SRM UNIVERSITY
LECTURE NOTES ON
PE2001-ANALYSIS OF POWER CONVERTER
Prepared by
Mr. R. Sridhar, AP/EEE
Ms. A. Geetha, AP/EEE
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RECTIFIER CIRCUIT
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INTRODUCTION
 IN THYRISTOR BASED RECTIFIERS, OUTPUT VOLTAGE CAN BE CONTROLLED. SO THEY ARE
TERMED AS CONTROLLED RECTIFIERS.
 CONTROLLED RECTIFIERS PRODUCE VARIABLE DC OUTPUT, WHOSE MAGNITUDE IS VARIED BY
PHASE CONTROL.
PHASE CONTROL
DC OUTPUT FROM RECTIFIER IS CONTROLLED BY CONTROLLING DURATION OF THE
CONDUCTION PERIOD BY VARYING THE POINT AT WHICH GATE SIGNAL IS APPLIED TO SCR.
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CONTROLLED RECTIFIERS ARE OF TWO TYPES,
1- FULLY CONTROLLED RECTIFIERS
DC CURRENT IS UNIDIRECTIONAL, BUT DC VOLTAGE HAS EITHER POLARITY. WITH ONE
POLARITY, FLOW OF POWER IS FROM AC SOURCE TO DC LOAD---RECTIFICATION.
WITH THE REVERSAL OF DC VOLTAGE BY THE LOAD, FLOW OF POWER IS FROM DC LOAD
TO AC SOURCE---INVERSION.
2- HALF CONTROLLED RECTIFIERS
HALF OF SCRS ARE REPLACED BY DIODES.
DC OUTPUT CURRENT AND VOLTAGE ARE UNIDIRECTIONAL. I.E., FLOW OF POWER IS FROM
AC SOURCE TO DC LOAD.
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Half-Wave Rectifier with R-L Load
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Half-Wave Rectifier with R-L Load (freewheeling diode)
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Full controlled Rectifier with R-L Load (freewheeling diode)
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Full controlled Rectifier with R-L Load
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Full controlled Rectifier with R-L Load with freewheeling diode(Bridge type)
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Full controlled Rectifier with RLE Load(Bridge type)
Continuous current mode
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Discontinuous current mode
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Full controlled Rectifier with RLE Load(Bridge type)
Inversion mode of operation
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• IN FULLY-CONTROLLED RECTIFIER, ONLY RECTIFICATION CAN BE OBTAINED BY
CONNECTING A FREEWHEELING DIODE ACROSS THE OUTPUT TERMINALS OF THE
RECTIFIER.
• ANOTHER METHOD OF OBTAINING RECTIFICATION IN BRIDGE RECTIFIERS IS
REPLACING HALF OF THE SCRS WITH DIODES. THESE CIRCUITS ARE CALLED
SEMICONTROLLED BRIDGE RECTIFIERS.
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Semi controlled Rectifier with R-L Load
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Semi controlled Rectifier with R-L Load with freewheeling diode
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Semi controlled Rectifier with RLE Load (Continuous current mode)
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Semi controlled Rectifier with RLE Load (Discontinuous current mode)
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WHY DUAL CONVERTER……?
• SEMI-CONVERTER ARE SINGLE QUADRANT CONVERTER (I.E) OVER ENTIRE FIRING ANGLE RANGE,
LOAD VOLTAGE & CURRENT IS SAME POLARITY
• SEMI-CONVERTER OPERATES ONLY IN RECTIFICATION MODE
• FULL-CONVERTER ARE TWO QUADRANT CONVERTER
• HERE THE CURRENT DIRECTION CANNOT REVERSED DUE TO UNIDIRECTIONAL PROPERTY OF SCR.
BUT VOLTAGE CAN BE REVERSED
• Α = 0 TO 90 -(VTG & CT IS + VE)-RECTIFIER
• Α = 90 TO 180 -(VTG IS -VE & CT IS +VE)-INVERTER
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WHAT …..?
• IN ORDER TO HAVE FOUR QUADRANT OPERATION WITHOUT ANY MECH CHANGEOVER
SWITCH WE GO FOR DUAL CONVERTER
• TWO CONVERTERS ARE CONNECTED BACK TO BACK TO THE LOAD CIRCUIT(IE)TWO
CONVERTERS IN ANTI-PARALLEL & CONNECTED TO SAME DC LOAD
• BY THIS ARRANGEMENT WE CAN REVERSE BOTH VTG & CT
• THUS FOUR QUADRANT OPERATION IS OBTAINED
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SINGLE PHASE DUAL CONVERTER
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GATING SEQUENCE
The average dc output voltage of converter 1 is
2Vm
Vdc1 
cos 1

The average dc output voltage of converter 2 is
2Vm
Vdc 2 
cos  2

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GATING SEQUENCE
In the dual converter operation one
converter is operated as a controlled rectifier
with  90 & the second converter is
operated as a line commutated inverter
0
in the inversion mode with   90

Vdc1  Vdc 2
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GATING SEQUENCE
2Vm


cos 1 
2Vm

cos  2 
2Vm
cos 1   cos  2

  cos  2 
or
cos  2   cos 1  cos   1 

 2    1  or
1   2   
radians
Which gives
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 2    1 
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OUTPUT WAVEFORM
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PRACTICAL DUAL CONVERTER
• THOUGH THEIR AVG OUTPUT VTG ARE EQUAL ,YET THEIR INST.VTG ARE OUT OF PHASE. THIS
RESULT IN VTG DIFFERENCE
• SO LARGE CIRCULATING CT FLOW BETWEEN TWO CONVERTERS BUT NOT THROUGH THE
LOAD
• CIRCULATING CT CAN BE LIMITED BY INSERTING A REACTOR BETWEEN THE TWO CONVERTERS
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EXP FOR INST.CIRCULATING CURRENT
• VO1 = INSTANTANEOUS OUTPUT VTG OF CONVERTER 1
• VO2 = INSTANTANEOUS OUTPUT VTG OF CONVERTER 2
• THE CIRCULATING CURRENT IR CAN BE DETERMINED BY INTEGRATING THE INSTANTANEOUS
VOLTAGE DIFFERENCE (WHICH IS THE VOLTAGE DROP ACROSS THE CIRCULATING CURRENT
REACTOR LR), STARTING FROM T = (2 - 1).
• IDEAL CONDTION
AS THE TWO
AVERAGE OUTPUT VOLTAGES DURING THE INTERVAL T = (+1) TO (2 - 1) ARE EQUAL AND
OPPOSITE THEIR CONTRIBUTION TO THE INSTANTANEOUS CIRCULATING CURRENT IR IS ZERO
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EXP FOR INST.CIRCULATING CURRENT
 t

  vr .d  t   ; vr   vO1  vO 2 
 2 1 

As the o/p voltage vO 2 is negative
1
ir 
 Lr
vr   vO1  vO 2 

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t


1
ir 
   vO1  vO 2  .d  t   ;
 Lr  2 1 

vO1  Vm sin  t for  2  1  to  t
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EXP FOR INST.CIRCULATING CURRENT
t
t


Vm
ir 
   sin  t.d  t    sin  t.d  t  
 Lr  2 1 

 2 1 
2Vm
ir 
 cos t  cos 1 
 Lr
The instantaneous value of the circulating current
depends on the delay angle.
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EXP FOR INST.CIRCULATING CURRENT
For trigger angle (delay angle) 1  0,
the magnitude of circulating current becomes min.
when  t  n , n  0, 2, 4,.... & magnitude becomes
max. when  t  n , n  1, 3, 5,....
If the peak load current is I p , one of the
converters that controls the power flow
may carry a peak current of

4Vm 
 Ip 
,
 Lr 

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EXP FOR INST.CIRCULATING CURRENT
where
I p  I L max 
Vm
 ,
RL
&
ir  max 
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4Vm

 max. circulating current
 Lr
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MODES OF OPERATION
•DUAL CONVERTER WITHOUT CIRCULATING
CURRENT
•DUAL CONVERTER WITH CIRCULATING
CURRENT
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DUAL CONVERTER WITHOUT CIRCULATING
CURRENT
• IN THIS MODE ONLY ONE CONVERTER IS OPERATED AT A TIME & NO NEED OF REACTOR
• WHEN CONVERTER 1 IS ON, 0 < 1 < 900
• VDC IS POSITIVE AND IDC IS POSITIVE
• ALLOW 10 TO 20MS TO LOAD CT TO REACH ZERO
• WHEN CONVERTER 2 IS ON, 0 < 2 < 900
• VDC IS NEGATIVE AND IDC IS NEGATIVE
• LOAD CT MAY DISCONTINUOUS OR CONTINUOUS BUT SATISFACTORY OPERATION IS DONE
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DUAL CONVERTER WITH CIRCULATING CURRENT
• IN THIS MODE, BOTH THE CONVERTERS ARE SWITCHED ON AND OPERATED AT THE SAME TIME &
REACTOR IS INSERTED
• THE TRIGGER ANGLES 1 AND 2 ARE ADJUSTED SUCH THAT (1 + 2) = 1800 (IE) 2 = (1800 - 1)
• WHEN 0 <1 <900, CONVERTER 1 OPERATES AS A CONTROLLED RECTIFIER AND CONVERTER 2
OPERATES AS AN INVERTER WITH 900 <2<1800
• IN THIS CASE VDC AND IDC, BOTH ARE POSITIVE
• WHEN 900 <1 <1800, CONVERTER 1 OPERATES AS AN INVERTER AND CONVERTER 2 OPERATED
AS A CONTROLLED RECTIFIER BY ADJUSTING ITS TRIGGER ANGLE 2 SUCH THAT 0 <2<900
• IN THIS CASE VDC AND IDC, BOTH ARE NEGATIVE
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FOUR QUADRANT OPERATION
Conv. 2
Inverting
2 > 900
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Conv. 2
Rectifying
2 < 900
Conv. 1
Rectifying
1 < 900
Conv. 1
Inverting
1 > 900
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MERITS OF DUAL CONVERTER WITH CIRCULATING CT
• THE CIRCULATING CURRENT MAINTAINS CONTINUOUS CONDUCTION OF BOTH THE
CONVERTERS OVER THE COMPLETE CONTROL RANGE, INDEPENDENT OF THE LOAD
• ONE CONVERTER ALWAYS OPERATES AS A RECTIFIER AND THE OTHER CONVERTER OPERATES
AS AN INVERTER, THE POWER FLOW IN EITHER DIRECTION AT ANY TIME IS POSSIBLE
• AS BOTH THE CONVERTERS ARE IN CONTINUOUS CONDUCTION WE OBTAIN FASTER DYNAMIC
RESPONSE. I.E., THE TIME RESPONSE FOR CHANGING FROM ONE QUADRANT OPERATION TO
ANOTHER IS FASTER
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DEMERITS OF DUAL CONVERTER WITH
CIRCULATING CT
• DUE TO REACTOR, SIZE & COST IS HIGH
• CIRCULATING CT GIVES RISE TO MORE LOSSES IN CONVERTER. SO THE EFFICIENCY & POWER
FACTOR IS LOW
• THE CONVERTER THYRISTORS SHOULD BE RATED TO CARRY A PEAK CURRENT MUCH GREATER
THAN THE PEAK LOAD CURRENT
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Effect of source Inductance in single phase rectifier
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Effect of source Inductance in single phase rectifier
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3-phase full controlled rectifier(RL)
• THE LINE-TO-NEUTRAL VOLTAGES ARE:
van  Vm sin  t
vbn
vcn
2
 Vm sin ( t 
)
3
2
 Vm sin ( t 
)
3
• THEN THE LINE-TO-LINE VOLTAGES ARE:

vab  van  vbn  3 Vm sin ( t  )
6

vbc  vbn  vcn  3 Vm sin ( t  )
2
5
vSRM
 vcn  van  3 Vm sin ( t  )
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6
3-phase full controlled rectifier(RL)
• THE AVERAGE OUTPUT VOLTAGE IS FOUND FROM :
Vdc 
3
 / 2 
 
/ 6 
vab d ( t ) 
3 3 Vm

cos
• THE RMS VALUE OF THE OUTPUT VOLTAGE IS :
Vrms
3


Vrms 
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 / 2 

/ 6 

v d ( t )

1/ 2
2
ab
1 3 3
3 Vm ( 
cos 2 )1/ 2
2
4
3-phase full controlled rectifier(RLE)
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3-phase full controlled rectifier(RLE)
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Rectification mode
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Inversion mode
Analysis for Rectification mode
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Analysis for Rectification mode
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Effect of source Inductance in three phase rectifier
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Effect of source Inductance in three phase rectifier
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3 phase Dual Converter
Due to instantaneous voltage differences between the output
voltages of converters, a circulating current flows through the
converters.
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This circulating
current is limited by a reactor.
12 PULSE CONVERTER
a) SERIES CONNECTION
b) PARALLEL CONNECTION
c)
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TRANSFORMER CONNECTION
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12 PULSE CONVERTER
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DC-DC CONVERTERS (CHOPPERS)
• THE OBJECTIVE IS TO CONVERT A FIXED DC VOLTAGE TO A VARIABLE
DC VOLTAGE
• IT IS POSSIBLE TO STEP UP AND STEP DOWN VOLTAGE.
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VOLTAGE STEP DOWN (BUCK CONVERTER)
First, suppose L=0, E=0.
The diode is not needed.
Va=(ton/T)Vs
k=ton/T is the duty cycle
VRMS=k1/2Vs
2
Pout=(kVs )/R
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VOLTAGE STEP UP (BOOST) CONVERTER
“On” mode:
VL=L(di/dt)
“Off” mode: Assume current
decreases at a constant rate. Then
Vo=Vs+VL
To ensure continuous current flow, a
capacitor is included.
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AVERAGE VALUE OF THE OUTPUT VOLTAGE
t1
1
Va   vO dt
T 0
t1
1
Va   VS dt
T 0
t1
Va  VS  ft1VS
T
Va  kVS
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Performance of a step up converter with resistive load
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DC-DC CONVERTER CLASSIFICATION
• FIRST QUADRANT CONVERTER
• SECOND QUADRANT
CONVERTER
• 1ST AND 2ND QUADRANT
CONVERTER
• 3RD AND 4TH QUADRANT
CONVERTER
• FOUR QUADRANT CONVERTER
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FIRST QUADRANT CHOPPER
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SECOND QUADRANT CHOPPER
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THIRD QUADRANT CHOPPER
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FOURTH QUADRANT CHOPPER
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1-2 AND 3-4 QUADRANT CONVERTERS
1st quad: S1, D4
2nd quad: S4, D1
3rd quad: S3, D2
4th quad: S2, D3
Polarity of the load EMF is reversed.
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FOUR QUADRANT CONVERTER
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FOUR QUADRANT CONVERTER
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FOUR QUADRANT CONVERTER
LOAD VOLTAGE EXPRESSIONS ARE
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Step-Down/Up (Buck-Boost) Converter
• The output voltage can be higher or lower than the input voltage
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Buck-Boost Converter: Waveforms
• Continuous conduction mode
Switch closed:
di L
VCC

dt
L
Switch open:
di L
vo

dt
L
Inductor Volt-second balance:
VCC DT
V (1  D )T
 o
0
L
L
 DVCC 
Vo  

1

D


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Buck-Boost: Limits of Cont./Discont. Conduction
• The output voltage is held constant
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Buck-Boost: Discontinuous Conduction
• This occurs at light loads
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Cuk DC-DC Converter
• The output voltage can be higher or lower than the input voltage
• Capacitor C1 stores and transfers energy from input to output
• When switch is ON, C1 discharges through the switch and transfers energy to the
output
• When switch is OFF, capacitor C1 is charged through the diode by energy from the
input and L1
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Cuk DC-DC Converter: Waveforms
• The capacitor voltage is
assumed constant (very large)
• Note phase inversion at the
output
Vo
 D 
 

Vd
1 D 
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SEPIC Converter
• Single-ended primary inductance converter (SEPIC)
• Can buck or boost the voltage
• Note that output is similar to buck-boost, but without a phase
inversion
• This circuit is useful for lithium battery powered equipment
Vo
 D 


Vd
1

D


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SEPIC Converter
Circuits for 2 different switching states
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ZETA CONVERTER
A Zeta converter performs a non-inverting buck-boost function similar to that of a SEPIC, which is an
acronym for Single-Ended Primary Inductance Converter. The Zeta topology is also similar to the SEPIC,
in that it uses two inductors, two switches and a capacitor to isolate the output from the input.
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ZETA CONVERTER
When analyzing Zeta waveforms it is helpful to keep in mind that at equilibrium, L1average current equals IIN and L2
average current equals IOUT, since there is no DC current through the flying cap CFLY. Also there is no DC voltage across
either inductor. Therefore, CFLY sees ground potential at its left side and VOUT at its right side, resulting in DC voltage
across CFLY being equal to VOUT.
When M1 is on, L1 and L2 are energized. D1 sees a potential of VIN+VOUT across it (see figures 3, 4, and 5). When M1
is off, energy stored in L1 and L2 is released. D1 is forward biased.
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ZETA CONVERTER
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ZETA CONVERTER
Output voltage is given by the following equation:
Where D is duty cycle. VOUT is plotted as a function of D in figure 6. As
can be seen, for D less than 0.5 the converter performs buck function and
for D larger than 0.5 it is a boost topology.
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RESONANT CONVERTER
 INTRODUCTION
 CLASSIFICATION
 CONCLUSION
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INTRODUCTION
 RESONANT
INVERTERS
ARE
ELECTRICAL
INVERTER
BASED
ON RESONANT CURRENT OSCILLATION. IT IS KNOWN AS DC TO DC CONVERTER OR DC
TO AC PWM INVERTER.
 MAIN FUNCTION IS TO REDUCE SWITCHING LOSSES OF THE DEVICES(MOSFET&IGBT).
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CLASSIFICATION
 THE RESONANT CONVERTER BROADLY CLASSIFIED INTO EIGHT TYPES. THOSE ARE:-
1.
SERIES RESONANT INVERTER
2.
PARALLEL RESONANT INVERTER
3.
CLASS E RESONANT CONVERTER
4.
CLASS E RESONANT RECTIFIER
5.
ZERO VOLTAGE SWITCHING(ZVS) RESONANT CONVERTER
6.
ZERO CURRENT SWITCHING(ZCS) RESONANT CONVERTER
7.
TWO QUADRANT ZVS RESONANT CONVERTER
8.
RESONANT DC-LINK INVERTER
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SERIES RESONANT INVERTER
 IT IS BASED ON RESONANT CURRENT OSCILLATION.
 SWITCHING DEVICE ARE PLACED IN SERIES WITH LOAD.
 THYRISTOR ARE WORK IN SWITCHING DEVICE.
 THIS TYPE OF INVERTER PRODUCES AN APPROXIMATELY SINUSOIDAL WAVE FORM AT
A HIGH FREQUENCY ,RANGING FROM 200HZ TO 100KHZ.
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CIRCUIT DIG. OF SERIES RESONANT CONVERTER
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Equivalent circuit dig.
Waveform
PARALLEL RESONANT INVERTER
 PARALLEL RESONANT INVERTER IS DUAL OF SERIES RESONANT INVERTER
 CURRENT IS CONTINUOUSLY CONTROLLED , THAT GIVES BETTER SHORT CIRCUIT
PROTECTION UNDER FAULT CONDITION
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CLASS E RESONANT CONVERTER
 IT HAS LOW SWITCHING LOSSES , YIELDING A HIGH EFFICIENCY OF MORE THAN 95%.
 USED IN LOW POWER APPLICATION & HIGH FREQUENCY ELECTRIC LAMP.
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CIRCUIT DIG. OF CLASS E RESONANT INVERTER & WAVE FORM
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CLASS E RESONANT RECTIFIER
 CLASS E RESONANT RECTIFIER IS BASED ON THE PRINCIPLE OF ZERO VOLTAGE
SWITCHING(ZVS) .
 THE DIODE TURN OFF AT ZERO VOLTAGE.
 A HIGH FREQUENCY DIODE RECTIFIER SUFFERS FROM DISADVANTAGE THAT IS
SWITCHING LOSSES , HARMONIC CONTENT.
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ZERO VOLTAGE SWITCHING(ZVS)
RESONANT CONVERTER
 THE ZVS RESONANT CONVERTER TURN ON & TURN OFF AT ZERO VOLTAGE.
 OUTPUT VOLTAGE CONTROL CAN BE ACHIEVED BY VARYING THE FREQUENCY &
OPERATES WITH CONSTANT OFF TIME CONTROL .
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ZERO CURRENT SWITCHING(ZCS)
RESONANT CONVERTER
 ZERO CURRENT SWITCHING(ZCS) RESONANT CONVERTER TURN ON & TURN OFF AT
ZERO CURRENT.
 THIS CONVERTER CAN OPERATE AT HIGHER RANGE FREQUENCY THAT IS 1MHZ TO
2MHZ.
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TWO QUADRANT ZVS RESONANT
CONVERTER
 IN THIS CONVERTER THE ZVS CONCEPT IS EXTENDED
 HERE FO > FS
 𝐹𝑜 =
1
2Π 𝐿𝐶
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RESONANT DC-LINK INVERTER
 THE DC LINK INVERTER IS SIMILAR TO THE PWM INVERTER .
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CONCLUSION
 IT IS USED FOR HIGH FREQUENCY APPLICATION.
 ZCS&ZVS BECOMES POPULAR AND THEY CAN TURN ON &TURN OFF AT ZERO
VOLTAGE&CURRENT AND ALSO ELIMINATE SWITCHING LOSSES.
 IN DC-LINK INVERTERS , A RESONANT CIRCUIT IS CONNECTED BETWEEN THE
INVERTER & DC SUPPLY.
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UNIT 4
AC VOLTAGE CONTROLLERS
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INTRODUCTION
• THE POWER FLOW INTO A LOAD CAN BE CONTROLLED BY VARYING THE RMS VALUE OF THE LOAD
VOLTAGE.
• THIS CAN BE ACCOMPLISHED BY THYRISTORS, AND THIS TYPE OF POWER CIRCUIT IS KNOWN AS AC
VOLTAGE CONTROLLERS.
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• THE MOST APPLICATION OF AC VOLTAGE CONTROLLERS ARE:
• INDUSTRIAL HEATING
• ON-LOAD TRANSFORMER TAP CHANGING
• LIGHT CONTROLS
• SPEED CONTROL OF INDUCTION MOTORS
• AC MAGNET CONTROLS
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• FOR POWER TRANSFER, TWO TYPES OF CONTROL ARE NORMALLY USED:
• ON-OFF CONTROL
• PHASE ANGLE CONTROL
• IN ON-OFF CONTROL, THYRISTOR SWITCHES CONNECT THE LOAD TO THE AC SOURCE FOR A FEW
CYCLES OF THE INPUT VOLTAGE AND THEN DISCONNECTED FOR A FEW CYCLES.
• IN PHASE CONTROL, THYRISTOR SWITCHES CONNECT THE LOAD TO THE AC SOURCE FOR A
PORTION OF EACH CYCLE.
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• THE AC VOLTAGE CONTROLLERS CAN BE CLASSIFIED INTO TWO TYPES:
• SINGLE-PHASE CONTROLLERS
• THREE-PHASE CONTROLLERS
• EACH TYPE CAN BE SUBDIVIDED INTO:
• UNIDIRECTIONAL OR HALF-WAVE CONTROL
• BIDIRECTIONAL OR FULL-WAVE CONTROL
• SINCE THE INPUT VOLTAGE IS AC, THYRISTORS ARE LINE COMMUTATED.
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PRINCIPLE OF ON-OFF CONTROL
• THE PRINCIPLE OF ON-OFF CONTROL CAN BE EXPLAINED WITH THE FOLLOWING SINGLE-PHASE
FULL-WAVE CONTROLLER.
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• THIS TYPE OF CONTROL IS APPLIED IN APPLICATIONS WHICH HAVE HIGH MECHANICAL INERTIA AND
HIGH THERMAL TIME CONSTANT.
• TYPICAL EXAMPLES ARE INDUSTRIAL HEATING AND SPEED CONTROL OF MOTORS.
• IF THE INPUT VOLTAGE IS CONNECTED TO LOAD FOR N CYCLES AND IS DISCONNECTED FOR M
CYCLES, THE OUTPUT LOAD VOLTAGE IS FOUND FROM:
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Vo  rms

n

 2 ( n  m)
Vo  rms  Vs

2
0
n
 Vs
mn

2 V sin  t d ( t ) 

2
s
1/ 2
2
k
• NOTE THAT K IS CALLED THE DUTY CYCLE, AND THE POWER FACTOR AND OUTPUT VOLTAGE VARY
WITH THE SQUARE ROOT OF K.
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PRINCIPLE OF PHASE CONTROL
• THE PRINCIPLE OF PHASE CONTROL CAN BE EXPLAINED WITH THE FOLLOWING CIRCUIT.
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• DUE TO THE PRESENCE OF DIODE D1, THE CONTROL RANGE IS LIMITED.
• THE RMS OUTPUT VOLTAGE CAN ONLY BE VARIED BETWEEN 70.7 TO 100%.
• THE OUTPUT VOLTAGE AND INPUT CURRENT ARE ASYMMETRICAL AND CONTAIN A DC COMPONENT.
• THIS CIRCUIT IS A SINGLE-PHASE HALF-WAVE CONTROLLER AND IS SUITABLE ONLY FOR LOW
POWER RESISTIVE LOADS, SUCH AS HEATING AND LIGHTING.
• SINCE THE POWER FLOW IS CONTROLLED DURING THE POSITIVE HALF-CYCLE OF INPUT VOLTAGE,
THIS TYPE OF CONTROLLER IS ALSO KNOWN AS UNIDIRECTIONAL CONTROLLER.
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• THE RMS VALUE OF THE OUTPUT VOLTAGE IS FOUND FROM:

2
1
2
2
Vo  {
[  2 Vs sin  t d ( t )  
2 Vs2 sin 2  t d ( t )]}1/ 2

2 
1
sin 2 1/ 2
Vo  Vs [
( 2   
)]
2
2
• THE AVERAGE VALUE OF THE OUTPUT VOLTAGE IS:

2
1
Vdc 
[
2 Vs sin  t d ( t )  


2
2 Vs
Vo 
(cos  1)
2
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2 Vs sin  t d ( t )]
110
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• THE FIRING PULSE OF T1 AND T2 ARE 180 DEGREES APART.
• THE RMS VALUE OF THE OUTPUT VOLTAGE IS:
 2
Vo  
 2



2 V sin  t d ( t ) 

2
s
1/ 2
2
sin 2 
1
Vo  Vs  (   
2 


1/ 2
• BY VARYING Α FROM 0 TO Π, VO CAN BE VARIED FROM VS TO 0.
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SINGLE-PHASE AC VOLTAGE CONTROLLERS WITH
INDUCTIVE LOAD
• IN PRACTICE, MOST LOADS ARE INDUCTIVE TO A CERTAIN EXTENT.
• A FULL-WAVE CONTROLLER WITH AN INDUCTIVE LOAD IS SHOWN NEXT.
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SINGLE PHASE AC VOLTAGE REGULATOR WITH RL LOAD
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• THE GATING SIGNALS OF THYRISTORS COULD BE SHORT PULSES FOR A CONTROLLER WITH A
RESISTIVE LOAD.
• HOWEVER, THEY ARE NOT SUITABLE FOR INDUCTIVE LOADS.
• WHEN THYRISTOR T2 IS FIRED, THYRISTOR T1 IS STILL CONDUCTING DUE TO THE INDUCTIVE LOAD.
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• BY THE TIME THE CURRENT OF T1 FALLS TO ZERO AND T1 IS TURNED OFF, THE GATE CURRENT OF T2
HAS ALREADY CEASED.
• CONSEQUENTLY, T2 WILL NOT BE TURNED ON.
• THIS DIFFICULTY CAN BE RESOLVED BY USING A CONTINUOUS GATE SIGNAL WITH A DURATION OF
Π - Α.
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• HOWEVER A CONTINUOUS GATE PULSE INCREASES THE SWITCHING LOSS OF THYRISTORS.
• IN PRACTICE A TRAIN OF PULSES WITH SHORT DURATION ARE USED TO OVERCOME THE LOSS
PROBLEM.
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• THE RMS VALUE OF THE OUTPUT LOAD VOLTAGE IS FOUND FROM:
 2
Vo  
 2

2
2
2
V
sin

t
d
(

t
)
 s



1/ 2
sin 2
sin 2  
1
Vo  Vs  (    

2
2 


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THREE-PHASE FULL-WAVE CONTROLLERS
• THE UNIDIRECTIONAL CONTROLLERS, WHICH CONTAIN DC INPUT CURRENT AND HIGHER HARMONIC
CONTENT DUE TO THE ASYMMETRICAL NATURE OF THE OUTPUT VOLTAGE WAVEFORM, ARE NOT
NORMALLY USED IN AC MOTOR DRIVES.
• A THREE-PHASE BIDIRECTIONAL CONTROL IS COMMONLY USED.
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30o
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• FOR 0 < Α < 60O:
 1   sin 2 
6 Vs  ( 

)
4
8
 6

1/ 2
Vo 
• FOR 60O < Α < 90O:
Vo 
1 
3 sin 2
6 Vs  (


16
  12
3 cos 2 
)
16

1/ 2
• FOR 90O < Α < 150O:
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Vo 
 1 5  sin 2
6 Vs  (



4
16
  24
3 cos 2 
)
16

1/ 2
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THREE-PHASE BIDIRECTIONAL DELTA-CONNECTED
CONTROLLERS
• IF THE TERMINALS OF A THREE-PHASE SYSTEM ARE ACCESSIBLE, THE CONTROL ELEMENTS (SCRS) AND
LOAD MAY BE CONNECTED IN DELTA.
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• SINCE THE PHASE CURRENT IN A NORMAL THREE-PHASE DELTA SYSTEM IS ONLY 1/√3 OF THE LINE
CURRENT, THE CURRENT RATINGS OF THE THYRISTORS ARE LESS.
• THE FOLLOWING FIGURE SHOWS THE WAVEFORMS FOR A DELAY ANGLE OF 120 DEGREES.
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60o
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• FOR RESISTIVE LOADS:
sin 2 
1
Vo  Vs  (   
2 


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UNIT 5
CYCLOCONVERTER
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SINGLE PHASE CYCLOCONVERTER
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INTRODUCTION
• A DEVICE WHICH CONVERTS INPUT POWER AT ONE FREQUENCY TO THE OUT PUT POWER AT
DIFFERENT FREQUENCY WITH ONE STAGE CONVERSION IS CALLED A CYCLOCONVERTER
• TYPES
STEP-UP CYCLOCONVERTER( FO > FS)
STEP-DOWN CYCLOCONVERTER ( FO < FS)
• DUE TO HIGH COST, NOT SPREAD WIDELY IN EARLY DAYS
• NOW WITH ADVENT OF HIGH POWER THYRISTOR, CYCLOCONVERTER BECOME POPULAR
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APPLICATION OF CYCLOCONVERTER
• SPEED CONTROL OF HIGH POWER AC DRIVE
• INDUCTION HEATING
• STATIC VAR COMPENSATION
• FOR CONVERTING VARIABLE SPEED ALTERNATOR VTG TO CONT FREQ OUTPUT VTG FOR USE
AS POWER SUPPLY IN AIRCRAFT OR SHIPBOARDS
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SINGLE PHASE TO SINGLE PHASE MID POINT TYPE
STEP-UP CYCLOCONVERTER WITH R LOAD
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WAVEFORM
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SINGLE PHASE TO SINGLE PHASE BRIDGE TYPE
STEP-UP CYCLOCONVERTER WITH R LOAD
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WAVEFORM
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1-Φ TO 1-Φ MID POINT TYPE STEP-DOWN
CYCLOCONVERTER WITH R LOAD
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OUTPUT VOLTAGE (VO) AND CURRENT (IO) WAVEFORM
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1-Φ TO 1-Φ MIDPOINT TYPE STEP-DOWN
CYCLOCONVERTER WITH R-L LOAD
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OUTPUT VOLTAGE (VO) AND CURRENT (IO)
WAVEFORM FOR DISCONTINUOUS CONDUCTION
MODE
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OUTPUT VOLTAGE (VO) AND CURRENT (IO)
WAVEFORM FOR CONTINUOUS CONDUCTION MODE
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1-Φ TO 1-Φ BRIDGE TYPE STEP-DOWN
CYCLOCONVERTER WITH R LOAD
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OUTPUT VOLTAGE (VO) AND CURRENT (IO)
WAVEFORM
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1-Φ TO 1-Φ BRIDGE-TYPE STEP-DOWN
CYCLOCONVERTER WITH R-L LOAD
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OUTPUT VOLTAGE (VO) AND CURRENT (IO)
WAVEFORM FOR DISCONTINUOUS CONDUCTION
MODE
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OUTPUT VOLTAGE (VO) AND CURRENT (IO)
WAVEFORM FOR CONTINUOUS CONDUCTION MODE
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THREE PHASE CYCLOCONVERTER
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THREE PHASE TO SINGLE PHASE CYCLOCONVERTERTOPOLOGY 1
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TOPOLOGY 2
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OUTPUT VOLTAGE
THE INPUT AND OUTPUT VOLTAGES ARE ADJUSTED TO BE EQUAL AND THE LOAD CURRENT CAN
FLOW IN EITHER DIRECTION. THUS,
V0  Vd  Vd 0 cos  p  Vd 0 cos  n
WHERE VD0 IS THE DC OUTPUT VOLTAGE OF EACH CONVERTER AT ZERO FIRING ANGLE AND
P AND N ARE THE INPUT AND OUTPUT FIRING ANGLES. FOR A 3 HALF-WAVE CONVERTER
VD0 =0.675VL AND VD0 = 1.35VL FOR THE BRIDGE CONVERTER (VL IS THE RMS LINE VOLTAGE).
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FIRING ANGLE
• VOLTAGE-TRACKING BETWEEN THE INPUT AND OUTPUT VOLTAGES IS ACHIEVED BY SETTING
THE SUM OF THE FIRING ANGLES TO . POSITIVE OR NEGATIVE VOLTAGE POLARITY CAN BE
ACHIEVED AS SHOWN BELOW
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THREE PHASE TO THREE PHASE CYCLOCONVERTER
• EACH PHASE GROUP FUNCTIONS AS A DUAL CONVERTER BUT THE FIRING ANGLE OF EACH
GROUP IS MODULATED SINUSOIDALLY WITH 2/3 PHASE ANGLE SHIFT -> 3 BALANCED
VOLTAGE AT THE MOTOR TERMINAL.
• AN INTER-GROUP REACTOR (IGR) IS CONNECTED TO EACH PHASE TO RESTRICT CIRCULATING
CURRENT.
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TOPOLOGY 1
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WAVEFORM
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TOPOLOGY 2
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REFERENCES
• 1. RASHID M.H., "POWER ELECTRONICS CIRCUITS, DEVICES AND APPLICATIONS", PRENTICE
HALL INDIA, THIRD EDITION, NEW DELHI, 2011.
• 2. P.C. SEN, “MODERN POWER ELECTRONICS”, WHEELER PUBLISHING CO, THIRD EDITION, NEW
DELHI, 2008.
• 3. NED MOHAN, UNDELAND AND ROBBIN, “POWER ELECTRONICS: CONVERTERS, APPLICATION
AND DESIGN”, JOHN WILEY AND SONS.INC, NEWYORK,REPRINT - 2009.
• 4. CYRIL W.LANDER, “POWER ELECTRONICS”, THIRD EDITION, MCGRAW HILL- 1993.
• www.nptel.ac.in, www.ieee.com, www.ocw.mit.edu
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