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.