Fairchild AN-9729 service manual

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AN-9729

LED Application Design Guide Using Half-Bridge LLC
Resonant Converter for 100W Street Lighting

Introduction

This application note describes the LED driving system
using a half-bridge LLC resonant converter for high
power LED lighting applications, such as outdoor or street
lighting. Due to the existence of the non-isolation DC-DC
converter to control the LED current and the light
intensity, the conventional PWM DC-DC converter has
the problem of low-power conversion efficiency. The half­bridge LLC converter can perform the LED current
control and the efficiency can be significantly improved.
Moreover, the cost and the volume of the whole LED
driving system can be reduced.

Consideration of LED Drive

LED lighting is rapidly replacing conventional lighting
sources like incandescent bulbs, fluorescent tubes, and
halogens because LED lighting reduces energy
consumption. LED lighting has greater longevity, contains
no toxic materials, and emits no harmful UV rays, which
are 5 ~ 20 times longer than fluorescent tubes and
incandescent bulbs. All metal halide and fluorescent
lamps, including CFLs, n contain mercury.

The amount of current through an LED determines the
light it emits. The LED characteristics determine the
forward voltage necessary to achieve the required level of
current. Due to the variation in LED voltage versus
current characteristics, controlling only the voltage across
the LED leads to variability in light output. Therefore,
most LED drivers use current regulation to support
brightness control. Brightness can be controlled directly
by changing the LED current.

Consideration of LLC Resonant
Converter

The attempt 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 high­frequency 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

© 2011 Fairchild Semiconductor Corporation www.fairchildsemi.com
Rev. 1.0.0 • 3/22/11

[1-7]

.

Among various kinds of resonant converters, the simplest
and most popular 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
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 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.

Figure 1. Half-Bridge, LC Series Resonant Converter

To overcome the limitation of series resonant converters,
the LLC resonant converter has been proposed
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
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 applications where the switching
loss is more dominant than the conduction loss.

In most practical designs, 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
larger than the LC series resonant inductor (Lr), the
magnetizing inductance in an LLC resonant converter is
just 3~8 times Lr, which is usually implemented by
introducing an air gap in the transformer.

[2-4].

In this

[8-12]

. The

AN-9729 APPLICATION NOTE

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

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

flowing current through the anti-parallel diode.



The rectifier network produces DC voltage by
rectifying the AC current with rectifier diodes and a
capacitor. The rectifier network can be implemented
as a full-wave bridge or center-tapped configuration
with capacitive output filter.

voltage switching (ZVS) over the entire operating range.
All essential parasitic elements, including junction
capacitances of all semiconductor 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 Fairchild’s
FLS-XS series. It includes explanation of the LLC
resonant converter operation principles, 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.

Figure 3. Schematic of Half-Bridge LLC

Resonant Converter

LLC Resonant Converter and
Fundamental Approximation

Figure 3 shows a 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, a considerable
amount of magnetizing current (Im) exists, 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.

In general, the LLC resonant topology consists of three
stages shown in Figure 3; square-wave generator, resonant
network, and rectifier network.



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

I

p

I

m

I

DS1

I

D

V

IN

V

d

V

gs1

V

gs2

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

© 2011 Fairchild Semiconductor Corporation www.fairchildsemi.com
Rev. 1.0.0 • 3/22/11 2

AN-9729 APPLICATION NOTE

sin( )

2

I t

π

ω

⋅

sin( ) 0

sin( ) 0

ω

= + >

= − <

sin( )

V t

ω

ac o

R R

ac o

R R

sin( )

V wt

π

⋅

π

ac o

R R

RO RI o

V n V n V

⋅

⋅ ⋅

L C L C

o

ω ω

= = = =

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

o

=

ac

(1)

and VRI is given as:

V V if t

RI o

V V if t

RI o

ω

(2)

where Vo is the output voltage.

The fundamental component of VRI is given as:

4

V

F

o

=

RI

π

(3)

Since harmonic components of VRI are not involved in the
power transfer, AC equivalent load resistance can be
calculated by dividing V

F

by Iac as:

RI

F

8 8

VV

RI

= = =

I I

ac o

o

2 2

π π

(4)

Considering the transformer turns ratio (n=Np/Ns), the
equivalent load resistance shown in the primary side is
obtained as:

2

8

n

=

2

π

(5)

By using the equivalent load resistance, the AC
equivalent circuit is obtained, as illustrated in Figure 6,
where V

F

and V

d

F

are the fundamental components of

RO

the driving voltage, Vd, and reflected output voltage,
VRO (nVRI), respectively.

pk

I

ac

V

IN

n=Np/N

Figure 6. AC Equivalent Circuit for LLC

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:

M

= = = =

V V V

d d in

=

2 2

ω ω ω

( 1) ( 1)( 1)

2 2

ω ω ω

p o o

where:

L L L R R m

= + = =

p m r ac o

L

Q

= = =

C R

C

r

L

V

d

+

-

s

F

V

d

r

L

m

Np:N

s

2

8

n

=

2

π

L

C

r

r

L

m

Resonant Converter

4

n V

o

F F

F F

ω

2

( ) ( 1)

m

ω

o

j m Q

− + − −

8

, ,

π

1 1 1

r

, ,

ω ω

r ac

o p

sin( )

π

4

V

in

sin( )

2

π

−

2

n

2

r r p r

+

V

V

(nV

O

R

o

-

F

Ro

F

)

RI

+

V

RI

-

R

ac

t

ω

2

t

ω

(6)

L

p

L

r

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.

Equation (6) shows the gain is unity at resonant frequency
(ωo), regardless of the load variation, which is given as:

( 1)

m

o

− ⋅

ω ω

2

n V

M at

I

o

I

=

ac

)sin(2wt

The gain of Equation (6) is plotted in Figure 7 for
different Q values with m=3, fo=100kHz, and fp=57kHz.

⋅

V

in o p

ω

2 2

−

2

p

1

(7)

As observed in Figure 7, the LLC resonant converter

4

V

F

o

=

RI

Figure 5. Derivation of Equivalent Load Resistance Rac

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.

The operating range of the LLC resonant converter is
limited by the peak gain (attainable maximum gain),
which is indicated with ‘*’ in Figure 7. Note that the peak
voltage gain does not occur at fo or fp. The peak gain
frequency where the peak gain is obtained exists between

© 2011 Fairchild Semiconductor Corporation www.fairchildsemi.com
Rev. 1.0.0 • 3/22/11 3

AN-9729 APPLICATION NOTE

p r

L C

/

r r

L C

1

=

r r

L C

( )

p r

L L

//( )

r lkp m lks

L L L n L

p lkp m

L L L

= +

ac

R

1:VM

//( ) //

r lkp m lks lkp m lkp

L L L n L L L L

= +

e

j m Q

− + ⋅ − ⋅ − ⋅

L C L C

V o

ω ω

= = = =

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; the full load condition should be worst
case for the resonant network design.

1

f

=

p

2

π

1

f

=

o

2

π

QR=

ac

In Figure 8, the effective series inductor (Lp) and shunt
inductor (Lp-Lr) are obtained by assuming n2L

lks=Llkp

and
referring the secondary-side leakage inductance to the
primary side as:

L L L

p m lkp

= + = +

2

(8)

When handling an actual transformer, equivalent circuit
with Lp and Lr is preferred since these values can be
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.

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

M

@

f

o

Figure 7. Typical Gain Curves of LLC Resonant

Converter (m=3)

Consideration for Integrated
Transformer

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 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 ineffective design.

for integrated transformer is obtained by:

ω

2

( ) ( 1)

m M

2

n V

⋅

M

O o

= =

V

in

2 2

ω ω ω

( 1) ( ) ( 1) ( 1)

− + ⋅ − ⋅ −

2 2

ω ω ω

p o o

=

2 2

ω ω ω

( 1) ( ) ( 1) ( 1)

2 2

ω ω ω

p o o

where:

2

R L

8

n

e

R m

ac

e

Q

= = =

o

= =

C R

,

2 2

M L

π

V r

1 1 1

L

r

, ,

ω ω

o p

e

r ac

⋅ − ⋅

ω

j m Q

2

ω

( ) ( 1)

2

ω

o

p

r r p r

m m

V

e

−

(9)

The gain at the resonant frequency (ωo) is fixed regardless
of the load variation, which is given as:

L

M M at

p

L L m

− −

p r

m

1

(10)

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

= +

L L L

= +

lkp m lkp

2

//

L

p

M

=

V

−

virtual gain caused by the leakage inductance in the
transformer secondary side.

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

© 2011 Fairchild Semiconductor Corporation www.fairchildsemi.com
Rev. 1.0.0 • 3/22/11 4

AN-9729 APPLICATION NOTE

p r

L C

/

r r

L C

f V

M M

=

r r

L C

1

2of

1

2Sf

1

f

=

p

2

π

1

f

=

o

2

π

Gain (M)

B

e

QR=

e

ac

@

o

Figure 9. Typical Gain Curves of LLC Resonant

Converter (m=3) Using an Integrated Transformer

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 street LED lighting systems where the reverse­recovery loss in the rectifier diode is severe. Below­resonance operation 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.

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 above the
resonant frequency may cause too much frequency
increase at light-load condition. Above-frequency
operation requires frequency skipping to prevent too much
increase of the switching frequency.

A

Loa d Increase

I

II

Below

Res onance

(fs<fo)

Figure 10. Operation Modes According to the

Operation Frequency

I

p

I

DS1

I

D

I

p

I

DS1

I

D

I

m

I

m

Figure 11. Waveforms of Each Operation Mode

Above

Res onance

f

o

(fs>fo)

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 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 limited above the peak gain frequency.

f

s

(I) fs< f

I

(II) fs> f

I

o

O

o

O

© 2011 Fairchild Semiconductor Corporation www.fairchildsemi.com
Rev. 1.0.0 • 3/22/11 5

AN-9729 APPLICATION NOTE

Even though the peak gain at a given condition can be

M

Capacitive
Region

Peak Gain

Inductive

Region

obtained 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

f

s

V

d

V

d

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. There is a trade-off between
the available gain range and conduction loss.

2.2

2.1

2

I

I

p

DS1

I

I

p

DS1

Reverse Recovery ZVS

Figure 12. Operation Waveforms for Capacitive

and Inductive Regions

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 startup. Typically 10~20% of the maximum gain is
used as a margin, as shown in Figure 13.

Gain (M)

Peak Gain

Maximum Operation
Gain

max

(M

)

10~20% of M

max

1.9

1.8

1.7

1.6

1.5

Peak Gain

1.4

1.3

1.2

m=5.0

1.1

1

0.2 0.4 0.6 0.8 1 1.2 1.4

m=9.0

0.3

0.5 0.7 0.9 1.1 1.3

m=6.0

m=7.0m=8.0

Q

m=4.5

m=4.0

m=3.5

m=2.25

m=2.5

m=3.0

Figure 14. Peak Gain (Attainable Maximum Gain)

vs. Q for Different m Values

f

o

f

s

Figure 13. Determining the Maximum Gain

© 2011 Fairchild Semiconductor Corporation www.fairchildsemi.com
Rev. 1.0.0 • 3/22/11 6