FAIRCHILD AN-4151

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Application Note AN-4151
Half-bridge LLC Resonant Converter Design Using
FSFR-series Fairchild Power Switch (FPS™)
Introduction
The effort to obtain ever-increasing power density of
switched-mode power supplies has been limited by the size
of passive components. Operation at higher frequencies
considerably reduces the size of passive components, such
as transformers and filters; however, switching losses have
been an obstacle to high-frequency operation. To reduce
switching losses and allow high-frequency operation,
resonant switching techniques have been developed.
These techniques process power in a sinusoidal manner and
the switching devices are softly commutated. Therefore, the
switching losses and noise can be dramatically reduced [17].
Among various kinds of resonant converters, the simplest and
most popular resonant converter is the LC series resonant
converter, where the rectifier-load network is placed in series
with the L-C resonant network, as depicted in Figure 1 [2-4].
In this configuration, the resonant network and the load act as
a voltage divider. By changing the frequency of driving
voltage Vd, the impedance of the resonant network changes.
The input voltage is split between this impedance and the
reflected load. Since it is a voltage divider, the DC gain of a
LC series resonant converter is always <1. At light-load
condition, the impedance of the load is very large compared
to the impedance of the resonant network; all the input
voltage is imposed on the load. This makes it difficult to
regulate the output at light load. Theoretically, frequency
should be infinite to regulate the output at no load.
Q1
Lr
Vin
n:1
Vd
Ro
Q2
+
VO
-
Cr
Figure 1. Half-bridge, LC Series Resonant Converter
To overcome the limitation of series resonant converters,
LLC resonant converter has been proposed [8-12]. LLC
resonant converter is a modified LC series resonant
converter implemented by placing a shunt inductor across
the transformer primary winding, as depicted in Figure 2.
When this topology was first presented, it did not receive
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
much attention due to the counterintuitive concept that
increasing the circulating current in the primary side with a
shunt inductor can be beneficial to circuit operation.
However, it can be very effective in improving efficiency
for high-input voltage application where the switching loss
is much more dominant than the conduction loss.
In most of the practical design, this shunt inductor is
realized using the magnetizing inductance of the
transformer. The circuit diagram of LLC resonant converter
looks much the same as the LC series resonant converter:
the only difference is the value of the magnetizing inductor.
While the series resonant converter has a magnetizing
inductance much larger than the LC series resonant
inductor (Lr), the magnetizing inductance in LLC resonant
converter is just 3~8 times Lr, which is usually
implemented by introducing an air gap in the transformer.
Q1
Lr
Vin
Q2
n:1
Ro
Lshunt
+
VO
( Lm )
Cr
Figure 2. Half-bridge LLC Resonant Converter
An LLC resonant converter has many advantages over a
series resonant converter; it can regulate the output over
wide line and load variations with a relatively small
variation of switching frequency. It can achieve zero
voltage switching (ZVS) over the entire operating range.
All essential parasitic elements, including junction
capacitances of all semi-conductor devices and the leakage
inductance and magnetizing inductance of the transformer,
are utilized to achieve soft-switching.
This application note presents design considerations of an
LLC resonant half-bridge converter employing FSFR-series
FPS™. It includes explanation of LLC resonant converter
operation principle, designing the transformer and resonant
network, and selecting the components. The step-by-step
design procedure explained with a design example helps
design the LLC resonant converter.
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AN4151 APPLICATION NOTE
1. LLC Resonant Converter and
Fundamental Approximation
Ip
Figure 3 shows the simplified schematic of a half-bridge
LLC resonant converter, where Lm is the magnetizing
inductance that acts as a shunt inductor, Lr is the series
resonant inductor, and Cr is the resonant capacitor.
Figure 4 illustrates the typical waveforms of the LLC
resonant converter. It is assumed that the operation
frequency is same as the resonance frequency, determined
by the resonance between Lr and Cr. Since the magnetizing
inductor is relatively small, there exists considerable
amount of magnetizing current (Im), which freewheels in
the primary side without being involved in the power
transfer. The primary-side current (Ip) is sum of the
magnetizing current and the secondary-side current referred
to the primary.
IDS1
ID
Vin
Vd
Vgs1
In general, the LLC resonant topology consists of three
stages shown in Figure 3; square wave generator, resonant
network, and rectifier network.
ƒ
ƒ
ƒ
Vgs2
The square wave generator produces a square wave
voltage, Vd, by driving switches Q1 and Q2 alternately
with 50% duty cycle for each switch. A small dead
time is usually introduced between the consecutive
transitions. The square wave generator stage can be
built as a full-bridge or half-bridge type.
The resonant network consists of a capacitor, leakage
inductances, and the magnetizing inductance of the
transformer. The resonant network filters the higher
harmonic currents. Essentially, only sinusoidal current
is allowed to flow through the resonant network even
though a square wave voltage is applied to the resonant
network. The current (Ip) lags the voltage applied to
the resonant network (that is, the fundamental
component of the square wave voltage (Vd) applied to
the half-bridge totem pole), which allows the
MOSFETs to be turned on with zero voltage. As
shown in Figure 4, the MOSFET turns on while the
voltage across the MOSFET is zero by flowing current
through the anti-parallel diode.
The rectifier network produces DC voltage by
rectifying the AC current with rectifier diodes and
capacitor. The rectifier network can be implemented as
a full-wave bridge or center-tapped configuration with
capacitive output filter.
Figure 4. Typical Waveforms of Half-bridge LLC
Resonant Converter
The filtering action of the resonant network allows use of
the fundamental approximation to obtain the voltage gain of
the resonant converter, which assumes that only the
fundamental component of the square-wave voltage input
to the resonant network contributes to the power transfer to
the output. Because the rectifier circuit in the secondary
side acts as an impedance transformer, the equivalent load
resistance is different from actual load resistance. Figure 5
shows how this equivalent load resistance is derived. The
primary-side circuit is replaced by a sinusoidal current
source, Iac, and a square wave of voltage, VRI, appears at the
input to the rectifier. Since the average of |Iac| is the output
current, Io, Iac, is obtained as:
I ac =
Vin
Q2
Ip
+
Lr
Vd
Im
-
Cr
2
sin(ωt )
VRI = +Vo
if sin(ωt ) > 0
VRI = −Vo
if sin(ωt ) < 0
(1)
(2)
where Vo is the output voltage.
The fundamental component of VRI is given as:
VRI F =
n:1
ID
Io
Ro
Lm
Rac =
+
π
sin(ωt )
(3)
VRI F
8 V
8
= 2 o = 2 Ro
I ac
π Io π
(4)
Considering the transformer turns ratio (n=Np/Ns), the
equivalent load resistance shown in the primary side is
obtained as:
VO
-
Rac =
Figure 3. Schematic of Half-bridge LLC
Resonant Converter
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
4Vo
Since harmonic components of VRI are not involved in the
power transfer, AC equivalent load resistance can be
calculated by dividing VRIF by Iac as:
Resonant network Rectifier network
IDS1
π ⋅ Io
and VRI is given as:
Square wave generator
Q1
Im
8n
π
2
2
Ro
(5)
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2
AN4151 APPLICATION NOTE
By using the equivalent load resistance, the AC equivalent
circuit is obtained, as illustrated in Figure 6, where VdF and
VROF are the fundamental components of the driving voltage,
Vd and reflected output voltage, VRO (nVRI), respectively.
where:
L p = Lm + Lr , Rac =
Lr 1
, ωo =
Q=
Cr Rac
+
+
VRI
-
Iac
I ac =
VRIF
Vo
VRI
π ⋅ Io
2
VRI F =
sin( wt )
4Vo
π
M =
Lr
sin( wt )
+
+
-
-
Np:Ns
Rac =
8n 2
π2
1
L p Cr
Ro
VRoF
Lm
Rac
2
2n ⋅ Vo (m − 1) ⋅ ω p
=
= 1 at ω = ωo (7)
Vin
ωo 2 − ω p 2
The operating range of the LLC resonant converter is
limited by the peak gain (attainable maximum gain), which
is indicated with ‘*’ in Figure 7. It should be noted that the
peak voltage gain does not occur at fo nor fp. The peak gain
frequency where the peak gain is obtained exists between fp
and fo, as shown in Figure 7. As Q decreases (as load
decreases), the peak gain frequency moves to fp and higher
peak gain is obtained. Meanwhile, as Q increases (as load
increases), the peak gain frequency moves to fo and the
peak gain drops; thus, the full load condition should be the
worst case for the resonant network design.
Ro
-
Lr
Cr
V dF
VO
VRI
Lm
n=Np/Ns
Lr
1
, ωp =
Lr Cr
The gain of Equation 6 is plotted in Figure 7 for different Q
values with m=3, fo=100kHz, and fp=57kHz. As observed
in Figure 7, the LLC resonant converter shows gain
characteristics that are almost independent of the load when
the switching frequency is around the resonant frequency,
fo. This is a distinct advantage of LLC-type resonant
converter over the conventional series resonant converter.
Therefore, it is natural to operate the converter around the
resonant frequency to minimize the switching frequency
variation.
Figure 5. Derivation of Equivalent Load Resistance Rac
Vin
Lp
Equation 6 shows the gain is unity at resonant frequency
(ωo), regardless of the load variation, which is given as:
VO
Ro
-
Cr
Ro , m =
As can be seen in Equation 6, there are two resonant
frequencies. One is determined by Lr and Cr, while the
other is determined by Lp and Cr.
Io
Vd
+
π
2
pk
I ac
Iac
8n 2
(nVRIF)
Figure 6. AC Equivalent Circuit for LLC Resonant
Converter
fp =
1
2π L p Cr
fo =
1
2π Lr Cr
2.0
Q=0.25
With the equivalent load resistance obtained in Equation 5,
the characteristics of the LLC resonant converter can be
derived. Using the AC equivalent circuit of Figure 6, the
voltage gain, M, is obtained as:
Q=
1.8
Lr / Cr
Rac
Q=1.0
1.6
Q=0.75
Gain ( 2nVo / Vin )
4n ⋅ Vo
sin(ωt )
VRO F n ⋅ VRI F
2n ⋅ Vo
M= F =
= π
=
F
4 Vin
Vd
Vd
Vin
sin(ωt )
(6)
π 2
ω 2
) ( m − 1)
ωo
=
ω2
ω ω2
( 2 − 1) + j ( 2 − 1)(m − 1)Q
ωp
ωo ωo
1.4
Q=0.50
Q=0.25
1.2
1.0
(
Q=1.0
M @ fo = 1
0.8
0.6
40
50
60
70
80
90
100
110
120
130
140
freq (kHz)
Figure 7. Typical Gain Curves of LLC Resonant
Converter (m=3)
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
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3
AN4151 APPLICATION NOTE
2. Consideration for Integrated
Transformer
2n ⋅ VO
M =
=
Vin
For practical design, it is common to implement the
magnetic components (series inductor and shunt inductor)
using an integrated transformer; where the leakage
inductance is used as a series inductor, while the
magnetizing inductor is used as a shunt inductor. When
building the magnetizing components in this way, the
equivalent circuit in Figure 6 should be modified as shown
in Figure 8 because the leakage inductance exists, not only
in the primary side, but also in the secondary side. Not
considering the leakage inductance in the transformer
secondary side generally results in an incorrect design.
Cr
Vd
+
Vin
Llks
Llkp
ω2
) m( m − 1)
ωo 2
=
2
ω
ω
ω2
( 2 − 1) + j ( ) ⋅ ( 2 − 1) ⋅ ( m − 1) ⋅ Q e
ωp
ωo ωo
where:
+
Vin
F
Cr
Lr
Lp-Lr
1
, ωp =
Lr Cr
1
L p Cr
Lp
Lp − Lr
m
m −1
=
at ω = ωo
(M V =
Lp
L p − Lr
ideal
transformer
Rac
The gain at the resonant frequency (ωo) is unity when using
individual core for series inductor, as shown in Equation 7.
However, when implementing the magnetic components
with integrated transformer, the gain at the resonant
frequency (ωo) is larger than unity due to the virtual gain
caused by the leakage inductance in the transformer
secondary side.
)
+
VROF
(nVRIF)
The gain of Equation 9 is plotted in Figure 10 for different Qe
values with m=3, fo=100kHz, and fp=57kHz. As observed in
Figure 9, the LLC resonant converter shows gain
characteristics almost independent of the load when the
switching frequency is around the resonant frequency, fo.
Figure 8. Modified Equivalent Circuit to Accommodate
the Secondary-side Leakage Inductance
In Figure 8, the effective series inductor (Lp) and shunt
inductor (Lp-Lr) are obtained by assuming n2Llks=Llkp and
referring the secondary-side leakage inductance to the
primary side as:
fp =
2.2
1
2π L p Cr
fo =
1
2π Lr Cr
Qe=0.25
Qe =
Lr = Llkp + Lm //(n 2 Llks ) = Llkp + Lm // Llkp
2.0
(8)
Lr / Cr
Rac e
Qe=1.00
1.8
Qe=0.75
Gain ( 2nVo / Vin )
L p = Lm + Llkp
When handling an actual transformer, equivalent circuit
with Lp and Lr is preferred since these values can be easily
measured with a given transformer. In an actual
transformer, Lp and Lr can be measured in the primary side
with the secondary-side winding open circuited and short
circuited, respectively.
Qe=0.50
1.6
Qe=0.25
1.4
1.2
M @ fo = M V
Qe=1.0
1.0
In Figure 9, notice that a virtual gain MV is introduced,
which is caused by the secondary-side leakage inductance.
By adjusting the gain equation of Equation 6 using the
modified equivalent circuit of Figure 9, the gain equation
for integrated transformer is obtained:
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
(10)
-
-
-
Lr 1
, ωo =
Cr Rac e
Ro
Lr = Llkp + Lm //(n 2 Llks )
1: M V
Qe =
M = MV =
n:1
L p = Llkp + Lm
L
8n 2 Ro
, m= p
Lr
π 2 MV 2
The gain at the resonant frequency (ωo) is fixed regardless
of the load variation, which is given as:
VRI
= Llkp + Lm // Llkp
Rac e =
VO
-
-
(9)
(
+
+
Lm
ω 2
) ⋅ (m − 1) ⋅ M V
ωo
ω2
ω
ω2
( 2 − 1) + j ( ) ⋅ ( 2 − 1) ⋅ (m − 1)Q e
ωp
ωo ωo
(
0.8
40
50
60
70
80
90
100
110
120
130
140
freq (kHz)
Figure 9. Typical Gain Curves of LLC Resonant
Converter (m=3) Using an Integrated Transformer
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AN4151 APPLICATION NOTE
3. Consideration of Operation Mode
and Attainable Maximum Gain
Operation Mode
The LLC resonant converter can operate at frequency
below or above the resonance frequency (fo), as illustrated
in Figure 10. Figure 11 shows the waveforms of the
currents in the transformer primary side and secondary side
for each operation mode. Operation below the resonant
frequency (case I) allows the soft commutation of the
rectifier diodes in the secondary side, while the circulating
current is relatively large. The circulating current increases
more as the operation frequency moves downward from the
resonant frequency. Meanwhile, operation above the
resonant frequency (case II) allows the circulating current
to be minimized, but the rectifier diodes are not softly
commutated. Below resonance operation is preferred for
high output voltage applications, such as Plasma Display
Panel (PDP) TV where the reverse recovery loss in the
rectifier diode is severe. Below resonance operation also
has a narrow frequency range with respect to the load
variation since the frequency is limited below the resonance
frequency even at no load condition.
Im
(I) fs < fo
1
2 fS
IDS1
IO
ID
(II) fs > fo
Ip
Im
IDS1
ID
IO
Figure 11. Waveforms of Each Operation Mode
Required Maximum Gain and Peak Gain
Above the peak gain frequency, the input impedance of the
resonant network is inductive and the input current of the
resonant network (Ip) lags the voltage applied to the
resonant network (Vd). This permits the MOSFETs to turn
on with zero voltage (ZVS), as illustrated in Figure 12.
Meanwhile, the input impedance of the resonant network
becomes capacitive and Ip leads Vd below the peak gain
frequency. When operating in capacitive region, the
MOSFET body diode is reverse recovered during the
switching transition, which results in severe noise. Another
problem of entering into the capacitive region is that the
output voltage becomes out of control since the slope of the
gain is reversed. The minimum switching frequency should
be well limited above the peak gain frequency.
On the other hand, above resonance operation has less
conduction loss than the below resonance operation. It can
show better efficiency for low output voltage applications,
such as Liquid Crystal Display (LCD) TV or laptop
adaptor, where Schottky diodes are available for the
secondary-side rectifiers and reverse recovery problems are
insignificant. However, operation at above the resonant
frequency may cause too much frequency increase at lightload condition. Above frequency operation requires
frequency skipping to prevent too much increase of the
switching frequency.
Gain (M)
1
2 fo
Ip
B
M
capacitive
region
A
peak gain
inductive
region
Load increase
I
fs
II
Below resonance
(fs<fo )
Above resonance
(f s>fo)
fo
Vd
Vd
Ip
Ip
IDS1
IDS1
fs
Figure 10. Operation Modes According to the
Operation Frequency
reverse recovery
ZVS
Figure 12. Operation Waveforms for Capacitive and
Inductive Regions
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
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5
AN4151 APPLICATION NOTE
The available input voltage range of the LLC resonant
converter is determined by the peak voltage gain. Thus, the
resonant network should be designed so that the gain curve
has an enough peak gain to cover the input voltage range.
However, ZVS condition is lost below the peak gain point,
as depicted in Figure 12. Therefore, some margin is
required when determining the maximum gain to guarantee
stable ZVS operation during the load transient and start-up.
Typically 10~20% of the maximum gain is used as a
margin for practical design, as shown in Figure 13.
2.2
2.1
2
1.9
1.8
peak gain
1.7
Gain (M)
peak gain
10~20% of Mmax
1.6
1.5
m=2.25
1.4
m=2.5
maximum operation gain
(Mmax)
1.3
m=3.0
1.2
m=6.0
m=9.0 m=8.0 m=7.0
1.1
m=3.5
m=4.0
m=4.5
m=5.0
1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Q
fo
fs
Figure 14. Peak Gain (Attainable Maximum Gain) vs.
Q for Different m Values
Figure 13. Determining the Maximum Gain
Even though the peak gain at a given condition can be
obtained by using the gain in Equation 6, it is difficult to
express the peak gain in explicit form. To simplify the
analysis and design, the peak gains are obtained using
simulation tools and depicted in Figure 14, which shows
how the peak gain (attainable maximum gain) varies with
Q for different m values. It appears that higher peak gain
can be obtained by reducing m or Q values. With a given
resonant frequency (fo) and Q value, decreasing m means
reducing the magnetizing inductance, which results in
increased circulating current. Accordingly, there is a tradeoff between the available gain range and conduction loss.
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
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6
AN4151 APPLICATION NOTE
4. Features of FSFR-series
Table 1.
FSFR-series is an integrated Pulse Frequency Modulation
(PFM) controller and MOSFETs specifically designed for
Zero Voltage Switching (ZVS) half-bridge converters with
minimal external components. The internal controller
includes an under-voltage lockout, optimized high-side /
low-side gate driver, temperature-compensated precise
current controlled oscillator, and self-protection circuitry.
Compared with discrete MOSFET and PWM controller
solution, FSFR-series can reduce total cost, component
count, size and weight, while simultaneously increasing
efficiency, productivity, and system reliability.
1
2
RT
This pin is to program the switching
frequency. Typically, opto-coupler and
resistor are connected to this pin to regulate
the output voltage.
4
CS
This pin is to sense the current flowing
through the low-side MOSFET. Typically
negative voltage is applied on this pin.
5
SG
This pin is the control ground.
7
8
1
2
3 4 5 6 7 8
RT SG LVcc
CON CS PG
9
9
10
VCTR
HVcc
This pin is the drain of the high-side
MOSFET, typically connected to the input
DC link voltage.
This pin is for enable/disable and protection.
When the voltage of this pin is above 0.6V,
the IC operation is enabled. Meanwhile,
CON when the voltage of this pin drops below
0.4V, gate drive signals for both MOSFETs
are disabled. When the voltage of this pin
increases above 5V, protection is triggered.
VDL
3
6
VDL
Pin Description
10
This pin is the power ground. This pin is
connected to the source of the low-side
MOSFET.
This pin is the supply voltage of the control
LVcc
IC.
PG
No connection.
This pin is the supply voltage of the highHVcc
side drive circuit.
This pin is the drain of the low-side
VCTR MOSFET. Typically transformer is
connected to this pin.
NC
Figure 15. Package Diagram
1.5μ s
Figure 16. Functional Block Diagram of FSFR-series
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
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7
AN4151 APPLICATION NOTE
Llks
Cr
Rdamp Dboot
LVcc
Vcc C
LVcc
Llk
p
VDL
HVcc
RT
Rmax Rmin
Vin
(From PFC
output)
CB
Np
Ns
Lm
Ns
RSS
CSS
RLPF
Co
Rbias
CHVcc
CON
Control
IC
VCTR
Integrated Llks D2
transformer
CLPF
SG
Vo
Rd
CF RF
KA431
CS
CDL
D1
PG
Rsense
Figure 17. Reference Circuit for Design Example of LLC Resonant Half-bridge Converter
5. Design Procedure
In this section, a design procedure is presented using the
schematic in Figure 17 as a reference. An integrated
transformer with center tap, secondary side is used and
input is supplied from power factor correction (PFC) preregulator. A DC/DC converter with 192W/24V output has
been selected as a design example. The design
specifications are as follows:
Vin min = VO. PFC 2 −
(Design Example) Assuming the efficiency is 92%,
P
192
Pin = o =
= 209W
0.92
E ff
Vin max = VO.PFC = 400V
Vin min = VO. PFC 2 −
[STEP-1] Define the system specifications
As a first step, define the following specification.
= 4002 −
Estimated efficiency (Eff): The power conversion
efficiency must be estimated to calculate the maximum
input power with a given maximum output power. If no
reference data is available, use Eff = 0.88~0.92 for lowvoltage output applications and Eff = 0.92~0.96 for highvoltage output applications. With the estimated efficiency,
the maximum input power is given as:
Pin =
E ff
2 ⋅ 209 ⋅ 20 × 10−3
= 349V
220 × 10−6
As discussed in the previous section, it is typical to operate
the LLC resonant converter around the resonant frequency
(fo) to minimize switching frequency variation. Since the
input of the LLC resonant converter is supplied from PFC
output voltage, the converter should be designed to operate
at fo for the nominal PFC output voltage.
(11)
As observed in Equation 10, the gain at fo is a function of m
(m=Lp/Lr). The gain at fo is determined by choosing that
value of m. While a higher peak gain can be obtained with
a small m value, too small m value results in poor coupling
of the transformer and deteriorates the efficiency. It is
typical to set m to be 3~7, which results in a voltage gain of
1.1~1.2 at the resonant frequency (fo).
(12)
Even though the input voltage is regulated as constant by
PFC pre-regulator, it drops during the hold-up time. The
minimum input voltage considering the hold-up time
requirement is given as:
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
2 PinTHU
CDL
[STEP-2] Determine the Maximum and
Minimum Voltage Gains of the Resonant
Network
Input voltage range (Vinmin and Vinmax): The maximum
input voltage would be the nominal PFC output voltage as:
Vin max = VO. PFC
(13)
where VO.PFC is the nominal PFC output voltage, THU is a
hold-up time, and CDL is the DC link bulk capacitor.
- Nominal input voltage: 400VDC (output of PFC stage)
- Output: 24V/8A (192W)
- Hold-up time requirement: 20ms (50Hz line freq.)
- DC link capacitor of PFC output: 220µF
Po
2 PinTHU
CDL
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8
AN4151 APPLICATION NOTE
With the chosen m value, the voltage gain for the nominal
PFC output voltage is obtained as:
M min
m @f=f
=
o
m −1
[STEP-4] Calculate Equivalent Load Resistance
With the transformer turns ratio obtained from Equation 16,
the equivalent load resistance is obtained as:
(14)
Rac =
which would be the minimum gain because the nominal
PFC output voltage is the maximum input voltage (Vinmax).
(Design Example)
The maximum voltage gain is given as:
Rac =
M max =
Vin max min
M
Vin min
(15)
Vin max min 400
M =
⋅ 1.12 = 1.28
Vin min
349
1
2π Q ⋅ f o ⋅ Rac
1
Lr =
(2π f o ) 2 Cr
Cr =
Gain (M)
Peak gain (available maximum gain)
1.28
8n2 Vo 2 8 ⋅ 9.02 ⋅ 242
=
= 197Ω
π 2 Po
π 2 ⋅ 192
With m value chosen in STEP-2, read proper Q value from
the peak gain curves in Figure 14 that allows enough peak
gain. Considering the load transient and stable zerovoltage-switching (ZVS) operation, 10~20% margin should
be introduced on the maximum gain when determining the
peak gain. Once the Q value is determined, the resonant
parameters are obtained as:
chosen as 5. The minimum and maximum gains are
obtained as:
VRO
m
5
M min = max
=
=
= 1.12
Vin
2
m −1
5 −1
Mmax
(17)
[STEP-5] Design the Resonant Network
(Design Example) The ratio (m) between Lp and Lr is
M max =
8n 2 Vo 2
π 2 Po
for Vinmin
Lp = m ⋅ Lr
(18)
(19)
(20)
(Design Example)
1.12
Mmin
M =
As calculated in STEP-2, the maximum voltage gain
(M max) for the minimum input voltage (Vinmin) is 1.28.
With 15% margin, a peak gain of 1.47 is required. m
has been chosen as 5 in STEP-2 and Q is obtained as
0.4 from the peak gain curves in Figure 19. By selecting
the resonant frequency as 100kHz, the resonant
components are determined as:
1
1
Cr =
=
= 20.2nF
2π Q ⋅ f o ⋅ Rac 2π ⋅ 0.4 ⋅ 100 × 103 ⋅ 197
1
1
Lr =
=
= 126 μ H
(2π f o ) 2 Cr (2π ⋅ 100 × 103 ) 2 ⋅ 20.2 × 10 −9
Vinmax
for
( VO.PFC )
m
= 1.12
m −1
fo
fs
Figure 18. Maximum Gain / Minimum Gain
Lp = m ⋅ Lr = 630 μ H
[STEP-3] Determine the Transformer Turns
Ratio (n=Np/Ns)
With the minimum gain (Mmin) obtained in STEP-2, the
transformer turns ratio is given as:
n=
Np
Ns
=
Vin max
⋅ M min
2(Vo + VF )
(16)
where VF is the secondary-side rectifier diode voltage drop.
(Design Example) assuming VF is 0.9V,
n=
Np
Ns
=
400
Vin max
⋅ M min =
⋅ 1.12 = 9.00
2(Vo + VF )
2(24 + 0.9)
Figure 19. Resonant Network Design Using the Peak
Gain (Attainable Maximum Gain)
Curve for m=5
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
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9
AN4151 APPLICATION NOTE
[STEP-6] Design the Transformer
2.0
The worst case for the transformer design is the minimum
switching frequency condition, which occurs at the
minimum input voltage and full-load condition. To obtain
the minimum switching frequency, plot the gain curve
using gain Equation 9 and read the minimum switching
frequency. The minimum number of turns for the
transformer primary-side is obtained as:
N p min =
1.8
f normal
f min
1.6
1.4
Mmax
1.2
n(Vo + VF )
2 f s ⋅ M V ⋅ ΔB ⋅ Ae
Mmin
(21)
min
1.0
where Ae is the cross-sectional area of the transformer core
in m2 and ΔB is the maximum flux density swing in Tesla,
as shown in Figure 20. If there is no reference data, use
ΔB =0.3~0.4 T.
0.8
0.6
40
50
60
70
80
90
100
110
120
130
140
Frequency (kHz)
Figure 21. Gain Curve
n (Vo+VF)/MV
VRI 1/(2fs)
100%
load
80%
load
60%
load
40%
load
20%
load
[STEP-7] Transformer Construction
-n (Vo+VF)/MV
ΔB
B
Figure 20. Flux Density Swing
Choose the proper number of turns for the secondary side
that results in primary-side turns larger than Npmin as:
N p = n ⋅ N s > N p min
(22)
Parameters Lp and Lr of the transformer were determined in
STEP-5. Lp and Lr can be measured in the primary side
with the secondary-side winding open circuited and short
circuited, respectively. Since LLC converter design
requires a relatively large Lr, a sectional bobbin is typically
used, as shown in Figure 22, to obtain the desired Lr value.
For a sectional bobbin, the number of turns and winding
configuration are the major factors determining the value of
Lr, while the gap length of the core does not affect Lr much.
Lp can be easily controlled by adjusting the gap length.
Table 2 shows measured Lp and Lr values with different
gap lengths. A gap length of 0.10mm obtains values for Lp
and Lr closest to the designed parameters.
2
Np
(Design Example) EER3542 core (Ae=107mm ) is
selected for the transformer. From the gain curve of
Figure 21, the minimum switching frequency is
obtained as 78kHz. The minimum primary-side turns
of the transformer is given as:
N p min =
=
N s2
N s1
n(Vo + VF )
2 f s min ΔB ⋅ 1.11 ⋅ Ae
9.0 × 24.9
= 30.5 turns
2 ⋅ 77 × 103 ⋅ 0.4 ⋅ 1.11 ⋅ 107 × 10−6
Choose Ns so that the resultant Np should be larger
than Npmin:
N p = n ⋅ N s = 1 × 9.0 = 9 < N p
Figure 22. Sectional Bobbin
Table 2. Measured Lp and Lr with Different Gap Lengths
min
N p = n ⋅ N s = 2 × 9.0 = 18 < N p
min
N p = n ⋅ N s = 3 × 9.0 = 27 < N p min
N p = n ⋅ N s = 4 × 9.0 = 36 > N p min
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
Gap length
Lp
Lr
0.0mm
0.05mm
2,295μH
943μH
123μH
122μH
0.10mm
630μH
118μH
0.15mm
488μH
117μH
0.20mm
419μH
115μH
0.25mm
366μH
114μH
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10
AN4151 APPLICATION NOTE
(Design Example)
VCr nom ≅
Final Resonant Network Design
Even though the integrated transformer approach in
LLC resonant converter design can implement the
magnetic components in a single core and save one
magnetic component, the value of Lr is not easy to
control in real transformer design. Resonant network
design sometimes requires iteration with a resultant Lr
value after the transformer is built. The resonant
capacitor value is also changed since it should be
selected among off-the-shelf capacitors. The final
resonant network design is summarized in Table 3 and
the new gain curves are shown in Figure 23.
Initial design
630µH
126H
20nF
100kHz
5
0.4
Final design
630µH
118µH
22nF
99kHz
5.34
0.36
M@fo
Minimum freq
1.14
78kHz
1.11
72kHz
(24)
However, the resonant capacitor voltage increases much
higher than this at overload condition or load transient.
Actual capacitor selection should be based on the OverCurrent Protection (OCP) trip point. With the OCP level,
IOCP, the maximum resonant capacitor voltage is obtained as:
VCr nom ≅
Vin max
I OCP
+
2
2 ⋅ π ⋅ f o ⋅ Cr
(25)
(Design Example)
Table 3. Final Resonant Network Design Parameters
Parameters
Lp
Lr
Cr
fo
m
Q
Vin max
2 ⋅ I Cr RMS
+
2
2 ⋅ π ⋅ f o ⋅ Cr
ICr RMS ≅
1
E ff
[
π Io 2
n(Vo + VF )
] +[
]2
2 2n
4 2 fo M V ( L p − Lr )
1
π ⋅8 2
9.0 ⋅ (24 + 0.9)
[
] +[
]2
0.92 2 2 ⋅ 9.0
4 2 ⋅ 99 × 103 ⋅ 1.11 ⋅ 512 × 10−6
= 1.32 A
=
The peak current in the primary side in normal
operation is:
I Cr peak = 2 ⋅ I Cr rms = 1.86 A
OCP level is set to 3.0A with 50% margin on ICrpeak:
VCr nom ≅
Vin max
2 ⋅ I Cr RMS
+
2
2 ⋅ π ⋅ f o ⋅ Cr
400
2 ⋅ 1.32
+
= 336V
2
2 ⋅ π ⋅ 99 × 103 ⋅ 22 × 10−9
V max
I OCP
≅ in +
2
2 ⋅ π ⋅ f o ⋅ Cr
=
VCr max
=
400
3
+
= 419V
2
2 ⋅ π ⋅ 99 ×103 ⋅ 22 ×10−9
A 630V rated low-ESR film capacitor is selected for the
resonant capacitor.
Figure 23. Gain Curve of the Final Resonant
Network Design
[STEP-9] Rectifier Network Design
[STEP-8] Select the Resonant Capacitor
When choosing the resonant capacitor, the current rating
should be considered because a considerable amount of
current flows through the capacitor. The RMS current
through the resonant capacitor is given as:
I Cr RMS ≅
1
E ff
[
π Io
2 2n
]2 + [
n(Vo + VF )
]2 (23)
4 2 fo M V ( L p − Lr )
When the center tap winding is used in the transformer
secondary side, the diode voltage stress is twice of the
output voltage expressed as:
VD = 2(Vo + VF )
The RMS value of the current flowing through each
rectifier diode is given as:
I D RMS =
The nominal voltage of the resonant capacitor in normal
operation is given as:
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
(26)
π
4
Io
(27)
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11
AN4151 APPLICATION NOTE
Meanwhile, the ripple current flowing through output
capacitor is given as:
ICo RMS = (
π Io
2 2
)2 − I o 2 =
π2 −8
8
LVcc
RT
(28)
Io
Rmax
π
2
I o ⋅ RC
PLoss.Co = ( I Co RMS ) 2 ⋅ RC
stress of the rectifier diode are:
VD = 2(Vo + VF ) = 2(24 + 0.9) = 49.8
4
I o = 6.28 A
The 100V/20A Schottky diode is selected for the
rectifier considering the voltage overshoot caused by
the stray inductance.
The RMS current of the output capacitor is:
I Co RMS = (
π Io
2 2
)2 − I o 2 =
π2 −8
8
π
2
I o ⋅ RC =
π
2
SG
⋅8⋅(
Soft-start: To prevent excessive inrush current and
overshoot of output voltage during start-up, increase the
voltage gain of the resonant converter progressively. Since
the voltage gain of the resonant converter is reversely
proportional to the switching frequency, the soft-start is
implemented by sweeping down the switching frequency
from an initial high frequency (f ISS) until the output voltage
is established, as illustrated in Figure 25. The soft-start
circuit is made by connecting RC series network on the RT
pin as shown in Figure 24. FSFR-series also has an internal
soft-start for 3ms to reduce the current overshoot during the
initial cycles, which adds 40kHz to the initial frequency of
the external soft-start circuit, as shown in Figure 25. The
actual initial frequency of the soft-start is given as:
f ISS = (
0.08
) = 0.50V
2
PG
Figure 24. Typical Circuit Configuration for RT Pin
I o = 3.857 A
When two electrolytic capacitors with ESR of 80mΩ
are used in parallel, the output voltage ripple is given
as:
ΔVo =
Control
IC
External S/S
(30)
(Design Example) The voltage stress and current
π
CSS
(29)
where RC is the effective series resistance (ESR) of the
output capacitor and the power dissipation is the output
capacitor is:
I D RMS =
RSS
Rmin
The voltage ripple of the output capacitor is:
ΔVo =
VDL
5.2k Ω 5.2k Ω
+
) × 100 + 40 (kHz ) (33)
Rmin
RSS
It is typical to set the initial frequency of soft-start (f ISS) as
2~3 times of the resonant frequency (fo).
The soft-start time is determined by the RC time constant:
The loss in electrolytic capacitors is:
TSS = 3 ~ 4 times of RSS ⋅ CSS
PLoss.Co = ( I Co RMS ) 2 ⋅ RC = 3.857 2 ⋅ 0.04 = 0.60W
(34)
fs
f ISS
40kHz
[STEP-10] Control Circuit Configuration
Control loop
take over
Figure 24 shows the typical circuit configuration for RT pin
of FSFR-series, where the opto-coupler transistor is
connected to the RT pin to control the switching frequency.
The minimum switching frequency occurs when the optocoupler transistor is fully tuned off, which is given as:
3ms
time
5.2k Ω
(31)
f min =
× 100( kHz )
Rmin
Assuming the saturation voltage of opto-coupler transistor is
0.2V, the maximum switching frequency is determined as:
f max = (
5.2k Ω 4.68k Ω
) × 100(kHz )
+
Rmin
Rmax
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
3~4 times of RC time constant
Figure 25. Frequency Sweep of the Soft-start
(32)
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12
AN4151 APPLICATION NOTE
(Design Example) The minimum frequency is 72kHz
I DS
in STEP-6. Rmin is determined as:
Rmin =
100 kHz
× 5.2k Ω = 7.2k
f min
VCS
Considering the output voltage overshoot during
transient (10%) and the controllability of the feedback
loop, the maximum frequency is set as 140kHz. Rmax
is determined as:
Rmax
Cr
VCS
4.68k Ω
=
fo × 1.40 5.2k Ω
(
−
)
100 kHz
Rmin
=
=
Np
CS
PG
SG
Rsense
Ns
Ns
IDS
4.68k Ω
= 7.1k Ω
99kHz × 1.4 5.2k Ω
(
−
)
100 kHz
7.2k Ω
Figure 27. Full-wave Sensing
Setting the initial frequency of soft-start as 250kHz
(2.5 times of the resonant frequency), the soft-start
resistor RSS is given as:
RSS =
Control
IC
(Design Example) Since the OCP level is determined
as 3A in STEP-8 and the OCP threshold voltage is 0.6V, a sensing resistor of 0.2Ω is used. The RC time
constant is set to 100ns (1/100 of switching period)
with 1kΩ resistor and 100pF capacitor.
5.2k Ω
f ISS − 40kHz 5.2k Ω
(
)
−
100kHz
Rmin
5.2k Ω
= 3.8k Ω
250kHz − 40kHz 5.2k Ω
(
)
−
100kHz
7.2k Ω
[STEP-11] Current Sensing and Protection
FSFR-series senses low-side MOSFET drain current as a
negative voltage, as shown in Figure 26 and Figure 27.
Half-wave sensing allows low-power dissipation in the
sensing resistor, while full-wave sensing has less switching
noise in the sensing signal. Typically, RC low-pass filter is
used to filter out the switching noise in the sensing signal.
The RC time constant of the low-pass filter should be
1/100~1/20 of the switching period.
Cr
Np
Ns
Ns
Control
IC
VCS
I DS
CS
SG
PG
Rsense
IDS
VCS
Figure 26. Half-wave Sensing
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
www.fairchildsemi.com
13
AN4151 APPLICATION NOTE
Design Summary
Figure 28 shows the final schematic of the LLC resonant half-bridge converter design example. EER3542 core with
sectional bobbin is used for the transformer. The efficiency at full load condition is around 94%.
Figure 28. Final Schematic of Half-bridge LLC Resonant Converter
- Core: EER3542 (Ae=107 mm2)
- Bobbin: EER3542 (Horizontal/section type)
EER3542
1
16
Np
Np
Ns1
N s2
1
3
1
2
N s1
Ns2
8
9
Figure 29. Transformer Structure
Pin(S → F)
Wire
Turns
Winding Method
Np
8→1
0.12φ×30 (Litz wire)
36
Section winding
Ns1
16 → 13
0.1φ×100 (Litz wire)
4
Section winding
Ns2
12 → 9
0.1φ×100 (Litz wire)
4
Section winding
Pin
Specification
Remark
Primary-side Inductance (Lp)
1－8
630μH ± 5%
Secondary windings open
100kHz, 1V
Equivalent Leakage Inductance (Lr)
1－8
118μH Max.
Short one of the secondary windings
100kHz, 1V
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
www.fairchildsemi.com
14
AN4151 APPLICATION NOTE
6. Experimental Verification
To show the validity of the design procedure presented in
this application note, the converter of the design example
has been built and tested. All the circuit components are
used as designed in the design example.
Figure 30 and Figure 31 show the operation waveforms at
full-load and no-load conditions for nominal input voltage.
As observed, the MOSFET drain-to-source voltage (VDS)
drops to zero by resonance before the MOSFET is turned
on and zero voltage switching is achieved.
Figure 32 shows the waveforms of the resonant capacitor
voltage and primary-side current at full-load condition. The
peak values of the resonant capacitor voltage and primaryside current are 325V and 1.93A, respectively, which are
well matched with the calculated values in STEP-8 of
design procedure section. Figure 33 shows the waveforms
of the resonant capacitor voltage and primary-side current
at output-short condition. For output-short condition, over
current protection (OCP) is triggered when the primaryside current exceeds 3A. The maximum voltage of the
resonant capacitor is a little bit higher than the calculated
value of 419V because the OCP trips at a level little bit
higher than 3A, due to the shutdown delay time of 1.5µs
(refer to the FSFR2100 datasheet).
Figure 31. Operation Waveforms at No-load Condition
Figure 34 shows the rectifier diode voltage and current
waveforms at full-load and no-load conditions. Due to the
voltage overshoot caused by stray inductance, the voltage
stress is a little bit higher than the value calculated in
STEP-9. Figure 35 shows the output voltage ripple at fullload and no-load conditions. The output voltage ripple is
well matched with the designed value in STEP-9.
Figure 32. Resonant Capacitor Voltage and Primaryside Current Waveforms at Full-load Condition
Figure 36 shows the measured efficiency for different load
conditions. Efficiency at full-load condition is about 94%.
Figure 33. Resonant Capacitor Voltage and Primaryside Current Waveforms for Output Short Protection
Figure 30. Operation Waveforms at Full-load Condition
Figure 34. Rectifier Diode Voltage and Current
Waveforms at Full-load Condition
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
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15
AN4151 APPLICATION NOTE
Figure 35. Output Voltage Ripple and Primary-side
Current Waveforms at Full-load Condition
Figure 37. Measured Efficiency
Figure 36. Soft-start Waveforms
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
www.fairchildsemi.com
16
AN4151 APPLICATION NOTE
7. References
[1] Robert L. Steigerwald, “A Comparison of Half-bridge
resonant converter topologies,” IEEE Transactions on
Power Electronics, Vol. 3, No. 2, April 1988.
[2] A. F. Witulski and R. W. Erickson, “Design of the series
resonant converter for minimum stress,” IEEE Transactions
on Aerosp. Electron. Syst., Vol. AES-22, pp. 356-363,
July 1986.
[3] R. Oruganti, J. Yang, and F.C. Lee, “Implementation of
Optimal Trajectory Control of Series Resonant Converters,”
Proc. IEEE PESC ’87, 1987.
[4] V. Vorperian and S. Cuk, “A Complete DC Analysis of the
Series Resonant Converter,” Proc. IEEE PESC’82, 1982.
[5] Y. G. Kang, A. K. Upadhyay, D. L. Stephens, “Analysis and
design of a half-bridge parallel resonant converter operating
above resonance,” IEEE Transactions on Industry
Applications Vol. 27, March-April 1991, pp. 386 – 395.
[6] R. Oruganti, J. Yang, and F.C. Lee, “State Plane Analysis of
Parallel Resonant Converters,” Proc. IEEE PESC ’85, 1985.
[7] M. Emsermann, “An Approximate Steady State and Small
Signal Analysis of the Parallel Resonant Converter Running
Above Resonance,” Proc. Power Electronics and Variable
Speed Drives ’91, 1991, pp. 9-14.
[8] Yan Liang, Wenduo Liu, Bing Lu, van Wyk, J.D, " Design
of integrated passive component for a 1 MHz 1 kW halfbridge LLC resonant converter", IAS 2005, pp. 2223-2228.
[9] B. Yang, F.C. Lee, M. Concannon, "Over current protection
methods for LLC resonant converter" APEC 2003, pp. 605 - 609.
[10] Yilei Gu, Zhengyu Lu, Lijun Hang, Zhaoming Qian,
Guisong Huang, "Three-level LLC series resonant DC/DC
converter" IEEE Transactions on Power Electronics
Vol.20, July 2005, pp.781 – 789.
[11] Bo Yang, Lee, F.C, A.J Zhang, Guisong Huang, "LLC
resonant converter for front end DC/DC conversion" APEC
2002. pp.1108 – 1112.
[12] Bing Lu, Wenduo Liu, Yan Liang, Fred C. Lee, Jacobus D.
Van Wyk, “Optimal design methodology for LLC Resonant
Converter,” APEC 2006. pp.533-538.
Author
Hang-Seok Choi / Ph. D
FPS Application Group / Fairchild Semiconductor
Phone: +82-32-680-1383
Fax: +82-32-680-1317
Email: [email protected]
Related Datasheets
FSFR2100
Important Notice
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HEREIN TO IMPROVE RELIABILITY, FUNCTION, OR DESIGN. FAIRCHILD DOES NOT ASSUME ANY LIABILITY ARISING OUT OF
THE APPLICATION OR USE OF ANY PRODUCT OR CIRCUIT DESCRIBED HEREIN; NEITHER DOES IT CONVEY ANY LICENSE
UNDER ITS PATENT RIGHTS, NOR THE RIGHTS OF OTHERS.
LIFE SUPPORT POLICY
FAIRCHILD’S PRODUCTS ARE NOT AUTHORIZED FOR USE AS CRITICAL COMPONENTS IN LIFE SUPPORT DEVICES OR
SYSTEMS WITHOUT THE EXPRESS WRITTEN APPROVAL OF THE PRESIDENT OF FAIRCHILD SEMICONDUCTOR
CORPORATION.
As used herein:
1.
Life support devices or systems are devices or systems
which, (a) are intended for surgical implant into the body,
or (b) support or sustain life, or (c) whose failure to perform
when properly used in accordance with instructions for use
provided in the labeling, can be reasonably expected to
result in significant injury to the user.
© 2007 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 10/9/07
2.
A critical component is any component of a life support
device or system whose failure to perform can be
reasonably expected to cause the failure of the life support
device or system, or to affect its safety or effectiveness.
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