dc-dc switch-mode converters - unlveebag/ee-442-642-dc-to-dc converters.pdf7-3 stepping down a dc...

7-1

DC-DC Switch-Mode

Converters

EE 442/642

7-2

Block Diagram of DC-DC Converters

7-3

Stepping Down a DC Voltage – Basic Concept

Any parasitic inductance in the above circuit will cause damage to the switch

In addition, the output voltage contains significant ripple..

dd

s

ono DVV

T

tV

s

on

T

tD Switch Duty Ratio: Average Output Voltage:

7-4

Pulse-Width Modulation in DC-DC Converters

s

on

T

tD Duty Ratio:

7-5

Step-Down (Buck) DC-DC Converter

dd

s

ono DVV

T

tV Output Voltage:

Filter corner frequency (fc) should

Be much lower than the

Switching frequency (fs)

7-6

Step-Down DC-DC Converter: Continuous Conduction

Mode

D

II

IVIV

DVV

do

oodd

do

7-7

Step-Down DC-DC Converter: boundary of

Continuous/Discontinuous Conduction Mode

Output Voltage:

Critical current below which

inductor current becomes

discontinuous:

ds

ods

odon

peakLoBLB

VDL

DT

VVL

DTVV

L

tiII

)1(2

)(2

)(22

1,

do DVV

7-8

Step-Down DC-DC Converter: Discontinuous

Conduction Mode (Constant Vd)

L

VTI

IID

D

V

V

dsLB

LBod

o

8

)4/(

max,

max,

2

2

Output Voltage:

where

max,

1

1

4

0)()(

LB

o

sosod

DI

I

TVDTVV

7-9

Step-Down DC-DC Converter: Limits of Cont./Discont.

Conduction Mode (Constant Vd)

7-10

Step-Down DC-DC Converter: Limits of Cont./Discont.

Conduction mode (Constant Vo)

If output voltage is kept constant,

Duty ratio for a given current:

2/1

max,

max,

)/(1

/

2)1(

2

Do

LBo

d

o

s

osLB

osLB

VV

II

V

VD

L

VTID

L

VTI

7-11

Step-Down Converter: Output Voltage Ripple

Consider continuous conduction mode.

Assume all the inductor ripple current

flows through the capacitor (with the

average current flows through the resistive

load. Then

222

)1(2

)1(8

),1(

),222

1(

1

s

cs

o

o

osL

sLco

f

fDD

LC

T

V

V

DL

VTI

TI

CC

QV

7-12

Step-Up (Boost) DC-DC Converter

• Output voltage must be greater than the input

7-13

Step-Up DC-DC Converter: Continuous Conduction

)1(

)1/(

)(

DII

IVIV

DVV

tVVtV

do

oodd

do

offodond

7-14

Step-Up DC-DC Converter: Effect of Parasitics

Parasitic elements are due to losses in the inductor, capacitor,

switch, and diode.

The duty-ratio is generally limited before the parasitic effects

become significant.

7-15

Step-Up DC-DC Converter: Limits of Cont./Discont.

Conduction

L

VTIDD

L

VTIDI

L

VTIDD

L

VTV

L

tiII

osoB

osdBoB

osLB

osd

onpeakLdBLB

27

2,)1(

2)1(

8),1(

222

1

max,

2

max,,

7-16

Step-Up DC-DC Converter: Discontinuous

Conduction (constant Vo)

2/1

max,

127

4

oB

o

d

o

d

o

I

I

V

V

V

VDFor constant Vo and variable Vd,

)2/(

0)(

1

1

LVTD

I

TVVDTV

ds

o

sodsd

7-17

Step-Up DC-DC Converter: Limits of Cont./Discont.

Conduction (constant Vo)

7-18

Step-Up DC-DC Converter Output Ripple

Consider continuous conduction mode.

Assume all the inductor ripple current

flows through the capacitor (with the

average current flows through the

resistive load. Then

ss

o

o

sosoco

TD

RC

DT

V

V

C

DT

R

V

C

DTI

C

QV

,

7-19

Step-Down/Up (Buck/Boost) DC-DC Converter

• The output voltage can be higher or lower than the

input voltage.

• Note the reverse polarity of the output voltage.

7-20

Buck-Boost Converter: Cont. Conduction Mode

odL

do

oodd

do

offoond

III

DDII

IVIV

DDVV

tVtV

/)1(

)1/(

0)(

Note:

7-21

Buck-Boost Converter: Limits of Cont./Discont.

Conduction

L

VTID

L

VTI

L

VTID

L

VTI

osoB

osoB

osLB

osLB

2,)1(

2

2),1(

2

max,

2

max,

7-22

Buck-Boost Converter: Disc. Conduction Mode

2/1

max,

oB

o

d

o

I

I

V

VDFor constant Vo and variable Vd,

)(2

0)(

1

1

1

DDTL

VI

I

DI

TVDTV

sd

L

d

o

sosd

7-23

Buck-Boost Converter: Limits of Cont./Discont.

Conduction

7-24

Buck-Boost Converter: Effect of Parasitics

In practice, the duty-ratio is limited to avoid these

parasitic effects from becoming significant.

7-25

Buck-Boost Converter: Output Voltage Ripple

Assume all the ripple current component of the diode current flows

through the capacitor and its average value flows through the load resistor.

ss

o

o

sosoco

TD

RC

DT

V

V

C

DT

R

V

C

DTI

C

QV

,

7-26

Cuk DC-DC Converter (Buck-Boost Converter)

7-27

Full-Bridge DC-DC Converter:

Possible Operation in all Four Quadrants

Applications:

• DC Motor Drives

• DC-AC Conversion at power frequency (UPS)

• DC-AC Conversion at high frequency (switch-mode power supplies)

7-28

Converter Waveforms: PWM with Bi-polar Voltage Switching

← triangular (rather than saw-tooth)

waveform is compared to vcontrol.

When vcontrol >vtri ,TA+,TB- are switched

ON, and (TB+,TA-) are switched OFF.

Duty cycle of (TA+,TB-): D1 = ton/Ts

=0.5(1+vcontrol/Vtri)

Duty cycle of (TB+,TA-): D2= (1- D1)

Vo = VAN - VBN = D1 Vd – D2Vd

= (2 D1 – 1) Vd = k.vcontrol

where k = Vd/Vtri

As D1: 0 →1, Vo: -Vd → Vd.

← Case where the average power flows

from Vd to Vo.

← Case where the average power flows

from Vo to Vd.

7-29

Converter Waveforms: Uni-polar Voltage Switching

← triangular waveform is compared to

vcontrol and -vcontrol .

When vcontrol >vtri ,TA+,TB- are switched

ON. When -vcontrol >vtri ,TB+,TA- are

switched ON.

Duty cycle of (TA+,TB-): D1 = ton/Ts

Duty cycle of (TB+,TA-): D2= (1- D1)

Vo = VAN - VBN = D1 Vd – D2Vd

= (2 D1 – 1) Vd = k.vcontrol

where k = Vd/Vtri

← Case where the average power flows

from Vd to Vo.

← Case where the average power flows

from Vo to Vd.

7-30

Output Ripple in Full Bridge Converter

2

11

22

,, 2 DDVVVV dormsormsr

dormsormsr VDDVVV 246 2

11

22

,,

(a)Bipolar switching:

(b)Unipolar switching:

7-31

Switch Utilization in DC-DC Converters

)/()(/ TTooTo IVIVPP Switch Utilization Ratio:

where VT and IT are the peak voltage and current

ratings of the switch.