Embed Size (px)
DESCRIPTION
Chapter 7 DC-DC Switch-Mode Converters. dc-dc converters for switch-mode dc power supplies and dc-motor drives these dc-dc converters are studied: step-down (buck) step-up (boost) step-up/ step-down (buck-boost) Cúk Full-bridge. Block Diagram of DC-DC Converters. - PowerPoint PPT Presentation
Citation preview
7-1
Chapter 7
DC-DC Switch-Mode Converters
• dc-dc converters for switch-mode dc power supplies and dc-motor drives
• these dc-dc converters are studied:
• step-down (buck)
• step-up (boost)
• step-up/ step-down (buck-boost)
• Cúk
• Full-bridge
7-2
Block Diagram of DC-DC Converters
7-3
Stepping Down a DC Voltage
• switching at constant frequency:
• pulse-width modulation (PWM) switching
offons ttT
vo
7-4
Pulse-Width Modulation (1)
• signal-level control voltage vcontrol generated by amplifying
the difference between actual output voltage and desired output voltage
• switch control signal generated by comparing vcontrol with
repetitive waveform
7-5
Pulse-Width Modulation (2)
• switch duty-cycle D is st
control
s
on
V
v
T
tD
ˆ
7-6
Step-Down (Buck) DC-DC Converter (1)
7-7
Step-Down (Buck) DC-DC Converter (2)
• average output voltage Vo
controlcontrol
st
do
dds
on
T
t
t
ds
o
vkvV
VV
VDVT
tdtdtV
TV
s
on
on
ˆ
or
01
0
7-8
R L C low-pass filter
CLfc 2
1
log401
log40 LC
7-9
Continuous conduction mode (1)
7-10
Continuous conduction mode (2)
DT
t
V
V
or
tTVtVV
dtvdtvdtv
s
on
d
o
onsoonod
T
t
L
t
L
T
L
s
on
ons
)()(
000
7-11
Continuous conduction mode (3)
• input power equals output power:
• step-down converter is equivalent to a dc transformer where the turns ratio is in the range 0-1
DV
V
I
I
IVIV
PP
o
d
d
o
oodd
od
1
7-12
Edge of Cont./Discont. Conduction
• Critical current below which inductor current becomes discontinuous:
L
VTIDV
L
TD
V
VV
L
TDVV
L
TDVV
L
tiI
dsLBd
s
d
od
sod
sod
onpeakLLB
8)1(
2
1
)1(2
1)(
2
1)(
2
1
2
1
max,
,
7-13
Discontinuous Conduction Mode
7-14
Discontinuous Conduction Mode (2)• Vo/Vd in the discontinuous mode
• integrating the inductor voltage over one time period,
• From the figure,
)1(
0)()(
1
1
D
D
V
V
TVDTVV
d
o
sosod
7-15
Discontinuous Conduction Mode (3)
L
VTI dsLB 8max,
7-16
Limits of Cont./Discont. Conduction with constant D
• The duty-ratio of 0.5 has the highest value of the critical current
• The boundary between the cont/discont mode is shown by the dashed curve
)1(4/8
max,
max,
DDIIL
VTI
LBLB
dsLB
7-17
Discont. Conduction mode with constant Vo
• in regulated dc power supplies Vo is kept constant by adjusting the duty ratio D• since Vd=Vo/D the average inductor current at the edge of cont/discont mode is
)1(2
)1(2
DL
VT
DVL
DTI
os
ds
LB
• when D=0 the maximum ILB,max is
L
VTI osLB 2max,
7-18
Discont. Conduction mode with constant Vo
2/1
max,max, /1
/
2
do
LBo
d
oosLB VV
II
V
VD
L
VTI
7-19
Step-Down Conv.: Output Voltage Ripple (1)
222
11 sLo
TI
CC
QV
Peak-peak voltage ripple:
7-20
Step-Down Conv.: Output Voltage Ripple (2)
)1(1
)(1
1
DTVL
I
T
tDtTV
LI
tVL
I
t
ILV
soL
s
ononsoL
offoL
Lo
During toff:
Computing :LI
7-21
Step-Down Conv.: Output Voltage Ripple (3)
LCf
f
fD
LC
DT
V
V
TI
CC
QV
I
DTVL
I
cs
cs
o
o
sLo
L
soL
2
1)1(
2
)1(
8
1
gives222
11
into ngsubstituti
)1(1
222
• ripple can be minimized by making fc of the low pass filter fc << fs
7-22
Step-Up (Boost) DC-DC Converter
• Output voltage is greater than the input
• main application: regulated dc power supplies
7-23
Step-Up DC-DC Converter Waveforms (1)
DV
V
DVV
DVVDVDV
DVVDV
T
tTVV
T
tV
tVVtV
d
o
od
ddod
dod
s
onsdo
s
ond
offdoond
1
1
)1(
)1(
)1)((
)(
)(
7-24
Effect of Parasitics
• The duty-ratio is generally limited before the parasitic effects become significant
7-25
Step-Up DC-DC Converter Waveforms (2)
• Assuming a lossless circuit Pd=Po
)1( DI
I
IVIV
d
o
oodd
Thus:• power remains the same• voltage increases• current decreases• equivalent to a DC transformer
7-26
Edge of Cont./Discont. Conduction (1)
)1(2
and 1
1
using2
12
1,
DDL
VTI
T
tD
DV
V
tL
V
iI
osLB
s
on
d
o
ond
peakLLB
7-27
Edge of Cont./Discont. Conduction (2)
• recognizing that the inductor current IL and the input current Id are the same Id= IL
• and
212
DDL
VTI osoB
)1(2
DDL
VTI osLB
• highest ILB at D=0.5
• highest IOB at D=1/3
L
VTI osLB 8max,
)1(27
2max, L
VTI osoB
)1( DII do
7-28
Edge of Cont./Discont. Conduction (3)
)1(2
DDL
VTI osLB 21
2DD
L
VTI osoB
7-29
Discont. Conduction (1)
• Occurs at light loads
7-30
Discont. Conduction (2)
)3(
constant remainspower since and
)2(
0)(
1
1
1
1
1
DI
I
D
V
V
TVVDTV
d
o
d
o
sodsd
7-31
Discont. Conduction (3)
10
1
,
1,
21
1
,2
,
0 0 1
,,
,
2
(3) using and
)(2
ngsubstituti2
22
1
1 1
DL
TVI
DDL
TVI
i
Di
T
T
iDT
DT
i
T
dttT
idtt
DT
i
TI
and
DTL
Vi
sd
sdd
peakL
peakL
s
s
peakLs
s
peakL
s
DT T
s
peakL
s
peakL
sd
sd
peakL
s s
7-32
sd
o
sd
o
d
o
sd
o
d
o
TVLI
DTVLI
V
V
DTV
LI
D
V
V
2
2
2
2
1
1
1
Discont. Conduction (4)
Solving Io in order to 1
Substituting above
7-33
2
max,
max,
2
14
27/
27
2
12
DDII
L
VTI
DDL
VTI
oBoBos
oB
osoB
Edge of Cont./Discont. Conduction with Vd constant
sd
o
sd
o
d
o
TVLI
DTVLI
V
V2
2 2
7-34
max,
2
max,
274
274
oB
o
d
o
oB
o
d
o
d
o
I
I
V
V
DI
I
V
V
V
V
Discont. Conduction with constant Vo (5)
L
VTI osoB 27
2max,
substituting IoB,max
We get
7-35
Discont. Conduction with Vo constant (6)
Solving for D
2/1
max,
127
4
oB
o
d
o
d
o
I
I
V
V
V
VD
7-36
Boost Converter Output Ripple (1)
7-37
Boost Converter Output Ripple (2)
• the ripple current flows through the capacitor and the average through R
ss
o
o
soo
soo
TD
RC
DT
V
VC
DT
R
VV
C
DTI
C
QV
(where =RC is the time const)
idiode
Io
7-38
Step-Down/Up (Buck-Boost) Converter
• The output voltage can be higher or lower than the input voltage
•The output voltage is negative
7-39
Buck-Boost DC-DC Converter: Waveforms
• equating the integral of inductor voltage over one period:
• D>0.5 means Vo>Vd• D<0.5 means Vo<Vd
•power is conserved Pd=Po:
do
sosd
VD
DV
TDVDTV
1
0)1)((
do ID
DI
1
7-40
• The average inductor current is
• Noting that average capacitor current is zero:
Limits of Cont./Discont. Conduction (1)
)1(2
12
12
1,
DL
VT
DL
VT
iI
os
ds
peakLLB
2)1(2
)1(1
DL
VTI
DII
ID
DIIII
osoB
LBoB
oBLBdLBoB
re-arranging:
Substituting:
7-41
Limits of Cont./Discont. Conduction (2)
• Maximum values obtained when D=0
2
max,
max,
)1(2
)1(2
)1(2
2
DL
VTI
DL
VTI
L
VTI
L
VTI
osoB
osLB
osoB
osLB
7-42
Discontinuous Conduction Mode (1)
• This occurs at light loads
• integrating the inductor voltage over one period
• and since Pd=Po
1
1 0)(
D
V
V
TVDTV
d
o
sosd
)2(1
DI
I
d
o
7-43
Discontinuous Conduction Mode (2)
DDL
TVI
i
Di
T
T
iDT
DT
i
T
dttT
idtt
DT
i
TI
and
DTL
Vi
sdL
peakL
peakL
s
s
peakLs
s
peakL
s
DT T
s
peakL
s
peakL
sL
sd
peakL
s s
)(2
ngsubstituti2
22
1
1
1
,
1,
21
1
,2
,
0 0 1
,,
,
1
7-44
Limits of Cont./Discont. Conduction
do
doB
dodo
doBdo
d
o
o
doBdo
d
oosoB
sd
Ldo
I
D
V
VI
III
D
V
VIII
I
IDDD
V
VIII
I
ID
L
VTI
DDTL
VIII
2max,
2max,
max,
1max,
1
1
)()(
)(
)2()1(2
)(2
dood VIVI /;
o
oBdo I
IVDV max,
7-45
Limits of Cont./Discont. Conduction with Vo constant
L
VTI
I
I
V
VD os
oBoB
o
d
o
2, max,
max,
7-46
Buck-Boost Converter: Effect of Parasitics
• The duty-ratio is limited to avoid these parasitic effects from becoming significant
7-47
Buck-Boost Converter: Output Voltage Ripple
ss
o
o
soo
soo
TD
RC
DT
V
VC
DT
R
VV
C
DTI
C
QV
(where =RC is the time const)
7-48
Cuk DC-DC Converter
• The output voltage can be higher or lower than the input voltage
• The output voltage is negative
• Capacitor C1 stores and transfers energy
• in steady state average inductor voltages VL1, VL2 are zero
• VC1 is larger than Vd and Vo: odC VVV 1
7-49
Cuk DC-DC Converter: Waveforms (1)
• VL1=Vd-VC1
• VL2=-Vo
• when switch T is off
7-50
Cuk DC-DC Converter: Waveforms (2)• when switch T is on
• VL1=Vd
• VL2=VC1-Vo
7-51
Cuk DC-DC Converter: Waveforms (3)• equating the integral voltages of L1, L2 over one period:
• thus
• and since Po=Pd
oC
soCso
dC
sdsCd
VD
V
DTVVTDVL
VD
V
DTVTDVVL
1
0)()1)((:2
)1(
1
0)1)((:1
1
1
1
1
D
D
V
V
d
o
1
D
D
I
I
d
o
1
7-52
Cuk DC-DC Converter: pros and cons
Advantages
• input current and output current have small ripple
•Disadvantages
• requirement of capacitor C1 with large ripple current capability
7-53
Full-Bridge DC-DC Converter
• Four quadrant operation is possible
• (TA+,TB-) (TA-,TB+) are switch pairs
• bipolar voltage switching: switches in each pair are activated simultaneously
• unipolar voltage switching: switches are activated independently
7-54
Bipolar voltage switching
4ˆ
at
4/ˆ)(
1
1
s
tri
control
controltri
stritri
T
V
vt
vvtt
T
tVtv
thus
ton of switch pair (TA+,TB-) is
1ˆ2
1
2
1
2ˆ2
12
1
1
tri
control
s
on
ss
tri
controlson
V
v
T
tD
TT
V
vTtt
7-55
• Duty-rate of pair (TA+,TB-)
• Duty-rate of pair (TA-,TB+)
• noting that
Bipolar voltage switching (2)
1
ˆ2
11
tri
control
s
on
V
v
T
tD
12 1 DD
dddBNANo VDVDVDVVV )12( 121
• D1 can vary between 0 and 1• Vo can vary between -Vd and +Vd
do VDV )12( 1
7-56
unipolar voltage switching
controltriBA
controltriBA
controltricontrolBA
vvifonTT
vvifonTT
vvvifonTT
,
,
,
• Duty-rate of switch TA+
• Duty-rate of switch TB+
• noting that
1
ˆ2
11
tri
control
s
on
V
v
T
tD
12 1 DD
dBNANo VDVVV )12( 1 • D1 can vary between 0.5 and 1• Vo can vary between 0 and Vd
7-57
Output Ripple in full-bridge DC converters
• unipolar voltage switching vs bipolar voltage switching:
• switching frequency is doubled
• ripple is reduced
• better frequency response
• better output voltage
• more complex switch control
unipolar
bipolar
ripple
7-58
Converter Comparison
• Buck, Boost, Buck-Boost, Cuk transfer energy in only one direction
• full-bridge is capable of bi-direccional power flow
• in Buck, Boost, switch utilization is good
• in Buck-Boost, Cuk, full-bridge switch utilization is poor
CONCLUSION
• Prefer Buck, Boost converters
• If higher and lower voltages needed, use Buck-Boost, Cuk
• If four-quadrant operation needed, use full-bridge
