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DC Choppers
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Introduction
Chopper is a static device. A variable dc voltage is obtained from a
constant dc voltage source.
Also known as dc-to-dc converter.
Widely used for motor control.
Also used in regenerative braking.
Thyristor converter offers greater efficiency,
faster response, lower maintenance, smaller
size and smooth control.
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Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Choppers are of Two Types
Step-down choppers.
Step-up choppers.
In step down chopper output voltage is lessthan input voltage.
In step up chopper output voltage is more
than input voltage.
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Principle Of
Step-down Chopper
V
i0
V0
Chopper
R
+
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A step-down chopper with resistive load.
The thyristor in the circuit acts as a switch.
When thyristor is ON, supply voltage appearsacross the load
When thyristor is OFF, the voltage across the
load will be zero.
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Vdc
v0
V
V/R
i0
Idc
t
t
tON
T
tOFF
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verage value of output or load voltage.
verage value of output or load current.
Time interval for which SCR conducts.
Time interval for which SCR is OFF.
Period of switching
dc
dc
ON
OFF
ON OFF
V A
I A
t
t
T t t
or chopping period.
1Freq. of chopper switching or chopping freq.f
T
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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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2
0
Average Output Current
RMS value of output voltage
1 ON
dcdc
ONdc
t
O o
VIR
tV V
I dR T R
V v dt T
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2
0
2
But during ,
Therefore RMS output voltage
1
.
.
ON
ON o
t
O
ON
O ON
O
t v V
V V dt T
tV
V t VT T
V d V
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2
2
Output power
But
Output power
O O O
OO
OO
O
P V I
VI
R
VP
RdV
PR
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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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Methods Of Control
The output dc voltage can be varied by the
following methods.
Pulse width modulation control or constant
frequency operation.
Variable frequency control or frequency
modulation control.
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Pulse Width Modulation
tONis varied keeping chopping frequency f&
chopping period T constant.
Output voltage is varied by varying the ON
time tON
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V0
V
V
V0
t
ttON
tON tOFF
tOFF
T
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Variable Frequency Control
Chopping frequency fis varied keeping either
tON or tOFF constant.
To obtain full output voltage range, frequency
has to be varied over a wide range. This method produces harmonics in the
output and for large tOFF load current may
become discontinuous
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v0
V
V
v0
t
t
tON
tON
T
T
tOFF
tOFF
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Step-down Chopper
With R-L Load
V
i0
V0
Chopper
R
LFWD
E
+
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When chopper is ON, supply is connected
across load.
Current flows from supply to load.
When chopper is OFF, load current continues
to flow in the same direction through FWD due
to energy stored in inductor L.
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Load current can be continuous or
discontinuous depending on the values of L
and duty cycle d
For a continuous current operation, load
current varies between two limits ImaxandImin
When current becomes equal to Imaxthechopper is turned-off and it is turned-on when
current reduces to Imin.
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Outputvoltage
Outputcurrent
v0
V
i0
Imax
Imin
t
t
tON
T
tOFF
Continuouscurrent
Outputcurrent
t
Discontinuouscurrent
i0
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22Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Expressions For
Load CurrentiOFor Continuous Current Operation When
Chopper Is ON (0 t tON)
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23Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
V
i0
V0
R
L
E
+
-
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24Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
min
min
Taking Laplace Transform
. 0
At 0, initial current 0
OO
O O O
O
O
diV i R L E
dt
V E
RI S L S I S iS S
t i I
IV EI SRR
SLS SLL
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25Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
min
Taking Inverse Laplace Transform
1
This expression is valid for 0 ,
i.e., during the period chopper is ON.
At the instant the chopper is turned off,
load c
R Rt tL L
O
ON
V Ei t e I e
R
t t
maxurrent is O ONi t I
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26Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
When Chopper is OFF
i0
R
L
E
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27Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
max
When Chopper is OFF 0
0
Talking Laplace 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
ERI S L SI S i
S
t
i I
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28Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
max
max
Taking Inverse Laplace Transform
1
O
R Rt tL L
O
I EI SR R
S LS S
L L
Ei t I e eR
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29Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
min
The expression is valid for 0 ,
i.e., during the period chopper is OFF
At the instant the chopper is turned ON or at
the end of the off period, the load current is
OFF
O OFF
t t
i t I
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30Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
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 E
i t e I eR
t t dT i t I
V EI e I e
I I
R
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31Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
max
min
From equation
1
At ,1
R Rt t
L LO
OFF ON O
OFF
Ei t I e eR
t t T t i t I t t d T
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32Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
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
dRT
L
RT
L
EI I e e
R
I
V EI e I eR
V e EI
R Re
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33Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
max
1 1
min max
min
max min
Substituting for in equation
1
we get,
1
1
is known as the steady state ripple.
d RT d RT
L L
dRT
L
RTL
I
EI I e e
R
V e EI
R Re
I I
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34Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
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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35Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
min max
min
max minmin
Assuming load current varies linearly
from to instantaneous
load current is given by
. 0O ON
O
I I
I ti I for t t dT
dT
I Ii I tdT
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36Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
2
0
0
2
max min
min
0
2
min max min2 2max min
min
0
RMS value of load current
1
1
21
dT
O RMS
dT
O RMS
dT
O RMS
I i dtdT
I I tI I dt
dT dT
I I I tI I
I I t dtdT dT dT
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37Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
1
2 2max 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 II I I I I
I i dtT
I II I t dt
T dT
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38Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
12 2
max min2
min min max min3
Effective input resistance is
CH
CH O RMS
i
S
I II d I I I I
I d I
VR
I
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39
Where
Average source currentS
S dc
i
dc
I
I dI
VR
dI
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40Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Principle Of Step-up Chopper
+
VOV
Chopper
CLOAD
DLI
+
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41Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Step-up chopper is used to obtain a load
voltage higher than the input voltage V. The values of Land Care chosen depending
upon the requirement of output voltage andcurrent.
When the chopper is ON, the inductor Lisconnected across the supply.
The inductor current Irises and the inductor
stores energy during the ONtime of thechopper, tON.
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42Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
When the chopper is off, the inductor current Iis forced to flow through the diode Dand 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 V dt
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43Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
A large capacitor C connected across the
load, will provide a continuous output voltage.
Diode Dprevents any current flow from
capacitor to the source.
Step up choppers are used for regenerative
braking of dc motors.
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44Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Expression For Output Voltage
Assume the average inductor current to be
during ON and OFF time of Chopper.
Voltage across inductor
Therefore energy stored in inductor
= . .
Where
When Chopper
period of chopper.
is ON
ON
ON
I
L V
V I t
t ON
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45Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
(energy is supplied by inductor to load)
Voltage across
Energy supplied by inductor
where period of Chopper.
Neg
When Chopper
lecting losses, energy stored in inductor
is OFF
O
O OFF
OFF
L V V
L V V It
t OFF
L
= energy supplied by inductor L
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46Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
WhereT = Chopping period or period
of switching.
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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47Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
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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48Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
For variation of duty cycle ' ' in the
range of 0 1 the output voltage
will vary in the range
O
O
d
d V
V V
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49Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Performance Parameters
The thyristor requires a certain minimum time toturn ONand turn OFF.
Duty cycle d can be varied only between a min.
& max. value, limiting the min. and max. valueof the output voltage.
Ripple in the load current depends inversely on
the chopping frequency, f.
To reduce the load ripple current, frequency
should be as high as possible.
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50Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Problem
A Chopper circuit is operating on TRC at a
frequency of 2 kHz on a 460 V supply. If the
load voltage is 350 volts, calculate the
conduction period of the thyristor in eachcycle.
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51Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
460 V, = 350 V, f = 2 kHz
1Chopping period
10.5 sec
2 10
Output voltage
dc
ONdc
V V
T
f
T m
tV VT
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52Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
Conduction period of thyristor
0.5 10 350
4600.38 msec
dc
ON
ON
ON
T V
t V
t
t
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53Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Problem
Input to the step up chopper is 200 V. The
output required is 600 V. If the conducting time
of thyristor is 200 sec. Compute Chopping frequency,
If the pulse width is halved for constant
frequency of operation, find the new outputvoltage.
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54Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
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
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55Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
6
6
Chopping frequency
1
1 3.33300 10
Pulse width is halved
200 10100
2ON
fT
f KHz
t s
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56Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
6
6
Frequency is constant
3.33
1300
Output voltage =
300 10200 300 Volts
300 100 10
ON
f KHz
T sf
TV
T t
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57Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Problem
A dc chopper has a resistive load of 20 and
input voltage VS= 220V. When chopper is ON,its voltage drop is 1.5 volts and chopping
frequency is 10 kHz. If the duty cycle is 80%,
determine the average output voltage and thechopper on time.
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58Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
220 , 20 , 10
0.80
= Voltage drop across chopper = 1.5 voltsAverage output voltage
0.80 220 1.5 174.8 Volts
S
ON
ch
ONdc S ch
dc
V V R f kHz
td
T
V
t
V V VT
V
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59Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
3
3
3
Chopper ON time,
1Chopping period,
1
0.1 10 secs 100 secs10 10
Chopper ON time,
0.80 0.1 10
0.08 10 80 secs
ON
ON
ON
ON
t dT
Tf
T
t dT
t
t
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60Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Problem
In a dc chopper, the average load current is 30
Amps, chopping frequency is 250 Hz, supply
voltage is 110 volts. Calculate the ON and OFF
periods of the chopper if the load resistance is2 ohms.
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61Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
30 , 250 , 110 , 2
1 1Chopping period, 4 10 4 msecs
250
&
30 20.545
110
dc
dcdc dc
dc
dc
I Amps f Hz V V R
Tf
VI V dVR
dVI
RI R
dV
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62Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
3 3
3
Chopper ON period,
0.545 4 10 2.18 msecs
Chopper OFF period,
4 10 2.18 10
1.82 10 1.82 msec
ON
OFF ON
OFF
OFF
t dT
t T t
t
t
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63Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
A dc chopper in figure has a resistive load of R= 10 and input voltage of V = 200 V. When
chopper is ON, its voltage drop is 2 V and the
chopping frequency is 1 kHz. If the duty cycle is
60%, determine
Average output voltage
RMS value of output voltage
Effective input resistance of chopper
Chopper efficiency.
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64Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
V
i0Chopper
+
R v0
200 , 10 , 2
0.60, 1 .
chV V R Chopper voltage drop V V
d f kHz
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65Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Average output voltage
0.60 200 2 118.8 VoltsRMS value of output 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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66Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
22
0
0 0
Effective input resistance of chopper is
118.811.88 Amps
10200
16.8311.88
Output power is
1 1
i
S dc
dcdc
i
S dc
dT dT
ch
O
V VR I I
VI
RV V
RI I
V VvP dt dt
T R T R
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67Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
2
2
0
0
0.6 200 22352.24 watts
10
Input power,
1
1
ch
O
O
dT
i O
dT
ch
O
d V VP
R
P
P Vi dtT
V V VP dt
T R
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68Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
0.6 200 200 22376 watts
10
Chopper efficiency,
100
2352.24100 99%
2376
ch
O
O
O
i
dV V V P
R
P
P
P
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69Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Problem
A chopper is supplying an inductive load with a
free-wheeling diode. The load inductance is 5 H
and resistance is 10.. The input voltage to the
chopper is 200 volts and the chopper is operatingat a frequency of 1000 Hz. If the ON/OFF time
ratio is 2:3. Calculate
Maximum and minimum values of load currentin one cycle of chopper operation.
Average load current
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70Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
5 , 10 , 1000 ,
200 , : 2 :3Chopping period,
1 1
1 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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71Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
23
5
3
3
53
1 10 0.6 msec5
ON OFF
OFF OFF
OFF
OFF
T t t
T t t
T t
t T
T
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72Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
3
3
max
1 0.6 10 0.4 msecDuty cycle,
0.4 10
0.41 10
Maximum value of load current is given by
1
1
ON OFF
ON
ON
dRT
L
RT
L
t T t
t
t
d T
V e EI
R Re
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73Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
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
RTL
V eI
R e
eI
e
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75
Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
3
0.4 10 1 10
5
min 10 1 10
5
max min
200 17.995 A10
1
Average load current
2
8.0047 7.9958 A
2
dc
dc
eI
e
I II
I
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76
Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Problem
A chopper feeding on RL load is shown infigure, with V = 200 V, R = 5, L = 5 mH, f
= 1 kHz, d = 0.5 and E = 0 V. Calculate
Maximum and minimum values of load
current.
Average value of load current.
RMS load current.
Effective input resistance as seen by source.
RMS chopper current.
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77
Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
3
V = 200 V, R = 5 , L = 5 mH,
f = 1kHz, d = 0.5, E = 0
Chopping period is
1 11 10 secs
1 10T
f
i0
v0
Chopper
R
LFWD
E
+
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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 current is given by
1
1
200 10
51
140 24.9 A
1
dRT
L
RT
L
V e EI
R Re
eI
e
eI
e
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79
Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
3
3
3
3
min
0.5 5 1 105 10
min 5 1 10
5 10
0.5
min 1
Minimum value of load current is given by
1
1
200 10
51
140 15.1 A
1
dRT
L
RT
L
V e EIR R
e
eI
e
eI
e
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80
Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
1 2
12 2
max min2
min min max min
Average value of load current is
2
for linear variation of currents
24.9 15.1 20 A2
RMS load current is given by
3
dc
dc
O RMS
I II
I
I II I I I I
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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 20.2 A
3
RMS chopper current is given by
0.5 20.2 14.28 A
O RMS
O RMS
ch O RMS
I
I
I d I
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82
Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
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
Cl ifi i Of Ch
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Classification Of Choppers
Choppers are classified as
Class A Chopper
Class B Chopper
Class C Chopper
Class D Chopper
Class E Chopper
Cl A Ch
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Class A Chopper
V
Chopper
FWD
+
v0
v0
i0
i0
L
OAD
V
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When chopper is ON,supply voltage Visconnected across the load.
When chopper is OFF, vO= 0 and the loadcurrent continues to flow in the same directionthrough the FWD.
The average values of output voltage andcurrent are always positive.
Class A Chopper is a first quadrant chopper .
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Class A Chopperis a step-down chopper in
which power always flows form source to load.
It is used to control the speed of dc motor.
The output current equations obtained in step
down chopper with R-Lload can be used to
study the performance of Class A Chopper.
i
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Output current
Thyristorgate pulse
Output voltage
ig
i0
v0
t
t
ttON
T
CH ON
FWD Conducts
Cl B Ch
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Class B Chopper
V
Chopper
+
v0
v0
i0
i0
L
E
R
D
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When chopper is ON, Edrives a currentthrough L and R in a direction opposite to thatshown in figure.
During the ON period of the chopper, theinductance Lstores energy.
When Chopper is OFF, diode Dconducts, and
part of the energy stored in inductor Lisreturned to the supply.
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Average output voltage is positive.
Average output current is negative.
Therefore Class B Chopperoperates in secondquadrant.
In this chopper, power flows from load tosource.
Class B Chopperis used for regenerativebraking of dc motor.
Class B Chopperis a step-up chopper.
Thyristorig
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Output current
Dconducts Chopper
conducts
Thyristorgate pulse
Output voltage
i0
v0
t
t
t
Imin
Imax
T
tONtOFF
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Expression for Output Current
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min
For the initial condition i.e.,
During the interval diode 'D' conduc
at 0
The solution of the ab
ts
voltage equation
ove equation is obtainedalong similar lines as in s
is given by
OO
O
LdiV Ri E
dt
i t I t
tep-down chopper
with R-L load
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min
max
max min
During the interval chopper is ON voltage
equation is g
1 0
At
1
0
iven by
OFF OFF
R Rt t
L LO OFF
OFF O
R Rt t
L L
OO
V Ei t e I e t t
Rt t i t I
V EI e I eR
LdiRi E
dt
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max
max
min
min max
Redefining the time origin, at 0
The solution for the stated initial condition is
1 0
At
1ON ON
O
R Rt t
L LO ON
ON O
R Rt t
L L
t i t I
Ei t I e e t t R
t t i t I
EI I e e
R
Class C Chopper
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Class C Chopper
V
Chopper
+
v0
D1
D2CH2
CH1
v0i0
i0
L
E
R
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Class C Chopperis a combination of Class Aand Class B Choppers.
For first quadrant operation, CH1is ON or D2conducts.
For second quadrant operation, CH2 is ON orD1conducts.
When CH1is ON, the load current is positive. The output voltage is equal to V & the load
receives power from the source.
When CH1is turned OFF, energy stored ininductance Lforces current to flow throughthe diode D2 and the output voltage is zero.
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Current continues to flow in positive direction.
When CH2is triggered, the voltage Eforcescurrent to flow in opposite direction through Land CH2.
The output voltage is zero.
On turning OFF CH2, the energy stored in theinductance drives current through diode D1
and the supply Output voltage is V, the input current becomes
negative and power flows from load to source.
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Average output voltage is positive
Average output current can take both positiveand negative values.
Choppers CH1& CH2 should not be turned ON
simultaneously as it would result in shortcircuiting the supply.
Class C Choppercan be used both for dc motorcontrol and regenerative braking of dc motor.
Class C Choppercan be used as a step-up orstep-down chopper.
Gate pulseof CH
ig1
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Gate pulseof CH2
of CH1
Output current
Output voltage
ig2
i0
V0
t
t
t
t
D1 D1D2 D2CH1 CH2 CH1 CH2ON ON ON ON
Class D Chopper
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Class D Chopper
V+ v0
D2
D1 CH2
CH1
v0
i0
L ER i0
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Class D is a two quadrant chopper.
When both CH1 and CH2are triggered
simultaneously, the output voltage vO= Vand
output current flows through the load. When CH1 and CH2 are turned OFF, the load
current continues to flow in the same direction
through load, D1and D2, due to the energystored in the inductor L.
Output voltage vO= - V.
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Average load voltage is positive if chopper ONtime is more than the OFF time
Average output voltage becomes negative if
tON < tOFF. Hence the direction of load current is always
positive but load voltage can be positive or
negative.
Gate pulseof CH1
ig1
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Gate pulseof CH2
Output current
Output voltage
Average v0
ig2
i0
v0
V
t
t
t
t
CH ,CH
ON1 2 D1,D2 Conducting
Gate pulseof CH1
ig1
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Gate pulseof CH2
Output current
Output voltage
Average v0
ig2
i0
v0
V
t
t
t
t
CH
CH1
2
D , D1 2
Class E Chopper
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Class E Chopper
V
v0
i0L ER
CH2 CH4D2 D4
D1 D3CH1 CH3
+
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Four Quadrant Operation
v0
i0
CH - CH ON
CH - D Conducts1 4
4 2
D D2 3- ConductsCH - D Conducts4 2
CH - CH ONCH - D Conducts
3 2
2 4
CH - D Conducts
D - D Conducts2 4
1 4
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Class E is a four quadrant chopper
When CH1 and CH4 are triggered, output
current iO flows in positive direction through
CH1 and CH4, and with output voltage vO= V. This gives the first quadrant operation.
When both CH1 and CH4are OFF, the energy
stored in the inductor L drives iOthrough D2and D3 in the same direction, but output
voltage vO= -V.
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Therefore the chopper operates in the
fourth quadrant. When CH2 and CH3are triggered, the load
current iO flows in opposite direction & output
voltage vO= -V.
Since both iO andvO are negative, the chopper
operates in third quadrant.
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When both CH2 and CH3are OFF, the load
current iOcontinues to flow in the same
direction D1andD4and the output voltage
vO= V.
Therefore the chopper operates in second
quadrant as vO is positive but iOis negative.
Eff Of S &
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Effect Of Source &
Load Inductance
The source inductance should be as small as
possible to limit the transient voltage. Also source inductance may cause
commutation problem for the chopper.
Usually an input filter is used to overcome theproblem of source inductance.
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The load ripple current is inversely
proportional to load inductance and chopping
frequency. Peak load current depends on load inductance.
To limit the load ripple current, a smoothing
inductor is connected in series with the load.
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Problem
For the first quadrant chopper shown in figure,express the following variables as functions of V,
R and duty cycle d in case load is resistive.
Average output voltage and current Output current at the instant of commutation
Average and RMS free wheeling diode current.
RMS value of output voltage RMS and average thyristor currents.
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V
i0
v0
Chopper
FWD
+
LOAD
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Average output voltage,
Average output current,
The thyristor is commutated at the instant
output current at the instant of commutation is
since V is the output v
ONdc
dc
dc
ON
tV V dV T
V dV
I R R
t t
V
R
oltage at that instant.
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2
00
Free wheeling diode (FWD) will never
conduct in a resistive load.
Average & RMS free wheeling diode
currents are zero.
1
But during
ONt
O RMS
O ON
V v dt T
v V t
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2
0
2
1
Where duty cycle,
ONt
O RMS
ON
O RMS
O RMS
ON
V V dt T
t
V V T
V dV
td
T
RMS value of thyristor current
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RMS value of thyristor current
= RMS value of load current
Average value of thyristor current
= Average value of load current
O RMSV
R
dVR
dV