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.
Power Electronics and 1
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Dr. Zainal Salam, UTM-JB
DC-DC Converter
(Chopper)
DEFINITION:
Converting the unregulated DC input to a
controlled DC output with a desired
voltage level.
• General block diagram:
DC supply
(from rectifier-
DC output LOAD
filter, battery,
fuel cell etc.)
Vcontrol
(derived from
feedback circuit)
• APPLICATIONS:
– Switched-mode power supply (SMPS), DC
motor control, battery chargers
Linear regulator
• Transistor is operated
in linear (active)
mode. + VCEce IL
+
• Output voltage Vin
RL Vo
Vo Vin Vce
LINEAR REGULATOR
• The transistor can be
conveniently + Vce
IL
modelled by an
RT
equivalent variable +
RL Vo
resistor, as shown. Vin
• Power loss is high at
EQUIVALENT
high current due to: CIRCUIT
Po I L 2 RT
or
Po Vce I L
Power Electronics and 3
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Switching Regulator
• Transistor is operated
in switched-mode:
+ Vce IL
– Switch closed:
Fully on (saturated) +
– Switch opened: Vin
RL
Vo
Fully off (cut-off)
SWITCHING REGULATOR
– When switch is open,
no current flow in it IL
– When switch is
closed no voltage SWITCH
+
drop across it. Vin
RL Vo
• Since P=V.I, no losses
occurs in the switch.
– Power is 100% EQUIVALENT CIRCUIT
transferred from Vo
source to load. Vin
– Power loss is zero
(ON) (OFF) (ON)
(for ideal switch): closed open closed
DT T
• Switching regulator is OUTPUT VOLTAGE
the basis of all DC-DC
converters
Power Electronics and 4
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Buck (step-down) converter
S L
+
Vd D C RL
Vo
CIRCUIT OF BUCK CONVERTER
iL
S + vL
+
Vd D RL Vo
CIRCUIT WHEN SWITCH IS CLOSED
S iL
+ vL
+
Vd RL Vo
D
CIRCUIT WHEN SWITCH IS OPENED
Power Electronics and 5
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Switch is turned on (closed)
• Diode is reversed + vL -
biased.
S iL +
+
C Vo
• Switch conducts Vd VD RL
inductor current
vL
• This results in
positive inductor VdVo
voltage, i.e: opened opened
closed closed
t
v L Vd Vo
• It causes linear Vo
increase in the iL
inductor current
iLmax
di IL
vL L L iLmin
dt
1
iL v L dt DT T
t
L
Power Electronics and 6
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Switch turned off (opened)
+ vL -
• Because of inductive
energy storage, i L S iL +
continues to flow. Vd C RL Vo
D
• Diode is forward
biased vL
VdVo
• Current now flows opened opened
(freewheeling) closed closed
through the diode. t
• The inductor voltage
can be derived as: Vo
iL
vL Vo iLmax
IL
iLmin
(1-D)T
t
DT T
Power Electronics and 7
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Dr. Zainal Salam, UTM-JB
Analysis
When the switch is closed (on) :
di
v L Vd Vo L L vL
dt
di V Vo Vd Vo
L d closed
dt L t
Derivative of iL is a positive
constant.Therefore iL must
increased linearly. iL
From Figure iL max
diL iL iL Vd Vo
IL iL
dt t DT L
V Vo
iL closed d
iL min
DT
L t
DT T
For switch opened,
di
v L Vo L L
dt
di Vo
L
dt L
di i i L Vo
L L
dt t (1 D )T L
V
iL opened o (1 D )T
L
Power Electronics and 8
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Steady-state operation
iL
Unstable current
t
iL Decaying current
t
iL Steady-state current
t
Steady - state operation requires that iL at the
end of switching cycle is the same at the
begining of the next cycle. That is the change
of iL over one period is zero, i.e :
iL closed iL opened 0
Vd Vo V
DTs o (1 D)Ts 0
L L
Vo DVd
Power Electronics and 9
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Dr. Zainal Salam, UTM-JB
Average, Maximum and
Minimum Inductor Current
iL
Imax
IL iL
Imin
t
Average inductor current Average current in R L
V
IL IR o
R
Maximum current :
iL Vo 1 Vo
I max I L (1 D)T
2 R 2 L
1 (1 D)
Vo
R 2 Lf
Minimum current :
iL 1 (1 D)
I min I L Vo
2 R 2 Lf
Inductorcurrent ripple :
iL I max I min
Power Electronics and 10
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Continuous Current Mode (CCM)
iL
Imax
Imin t
0
From previous analysis,
iL 1 (1 D)
I min I L Vo
2 R 2 Lf
For continuous operation, I min 0,
1 (1 D)
Vo 0
R 2 Lf
(1 D)
L Lmin R
2f
This is the minimum inductor current to
ensure continous mode of operation.
Normally L is chosen b be Lmin
Power Electronics and 11
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Output voltage ripple
KCL, Capacitor current :
ic iL iR L iL iR
The charge can be witten as : +
iC
Q CVo Vo
Q CV
Q
o Vo
C imax
iL
Use triangle area formula :
iL=IR
1 T i
Q L Vo/R imin
2 2 2
0
TiL iC
8
Ripple voltage (Peak - to peak)
0
TiL (1 D)
Vo
8C 8 LCf 2
So, the ripple factor,
V (1 D)
r o
Vo 8 LCf 2
Note : Ripple can be reduced by :
1) Increasing switching frequency
2) Increasing inductor size
3) Increasing capacitor size.
Power Electronics and 12
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Basic design procedures
SWITCH L
Lmin= ?
RL
L = 10Lmin
Vd Po = ?
f=? D
(input C Io = ?
D=? ripple ?
spec.)
TYPE ?
• 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 i 2
I L, RMS I L L
3
Power Electronics and 13
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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 14
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Boost (step-up) converter
L D
Vd C +
S
RL Vo
CIRCUIT OF BOOST CONVERTER
iL L D
+ vL
Vd +
S C
RL Vo
CIRCUIT WHEN SWITCH IS CLOSED
L
D
+ vL -
+
Vd C RL
S Vo
CIRCUIT WHEN SWITCH IS OPENED
Power Electronics and 15
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Dr. Zainal Salam, UTM-JB
Boost analysis:switch closed
iL
L D
+ vL
+
Vd C vo
S
v L Vd Vd
di
L L v L
CLOSED
dt
t
diL Vd
V d V o
dt L
diL iL iL
i iL
t DT
L
dt
di V
L d
dt L DT T t
Vd DT
iL closed
L
Power Electronics and 16
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Dr. Zainal Salam, UTM-JB
Switch opened
iL
D
+ vL -
+
Vd C vo
S
-
v L Vd Vo
diL
L Vd
dt
di V Vo vL
L d OPENED
dt L t
diL iL V d V o
dt t
iL iL
iL
(1 D)T
( 1-D )T
t
diL Vd Vo
DT T
dt L
Vd Vo (1 DT )
iL opened
L
Power Electronics and 17
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Dr. Zainal Salam, UTM-JB
Steady-state operation
iL closed iL opened 0
Vd DT Vd Vo (1 D )T
0
L L
Vd
Vo
1 D
• 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 18
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Dr. Zainal Salam, UTM-JB
Average, Maximum, Minimum
Inductor Current
Input power Output power
Vo 2
Vd I d
R
2
Vd
(1 D) Vd 2
Vd I L
R (1 D) 2 R
Average inductor current :
Vd
IL
(1 D) 2 R
Maximum inductor current :
iL Vd V DT
I max I L d
2 (1 D) 2 R 2L
Minimum inductor current :
iL Vd V DT
I min I L d
2 (1 D) 2 R 2L
Power Electronics and 19
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Dr. Zainal Salam, UTM-JB
L and C values
For CCM,
I min 0 Vd
vL
Vd V DT
2
d 0
(1 D) R 2L
D1 D 2 TR
Lmin VdVo
2 Imax
D1 D 2 R
iL
Imin
2f
Ripple factor iD Imax
V
Q o DT CVo
Imin
R
Io=Vo / R
Vo DT Vo D
Vo
RCf RCf ic
V D
r o
Vo RCf
Q
DT T
Power Electronics and 20
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Examples
• The boost converter has the following parameters: V d=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 21
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Dr. Zainal Salam, UTM-JB
Buck-Boost converter
S
D
+
Vd C
L RL Vo
RL
CIRCUIT OF BUCK-BOOST CONVERTER
S D
+ +
Vd iL vL Vo
CIRCUIT WHEN SWITCH IS CLOSED
S D
+ +
Vd iL vL
Vo
CIRCUIT WHEN SWITCH IS OPENED
Power Electronics and 22
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Dr. Zainal Salam, UTM-JB
Buck-boost analysis
Vd
Switch closed vL
di
v L Vd L L
dt
diL Vd VdVo
dt L Imax
iL iL Vd iL
Imin
t DT L
V DT
(iL ) closed d Imax
L iD
Switch opened Imin
di
v L Vo L L Io=Vo / R
dt
di V
L o i c
dt L
iL iL Vo Q
t (1 D )T L DT T
Vo (1 D )T
(iL ) opened
L
Power Electronics and 23
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Output voltage
Steady state operation :
iL(closed ) iL(opened ) 0
Vd DT Vo (1 D)T
0
L L
Output voltage :
D
Vo Vs
1 D
• 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.
Power Electronics and 24
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Dr. Zainal Salam, UTM-JB
Average inductor current
Assuming no power loss in the converter,
power absorbed by the load must equal
power supplied the by source, i.e.
Po Ps
Vo2
Vd I s
R
But average source current is related to
average inductor current as :
Is ILD
Vo2
Vd I L D
R
Substituting for Vo ,
Vo2 Po Vd D
IL
Vd RD Vd D R (1 D ) 2
Power Electronics and 25
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Dr. Zainal Salam, UTM-JB
L and C values
Max and min inductor current,
iL Vd D Vd DT
I max I L 2
2 R (1 D ) 2L
iL Vd D V DT
I min I L d
2 R (1 D ) 2 2L
For CCM
Vd D V DT
2
d 0
R (1 D ) 2L
(1 D ) 2 R
Lmin
2f
Output voltage ripple,
Vo
Q DT CVo
R
Vo DT Vo D
Vo
RC RCf
V D
r o
Vo RCf
Power Electronics and 26
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Dr. Zainal Salam, UTM-JB
Converters in CCM: Summary
Buck
Vo
S L D
V + Vd
D C RL
Vo Vo 1 D
d
Vo 8 LCf 2
(1 D ) R
Lmin
2f
L Boost
D
Vo 1
V + Vd 1 D
C Vo
S Vo D
d
RL Vo RCf
D (1 D ) 2 R
Lmin
2f
S Buck Boost
Vo D
D +
V C Vo
Vd 1 D
L RL
d
Vo D
Vo RCf
(1 D) 2 R
Lmin
2f
Power Electronics and 27
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Control of DC-DC converter:
pulse width modulation (PWM)
Vo (desired)
+ Vcontrol Switch control
signal
Vo (actual) Comparator
-
Sawtooth
Waveform Sawtooth
Waveform
Vcontrol 1
Vcontrol 2
Switch
control
ton 2 signal
ton 1
T
Power Electronics and 28
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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 29
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Linear and SMPS block diagram
Basic Block diagram of linear power supply
C E
Vce=Vd-Vo +Vo DC Regulated
DC Unregulated
B +
+
Base/gate RL
Vd Drive Vo
Line
Input -
1 / 3 -
Rectifier/ Error Vo
50/60 Hz Filter Amp.
Isolation
Transformer
Vref
Basic Block diagram of SMPS
DC-DC CONVERSITION AND
DC ISOLATION
DC
Unregulated Regulated
High
RECTIFIER Frequency
EMI
AND
FILTER rectifier Vo
FILTER
and
filter
Vref
Base/
PWM error
gate
Controller Amp
drive
Power Electronics and 30
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High frequency transformer
Basic function :
1) Input - output electrical isolation
2) step up/down time - varying voltage
Basic input - output relationship
v1 N1
;
v2 N 2
i1 N 2
i2 N1
Models :
i1 N1 N2 i2
+ +
V1 V2 Ideal model
i1 N1 N2 i2
+ +
Lm Model used for
V1 V2
most PE application
Power Electronics and 31
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Flyback Converter
+
C R Vo
Vd LM
Flyback converter circuit
iD
iS i1 N1 N2
+
+ + vD
iLM v2 iC iR Vo
v1
Vd
+
+ vSW i2
Model with magnetising
inductance
Power Electronics and 32
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Operation: switch closed
0 N1 N2
is=iLM
+
+
iLM v2
v1 Vo
Vd +
v1=Vs 0
diLm
v1 Vd Lm
dt
diLm iLm iLm Vd
dt dt DT Lm
iLm
closed
Vd DT
Lm
On the load side of the transformer,
N2 N2
N Vd N
v2 v1
1 1
N
v D Vo Vd 2 0, i.e. diode turned off
N
1
Therefore,
i2 0 and i1 0
Power Electronics and 33
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Dr. Zainal Salam, UTM-JB
Switch opened
iD
N1 N2
+ +
iLM v1 v2= VS Vo
Vs +
+ vSW
N
v1 Vo 1
N
2
But v2 Vo
N N
v1 v2 1 Vo 1
N N
2 2
di N
v1 Lm L m Vo 1
N
dt 2
diL m iL m iL m Vo N1
N
dt dt 1 D T Lm 2
V (1 D )T N1
iL m open o
N
Lm 2
Voltage across the switch :
N
vSW Vd Vo 1
N
2
Power Electronics and 34
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Output voltage
For steady - state operation,
iL closed iL opened 0
m m
Vd DT Vo 1 D T N1
N 0
Lm Lm 2
D N 2
Vo Vd N
1 D 1
• 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 35
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Dr. Zainal Salam, UTM-JB
Flyback waveforms
Ps P0 Vs
V0 2 v1
Vd I s
R
I s is related to I Lm as : -V(N1 /N2)
Is
I Lm DT
T
I Lm D
iLm
iLM
Solving for I Lm
is
Vd I Lm D
V02
R
t
2
V0
I Lm
Vd DR iD
I Lm can written as :
2 iC
Vd D N2
I Lm
2 N
(1 D ) R 1
Vo/ R
V0 N 2
DT T t
N
(1 D ) R 1
Power Electronics and 36
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Dr. Zainal Salam, UTM-JB
Max, Min inductor current
iLm
I Lm I Lm
,max 2
2
Vd D N 2 V d DT
2 N
(1 D ) R 1 2 Lm
iLm
I Lm ,min I Lm
2
2
Vd D N 2 Vd DT
2 N
(1 D ) R 1 2 Lm
For CCM, I Lm , min 0
2
Vd D N2 Vd DT Vd D
2 N
(1 D ) R 1 2 Lm 2 Lm f
2
V (1 D) R N1 2
Lm min d
N
2f 2
Ripple calculatio n is similar to boost,
V0 D
r
V0 RCf
Power Electronics and 37
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Dr. Zainal Salam, UTM-JB
Example
The Flyback converter has these specifications:
DC input voltage: 40V
Output voltage: 25V
Duty cycle: 0.5
Rated load: 62.5W
Max peak-peak inductor current ripple:
25% of the average inductor current.
Maximum peak-peak output voltage: 0.1V
Switching frequency: 75kHz
Based on the abovementioned specifications, determine
a) Transformer turns ratio
b) Value of magnetizing inductor Lm.
c) Maximum and minimum inductor current.
d) Value of capacitor C.
Power Electronics and 38
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Full-bridge converter
SW1 SW3
Lx
+ + +
NS vx Vo
C R
vp
VS
NS
SW4 SW2
SW1,SW2
DT T
SW3,SW4
T T
DT
VP 2 2
VS
-VS
Vx
N
VS S
N
P
DT T T T
DT
2 2
Power Electronics and 39
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Dr. Zainal Salam, UTM-JB
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
Ns
Vo 2Vs D
Np
Power Electronics and 40
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Dr. Zainal Salam, UTM-JB