ch7 lecture

7/30/2019 CH7 Lecture

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Full-wave And Three- PhaseRectifiers

(Converting AC to DC)4-1 Introduction The average current in AC source is zero

in the full-wave rectifier, thus avoiding problemsassociated with nonzero average source currents,particularly in transformers.

The output of the full-wave rectifier has inherentlyless ripple than the half-wave rectifier.

Uncontrolled and controlled single-phase and three-phase full-wave converters used as rectifiers areanalyzed.


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4-2 Single-phase full-wave rectifiers

Fig. 4-1 Bridge rectifier

The lower peak diode voltage make it more suitablefor high-voltage applications.


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Resistive load

0

sin , 0( )

sin , 2

Vm t t v t

Vm t t

0

1( ) sin( ) ( ) 2 m

o m

VV avg V t d t

2( )

( )o m

o

V VI avg

R R

mI2

rmsI

Power absorbed by the load resistor

2

R rmsP I R

power factorPf=1


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R-L load Fig

Fig. (a) Bridge rectifier with R-L load(b) Voltages and Current(c) Diode and source when the

inductance is large and thecurrent nearly constant


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Resistive load

0

56

6

11

5 22 2 65

6 2 2

6

6

sin , 56 6

( )

sin , 5 33 2

1 3 3( ) sin( ) ( ) 0.827 0.477

223

31 sin(2 )( ) sin ( ) ( )

2 4 23

0.707 1.

m

m

m

m

mo m m Lm

o

m

V t tv t

V t t

VV avg V t d t V V

V tV rms V t d t t

V

22 LmV

( ) 0.627( ) o mo

V avg V I avg

R R

mI

2rmsI

Power absorbed by the load resistor2

R rmsP I R power factorPf=1


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Voltages across the diodesVD1 and VD2


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Three-phase rectifiers

Resistive load :

Fig. Three phase full bridge rectifier


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Resistive load

0

3

0

11

22 2 3

3 2 2

0

0

sin , 03

( )2

sin , 3 3

1 3( ) sin( ) ( ) 0.955

3

31 sin(2 )( ) sin ( ) ( )

2 23

0.707 1.22

m

m

Lm

Lm

Lmo Lm Lm

L

o L

m Lm

V t tv t

V t t

VV avg V t d t V

V tV rms V t d t t

V V

( ) 0.627( ) o mo

V avg V I avg

R R

mI

2rmsI

Power absorbed by the load resistor2

R rmsP I R power factorPf=1


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A transition of the highest line-to-line voltage must take place

every

.

Because of the six transitions that occur for each periodof the source voltage, the circuit is called a six-pulse

rectifier.

Diode turn on in the sequence 1,2,3,4,5,6,1,..

00606/360

25

63

41

DDc

DDb

DDa

iii

iii

iii


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Each diode conducts one-third of the time, resulting in

avgoavgD II ,,3

1

rmsormsD II ,,3

1

rmsormsS II ,,3

2

Apparent power from the three-phase source is

rms,Srms,LL IVS 3


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...,,,n,)n(

VV

V.

V)wt(wtdsinV/V

)tnwcos(VVo)t(v

LL,m

n

LL,m

LL,m/

/LL,m

..,,n

n

181261

6

950

3

3

1

2

32

30

0

18126

0

Since the output voltage is periodic with period 1/6 of the acsupply voltage, the harmonics in the output are of order 6k,k=1,2,3,Adevantageoutput is inherently like a dc voltage, and the high-

frequency low-amplitude harmonics enable filters to be effective.


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For a dc load current (constant I0) --- Fig4.17


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Twelve-Pulse rectifier


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The purpose of the transformer connection is to introduce

phase shift between the source and bridge.

This results in inputs to two bridges which are

apart. The two bridge outputs are similar, but also shifted by

0

30

030

030

.

The delay angles for the bridge are typically the same.

, , ,

, ,

3 3 6m L L m L L m L Lo o Y o

V V VV V V

The peak output of the twelve-pulse converter occurs midway

between alternate peaks of the six-pulse converters. Adding the

voltages at that point gives

, , ,2 cos(15 ) 1.932o peak m L L m L LV V V


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Primary line voltages

Line voltages for secondary star Line voltages for secondary delta


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Voltages across the diode D1


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7 /12

( )

5 /12

1

27 /12

2 2

( )

5 /12

1sin . ( ) 0.988616

60.988616 1.932 1.91

1 sin . ( ) 0.988668

6

0.988616 1.932 1.9101

o Avg m m

mL L mL L

o rms m m

mL L mL L

V V t d t V

V V

V V t d t V

V V

Since a transition between conducting Diodes every ,

there are a total of 12 such transitions for each period of the

ac source. The output has harmonic frequencies which are multiple

of 12 times the source fre. (12k k=1,2,)

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ch7 lecture

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