Design Considerations
for an LLC Resonant Converter
Hangseok Choi
Power Conversion Team
www.fairchildsemi.com
1. Introduction
Growing demand for higher power
density and low profile in power
converter has forced to increase
switching frequency
High frequency
operation
However, Switching Loss has been
an obstacle to high frequency
operation
Overlap of voltage and current
2
Capacitive loss
Reverse recovery loss
1. Introduction
Resonant converter: processes power in a sinusoidal manner and
the switching devices are softly commutated
9 Voltage across the switch drops to zero before switch turns on (ZVS)
• Remove overlap area between V and I when turning on
• Capacitive loss is eliminated
Series resonant converter / Parallel resonant converter
3
1. Introduction
Series Resonant (SR) converter
resonant network
Q1
Ip
Vin
Vd
n:1
Ro
Lr
VO
Q2
Lm
Ids2
+
Cr
The resonant inductor (Lr) and resonant capacitor (Cr) are in series
The resonant capacitor is in series with the load
9 The resonant tank and the load act as a voltage dividerÆ DC gain is always
lower than 1 (maximum gain happens at the resonant frequency)
9 The impedance of resonant tank can be changed by varying the frequency
of driving voltage (Vd)
4
1. Introduction
Series Resonant (SR) converter
Advantages
9 Reduced switching loss and EMI through ZVS Æ Improved
efficiency
9 Reduced magnetic components size by high frequency operation
Drawbacks
9 Can optimize performance at one operating point, but not with wide
range of input voltage and load variations
9 Can not regulate the output at no load condition
9 Pulsating rectifier current (capacitor output): limitation for high
output current application
5
1. Introduction
Parallel Resonant (PR) converter
resonant network
Q1
Ip
Vin
Vd
Q2
n:1
Ro
Llkp
Cr
+
VO
-
Ids2
The resonant inductor (Lr) and resonant capacitor (Cr) are in series
The resonant capacitor is in parallel with the load
9 The impedance of resonant tank can be changed by varying the
frequency of driving voltage (Vd)
6
1. Introduction
Parallel Resonant (PR) converter
Advantages
9 No problem in output regulation at no load condition
9 Continuous rectifier current (inductor output): suitable for high
output current application
Drawbacks
9 The primary side current is almost independent of load condition:
significant current may circulate through the resonant network,
even at the no load condition
9 Circulating current increases as input voltage increases: limitation
for wide range of input voltage
7
1. Introduction
What is LLC resonant converter?
9 Topology looks almost same as the conventional LC series
resonant converter
9 Magnetizing inductance (Lm) of the transformer is relatively small
and involved in the resonance operation
9 Voltage gain is different from that of LC series resonant converter
LC Series resonant converter
resonant network
Q1
Ip
Vin
Vd
Ro
Lr
Ids2
+
VO
Lm
resonant network
Q1
n:1
Q2
8
LLC resonant converter
Ip
Vin
Vd
Q2
Ids2
Io
ID
Ro
Lr
+
VO
Im
Lm
Cr
n:1
Cr
1. Introduction
Features of LLC resonant converter
- Reduced switching loss through ZVS: Improved efficiency
- Narrow frequency variation range over wide load range
- Zero voltage switching even at no load condition
- Typically, integrated transformer is used instead of discrete magnetic
components
9
1. Introduction
Integrated transformer in LLC resonant converter
9 Two magnetic components are implemented with a single core (use
the primary side leakage inductance as a resonant inductor)
9 One magnetic components (Lr) can be saved
9 Leakage inductance not only exists in the primary side but also in
the secondary side
9 Need to consider the leakage inductance in the secondary side
Q1
Integrated transformer
Q1
Vin
n:1
Vd
Q2
Io
ID
Ro
Lr
+
VO
Lm
Ip
Vin
Vd
Q2
10
Cr
Ids2
Ro
+
VO
Im
Lm
Ids2
Llks
Llkp
Io
ID
n:1
Cr
2. Operation principle and Fundamental Approximation
Square wave generator: produces a square wave voltage, Vd by driving switches,
Q1 and Q2 with alternating 50% duty cycle for each switch.
Resonant network: consists of Llkp, Llks, Lm and Cr. The current lags the voltage
applied to the resonant network which allows the MOSFET’s to be turned on
with zero voltage.
Rectifier network: produces DC voltage by rectifying AC current
Ip
Im
Square wave generator
resonant network
Q1
Ip
Vin
Vd
Q2
Llks
Llkp
Ro
+
VO
Im
Lm
Ids2
Io
ID
n:1
Ids2
Rectifier network
-
ID
Vd
(Vds2)
Cr
Vgs1
Vgs2
11
Vin
2. Operation principle and Fundamental Approximation
The resonant network filters the higher harmonic currents. Thus, essentially
only sinusoidal current is allowed to flow through the resonant network even
though a square wave voltage (Vd) is applied to the resonant network.
Fundamental approximation: assumes that only the fundamental component of
the square-wave voltage input to the resonant network contributes to the power
transfer to the output.
The square wave voltage can be replaced by its fundamental component
Vd
Resonant
netw ork
12
Isec
Ip
Isec
Ip
Vd
Resonant
netw ork
2. Operation principle and Fundamental Approximation
Because the rectifier circuit in the secondary side acts as an impedance
transformer, the equivalent load resistance is different from actual load resistance.
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.
The equivalent load resistance is
obtained as
I ac
pk
Io
+
Iac
+
VRI
VO
Ro
-
Rac =
F
8 Vo
8
VRI
VRI
=
=
=
Ro
2
2
F
π Io π
I ac
I ac
I ac =
Iac
VRIF
VRI
13
-
F
Vo
π ⋅ Io
VRI F =
2
sin( wt )
4Vo
π
sin( wt )
2. Operation principle and Fundamental Approximation
AC equivalent circuit (L-L-L-C)
Vin
Vd
+
Cr
Llks
Llkp
+
+
-
-
n:1
Rac =
π2
Ro
-
VdF
=
ω 2 Lm Rac Cr
ω2
ω2
2
jω ⋅ (1 − 2 ) ⋅ ( Lm + n Llks ) + Rac (1 − 2 )
ωo
ωp
Ro
n2Llks
Cr
F
VRI
Lm
8n 2
VO
4n ⋅ Vo
sin(ωt )
VRO
2n ⋅ Vo
n ⋅ VRI
π
M= F =
=
=
4 Vin
Vd
Vd F
Vin
sin(ωt )
π 2
F
Rac =
Llkp
Lm
Rac
VROF
ωo =
8n 2
π2
Ro
1
, ωp =
Lr Cr
1
L p Cr
Lp = Lm + Llkp , Lr = Llkp + Lm //(n 2 Llks )
- Lr is measured in primary side with secondary winding short circuited
- Lp is measured in primary side with secondary winding open circuited
14
2. Operation principle and Fundamental Approximation
Simplified AC equivalent circuit (L-L-C)
Cr
Vd
+
Vin
Llks
Llkp
+
+
Ro
-
-
ω2 k
( 2)
ωp k +1
VO
VRI
Lm
Assuming Llkp=n2Llks
n:1
M=
2n ⋅ VO
=
Vin
-
ω
ω2
ω2
(k + 1) 2
j ( ) ⋅ (1 − 2 ) ⋅ Q
+ (1 − 2 )
ωo
ωo
ωp
2k + 1
Lr = Llkp + Lm //(n Llks )
2
= Llkp + Lm // Llkp
L p = Llkp + Lm
Cr
VinF
1:
Q=
Lp
L p − Lr
Rac
VROF
M=
- Lr is measured in primary side with secondary winding short circuited
- Lp is measured in primary side with secondary winding open circuited
15
k=
Lm
Llkp
Expressing in terms of Lp and Lr
Lr
Lp-Lr
Lr / Cr
Rac
2n ⋅ VO
=
Vin
ω 2 Lp − Lr
( 2)
Lp
ωp
Lp
ω
ω2
ω2
+ (1 − 2 )
j ( ) ⋅ (1 − 2 ) ⋅ Q
Lr
ωo
ωo
ωp
2. Operation principle and Fundamental Approximation
Gain characteristics
LLC resonant C onverter
fp
9 Two resonant frequencies (fo and fp)
exist
9 The gain is fixed at resonant frequency
(fo) regardless of the load variation
fo
2.0
Q=
Q=0.2
1.8
Lr / Cr
Rac
Q= 1
Q = 0.8
1.6
Q = 0.6
Lp
Lp − Lr
Q = 0.4
1.4
G ain
M @ω =ωo
k +1
=
=
k
Q = 0.2
1.2
9 Peak gain frequency exists between fo
and fp
9 As Q decreases (as load decreases),
the peak gain frequency moves to fp and
higher peak gain is obtained.
9 As Q increases (as load increases),
peak gain frequency moves to fo and the
peak gain drops
16
Q=1
1.0
M=
0.8
k +1
=
k
Lp
Lp − Lr
0.6
40
50
60
70
80
90
freq (kH z)
100
110
120
130
140
2. Operation principle and Fundamental Approximation
Peak gain (attainable maximum gain) versus Q for different k values
2.4
2.2
Peak Gain
2.0
k=1.5
1.8
k=1.75
k=2
1.6
k=2.5
1.4
k=3
1.2
k=4
k=5
k=7
k=9
1
0.2
0.4
0.6
0.8
Q
17
1
1.2
1.4
3. Design procedure
Design example
- Input voltage: 380Vdc (output of PFC stage)
- Output: 24V/5A (120W)
- Holdup time requirement: 17ms
- DC link capacitor of PFC output: 100uF
PFC
DC/DC
ID
Q1
Ip
VDL
CDL
Vd
Q2
Np:Ns
Llks
Llkp
Im
-
Lm
Ids2
18
VO
+
Cr
Ro
3. Design procedure
[STEP-1] Define the system specifications
9 Estimated efficiency (Eff)
9 Input voltage range: hold up time should be considered for minimum input voltage
Vin min = VO. PFC 2 −
19
2 PinTHU
CDL
3. Design procedure
[STEP-2] Determine the maximum and minimum voltage gains of the
resonant network by choosing k ( k = Lm / Llkp )
- it is typical to set k to be 5~10, which results in a gain of 1.1~1.2 at fo
M
M
min
max
VRO
Lm + n 2 Llks Lm + Llkp k + 1
= max =
=
=
Vin
Lm
Lm
k
2
Vin max min
= min M
Vin
Gain (M)
Peak gain (available maximum gain)
1.36
Mmax
for Vinmin
1.14
Mmin
M=
k +1
= 1.14
k
fo
20
for Vinmax
fs
3. Design procedure
[STEP-3] Determine the transformer turns ratio (n=Np/Ns)
Vin max
n=
=
⋅ M min
N s 2 (Vo + VF )
Np
[STEP-4] Calculate the equivalent load resistance (Rac)
8n 2 Vo 2
Rac = 2
π Po
21
3. Design procedure
[STEP-5] Design the resonant network
- With k chosen in STEP-2, read proper Q from gain curves
k = 7 , M max = 1.36
peak gain = 1.36 × 110% = 1.5
22
3. Design procedure
[STEP-6] Design the transformer
- Plot the gain curve and read the minimum switching frequency. Then, the minimum
number of turns for the transformer primary side is obtained as
N p min =
23
n(Vo + VF )
2 f s min ⋅ ΔB ⋅ Ae
3. Design procedure
[STEP-7] Transformer Construction
- Since LLC converter design results in relatively large Lr, usually sectional bobbin is typically
used
- # of turns and winding configuration are the major factors determining Lr
- Gap length of the core does not affect Lr much
- Lp can be easily controlled with gap length
Np=52T
Ns1=Ns2=6T
Bifilar
Design value: Lr=234uH, Lp=998uH
24
3. Design procedure
[STEP-8] Select the resonant capacitor
I Cr
25
RMS
π Io
n(V + 2 ⋅ VF ) 2
≅ [
] +[ o
]
2 2n
4 2 f o Lm
2
VCr
max
Vin max
2 ⋅ I Cr RMS
≅
+
2
2 ⋅ π ⋅ f o ⋅ Cr
4. Conclusion
Using a fundamental approximation, gain equation has
been derived
Leakage inductance in the secondary side is also
considered (L-L-L-C model) for gain equation
L-L-L-C equivalent circuit has been simplified as a
conventional L-L-C equivalent circuit
Practical design consideration has been presented
26
Appendix - FSFR-series
Variable frequency control with 50% duty cycle for half-bridge resonant
converter topology
High efficiency through zero voltage switching (ZVS)
Internal Super-FETs with Fast Recovery Type Body Diode (trr=120ns)
Fixed dead time (350ns)
Up to 300kHz operating frequency
Pulse skipping for Frequency limit (programmable) at light load condition
Simple remote ON/OFF control
Various Protection functions: Over Voltage Protection (OVP), Over Current
Protection (OCP), Abnormal Over Current Protection (AOCP), Internal Thermal
Shutdown (TSD)
27
Appendix - FSFR-series demo board
28
Appendix - FSFR-series demo board
29
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