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Consideration of Gain Distortion Under Light Load Conditions
In An LLC Resonant Converter
Jintae, Kim / Fairchild Korea Semiconductor
Abstract
In an LLC resonant converter, it is well known that input to output voltage conversion ratio decreases as
operating frequency increases under ZVS (Zero Voltage Switching) operating region. However, practical gain of
the converter could be increased under light load conditions as the operating frequency increases due to stray
capacitance existing parallel with the primary side winding of a high frequency transformer. Power supply
designers can be confronted with the phenomenon of output voltage increase under light load condition and
especially no load condition even though the operating frequency increase to regulate output voltage. In this
paper, root cause the phenomenon will be analyzed and solutions to avoid will be suggested.
Introduction
Recently, the LLC resonant converter has received a lot of attention as a result of some outstanding advantages,
such as achieving high efficiency through Zero Voltage Switching (ZVS) and having a narrow operating
frequency variation under overall load conditions - despite the fact that the design of the converter is somewhat
complicated. The LLC resonant converter is widely used in home appliances, street lamps chargers, and various
other electric devices. It is well known that the LLC resonant converter regulates output voltage with adjusting
the operating frequency. Generally, voltage conversion ratio, namely a gain values under ZVS operating region
theoretically decreases as the operating frequency increases. However, practical a gain value can be increased at
light load conditions unlike the ideal gain curve even though operating frequency increases. This gain distortion
is mainly caused by parasitic components, i.e. resonant inductances and stray capacitances distributed to the
high frequency transformer. In order to avoid undesirable output voltage increases in the light load condition,
the parasitic components have to be taken into account in the design phase.
In this paper, the cause of gain curve distortion by the parasitic components will be discussed in detail and
solutions will be suggested.
Operation Principle of an LLC Resonant Converter
Figure 1 shows a basic circuit of an LLC resonant converter. Generally, the LLC resonant converter consists of a
controller with MOSFETs, a resonant network and a rectifier network. The controller delivers a gate signal with
50% duty ratio to two MOSFETs alternatively and changes operating frequency of load variations to regulate
the output voltage, Vout, which is called PFM (Pulse Frequency Modulation). The resonant network is comprised
of two resonant inductors and one resonant capacitor (L-L-C). Basically, the resonant inductances, Lr and Lm and
capacitor, Cr act as a voltage divider whose impedance is varied by the operation frequency so that the desirable
output voltage can be obtained, as shown in Equation 1. For a practical design, the resonant network can be
made of a magnetizing inductance, Lm and leakage inductance, Llk of a high frequency transformer with general
bobbin or a sectional one as shown in Figure 2. Finally, the rectifier network rectifies sinusoidal waveforms
from the resonant network and delivers to the output stage.
n  Vout 
Rac || Lm
1
Cr
 Lr  Rac || Lm
 Vd
… Equation 1
where Vd is input voltage and Rac is load resistance.
Even though the input voltage, Vd is a square waveform controlled by two MOSFETs, it could also be
considered as a sinusoidal waveform by the fundamental approximation. With this approximation, the voltage
conversion ratio can be expressed as shown in Equation 2.
2
M 
2n  Vo

Vin
    m  1
  
r

2
… Equation 2
2
2
2

 


2
 


    1            1  (m  1)  Q 
p
r
r



 
2
Where,
Lp
m
,
Lr
r 
1
, p 
Lr Cr
1
1
, and Q 
Rac
L p Cr
Lr
and Rac and Vd can be expressed
Cr
V
8  n 2  Vout
and in respectively.
2
2
  I out
As can be seen in Equation 2, there are two resonant frequencies. One is ωp which is determined by (Lm + Lr)
and Cr and the other is ωr which is determined by Lr and Cr. By using this equation, a voltage conversion ratio
of the converter, namely gain curve, can be plotted with according to the variation of operating frequency &
load as shown in Figure 3.
In Figure 3, the highest value indicated with ‘+’ for each curve is called ‘peak gain’ and is placed between two
resonant frequencies, ωp and ωr. As output load increases more and more, a value of the peak gain lessens and
the position of peak gain moves to a higher frequency. Meanwhile, it can be seen that the resonant gain indicated
with ‘×’ at ωr is fixed even though the output load varies. The gain curve demonstrates that the gain decreases
and output voltage reduces when the operating frequency applied to the resonant network increases in the ZVS
region.
Practical Voltage Conversion Ratio of an LLC resonant Converter
Figure 4 shows a practical circuit of an LLC resonant converter with stray capacitance. The stray capacitance is
usually dependant upon the transformer winding structures and the output capacitance of rectifiers on the
secondary side. Generally these parameters will not affect a gain curve under some load on the output, however
influence for a gain distortion could become more as the load resistance, Rac increases, which finally makes the
converter operate undesirably.
Considering the stray capacitance, especially one distributed to the primary side winding of a high frequency
transformer, a voltage divide equation of L-L-C impedance can be expressed by the following:
Cr || Rac || Lm
1
n  Vout 
 1

Cr  Lr   Cr || Rac || Lm 
1
 Vd …Equation 3
And the voltage conversion ratio of the converter can be also calculated with the fundamental approximation:
2
M
    m  1
  
r 

2n  V o

Vin
2
2
2
2


 
  m  1  1   
  (m  1)  Q       1





    

  
   r 

r
s 
r 
  p  




2
… Equation 4
where,
m
Lp
Lr
,
r 
1
, p 
Lr Cr
1
, s 
L p Cr
1
1
, and Q 
Rac
Lr Cs
Lr
and Rac and Vd can be
Cr
V
8  n 2  Vout
expressed
and in respectively.
2
2
  I out
In Equation 4, three resonant frequencies can be observed. Two resonant frequencies are same as one of the
ideal voltage conversion ratios; ωp and ωr are determined by {(Lm + Lr) & Cr} and {Lr & Cr} respectively. The
rest is ωs, and this is formed by the resonant inductance and stray capacitance (Lr + Cs). A voltage conversion
ratio of the equation can be plotted according to load conditions of 20%, 10% and no-load as shown in Figure 5.
In figure 5, it can be observed that while operating frequency increases, the voltage gain decreases, but increases
slowly after the operating frequency passes the resonant frequency formed by Lr and Cr. The rate of gain
increases more and more as the load of the output reduces. If this practical fact isn’t taken into account, the
designed converter will not control the output voltage.
Overcoming the Gain Distortion in an LLC resonant converter
Stray capacitance causing gain distortion is usually dependant upon the stray capacitance that is distributed to
the high frequency transformer, especially primary side winding so that it is impossible to avoid the gain
distortion unless it is removed. Stray capacitance in high frequency transformers usually increases as the
distance between each winding layer decreases, and / or the number of winding layers increases. Simple ways to
reduce stray capacitance are to lengthen the distance between the layers of the primary side winding, add more
insulation tape between each layer, and reduce the number of winding layers. Unfortunately, these ways cannot
remove the parasitic capacitance completely; therefore, it needs an easy way to avoid it rather than to remove it.
Some ways to avoid gain distortion include:
a) Burst Mode Operation
The burst mode function is one of the well-known ways to regulate the output voltage in a conventional
converter controlled by PWM (Pulse Width Modulation) when a controller is under a range not to regulate an
output voltage at no load condition due to a saturation voltage of transistor built in photo-coupler. This function
is traditionally used not only to increase efficiency under light load conditions but to also avoid the case of not
controlling an output voltage. It can be also implemented in an LLC resonant converter. Figure 6 shows a
typical LLC resonant converter using FSFR-series designed especially for a resonant converter by Fairchild
Semiconductor and its burst mode operating waveforms. A maximum & minimum operating frequency can be
easily set by the resistors, Rmax & Rmin. When the operating frequency increases up to maximum frequency set
by Rmax and a voltage on ‘CON’ pin decreases to the burst-on-threshold level, the controller goes into the burst
mode operation. Therefore, a maximum frequency is set at front of a frequency of starting to increase gain by
the parasitic capacitance and leakage inductance and then if the load condition becomes light and the operating
frequency increases to the maximum frequency, the controller can regulate the output voltage under the burst
mode operation without any gain distortion.
b) Increasing M Factor
Table 1 shows an example of designed L-L-C parameters for 4 and 10 of m factor, with the same input & output
voltage and current electrical specifications. As shown in the Table 1, the resonant inductance, Lr of m for 4 is
relatively higher than one of m for 10. As mentioned above, the resonant frequency, ωs which generates the gain
distortion is formed by Lr and Cs. If either Lr or Cs decreases, it can push up ωs to higer frequency. Hence, it
could prevent the increase of the output voltage of the LLC converter under no load condition.
Table 1. An example of designed key LLC parameters with m factor of 10 & 4
4
m factor
10
Required Maximum Gain
1.33
Turn-ratio (n1)
8.0
AC Resistor (Rac)
169 [ohm]
Q factor
0.28
0.6
Resonant Frequency
100 [kHz]
Resonant capacitor, Cr
33.6 [nF]
16.2 [nF]
Resonant Inductance, Lr
75.36 [uH]
156.1[uF]
c) Adding Dummy Resistor
Adding a dummy resistor is the best simple way to remove the gain distortion. As mentioned above, the gain
distortion occurs with light or no load condition. By adding a dummy resistor, a required maximum operating
frequency of the LLC resonant converter is put at the front of a frequency of the beginning of gain distortion.
However, this way cannot be applied to applications in which stand-by power is prioritized due to power
dissipation by the dummy resistor. It is usually used at power supplied for the LCD TV which is composed with
an auxiliary power supply and LLC resonant converter.
An LLC resonant converter attracts a lot attention due to its many outstanding advantages, including optimal
design procedure. However, the gain distortion generated by parasitic capacitance and leakage inductance are
barely known. Many engineers - when confronted with the case of not regulating an output voltage, which is
increased under no load condition - are embarrassed. The proposed solutions in this paper prevents gain
distortion and allows the controlling of an output voltage in spite of no load condition.
Q1
Rectifier network
Resonant network
n:1
Controller
Vin
Iout
Vd
+
Lr
Q2
Rout
Lm
Vout
-
Controller & MOSFETs
Cr
Transformer
Lr
Lm
Rac
Cr
Figure 1. A basic circuit of an LLC resonant converter
Inductor
Transformer
n:1
Lr
Integrated Transformer
n:1
Llk,se
Llk,pri
c
Lm
Lm
Cr
Cr
(a)
(b)
gain
Figure 2. A high frequency inductor & transformer with general bobbin (a)
and an integrated transformer with a sectional bobbin (b)
ZVS region
Below region
Above region
Load increase
peak gain
ZCS region
ωp
ωr
frequency
Figure 3. Voltage conversion ratio of an LLC resonant converter according to the operating frequency & load
variation
Controller
Q1
Vin
n:1
Iout
Vd
Cstray
Lr
+
Q2
Cstray
Rout
Lm
Vout
-
Cstray
Cr
Transformer
Lr
Lm
Cstray
Rac
Cr
gain
Figure 4. A practical LLC resonant converter with stray capacitance
No load @ Ideal
20% Load @ Practical
10% Load @ Practical
No load @ Practical
rease
to inc
s
t
r
a
st
Gain
ωp ωr
ωs
frequency
Figure 5. Ideal & practical voltage conversion ratio of an LLC resonant converter according to the operating
frequency & load variation
Cr
VIN
iCr
Vcc
LVCC
vCON
vCTR
VDL
vCON
RT
Rmax
Rmin
CON
FSFR-series
HVCC
iCr
CTR
vCTR
CS
SG
PG
Figure 6. Typical LLC resonant converter using FSFR-series and its burst mode operating waveforms