan Liang, Fred C. Lee, Jacobus D. van Wyk
Center for Power Electronics Systems
Virginia Polytechnic Institute and State University
674 Whittemore Hall
Blacksburg, VA 24061 USA
Abstract: Although LLC resonant converter can achieve wide
operation range with high efficiency, lack of design methodology
makes it difficult to be implemented. In this paper, based on the
theoretical analysis on the operation principles during normal
condition and holdup time, the relationship between converter
efficiency and operation range with different circuit parameters
has be revealed. An optimal design methodology has been
developed based on the revealed relationship. A 1MHz, 1kW
LLC converter is designed to verify the proposed method.
converter becomes the most attractive topology due to its high
efficiency and wide operation range.
Cr
Vin
Lr
n:1:1
Vo
Lm
R
L
I.
I
NTRODUCTION
With the development of power conversion technology,
power density becomes the major challenge for front-end
AC/DC converters [1] [2] [3]. Although increasing switching
frequency can dramatically reduce the passive component
size, its effectiveness is limited by the converter efficiency and
thermal management design. Meanwhile, to meet the holdup
time requirement, bulky capacitors have to be used to provide
the energy during holdup time, which is only affected by
DC/DC stage operation input voltage range [1]. The
relationship between holdup time capacitor requirement and
minimum DC/DC stage input voltage for different front-end
converter power levels is shown in Figure 1. Apparently, wide
operation range DC/DC stage can reduce the holdup time
capacitor requirement and improve the system power density.
However, when the minimum voltage is less than 200V, very
limited effects can be observed.
Figure 2. LLC Resonant Converter.
2
Q=0.3
1.5
nVo/(Vin/2)
ZCS
ZVS
1
Q=1
0.5
0.2
0.4
0.6
0.8
f/f0
1
1.2
1.4
Figure 3. Gain Characteristic of LLC Converter.
Figure 1. Holdup time capacitor requirement for DC/DC stage with
different minimum input voltage.
To reduce the holdup time capacitor requirement,
different research efforts have been implemented, by using
extra holdup time extension circuit or by developing better
topologies [4][5][6]. Among different solutions, LLC resonant
The LLC resonant converter topology is shown in Figure
2. By utilizing the transformer magnetizing inductance, LLC
converter modifies the gain characteristic of series resonant
converter (SRC). Its voltage gain characteristics for different
loads are shown in Figure 3, due to the half bridge structure,
the output voltage is normalized with half of the input voltage.
Comparing with SRC, the converter can achieve both Buck
mode and Boost mode. When the switching frequency is
higher than resonant frequency, voltage gain of LLC converter
is always less than one, and it operates as an SRC converter
and zero voltage switching (ZVS) can be achieved. When the
switching frequency is lower than resonant frequency, for
different load conditions, both ZVS and zero current switching
(ZCS) could be achieved. At the boundary of ZVS and ZCS
regions, as shown in the dashed line in Figure 3, converter
voltage gain reaches it maximum value.
0-7803-9547-6/06/$20.00 ©2006 IEEE.
533
According to the circuit operation analysis [4], at the
resonant frequency, because the impedance of resonant tank,
constructed by L
r
and C
r
, is zero, input and output voltages are
virtually connected together. Thus, converter voltage gain is
equal to one for all the load conditions. When the input AC
line exists, DC/DC stage input voltage is generated by PFC
stage and it is regulated at 400V. At this condition, by
choosing a suitable transformer turns ratio, converter could
always operate at resonant frequency. Therefore, the
conduction loss and switching loss can be minimized. During
holdup time, energy transferred to the load comes from bulky
holdup time capacitor. While DC/DC input voltage keeps
decreasing, converter reduces its switching frequency to
operate in Boost mode and regulate output voltage. Due to the
complexity of resonant tank, design of the LLC resonant
converter needs to consider three key elements, resonant
frequency, characteristic factor, and inductor ratio,
1
f
0
=
(1)
2
π
L
r
C
r
Q
=
L
n
=
L
r
/
C
r
n
2
R
L
m
L
r
(2)
(3)
different load conditions. For most of the time, front-end
converter is operating under this operation mode. Therefore,
the efficiency at resonant frequency is the key aspect for the
LLC converter performance.
According to the operation of LLC resonant converter, at
resonant frequency, resonant tank current is a pure sinusoidal
waveform as shown in Figure 4. The dashed line is the
magnetizing inductor current. The equivalent circuit of the
operation is shown in Figure 5. At first half line cycle,
resonant tank current i
r
resonates up. At the same time, output
voltage is applied to magnetizing inductor. Therefore, the
magnetizing inductor current increases linearly. At the end of
this half switching cycle, primary switch turns off with peak
magnetizing inductor current, and the other switch turns on
under ZVS condition with same current. During the other half
line cycle, the resonant tank current keeps resonant and output
voltage is applied to the magnetizing inductor with reverse
polarity. Therefore, the magnetizing inductor current
decreases linearly. Thus, a square wave voltage is applied to
the magnetizing inductor, and the magnetizing inductor
current is a triangle shape as shown in the dashed line in
Figure 4. Moreover, at the end of each half switching cycle,
magnetizing inductor current reaches its maximum value and
the resonant tank current gets the same value at the same time.
i
r
Here f
0
is the resonant frequency, which defines the
switching frequency of LLC resonant converter. The
characteristic factor Q is the ratio between the characteristic
impedance and the load. L
n
is defined as the ratio between the
magnetizing inductance and the resonant inductance.
Although different literatures [9]-[11] have discussed
operation principles and benefits of the topology, there is no
design guideline developed. Moreover, instead of simply
choosing Q value in the conventional SRC or PRC design,
LLC requires defining two coupled elements L
n
and Q.
Apparently, try and error method could result in a good
design. However, it is time consuming and not cost effective.
As a result, the topology is difficult to be adopted by the
industries. In this paper, based on the analysis of LLC
resonant converter at different operation conditions, including
the normal operation and during holdup time, an optimal
design methodology has been developed. Based on the
developed method, designed LLC converter can achieve
maximum efficiency with desired operation range, which is
verified by a 1MHz LLC resonant converter.
II. C
IRCUIT
O
PERATION
A
NALYSIS
O
F
LLC R
ESONANT
C
ONVERTER
A. Normal Operation Analysis
At normal operation condition, LLC converter input
voltage is regulated by PFC stage. From the gain characteristic
curves shown in Figure 3, converter gain can keep constant at
resonant frequency. Therefore, by designing a suitable
transformer turns-ratio to make the converter voltage gain
equal to one, at normal operation condition, LLC resonant
converter can always operate at its resonant frequency for
i
m
0
T /2
T
Figure 4. Resonant Tank Current Waveform at Resonant Frequency.
Lr
i
r
V
in
/2
Cr
Lm
i
m
nv
o
Figure 5. Equivalent circuit at resonant frequency.
The magnetizing inductor peak current can be determined
nV
o
(4)
by
I
pk
=
T
L
m
4
Here n is the transformer turns ratio between the primary
side and secondary side, V
O
is the output voltage, T is the
switching cycle and L
m
is magnetizing inductance.
Since the resonant tank current at resonant frequency is a
sinusoidal wave, it can be represented by the equation
I
r
=
2
I
rms
sin(2
π
f
0
+
φ
)
(5)
Here I
rms
is the resonant tank RMS current, and f
0
is the
resonant frequency and
φ
is the initial angle of the resonant
tank current, which represent the phase difference between the
534
resonant tank current and magnetizing inductor current.
According to the current waveforms, at the end of each half
switching cycle, magnetizing inductor current is equal to the
resonant tank current, which means
nV
o
(6)
2
I
rms
sin(
φ
)
=
L
m
T
/ 4
On the other hand, the difference between resonant tank
current and magnetizing inductor current is the current
transferred to the load, thus
T
/2
∫
0
(
i
r
−
i
m
)
dt
=
V
O
T
nR
L
2
(7)
Here R
L
is the load resistance, n is the transformer turns
ratio.
By summarizing these equations, the resonant tank RMS
current can be solved as
I
rms
1
V
O
=
8
nR
L
2
n
4
R
L
2
T
2
L
m
2
+
8
π
2
(8)
off loss, which is also depends on the magnetizing inductance.
Therefore, to design a high efficiency LLC resonant converter,
it is essential to find a suitable magnetizing inductor.
B. Holdup Time Operation Analysis
During the holdup time, input AC line doesn’t exist and
PFC stage no longer provides energy to DC/DC stage. All the
energy transferred to the load during holdup time is purely
coming from holdup time capacitor. Therefore, the input
voltage of DC/DC stage will keep decreasing during holdup
time. To maintain regulated output voltage, switching
frequency of the LLC resonant needs to be reduced so that the
converter gain can be boosted up. Different from PWM
converters, LLC converter could achieve highest efficiency at
high input voltage. During holdup time, the converter operates
far away from its resonant point and has less efficiency.
However, the holdup time only requires 20mS, and low
efficiency could be tolerated and would not cause excess
thermal stress.
Because the transformer turns ratio is a fixed value, the
required gain is determined by the relationship between the
input and output voltage, which can be represented by
g
=
nV
O
V
in
/ 2
Here V
O
is the output voltage, n is transformer turns-ratio,
R
L
is load resistance, T is switching cycle at resonant
frequency, and L
m
is the magnetizing inductance.
Since the resonant tank current continuously flows trough
the primary side switches, its RMS value determines the
primary side conduction loss. Comparing with the load current
reflected to primary side, resonant tank RMS current is only
related to the magnetizing inductance, the load resistance and
the switching cycle. While the switching cycle and load
resistance are predetermined values for certain converter
specifications, resonant tank RMS current is only determined
by the magnetizing inductance.
Besides the primary side conduction loss, secondary side
rectifier conduction loss is also a major concern. For diode
rectifier, its conduction loss major comes from diode forward
voltage drop and is proportional to the average output current.
However, if considering synchronous rectification, it is also
desirable to minimize the secondary side RMS current. Since
we already get the formulas for both the resonant tank current
and magnetizing inductor current, secondary side current can
be easily calculated. Based on previous analysis, secondary
RMS can be expressed as
I
RMS
_
S
=
1
V
O
4
nR
L
5
π
2
−
48
n
4
R
L
T
2
+
1
2
12
π
2
L
m
(10)
Here, g is the required voltage gain for LLC converter, V
O
is the output voltage and V
in
is the input voltage. From this
equation, lower the input voltage, higher the voltage gain is
required.
As shown in Figure 1, the holdup time capacitor
requirement is largely affected by the operation range of the
DC/DC stage. Wider operation range can dramatically reduce
the holdup time capacitor requirement and improve the whole
converter power density. Therefore, wide operation range of
DC/DC stage is desired.
The operation range of LLC converter is decided by the
peak voltage gain that can be achieved. At normal operation
mode, input voltage is 400V and LLC has a voltage gain equal
to one. If the converter can achieve a maximum gain of 2, it
will be able to regulate output voltage with 400/2=200V input.
Obviously, the higher the peak gain, the wider the operation
range of LLC resonant converter.
I
Lr
(9)
I
Lm
0
From this equation, same as the primary side RMS
current, secondary side RMS current is also entirely
determined by the magnetizing inductance.
Based on the analysis o the LLC resonant converter
operating at resonant frequency, the converter conduction loss
is mainly affected by the magnetizing inductance, instead of
resonant inductor or the resonant capacitor. At the same time,
the primary side switches can achieve ZVS for all the load
conditions, the switching loss is mainly coming from the turn
T/2
Figure 6. Resonant tank current at peak gain point
From gain characteristic curves in Figure 3, the peak gain
happens when the circuit is running at the boundary of zero
current switching (ZCS) and zero voltage switching (ZVS)
modes. The resonant tank current at this condition is shown in
Figure 6. In each half switching cycle, the magnetizing
inductor is firstly charged by the output voltage. After that, it
535
participates in the resonance (the resonant tank is constructed
by L
r
, C
r
and L
m
) and transfers it stored energy to the resonant
capacitor. At the end of each half switching cycle, its current
is reset to zero. Therefore, entire energy stored in the
magnetizing inductor can be transferred to the load, and the
converter gain reaches its peak value. Although the peak gain
can be calculated based on the current waveform, it is difficult
to solve the equations and get the analytical solution.
Therefore, to simplify the analysis, peak gains at different L
n
and Q combinations are simulated based on the simulation tool
Simplis, which can automatically reach the circuit steady state
within short simulation time. The peak gains for different L
n
and Q values are summarized in the contour curves in Figure
7. In this set of curves, each line shows the combinations of
different L
n
and Q values that can achieve same peak voltage
gain. For instance, if we want to design a converter with a
peak gain of 1.3, any combination of L
n
and Q along the line
1.3 can be chosen as a valid design.
1
0.95
purely determined by the magnetizing inductance, as shown in
the following equation:
I
rms
1
V
O
=
8
nR
L
2
n
4
R
L
2
T
2
L
m
2
+
8
π
2
(11)
I
RMS
_
S
=
1
V
O
4
nR
L
5
π
2
−
48
n
4
R
L
T
2
12
π
2
L
m
2
+
1
(12)
0.85
0.75
0.65
1.
3
0.55
0.45
1 .3
0.35
0.25
0.15
0.05
1.6
2
1.6
1.3
2. 5
3
1
3
5
7
2 .5
3
9
11
13
2
2.5
3
15
17
1.6
2
19 20
Ln
Figure 7. Relationship between converter peak gain and L
n
, Q
Apparently, peak gain is affected by both L
n
and Q
values. By reducing L or Q value, higher peak gain can be
achieved.
III. D
ESIGN
M
ETHODOLOGY FOR
LLC R
ESONANT
C
ONVERTER
The LLC resonant converter design goal is to achieve
minimum loss with the capability of achieve required
maximum gain to ensure wide operation range. According to
previous analysis, the relationships between the design
parameters L
n
and Q with the converter performance,
especially the conduction loss and the operation range, is
revealed. These relationships can be used to develop an
optimal design methodology of LLC resonant converter.
LLC resonant converter operates under normal operation
condition at most of the time. When the input Ac line exists,
the DC/DC stage input voltage is a regulated 400V. Therefore,
LLC converter could always operates at resonant frequency
and achieve optimal efficiency. Thus, it is essential to
minimize the loss when converter operates at resonant
frequency. Based on the operation analysis at resonant
frequency, both the primary and secondary conduction loss is
Therefore, to minimize conduction loss, the magnetizing
inductance should be maximized to reduce RMS currents on
primary side and secondary side. In turn, the copper loss of the
magnetic components can also be reduced.
To achieve high power density, high switching frequency
is always desired, because the passive component size reduces
dramatically with increasing switching frequency. However,
the switching loss increases linearly with the switching
frequency. Therefore, it is also important to minimize the LLC
converter switching loss.
Based on the operation analysis, LLC converter primary
side switches can achieve ZVS turn on for all the load
conditions. However, the ZVS condition is ensured by the
peak magnetizing current, which can be calculated as
nV
o
(13)
I
pk
=
T
L
m
4
Here, n is transformer turns ratio, V
O
is output voltage, L
m
is the magnetizing inductance and T is the switching cycle.
During the primary side switches commutating period, due to
the large magnetizing inductance, the magnetizing inductor
current can be assumed to be constant. To ensure ZVS turn on,
the peak magnetizing inductor current should be able to
discharge MOSFETs junction capacitors within dead time,
which can be represented by
I
pk
>
2
V
bus
C
j
t
dead
1.6
1.3
2
1.6
Q
2
2.5
3
(14)
Here V
bus
is input bus voltage, C
j
is MOSFET junction
capacitance and t
dead
is the dead time.
Although the large turn off current can ensure soft
switching condition, it results in larger turn off loss, because
primary side switches turning off is hard switching. Therefore
smaller turn off current is desirable to reduce turn off loss.
By summarizing previous analysis, to achieve minimum
conduction loss, the magnetizing inductance is required to be
as large as possible. To ensure minimum switching loss, the
magnetizing inductor needs to be smaller enough to achieve
ZVS condition and large enough to have smaller turn off
current. Therefore, considering both conduction loss and
switching loss, the optimally designed L
m
should make the
primary side turn off current exactly the same as ZVS
requirement. Thus,
T
⋅
t
dead
(15)
L
m
=
16
C
j
536
According to the definition of L
n
and Q
L
n
=
L
m
L
r
L
r
C
r
n
2
R
L
(16)
we need to further consider the L
n
and Q impacts on the circuit
operations.
1
0.95
1.6
0.85
0.75
0.65
1.3
2
Q
=
(17)
Q
1.
3
1 .6
together with the resonant frequency
1
f
0
=
2
π
L
r
C
r
we can calculate magnetizing inductance as
2
π
f
0
L
n
Q
L
m
=
n
2
R
L
0.55
0.45
(18)
1 .3
2
2. 5
3
2.5
3
1
3
5
0.35
0.25
0.15
0.05
1.6
2
1.6
1.3
(19)
2.5
3
7
9
11
13
2
1.6
2.5
3
15
17
2
19 20
Based on this equation, it can be seen that, as long as the
production of L
n
and Q keeps constant, L
m
is a fixed value. Or
in other words, for a designed magnetizing inductance, the
relationship between L
n
and Q is fixed. Once an L
n
value is
chosen, the corresponding Q value can be designed.
Besides the converter efficiency, the other major aspect of
LLC converter is its operation range. Although the converter
efficiency is mainly defined by the magnetizing inductance,
the L
n
and Q value could affect the gain characteristic of LLC
resonant converter. As discussed before, wide operation range
LLC resonant converter can reduce the holdup time capacitor
requirement and improve system power density. To achieve
the desired operation range, peak gain is required to be higher
than certain level.
A 200 kHz 1kW LLC resonant converter with operation
range from 250V to 400V is chosen as an example. In this
case, the peak voltage gain is required to be larger than
400/250=1.6. From Figure 7, all the L
n
and Q combinations
below line 1.6 could meet the gain requirement. However, this
results in infinite solutions for the converter design.
Furthermore, considering normal operation efficiency,
magnetizing inductance is expected to be maximized. Based
on the analysis on the magnetizing inductance, we can get the
magnetizing inductance should be
T
⋅
t
dead
L
m
=
16
C
ds
Ln
Figure 8. Design example of LLC converter
As shown in Figure 9, the gain characteristics for different
L
n
values are summarized. It shows that the larger L
n
will
increase the frequency range of LLC resonant converter.
Although at normal operation condition, PFC stage generates a
regulated 400V bus, due to the line frequency ripple, LLC
converter still needs to do switching frequency modulation to
regulated output voltage. Therefore, the switching frequency
range should be as small as possible, which requires a
minimum L
n
value. However, larger L
n
makes it easier to use
the transformer leakage inductance to realize the resonant
inductor. Therefore, trade off between the converter size and
efficiency can be carried out and determine the L
n
value.
Based on the chosen L
n
and Q values, L
r
and C
r
can be
calculated accordingly.
3.5
3
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
f/f0
0.8
1
1.2
Mormolized Gain
Ln=10
Ln=14
Ln=16
Ln=20
(20)
For 200 kHz switching frequency and 100nS dead time,
together with 450pF C
j
(IXFH21N50), we can easily calculate
the magnetizing inductance should be around 70uH.
Therefore, for required magnetizing inductance of 70uH,
a marked line can be added to Figure 7, the peak gain curves,
as shown in Figure 8. All the designs along the marked line
will have the same magnetizing inductance, which ensures
maximum efficiency at normal operation condition.
Comparing with peak gain curves, L
n
has to be larger than 5.5
to meet the gain requirement. However, along the marked line,
there could be infinite solutions for the valid design. To
further pickup a suitable value for the L
n
and Q combination,
Figure 9. L
n
impacts on LLC converter voltage gain
IV. E
XPERIMENTAL IMPLEMENTATION
To verify the theoretical analysis, a 1MHz, 1kW LLC
resonant converter with wide input voltage range (200V to
400V) and 48V output is designed based on the proposed
methodology. To ensure soft switching and minimize turn off
loss, the magnetizing inductance is chosen as 14uH. L
n
is
designed as 17 to utilize the transformer leakage inductance,
which results in a 0.8uH resonant inductance. The resonant
capacitor can be designed accordingly as 33nF.
537
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