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Power Electronics 22
Introduc
tion
Chopper is a static device.
A variable dc voltage is obtained from aconstant dc voltage source.
Also known as dc-to-dc converter. Widely used for motor control.
Also used in regenerative braking.
Thyristor converter offers greaterefficiency, faster response, lowermaintenance, smaller size and smoothcontrol.
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Power Electronics 33
Choppers are of Two Types
y Step-down choppers.
y Step-up choppers.
y In step down chopper outputvoltage is less than input voltage.
y In step up chopper output voltage
is more than input voltage.
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Power Electronics 55
A step-down chopper with resistiveload.
The thyristor in the circuit acts as aswitch.
When thyristor is ON, supplyvoltage appears across the load
When thyristor is OFF, the voltageacross the load will be zero.
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Power Electronics 66
Vdc
v0
V
V/R
i0
Idc
t
t
tON
T
tOFF
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Power Electronics 77
verage value of output or load voltage.
verage value of output or load current.
Time interval for which SCR conducts.
Time interval for which SCRis OFF.
Period ofswitching
dc
dc
ON
OFF
ON OFF
V A
I A
t
t
T t t
!
!
!
!
! !or chopping period.
1Freq. of chopperswitching or chopping freq.f
T! !
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Power Electronics 88
Average Output Voltage
.
duty cycle
ONdc
ON OFF
ONdc
ON
tV V
t t
tV V V d
T
tbut d t
!
! !
! !
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Power Electronics 99
2
0
Average Output Current
RMS value of output voltage
1 ON
dcdc
ONdc
t
O o
VI
R
tV VI d R T R
V dtT
!
! !
!
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Power Electronics 1010
2
0
2
But during ,
Therefore RMS output voltage
1
.
.
ON
ON o
t
O
ON
O ON
O
t V
V V dt T
tV
V t VT T
V d V
!
!
! !
!
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Power Electronics 1111
2
2
Outputpo er
But
Outputpo er
O O O
OO
OO
O
P V I
VI
VP
RdV
PR
!
!
@
!
!
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Power Electronics 1212
Effective input resistance of chopper
The output voltage can be varied by
varying the duty cycle.
i
dc
i
VR
I
RR
d
!
!
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Power Electronics 1313
Methods Of Control
The output dc voltage can be variedby the following methods.
Pulse width modulation control orconstant frequency operation.
Variable frequency control.
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Power Electronics 1414
Pulse Width Modulation
tON is varied keeping choppingfrequency f& chopping period T
constant. Output voltage is varied by varying
the ON time tON
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Power Electronics 1515
V0
V
V
V0
t
ttON
tON tOFF
tOFF
T
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Power Electronics 1616
Variable Frequency Control
Chopping frequency fis variedkeeping either tON or tOFF constant.
To obtain full output voltage range,frequency has to be varied over awide range.
This method produces harmonics in
the output and for large tOFF loadcurrent may become discontinuous
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Power Electronics 1717
v0
v0
t
t
tON
tON
T
T
tOFF
tOFF
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Power Electronics 1818
Step-down Chopper
With R-L Load
V
i
V0
Chopp r
LFWD
E
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Power Electronics 1919
When c
hopper is ON, supply is connectedacross load.
Current flows from supply to load.
When chopper is OFF, load current
continues to flow in the same directionthrough FWD due to energy stored ininductor L.
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Power Electronics 2020
Load current can be continuous ordiscontinuous depending on the values of
Land duty cycle d For a continuous current operation, load
current varies between two limits Imaxand I
min When current becomes equal to Imax the
chopper is turned-off and it is turned-onwhen current reduces to Imin.
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Power Electronics 2121
Outputvoltage
Outputcurrent
v0
V
i0
Imax
Imin
t
t
tON
T
tOFF
Continuouscurrent
Outputcurrent
t
Discontinuouscurrent
i0
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Power Electronics 2222
Expressions ForLoad Current
iO For Continuous Current Operation
WhenChopperIs ON (0e te tON)
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Power Electronics 2323
V
i0
V0
R
L
E
+
-
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Power Electronics 2424
min
min
Taking Laplace Transform
. 0
t 0, initial current 0
O
O
O O O
O
O
di
Vi
R L Edt
V E
RI S L S I S iS S
t i I
IV EI SRR
SLS SLL
!
! -
! !
!
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Power Electronics 2525
min
Taking Inverse aplace Transform
1
This expression is valid for0 ,
i.e., during the period chopperis ON.
Atthe instantthe chopperisturned off,
load c
R Rt t
L L
O
O N
V Ei t e I e
R
t t
! - e e
maxurrentis O O Ni t I!
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Power Electronics 2626
When Chopperis OFF
i0
R
L
E
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Power Electronics 2727
max
When Chopperis OFF 0
0
Talking aplace transform
0 0
Redefining time origin we have at 0,
initial current 0
OFF
OO
O O O
O
t t
diRi L E
dt
E RI S L SI S i
S
t
i I
e e
!
! -
!
!
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Power Electronics 2828
max
max
Taking Inverse aplace Transform
1
O
R Rt tL L
O
I EI S
R RS LS S
L L
Ei t I e eR
@ !
! -
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Power Electronics 2929
min
The expression is vali for0 ,
i.e., during the period chopperisOFF
tthe instantthe chopperisturned ON or at
the end ofthe offperiod, the load currentis
OFF
O OFF
t t
i t I
e e
!
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Power Electronics 3030
min
max
max
max min
min
From equation
1
At ,
To Find &
1
R Rt t
L L
O
ON O
dRT dRT
L L
V Ei t e I eR
t t dT i t I
V E I e I e
I I
R
! -
! ! !
@ !
-
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Power Electronics 3131
max
min
From equation
1
At ,1
R R
t tL LO
OFF ON O
OFF
Ei t I e eR
t t T t i t It t d T
! -
! ! !! !
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Power Electronics 3232
1 1
min max
min
max min
max
1
Substituting for in equation
1
we get,
1
1
d RT d RT
L L
dRT dRT
L L
dRTL
RT
L
E
I I e eR
I
V E I e I eR
V e EI
R Re
@ ! -
!
-
!
-
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Power Electronics 3333
max
1 1
min max
min
max min
ubstituting for in equation
1
e get,
1
1
is kno n asthe steadystate ripple.
d RT d RT
L L
dRT
L
RTL
I
E I I e e
R
V e EI
R Re
I I
! -
!
-
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Power Electronics 3434
max min
max min
Therefore peak-to-peak ripple current
Average output voltage
.
Average output current
2
dc
dc approx
I I I
V d V
I II
( !
!
!
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Power Electronics 3535
min max
min
max minmin
Assuming load current varies linearlyfrom to instantaneous
load currentis given by
. 0O ON
O
I I
I ti I for t t dT
dT
I Ii I t
dT
(! e e
!
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Power Electronics 3636
2
0
0
2
max min
min
0
2
min max min2 2max minmin
0
RMS value ofload current
1
1
21
dT
O RMS
dT
O RMS
dT
O RMS
I i dtdT
I I t I I dt
dT dT
I I I t I I I I t dtdT dT dT
!
!
-
! -
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Power Electronics 3737
12 2
max min2
min min max min
2
0
0
2
max minmin
0
RMS value of output current
3
RMS chopper current
1
1
O RMS
dT
CH
dT
CH
I I I I I I I
I i dtT
I I I I t dt
T dT
!
-
!
!
-
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Power Electronics 3838
12 2
max min2
min min max min3
Effective input resistance is
CH
CH O RMS
i
S
I I I d I I I I
I d I
VR
I
!
-
!
!
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Power Electronics 3939
WhereAverage source currentS
S dc
i
dc
I
I dI
VR
dI
!
!
@ !
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Power Electronics 4040
Principle Of Step-up Chopper
+
VOV
Chopper
CLOA
D
DLI
+
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Power Electronics 4141
Step-up chopper is used to obtain a loadvoltage higher than the input voltage V.
The values ofL and Care chosendepending upon the requirement of
output voltage and current. When the chopper is ON, the inductor L is
connected across the supply.
The inductor current Irises and the
inductor stores energy during the ONtime of the chopper, tON.
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Power Electronics 4242
When the chopper is off, the inductorcurrent I is forced to flow through thediode D and load for a period, tOFF.
The current tends to decrease resulting inreversing the polarity of induced EMF in L.
Therefore voltage across load is given by
. .,O OdI
V V L i e V Vdt
! "
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Power Electronics 4343
A large capacitor C connectedacross the load, will provide a
continuous output voltage . Diode D prevents any current flow
from capacitor to the source.
Step up choppers are used for
regenerative braking of dc motors.
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Power Electronics 44
44
Expression For OutputVoltageAssume the average inductor currentto be
during ON and OFF time of Chopper.
Voltage acrossinductor
Therefore energystored in inductor
= . .
Where
When Chopper
period of chopper.
is ON
ON
ON
I
L V
V I t
t ON
!
!
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Power Electronics 45
45
(energyissupplied byinductorto load)
Voltage across
Energysupplied byinductor
where period of Chopper.
Neg
When Chopper
lecting losses, energystored in inductor
is OFF
O
O OFF
OFF
L V V
L V V It
t OFF
L
!
!
!
= energysupplied byinductorL
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Power Electronics 46
46
? A
WhereT = Chopping period orperiod
ofswitching.
ON O OFF
ON OFF
O
OFF
O
ON
VIt V V It
V t tV
t
TV V
T t
@ !
!
!
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Power Electronics 47
47
1
1
1
1
Where duty cyle
ON OFF
OON
O
ON
T t t
V Vt
T
V Vd
td
T
!
!
@ !
! !
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Power Electronics 48
48
For variation ofduty cycle ' ' in the
range of 0 1 the output voltage
ill varyin the range
O
O
d
d V
V V
g
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Power Electronics 49
49
Performance Parameters The thyristor requires a certain minimum time to turn
ONand turnOFF.
Duty cycle dcan be varied only between a min. &
max. value, limiting the min. and max. value ofthe
output voltage.
Ripple inthe load current depends inversely onthe
chopping frequency, f.
To reduce the load ripple current, frequency shouldbe as high as possible.
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Power Electronics 50
50
Problem
AChopper circuitisoperatingonTRCata frequencyof 2 kHzona
460V
supply.If theloadvoltageis350 volts, calculate the conductionperiodof the thyristorineach cycle.
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Power Electronics 51
51
3
460V, 350V, f 2 kHz
1Chopping period
10.5 sec
2 10
Output voltage
dc
ONdc
V V
T
f
T m
tV V
T
!
!
! !v
!
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Power Electronics 52
52
3
Conductionperiod ofthyristor
0.5 10 350
4600.38msec
dcON
ON
ON
T Vt
V
t
t
v!
v v!
!
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Power Electronics 53
53
Problem
Input to thestep up chopperis 200 V.Theoutputrequiredis 600 V.If the
conducting timeof thyristoris 200 Qsec.Compute
Chopping frequency,
If thepulse widthishalved for
constant frequencyofoperation, findthenewoutput voltage.
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Power Electronics 54
54
6
200 , 200 , 600
600 200200 10
Solving for
300
ON dc
dc
ON
V V t s V V
TV V
T tT
T
T
T s
Q
Q
! ! !
!
! v
!
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Power Electronics 55
55
6
6
Chopping frequency
1
1 3.33300 10
Pulse i th is halved
200 10100
2ON
fT
f KHz
t sQ
!
! !v
v@ ! !
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Power Electronics 56
56
6
6
Frequencyis constant
3.33
1300
Output voltage
300 10200 300Volts
300 100 10
ON
f KHz
T sf
TV
T t
Q
@ !
! !
@
v! !
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Power Electronics 57
57
Problem
Adc chopperhasaresistiveloadof 20;
andinput voltageVS = 220V. Whenchopperis ON, its voltagedropis 1.5voltsand chopping frequencyis 10 kHz.If theduty cycleis 80%, determine the
averageoutput voltageand the chopperon time.
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Power Electronics 58
58
220 , 20 , 10
0.80
= Voltage drop across chopper = 1.5 volts
Average output voltage
0.80 220 1.5 174.8 Volts
S
ON
ch
ONdc S ch
dc
V V R f kHzt
dT
V
tV V VT
V
! ! ; !
! !
!
! !
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Power Electronics 59
59
3
3
3
3
ChopperONtime,
1Chopping period,
10.1 10 secs 100 secs10 10
ChopperONtime,
0.80 0.1 10
0.08 10 80 secs
ON
ON
ON
ON
t dT
Tf
T
t dT
t
t
!
!
! ! v !v
!
! v v
! v !
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Power Electronics 60
60
Problem
Inadc chopper, theaverageloadcurrentis 30 Amps, choppingfrequencyis 250 Hz, supply voltageis 110 volts.Calculate the ONandOFFperiodsof the chopperif theloadresistanceis 2 ohms.
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Power Electronics 61
61
3
30 , 250 , 110 , 21 1
Chopping period, 4 10 4 msecs250
30 20.545
110
dc
dcdc dc
dc
dc
I Ampsf Hz V V R
Tf
V I V dV R
dVI
RI R
dV
! ! ! ! ;
! ! ! v !
! !
@ !
v! ! !
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Power Electronics 62
62
3
3 3
3
Chopper ON period,
0.545 4 10 2.18msecsChopper OFF period,
4 10 2.18 10
1.82 10 1.82msec
ON
OFF ON
OFF
OFF
t dT
t T t
t
t
! ! v v !
!
! v v
! v !
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Power Electronics 63
63
Adc chopperin figure hasaresistiveloadof R = 10; andinput voltageof V
= 200 V. When chopperis ON, its voltagedropis 2 Vand the chopping frequencyis
1 kHz.If theduty cycleis 60%,determine
Averageoutput voltage
RMS valueofoutput voltage Effectiveinputresistanceof chopper
Chopperefficiency.
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Power Electronics 64
64
V
iChopper
+
v0
200 , 10 , 2
0.60, 1 .
chV V R Chopper voltage drop V V
d f kHz
! ! ; !
! !
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Power Electronics 65
65
? A
Average output voltage
0.60 200 2 118.8VoltsRMS value ofoutput voltage
0.6 200 2 153.37 Volts
dc ch
dc
O ch
O
V d V V
V
V d V V V
!
! !
!
! !
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Power Electronics 66
66
22
0
0 0
Effective input resistance of chopperis
118.811.88Amps
10200
16.8311.88
Outputpoweris
1 1
i
S dc
dcdc
i
S dc
dT dT
ch
O
V VRI I
VI
RV V
RI I
V V P dt dt
T R T R
! !
! ! !
! ! ! ! ;
! !
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Power Electronics 67
67
? A
2
2
0
0
0.6 200 22352.24 watts
10
Inputpower,
1
1
ch
O
O
dT
i O
dT
ch
O
d V V
P R
P
P Vi dtT
V V V P dt
T R
!
! !
!
!
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Power Electronics 68
68
? A0.6 200 200 22376 watts
10
Chopper efficiency,
100
2352.24100 99%
2376
ch
O
O
O
i
dV V V P
R
P
P
P
L
L
!
v ! !
! v
! v !
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Power Electronics 69
69
Problem A chopper is supplying an inductive loadwith a
free-wheelingdiode. The load inductance is 5 H
and resistance is 10;.. The inputvoltage to the
chopper is 200 volts andthe chopper isoperating ata frequency of1000 Hz. Ifthe
ON/OFFtime ratio is 2:3. Calculate
Maximum andminimum values of loadcurrent in one cycle ofchopper operation.
Average loadcurrent
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Power Electronics 70
70
5 , 10 , 1000 ,
200 , : 2 : 3
Chopping period,
1 11 msecs1000
2
32
3
ON OFF
ON
OFF
ON OFF
L H R f Hz
V V t t
T f
t
t
t t
! ! ; !
! !
! ! !
!
!
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Power Electronics 71
71
3
2
3
53
3
53
1 10 0.6 msec5
ON OFF
OFF OFF
OFF
OFF
T t t
T t t
T t
t T
T
!
!
!
!
! v v !
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Power Electronics 72
72
3
3
3
max
1 0.6 10 0.4 msec
Duty cycle,
0.4 100.41 10
Maximum value of load currentis given by
1
1
ON OFF
ON
ON
dRT
L
RT
L
t T t
t
td T
V e EI
R Re
!
! v !
v! ! !v
!
-
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Power Electronics 73
73
3
3
max
0.4 10 1 10
5
max 10 1 10
5
Since there is no voltage source in
the load circuit, E 0
1
1
200 110
1
dRT
L
RT
L
V e
I Re
eI
e
v v v
v v
@ ! -
! -
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Power Electronics 74
74
3
3
0.8 10
max 2 10
max
min
120
1
8.0047A
Minimum value ofload current ith E 0
is given by
1
1
dRT
L
RT
L
eI
e
I
V eIR
e
v
v
! -
!
!
-
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Power Electronics 75
75
3
3
0.4 10 1 10
5
min 10 1 10
5
max min
200 17.995A10
1
Average load current
2
8.0047 7.995 8A2
dc
dc
eI
e
I II
I
v v v
v v
! ! -
!
! }
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Power Electronics 76
76
Problem A chopper feedingon RLloadisshownin
figure, withV= 200 V, R = 5;, L= 5mH, f= 1 kHz, d= 0.5and E= 0 V.Calculate
Maximumandminimum valuesofloadcurrent.
Average valueofloadcurrent.
RMSloadcurrent. Effectiveinputresistanceasseen bysource.
RMS choppercurrent.
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Power Electronics 77
77
3
3
V 200V, R 5 , L 5mH,
f 1kHz, d 0.5, E 0Chopping period is
1 11 10 secs
1 10
T
f
;
! ! ! v
v i0
v0
C er
R
LFW
E
+
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Power Electronics 78
78
Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
3
3
3
max
0.5 5 1 10
5 10
max 5 1 10
5 10
0.5
max 1
Maximum value of load currentis given by
1
1
200 10
51
140 24.9A
1
dRTL
RT
L
V e EI
R Re
eI
e
eI
e
v v v
v
v v
v
!
-
! -
! ! -
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Power Electronics 79
79
Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
3
3
3
min
0.5 5 1 10
5 10
min 5 1 10
5 10
0.5
min 1
Minimum value ofload currentis given by
1
1
200 10
51
140 15.1 A
1
dRT
L
RT
L
V e EI
R Re
eI
e
eI
e
v v vv
v v
v
!
-
! -
! !
-
8/8/2019 DC Choppers VIT
80/89
Power Electronics 80
80
Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
1 2
12 2
max min2
min min max min
Average value ofload currentis
2
for linear variation ofcurrents
24.9 15.1 20 A2
RMS load currentis given by
3
dc
dc
O RMS
I II
I
I I I I I I I
!
@ ! !
!
-
8/8/2019 DC Choppers VIT
81/89
Power Electronics 81
81
Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
12 2
2
1
2
24.9 15.115.1 15.1 24.9 15.1
3
96.04228.01 147.98 20.2A
3
RMS chopper currentis given by
0.5 20.2 14.28A
O RMS
O RMS
ch O RMS
I
I
I d I
!
-
! ! -
! ! v !
8/8/2019 DC Choppers VIT
82/89
Power Electronics 82
82
Effective input resistance is
= Average source current
0.5 20 10 A
Therefore effective input resistance is
20020
10
i
S
S
S dc
S
i
S
VRI
I
I dI
I
VR
I
!
!
! v !
! ! ! ;
8/8/2019 DC Choppers VIT
83/89
Power Electronics 83
83
Classification Of Choppers
Choppers are classified as
Class A Chopper
Class B Chopper
Class CChopper
Class D Chopper
Class E Chopper
8/8/2019 DC Choppers VIT
84/89
Power Electronics 84
84
Class A Chopper
V
Chopper
FWD
+
v0
v0
i0
i0
LOAD
V
8/8/2019 DC Choppers VIT
85/89
Power Electronics 85
85
Class B Chopper
V
Chopper
+
v0
v0
i0
i0
L
E
R
D
8/8/2019 DC Choppers VIT
86/89
Power Electronics 86
86
Class C Chopper
V
e
+
v0
D1
D2
CH2
CH1
v0i0
i0
L
E
8/8/2019 DC Choppers VIT
87/89
Power Electronics 87
87
Class D Chopper
V+ v0
D2
D1 C 2
C 1
v0
i0
L ER i0
8/8/2019 DC Choppers VIT
88/89
Power Electronics 88
88
Class E Chopper
V
v
0
i0L ER
CH2 H2 4
1H1 H3
+
8/8/2019 DC Choppers VIT
89/89
Four Quadrant Operationv0
i0
CH CH ON
CH Conducts1 4
4 2
2 Conducts
CH Conducts4 2
CH CH ON
CH Conducts3 2
2 4
CH Conducts
Conducts2 4
1 4