DC Choppers N

1Prof. T.K. Anantha Kumar, E&E Dept., MSRIT

DC Choppers


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.


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.


Principle Of Step-down Chopper

V

i0

V 0

C hopper

R

+


• 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.


V d c

v 0

V

V /R

i0

Id c

t

t

tO N

T

tO F F


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 AI AttT t t

or chopping period.1 Freq. of chopper switching or chopping freq.fT


Average Output Voltage

.

duty cycle

ONdc

ON OFF

ONdc

ON

tV Vt t

tV V V dT

tbut dt


2

0

Average Output Current

RMS value of output voltage

1 ON

dcdc

ONdc

t

O o

VIR

tV VI dR T R

V v dtT

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

2

0

2

But during , Therefore RMS output voltage

1

.

.

ON

ON o

t

O

ONO ON

O

t v V

V V dtT

tVV t VT T

V d V


2

2

Output power

But

Output power

O O O

OO

OO

O

P V IV

IR

VPRdVP

R


Effective input resistance of chopper

The output voltage can be varied by varying the duty cycle.

idc

i

VRIRRd


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.


Pulse Width Modulation

• tON is varied keeping chopping frequency ‘f’ & chopping period ‘T’ constant.

• Output voltage is varied by varying the ON time tON


V 0

V

V

V 0

t

ttO N

tO N tO F F

tO F F

T


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


v 0

V

V

v 0

t

t

tO N

tO N

T

T

tO F F

tO F F


Step-down ChopperWith R-L Load

V

i0

V 0

C hopper

R

LFW D

E

+


• 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’.


• 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.


O utputvo ltage

O utputcurrent

v 0

V

i0

Im a x

Im in

t

t

tO N

T

tO F F

C ontinuouscurrent

O utputcurrent

t

D iscon tinuouscurrent

i0


Expressions For Load Current

iO For Continuous Current Operation When

Chopper Is ON (0 t tON)


V

i0

V 0

R

L

E

+

-


min

min

Taking Laplace Transform

. 0

At 0, initial current 0

OO

O O O

O

O

diV i R L Edt

V ERI S L S I S iS S

t i I

IV EI S RR SLS SLL


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 eR

t t

maxurrent is O ONi t I


When Chopper is OFFi0

R

L

E


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 Edt

ERI S L SI S iS

t

i I


max

max

Taking Inverse Laplace Transform

1

O

R Rt tL L

O

I EI S R RS LS SL L

Ei t I e eR


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


min

max

max

max min

min

From equation

1

At ,

To Find &

1

R Rt tL L

O

ON O

dRT dRTL L

V Ei t e I eR

t t dT i t I

V EI e I e

I I

R


max

min

From equation

1

At ,

1

R Rt tL L

O

OFF ON O

OFF

Ei t I e eR

t t T t i t I

t t d T


1 1

min max

min

max min

max

1

Substituting for in equation

1

we get,

1

1

d RT d RTL L

dRT dRTL L

dRTL

RTL

EI I e eR

I

V EI e I eR

V e EIR R

e


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 RTL L

dRTL

RTL

I

EI I e eR

V e EIR R

e

I I


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


min max

min

max minmin

Assuming load current varies linearlyfrom to instantaneous load current is given by

. 0O ON

O

I I

I ti I for t t dT

dTI Ii I t

dT


20

0

2

max minmin

0

2min max min2 2max min

min0

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 II I t dtdT dT dT


12 2

max min2min min max min

20

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


12 2

max min2min min max min3

Effective input resistance is

CH

CH O RMS

iS

I II d I I I I

I d I

VRI


Where Average source currentS

S dc

idc

I

I dI

VRdI


Principle Of Step-up Chopper

+

V OV

C hopper

CLOAD

DLI

+


• 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.


• 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

. ., O OdIV V L i e V Vdt


• 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.


Expression For Output VoltageAssume 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 tt ON


(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


Where T = Chopping period or period

of switching.

ON O OFF

ON OFFO

OFF

OON

VIt V V It

V t tV

t

TV VT t


1

1

11

Where duty cyle

ON OFF

OON

O

ON

T t t

V V tT

V Vd

tdT


For variation of duty cycle ' ' in the range of 0 1 the output voltage will vary in the range

O

O

dd V

V V


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.


Classification Of Choppers

• Choppers are classified as – Class A Chopper– Class B Chopper– Class C Chopper– Class D Chopper– Class E Chopper


Class A Chopper

V

C hopper

FW D

+

v 0

v 0

i0

i0

LOAD

V


• 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 .


• 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.


O utput curren t

Thyristo rgate pu lse

O utpu t vo ltage

ig

i0

v0

t

t

ttO N

T

C H O N

FW D C onduc ts


Class B Chopper

V

C hopper

+

v 0

v 0

i0

i0

L

E

R

D


• 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.


• 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.


O utpu t curren t

D con d u cts C h o pp e r

con d u cts

Thyristo rgate pu lse

O utpu t vo ltage

ig

i0

v 0

t

t

t

Im in

Im ax

T

tO NtO F F


Expression for Output Current


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 Edt

i t I t

tep-down chopper with R-L load


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 tL L

O OFF

OFF O

R Rt tL L

OO

V Ei t e I e t tR

t t i t I

V EI e I eR

Ldi Ri Edt


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 tL L

O ON

ON O

R Rt tL L

t i t I

Ei t I e e t tR

t t i t I

EI I e eR


Class C Chopper

V

C hopper

+

v0

D 1

D 2C H 2

C H 1

v 0i0

i0

L

E

R


• 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.


• 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.


• 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.


G ate pu lseof C H 2


O utput curren t

O utpu t vo ltage

ig 1

ig 2

i0

V 0

t

t

t

t

D 1 D 1D 2 D 2C H 1 C H 2 C H 1 C H 2O N O N O N O N


Class D Chopper

V+ v 0

D 2

D 1 C H 2

C H 1

v 0

i0

L ER i0


• 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 .


• 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.




O utpu t curren t

O utput vo ltage

Average v 0

ig 1

ig 2

i0

v 0

V

t

t

t

t

C H ,C HO N1 2 D 1,D 2 Conducting


G ate pu lseo f C H 2

G ate pulseof C H 1

O utpu t curren t

O utpu t vo ltage

Average v0

ig 1

ig 2

i0

v 0

V

t

t

t

t

C HC H

1

2

D , D1 2


Class E Chopper

V

v 0

i0L ER

C H 2 C H 4D 2 D 4

D 1 D 3C H 1 C H 3

+


Four Quadrant Operationv 0

i0

C H - C H O NC H - D C onduc ts

1 4

4 2

D D2 3 - ConductsC H - D C onduc ts4 2

C H - C H O NC H - D C onduc ts

3 2

2 4

C H - D C onduc tsD - D C onducts

2 4

1 4


• 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.


• 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.


• 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.


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.


• 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.


V

i0

v 0

C hopper

FW D

+

LOAD


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

dcdc

ON

tV V dVT

V dVIR R

t tVR

oltage at that instant.


20

0

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 dtT

v V t


2

0

2

1

Where duty cycle,

ONt

O RMS

ONO RMS

O RMS

ON

V V dtT

tV VT

V dV

tdT


RMS value of thyristor current = RMS value of load current

Average value of thyristor current= Average value of load current

O RMSV

RdVR

dVR

DC Choppers N

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