dc choppers by T08G2Yz

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									                           DC Choppers




Power Electronics by Prof. M. Madhusudhan Rao   1
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    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.
Power Electronics by Prof. M. Madhusudhan Rao      2
  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 less
     than input voltage.
    In step up chopper output voltage is more
     than input voltage.

Power Electronics by Prof. M. Madhusudhan Rao      3
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Principle Of
Step-down Chopper
                                 Chopper
                                                i0
                                                         +


   V                                                 R       V0



                                                         
Power Electronics by Prof. M. Madhusudhan Rao                     4
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• A step-down chopper with resistive load.
• The thyristor in the circuit acts as a switch.
• When thyristor is ON, supply voltage appears
  across the load
• When thyristor is OFF, the voltage across the
  load will be zero.

Power Electronics by Prof. M. Madhusudhan Rao      5
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
        v0
         V

                                                Vdc

                                                      t
                   tON           tOFF
         i0


      V/R
                                                Idc
                                                      t
                           T

Power Electronics by Prof. M. Madhusudhan Rao             6
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Vdc  Average value of output or load voltage.
I dc  Average value of output or load current.
tON  Time interval for which SCR conducts.
tOFF  Time interval for which SCR is OFF.
T  tON  tOFF  Period of switching or chopping period.
   1
f   Freq. of chopper switching or chopping freq.
   T
 Power Electronics by Prof. M. Madhusudhan Rao      7
   Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   Average Output Voltage
                   tON        
          Vdc  V             
                   tON  tOFF 
                   tON 
          Vdc  V        V .d
                   T 
        tON           
   but                  d  duty cycle
        t             
Power Electronics by Prof. M. Madhusudhan Rao   8
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    Average Output Current
              Vdc
       I dc 
               R
              V  tON  V
       I dc          d
              R T  R
    RMS value of output voltage
                             tON
                1
           VO                 v dt
                                    2
                                    o
                T              0
Power Electronics by Prof. M. Madhusudhan Rao   9
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    But during tON , vo  V
   Therefore RMS output voltage
                                    tON
                    1
               VO                     
                                                2
                                         V dt
                    T                  0

                                   2
                    V       tON
               VO    tON      .V
                    T        T
               VO  d .V
Power Electronics by Prof. M. Madhusudhan Rao       10
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   Output power PO  VO I O
                     VO
   But          IO 
                      R
    Output power
                                                 2
                                          V
                                     PO        O

                                           R
                                              2
                                          dV
                                     PO 
                                            R
Power Electronics by Prof. M. Madhusudhan Rao        11
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Effective input resistance of chopper
             V
        Ri 
             I dc
             R
       Ri 
             d
The output voltage can be varied by
varying the duty cycle.
Power Electronics by Prof. M. Madhusudhan Rao   12
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
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.



Power Electronics by Prof. M. Madhusudhan Rao     13
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Pulse Width Modulation
• tON is varied keeping chopping frequency ‘f’ &
  chopping period ‘T’ constant.
• Output voltage is varied by varying the ON
  time tON




Power Electronics by Prof. M. Madhusudhan Rao   14
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   V0
     V

          tON         tOFF

                                                t
                       T
   V0

     V



                                                t
                tON        tOFF
Power Electronics by Prof. M. Madhusudhan Rao       15
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Variable Frequency Control
• Chopping frequency ‘f’ is 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

Power Electronics by Prof. M. Madhusudhan Rao   16
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    v0
     V


               tON              tOFF
                                                t
                         T
    v0

     V


               tON           tOFF
                                                t
                     T
Power Electronics by Prof. M. Madhusudhan Rao       17
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Step-down Chopper
With R-L Load
                Chopper
                                                i0
                                                             +
                                                         R

 V                                                               V0
                                        FWD              L

                                                     E
                                                             
Power Electronics by Prof. M. Madhusudhan Rao                         18
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• 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’.
Power Electronics by Prof. M. Madhusudhan Rao   19
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• 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 Imax and Imin
• When current becomes equal to Imax the
  chopper is turned-off and it is turned-on when
  current reduces to Imin.
Power Electronics by Prof. M. Madhusudhan Rao   20
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
  v0
                                                Output
                                                voltage
   V
             tON           tOFF
                                                          t
                     T
   i0                                                Output
 Imax                                                current

                                                Continuous
  Imin                                           current
                                                       t
   i0                                                Output
                                                     current
                                                Discontinuous
                                                   current
                                                       t
Power Electronics by Prof. M. Madhusudhan Rao                   21
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
             Expressions For
               Load Current
   iO For Continuous Current Operation
                  When
        Chopper Is ON (0  t  tON)



Power Electronics by Prof. M. Madhusudhan Rao   22
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                                                i0
                                                             +
                                                         R

V                                                                V0
                                                         L

                                                     E
                                                             -
Power Electronics by Prof. M. Madhusudhan Rao                    23
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                 diO
    V  iO R  L     E
                 dt
    Taking Laplace Transform

       RI O  S   L  S .I O  S   iO  0   
    V                                               E
    S                                            S
    At t  0, initial current iO  0    I min
                 V E       I min
    IO  S              
                      R        R
               LS  S   S 
                      L        L
Power Electronics by Prof. M. Madhusudhan Rao            24
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
 Taking Inverse Laplace Transform
            V E        t 
                          R               R
                                           t
 iO  t        1  e   L
                                I min e   L
              R             
                              
 This expression is valid for 0  t  tON ,
 i.e., during the period chopper is ON.
 At the instant the chopper is turned off,
 load current is iO  tON   I max
Power Electronics by Prof. M. Madhusudhan Rao     25
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
When Chopper is OFF
                                   i0

                                             R


                                             L

                                         E

Power Electronics by Prof. M. Madhusudhan Rao    26
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
  When Chopper is OFF  0  t  tOFF 
              diO
  0  RiO  L     E
              dt
  Talking Laplace transform

  0  RI O  S   L  SI O  S   iO  0   
                                                 E     
                                             S
  Redefining time origin we have at t  0,
  initial current iO  0               
                                           I   max
Power Electronics by Prof. M. Madhusudhan Rao              27
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
              I max        E
 IO  S          
             S
                  R          R
                      LS  S  
                  L          L
Taking Inverse Laplace Transform
                              R
                              t      E         R
                                                 t   
iO  t   I max e            L
                                      1  e    L
                                                      
                                      R              
Power Electronics by Prof. M. Madhusudhan Rao             28
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
The expression is valid for 0  t  tOFF ,
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
                              iO  tOFF   I min
 Power Electronics by Prof. M. Madhusudhan Rao      29
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   Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
To Find I max & I min
From equation
                          V E        t 
                                        R               R
                                                         t
               iO  t        1  e   L
                                              I min e   L
                            R             
                                            
At             t  tON  dT , iO  t   I max
                           V E                
                                                  dRT
                                                                     
                                                                        dRT
               I max          1  e
                                                   L
                                                          I min e
                                                                         L
                             R                         
Power Electronics by Prof. M. Madhusudhan Rao                                 30
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
From equation
                                                 R
                                                 t    E         R
                                                                  t   
                 iO  t   I max e              L
                                                       1  e    L
                                                                       
                                                       R              
At               t  tOFF  T  tON , iO  t   I min
                 t  tOFF  1  d  T
Power Electronics by Prof. M. Madhusudhan Rao                          31
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                                
                                
                                      1 d  RT 
                                    1 d  RT
                                    
                              E
       I min  I max e L
                             1  e L 
                              R                
                                                 
Substituting for I min in equation
                       V E                     
                                                     dRT
                                                                        
                                                                             dRT
             I max         1  e
                                                      L
                                                             I min e
                                                                              L
                         R                                
we get,
                              
                                 dRT
                                                 
                       V 1  e L                 E
             I max   
                       R      
                                  RT              R
                          1 e L
                                                
                                                 
Power Electronics by Prof. M. Madhusudhan Rao                                      32
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Substituting for I max in equation
                           
                               1 d  RT          
                                                      1 d  RT 
                                             E
      I min  I max e              L
                                             1  e L 
                                             R                 
                                                                 
we get,
                         dRT
              V  e  1 E  L
      I min                
               R L  RT    R
                   e 1 
                         
 I max  I min  is known as the steady state ripple.
Power Electronics by Prof. M. Madhusudhan Rao                        33
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Therefore peak-to-peak ripple current
                 I  I max  I min
Average output voltage
                 Vdc  d .V
Average output current
                       I max  I min
      I dc approx  
                             2
Power Electronics by Prof. M. Madhusudhan Rao   34
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Assuming load current varies linearly
from I min to I max instantaneous
load current is given by

      iO  I min        
                           I  .t         for 0  t  tON  dT 
                     dT
                    I max  I min 
      iO  I min                 t
                         dT       
Power Electronics by Prof. M. Madhusudhan Rao                        35
                                                                     35
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
RMS value of load current
                     dT
                1
                    
                        2
I O RMS              i0 dt
               dT    0


                                     I max  I min  t  dt
                                                       2
                1
                     dT
                          
I O RMS    
               dT    
                     0
                           I min 
                                           dT
                                                        
                                                        
                           2        I max  I min  2 2 I min  I max  I min  t 
                     dT                               2
                1
I O RMS    
               dT         I min  
                                         dT
                                                     t 
                                                                   dT
                                                                                     dt
                                                                                    
                     0                                                             


  Power Electronics by Prof. M. Madhusudhan Rao                                    36
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    Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
RMS value of output current
                                                                1
              2        I max  I min   I I  I 
                                        2                       2
I O RMS    I min                       min  max min  
             
                              3                            
                                                            
RMS chopper current
                 dT
         1
                 i dt
                      2
I CH                  0
         T        0

                                                    2
                             I max  I min     
                 dT
         1
I CH   
         T         I min   dT
                 0          
                                                 t  dt
                                                 
Power Electronics by Prof. M. Madhusudhan Rao                       37
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                                                              1
            2        I max  I min   I I  I 
                                                  2           2
I CH    d  I min                       min  max min  
           
                            3                            
                                                          
                            I CH  d I O RMS 
Effective input resistance is
                                 V
                            Ri 
                                 IS
  Power Electronics by Prof. M. Madhusudhan Rao        38
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    Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Where
                 I S  Average source current


                 I S  dI dc


                       V
                Ri 
                      dI dc
Power Electronics by Prof. M. Madhusudhan Rao   39
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    Principle Of Step-up Chopper

       I           L                            D
                                                            +
              +          

                                                        L
                                                    C   O    VO
V                                                       A
                                                        D
                       Chopper

                                                            
Power Electronics by Prof. M. Madhusudhan Rao               40
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  Prof. 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 L and C are chosen depending
  upon the requirement of output voltage and
  current.
• When the chopper is ON, the inductor L is
  connected across the supply.
• The inductor current ‘I’ rises and the inductor
  stores energy during the ON time of the
  chopper, tON.
Power Electronics by Prof. M. Madhusudhan Rao       41
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• When the chopper is off, the inductor current I
  is forced to flow through the diode D and load
  for a period, tOFF.
• The current tends to decrease resulting in
  reversing the polarity of induced EMF in L.
• Therefore voltage across load is given by

                   dI
        VO  V  L    i.e., VO  V
                   dt
Power Electronics by Prof. M. Madhusudhan Rao   42
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• A large capacitor ‘C’ connected across 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.

Power Electronics by Prof. M. Madhusudhan Rao    43
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Expression For Output Voltage
  Assume the average inductor current to be
  I during ON and OFF time of Chopper.
  When Chopper is ON
  Voltage across inductor L  V
  Therefore energy stored in inductor
                 = V .I .tON
  Where tON  ON period of chopper.
Power Electronics by Prof. M. Madhusudhan Rao   44
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
When Chopper is OFF
(energy is supplied by inductor to load)
Voltage across L  VO  V
Energy supplied by inductor L  VO  V  ItOFF
where tOFF  OFF period of Chopper.
Neglecting losses, energy stored in inductor
L = energy supplied by inductor L
Power Electronics by Prof. M. Madhusudhan Rao   45
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
  VItON  VO  V  ItOFF
                    V tON  tOFF 
         VO 
                             tOFF
            T 
    VO  V          
            T  tON 
  Where
          T = Chopping period or period
              of switching.
Power Electronics by Prof. M. Madhusudhan Rao   46
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                T  tON  tOFF
                      
               1 
      VO  V          
                   tON
               1     
                   T 
               1 
     VO  V        
               1 d 
          tON
Where d         duty cyle
           T
Power Electronics by Prof. M. Madhusudhan Rao   47
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
For variation of duty cycle ' d ' in the
range of 0  d  1 the output voltage VO
will vary in the range V  VO  



Power Electronics by Prof. M. Madhusudhan Rao   48
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
     Performance Parameters
• The thyristor requires a certain minimum time to
  turn ON and turn OFF.
• Duty cycle d can be varied only between a min.
  & max. value, limiting the min. and max. value
  of 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.
  Power Electronics by Prof. M. Madhusudhan Rao   49
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    Prof. 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 each
  cycle.



Power Electronics by Prof. M. Madhusudhan Rao    50
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
V  460 V, Vdc = 350 V,                          f = 2 kHz
                                              1
Chopping period                            T
                                              f
                                                    1
                                           T         3
                                                          0.5 m sec
                                                2 10
                                                  tON 
Output voltage                             Vdc       V
                                                  T 
Power Electronics by Prof. M. Madhusudhan Rao                     51
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
  Conduction period of thyristor
              T  Vdc
        tON 
                V
                      3
              0.5 10  350
        tON 
                    460
        tON  0.38 msec
Power Electronics by Prof. M. Madhusudhan Rao   52
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  Prof. 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 output
     voltage.

Power Electronics by Prof. M. Madhusudhan Rao   53
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
 V  200 V , tON  200  s, Vdc  600V
                  T 
         Vdc  V          
                  T  tON 
                            T       
         600  200               6 
                     T  200  10 
  Solving for T
         T  300  s
Power Electronics by Prof. M. Madhusudhan Rao   54
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   Chopping frequency
               1
           f 
               T
                   1
           f          6
                           3.33KHz
               300 10
   Pulse width is halved
                                                6
                             200 10
                   tON                              100  s
                                 2
Power Electronics by Prof. M. Madhusudhan Rao                    55
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Frequency is constant
            f  3.33KHz
               1
            T   300  s
               f
                      T 
 Output voltage = V          
                      T  tON 
                                 300 106 
                           200                 6 
                                  300  100 10     300 Volts
                                                   
  Power Electronics by Prof. M. Madhusudhan Rao               56
                                                              56
    Prof. 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 the
  chopper on time.

Power Electronics by Prof. M. Madhusudhan Rao   57
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
 VS  220V , R  20, f  10 kHz
      tON
 d        0.80
       T
 Vch = Voltage drop across chopper = 1.5 volts
  Average output voltage
                       tON 
                Vdc        VS  Vch 
                       T 
                Vdc  0.80  220  1.5   174.8 Volts
Power Electronics by Prof. M. Madhusudhan Rao            58
                                                         58
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Chopper ON time,                        tON  dT
                                           1
Chopping period,                        T
                                           f
             1            3
      T           0.110 secs  100 μsecs
         10 10 3

Chopper ON time,
             tON  dT
                                                3
             tON  0.80  0.110
             tON  0.08 103  80 μsecs
Power Electronics by Prof. M. Madhusudhan Rao        59
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  Prof. 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 is 2 ohms.



Power Electronics by Prof. M. Madhusudhan Rao   60
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
I dc  30 Amps, f  250 Hz , V  110 V , R  2
                        1     1
Chopping period, T              4 10 3  4 msecs
                         f 250
             Vdc
      I dc       & Vdc  dV
               R
              dV
     I dc 
               R
            I dc R 30  2
      d                  0.545
              V     110
 Power Electronics by Prof. M. Madhusudhan Rao    61
                                                  61
   Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Chopper ON period,
                                                3
              tON  dT  0.545  4 10  2.18 msecs
Chopper OFF period,
      tOFF  T  tON
                                     3         3
              tOFF  4  10  2.18 10
                                          3
              tOFF  1.82 10  1.82 msec
Power Electronics by Prof. M. Madhusudhan Rao        62
                                                     62
  Prof. 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.
Power Electronics by Prof. M. Madhusudhan Rao      63
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                  Chopper
                                                 i0
                                                        +



    V                                                 R v0



                                                        

V  200 V , R  10, Chopper voltage drop Vch  2V
d  0.60, f  1 kHz.
 Power Electronics by Prof. M. Madhusudhan Rao               64
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   Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Average output voltage
             Vdc  d V  Vch 
             Vdc  0.60  200  2  118.8 Volts
RMS value of output voltage
             VO  d V  Vch 
             VO  0.6  200  2   153.37 Volts
Power Electronics by Prof. M. Madhusudhan Rao      65
                                                   65
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   Effective input resistance of chopper is
                    V   V
                Ri  
                    I S I dc
                       Vdc 118.8
                I dc              11.88 Amps
                         R     10
                       V    V     200
                Ri                   16.83
                       I S I dc 11.88
   Output power is
                                                    V  Vch 
                             dT   2            dT                2
                              1 v         1
                   PO   dt     0
                                                                    dt
                              T 0 R Rao T      0
                                                        R                 66
Power Electronics by Prof. M. Madhusudhan                                 66
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                      d V  Vch 
                                                2

                 PO 
                           R
                          0.6  200  2
                                                    2

                 PO                                     2352.24 watts
                                   10
   Input power,
                             dT
                      1
                 Pi 
                      T       Vi dt
                              0
                                    O


                      1
                              dT
                                V V  Vch 
                 PO 
                      T        R dt
                              0
Power Electronics by Prof. M. Madhusudhan Rao                             67
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
            dV V  Vch 
      PO 
                  R
            0.6  200  200  2
      PO                         2376 watts
                    10
Chopper efficiency,
                 PO
                100
                 Pi
                 2352.24
                       100  99%
                  2376
Power Electronics by Prof. M. Madhusudhan Rao   68
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  Prof. 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 operating
  at a frequency of 1000 Hz. If the ON/OFF time
  ratio is 2:3. Calculate
   – Maximum and minimum values of load current
     in one cycle of chopper operation.
   – Average load current
  Power Electronics by Prof. M. Madhusudhan Rao   69
                                                  69
    Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
  L  5 H , R  10, f  1000 Hz,
  V  200 V , tON : tOFF  2 : 3
  Chopping period,
            1      1
        T           1 msecs
             f 1000
         tON 2
             
        tOFF 3
                         2
                 tON     tOFF
                         3
Power Electronics by Prof. M. Madhusudhan Rao   70
                                                70
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
     T  tON  tOFF
                       2
                    T  tOFF  tOFF
                       3
        5
     T  tOFF
        3
                               3
                     tOFF      T
                               5
        3     3
     T  110  0.6 msec
        5
Power Electronics by Prof. M. Madhusudhan Rao   71
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
             tON  T  tOFF
             tON  1  0.6  103  0.4 msec
Duty cycle,
                                                3
         tON 0.4 10
     d             3
                          0.4
          T     110
Maximum value of load current is given by
                                      
                                           dRT
                                                 
                       V 1  e             L
                                                  E
             I max   
                       R       
                                  RT              R
                          1 e L
                                                
                                                 
Power Electronics by Prof. M. Madhusudhan Rao           72
                                                        72
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   Since there is no voltage source in
   the load circuit, E = 0
                                    
                                       dRT
                                                   
                             V 1  e L            
                  I max   
                             R      
                                        RT         
                                1 e L
                                                  
                                                   
                                               
                                                  0.4101103   
                             200 1  e                 5
                                                                  
                   I max                101103               
                             10         
                                  1 e 5
                                                                 
                                                                  
Power Electronics by Prof. M. Madhusudhan Rao                         73
                                                                      73
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                             1  e        0.8103   
                I max    20       2103
                                                       
                              1 e
                                                      
                                                       
                I max    8.0047A
 Minimum value of load current with E = 0
 is given by
                             dRT    
                          V  e L  1
                I min   
                          R  RT     
                            
                             e L 1 
                                     
Power Electronics by Prof. M. Madhusudhan Rao              74
                                                           74
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                               
                          0.4101103
        200  e               1
                                5
I min                             7.995 A
        10  10110            
                        3

               e 5 1 
                               
Average load current
                I max  I min
         I dc 
                      2
                8.0047  7.995
         I dc                     8 A
                         2
Power Electronics by Prof. M. Madhusudhan Rao   75
                                                75
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    Problem
• A chopper feeding on RL load is shown in
  figure, 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.
Power Electronics by Prof. M. Madhusudhan Rao        76
                                                     76
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   V = 200 V, R = 5 , L = 5 mH,
   f = 1kHz, d = 0.5, E = 0
   Chopping period is
      1      1          3
   T            110 secs
      f 110   3
                    Chopper
                                                      i0
                                                                   +
                                                               R

                                                                       v0
                                                FWD            L

                                                           E
Power Electronics by Prof. M. Madhusudhan Rao                      77
                                                                    77
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
  Maximum value of load current is given by
                                
                                   dRT
                                         
                         V 1  e L  E
               I max                       
                         R       
                                    RT 
                                               R
                            1 e
                           
                                     L
                                         
                                         
                                    
                                       0.551103   
                         200 1  e       5103
                                                     
               I max                   51103    0
                          5            
                               1  e 5103         
                                                    
                            1  e0.5 
               I max    40       1 
                                          24.9 A
                             1 e 
Power Electronics by Prof. M. Madhusudhan Rao              78
                                                           78
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   Minimum value of load current is given by
                              dRT         
                           V  e  1 E
                                  L
                 I min                       
                           R L  RT         R
                              e 1 
                                          
                                   0.551103    
                                                  1
                                            3
                           200  e 510
                 I min          51103          0
                            5
                                 e 5103  1 
                                                   
                               e0.5  1 
                 I min    40  1          15.1 A
                               e 1 
Power Electronics by Prof. M. Madhusudhan Rao             79
                                                          79
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Average value of load current is
                I1  I 2
         I dc 
                   2
for linear variation of currents
             24.9  15.1
     I dc               20 A
                  2
RMS load current is given by
                                                                     1
                   2           I max  I min   I I  I 
                                                2                    2
I O RMS    I min                               min  max min  
                   Prof. M. Madhusudhan Rao
                                         3                         
                                                                    
                                                                    80
Power Electronics by                                                80
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                                                              1
                       24.9  15.1  15.1 24.9  15.1 
                                                 2            2
I O RMS     15.1 
                    2
                                                       
               
                             3                          
                                                         
                                                     1
                       96.04                       2
I O RMS    228.01         147.98  20.2 A
                         3           
RMS chopper current is given by
      I ch  d I O RMS   0.5  20.2  14.28 A
 Power Electronics by Prof. M. Madhusudhan Rao           81
                                                         81
   Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    Effective input resistance is
                        V
                   Ri 
                        IS
    I S = Average source current
                   I S  dI dc
                   I S  0.5  20  10 A
    Therefore effective input resistance is
                       V 200
                   Ri       20
                       IS 10
Power Electronics by Prof. M. Madhusudhan Rao   82
                                                82
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Classification Of Choppers
• Choppers are classified as
    –   Class A Chopper
    –   Class B Chopper
    –   Class C Chopper
    –   Class D Chopper
    –   Class E Chopper


Power Electronics by Prof. M. Madhusudhan Rao   83
                                                83
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    Class A Chopper
                                      i0                v0
                                                    +

               Chopper
                                              L
                                              O     v0 V
V                                             A
                         FWD                  D


                                                                 i0



    Power Electronics by Prof. M. Madhusudhan Rao            84
                                                             84
      Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• When chopper is ON, supply voltage V is
  connected across the load.
• When chopper is OFF, vO = 0 and the load
  current continues to flow in the same direction
  through the FWD.
• The average values of output voltage and
  current are always positive.
• Class A Chopper is a first quadrant chopper .
Power Electronics by Prof. M. Madhusudhan Rao   85
                                                85
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Class A Chopper is 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-L load can be used to
  study the performance of Class A Chopper.

Power Electronics by Prof. M. Madhusudhan Rao   86
                                                86
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
ig                                                Thyristor
                                                  gate pulse

                                                                  t
i0
                                                 Output current


      CH ON
                                                                  t
v0                  FWD Conducts
                                                Output voltage



                                                                  t
        tON
              T
Power Electronics by Prof. M. Madhusudhan Rao                     87
                                                                  87
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    Class B Chopper

                   D
                                        i0                        v0
                                                        +
                                                    R

V                                                   L v0

                       Chopper
                                                    E       i0
                                                        

    Power Electronics by Prof. M. Madhusudhan Rao                 88
                                                                  88
      Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• When chopper is ON, E drives a current
  through L and R in a direction opposite to that
  shown in figure.
• During the ON period of the chopper, the
  inductance L stores energy.
• When Chopper is OFF, diode D conducts, and
  part of the energy stored in inductor L is
  returned to the supply.
Power Electronics by Prof. M. Madhusudhan Rao   89
                                                89
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Average output voltage is positive.
• Average output current is negative.
• Therefore Class B Chopper operates in second
  quadrant.
• In this chopper, power flows from load to
  source.
• Class B Chopper is used for regenerative
  braking of dc motor.
• Class B Chopper is a step-up chopper.
Power Electronics by Prof. M. Madhusudhan Rao   90
                                                90
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   ig
                                                Thyristor
                                                gate pulse

                                                                        t
   i0    tOFF       tON

                T
                                                                        t
                                                Output current
 Imax
 Imin
           D
        conducts Chopper
                 conducts
  v0                                                   Output voltage



                                                                        t

Power Electronics by Prof. M. Madhusudhan Rao                           91
                                                                        91
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
  Expression for Output Current




Power Electronics by Prof. M. Madhusudhan Rao   92
                                                92
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
During the interval diode 'D' conducts
voltage equation is given by
             LdiO
        V          RiO  E
               dt
For the initial condition i.e.,
            iO  t   I min at t  0
The solution of the above equation is obtained
along similar lines as in step-down chopper
with R-L load
Power Electronics by Prof. M. Madhusudhan Rao    93
                                                 93
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
             V E                       R
                                         t                  R
                                                              t
 iO  t       1  e
                                         L
                                                 I min e
                                                              L
                                                                   0  t  tOFF
               R                              
At t  tOFF               iO   t   I max

                V E                 R
                                       tOFF
                                                               R
                                                               tOFF
   I max           1  e  I min e
                                       L                       L
                  R      
During the interval chopper is ON voltage
equation is given by
                LdiO
       0                   RiO  E
                  dt M. Madhusudhan Rao                                           94
Power Electronics by Prof.                                                        94
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Redefining the time origin, at t  0 iO  t   I max
The solution for the stated initial condition is
                       R
                       t    E                  R
                                                  
                                                 t
iO  t   I max e     L
                             1  e             L
                                                                 0  t  tON
                             R                   
At t  tON                               iO  t   I min
                           R
                           tON      E                R
                                                       tON   
 I min  I max e          L
                                     1  e           L
                                                              
                                     R                       
Power Electronics by Prof. M. Madhusudhan Rao                               95
                                                                            95
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    Class C Chopper

                 CH1                    D1
                                             i0             v0
                                                        +

V                                                   R

                 CH2                    D2          L v0

                           Chopper
                                                                      i0
                                                    E
                                                        
    Power Electronics by Prof. M. Madhusudhan Rao                96
                                                                 96
      Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Class C Chopper is a combination of Class A
  and Class B Choppers.
• For first quadrant operation, CH1 is ON or D2
  conducts.
• For second quadrant operation, CH2 is ON or
  D1 conducts.
• When CH1 is ON, the load current is positive.
• The output voltage is equal to ‘V’ & the load
  receives power from the source.
• When CH1 is turned OFF, energy stored in
  inductance L forces current to flow through the
  diode D2 and the output voltage is zero.
Power Electronics by Prof. M. Madhusudhan Rao   97
                                                97
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Current continues to flow in positive direction.
• When CH2 is triggered, the voltage E forces
  current to flow in opposite direction through L
  and CH2 .
• The output voltage is zero.
• On turning OFF CH2 , the energy stored in the
  inductance drives current through diode D1 and
  the supply
• Output voltage is V, the input current becomes
  negative and power flows from load to source.
Power Electronics by Prof. M. Madhusudhan Rao    98
                                                 98
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Average output voltage is positive
• Average output current can take both positive
  and negative values.
• Choppers CH1 & CH2 should not be turned
  ON simultaneously as it would result in short
  circuiting the supply.
• Class C Chopper can be used both for dc motor
  control and regenerative braking of dc motor.
• Class C Chopper can be used as a step-up or
  step-down chopper.
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 ig1
                                                     Gate pulse
                                                      of CH1

                                                                             t
 ig2                                                          Gate pulse
                                                               of CH2
                                                                             t
 i0
                                                            Output current

                                                                             t

       D1   CH1    D2    CH2    D1    CH1       D2    CH2
            ON           ON           ON              ON
 V0
                                                                  Output voltage


                                                                             t
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
    Class D Chopper
                                                           v0
                  CH1                                 D2

                                R i0      L      E
V
                            +           v0                      i0

                    D1                          CH2



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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Class D is a two quadrant chopper.
• When both CH1 and CH2 are triggered
  simultaneously, the output voltage vO = V and
  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, D1 and D2 , due to the energy
  stored in the inductor L.
• Output voltage vO = - V .
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• Average load voltage is positive if chopper
  ON time 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.


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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
ig1
                                                 Gate pulse
                                                  of CH1

                                                                  t
ig2                                             Gate pulse
                                                 of CH2
                                                                  t
 i0
                                                   Output current



                                                                  t
      CH1,CH2          D1,D2 Conducting
        ON
 v0
                                                 Output voltage
 V
                                                Average v0
                                                                  t


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ig1
                                                Gate pulse
                                                 of CH1

                                                                   t
ig2                                             Gate pulse
                                                 of CH2
                                                                   t
i0
                                                       Output current

      CH1
      CH2
                                                                   t
            D1, D2
v0                                              Output voltage
V

                                                                   t
                                                      Average v0

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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Class E Chopper

          CH1                    D1                  CH3     D3

                               i0     R         L    E
V
                             +                           
                                                v0
          CH2                    D2                  CH4     D4


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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Four Quadrant Operation
                                         v0
     CH2 - D4 Conducts                          CH1 - CH4 ON
      D1 - D4 Conducts                          CH4 - D2 Conducts

                                                            i0

        CH3 - CH2 ON                          D2 - D3 Conducts
     CH2 - D4 Conducts                        CH4 - D2 Conducts
Power Electronics by Prof. M. Madhusudhan Rao                       107
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• 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 CH4 are OFF, the energy
  stored in the inductor L drives iO through D2
  and D3 in the same direction, but output
  voltage vO = -V.
Power Electronics by Prof. M. Madhusudhan Rao   108
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Therefore the chopper operates in the
  fourth quadrant.
• When CH2 and CH3 are triggered, the load
  current iO flows in opposite direction & output
  voltage vO = -V.
• Since both iO and vO are negative, the chopper
  operates in third quadrant.
Power Electronics by Prof. M. Madhusudhan Rao   109
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• When both CH2 and CH3 are OFF, the load
  current iO continues to flow in the same
  direction D1 and D4 and the output voltage
  vO = V.
• Therefore the chopper operates in second
  quadrant as vO is positive but iO is negative.
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   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 the
  problem of source inductance.
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• 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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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
      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.
  Power Electronics by Prof. M. Madhusudhan Rao   113
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    Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                                                 i0
                                                          +
                        Chopper
                                                      L
                                                      O   v0
V                                          FWD        A
                                                      D


                                                          

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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                                tON 
Average output voltage, Vdc         V  dV
                                T 
                               Vdc dV
Average output current, I dc      
                                R      R
The thyristor is commutated at the instant t  tON
                                                  V
 output current at the instant of commutation is
                                                  R
since V is the output voltage at that instant.
 Power Electronics by Prof. M. Madhusudhan Rao   115
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   Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Free wheeling diode (FWD) will never
conduct in a resistive load.
 Average & RMS free wheeling diode
currents are zero.
                                            tON
                                 1
                                                v dt
                                                    2
               VO RMS                             0
                                 T              0

But             vO  V during tON
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
                                            tON
                                 1
                                               
                                                    2
                VO RMS                          V dt
                                 T              0

                                    tON 
                VO RMS        V      
                                           2

                                    T 
                VO RMS   dV
                      tON
Where duty cycle, d 
                       T
Power Electronics by Prof. M. Madhusudhan Rao            117
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
  RMS value of thyristor current
                 = RMS value of load current
                    VO RMS 
                
             R
            dV
        
            R
  Average value of thyristor current
                = Average value of load current
                      dV
                 
                       R
Power Electronics by Prof. M. Madhusudhan Rao     118
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Impulse
Commutated Chopper
• Impulse commutated choppers are widely used
  in high power circuits where load fluctuation is
  not large.
• This chopper is also known as
   – Parallel capacitor turn-off chopper
   – Voltage commutated chopper
   – Classical chopper.
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
           LS                       T1          iT1

 +                a    +                               IL             +
                  b _C              T2
                        iC                            FWD
                                                            L
                                                            O
VS                                                          A     vO
                                                            D

                             L           D1
 _                                                                _

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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• To start the circuit, capacitor ‘C’ is initially
  charged with polarity (with plate ‘a’ positive)
  by triggering the thyristor T2.
• Capacitor ‘C’ gets charged through VS, C, T2
  and load.
• As the charging current decays to zero thyristor
  T2 will be turned-off.
• With capacitor charged with plate ‘a’ positive
  the circuit is ready for operation.
• Assume that the load current remains constant
  during the commutation process.
Power Electronics by Prof. M. Madhusudhan Rao   121
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• For convenience the chopper operation is
  divided into five modes.
    – Mode-1
    – Mode-2
    – Mode-3
    – Mode-4
    – Mode-5

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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Mode-1 Operation
             LS                             T1

 +                          +                              IL
                  VC        _C                        iC
                                                                L
VS                                                              O
                                                                A
                                                                D
                                    L            D1
  _
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Thyristor T1 is fired at t = 0.
• The supply voltage comes across the load.
• Load current IL flows through T1 and load.
• At the same time capacitor discharges through
  T1, D1, L1, & ‘C’ and the capacitor reverses its
  voltage.
• This reverse voltage on capacitor is held
  constant by diode D1.
Power Electronics by Prof. M. Madhusudhan Rao    124
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
   Capacitor Discharge Current
                      C
         iC  t   V   sin  t
                      L
                         1
   Where            
                        LC
   & Capacitor Voltage
                                    VC  t   V cos  t
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
 Mode-2 Operation
                      IL
 +            LS             _                   IL
                  VC             C                    L
VS                           +              T2        O
                                                      A
                                                      D
 _

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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Thyristor T2 is now fired to commutate
  thyristor T1.
• When T2 is ON capacitor voltage reverse
  biases T1 and turns if off.
• The capacitor discharges through the load from
  –V to 0.
• Discharge time is known as circuit turn-off
  time.
Power Electronics by Prof. M. Madhusudhan Rao   127
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Circuit turn-off time is given by
                  VC  C
             tC 
                    IL
Where I L is load current.
t C depends on load current, it must be designed
for the worst case condition which occur at the
maximum value of load current and minimum
value of capacitor voltage.
 Power Electronics by Prof. M. Madhusudhan Rao    128
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   Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Capacitor recharges back to the supply voltage
  (with plate ‘a’ positive).
• This time is called the recharging time and is
  given by
                    VS  C
               td 
                       IL
• The total time required for the capacitor to
  discharge and recharge is called the
  commutation time and it is given by tr  tC  td
Power Electronics by Prof. M. Madhusudhan Rao   129
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• At the end of Mode-2 capacitor has recharged
  to VS and the free wheeling diode starts
  conducting.




Power Electronics by Prof. M. Madhusudhan Rao   130
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Mode-3 Operation

                        IL
   +            LS            +                       IL
                    VS        _C                T2          L
VS                                                          O
                                                            A
                                                     FWD    D
   _
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• FWD starts conducting and the load current
  decays.
• The energy stored in source inductance LS is
  transferred to capacitor.
• Hence capacitor charges to a voltage higher
  than supply voltage, T2 naturally turns off.


Power Electronics by Prof. M. Madhusudhan Rao    132
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
 The instantaneous capacitor voltage is
                                                LS
                 VC  t   VS  I L               sin  S t
                                                C
 Where
                                 1
                 S 
                                 LS C
Power Electronics by Prof. M. Madhusudhan Rao                  133
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Mode-4 Operation
              LS

  +                          +                        IL
                  VC         _C                            L
                                                D1         O
VS
                                                           A
                                     L                     D
  _                                                  FWD

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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Capacitor has been overcharged i.e. its voltage
  is above supply voltage.
• Capacitor starts discharging in reverse
  direction.
• Hence capacitor current becomes negative.
• The capacitor discharges through LS, VS, FWD,
  D1 and L.
• When this current reduces to zero D1 will stop
  conducting and the capacitor voltage will be
  same as the supply voltage
Power Electronics by Prof. M. Madhusudhan Rao   135
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Mode-5 Operation

              IL
                             L            • Both thyristors are off
        FWD                  O
                             A              and the load current
                             D              flows through the FWD.
                                          • This mode will end once
                                            thyristor T1 is fired.
Power Electronics by Prof. M. Madhusudhan Rao                   136
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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
 ic                        Capacitor Current
                             IL
 0                                                   t
 Ip
iT1
                Ip
 IL                        Current through T1
                                                 t
 0


 Power Electronics by Prof. M. Madhusudhan Rao           137
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   Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
  vT1
    Vc                                         Voltage across T1
                                                              t
     0
   vo
Vs+Vc
   Vs                                   Output Voltage
                                                              t
   vc

  Vc
                                                              t
              Capacitor Voltage
  -Vc
                                   tc
                                          td
  Power Electronics by Prof. M. Madhusudhan Rao                    138
                                                                   138
    Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
Disadvantages
• A starting circuit is required and the starting
  circuit should be such that it triggers thyristor
  T2 first.
• Load voltage jumps to almost twice the supply
  voltage when the commutation is initiated.
• The discharging and charging time of
  commutation capacitor are dependent on the
  load current and this limits high frequency
  operation, especially at low load current.
Power Electronics by Prof. M. Madhusudhan Rao    139
                                                 139
  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT
• Chopper cannot be tested without connecting
  load.
• Thyristor T1 has to carry load current as well
  as resonant current resulting in increasing its
  peak current rating.



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  Prof. T.K. Anantha Kumar, E&E Dept., MSRIT

								
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