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Power Electronics andDrives (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.
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DC-DC Converter(Chopper)
DEFINITION: Converting the unregulated DC input to acontrolled DC output with a desiredvoltage 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
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
3
Linear regulator• Transistor is operated
in linear (active)mode.
• Output voltage
• The transistor can beconvenientlymodelled by anequivalent variableresistor, as shown.
• Power loss is high athigh current due to:
Lceo
T Lo
I V P
R I P
or
2
+
V oRL
+ V CEce I L
LINEAR REGULATOR
RT
EQUIVALENTCIRCUIT
V in
RL
+ V ce I L
V inV o
+
ceino V V V
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
4
Switching Regulator
• Transistor is operatedin switched-mode : – Switch closed:
Fully on (saturated) – Switch opened:
Fully off (cut-off)
– When switch is open,no current flow in it
– When switch isclosed no voltagedrop across it.
• Since P=V.I , no losses occurs in the switch. – Power is 100%
transferred fromsource to load.
– Power loss is zero(for ideal switch):
• Switching regulator isthe basis of all DC-DCconverters
+
V o
RL
+ V ce I L
SWITCHING REGULATOR
EQUIVALENT CIRCUIT
V in
RL
I L
V inV o
+
(ON)closed
(OFF)open
(ON)closed
DT T
OUTPUT VOLTAGE
V o
SWITCH
V in
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
5
Buck (step-down) converter
V d
L
D C RL
S
+
V o
V o
+
CIRCUIT OF BUCK CONVERTER
CIRCUIT WHEN SWITCH IS CLOSED
CIRCUIT WHEN SWITCH IS OPENED
V o
+
i L
V d D RL
S
V d D RL
S
+ v L
+ v L
i L
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
6
Switch is turned on (closed)
• Diode is reversedbiased.
• Switch conductsinductor current
• This results inpositive inductorvoltage, i.e:
• It causes linearincrease in theinductor current
od L V V v
dt v L
i
dt di Lv
L L
L L
1
V d V D
+ v L -
C RL
+V o
V d V o
V o
closedopened
closedopened
t
DT T t
i Lmin
i Lmax
I L
v L
i L
i L
+S
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
7
Switch turned off (opened)
• Because of inductiveenergy storage, i Lcontinues to flow.
• Diode is forward
biased
• Current now flows(freewheeling)through the diode.
• The inductor voltagecan be derived as:
o L V v
V d
+ v L -
C RL
+V o
V d V o
V o
closedopened
closedopened
t
DT T t
i Lmin
i Lmax
I L
v L
i L
i L
S
D
(1-D)T
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
8
Analysis
T D LV
i
LV
T Di
t i
dt di
LV
dt di
dt di
LV v
DT L
V V i
LV V
DT i
t i
dt di
i
i L
V V dt
didt
di LV V v
oopened L
o L L L
o L
Lo L
od closed L
od L L L
L
L
od L
Lod L
)1(
)1(
opened,switchFor
FigureFrom
linearly.increasedmusthereforeconstant.T
positiveais of Derivative
:(on)closedisswitchWhen the
I L
i L max
DT T
i L
V d V o
v L
t
t
i L min
closed
i L
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
9
Steady-state operation
d o
so
sod
opened Lclosed L
L
L
DV V
T D LV
DT L
V V
ii
i
i
0)1(
0
:i.ezero,isperiodoneoverof
changetheisThatcycle.nexttheof begining
at thesametheiscycleswitchingof endat thethatrequiresoperationstate-Steady
i L
Unstable current
Decaying current
Steady-state current
t
t
t
i L
i L
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
10
minmax
min
max
L
:ripplecurrentInductor
2)1(1
2
:currentMinimum
2)1(1
)1(212
:currentMaximum
RincurrentAveragecurrentinductorAverage
I I i
Lf D
RV i I I
Lf D
RV
T D LV RV i I I
RV
I I
L
o L
L
o
oo L L
o R L
Average, Maximum andMinimum Inductor Current
I L
I max
I min
i L
i L
t
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
11
Continuous Current Mode (CCM)
min
min
min
min
bebchosenis Normally
operation.of modecontinousensure current toinductorminimumtheisThis
2)1(
02
)1(1
,0 operation,continuousFor
2)1(1
2
analysis,previousFrom
L L
R f D
L L
Lf D
RV
I
Lf D
RV
i I I
o
o L
L
i L
I max
I mint
0
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
12
Output voltage ripple
size.capacitorIncreasing3)
sizeinductorIncreasing2)
frequencyswitchingIncreasing1)
:byreducedbecanRipple:Note8
)1(
factor,rippletheSo,
8
)1(8
peak)to-(Peak voltageRipple
8
2221
:formulaareatriangleUse
:aswittenbecanchargeThe
:currentCapacitorKCL,
2
2
LCf
D
V
V r
LCf
DC iT
V
iT
iT Q
C Q
V
V C Q
CV Q
iii
o
o
Lo
L
L
oo
o
R Lc
i L
i L
=I R
i max
imin
V o
+
V o / R
i RL i L
iC
iC
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
13
Basic design procedures
Vd(inputspec.)
SWITCH
f = ?D = ?TYPE ?
D
L
Lmin = ?
L = 10L min
Cripple ?
RL
Po = ?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 L min . Choose L>>10 L min • 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 I p /3, where I p is the peak capacitor current givenby i L /2.
• ECAPs can be used
• Wire size consideration: – Normally rated in RMS. But i L is known as peak. RMS value
for i L is given as:
22
, 32
L
L RMS Li
I I
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Power Electronics andDrives (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 minimuminductor 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 is125W. (a) Determine the duty cycle, (b) value of L to limit thepeak inductor current to 6.25A, (c) value of capacitance to limitthe output voltage ripple factor to 0.5%.
• Design a buck converter such that the output voltage is 28Vwhen the input is 48V. The load is 8Ohm. Design the convertersuch that it will be in continuous current mode. The outputvoltage ripple must not be more than 0.5%. Specify thefrequency and the values of each component. Suggest the powerswitch also.
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
15
Boost (step-up) converter
V d
L D
C
RL
S
V d
L D
CRL
S
V d
LD
C RLS
+ v L
+
V o
+ v L -
V o
+
CIRCUIT OF BOOST CONVERTER
CIRCUIT WHEN SWITCH IS CLOSED
CIRCUIT WHEN SWITCH IS OPENED
V o
+
i L
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
16
Boost analysis:switch closed
L DT V
i
LV
dt di
DT i
t i
dt di
LV
dt di
dt
di L
V v
d closed L
d L
L L L
d L
L
d L
DT T
i L
v L CLOSED
t
t
V d
V d V o
i L
V d
LD
CS
+ v L
i L
+vo
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
17
Switch opened
L
DT V V i
LV V
dt di
T Di
t i
dt di
LV V
dt di
dt di
L
V V v
od opened L
od L
L
L L
od L
L
od L
)1(
)1(
DT T
( 1-D )T
i L
v L OPENED
t
t
V d
V d V o
i L
V d
D
CS
+ v L -
i L
+vo
-
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
18
Steady-state operation
D
V V
LT DV V
L DT V
ii
d o
od d
opened Lclosed L
1
0)1(
0
• Boost converter produces output voltage that isgreater or equal to the input voltage.
• Alternative explanation:
– when switch is closed, diode is reversed. Thusoutput is isolated. The input supplies energy toinductor.
– When switch is opened, the output stagereceives energy from the input as well as fromthe inductor. Hence output is large.
– Output voltage is maintained constant byvirtue of large C.
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
19
Average, Maximum, MinimumInductor Current
L DT V
R D
V i I I
L DT V
R D
V i I I
R D
V I
R D
V R D
V
I V
RV
I V
d d L L
d d L L
d L
d
d
Ld
od d
2)1(
2
:currentinductorMinimum
2)1(
2
:currentinductorMaximum
)1(
:currentinductorAverage
)1(
)1(
powerOutputpowerInput
2min
2max
2
2
2
2
2
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
20
L and C values
RCf D
V V
r
RCf
DV
RCf
DT V V
V C DT RV
Q
f R D D
TR D D L
L DT V
R D
V
I
o
o
ooo
oo
d d
factorRipple
21
21
02)1(
0
CCM,For
2
2
min
2
min
I max
I min
I min
I max
ic
i D
i L
V d
v L
V d V o
I o=V o / R
DT T
Q
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
21
Examples
• The boost converter has the following parameters: V d=20V,D=0.6, R=12.5ohm, L=65uH, C=200uF, f s=40KHz. Determine(a) output voltage, (b) average, maximum and minimuminductor current, (c) output voltage ripple.
• Design a boost converter to provide an output voltage of 36Vfrom a 24V source. The load is 50W. The voltage ripple factormust be less than 0.5%. Specify the duty cycle ratio, switching
frequency, inductor and capacitor size, and power device.
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
22
Buck-Boost converter
V d L
D
C RL
S+
V o
V o
+
CIRCUIT OF BUCK-BOOST CONVERTER
CIRCUIT WHEN SWITCH IS CLOSED
CIRCUIT WHEN SWITCH IS OPENED
V o
+
i LV d v L
+
i L
V d
v L
+
D
DS
S
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
23
Buck-boost analysis
DT T
I min
I max
ic
i D
i L
V d
v L
Q
V d V o
I o=V o / R
I max
I min
LT DV
i
LV
T Di
t i
LV
dt di
dt di
LV v
L DT V
i
LV
DT i
t i
LV
dt di
dt di
LVd v
oopened L
o L L
o L
Lo L
d closed L
d L L
d L
L L
)1()(
)1(
openedSwitch
)(
closedSwitch
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
24
Output voltage
• NOTE: Output of a buck-boost converter either behigher 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 closedand transferred to load when switch is opened.
D DV
LT DV
L DT V
s
od
opened iLclosed iL
1V
:tageOutput vol
0)1(
0
:operationstateSteady
o
)()(
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
25
Average inductor current
2
2
2
2
)1(
,forngSubstituti
:ascurrentinductoraverage
torelatediscurrentsourceaverageBut
i.e.source,bythesuppliedpower
equalmustloadby the absorbedpower
converter,in thelosspowernoAssuming
D R
DV DV
P RDV
V I
V
D I V RV
D I I
I V RV
PP
d
d
o
d
o L
o
Ld o
Ls
sd o
so
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
26
L and C values
RCf D
V V
r
RCf DV
RC DT V
V
V C DT RV
f R D
L
L DT V
D R
D
L DT V
D R
DV i I I
L DT V
D R DV i I I
o
o
ooo
oo
d
d d L L
d d L L
Q
ripple,tageOutput vol
2)1(
02)1(
V
CCMFor
2)1(2
2)1(2
current,inductorminandMax
2
min
2d
2min
2max
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
27
Converters in CCM: Summary
V d
L
D
C RL
S
+
V o
f R D
L
LCf
DV V
DV
V
o
o
d
o
2)1(
8
1
Buck
min
2
f R D D
L
RCf D
V V
DV V
o
o
d
o
2)1(
11
Boost
2
min
f R D
L
RCf D
V V
D
D
V
V
o
od
o
2)1(
1
BoostBuck
2
min
V
d
L
D C RL
S
+
V o
V
d
L D
CRL
S
+V
o
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Power Electronics andDrives (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 controlsignal
SawtoothWaveform
Vcontrol 1
Switchcontrolsignalton 2
T
Vcontrol 2
ton 1
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Power Electronics andDrives (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 powersupply-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)
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30
Linear and SMPS block diagramBasic Block diagram of linear power supply
Basic Block diagram of SMPS
Base/gateDrive
ErrorAmp.
LineInput
3 / 150/60 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
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
31
High frequency transformer
:Models
;
iprelationshoutput-inputBasic
voltagevarying-meup/down tistep2)isolationelectricaloutput-Input 1)
:functionBasic
1
2
2
1
2
1
2
1
N N
ii
N
N
v
v
V 1 V2
++i1 i2 N 1 N 2
Ideal model
V 1 V 2
++
i1 i2 N 1 N 2
Model used formost PE application
Lm
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
32
Flyback Converter
V d
+
V o
V d
N 1 N 2i1
i2
+
v2v1
+
i LM
i D
+ v D
iC i R
C R
vSW +
+
iS
L M
V o
Flyback converter circuit
Model with magnetisinginductance
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
33
Operation: switch closed
V d
V o
N 2
+
0
0
v1
v1=V s
i LM
is=i LM
+
N 1
+
v2
0and0
Therefore,
off turneddiodei.e. ,0
er,transformtheof sideloadOn the
12
1
2
1
2
1
212
1
ii
N N V V v
N N
V N N
vv
L
DT V i
LV
DT iL
dt iL
dt diL
dt di
LV v
d o D
d
m
d
closed L
m
d mmm
Lmmd
m
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
34
Switch opened
s
+
v1
+
i LM
N 1 N 2
v2= V S+
+
V o
i D
vSW
2
1
2
1
2
1
211
2
1
2
121
2
2
11
:switchtheacrossVoltage
)1(
1
But
N N
V V v
N N
LT DV
i
N N
LV
T D
i
dt
i
dt
di
N N V
dt di Lv
N N
V N N
vv
V v N
N V v
od SW
m
oopenm L
m
om Lm Lm L
om Lm
o
o
o
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
35
Output voltage
1
22
1
1
01
0
operation,state-steadyFor
N N
D D
V V
N N
LT DV
L DT V
ii
d o
m
o
m
d
opened Lclosed L mm
• Input output relationship is similar to buck-boostconverter.
• Output can be greater of less than input,dependingupon D.
• Additional term, i.e. transformer ratio is present.
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36
Flyback waveforms
i Lm
is
t
t
i D
iC
v1
-V(N 1 /N 2)
V o / R
V s
DT T
i L
1
20
2
1
22
20
20
20
0
)1(
)1(
:asncan writte
forSolving
:as torelatedis
N N
R DV
N N
R D
DV I
I
DRV V
I
RV
D I V
I
D I T
DT I I
I I R
V I V
PP
d L
L
d L
Ld
L
L L
s
Ls
sd
s
m
m
m
m
m
mm
m
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
37
Max, Min inductor current
RCf D
V V
r
N
N
f
R DV L
f L DV
L DT V
N N
R D
DV
I
L DT V
N N
R D
DV
i I I
L DT V
N N
R D
DV
i I I
d m
m
d
m
d d
L
m
d d
L
L L
m
d d
L L L
m
m
mm
m
mm
0
0
2
2
12
min
2
1
22
min
2
1
22
min,
2
1
22
max,
boost,similar toisncalculatioRipple2
)1(
22)1(
0,CCM,For
2)1(
2
2)1(
2
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Power Electronics andDrives (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 L m.c) Maximum and minimum inductor current.
d) Value of capacitor C.
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Power Electronics andDrives (Version 3-2003)Dr. Zainal Salam, UTM-JB
39
Full-bridge converter
SW2SW4
SW3
V S
N S
N S
+
v x C
L x
R+
V o
+
v p
SW1
SW1,SW2
SW3,SW4DT T
2T DT
T 2V P
V S
-V S
V x
P
SS N
N V
DT 2T
DT T 2
T
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Full bridge: basic operation
• Switch “pair”: [S1 & S2];[S3 & S4].
• Each switch pair turn on at a time as shown. Theother pair is off.
• “AC voltage” is developed across the primary.Then transferred to secondary via high frequencytransformers.
• On secondary side, diode pair is “high frequencyfull wave rectification”.
• The choke (L) and (C ) acts like the “buck converter” circuit.
• Output Voltage
D N N
V V p
sso
2