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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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 −=
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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 lossesoccurs 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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
dtdi
Lv
LL
LL
1
Vd VD
+ vL -
C RL
+
−
Vo
Vd−Vo
−Vo
closedopened
closedopened
t
DT Tt
iLmin
iLmax
IL
vL
iL
iL
+
−
S
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
8
Analysis
( )
( ) TDLV
i
LV
TDi
ti
dtdi
LV
dtdi
dtdi
LVv
DTL
VVi
LVV
DTi
ti
dtdi
i
iL
VVdt
didt
diLVVv
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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
9
Steady-state operation
( ) ( )
do
so
sod
openedLclosedL
L
L
DVV
TDLV
DTL
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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
VR
ViII
RV
II
L
oL
L
o
ooLL
oRL
−=∆
��
���
� −−=∆−=
��
���
� −+=
��
���
� −+=∆+=
==�
=
Average, Maximum and Minimum Inductor Current
IL
Imax
Imin
iL
∆iL
t
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
11
Continuous Current Mode (CCM)
min
min
min
min
be bchosen is Normally operation. of mode continous ensure
current toinductor minimum theis This2
)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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
12
Output voltage ripple
size.capacitor Increasing 3)sizeinductor Increasing 2)frequency switching Increasing 1)
:by reduced becan Ripple :Note8
)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
DVV
r
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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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:2
2, 3
2��
���
�∆+= LLRMSL
iII
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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.
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
CIRCUIT WHEN SWITCH IS CLOSED
CIRCUIT WHEN SWITCH IS OPENED
Vo
+
−
−
iL
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
16
Boost analysis:switch closed
( )LDTV
i
LV
dtdi
DTi
ti
dtdi
LV
dtdi
dtdi
L
Vv
dclosedL
dL
LLL
dL
L
dL
=∆
=�
∆=∆
∆=
=�
=
=
DT T
iL
vL CLOSED
t
t
Vd
Vd− Vo
∆iL
Vd
L D
CS
+ vL −
iL
+vo−
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
17
Switch opened
( ) ( )L
DTVVi
LVV
dtdi
TDi
ti
dtdi
LVV
dtdi
dtdi
L
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
-
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
18
Steady-state operation
( ) ( )( )
DV
V
LTDVV
LDTV
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.
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
19
Average, Maximum, Minimum Inductor Current
LDTV
RD
ViII
LDTV
RD
ViII
RD
VI
RD
VRD
V
IV
RV
IV
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
−−
=∆−=�
+−
=∆+=�
−=�
−=
��
���
�
−=
=
=
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
20
L and C values
( )
( )
RCfD
VV
r
RCfDV
RCfDTV
V
VCDTR
VQ
fRDD
TRDDL
LDTV
RD
V
I
o
o
ooo
oo
dd
=∆=
==∆
∆=��
���
�=∆
−=
−=
≥−−
≥
factor Ripple
21
21
02)1(
0CCM,For
2
2
min
2
min
Imax
Imin
Imin
Imax
ic
iD
iL
Vd
vL
Vd−Vo
Io=Vo / R
DT T
∆Q
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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.
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
22
Buck-Boost converter
Vd L
D
C RL
S+
Vo
−
Vo
+
CIRCUIT OF BUCK-BOOST CONVERTER
CIRCUIT WHEN SWITCH IS CLOSED
CIRCUIT WHEN SWITCH IS OPENED
Vo
+
−
−
iLVd vL
+
−
iLVd vL
+
−
D
DS
S
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
23
Buck-boost analysis
DT T
Imin
Imax
ic
iD
iL
Vd
vL
∆Q
Vd−Vo
Io=Vo / R
Imax
Imin
LTDV
i
LV
TDi
ti
LV
dtdi
dtdi
LVv
LDTV
i
LV
DTi
ti
LV
dtdi
dtdi
LVdv
oopenedL
oLL
oL
LoL
dclosedL
dLL
dL
LL
)1()(
)1(
openedSwitch
)(
closedSwitch
−=∆�
=−∆=
∆∆
=�
==
=∆�
=∆=∆
∆
=�
==
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
LTDV
LDTV
s
od
openediLclosediL
1V
:tageOutput vol
0)1(
0:operation stateSteady
o
)()(
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
DVDV
PRDV
VI
V
DIVR
V
DII
IVR
V
PP
d
d
o
d
oL
o
Ldo
Ls
sdo
so
−===�
=�
=
=
=
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
26
L and C values
RCfD
VV
r
RCfDV
RCDTV
V
VCDTR
V
fRD
L
LDTV
DR
D
LDTV
DR
DViII
LDTV
DR
DViII
o
o
ooo
oo
d
ddLL
ddLL
=∆=
==∆
∆=��
���
�=∆
−=�
=+−
−−
=∆−=�
+−
=∆+=�
Q
ripple, tageOutput vol2
)1(
02)1(
V
CCMFor
2)1(2
2)1(2
current,inductor min andMax
2
min
2d
2min
2max
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
27
Converters in CCM: Summary
Vd
L
DC RL
S
+Vo
−
fRD
L
LCf
DVV
DVV
o
o
d
o
2)1(
8
1
Buck
min
2
−=
−=∆
=
fRDD
L
RCfD
VV
DVV
o
o
d
o
2)1(
11
Boost
2
min−=
=∆−
=
fRD
L
RCfD
VV
DD
VV
o
o
d
o
2)1(
1
BoostBuck
2
min−=
=∆−
−=
−
Vd
L
D C RL
S+Vo
−
Vd
L D
CRL
S
+Vo
−
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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)
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
30
Linear and SMPS block diagramBasic Block diagram of linear power supply
Basic Block diagram of SMPS
Base/gateDrive
ErrorAmp.
LineInput
φφ 3/1
50/60 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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
NN
ii
NN
vv
=
=
V1V2
+
−
+
−
i1 i2N1 N2
Ideal model
V1V2
+
−
+
−
i1 i2N1 N2
Model used formost PE application
Lm
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
33
Operation: switch closed
Vd
Vo
N2
+
−
0
0
v1
v1=Vs
iLM
is=iLM+
−
N1
+
−v2
( )
0 and 0Therefore,
off turneddiode i.e. ,0
er, transform theof side load On the
12
1
2
1
2
1
212
1
==
<���
����
�−−=
���
����
�=���
����
�=
=∆�
=∆=∆=
==
ii
NN
VVv
NN
VNN
vv
LDTV
i
LV
DTiL
dtiL
dtdiL
dtdi
LVv
doD
d
m
dclosedL
m
dmmm
Lmmd
m
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
NN
VVv
NN
LTDV
i
NN
LV
TD
i
dt
i
dt
di
NN
Vdt
diLv
NN
VNN
vv
Vv
NN
Vv
odSW
m
oopenmL
m
omLmLmL
omL
m
o
o
o
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
35
Output voltage
( ) ( )( )
���
����
���
���
�−
=�
=���
����
�−−�
=∆+∆
1
2
2
1
1
01
0operation, state-steadyFor
NN
DD
VV
NN
LTDV
LDTV
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.
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
36
Flyback waveforms
iLm
is
t
t
iD
iC
v1
-V(N1 /N2)
−Vo/ R
V s
DT T
∆iLM( )
( )
���
����
�
−=
���
����
�
−=
=�
=
==
=
=
1
20
2
1
22
20
20
20
0
)1(
)1(
:asn can writte
for Solving
:as torelated is
NN
RDV
NN
RD
DVI
I
DRVV
I
RV
DIV
I
DIT
DTII
IIR
VIV
PP
dL
L
dL
Ld
L
LL
s
Ls
sd
s
m
m
m
m
m
mm
m
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
37
Max, Min inductor current
( )
RCfD
VV
r
NN
fRDV
L
fLDV
LDTV
NN
RD
DV
I
LDTV
NN
RD
DV
iII
LDTV
NN
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
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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 Lm. c) Maximum and minimum inductor current.d) Value of capacitor C.
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
39
Full-bridge converter
SW2SW4
SW3
VS
NS
NS
+
−vx C
Lx
R+
−Vo
+
−
vp
SW1
SW1,SW2
SW3,SW4 DT T
2T DT
T +2VP
VS
-VS
Vx
���
����
�
P
SS N
NV
DT2T
DTT +2
T
Power Electronics and Drives (Version 3-2003)
Dr. Zainal Salam, UTM-JB
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
DNN
VVp
sso ⋅
��
�
�
��
�
�= 2
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