power electronics and drives (version 3-2003) dr. zainal salam, utm-jb 1 chapter 3 dc to dc...

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.

DC-DC Converter (Chopper)

DEFINITION: Converting the unregulated DC input to a

controlled DC output with a desired voltage 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


3

Linear regulator• Transistor is operated

in linear (active) mode.

• Output voltage

• The transistor can be conveniently modelled by an equivalent variable resistor, as shown.

• Power loss is high at high current due to:

Lceo

TLo

IVP

RIP

or

2

+

VoRL

+ VCEce IL

LINEAR REGULATOR

RT

EQUIVALENTCIRCUIT

Vin

RL

+ Vce IL

VinVo

+

ceino VVV


4

Switching Regulator

• Transistor is operated in switched-mode:– Switch closed:

Fully on (saturated)– Switch opened:

Fully off (cut-off)

– When switch is open, no current flow in it

– When switch is closed no voltage drop across it.

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

transferred from source to load.

– Power loss is zero (for ideal switch):

• Switching regulator is the basis of all DC-DC converters

+

Vo

RL

+ Vce IL

SWITCHING REGULATOR

EQUIVALENT CIRCUIT

Vin

RL

IL

VinVo

+

(ON)closed

(OFF)open

(ON)closed

DT T

OUTPUT VOLTAGE

Vo

SWITCH

Vin


5

Buck (step-down) converter

Vd

L

D C RL

S

+

Vo

Vo

+

CIRCUIT OF BUCK CONVERTER

CIRCUIT WHEN SWITCH IS CLOSED

CIRCUIT WHEN SWITCH IS OPENED

Vo

+

iL

Vd D RL

S

Vd D RL

S

+ vL

+ vL

iL


6

Switch is turned on (closed)

• Diode is reversed biased.

• Switch conducts inductor current

• This results in positive inductor voltage, i.e:

• It causes linear increase in the inductor current

odL VVv

dtvL

i

dt

diLv

LL

LL

1

Vd VD

+ vL -

C RL

+

Vo

Vd Vo

Vo

closedopened

closedopened

t

DT Tt

iLmin

iLmax

IL

vL

iL

iL

+

S


7

Switch turned off (opened)

• Because of inductive energy storage, iL

continues to flow.

• Diode is forward biased

• Current now flows (freewheeling) through the diode.

• The inductor voltage can be derived as:

oL Vv

Vd

+ vL -

C RL

+

Vo

Vd Vo

Vo

closedopened

closedopened

t

DT Tt

iLmin

iLmax

IL

vL

iL

iL

S

D

(1-D)T


8

Analysis

TDL

Vi

L

V

TDi

ti

dtdi

L

V

dtdi

dtdi

LVv

DTL

VVi

L

VV

DTi

ti

dtdi

i

iL

VV

dtdi

dtdi

LVVv

oopenedL

oLLL

oL

LoL

odclosedL

odLLL

L

L

odL

LodL

)1(

)1(

opened,switch For

Figure From

linearly. increased

must hereforeconstant.T

positive a is of Derivative

:(on) closed isswitch When the

IL

iL max

DT T

iL

Vd Vo

vL

t

t

iL min

closed

iL


9

Steady-state operation

do

so

sod

openedLclosedL

L

L

DVV

TDL

VDT

L

VV

ii

i

i

0)1(

0

:i.e zero, is period oneover of

change theisThat cycle.next theof begining

at the same theis cycle switching of end

at the that requiresoperation state-Steady

iL Unstable current

Decaying current

Steady-state current

t

t

t

iL

iL


10

minmax

min

max

L

:ripplecurrent Inductor

2)1(1

2

:current Minimum

2)1(1

)1(21

2

:current Maximum

Rin current Average currentinductor Average

IIi

LfD

RV

iII

LfD

RV

TDL

V

R

ViII

R

VII

L

oL

L

o

ooLL

oRL

Average, Maximum and Minimum Inductor Current

IL

Imax

Imin

iL

iL

t


11

Continuous Current Mode (CCM)

min

min

min

min

be bchosen is Normally

operation. of mode continous ensure

current toinductor minimum theis This

2)1(

02

)1(1

,0 operation, continuousFor

2)1(1

2

analysis, previous From

LL

RfD

LL

LfD

RV

I

LfD

RV

iII

o

oL

L

iL

Imax

Imint

0


12

Output voltage ripple

size.capacitor Increasing 3)

sizeinductor Increasing 2)

frequency switching Increasing 1)

:by reduced becan Ripple :Note

8

)1(

factor, ripple theSo,

8

)1(8

peak) to-(Peak voltageRipple8

2221

:formula area triangleUse

:as witten becan charge The

:currentCapacitor KCL,

2

2

LCf

DV

Vr

LCf

DCiT

V

iT

iTQ

CQ

V

VCQ

CVQ

iii

o

o

Lo

L

L

oo

o

RLc

iL

iL=IR

imax

imin

0

0

Vo

+

Vo/R

iRL iL

iC

iC


13

Basic design procedures

Vd(inputspec.)

SWITCH

f = ?D = ?TYPE ?

D

L

Lmin= ?L = 10Lmin

Cripple ?

RLPo = ?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 Lmin. Choose L>>10 Lmin

• 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 Ip/3, where Ip is the peak capacitor current given by iL/2. • ECAPs can be used

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

iL is given as:

22

, 3

2

L

LRMSLi

II


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 minimum inductor 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 is 125W. (a) Determine the duty cycle, (b) value of L to limit the peak inductor current to 6.25A, (c) value of capacitance to limit the output voltage ripple factor to 0.5%.

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


15

Boost (step-up) converter

Vd

L D

C

RL

S

Vd

L D

CRL

S

Vd

LD

C RLS

+ vL

+

Vo

+ vL -

Vo

+

CIRCUIT OF BOOST CONVERTER



Vo

+

iL


16

Boost analysis:switch closed

L

DTVi

L

V

dt

diDT

i

t

i

dt

diL

V

dt

didt

diL

Vv

dclosedL

dL

LLL

dL

L

dL

DT T

iL

vLCLOSED

t

t

Vd

Vd Vo

iL

Vd

L D

CS

+ vL

iL

+vo


17

Switch opened

L

DTVVi

L

VV

dt

di

TD

it

i

dt

diL

VV

dt

didt

diL

VVv

odopenedL

odL

L

LL

odL

L

odL

)1(

)1(

DT T

( 1-D )T

iL

vL OPENED

t

t

Vd

Vd Vo

iL

Vd

D

CS

+ vL -

iL

+vo

-


18

Steady-state operation

D

VV

L

TDVV

L

DTV

ii

do

odd

openedLclosedL

1

0)1(

0

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

• Alternative explanation:

– when switch is closed, diode is reversed. Thus output is isolated. The input supplies energy to inductor.

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

– Output voltage is maintained constant by virtue of large C.


19

Average, Maximum, Minimum Inductor Current

L

DTV

RD

ViII

L

DTV

RD

ViII

RD

VI

RD

V

R

D

V

IV

R

VIV

ddLL

ddLL

dL

d

d

Ld

odd

2)1(

2

:currentinductor Minimum

2)1(

2

:currentinductor Maximum

)1(

:currentinductor Average

)1(

)1(

powerOutput powerInput

2min

2max

2

2

2

2

2


20

L and C values

RCfD

V

Vr

RCf

DV

RCf

DTVV

VCDTR

VQ

fRDD

TRDDL

L

DTV

RD

V

I

o

o

ooo

oo

dd

factor Ripple

21

21

02)1(

0

CCM,For

2

2

min

2

min

Imax

Imin

Imin

Imax

ic

iD

iL

Vd

vL

Vd Vo

Io=Vo / R

DT T

Q


21

Examples

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

• Design a boost converter to provide an output voltage of 36V from a 24V source. The load is 50W. The voltage ripple factor must be less than 0.5%. Specify the duty cycle ratio, switching frequency, inductor and capacitor size, and power device.


22

Buck-Boost converter

Vd L

D

C RL

S

RL

+

Vo

Vo

+

CIRCUIT OF BUCK-BOOST CONVERTER



Vo

+

iLVd vL

+

iLVd vL

+

D

DS

S


23

Buck-boost analysis

DT T

Imin

Imax

ic

iD

iL

Vd

vL

Q

Vd Vo

Io=Vo / R

Imax

Imin

L

TDVi

L

V

TD

i

t

iL

V

dt

didt

diLVv

L

DTVi

L

V

DT

i

t

iL

V

dt

didt

diLVdv

oopenedL

oLL

oL

LoL

dclosedL

dLL

dL

LL

)1()(

)1(

openedSwitch

)(

closedSwitch


24

Output voltage

• NOTE: Output of a buck-boost converter either be higher 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 closed and transferred to load when switch is opened.

DD

V

L

TDV

L

DTV

s

od

openediLclosediL

1V

:tageOutput vol

0)1(

0

:operation stateSteady

o

)()(


25

Average inductor current

2

2

2

2

)1(

,for ngSubstituti

:ascurrent inductor average

torelated iscurrent source averageBut

i.e. source,by thesuppliedpower

equalmust load by the absorbedpower

converter, in the losspower no Assuming

DR

DV

DV

P

RDV

VI

V

DIVR

V

DII

IVR

V

PP

d

d

o

d

oL

o

Ldo

Ls

sdo

so


26

L and C values

RCfD

V

Vr

RCf

DV

RC

DTVV

VCDTR

V

fRD

L

L

DTV

DR

D

L

DTV

DR

DViII

L

DTV

DR

DViII

o

o

ooo

oo

d

ddLL

ddLL

Q

ripple, tageOutput vol

2)1(

02)1(

V

CCMFor

2)1(2

2)1(2

current,inductor min andMax

2

min

2d

2min

2max


27

Converters in CCM: Summary

V

dL

DC RL

S

+

Vo

f

RDL

LCf

D

V

V

DV

V

o

o

d

o

2

)1(

8

1

Buck

min

2

fRDD

L

RCfD

V

V

DV

V

o

o

d

o

2)1(

11

Boost

2

min

f

RDL

RCf

D

V

V

D

D

V

V

o

o

d

o

2

)1(

1

BoostBuck

2

min

V

d

L

D C RL

S+Vo

V

d

L D

CRL

S

+Vo


28

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

Comparator

Vcontrol

SawtoothWaveform

Vo (desired)

Vo (actual)

+

-

Switch control signal

SawtoothWaveform

Vcontrol 1

Switchcontrolsignalton 2

T

Vcontrol 2

ton 1


29

Isolated DC-DC Converter

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

• Advantages of switched mode over linear power supply-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)


30

Linear and SMPS block diagram

Basic Block diagram of linear power supply

Basic Block diagram of SMPS

Base/gateDrive

ErrorAmp.

LineInput

3/1

50/60 HzIsolation

Transformer

Rectifier/Filter

+

Vd

-

Vce=Vd-Vo

C E

B

Vo

Vref

RL

+Vo

+

Vo

-

DC Unregulated

DC Regulated

EMIFILTER

RECTIFIERAND

FILTER

HighFrequency

rectifierandfilter

Base/gatedrive

PWMController

errorAmp

Vo

Vref

DCRegulated

DC-DC CONVERSITION ANDISOLATIONDC

Unregulated


31

High frequency transformer

: Models

;

iprelationshoutput -input Basic

voltage varying- meup/down ti step 2)

isolation electricaloutput -Input 1)

:function Basic

1

2

2

1

2

1

2

1

N

N

i

i

N

N

v

v

V1V2

+

+

i1 i2N1 N2

Ideal model

V1V2

+

+

i1 i2N1 N2

Model used formost PE application

Lm


32

Flyback Converter

Vd

+

Vo

Vd

N1 N2i1

i2

+

v2v1

+

iLM

iD

+ vDiC

iR

C R

vSW+

+

iS

LM

Vo

Flyback converter circuit

Model with magnetisinginductance


33

Operation: switch closed

Vd

Vo

N2

+

0

0

v1

v1=Vs

iLM

is=iLM+

N1

+

v2

0 and 0

Therefore,

off turneddiode i.e. ,0

er, transform theof side load On the

12

1

2

1

2

1

212

1

ii

N

NVVv

N

NV

N

Nvv

L

DTVi

L

V

DT

iL

dt

iL

dt

diLdt

diLVv

doD

d

m

dclosedL

m

dmmm

Lmmd

m


34

Switch opened

Vs

+

v1

+

iLM

N1 N2

v2= VS

+

+

Vo

iD

vSW

2

1

2

1

2

1

2

11

2

1

2

121

2

2

11

:switch theacross Voltage

)1(

1

But

N

NVVv

N

N

L

TDVi

N

N

L

V

TD

i

dt

i

dt

di

N

NV

dt

diLv

N

NV

N

Nvv

Vv

N

NVv

odSW

m

oopenmL

m

omLmLmL

omL

m

o

o

o


35

Output voltage

1

2

2

1

1

01

0

operation, state-steadyFor

N

N

DD

VV

N

N

L

TDV

L

DTV

ii

do

m

o

m

d

openedLclosedL mm

• Input output relationship is similar to buck-boost converter.

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

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


36

Flyback waveforms

iLm

is

t

t

iD

iC

v1

-V(N1 /N2)

Vo/ R

Vs

DT T

iLM

1

20

2

1

22

20

20

20

0

)1(

)1(

:asn can writte

for Solving

:as torelated is

N

N

RD

V

N

N

RD

DVI

I

DRV

VI

R

VDIV

I

DIT

DTII

IIR

VIV

PP

dL

L

dL

Ld

L

LL

s

Ls

sd

s

m

m

m

m

m

mm

m


37

Max, Min inductor current

RCfD

V

Vr

N

N

f

RDVL

fL

DV

L

DTV

N

N

RD

DV

I

L

DTV

N

N

RD

DV

iII

L

DTV

N

N

RD

DV

iII

dm

m

d

m

dd

L

m

dd

LLL

m

dd

LLL

m

mmm

mmm

0

0

2

2

12

min

2

1

22

min

2

1

22

min,

2

1

22

max,

boost, similar to isn calculatio Ripple

2

)1(

22)1(

0, CCM,For

2)1(

2

2)1(

2


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, determine• Transformer turns ratio• Value of magnetizing inductor Lm. • Maximum and minimum inductor current.• Value of capacitor C.


39

Full-bridge converter

SW2SW4

SW3

VS

NS

NS

+

vx C

Lx

R

+

Vo

+

vp

SW1

SW1,SW2

SW3,SW4DT T

2

T DTT

2VP

VS

-VS

Vx

P

SS N

NV

DT2

TDT

T

2T


40

Full bridge: basic operation

• Switch “pair”: [S1 & S2];[S3 & S4].

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

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

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

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

• Output Voltage

DN

NVV

p

sso

2

power electronics and drives (version 3-2003) dr. zainal salam, utm-jb 1 chapter 3 dc to dc...

Documents

power electronics

drives version

zainal salam

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