A. K. Gautam

Choppers

Fixed DC Supply Variable DC Output

?By: Aniruddha Kr. Gautam

A. K. Gautam

• A chopper is a static device which is used to obtain a variable dc voltage from a constant dc voltage source.

• Also known as dc‐to‐dc converter.• It offers greater efficiency, faster response, lower

maintenance, smaller size and smooth control.• Widely used in trolley cars, battery operated

vehicles, traction motor control, control of large number of dc motors, etc…

• Also used in regenerative braking of dc motors to return energy back to supply and also as dc voltage regulators.

A. K. Gautam

METHODS OF CONTROL:

The output dc voltage can be verified by the following methods.• Constant Frequency Control or Pulse width modulation control• Variable Frequency Control

PULSE WIDTH MODULATION

In Pulse width modulation the pulse width ton of the output waveform is varied keeping chopping frequency ’f’ and hence chopping period ‘T’ constant. Therefore output voltage is varied by varying the ON time, ton . Figure shows the output voltage waveform for different ON times.

VARIABLE FREQUENCY CONTROL

In this method of control, chopping frequency f is varied keeping either ton or toff constant. This method is also known as frequency modulation.

In frequency modulation to obtain full output voltage, range of frequency has to be varied over a wide range. This method produces harmonics in the output and for large toff load current may be discontinuous.

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V 0

V

V

V 0

t

ttO N

tO N tO F F

tO F F

T

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v 0

V

V

v 0

t

t

tO N

tO N

T

T

tO F F

tO F F

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Basic DC to DC converters• Buck converter (Step-down converter)• Boost converter (Step-up converter)• Buck-Boost converter (Step-down/step-up converter)

and• Cuk converter

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Buck converter (Step-down converter)

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• Diode is reversed biased. Switch conducts inductor current

• This results in positive inductor voltage, i.e.: VL=Vd-VO

• It causes linear increase in the inductor current.

Circuit operation when switch is turned on (closed)

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Operation when switch turned off (opened)

• Because of inductive energy storage, iL continues to flow.

• Diode is forward biased.• Current now flows through

the diode and,

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Analysis for switch closed

• The inductor voltage

• Since the derivative if iL is a positive constant. Therefore iL must increase linearly.

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Analysis for switch opened

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Steady-state operation

• Steady state operation requires that iL

• Steady state operation requires that iL at the end of switching cycle is the same at the beginning of the next cycle. That is change of iL over one period is zero. i.e.

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Steady State Time Domain Analysis of Type-A Chopper

O utpu tvo ltage

O utpu tcurrent

v 0

V

i0

Im a x

Im in

t

t

tO N

T

tO F F

C ontinuouscurrent

O utpu tcurrent

t

D iscon tinuouscurrent

i0

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Expressions For Load Current iO For Continuous Current Operation When Chopper is ON (0 t tON)

V

i0

V 0

R

L

E

+

-

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Steady State Ripple

)26.2.........(....................

1

11

1

1

1

1

1

1

1

1

)(

minmax

a

aonaon

aa

aonaon

a

aon

a

aon

a

aon

TT

TTTTTS

TTTT

TTTT

TT

TTS

TT

TT

TT

TTS

e

ee

R

V

ee

ee

e

e

R

V

e

e

e

e

R

VII

The ripple current given by the equation is seen to be independent of load current emf E With Ton= αT and T-Ton = (1-α)T can be written as

a

a

T

a

TT

TTT

S

e

ee

R

VII

1

111

minmax

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Limit of Continuous Conduction

• In a chopper if Ton is reduced , Toff increases for a constant chopping period T.

• As Ton gets low and Toff goes high so current I may fall to zero.• As in step down chopper current cannot go reverse so for limit current can

go to only zero from Imin (Eqn. 2.20)• We can get value of α is obtain by equating the above equation.

)27.2.......(....................11ln

1

1

01

1

'

min

a

a

a

on

a

a

on

TT

aon

STT

TT

TT

TT

S

emT

T

T

T

mV

E

e

e

R

E

e

e

R

VI

A. K. Gautam

• So for Given Value of E, VS, T and Ta; if duty cycle is α’ then current goes at just continuous point.

• If actual duty cycle is less than α’ , load current will be discontinuous.

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CCM and DCM of Buck Converter

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Step Up (Boost)Chopper

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• A boost converter (step-up converter) is a DC-to-DC power converter with an output voltage greater than its input voltage.

• It is a class of switched-mode power supply (SMPS) containing at least two semiconductor switches (a diode and a transistor) and at least one energy storage element, a capacitor, inductor, or the two in combination. 

• Boost converter is also used as the voltage increase mechanism in the circuit known as the 'Joule thief'. 

• For a step-up chopper we can obtain an average output voltage V0 greater than input voltage.  

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• 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:

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• 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.

. ., O O

dIV V L i e V V

dt

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Operating Principle

• The key principle that drives the boost converter is the tendency of an inductor to resist changes in current.

Mode 1 (On State):

When the switch is closed, current flows through the inductor in clockwise direction and the inductor stores the energy. Polarity of the left side of the inductor is positive.

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Mode 2 (Off State)

When the switch is opened, current will be reduced as the impedance is higher. Therefore, change or reduction in current will be opposed by the inductor. Thus the polarity will be reversed (means left side of inductor will be negative now). As a result two sources will be in series causing a higher voltage to charge the capacitor through the diode D.

Here the switch is open and the only path offered to inductor current is through the flyback diode D, the capacitor C and the load R.

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Mode of conduction

Continuous Conduction mode:• When a boost converter operates in continuous mode, the current through

the inductor (IL) never falls to zero.

• During the On-state, the switch S is closed, which makes the input voltage (Vi) appear across the inductor.

• Change in current (IL) flowing through the inductor during a time period (t) by the formula:

• At the end of the On-state, the increase of IL is therefore:L

V

t

I iL

i

DT

iL VL

DTdtV

LI

on 0

1

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• D is the duty cycle. It represents the fraction of the commutation period T during which the switch is On.

• D ranges between 0 (S is never on) and 1 (S is always on).• During the Off-state, the switch S is open, so the inductor

current flows through the load. If we consider zero voltage drop in the diode, and a capacitor large enough for its voltage to remain constant, the evolution of IL is:

• Therefore, the variation of IL during the Off-period is:

dt

dILVV L

oi

L

TDVV

L

dtVVI oi

T

DT

oiLoff

1)()(

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• considering that the converter operates in steady-state conditions, so the amount of energy stored in each of its components has to be the same at the beginning and at the end of a commutation cycle. In particular, the energy stored in the inductor is given by:

• So, the inductor current has to be the same at the start and end of the commutation cycle. This means the overall change in the current (the sum of the changes) is zero:

2

2

1LLIE

0

1

0

L

TDVV

L

DTVII

II

oiiLl

Ll

offon

offon

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• Expression shows that the output voltage is always higher than the input voltage (as the duty cycle goes from 0 to 1), and that it increases with D,

o

i

i

o

V

VD

DV

V

1

1

1

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Discontinuous Conduction mode:

• If the ripple amplitude of the current is too high, the inductor may be completely discharged before the end of a whole commutation cycle. 

• Occurs under light loads. • Here the current through the inductor falls to zero

during part of the period.• As the inductor current at the beginning of the cycle

is zero, its maximum value: 

)( DTtatL

DTVI iLMax

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• During the off-period, IL falls to zero after :

• The load current Io is equal to the average diode current (ID). Also the diode current is equal to the inductor current during the off-state. Therefore the output current can be written as:

io

i

iL

VV

DVSo

L

TVVI

Max

,

0)( 0

o

i

i

o

io

i

io

iio

LDo

LI

TDV

V

VSo

VVL

TDV

VV

DV

L

DTVISo

III Maz

21,

22,

2

2

22

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(CCM) and (DCM) of boost

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Types of Choppers

• Type A Chopper or First–Quadrant Chopper• Type B Chopper or Second-Quadrant Chopper• Type-C chopper or Two-quadrant type-A

Chopper• Type-D Chopper or Two-Quadrant Type–B

Chopper• Type-E chopper or the Fourth-Quadrant

Chopper

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Type A Chopper or First–Quadrant Chopper

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• 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 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

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Type B Chopper or Second-Quadrant Chopper

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• 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 and average output current is negative.

• 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.

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Type-C chopper or Two-quadrant type-A Chopper

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• 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.

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• 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.

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Type-D Chopper or Two-Quadrant Type –B Chopper

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• 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.

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Type-E chopper or the Fourth-Quadrant Chopper

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• Class E is a four quadrant chopper• When CH1 and CH4 are triggered, output current

iO flows in positive direction through CH1 and CH4 , and with output voltage vO = V.

• This gives the first quadrant operation.• When both CH1 and 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.

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• 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 andD4 and the output voltage vO = V.

• Therefore the chopper operates in second quadrant as vO is positive but iO is negative.