DC – DC Converter (Chopper)

7/31/2019 DC DC Converter (Chopper)

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6/1/2012

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DC DCConverter(Chopper)

DCtoDCCONVERTER

(CHOPPER)

Buckconverter

Boostconverter

BuckBoostconverter


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DCDCConverter

(Chopper)DEFINITION:

ConvertingtheunregulatedDCinputtoacontro e outputw t a es re voltagelevel.

Generalblockdiagram:

LOAD

DC supply

(from rectifier-

filter, battery,

fuel cell etc.)

DC output

control

(derived from

feedback circuit)

APPLICATIONS: Switchedmodepowersupply(SMPS),DC

motorcontrol,batterychargers

Linearregulator

Transistorisoperatedinlinear

(active)mode.

Outputvoltage

+

Vo

RL

+ VCEce

IL

Vin

Thetransistorcanbeconveniently

modelledbyanequivalentvariable

resistor,asshown.

LINEAR REGULATOR

RT

RL

+ Vce

I

L

V

+

ceino VVV =

dueto:

EQUIVALENT

CIRCUIT

ino

Lceo

TLo

IVP

RIP

=

=

or

2


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SwitchingRegulator Transistorisoperatedinswitched

mode: Switchclosed: Fullyon(saturated)

Switchopened: Fullyoff(cutoff)

+

Vo

RL

+ Vce

IL

SWITCHING REGULATOR

Vin

Whenswitchisopen,nocurrentflowinit

Whenswitchisclosednovoltagedropacrossit.

SinceP=V.I,nolosses occursintheswitch. Poweris100%transferredfromsourceto EQUIVALENT CIRCUIT

RL

IL

Vin

Vo

+

SWITCH

.

Powerlossiszero

(foridealswitch):

SwitchingregulatoristhebasisofallDCDCconverters

(ON)

closed

(OFF)

open

(ON)

closed

DT T

OUTPUT VOLTAGE

o

Vin

Buck(stepdown)converter

Vd

L

DC R

L

S

+

Vo

Vo

CIRCUIT OF BUCK CONVERTER

CIRCUIT WHEN SWITCH IS CLOSED

+

iL

Vd D RL

S + vL

Vo

+

CIRCUIT WHEN SWITCH IS OPENED

Vd D

RL

S

+ vL

iL


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Switchis turnedon(closed)

Diodeisreversedbiased.

Switchconductsinductor

current

Thisresultsinpositiveinductor

Vd VD

+ vL

-

C RL

+

Vo

iL

+

S

voltage,i.e:

Itcauseslinearincreaseinthe

inductorcurrent

odL VVv =

VdV

o

closed

openedclosed

opened

t

vL

=

=

dtvL

i

dtdiLv

LL

LL

1

o

DT Tt

iLmin

iLmax

IL

iL

Switchturnedoff(opened)

Becauseofinductiveenergy

storage,iL

continuestoflow.V

d

+ vL

-

C RL

+

Vo

iL

S

D

Dio eis orwar iase

Currentnowflows(freewheeling)

throughthediode.

VdV

o

closed opened closed opened

t

vL

derivedas:

oL Vv =

o

DT T

t

iLmin

iLmax

IL

iL

(1-D)T


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Analysis

When the switch is closed (on):

Derivative of is a positive constant.Therefore

d oL LL d o

L L

V Vdi div V V L

dt dt L

i i

= = =

VdVo

vL

t

closed

( )

must increased linearly. From Figure:

d oL L L

d oL closed

V Vdi i i

dt t DT L

V Vi DT

L

= = =

=

For switch opened,

IL

iL max

DT T

iL

t

iL min

iL

( )

(1 )

(1 )

oL L

L o

oL L L

oL opened

Vdi di

v V L dt dt L

Vdi i i

dt t D T L

Vi D T

L

= = =

= = =

=

Steadystateoperation

iL

Unstable current

t

Decaying current

Steady-state current

t

t

iL

iL

( ) ( )

Steady-state operation requires that at the end of switching cycle is the same at the

begining of the next cycle. That is the change of over one period is zero, i.e:

0

L

L

L Lclosed opened

d o

i

i

i i

V V

L

+ =

(1 ) 0o

s s o d

VDT D T V DV

L

= =


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LAverage inductor current Average current in R

oL R

VI I

R

=

= =

Average,MaximumandMinimum

InductorCurrent

max

min

Maximum current:

1 1 (1 )(1 )

2 2 2

Minimum current:

o oLL o

LL

V Vi DI I D T V

R L R Lf

iI I

= + = + = +

= i

L

1 (1 )2

Inductor current ripple:

oDV

R Lf =

max min

Li I I =

IL

Imax

Imin

iL

t

ContinuousCurrentMode(CCM)

min

From previous analysis,

2

LL

iI I

=

iL

Imax

min

)

2

For continuous operation, 0,

1 (1 )0

2

1

o

o

VR Lf

I

DV

R Lf

D

=

Imin

t0

min2

This is the minimum inductor current to ensure continous mode

of operatio

f =

min

n.

Normally is chosen b beL L>>


7/15


8/15

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CalculateLmin.ChooseL>>10Lmin

CalculateCforripplefactorrequirement. Capacitorratings:

mustwithstandpeakoutputvoltage

.triangularw/fisIp/3,whereIp isthepeakcapacitorcurrentgivenbyi

L/2.

ECAPscanbeused

Wiresizeconsideration:

NormallyratedinRMS.ButiL

isknownaspeak.RMSvaluefori

Lisgivenas:

22

,3

2

+= LLRMSLi

II

Problems Abuckconverterissuppliedfroma50Vbatterysource.Given

L=400uH,C=100uF,R=20Ohm,f=20KHzandD=0.4.Calculate:

(a)outputvoltage(b)maximumandminimuminductor

current,(c)outputvoltageripple.

Abuckconverterhasaninputvoltageof50Vandoutputof

25V.Theswitchingfrequencyis10KHz.Thepoweroutputis

125W.(a)Determinethedutycycle,(b)valueofLtolimitthe

peakinductorcurrentto6.25A,(c)valueofcapacitanceto

limittheoutputvoltageripplefactorto0.5%.

whentheinputis48V.Theloadis8Ohm.Designthe

convertersuchthatitwillbeincontinuouscurrentmode.The

outputvoltageripplemustnotbemorethan0.5%.Specify

thefrequencyandthevaluesofeachcomponent.Suggestthe

powerswitchalso.


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Boost(stepup)converter

Vd

L D

C

RL

S +

Vo

Vd

LD

CR

LS

+ vL

Vo

CIRCUIT OF BOOST CONVERTER


+

iL

Vd

L

D

C RLS

+ vL

-

Vo

+


Boostanalysis:switch closed

Vv dL = Vd

LD

CS

+ vL

iL

+

vo

DT

i

t

i

dt

di

LV

dtdi

dtL

LLL

dL

L

=

=

=

=

vL

CLOSED

t

Vd

( )L

DTVi

Ldt

dclosedL

dL

=

=

DT T

iL

t

VdV

o

iL


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Switchopened

dt

diL

VVv

L

odL

=

=V

d

D

CS

+ vL-

iL

+

vo

-

TD

i

t

i

dt

di

Ldt

L

LL

odL

)1(

=

=

=

vL OPENED

t

Vd

VdV

o

( )( )

L

DTVVi

L

VV

dt

di

odopenedL

odL

)1(

=

=

DT T

( 1-D )T

iL

t

iL

Steadystateoperation

( ) ( )

( )

0

(1 )0

1

L Lclosed opened

d od do

i i

V V D T V DT V V

L L D

+ =

+ = =

Boostconverterproducesoutputvoltagethatisgreateror

equaltotheinputvoltage.

Alternativeexplanation:

whenswitchisclosed,diodeisreversed.Thusoutputis

isolated.Theinputsuppliesenergytoinductor.

ensw c sopene , eou pu s agerece vesenergy

fromtheinputaswellasfromtheinductor.Henceoutputis

large.

OutputvoltageismaintainedconstantbyvirtueoflargeC.


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Average,Maximum,MinimumInductorCurrent

2

2 2

2

Input power Output power

(1 )

d

o d

d d d L

V

DV VV I V I

=

= = =

2

Average inductor current:

(1 )

Maximum inductor current:

dL

VI

D R

=

max 2

min

2 (1 ) 2

Minimum inductor current:

2 (1

d dLL

dLL

V V DT i

I I D R L

ViI I

= + = +

= =

2) 2

dV DT

D R L

LandCvalues

min

2

For CCM,

0

0(1 ) 2

d d

I

V V DT

D R L

I

max

Vd

vL

VdV

o

( ) ( )2 2

min

1 1

2 2

Ripple factor

o

D D TR D D RL

f

VQ DT C V

= =

= =

Imax

Imin

Imin

iD

L

o oo

o

o

R

V DT V DV

RCf RCf

V Dr

V RCf

= =

= =

ic

Io=V

o/ R

DT T

Q


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Problems

Theboostconverterhasthefollowingparameters:Vd=20V,

D=0.6,R=12.5ohm,L=65H,C=200F,fs=40KHz.Determine(a)

outputvoltage,(b)average,maximumandminimuminductor

current,(c)outputvoltageripple.

Designaboostconvertertoprovideanoutputvoltageof36V

froma24Vsource.Theloadis50W.Thevoltageripplefactor

mustbelessthan0.5%.Specifythedutycycleratio,switching

frequency,inductorandcapacitorsize,andpowerdevice.

BuckBoostconverter

Vd L

D

CRL

S

+

Vo

Vo

CIRCUIT OF BUCK-BOOST CONVERTER

+

iLVd vL

+

DS

Vo

+



iLVd vL

+

DS


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BuckboostanalysisV

d

vL

VdV

o

Imax

Switch closed

dL LL

Vdi div Vd L

dt dt L

Vi i

= = =

Imin

Imax

iD

iL

Imin

( )

Switch opened

d

L closed

oL L

t DT L

V DTi

L

Vdi div V L

= =

=

= = =

DT T

ic

Q

o o

(1 )

(1 )( )

oL L

oL opened

dt dt L

Vi i

t D T L

V D Ti

L

= =

=

Outputvoltage

( ) ( )

Steady state operation:

(1 )0 0d o

iL c losed iL opened

V DT V D T

L L

+ = + =

NOTE:Outputofabuckboostconvertereitherbehigheror

lowerthaninput.

IfD>0.5,outputishigherthaninput

oOutput voltage: V1

sV

D =

. ,

Outputvoltageisalwaysnegative.

Notethatoutputisneverdirectlyconnectedtoload.

Energyisstoredininductorwhenswitchisclosedand

transferredtoloadwhenswitchisopened.


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Averageinductorcurrent

2

Assuming no power loss in the converter, power absorbed by the load

must equal power supplied the by source, i.e.

But average source current is related to average inductor current as:

oo s d sP P V I

R= =

2

Substituting for ,

os L d L

o

VI I D V I D

R

V

= =

2

2(1 )o o dL

d d

V P V DI

V RD V D R D= = =

LandCvalues

max 2

Max and min inductor current,

2 (1 ) 2

d dLL

V D V DT iI I

R D L

= + = +

min 2

2

dmin2

2 (1 ) 2

For CCM

V (1 )0

(1 ) 2 2

d dLL

d

I IR D L

D V DT D RL

R D L f

= =

+ = =

,

Q o o

o o oo

o

VDT C V

R

V DT V D V DV r

RC RCf V R

= =

= = = =

Cf


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6/1/2012

ConvertersinCCM:Summary

2

Buck

1

8

o

d

o

o

V

DV

V D

V LCf

=

=

V

d

L

D C RL

S

+

Vo

min2

Lf

=

2

min

1Boost

1

(1 )

o

d

o

o

V

V D

V D

V RCf

D D RL

=

=

=

V

d

L D

C

RL

S

+

Vo

V

d

L

D

C RL

S

+

Vo

2

min

Buck Boost1

(1 )

2

o

d

o

o

V DV D

V D

V RCf

D RL

f

=

=

=

ControlofDCDCconverter:

pulsewidthmodulation(PWM)

Comparator

Vcontrol

Vo(desired)

Vo

(actual)

+

-

Switch control

signal

Sawtooth

Waveform Sawtooth

Waveform

Vcontrol 1

Vcontrol 2

Switch

control

signalton 2

T

ton 1

Documents

DC – DC Converter (Chopper)