DC-DC ConvertersDC DC Converters

충북대학교 전자정보대학 김영석

2 12 92012.9

1

Ref: Dr. M.H. Rashid

Step Down ConverterStep-downStep down

SW closed (t1) => 부하에 전압 전달

SW open => 부하 전압은 0

fttkratioduty ==:)( 1시비율

부하 전압은

t1 짧을수록 전압 감소

kVV

ftT

kratioduty

saverageo

s

⎞⎛

=

==

:

:)(

2/1

)(

1

전압출력평균

시비율

RVV

VkdtvT

V s

kT

ormso =⎟⎠⎞

⎜⎝⎛= ∫

1 : 2/1

0

2)(

입력저항유효본전원에서

실효치전압의출력

kR

RkVV

IVR

s

s

averageo

si ===

/:

)(

입력저항유효본전원에서

동작 모드동작 모드

Constant frequency operation => PWM(Pulse width modulation)

Variable frequency operation

8/28/2012 EEL 4242 by Dr. M.H. Rashid 2

Variable frequency operation

Step Down Operation with RL Load

3

Modes of Operationdi1

1

1 1( 0)

SdiV Ri L Edt

For i t I

= + +

= =

( )/ /1 1

1 1 2

( ) 1

( )

tR L tR LSV Ei t I e eR

i t t kT I

− −−= + −

= = =

220 diRi L E

dt= + +

( )2 2

/ /2 2

( 0)

( ) 1tR L tR L

dtFor i t I

Ei t I e e− −

= =

= − −( )2 2

2 2 3 3 1

( ) 1

( (1 ) )

i t I e eR

i t t k T I I I= = − = =

4

Modes of Operation( )

( )

/ /2 1

(1 ) / (1 ) /

1

(1 ) 1

kTR L kTR LS

k TR L k kTR L

V EAt t kT I I e eR

E TR TAt t k T I I I

− −

− − − −

−= = + −

k k⎛ ⎞ ⎛ ⎞

( )( ) / ( ) /3 1 2(1 ) 1k k kAt t k T I I I e e z

R L τ= − = = − − = =

1 2

(1 )

1 11 1

1

kz kzS S

z z

kz z k zS

V Ve E e EI IR e R R e R

V e e eI I I

−

−

− − − −

⎛ ⎞ ⎛ ⎞− −= − = −⎜ ⎟ ⎜ ⎟− −⎝ ⎠ ⎝ ⎠

− + −Δ = =2 1 1

( ) 0 0.5

zI I IR e

d I kdk

−Δ = − =−

Δ= =

max tanh4 4

S SV VRIR fl fL

Δ =

리플전류는 주파수에 반비례

5

Discontinuous Operation 0I

22 1 RILt ln

R E⎛ ⎞= +⎜ ⎟⎝ ⎠( )

1

/1

0

( ) 1 tR LS

IV Ei t e

R−

=−

= −

( )1 1 kzSV EL ln eR E

−−⎛ ⎞= + −⎜ ⎟⎝ ⎠

( )

( )1 1 2( )

Ri t t kT I

V E= = =

− ( )2 1 kzSV EAt t kT I eR

−= = −Mode 2

Mode 1

6

Step-Up Operation

Step-upp p

SW closed (t1) => 인덕터에 전류 흐르고 에너지 저장

SW open => 인덕터 축적에너지는 D1을 통해 부하에 전달

t1 길수록 승압전압 상승

Vdi

kVtVILVv

tLVI

dtdiLv

ssso

sL

=+=Δ

+=

=Δ∴=

1)1(

,

1

1

ktt sso −1)(

22

7

Step-Up Operation

111 )( , :1 It

LVti

dtdiLVMode s

s +==

222 )( , :2 It

LEVtiE

dtdiLVMode s

s +−

=+=

8

Step-Up Operation

1 ( ) SVdiV L i I11 1( )

( )

SS

S

V L i t t Idt L

VI i t kT kT I

= = +

+

Mode 1

2 1 1( ) SI i t kT kT IL

= = = +

( )

22

/ /( )

S

tR L tR LS

diV Ri L Edt

V E

= + +

− ( )

( )

/ /2 2

(1 ) (1 )1 2 2

( ) 1

( (1 )) 1

tR L tR LS

k z k zS

V Ei t e I eR

V EI i t k e I eL

− −

− − − −

= − +

−= = − = − +( )1 2 2

(1 )

2 (1 )

( ( ))

1

k zS S

k z

LV kz V EeI

R e R

− −

− −

−= +

−

2 2 1(1 )

11

S S Sk z

V kz V E VI I I I kTR e R L− −

−= + Δ = − =

−Mode 2

9

Converter Classifications

10

1st Quadrant Converter

• Both the voltage and the current are positiveSt d t• Step-down converters

11

2nd Quadrant Converter

• Both the voltage is positive and the current is negativecurrent is negative

12

2nd Quadrant Converter

0 LL

diL Ri Edt

E

= + + Mode 1

( )/ /1

1 1 2

( ) 1

( )

tR L tR LL

L

Ei t I e eR

At t t kT i t t kT I

− −= − −

= = = = =1 1 2( )LAt t t kT i t t kT I

LS L

diV Ri L Edt

V E

= + +

( )/ /2( ) 1

(1 ) ( (1 ) )

tR L tR LSL

V Ei t I e eR

At t t k T i t t k T I

− −−= + −

2 2 1(1 )

1 2

(1 ) ( (1 ) )

11 1

Lk z kz z

S Sz z

At t t k T i t t k T IV Ve E e e EI IR R R R

− − − −

− −

= = − = = − =

− −= − = − Mode 2

13

1 21 1z zR e R R e R− −− −

1st and 2nd Quadrant Converter

• S1 and D4: 1st Quadrantd• S4 and D1: 2nd Quadrant

14

3rd and 4th Quadrant Converter

• S3 and D2: 3rd• S2 and D3: 4th

15

Four Quadrant Converter

16

Switching Mode Regulators

St /d + C t l > S it hi d l t sStep-up/down conv. + Control => Switching mode regulators

보통 PWM 사용, fs ~ ft/100

종류종류

Buck Regulator

Boost Regulator

Buck-Boost Regulator

Cuk Regulator

17

Buck Regulator M d 1: Q1 ON Q1/L/C/R 전류 흐름 전류 증가Mode 1: Q1 ON, Q1/L/C/R 전류 흐름, 전류 증가

Mode 2: Q1 OFF, Dm/L/C/R 전류 흐름, 전류 감소

18

Buck Regulator

(1 )a S S a

S

V kV I kIV k kI

= =

−Δ =

(1 )S

IfL

V k kIV

Δ =

−ΔΔ = = 28 8CV

fC f CLΔ = =

• The critical values for a continuous• The critical values for a continuous inductor current and capacitor voltage

(1 )2c

k RL Lf

−= =

2

116c

kC CLf−

= =

19

Boost Regulator

20

Boost Regulator

V I V k

( )1 1

S a Sa S

V I V kV I Ik k fL

I V V I k

= = Δ =− −

−( )a a S aC

a

I V V I kVV fC fC

−Δ = =

• The critical values for a continuous inductor current and capacitor voltageinductor current and capacitor voltage

( )1k k RL L

−( )2cL L

fkC C

= =

2cC CfR

= =

21

Buck-Boost Regulator

Buck-Boost Reg. = Inverting or Flyback Reg. (Vo 극성 Vs와 반대)

Mode 1: Q1 ON, Dm OFF, Q1/L전류 흐름, 전류 증가

Mode 2: Q1 OFF, Dm ON, Dm/L/C/R 전류 흐름, 전류 감소

22

Buck-Boost Regulator

1 1S a S

a SkV kI V kV I I

k k fLI V I k

= = Δ =− −

( )a a a

Ca S

I V I kVV V fC fC

Δ = =−

• The critical values for a continuous inductor current and capacitor voltageinductor current and capacitor voltage

( )1k k RL L

−= =

2cL Lf

kC C

= =

= =2cC C

fR

23

Cuk Regulator

Buck-Boost 기능

Vo 극성 Vs와 반대

24

Cuk Regulator

1 1S a

a SkV kIV I

k k= =

− −

1 21 2

S SV k V kI IfL fL

Δ = Δ =

( )1

1 1

1( )

SS SC

S a

I kI VVV V fC fC

−Δ = =

−

2 2 22 2 2 2

(1 )8 8

a SC

V k kVVC L f C L f

−Δ = =

25

Cuk Regulator

• The critical values for a continuous inductor current and capacitor voltage

( )21 k RL L

−= =

( )

1 1 21

cL Lkfk R

L L

= =

−= =2 2

1 1

2c

c

L Lf

kC Cf

= =

= =1 1

2 2

21

8

c

c

fR

C CfR

= =8 fR

26

Input Filter

Chopper에 의해 발생한 고조파를 제거함

2

0⎟⎟⎠

⎞⎜⎜⎝

⎛=

nffII nhns

27

Ex 9-14Buck Con. Vs=110V, Va=60V, Ia=20A, f=20kHz, 피크 대 피크 맥동은 부하전압에 대해서 2.5%, 부하전류에 대해서 5%, 필터 Le전류에 대해서 10% (a) Le, L, Ce? (b) PSPICE 시뮬레이션

VV 60

VkkVV

AV

IVR

sa

a

a

5455.060 ,

32060

==∴=

Ω===

VVVVAAkII

V

ac

as

sa

5.1025.060%5.291.10205455.0

110,

=×=×=Δ=×==

AAIIAAII

a

aL

ac

21.020%10105.020%5

=×=×=Δ=×=×=Δ

FAIC

HVVkHzAVVV

VfIVVVL

ss

asae μ

3382

82.681110202

)60110(60)(

Δ

=××

−=

××Δ−

=

HkHA

VfI

VkLVkTIIL

FkHzVfV

C

cc

LL

c

μ

μ

91.40201

5.15455.0 ,

33.82085.18

=×

=ΔΔ

=∴Δ≈Δ

=Δ

=××

=×Δ

=

28

kHzAfIkTt Lc μ

2011 ××Δ

Ex 9-14 (continued)PSPICE 시뮬레이션

Va=Vc=59.5V, Ia=19.8A, I(av)=19.8A,ΔVc=1.8V, ΔI=2.0A, ΔIL=0.33A

29