LLC DC/DC

Analysis and Implementation for A Half-Bridge DC/DC LLC Resonant Converter

I

DC/DCPWM

PWM

LLCDC/DC

(1)

(SRC)(2)(PRC)(3)

(SPRCLCC)

LLCLCC

LLC(1)

(2)(3)()

(4)

IsSpice

LLC

LLC V 150=DCV

V 24=oV W100=oP % 88.9=h

II

Abstract

In general, front-end DC/DC converters are classified into two types of

pulsewidth modulation converters and resonant converters. Since a PWM converter

is operating in hard switching, it leads to large switching losses so that the

efficiency is degraded. A resonant converter with soft switching is thereby

developed to reduce the switching loss and increase the efficiency. Therefore, an

LLC resonant converter is investigated in this thesis. It is employed as the front-end

DC/DC converter with high efficiency, high power density and high reliability on its

performances.

In the thesis, three types of traditional resonant converters are introduced. They

are series resonant converter (SRC), parallel resonant converter (PRC) and series

parallel resonant converter (SPRC, or LCC). The switching frequencies of these

converters must increase to maintain a regulated output voltage, when the input

voltage increases and the load becomes light. However, more circulating energy will

be resulted form the higher switching frequencies.

To proceed, the operating principle of an LLC resonant converter is presented.

Its performances are compared with those of an LCC resonant converter. The LLC

resonant converter exhibits the advantages over LCC converter. The main switches

achieve ZVS operation and rectifier diodes have no reverse recovery current. The

ZVS operation region of the converter increases when the loads become light. The

circulating energy is still small even if the input voltage increases.

Finally, the theoretical analysis is validated by IsSpice simulations and

experimental results. It reveals that the LLC resonant converter achieves ZVS

operation despite variations in input voltage and load resistance. A prototype of

W100 output LLC resonant converter with efficiency of % 88.9 is implemented in

this thesis.

III

..................................................................................................................... I

.................................................................................................................... II

.......................................................................................................................... III

....................................................................................................................V

............................................................................................................ 1-1

1.1 .................................................................................... 1-1

1.2 DC/DC.......................................................... 1-2

1.3 ........................................................................................ 1-3

1.4 ........................................................................................ 1-3

1.5 ................................................................................................ 1-4

........................................................................ 2-1

2.1 ............................................................ 2-1

2.2 ................................................................................ 2-2

2.2.1 ............................... 2-2

2.2.2 ........................................................... 2-3

............................................................ 3-1

3.1 ........................................................................ 3-1

3.2 ........................................................................ 3-6

3.3 .................................................................. 3-11 3.4 SRCPRC LCC ................................ 3-13

3.5 LLC ..................................................................... 3-14

LLC............................................................................ 4-1

4.1 LLC ............................................................................... 4-1

4.2 LLC LCC .................................. 4-4

4.3 LLC ........................................... 4-9

IV

4.3.1 (II) ................................................................................ 4-11

4.3.2 (I) ................................................................................. 4-11

4.3.3 (III)............................................................................... 4-12

LLC DC/DC.......... 5-1

5.1 LLC ................................................... 5-1

5.2 LLC ................................................... 5-3

............................................................................ 6-1

6.1 ........................................................................ 6-1

6.1.1( rL , rC , mL ) ..................................... 6-2

6.1.2 oC ................................................... 6-5

6.2 ........................................................................ 6-7

LLC ................................................................ 7-1

7.1 IsSpice .................................................................. 7-1

7.2 ................................................................................... 7-3

7.3 ........................................................... 7-5

7.4 ....................................................................................... 7-8

7.5 ..................................................................... 7-12

7.6 ............................................................................................. 7-16

........................................................................................ 8-1

8.1 ........................................................................................................ 8-1

8.2 ................................................................................................ 8-1

V

1.1 .......................................................................... 1-1

1.2 .......................................................................... 1-2

1.3 .......................................................................... 1-2

2.1 / ................................................. 2-2

2.2 ZVS/ ............................................................. 2-3

2.3 ZCS/.............................................................. 2-3

2.4 .............................................................. 2-4

2.5 ...................................................................... 2-5

2.6 ...................................................................... 2-5

3.1 .................................................................. 3-1

3.2 (SRC)................................................................ 3-1

3.3 ( 1S , 2S ) ............................................................ 3-2

3.4 (a)+ (b) eqR ....................................... 3-2

3.5 .................................................................................. 3-3

3.6 .............................................................. 3-5

3.7 ...................................................................... 3-6

3.8 (PRC)................................................................ 3-6

3.9 (a)+ (b) eqR ............................... 3-7

3.10 .................................................................................. 3-8

3.11 .................................................................... 3-10

3.12 .................................................................... 3-10

3.13 (LCC).......................................................... 3-11

3.14 ............................................................................ 3-11

3.15 ................................................................ 3-12

3.16 ................................................................ 3-12

VI

3.1 ......................................................... 3-14

3.17 LLC......................................................................... 3-14

4.1 LLC........................................................................... 4-1

4.2 (a)LCC (b)LLC........................................ 4-1

4.1 Q ..................................................................................... 4-3

4.3 .............................................................................................. 4-4

4.4 LLC....................................................................... 4-4

4.5 (a) )(wX eqR (b) ZCSZVS .................................... 4-6

4.6 (a)ZCSZVS (b)LCC ........................ 4-7

4.7 (a) )(wX eqR (b) ZCSZVS .................................... 4-8

4.8 (a)ZCSZVS (b)LLC......................... 4-9

4.9 LLC..................................................................... 4-10

4.10 LLC................................................................. 4-10

4.11 LLC(II) ........................................................... 4-11

4.12 LLC(I)............................................................. 4-12

4.13 LLC(III) .......................................................... 4-12

5.1 LLC........................................................................... 5-1

5.2 ++...................................................... 5-1

5.3 ( 1v , 1i ) .............................................. 5-2

5.4 (a) LLC (b) .................................................. 5-3

5.5 .............................................................................. 5-4

5.6 .............................................................................. 5-4

5.7 .............................................................................. 5-6

5.8 .............................................................................. 5-7

5.9 .............................................................................. 5-9

5.10 ............................................................................ 5-10

5.11 ............................................................................ 5-11

5.12 1v 1i .............................................. 5-12

VII

5.13 LLC......................................... 5-12

6.1 LLC........................................................... 6-1

6.1 LLC....................................................... 6-1

6.2 (a)LLC( rL , rC , mL )................................ 6-2

6.2 (b)LLC oC ............................................. 6-2

6.3 (a)LLC (b) ....................................... 6-2

6.4 ( rL , rC )................................................................ 6-5

6.2 .............................................................................................. 6-5

6.5 .......................................................................................... 6-6

6.3 LLC................................................... 6-7

6.6 LLC........................................... 6-8

6.7 (1gs

v ,2gs

v )....................................................................... 6-8

6.8 LLC....................................................... 6-9

7.1 LLC....................................................... 7-1

7.2 1S 1gsv 1Sv ............................................................... 7-1

7.3 2S 2gsv 2Sv ............................................................... 7-2

7.4 rL

i mL

i ..................................................... 7-2

7.5 oi ........................................................................... 7-3

7.6 rC

v ..................................................................................... 7-3

7.7 ZVS:1S ..................................................................................... 7-3

7.8 ZVS:2S .................................................................................... 7-3

7.9 rL

i V 24 ,kHz 50 ,V 150 === osDC VfV .................................. 7-4

7.10 oi V 24 ,kHz 50 ,V 150 === osDC VfV ............... 7-4

7.11 rC

v V 24 ,kHz 50 ,V 150 === osDC VfV ......................... 7-4

7.12 .......................................................................................... 7-5

7.13 ............................................................................... 7-5

7.14 .............................................................. 7-5

7.1 .......................................................................................... 7-6

VIII

7.15 rL

i V 140=DCV kHz 50=sf V 34.22=oV ........................ 7-6

7.16 rL

i V 140=DCV kHz 1.48=sf V 24=oV .......................... 7-6

7.17 rL

i V 160=DCV kHz 50=sf V 56.25=oV ........................ 7-6

7.18 rL

i V 140=DCV kHz 7.56=sf V 24=oV .......................... 7-6

7.2 .................................................................................................. 7-7

7.19 rL

i W= 10R kHz 50=sf V 2.25=oV ............................... 7-7

7.20 rL

i W= 10R kHz 9.53=sf V 24=oV .............................. 7-7

7.21 rL

i W= 5R kHz 50=sf V 3.722=oV .............................. 7-7

7.22 rL

i 5 W=R kHz 9.14=sf V 24=oV ................................ 7-7

7.23 LLC........................................................... 7-7

7.24 .......................................................................... 7-7

7.25 .......................................................................... 7-8

7.26 )(~)(~ svsv ctrlo ......................................................... 7-8

7.27 .................................................................................. 7-9

7.28 0>k ............................................................................... 7-10

7.29 0

IX

7.40 rL

i W= 5R kHz 9.48=sf V 24=oV .............................. 7-13

7.5 oV ............................................................................ 7-14

7.41 ........................................................ 7-14

7.42 .................................................................... 7-14

7.43 ........................................................ 7-15

7.44 ............................................................................................ 7-15

1-1

1.1

(power supply)

(power density)

(DPSDistribute Power

System)1.1DC/DC

DC/DC

V 400~300 DC/DC

V 400~300 (DC bus) V 4812

DC/DC

EMI filter

front endDC/DC

converter

DC bus(12/48V)

on-boardconverter #1

high voltageVRM

PFC

300-400V

AC/DC on-board

converter #3low voltage

VRM

on-boardconverter #2

1.1

1-2

1.2 DC/DC

DC/DCPWM

PWM

PWM

(1)(SRC : Series Resonant Converter)

(2)(PRC: Parallel Resonant Converter)

(3)(SPRC LCC: Series Parallel Resonant Converter)

( V 400 )

1.2

h

inVV 300 V 004

1.2

LLC

1.3

h

inVV 300 V 004

1.3

1-3

DC/DC

(1) (efficiency)

(2) (line regulation)

(3) (load regulation)

1.3

[Bha93][Yan03](SRC)

[KUS91][Yan03](PRC)

[Ste88] [Yan03](SPRC)

[YLZH02][LLLW05](LLC)

1.4

(1) (SRC, PRC, SPRC)

(2) LLCIsSpice

(3) LLC

1-4

1.5

LLC

LLCDC/DC

LLC

2-1

2.1

2.2

2.1

on/off

(1)

(2)

2-2

(3)

2.1

)(tv

t

)(ti

t

)(tv

)()()( titvtp =

2.1 /

2.2

2.1

2.2.1

) ,( CL

/2.1/

on

off

on

on

(ZVS: Zero Voltage Switching)2.2

off

off

(ZCS: Zero Current Switching)2.3

2-3

)(tis)(tvs

onoff: S

2.2 ZVS/

)(tis)(tvs)(tvs

offon: S

2.3 ZCS/

2.2.2

l (RC: Resonant Converter)

(SRC)

(PRC)(LCC)LLC

SRCPRCLCC

LLC

2.4(ZVS/ZCS)

ZVS/ZCS

2-4

CL

Rgv

gi

inZ

2.4

(1) ZVS

2.4 inZ

gi gv

/

onoff ZVS

(2) ZCS

2.4 inZ

gi gv

/

offon ZCS

l (QRC: Quasi-Resonant Converter)

/ZVS/ZCS

( L ,C )/

(1)

2.5

(a) 2.5(a) rL Lri

( dtdis )

2-5

rLS

rLSii =

rLS

rLSii =

rC

rCv+ -

rLS

rLSii =

rC

rCv+ -

SD

Sv Si

off on

t

Sv Si

off on toff on

SvSi

off on t

Sv

off

(a)offon (b)onoff (c) ( ) 0tiS

2.5

(b) 2.5(b)on Lri

off rC rr CL -

Lri offZCS

(c) 2.5(c)

Lri

offZCS

(2)

2.6

S S

rCrC

v+ -

+ -SvrC

rCv+ -

+ -Sv

rLS

rC

rCv+ -

+ -SvrL

SD

SiSvonoff

t

SvSi

offon toffon

Si Si

offon t

Sv

on

(a)onoff (b)offon (c) ( ) 0tvS

2.6

(a) 2.6(a) rC

( dtdvs )

2-6

(b) 2.6(b)offrC

v

on rL rr CL -

rC

v onZCS

(c) 2.6(c)

rC

v

onZVS

l (MRC: Multi-Resonant Converter)

ZVS

3-1

3.1

(SRC)(PRC)

(LCC)LLC

dcV

3.1

3.1

(SRC)3.2( 1S , 2S )

1S 2S 1S 2S

gv ( 1S , 2S )

(dead time) dT

xv (non-overlapping square wave)3.3

DCV

1C

2C

1S1S

D

2S 2SD

gvrL rC

oC R

1D

2D3D

4D

acv

gi

oV

aci

3.2 (SRC)

3.4(a)

3.4(b)3.4(b)

3.4

3-2

t

t

sDT sDTdT

sT

offon

2

1

SS

offon

2

1

SS

offon

1

2

SS

DCV

DCV-

)(tS

)(tvg

3.3 ( 1S , 2S )

oC R

1D

2D3D

4D

acv

aci

oVacv

aci

eqRxi

)(tvg)(tvg

rL rCrL rC

DCV

DCV-

DCV

DCV-

(a) (b)

3.4 (a)+ (b) eqR

sf rf

aci

sf (fundamental component)( rL ,

rC ) )(tiac

)sin()( tIti smac w= (3-1)

oC R(Cutoff

frequency) soc fRCf

3-3

m

T

sms

T

xs

Tx

I

dttIT

dttiT

ti sss

p

w

2

)sin(1 )(1)(

0

0

=

== (3-3)

(3-2) RIV mo )2( p= )(tvac oV )(tiac )(tvac

( )

==0)( ,0)( ,

)(sgn)(tiVtiV

tiVtvaco

acoacoac (3-4)

)sgn(

=0 ,10 ,1

:)sgn(xx

x (3-5)

oV )(tvac (Fourier series)

=

++=1

0 )sin()cos(2

)(n

snsnac tnbtnaatv ww (3-6)

)(tvac 0=na

oT

T so

T

sos

V dtt-V dttVT

b ss

s

p4)sin()()sin(2

2

2

0 1=

+= (3-7)

)(tvac

)sin(4)sin(1)( tVtbv sosfdlac wpw == (3-8)

(3-1)(3-2) (3-8)3.4(b)

R

RIV

tI

tV

iv

Rm

o

sm

so

fdlac

fdlaceq

2

)(

)(

8

244)sin(

)sin(4

p

pppw

wp

=

==

== (3-9)

3.23.5 rCrL

RReq 28

p=)( fdlgv )( fdlacv)(tig

3.5

3-4

)(1

1

)1(1

1

1)()(

)(

)(

ssQ

LsCLsL

RL

RsC

sL

Rsvsv

r

rs

rrrrr

r

eq

rr

eqr

r

eq

fdlg

fdlac

ww

www

++=

++=

++=

(3-10)

(quality factor) eqrrs RLQ w=: (resonant frequency)

rrr CL1:=w (characteristic impedance) rro CLZ =:

3.5(3-10) gi )( fdlgv

)(1

11

)(1)(

)()(

)(

)(

)(

ssQR

svRsv

svsi

r

rs

eq

fdlgeq

fdlac

fdlg

g

ww

++=

=

(3-11)

)(1

11)(

)(

)(

ww

www

w

r

rs

eqfdlg

g

jjQRjvji

-+= (3-12)

--= - )(tan

)()( 1

)( s

r

r

ss

sfdlg

sg Qjv

jiww

ww

w

w (3-13)

rs ww > sw gi

)( fdlgv 3.6

3.6

(1) rs ff > 1>rs ww

(ZVS)

(2) rs ff < 1

3-5

region operating

r

s

ww

)()(

)(

)(

w

w

jvjv

fdlg

fdlac

inV

R

sticCharacteriGain Voltage

Q

3.6

(3) gV B

( sQ )A )(Bsf )( Asf

(4) R gV oV

CA )(Csf )( Asf

MOSFETZVS

sf rf MOSFET

(switching loss)3.6

:

:

( R sQ )3.6BA

sw

:

R

sf 3.7 rs ff > sf

(3-13) gi gv

3-6

(circulating energy)

)(tvg

)(tig

)(tvg

)(tig

1sT

2sT

VVin 3001 =

VVin 4002 =

2112 ssss TTff >> 3.7

3.2

(PRC)3.8

( 1S , 2S )SRC3.3

3.33.9(a)

3.9(b) oL

DCV

1C

2C

1S 1SD

2S 2SD

gvrL

pC

oC R

1D

2D3D

4D

acv

aci

oV

oL

gi

3.8 (PRC)

3.1

)(tvac

)sin()( tVtv smac w= (3-14)

3-7

oC R

1D

2D3D

4Dacv

aci

oVacv

aci

eqRoI

yv

yv

)(tvg

rL

rC

DCV

DCV-

)(tvg

rL

rC

DCV

DCV-

(a) (b) 3.9 (a)+ (b) eqR

)(tvac )(tv y

sT

yo tvV )(= (3-15)

)sin()()( tVtvtv smacy w==

mT

sms

T

ys

TyVdttV

Tdttv

Ttv ss

s pw

2 )sin(1 )(1)(

0

0 === (3-16)

(3-16) mo VV )2( p= )(tiac oI

)(tvac )(tiac

( )

==0)( ,0)( ,

)(sgn)(tvItvI

tvItiaco

acoacoac (3-17)

oI )(tiac

=

++=1

0 )sin()cos(2

)(n

snsnac tnbtnaati ww (3-18)

0=na

oT

T so

T

sos

I dtt-I dttIT

b ss

s

p4)sin()()sin(2

2

2

0 1=

+= (3-19)

)(tiac

)sin(4)sin(1)( tItbi sosfdlac wpw == (3-20)

3.9(b)

3-8

RtI

tV

iv

Rso

so

fdlac

fdlaceq 8)sin(4

)sin(2

2

)(

)( p

wp

wp

=== (3-21)

3.83.10

pC

rL

RReq 8

2p=)( fdlgv )( fdlacv

)(tig

3.10

1)(1)(

1

1

1

)//1(

//1

)()(

2

2

)(

)(

++=

++=

+=

rpr

eq

rrr

eqr

r

eqr

fdlg

fdlac

sQ

s

RsLCLs

RsC

sL

RsC

svsv

ww

(3-22)

)(: rreqp LRQ w= rrr CL1:=w

rro CLZ =:

3.10(3-22) gi )( fdlgv

1)(1)(

)(11

1

11

)//1(

1)(

)(

2

2

)(

++

+=

++

+=

+=

rpr

rp

eq

eq

rrr

req

eq

eqr

rfdlg

g

sQ

s

sQ

R

sRLsCL

CsRR

RsC

sLsvsi

ww

w

(3-23)

3-9

1)(1)(

)(11

)()(

2)( ++-

+=

rpr

rp

eqfdlg

g

jQ

jQ

Rjvji

ww

ww

ww

w

w (3-24)

-+-=

+

--

-+

+-=

-+

+-=

>

---=

-

-

--

--

1)()()(1tan

180

1)(

)(1

)(1

1)(

)(1

)(

tan180

1)(

)(1

tan)(tan180

, 1)(

)(1

tan180)(tan)(

)(

21

2

2

1

2

11

2

11

)(

r

s

r

sp

r

s

p

r

s

r

s

p

r

sp

r

s

r

s

p

r

sp

r

s

r

s

p

r

sp

rs

r

s

r

s

p

r

sp

sfdlg

sg

QQ

QQ

QQ

QQ

QQ

jvji

ww

ww

ww

ww

ww

ww

ww

ww

ww

ww

ww

ww

ww

ww

ww

ww

w

w

(3-25)

rs ww > sw gi

)( fdlgv 3.11

>-+

+

> 3.12

sf (3-25) gi gv

(circulating energy)PRC

SRC

PRC

3-11

SRC

3.3

(SPRC, or LCC)3.13

DCV

1C

2C

1S 1SD

2S 2SD

gvrL

pC

oC R

1D

2D3D

4D

oV

oL

rC

acv

acigi

3.13 (LCC)

SRC

pC

PRC( rL , rC )

PRC rL ( rL , rC )

3.9

LCC3.14

RReq 8

2p=)( fdlgv

)( fdlacv

)(tig

3.14

111

)//1(1

//1

)()(

2 ++++=

++=

r

p

reqeq

rpr

eqpr

r

eqp

g

ac

CC

CsRRsLCLs

RsCsC

sL

RsC

svsv

(3-27)

3.15

3-12

rs

ww

sticCharacteriGain Voltage

inV

R

)()(

)(

)(

w

w

jvjv

fdlg

fdlac

3.15

3.15:

:

( RQ)BA

QSRCPRCPRC

ZVS

:

R

sf CA

3.16

)(tvg

)(tiac

)(tvg

)(tiac

3.16

3-13

3.4 SRCPRCLCC

n

(1) SRC3.7

(2) PRC pQ sQ PRC

PRCSRC

(3) LCCSRC pC

pC LCCSRCPRC

( rL , rC )

LCCPRC

n

(1) SRC3.6 sQ R

sf

(2) PRC3.11 pQ R

sf SRC

(3) LCCSRCPRCSRCPRC

n

sf

n

3.1

3-14

3.1

SRC PRC LCC (SPRC)

(

)

3.5 LLC

SRCPRCLCC

V 400~300

LLC3.17

2D

DCV

1S 1SD

2S 2SD

gvrL rC

oC RoV

1D

2i

3i

2v

3v

mL 1v

1irLi1:1:n

rCv mLi

oi

3.17 LLC

rL mL rC LCC

(LCD: Liquid Crystal Display)(PDP: Plasma Display Panel)

4-1

LLC

3.1

LLC4.14.2

LLC4.3LLC

(II)

4.1 LLC

4.1LLCLCC pC

mL 4.2LLC

( 0=eqR )

rrr CL1:1 =w ( =eqR )

rmrr CLL )(1:2 +=w RnReq22 )8( p= 3.1

2D

DCV

1S 1SD

2S 2SD

gvrL rC

oC RoV

1D

2i

3i

2v

3v

mL 1v

1irLg ii =1:1:n oi

4.1 LLC

mL

rL

eqR

rC

eqR)( fdlgv

)( fdlacv )( fdlacv

)( fdlgv

)(tig)(tig rL rC

(a) (b)

4.2 (a)LCC (b)LLC

4-2

4.2(b)

1)(

)//(1//

)()(

23

2

)(

)(

++++=

++=

sRLsCLCLs

RLCL

CLs

RsLsC

sL

RsLsvsv

eq

mrmrr

eq

mrr

rm

eqmr

r

eqm

fdlg

fdlac

(4-1)

Lin

Q eqR rL mL rC

(4-1)

m

eq

eq

m

LR

ssRL -

==+ 01 (4-2)

0)( 23 =+++ sRLsCLCLs

RLCL

eq

mrmrr

eq

mrr (4-3)

01// m

2 =++rrr

eq

CLs

LLR

s (4-4)

rm LL >>

012 =++

rrr

eq

CLs

LR

s (4-5)

rr

nr

eqn CLL

R 1, 2 2 == wzw (4-6)

( rrm LLL // )

eq

r

r

RCL

Q ==z21 (4-7)

W= 7.5R 5.2=n W== 9.28)8( 22 RnReq p H 65 m=rL

4-3

H 273 m=mL F 60 nCr = (4-1)

011045.91003.2103.69 -62-113-17 =+++ sss (4-8)

-=

-=5

3,2

51

10)97.307.2(

1035.1

js

s (4-9)

( )( )

1025

1052

55

1005.20, 1014.42

01005.201014.4

010)97.307.2( 10)97.307.2(

==

=++

=-+++

nn

ss

jsjs

wzw

(4-10)

Q

1.0821

==z

Q (4-11)

(4-7)( rmr LLL // )

14.1=Q (4-12) Q(4-7)4.14.1 eqR

Q Q

4.1 Q

][ WeqR Q eqrr RCLQ /=

5.1 6.49 6.5

10.1 3.23 3.25

15.2 2.14 2.17

20.3 1.58 1.62

28.9 1.08 1.14

35.5 0.86 0.93

40.5 0.78 0.81

76 1.51 0.43

101.3 2.04 0.32

4-4

4.2(b)A

r

rr

rr sC

CLssC

sLsZ 11)(2

1+

=+= (4-13)

eqm

eqmeqm RsL

RsLRsLsZ

+

== //)(2 (4-14)

4.3Q

H 65 m=rLF 60C nr =

W= 9.28eqRH 273 m=mL

w51006.51 =

rrCL

W= 9.32r

r

CL

51006.1 =m

eq

LR

)(1 wjZ

)(2 wjZQ

4.3

4.2 LLCLCC

(4-1) H 65 m=rL H 273 m=mL F 60 nCr = LLC

4.4Q(4-7)Q

16.1 rf14.1 rf12.1 rf1rf18.0 rf16.0 rf12.0 rf 14.0 rf

AC

B

)()(

)(

)(

jvjv

fdlg

fdlac

0.5

1

1.5

2

2.5

3

0

=Q 13

3.23

1.08

1.51

2.04

W= 5.2eqR

W= 1.10eqR

W= 76eqR

W= 101.3eqR

W= 9.28eqR

4.4 LLC

4-5

4.4

R

sw 4.4BA

A sw ( rL , rC ) 1rw ( rL , rC )

LLC

( R)4.4BC

3.2PRC

Lin

( eqR )

(1) LCCZVS

(2) LLCZVS

LCC ZVS

4.2(a)LCC

)()(:1

)1(

)//(1)(

)//(1)(

222

2

www

ww

w

ww

ww

jXRCR

CRjRC

Lj

RCjCj

LjjZ

RsCsC

sLsZ

peq

peqeq

rr

eqpr

rin

eqpr

rin

+=+-

+-=

++=

++=

(4-15)

( )

++--=

+=

ppeqprr

peq

eq

CCRCCLX

CRR

R

wwwwww

ww

)(1111)(

1)(

2

222 (4-16)

)(wX eqR 4.5(a)

4-6

eqR 0)( =wX

w critw (4-16)

( ) 0)(1111)( 2 =+

+--=pcritpeqcritpcritrcrit

rcritcrit CCRCCLX

wwwwww (4-17)

(1) 0=eqR 0: == eqRcrit ww

rr

RrR

rR CLCL

eq

eq

eq

101 00

0 ==- ==

= www (4-18)

(2) =eqR == eqRcrit ww :

)//(

1011

prrR

pRrRrR CCLCC

Leq

eqeq

eq==-- =

=== www

w (4-19)

rpr CCC

4.5(a) critww > 0)( >wX )( wjZ in

LCC gi gv ZVS

critww < 0)( eqRs ww W= 20eqR ZVS 20=> eqRs ww

4-7

( W= 20eqR ) 2010 == < eqeq RR ww LCC

ZVS

eqR

w

)()(

)(

)(

w

w

jvjv

fdlg

fdlac

critw

1020

0 10=eqRw 20=eqRw0=eqRw 10=eqRw 20=eqRw =eqRw

ZVS

ZCS

)(

20

=eqR

10=eq

R

(a) (b)

4.6 (a)ZCSZVS (b)LCC

( W= 2010eqR ) critw

1020 == > eqeq RR ww ZVS

sw 20=> eqRs ww sw

(1) ZVS crits ww >

(2) ( eqR ) critw ZVS sw

LLC ZVS

4.2(b)LLC

)()(:

)1(

)//(1)(

)//(1)(

222

222

www

ww

ww

ww

ww

jXRLR

RLjRLC

Lj

RLjCj

LjjZ

RsLsC

sLsZ

meq

eqmeqm

rr

eqmr

rin

eqmr

rin

+=+

++-=

++=

++=

(4-20)

4-8

+-+-=

+=

22

3

222

22

)()(1)(

)(

eqm

mm

rr

meq

eqm

RLLL

CLX

LRRL

R

ww

ww

ww

ww

w (4-21)

)(wX eqR 4.7(a)

eqR 0)( =wX

w critw (4-21)

0)(

)(1)( 223

=+

-+-=eqmcrit

mcritmcrit

rcritrcritcrit RL

LLC

LXw

ww

www (4-22)

(3) 0=eqR 0: == eqRcrit ww

rr

RrR

rR CLCL

eq

eq

eq

101 00

0 ==- ==

= www (4-23)

(4) =eqR == eqRcrit ww :

rmr

RmRrR

rR CLLL

CL

eqeq

eq

eq )(101

+==+- ==

== www

w (4-24)

rmr LLL >+ )( == > eqeq RR ww 0 4.7(a) eqR critw

4.7(b) eqR critw critww >

4.7(a) critww > 0)( >wX )( wjZ in

LLC gi gv ZVS

critww < 0)(

4-9

4.4 10=eqR 20=eqR

4.8(b)4.8(a) W= 10eqR ZVS

10=> eqRs ww W= 20eqR ZVS 20=> eqRs ww

( W= 20eqR ) 2010 == > eqeq RR ww LLC

ZVS

eqR

w

)()(

)(

)(

w

w

jvjv

fdlg

fdlac

1020

critw0 10=eqRw20=eqRw0=eqRw10=eqRw20=eqRw=eqRw

)( 20

=eqR

10=eq

R

(a) (b)

4.8 (a)ZCSZVS (b)LLC

( W= 2010eqR ) critw

1020 == < eqeq RR ww 10=> eqRs ww 20=> eqRs ww 10=eqR

ZVSZVS

(1) ZVS crits ww >

(2) ( eqR ) critw ZVS sw

4.3 LLC

LLC4.9

H 65 m=rL H 273 m=mL F 06 nCr = (a)(b)Region (I)

Region (II)Region (III)

4-10

14.1 rf12.1 rf1rf18.0 rf16.0 rf12.0 rf 14.0 rf

AC

B

=Q W= 5.2eqR

W= 1.10eqR

W= 76eqR

W= 101.3eqR

W= 9.28eqR

2rf

)(a )(b

4.9 LLC

4.2(b)(4-1) gi )( fdlgv

1)(

//1

)//(1//

)()(

)()(

)()(

)(

23

2

)()(

)(

)(

++++

+

=

++

=

==

sRL

sCLCLsR

LCL

sCsR

CL

RsLRsLsC

sL

RsL

svsi

svsv

svsi

sY

eq

mrmrr

eq

mrr

req

rm

eqmeqm

rr

eqm

fdlac

g

fdlg

fdlac

fdlg

g

(4-25)

LLC4.10 H 65 m=rL

H 273 m=mL F 06 nCr =

16.1 rf14.1 rf12.1 rf1rf18.0 rf16.0 rf12.0 rf 14.0 rf

)()(

)( wwjv

ji

fdlg

g

=Q

4.10 LLC

4-11

)()()( )( www jvjijY fdlgg= ZVS

gi gv 0)(

4-12

1.5=Q 4.10

ZVS

oi

gv

mLi

rLi

1v

4.12 LLC(I)

4.11( 0tt < )off

4.114.12 1rs ff > 1rs TT <

rL

i mL

i mL

1i

1D 2D (reverse recovery current)

4.3.3 (III) 2rs ff <

4.13 kHz 13=sf

oi

gv

1v

mLi

rLi

4.13 LLC(III)

4-13

kHz 35.32 =rf 1.5=Q 4.10

ZCSrL

i gv 4.13

MOSFETZVS

(a) Region (I)Region (II)ZVS regions

(b) Region (III)ZCS region

Region (I) 1D 2D Region (II)

5-1

LLCDC/DC

LLC(II)

Lin

LLC

5.1 LLC

5.1LLC

5.2

oC oV Lin

5.2

5.2

2D

DCV

1S 1SD

2S 2SD

gvrL rC

oC RoV

1D

2i

3i

2v

3v

mL 1v

1irLi1:1:n

rCv mLi

oi

5.1 LLC

3Dv

oV

2Dv

2i

3i

2v

3v

1v

1i1:1:n

1D

2D

5.2 ++

5-2

5.2

01 >i 01 01i (5-1) 0312 >+= inii ( on1 D , off2 D ) oo nVvVv == 12

=- oVvD 32 on 32 vv = oVVo -= off2 D

(2) < 01i (5-1) 0123 >-= niii ( off1 D , on2 D ) oo nVvVv -=-= 13

= oVvD 21 on 32 vv = oVVo -= off1 D

(3) 321 vvnv == ovv 2 ovv - 3 oo nVvnV - 1

01 >i 132 niiiio =+= 01

5-3

5.4(a)LLC

5.35.4(b)

5.4(b)LLC

mL 1v

1i

5.3

2D

DCV

1S 1SD

2S 2SD

gvrL rC

oC RoV

1D

2i

3i

2v

3v

mL 1v

1i1:1:n

rCv mLi DCV

1S 1SD

2S 2SD

gvrL rC

mLrC

v mLirL

irL

ioi

(a) (b)

5.4 (a) LLC (b)

5.2 LLC

(1) sT oC ovD

oV sT ov oV

(2)

(3)

LLC sT

(1) [ - 0tt ]( 1S off 2S on 1SD off 2SD off)

( 1S , 2S )(off, on)

5.35.5(b)

-= 0tt 2S onoff

rL mL rC

5-4

mL 1v

1i

DCV

1S 1SD

2S 2SD

gvrL rC

mLrC

v mLi

DCV

mL1v

1S 1SD

2S 2SD

gvrL rC

rCv mLi

[ ])( 5tvCr

[ ])( 5tiLr[ ])( 5tiLm

0

1v

1i

onV

onV-

-0t

0Lri

(3) [ 1t , 2t ]( 1S on 2S off off1 SD 2SD off)

1tt = 1SD 1S

on5.7(a) 0>Lri

mL onV ( rL , rC )

5.7(b)

mL 1v

1i

DCV

1S 1SD

2S 2SD

gvrL rC

mLrC

v mLi

onV

1i

DCV

1S 1SD

2S 2SD

gvrL rC

mL

rCv mLi

[ ])( 1tvCr

[ ])( 1tiLr[ ])( 1tiLm

0

1v

1i

onV

onV-

2t 1t

0>rL

i 0>rL

i

(a) (b) (c) 5.7

=

=

--=

oL

m

LC

r

CoDCL

r

nVdt

tdiL

tidt

tdvC

tvnVVdt

tdiL

m

r

r

r

r

)(

)()(

)()(

(5-13)

0)( 1 =ti rL )( 1tv rC )( 1tiLm

5-7

( )

--=

-+-+--+=

---

=

)()()(

)(sin)()(cos)()(

)(sin)(

)(

11

1111111

111

1

tittLnVti

nVVttZtittVtvnVtv

ttZ

nVtvVti

mm

rrr

r

r

Lm

oL

oDCrrLrDCCoC

rr

oCDCL

ww

w

(5-14)

rrr CLZ =:1 rrr CL1:1 =w 0)( 11 - ttrw [ ]21 , ttt )(sin 11 ttr -w

)()(sin 1111 tttt rr -- ww (5-15)

(5-14) )()( 22 titi LmLr = 0)( 1 =ti rL

)()()()(

1121211

1 tittLnVtt

ZnVtvV

m

rL

m

or

r

oCDC --=---

w (5-16)

1

11

1122 )(

)(:

r

DCCor

m

o

L

ZVtvnV

LnV

tittT

r

m

-++

=-=w

(5-17)

Lri Lmi

01 =i 5.3 oo nVvnVi -= 11 0 mL

(4) [ 2t , 3t ]( 1S on 2S off 1SD off 2SD off)

01 =i

5.8(b)( rL rC mL )

mL 1v

1i

DCV

1S 1SD

2S 2SD

gvrL rC

mLrC

v mLi

1v

DCV

1S 1SD

2S 2SD

gvrL rC

mL

rCv mLi

[ ])( 2tvCr

[ ])( 2tiLr[ ])( 2tiLm

0

1v

1i

onV

onV-

2t

3t0>rL

i 0>rL

i

(a) (b) (c)

5.8

5-8

--=

=

--=

)()()(

)()(

)()()(

tvtvVdt

tdiL

tidt

tdvC

tvtvVdt

tdiL

rr

m

r

r

rm

r

CLDCL

m

LC

r

CLDCL

r

(5-18)

)()( 22 titi mr LL = )( 2tv rC

( )

=

+-+--=

--

+-=

)()(

)(sin)()(cos)()(

)(sin)(

)(cos)()(

2222222

222

2222

titiVttZtittVtvtv

ttZ

tvVtttiti

rm

rrr

r

rr

LL

DCrrLrDCCC

rr

CDCrLL

ww

ww

(5-19)

rrmr CLLZ )(:2 += rrmr CLL )(1:2 +=w (5-15)

( )( ))(

)()(:

22

232233 tvV

titiZttT

r

rr

CDCr

LLr

-

-=-=

w (5-20)

)()(1 rmmCDC LLLvVv r +-=

oo nVvnV - 1 1S 1SD (on, off)

0)( 3 >ti rL 1S onoff

(5) [ 3t , 4t ]( off1 S onoff2 S 1SD off on2 SD )

3tt = 1S onoff 0>rLi

rL

i 2S

D 2S

D

5.9(a) 2S offon 2S

ZVS

5.8(a)5.9(a) 2S 3tt = onoff gv

DCV 0 V )()( 33 -+ = tvtv rr CC 5.8(b) =D=D mLvv1

)( mrmDC LLLV +- (5-8) )()( 331 ++ = tvtv mL

onVtv -=+ )( 31 5.9(b)

5-9

mL 1v

1i

DCV

1S 1SD

2S 2SD

gvrL rC

mLrC

v mLi

DCV

1S 1SD

2S 2SD

gvrL rC

mL

rCv mLi

onV-

1i[ ])( 3tvCr

[ ])( 3tiLr[ ])( 3tiLm

)(on off

0

1v

1i

onV

onV-

-3t

+3t

4t

0>rL

i 0>rL

i

(a) (b) (c)

5.9

5.9(b)

-=

=

-=

oL

m

LC

r

CoL

r

nVdt

tdiL

tidt

tdvC

tvnVdt

tdiL

m

r

r

r

r

)(

)()(

)()(

(5-21)

)( 3ti rL )( 3tv rC )( 3tiLm

( )

---

=

+-+--=

--

+-=

)()()(

)(sin)()(cos)()(

)(sin)(

)(cos)()(

33

3113313

311

3313

tittLnVti

nVttZtittnVtvtv

ttZ

tvnVtttiti

mm

rrr

r

rr

Lm

oL

orrLroCC

rr

CorLL

ww

ww

(5-22)

rrr CLZ =:1 rrr CL1:1 =w 0)( 4 =tiLr

-=-= -

oC

rL

r nVtvZti

ttTr

r

)()(

tan1:3

131

1344 w

(5-23)

Lri ( 0)( 4 =ti rL ) 2SD

Lri

(6) [ 4t , 5t ]( 1S off 2S on 1SD off off2 SD )

4tt = 2SD 2S

on5.10(a) mL

onV- ( rL , rC )5.10(b)

5-10

mL 1v

1i

5.3

DCV

1S 1SD

2S 2SD

gvrL rC

mLrC

v mLi

mL

DCV

1S 1SD

2S 2SD

gvrL rC

rCv mLi mLi

onV-

1i[ ])( 4tvCr

[ ])( 4tiLr[ ])( 4tiLm

0

1v

1i

onV

onV-5t4t

0k 7.28 k

(unstable)

(b) 0

7-10

Im

agin

ary

Axi

s

Imag

inar

y A

xis

0=s1500-=s20000-=s 0=s1500-=s20000-=s

7.28 0>k 7.29 0

7-11

s 0.0425=st

Am

plitu

de

Mag

nitu

de (d

B)

Phas

e (d

eg)

GM

PM

s 0425.0=st

7.32 ssC /001)( -= 7.33 ssC /001)( -=

(3)

ssC /001)( -= 7.30

ovrefvctrlv~e~

41

s100- 2)-(7

7.34

7.34(7-2)

93.77)(s )1399( )102(

1005.1)(~)(~

4

10

+++

=sssv

sv

ref

o (7-3)

refv~ ov~ 7.35

7.35

7-12

7.35 kHz 50Hz 14.7srad 92.3BW =

7-13

div/A 1

div/s 5.2 m

rLi

div/A 1

div/s 5.2 m

rLi

7.37

rLi V 140=DCV 7.38 rLi V 160=DCV

kHz 8.46=sf V 24=oV kHz 5.53=sf V 24=oV

W= 107.5R kHz 2.5250 =sf

7.4

][ WR ]kHz[ sf ]V[ oV

5.7 50 24

10 52.2 24

5 48.9 24

7.39~40 sf oV

rLi

div/A 1

div/s 5.2 m

div/A 1

div/s 5.2 m

rLi

rLi

7.39

rLi W= 10R 7.40

rLi W= 5R

kHz 2.52=sf V 24=oV kHz 9.48=sf V 24=oV

(3) DCV R7.5

7-14

7.5 oV

]V[ DCV ][ WR ]kHz[ sf ]V[ oV

150 5.7 50 24

158 5.7 53.3 24

150 10 52.3 24

(a) 7.41( V 158150 )( V 24=oV )

(a) V 158150 (b) V 150581

(V1 V/divACH0.5 s/div)

7.41

(b) 7.42( V 158150 ) sf

( V 24=oV )

(a) V 150DC =V kHz 50=sf (b) V 158DC =V kHz 3.35=sf

7.42

7-15

(c) 7.43( W 105.7 )

(a) W 107.5 (b) W 7.510 (V1V/divACH0.2 s/div)

7.43

LLC7.44

ccV+

Wk 10

Wk 10

ccV-

Wk2

ccV+

ccV+

ccV-

Wk2

1gsv

1:1W 10

Wk 10

F 1 m F 1m

ccV+

ccV+

2gsv

1:1W 10

Wk 10

F 1m F 1m

W= k 100aR

k 50

k 50

-k 50

k 50

-

k 10

ccV+

-

k .33

k 01

ev~refv

2D

DCV

1S1S

D

2S2SD

gvrL rC

oC RoV

1D

2i

3i

2v

3v

mL 1v

1irLi1:1:n

rCv mLi

oi

-

k 10

ccV+

k 001-

k 05

k 05

-k 05

k 05

biasV

F1.0 m

ctrlv~ctrlbias vV~+

4046

ccV+

F2.2 n

k 01

k 1-

F10 n

k 100

F1.0 m

7.44

7-16

7.6

(1) :

rL

lkL rL

(2) MOSFET

DS(on)r

DS(on)r

1.5

(3)

(a)(fast recovery

diodes)(b)(ultra-fast recovery diodes)(c)

(SBD: Schottky Barrier Diode)

0.8 V

1.2 V

(4)

(aluminum electrolytic capacitor)

(ESR: Equivalent Series Resistance)

ESR

8-1

8.1

LLC

1.

2. LLC

QLin

Q eqR rL mL rC

3. LLCLin

4. LLC

Lin

5.

6. IsSpice

W100=oP LLC % 88.9

8.2

1.

W100

W300

2.

8-2

LLC

kHz 50 kHz 100

3.

1

4.

Q

Ref-1

[Bha90] Bhat, A. K. S., Analysis, Optimization and Design of A

Series-Parallel Resonant Converter, Proc. IEEE APEC, pp.

155-164, 1990.

[Bha92] Bhat, A. K. S., Fixed-Frequency PWM Series-Parallel Resonant

Converter, IEEE Trans. on Industry Applications, Vol. 28, No. 5, pp.

1002-1009, 1992.

[Bha93] Bhat, A. K. S., Analysis and Design of a Series-Parallel Resonant

Converter, IEEE Trans. on Power Electronics, Vol. 8, No. 1, pp.

1-11, 1993.

[Bha93] Bhat, A. K. S., Analysis and Design of a Modified Series Resonant

Converter, IEEE Trans. on Power Electronics, Vol. 8, No. 6, pp.

423-430, 1993.

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[96] DC-DC

1996

[97] PWMDC-DC

1997

[98]

1998

[99]

1999

[01]

Ref-3

2001

[02]

2002

[03] AC/DC

2003

[04] DC/DC

2004

[05] DC/DC

2005

[05]

DC/DC

2005

[06]

DC/DC

2006

[98] 19982

Name Chih-Hao Tsai

1982/12/20

121 10 3

(02) 24985832

[97 ]

[94 ]

[90 ]

[87 ]

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