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Example 2

A dc step down chopper has aninductive load of 1 ohm resistance and

10 mH inductance. Source voltage is 24

V. The chopper operates at a frequencyof 100 Hz with on-time of 5 ms.

Determine

(a) the average load current

(b) maximum and minimum load

currents.

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Solution

(a) Period 10010001 fT ms10 And duty cycle 105 Tton 5.0

Average output voltage245.0 So VV V12

Average load current

112 RVI oo A12

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Solution(b) During the on-period )exp(1)exp()( 1 LRt

R

VLtRIti So

At the end of the on-period

5.010)1105.0( LTRLtR and

)5.0exp(11

24)5.0exp(12 II

44.9607.0 12 II (b.1)During the off-period )exp()( 2 LtRItio

At the end of the off-period

5.010)1105.0()1( LTRLtR and

)5.0exp(21 II

21 607.0 II (b.2)

Substitute (b.2) into (b.1):

44.9)607.0(607.0 22 II which gives A95.142 I

95.14607.0607.0 21 II A07.9

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DC step-up chopper operation

The dc chopper can also be used to stepup a dc voltage.

The circuit of a step-up chopper is

given on the next slide.

To obtain an average value of the

output voltage greater than VS, acapacitor must be connected in parallel

with the load.

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DC step-up chopper circuit

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When the switch Sis turned on for

time ton

, the current rises linearly in

the inductor and energy is stored.

When the switch is turned off for

time toff, the inductor voltage

reverses and acts together with the

input voltage to forward bias thediode. It then transfers energy to

the capacitor.

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When the switch is turned on again,- the load current is maintained by the

capacitor,

- energy is stored in the inductor and

- the cycle starts again.

Assuming a continuous source current

the waveform for the current in the

inductor would be as shown on the next

slide.

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During the chopper on-period, the

voltage across the inductor is

From this

Over the on-time of ton, the source

current changes by

dt

diLVv ssL

tL

Vi ss

ons

s tL

VI

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During the off-periodAnd hence the average output voltage

This simplifies to

dt

diLVv

s

so

tiLVV sso

off

sso

t

ILVV

s

off

onso Vt

tVV

off

onso

t

tVV 1

T

TVV so )1(1

1

s

o

VV

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If the capacitor is sufficiently large,

the output voltage will be

continuous and vo will become the

average value Vo.

The above equation shows that the

load voltage can be stepped up by

varying the duty cycle .

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If losses are neglected and the capacitoris very large

Or the average source current

Therefore,

ooss IVIV

osos IVVI )(

the average source current )1( os II

the maximum source current )2(2 sss III

the minimum source current )2(1 sss III

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Example 4The step-up chopper is to deliver 3A into

a resistive load R of 10 ohms. The source

voltage is 12 V, L = 20H and the

chopper frequency is 50 kHz. Thecapacitor is very large. Determine

(a) the on-time of the chopper

(b) the average, minimum and maximum

source current.

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Solution(a)The average voltage 310 oo RIV V30

From equation (4.12),

30121 os VV 4.0

Therefore 6.0

(b)Period )105(101 46 fT s20 206.0

Tton

s12

12)2012()( onss tLVI A2.7

)6.01(3)1( os

II A5.7

6.3-5.7)2(1 ss III A9.3

6.35.7)2(2 ss III A1.11

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Transfer of powerfrom a lower voltagesource to a higher voltage source

The step-up chopper can be used to

transfer power from a lower voltage

source to a higher voltage source asshown on the next slide

The voltage E and inductance L couldbe representing a dc motor supplying

power to the dc supply during braking.

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For continuous source current, the

current waveform would be similar to

the waveform in Figure 4.5. repeated on

the next slide.

During the chopper on-period, thevoltage across the inductor is

This gives the source current as

dt

diLEvL

1)( ItL

Eti

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I1is the initial current for the on-period.During the off-period

For the system to be stable the current

should fall.Thus or

The source current during off-period isgiven by

dt

diLVE s

0dt

diLVE s

sVE

2)( ItL

VEti s

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Switch-Mode DC Power SuppliesSwitch-mode mode dc power supplies use

dc choppers to convert unregulated dc inputinto regulated dc output.

The regulation is achieved by pulse-widthmodulation and the switching device is

normally power BJT, MOSFET or IGBT.

At the output of the dc chopper is a smallfilter which is treated as an integral part of

the chopper.

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Switch-mode dc power supplies contdThe load is represented by an equivalent

resistance which is usually the case inswitch mode dc power supplies.

Two basic converter topologies, namelystep-down (buck) converter and step-up

(boost) converter are discussed.

Other topologies like buck-boost and Cukconverters are combinations of the two

basic topologies.

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Step-Down (Buck) DC-To-DC ConverterThis converter provides an average output

voltage lower than the dc input voltage.

Where the input voltage is ac, the converter

is very often used with an isolation

transformer. In such converters, the ac input

is first rectified and smoothed.

The smoothed dc is then chopped at a highfrequency to feed the isolation transformer

which is ferrite cored transformer, much

smaller than its 50 Hz counterpart.

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Step-down (Buck) dc-to-dc convertercontd

The figure on the next slide shows

the circuit of non-isolated converter

using a power BJT as switch.

It is like the step-down chopper in

Figure 4.2 and it operates in thesame manner as that step-down

chopper.

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Buck converter contdWaveforms in the converter are shown on

the next slide.

They are obtained under the assumption that

the capacitance is very large thus causing

the output voltage vo(t)to be equal to Vo

(the average output voltage).

This assumption is very reasonable becausein switch mode dc power supplies, the

percentage ripple in the output is usually

less than 1 %.

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Buck converter contdDepending on the switching frequency,

filter inductance and capacitance, the

inductance current may be continuous

or discontinuous,giving a mode ofoperation called

- the continuous conduction mode

(CCM) and

- discontinuous conduction mode

(DCM) respectively.

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Buck converter contd

It is not common to mix these twooperating modes because they

require different control algorithms.

We consider only the CCM.

When the transistor is turned on andoff, the voltage across the diode will

be as shown on the next slide.