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Power Electronics and Drives (Version 3-2003) Dr. Zainal Salam, UTM-JB 1 Chapter 3 DC to DC CONVERTER (CHOPPER) General Buck converter Boost converter Buck-Boost converter Switched-mode power supply Bridge converter Notes on electromagnetic compatibility (EMC) and solutions.
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

1

Chapter 3

DC to DC CONVERTER(CHOPPER)

• General• Buck converter• Boost converter• Buck-Boost converter

• Switched-mode power supply• Bridge converter• Notes on electromagnetic compatibility

(EMC) and solutions.

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DC-DC Converter(Chopper)

DEFINITION: Converting the unregulated DC input to acontrolled DC output with a desiredvoltage level.

• General block diagram:

LOAD

Vcontrol(derived from

feedback circuit)

DC supply(from rectifier-filter, battery,fuel cell etc.)

DC output

• APPLICATIONS: – Switched-mode power supply (SMPS), DC

motor control, battery chargers

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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

3

Linear regulator• Transistor is operated

in linear (active)mode.

• Output voltage

• The transistor can beconvenientlymodelled by anequivalent variableresistor, as shown.

• Power loss is high athigh current due to:

Lceo

T Lo

I V P

R I P

or

2

+

V oRL

+ V CEce I L

LINEAR REGULATOR

RT

EQUIVALENTCIRCUIT

V in

RL

+ V ce I L

V inV o

+

ceino V V V

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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

4

Switching Regulator

• Transistor is operatedin switched-mode : – Switch closed:

Fully on (saturated) – Switch opened:

Fully off (cut-off)

– When switch is open,no current flow in it

– When switch isclosed no voltagedrop across it.

• Since P=V.I , no losses occurs in the switch. – Power is 100%

transferred fromsource to load.

– Power loss is zero(for ideal switch):

• Switching regulator isthe basis of all DC-DCconverters

+

V o

RL

+ V ce I L

SWITCHING REGULATOR

EQUIVALENT CIRCUIT

V in

RL

I L

V inV o

+

(ON)closed

(OFF)open

(ON)closed

DT T

OUTPUT VOLTAGE

V o

SWITCH

V in

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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

5

Buck (step-down) converter

V d

L

D C RL

S

+

V o

V o

+

CIRCUIT OF BUCK CONVERTER

CIRCUIT WHEN SWITCH IS CLOSED

CIRCUIT WHEN SWITCH IS OPENED

V o

+

i L

V d D RL

S

V d D RL

S

+ v L

+ v L

i L

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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

6

Switch is turned on (closed)

• Diode is reversedbiased.

• Switch conductsinductor current

• This results inpositive inductorvoltage, i.e:

• It causes linearincrease in theinductor current

od L V V v

dt v L

i

dt di Lv

L L

L L

1

V d V D

+ v L -

C RL

+V o

V d V o

V o

closedopened

closedopened

t

DT T t

i Lmin

i Lmax

I L

v L

i L

i L

+S

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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

7

Switch turned off (opened)

• Because of inductiveenergy storage, i Lcontinues to flow.

• Diode is forward

biased

• Current now flows(freewheeling)through the diode.

• The inductor voltagecan be derived as:

o L V v

V d

+ v L -

C RL

+V o

V d V o

V o

closedopened

closedopened

t

DT T t

i Lmin

i Lmax

I L

v L

i L

i L

S

D

(1-D)T

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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

8

Analysis

T D LV

i

LV

T Di

t i

dt di

LV

dt di

dt di

LV v

DT L

V V i

LV V

DT i

t i

dt di

i

i L

V V dt

didt

di LV V v

oopened L

o L L L

o L

Lo L

od closed L

od L L L

L

L

od L

Lod L

)1(

)1(

opened,switchFor

FigureFrom

linearly.increasedmusthereforeconstant.T

positiveais of Derivative

:(on)closedisswitchWhen the

I L

i L max

DT T

i L

V d V o

v L

t

t

i L min

closed

i L

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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

9

Steady-state operation

d o

so

sod

opened Lclosed L

L

L

DV V

T D LV

DT L

V V

ii

i

i

0)1(

0

:i.ezero,isperiodoneoverof

changetheisThatcycle.nexttheof begining

at thesametheiscycleswitchingof endat thethatrequiresoperationstate-Steady

i L

Unstable current

Decaying current

Steady-state current

t

t

t

i L

i L

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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

10

minmax

min

max

L

:ripplecurrentInductor

2)1(1

2

:currentMinimum

2)1(1

)1(212

:currentMaximum

RincurrentAveragecurrentinductorAverage

I I i

Lf D

RV i I I

Lf D

RV

T D LV RV i I I

RV

I I

L

o L

L

o

oo L L

o R L

Average, Maximum andMinimum Inductor Current

I L

I max

I min

i L

i L

t

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11

Continuous Current Mode (CCM)

min

min

min

min

bebchosenis Normally

operation.of modecontinousensure current toinductorminimumtheisThis

2)1(

02

)1(1

,0 operation,continuousFor

2)1(1

2

analysis,previousFrom

L L

R f D

L L

Lf D

RV

I

Lf D

RV

i I I

o

o L

L

i L

I max

I mint

0

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Output voltage ripple

size.capacitorIncreasing3)

sizeinductorIncreasing2)

frequencyswitchingIncreasing1)

:byreducedbecanRipple:Note8

)1(

factor,rippletheSo,

8

)1(8

peak)to-(Peak voltageRipple

8

2221

:formulaareatriangleUse

:aswittenbecanchargeThe

:currentCapacitorKCL,

2

2

LCf

D

V

V r

LCf

DC iT

V

iT

iT Q

C Q

V

V C Q

CV Q

iii

o

o

Lo

L

L

oo

o

R Lc

i L

i L

=I R

i max

imin

V o

+

V o / R

i RL i L

iC

iC

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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

13

Basic design procedures

Vd(inputspec.)

SWITCH

f = ?D = ?TYPE ?

D

L

Lmin = ?

L = 10L min

Cripple ?

RL

Po = ?Io = ?

• Calculate D to obtain required output voltage.

• Select a particular switching frequency (f) and device – preferably f>20KHz for negligible acoustic noise – higher fs results in smaller L and C. But results in higher losses.

Reduced efficiency, larger heat sink. – Possible devices: MOSFET, IGBT and BJT. Low power MOSFET can

reach MHz range.• Calculate L min . Choose L>>10 L min • Calculate C for ripple factor requirement.

– Capacitor ratings:• must withstand peak output voltage• must carry required RMS current. Note RMS current for

triangular w/f is I p /3, where I p is the peak capacitor current givenby i L /2.

• ECAPs can be used

• Wire size consideration: – Normally rated in RMS. But i L is known as peak. RMS value

for i L is given as:

22

, 32

L

L RMS Li

I I

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14

Examples• A buck converter is supplied from a 50V battery source. Given

L=400uH, C=100uF, R=20 Ohm, f=20KHz and D=0.4.

Calculate: (a) output voltage (b) maximum and minimuminductor current, (c) output voltage ripple.

• A buck converter has an input voltage of 50V and output of 25V. The switching frequency is 10KHz. The power output is125W. (a) Determine the duty cycle, (b) value of L to limit thepeak inductor current to 6.25A, (c) value of capacitance to limitthe output voltage ripple factor to 0.5%.

• Design a buck converter such that the output voltage is 28Vwhen the input is 48V. The load is 8Ohm. Design the convertersuch that it will be in continuous current mode. The outputvoltage ripple must not be more than 0.5%. Specify thefrequency and the values of each component. Suggest the powerswitch also.

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15

Boost (step-up) converter

V d

L D

C

RL

S

V d

L D

CRL

S

V d

LD

C RLS

+ v L

+

V o

+ v L -

V o

+

CIRCUIT OF BOOST CONVERTER

CIRCUIT WHEN SWITCH IS CLOSED

CIRCUIT WHEN SWITCH IS OPENED

V o

+

i L

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16

Boost analysis:switch closed

L DT V

i

LV

dt di

DT i

t i

dt di

LV

dt di

dt

di L

V v

d closed L

d L

L L L

d L

L

d L

DT T

i L

v L CLOSED

t

t

V d

V d V o

i L

V d

LD

CS

+ v L

i L

+vo

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17

Switch opened

L

DT V V i

LV V

dt di

T Di

t i

dt di

LV V

dt di

dt di

L

V V v

od opened L

od L

L

L L

od L

L

od L

)1(

)1(

DT T

( 1-D )T

i L

v L OPENED

t

t

V d

V d V o

i L

V d

D

CS

+ v L -

i L

+vo

-

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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB

18

Steady-state operation

D

V V

LT DV V

L DT V

ii

d o

od d

opened Lclosed L

1

0)1(

0

• Boost converter produces output voltage that isgreater or equal to the input voltage.

• Alternative explanation:

– when switch is closed, diode is reversed. Thusoutput is isolated. The input supplies energy toinductor.

– When switch is opened, the output stagereceives energy from the input as well as fromthe inductor. Hence output is large.

– Output voltage is maintained constant byvirtue of large C.

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19

Average, Maximum, MinimumInductor Current

L DT V

R D

V i I I

L DT V

R D

V i I I

R D

V I

R D

V R D

V

I V

RV

I V

d d L L

d d L L

d L

d

d

Ld

od d

2)1(

2

:currentinductorMinimum

2)1(

2

:currentinductorMaximum

)1(

:currentinductorAverage

)1(

)1(

powerOutputpowerInput

2min

2max

2

2

2

2

2

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20

L and C values

RCf D

V V

r

RCf

DV

RCf

DT V V

V C DT RV

Q

f R D D

TR D D L

L DT V

R D

V

I

o

o

ooo

oo

d d

factorRipple

21

21

02)1(

0

CCM,For

2

2

min

2

min

I max

I min

I min

I max

ic

i D

i L

V d

v L

V d V o

I o=V o / R

DT T

Q

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21

Examples

• The boost converter has the following parameters: V d=20V,D=0.6, R=12.5ohm, L=65uH, C=200uF, f s=40KHz. Determine(a) output voltage, (b) average, maximum and minimuminductor current, (c) output voltage ripple.

• Design a boost converter to provide an output voltage of 36Vfrom a 24V source. The load is 50W. The voltage ripple factormust be less than 0.5%. Specify the duty cycle ratio, switching

frequency, inductor and capacitor size, and power device.

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22

Buck-Boost converter

V d L

D

C RL

S+

V o

V o

+

CIRCUIT OF BUCK-BOOST CONVERTER

CIRCUIT WHEN SWITCH IS CLOSED

CIRCUIT WHEN SWITCH IS OPENED

V o

+

i LV d v L

+

i L

V d

v L

+

D

DS

S

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23

Buck-boost analysis

DT T

I min

I max

ic

i D

i L

V d

v L

Q

V d V o

I o=V o / R

I max

I min

LT DV

i

LV

T Di

t i

LV

dt di

dt di

LV v

L DT V

i

LV

DT i

t i

LV

dt di

dt di

LVd v

oopened L

o L L

o L

Lo L

d closed L

d L L

d L

L L

)1()(

)1(

openedSwitch

)(

closedSwitch

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24

Output voltage

• NOTE: Output of a buck-boost converter either behigher or lower than input.

– If D>0.5, output is higher than input – If D<0.5, output is lower input

• Output voltage is always negative.

• Note that output is never directly connected to load.

• Energy is stored in inductor when switch is closedand transferred to load when switch is opened.

D DV

LT DV

L DT V

s

od

opened iLclosed iL

1V

:tageOutput vol

0)1(

0

:operationstateSteady

o

)()(

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25

Average inductor current

2

2

2

2

)1(

,forngSubstituti

:ascurrentinductoraverage

torelatediscurrentsourceaverageBut

i.e.source,bythesuppliedpower

equalmustloadby the absorbedpower

converter,in thelosspowernoAssuming

D R

DV DV

P RDV

V I

V

D I V RV

D I I

I V RV

PP

d

d

o

d

o L

o

Ld o

Ls

sd o

so

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26

L and C values

RCf D

V V

r

RCf DV

RC DT V

V

V C DT RV

f R D

L

L DT V

D R

D

L DT V

D R

DV i I I

L DT V

D R DV i I I

o

o

ooo

oo

d

d d L L

d d L L

Q

ripple,tageOutput vol

2)1(

02)1(

V

CCMFor

2)1(2

2)1(2

current,inductorminandMax

2

min

2d

2min

2max

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27

Converters in CCM: Summary

V d

L

D

C RL

S

+

V o

f R D

L

LCf

DV V

DV

V

o

o

d

o

2)1(

8

1

Buck

min

2

f R D D

L

RCf D

V V

DV V

o

o

d

o

2)1(

11

Boost

2

min

f R D

L

RCf D

V V

D

D

V

V

o

od

o

2)1(

1

BoostBuck

2

min

V

d

L

D C RL

S

+

V o

V

d

L D

CRL

S

+V

o

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Control of DC-DC converter:pulse width modulation (PWM)

Comparator

Vcontrol

SawtoothWaveform

Vo (desired)

Vo (actual)

+

-

Switch controlsignal

SawtoothWaveform

Vcontrol 1

Switchcontrolsignalton 2

T

Vcontrol 2

ton 1

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Isolated DC-DC Converter

• Isolated DC-DC requires isolation transformer• Two types: Linear and Switched-mode

• Advantages of switched mode over linear powersupply-Efficient (70-95%)

-Weight and size reduction

• Disadvantages-Complex design-EMI problems

• However above certain ratings,SMPS is the only feasible choice

• Types of SMPS-Flyback

-forward-Push-pull-Bridge (half and full)

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Linear and SMPS block diagramBasic Block diagram of linear power supply

Basic Block diagram of SMPS

Base/gateDrive

ErrorAmp.

LineInput

3 / 150/60 HzIsolation

Transformer

Rectifier/ Filter

+

Vd

-

Vce =Vd-Vo

C E

B

Vo

Vref

RL

+Vo

+

Vo

-

DC UnregulatedDC Regulated

EMIFILTER

RECTIFIERAND

FILTER

HighFrequency

rectifierandfilter

Base/ gatedrive

PWMController

errorAmp

Vo

Vref

DCRegulated

DC-DC CONVERSITION ANDISOLATIONDC

Unregulated

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High frequency transformer

:Models

;

iprelationshoutput-inputBasic

voltagevarying-meup/down tistep2)isolationelectricaloutput-Input 1)

:functionBasic

1

2

2

1

2

1

2

1

N N

ii

N

N

v

v

V 1 V2

++i1 i2 N 1 N 2

Ideal model

V 1 V 2

++

i1 i2 N 1 N 2

Model used formost PE application

Lm

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Flyback Converter

V d

+

V o

V d

N 1 N 2i1

i2

+

v2v1

+

i LM

i D

+ v D

iC i R

C R

vSW +

+

iS

L M

V o

Flyback converter circuit

Model with magnetisinginductance

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Operation: switch closed

V d

V o

N 2

+

0

0

v1

v1=V s

i LM

is=i LM

+

N 1

+

v2

0and0

Therefore,

off turneddiodei.e. ,0

er,transformtheof sideloadOn the

12

1

2

1

2

1

212

1

ii

N N V V v

N N

V N N

vv

L

DT V i

LV

DT iL

dt iL

dt diL

dt di

LV v

d o D

d

m

d

closed L

m

d mmm

Lmmd

m

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34

Switch opened

s

+

v1

+

i LM

N 1 N 2

v2= V S+

+

V o

i D

vSW

2

1

2

1

2

1

211

2

1

2

121

2

2

11

:switchtheacrossVoltage

)1(

1

But

N N

V V v

N N

LT DV

i

N N

LV

T D

i

dt

i

dt

di

N N V

dt di Lv

N N

V N N

vv

V v N

N V v

od SW

m

oopenm L

m

om Lm Lm L

om Lm

o

o

o

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Output voltage

1

22

1

1

01

0

operation,state-steadyFor

N N

D D

V V

N N

LT DV

L DT V

ii

d o

m

o

m

d

opened Lclosed L mm

• Input output relationship is similar to buck-boostconverter.

• Output can be greater of less than input,dependingupon D.

• Additional term, i.e. transformer ratio is present.

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36

Flyback waveforms

i Lm

is

t

t

i D

iC

v1

-V(N 1 /N 2)

V o / R

V s

DT T

i L

1

20

2

1

22

20

20

20

0

)1(

)1(

:asncan writte

forSolving

:as torelatedis

N N

R DV

N N

R D

DV I

I

DRV V

I

RV

D I V

I

D I T

DT I I

I I R

V I V

PP

d L

L

d L

Ld

L

L L

s

Ls

sd

s

m

m

m

m

m

mm

m

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37

Max, Min inductor current

RCf D

V V

r

N

N

f

R DV L

f L DV

L DT V

N N

R D

DV

I

L DT V

N N

R D

DV

i I I

L DT V

N N

R D

DV

i I I

d m

m

d

m

d d

L

m

d d

L

L L

m

d d

L L L

m

m

mm

m

mm

0

0

2

2

12

min

2

1

22

min

2

1

22

min,

2

1

22

max,

boost,similar toisncalculatioRipple2

)1(

22)1(

0,CCM,For

2)1(

2

2)1(

2

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38

ExampleThe Flyback converter has these specifications:DC input voltage: 40VOutput voltage: 25VDuty cycle: 0.5Rated load: 62.5WMax peak-peak inductor current ripple:25% of the average inductor current.Maximum peak-peak output voltage: 0.1VSwitching frequency: 75kHz

Based on the abovementioned specifications, determinea) Transformer turns ratiob) Value of magnetizing inductor L m.c) Maximum and minimum inductor current.

d) Value of capacitor C.

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39

Full-bridge converter

SW2SW4

SW3

V S

N S

N S

+

v x C

L x

R+

V o

+

v p

SW1

SW1,SW2

SW3,SW4DT T

2T DT

T 2V P

V S

-V S

V x

P

SS N

N V

DT 2T

DT T 2

T

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Full bridge: basic operation

• Switch “pair”: [S1 & S2];[S3 & S4].

• Each switch pair turn on at a time as shown. Theother pair is off.

• “AC voltage” is developed across the primary.Then transferred to secondary via high frequencytransformers.

• On secondary side, diode pair is “high frequencyfull wave rectification”.

• The choke (L) and (C ) acts like the “buck converter” circuit.

• Output Voltage

D N N

V V p

sso

2


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