Current Mode Converter

Shen-Yaur Chen

• Limited value of error voltage provides peak current protection

• No Soft-start mechanism is required

• Modules share a common error voltage

• Peak Current in each is kept the same

PWM Converter with Current-Mode Control

PWM Switch Model

• Limited value of error voltage provides peak current protection

• No Soft-start mechanism is required

• Modules share a common error voltage

• Peak Current in each is kept the same

2

1

m D

m D

2

11

O O

m DI I I

m D

n

n O

DI I

D

Subharmonic

0.5 UnstableD

External Ramp (Stabilized Ramp, Compensated Ramp)

2 2

1 1

1 Stable D>0.5n

C Cn O

C C

m m m mI I

m m m m

Average Model

• R. D. Middlebrook, “Topics in Multiple-Loop Regulations and Current-Mode Programming,” in proc. IEEE Power Electron. Spec. Conf., Rec., 1985, pp. 716-732.

1 2

: average current

L i C C

L

i R v M dT m dT

i

Current Average

Perturbed

1 1 1

2 2 2

d=D+d

M

M

m m

m m

LL L

c c c

i I i

v V v

11 2 2L Ci Ci R v M M T d DT m

1

g o

i

v vm R

L

2

o

i

vm R

L

c L g om i f rd F v R i k v k v

1

1

12

2c L i

C

d v i R DT mM M

1

1

2mC

FM M

2

2

if

ir

DTRk

LDTR

kL

Complete Small Signal Model

Exact Average

• G. C. Verghese, C. A. Bruzos, and K. N. Mahabir, “Averaged and Sampled-Data Models for PCM Control: A Reexamination,” in proc. IEEE Power Electron. Spec. Conf., Rec., 1989, pp. 3-13.

Exact Average

1 22 2L i C Ci R v M dT d m dT d m dT

2 21 22 2L Ci Ci R v M T d D T m D T m

2 21 2

12 2c L i

C

d v i R D T m D T mM T

1

g o

i

v vm R

L

2

o

i

vm R

L

2

2

1 22

1

f i

ir

mc

Dk TR

LTR

k DL

Fm T

Ridley’s Model

• R. B. Ridley, A New small-signal Model for Current-Mode Control, Ridley Engineering, Inc.,July 1999.

Ridley's Model

Current Programmed Converter

Peak Current Mode Converter

Current-Mode Converter with Fixed Input and Output Voltages

(a)Buck (b)Boost

(c)Buck-Bust

Generic Current-Mode Cell

PWM Switch Model

Small-Signal Model of the Current-mode Cell with Fixed Voltage

Modulation Gain

m

1 F

( )n e sS S T

Modulation Gain

tan i Ln

s s

AB R iS

dT DT

tan Tme

s s

BC VS

dT T

ˆ

ˆ( )

c

n e s

v AC AB BC

S S dT

ˆ 1 1ˆ ( )m

c n e s c n s

dF

v S S T m S T

1 ec

n

Sm

S

Sampling Gain

ˆ( 1) ( ) ( 1)i L f eR i k S S t k

ˆ( ) ( ) ( 1)i L n eR i k S S t k

( 1) ( )L Li k i k

f e

n e

S S

S S

1 ( 1) (1 ) ( 1)L c

i

i k v kR

Control Perturbation

k k +1

ˆ( )si n

t

(exact)

(b)

Sn Sf

Se

ˆ( )si k

(a)

ˆc cV v

(c)

k

ˆ( )si n

t

(approx)

k +1

Discret Time Response

1 ( 1) ( ) (1 ) ( 1)L L c

i

i k i k v kR

Subharmonics oscilla n tio1 Oscillation

f

n

Without external Ramp

S

= 1S

Cycle D 0.5Duty

( ) 1( ) (1 )

( )L

ic

i z zH z

R zv z

SystemSample and Hold

1 F(s)=H(e ) (1 e )

1 1 e 1 =

e

s s

s

s

sT sT

s

sT

sTi s

sT

R sT

z Transform

i

f

ii

( ) F ( )

( )

S

1 F ( )

ap ac cpL

i cpi acn

n f

V V Vi ss

sL sLd s

RVRVS

L LS S

sR s

m

1

1 1

( )

F

( )

n e s

m ii s

F F sR

S

s

T

T

S

( )1 1 1

R 1 ( ) ( )

( )1

s

s

s

sTm i

sTi s m i i e

se sT

F F se

sT e F F s R H s

sTH s

e

' Aproximation

Pade s

2

2( ) 1e

n z n

s sH s

Q

2z

ns

Q

T

Complete Small-Signal Model for Current-Mode Control

Invarient Small-Signal Model for Current-Mode Control

Small-signal Model for the Generic Current Cell

Generic Current Cell with Fixed Voltage During Off-Time

'

2f s

i L c s e

s d TR i v dT S

'

off

on off

on

on off

vd

v v

vd

v v

2

2e s sL

ap ion

DS T D Ti

V R Lv

'

'

0

1

m f on i L

apon

Lf

i m apon

d F k v R i

Vv d

D

i Dk

R F Vv

' 12

s if

DT R Dk

L

2n s

i L c s e

s dTR i v dT S

' '2

2e s sL

ap ioff

D S T D Ti

V R Lv

'

'

'

m i r off

offi r off

apm

d F R i k v

vR i k v

VF

D

''1Lr

i m apoff

i Dk

R F Vv

'2'

2s i

r

D T Rk

L

Feedforward Gain

'

' '

Buck Converter

12

2

s if f

s ir r f

DT R Dk k

L

T Rk k k

L

Current Loop Gain

Buck Converterˆ 0

ˆˆˆ

1//

11

//

ˆˆ

1//

g

gL g

l c

l c

o L c

c c

v

V di V Yd

sL R R RsC

YsL R R R

sC

v i Z

Z R RsC

令

Buck Converter

ˆ

ˆ 1

i m g i e

m g coc

c i r m g c

T s F V YR H s

F V YZv sT s

v s T s k F V Z

gC O

DVI I

R

1

1C

CC

R Cs kZ

s R R C

11R s

RYs

2

20 0

1ps

s ss

Q

0

1

LC

0

1ps

C

QL

CRR

Current Loop Gain

i '

1T ( ) ( )

( ) es c

L sCRs H s

RT m D s

2

20 0

( ) 1

1

ps

ps

o c

s ss

Q

QL

CRR

1o

LC

Control-to-output

'

1( ) ( )

1 0.5

op h

sic c

v RF s F s

RTRv m DL

p

1F ( )

1

c

p

sCRs

s

'1( 0.5)s

p c

Tm D

CR LC

h 2

2

1F ( )

1n p n

ss sQ

p '

1Q

( 0.5)cm D

Audio Susceptibility'

'

s

(1 )2

( ) ( )0.5

RT

co

p h

g c

DD m D

vF s F s

Lv m D

Boost Converter

RC

L

Vi

PWM

Ri

Duty cycle

Mod--+

c

a

p

Sensed CurrentTs

External Ramp

Se

Sn

Control Vc

d

Boost Converter

2s i

f

T Rk

L

2(1 )

2s i

r

D T Rk

L

L

rc

CRiv

dD

Vap ˆ

dI cˆ

v

ovi

vDˆ

p

a

Zc

dFm

kf

+

+

+

kr

PWM

Cr

i

-

cv

He(s) Ri

Boost Converter

1

1

ˆ ˆˆ

ˆˆ ˆ(1 )

1

(1 )

o

c

oc

Dv vi

Z

i D i I d

Z r sL

VI

D R

Boost Converter

1

1//

ˆˆ

1 ˆˆˆ [(1 ) ](1 )

ˆˆ ˆ

ˆˆˆ

1

cc

o c

oo l c

oo

oo

Z R rsC

v Z i

Vv D i d Z

D R

Vv v d

D

Z i V dv

D

Boost Converter

21

21

1ˆ( )

ˆ (1 )

1 ˆˆ 1

ˆ (1 ) ( )

ˆ (1 )( )

co

lpi

c

Lc

om c

c

o

opi

ZV

i RT s

Z D Zd

v

D Rv D Z i

T s

v D R ZT s Z

D Z Ri

Boost Converter

2 2

ˆ ˆˆ ˆ

( ) ( ) ( )

1

1 2

c r o im

i m pi i e

S

zi

o oe

c

d F v k v Ri

T s F T s R H s

sH s

D m T s s

2

2

1

( ) (1 )

2 ( ) (1 )

1

2(1 )

ec

n

C L C

C

Sm

S

C r R r R r D L

LC R r r D R

L

D R C

2

0

2

1 1

( )

1 2

( / 2 )

( ) 1

2

C

ziC

ez n n

ns

z

D R r D

LC R r LC

C R r CR

s sH s

Q

T

Q

dcv

+

+

+

- ov

Ti(s)

Fm Tpi(s) Tm(s)

He(s) Ri

kr

i