AN-9729 datasheet(3/17 Pages) FAIRCHILD

Part #	AN-9729

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

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AN-9729

APPLICATION NOTE

www.fairchildsemi.com

Rev. 1.0.1 • 11/16/12

3

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:

sin(

)

2

o

ac

I

t









(1)

and VRI is given as:

sin(

)

0

sin(

)

0

RI

o

RI

o

VV

if

t

VV

if

t











(2)

where Vo is the output voltage.

The fundamental component of VRI is given as:

4

sin(

)

F

o

RI

V

Vt







(3)

Since harmonic components of VRI are not involved in the

power transfer, AC equivalent load resistance can be

calculated by dividing VRI

F by Iac as:

22

88

F

o

RI

ac

o

ac

o

V

RR

II







(4)

Considering the transformer turns ratio (n=Np/Ns), the

equivalent load resistance shown in the primary side is

obtained as:

2

8

ac

o

n

RR





(5)

By using the equivalent load resistance, the AC

equivalent circuit is obtained, as illustrated in Figure 6,

where Vd

F and VROF are the fundamental components of

the driving voltage, Vd, and reflected output voltage,

VRO (nVRI), respectively.

pk

ac

I

4

sin(

)

F

o

RI

V

Vwt





)

sin(

2

wt

I

o

ac



 

Figure 5. Derivation of Equivalent Load Resistance Rac

VO

Lm

Lr

Cr

Ro

VIN

Vd

F

(nVRI

F)

Lm

Lr

Cr

Rac

Np:Ns

Vd

+

-

+

VRI

n=Np/Ns

2

8

ac

o

n

R





+

-

VRo

F

Figure 6. AC Equivalent Circuit for LLC

Resonant Converter

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:

2

22

4

sin(

)

2

4

sin(

)

2

() (

1)

(1)

(

1)(

1)

o

FF

RORI

o

FF

in

dd

in

o

po

o

nV

t

Vn V

n V

M

V

VV

V

t

m

jm

Q











 















(6)

where:

2

8

,,

11

1

,,

p

pm

r

ac

o

r

op

rac

rr

p

r

L

n

LL

L

R

m

L

Q

CR

LC

L C













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:

2

22

(1)

2

1

p

o

in

o

p

m

nV

Mat

V



 















(7)

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.

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

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