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Contents
Manual for K-Notes ................................................................................. 2
Power Semi-Conductor Devices .............................................................. 3
Phase Controlled converter .................................................................. 10
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Chopper ................................................................................................ 15
Inverters................................................................................................ 21
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AC - AC Converters ................................................................................ 26
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© 2014 Kreatryx. All Rights Reserved.
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Manual for K-Notes
Why K-Notes?
Towards the end of preparation, a student has lost the time to revise all the chapters
from his / her class notes / standard text books. This is the reason why K-Notes is
specifically intended for Quick Revision and should not be considered as comprehensive
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study material.
What are K-Notes?
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A 40 page or less notebook for each subject which contains all concepts covered in GATE
Curriculum in a concise manner to aid a student in final stages of his/her preparation. It
is highly useful for both the students as well as working professionals who are preparing
for GATE as it comes handy while traveling long distances.
When do I start using K-Notes?
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It is highly recommended to use K-Notes in the last 2 months before GATE Exam
(November end onwards).
How do I use K-Notes?
Once you finish the entire K-Notes for a particular subject, you should practice the
respective Subject Test / Mixed Question Bag containing questions from all the Chapters
to make best use of it.
© 2014 Kreatryx. All Rights Reserved.
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Power Semi-Conductor Devices
Properties of ideal switch
1.
Conduction state , VON  0,    ION  
2.
Blocking state , VOFF  0,    VOFF  
3.
Ideal switch can change its state instantaneously TON  0 , TOFF  0
4.
No power loss while switching.
5.
Stable under all operating conditions.
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Classification of switches
1.
Uncontrolled switch (Passive switch)
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Switching state cannot be controlled by any control signal E.g. Diode
2.
Semi-controlled switch
Only one switching state can be controlled by an external control signal. E.g. SCR
3.
Fully controlled switch
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If both switching states can be controlled by switchable control signal. E.g. BJT, MOSFET.
Other Classification
1.
Unipolar switch
The switch can block only one polarity of voltage when it is in OFF state.
2.
Bipolar switch
This switch can block both polarity of voltage when it is in blocking state.
3.
Unidirectional switch
This switch can carry current in only one direction when it is in conduction state.
4.
Bidirectional switch
This switch can carry current in both the directions when it is in conduction state.
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Ideal characteristics of power semiconductor switches
Device
Diode
Characteristic
BJT
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MOSFET
IGBT
SCR
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GTO
TRIAC
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Power loss in a switch
1) The average power has in a switch is given by
1 T
P   vidt
T o
Where v = instantaneous voltage
i = instantaneous current
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2) If the device is modeled as a resistance, as in case of a MOSFET
2
2
P  Irms
R ON  Vrms
R ON
3) If the device is modeled as a voltage source.
P  V Iavg
Silicon Controlled Rectifier
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
In forward blocking mode, J1 , J3 are forward biased and J2 is reverse biased.

In forward conduction mode, J2 breakdown, J1 , J3 are forward biased.

In reverse blocking mode, J1 , J3 are reverse biased & J2 is forward biased.
Latching Current
This is the minimum value of anode current above which SCR turns ON. This is related to
minimum gate pulse width requirement for SCR.
Holding current
Minimum value of anode current below which SCR turns OFF.
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 di 
Slope of characteristics =  
 dt 
If ta  trr
Area under the curve = QR
1
QR  IRM trr
2


IRM  di dt trr
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QR 
1 di 2
trr
2 dt
Device & Circuit Turn-off time

Device turn off time, tq  trr  tgr
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trr = reverse recovery time
t gr = gate recovery time

Circuit turn-off time  t c  is the time period for which communication circuit applies reverse

voltage across SCR after anode current becomes zero.
For successful communication, tc  tq
Turn-ON methods of SCR
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1) Forward voltage triggering
If VAK  VBO , then J2 breakdown & SCR conducts. This can damage the SCR.
2)
dV
Triggering
dt
dv
dv
Ic  C j
, if
is high, charging current increase and SCR conducts when Ic  Ilatching .
dt
dt
3) Light Triggering
If light is incident on J2 , charge carriers are generated and J2 starts conducting.
4) Thermal Triggering
When temperature is increased then charge carriers are generated & SCR conducts.
5) Gate Triggering
By applying gate pulse in SCR, VBO is lowered and SCR can easily conduct.
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Static V-I characteristics of SCR
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Communication of thyristor
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Communication is defined as process of turning OFF the thyristor.
Types of Commutations:
1. Natural or line communication
In this case nature of supply supports the commutation.
E.g. Rectifier, AC voltage controllers, Step-down cyclo-converters.
2. Forced Commutation
1) Class A commutation

Circuit should be under-damped.

R2 

Ringing frequency, r 

Thyristor conducts for a period of =
4L
for damped oscillations.
C
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1
R2
 2
LC 4L

r
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2) Class-B commutation or current commutation
a)
 ITM peak  Io
C
 IP
L
c) Time required to turn OFF TM after TA ON
b)
 ITA peak  Vs
I 
  LC  LC sin1  o 
 Ip 
 
d) Conduction time of TA   LC
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e) tCM 
CVR
= circuit turn off time
Io

I
Where VR  VS cos sin1  o
 Ip


Other Implementation

I
tCM     2 sin1  o
 Ip



  LC
 
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 
 
 
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Rest all parameters remains same.
3) Class-C commutation or Impulse commutation

 I T1 peak
V
2V 
 S  S 
 R1 R 2 

 I T2 peak
V
2V 
 S  S 
 R 2 R1 

tC1  R1 ln2 

tC2  R 2 ln2 
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Class-D commutation or voltage commutation
C
L

 ITM peak  Io  VS

 ITA peak  Io

 TON min for TM  

tCM 

Conduction time of TA  2tCM 

 VO avg
LC
CVs
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Io

2CVs
Io
VS
 TON  2tCM  , T = Switching internal
T
Thermal Protection of SCR
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 jc = Thermal resistance b/w J & C
CS = Thermal resistance b/w C & S
SA = Thermal resistance b/w S & A
Unit of   0 C / w
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In electrical circuit representation
TjA = Temperature difference b/w J & A
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Phase Controlled converter
Form factor
V
FF  or
Vo
Vor : rms value of output voltage.
Vo : Average value of output voltage.
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Ripple Factor
RF =
FF2  1
Distortion factor
V
DF  01
Vor
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V01 : rms value of fundamental components of Vo
Vor : rms value of output voltage.
Total harmonic Distortion
THD 
1
1
DF2
Single phase half wave uncontrolled rectifier
VO
IO
ϒ
IO max 
R – load
Vm

Vm
R


2
RL – Load
Vm
1  cos  
2
Vm
1  cos  
2R
   
  2 , 
L – Load
0
Vm
L
2
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
 = Extinction angle, Angle at which ω goes to zero.

If a free-wheeling diode is connected across the load (RL) that behaves as R-load as output
voltage goes to zero after t   when FD conducts.
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Single phase half wave controlled rectifier
i)
R – load

VO avg 
Vm
1  cos  
2

IO avg 
Vm
1  cos  
2R

Vor 
Vm2 
sin2 
    

4 
2 

Input power factor =
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VS 

ii)
α = firing angle
R – L load
2
Vor
R
VS IS
Vm
Vor
VS
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2

Voavg 
Vm
 cos   cos  
2

Io avg 
Vm
 cos   cos  
2R
Vm


Vor 
     12  sin2  sin2 
2 

Circuit turn off time, t c 
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 2   

Single phase full – wave rectifier
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VO
IS1
IS
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DF
1
full converter
2Vm
cos 

2 2
Io

Io
Semi converter
Vm
1  cos  

2 2
I cos 
2
 O
IO
2 2



2 2
   
cos 
DPF
IPF
1
cos 
cos 
2
2
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2 2
cos 

2
1  cos  
   
DPF: Displacement power factor = cos  angle b w VS & IS1 
IS1 = fundamental components of IS
IPF: Input power factor
IPF = DPF x DF
DF: Distortion factor
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In case of continuous conductions, outgoing thyristors stop conduction before incoming
thyristor start
Load
R – load
R – L load
RLE – load
1
1
Full converter
V
Vo  m 1  cos  

V
Vo  m  cos   cos  

V

Vo   m  cos   cos    E        
 

Semi – converter
V
Vo  m 1  cos  

V
Vo  m 1  cos  

1
Vo   Vm 1  cos    E       

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Three phase half wave controlled rectifier
Vo 
3Vml
cos 
2
Vml : Peak value of line voltage
1 3 3

Vor  Vmp  
cos2 
 2 8

1
2
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Vmp : Peak value of phase voltage
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Three phase full wave rectifier
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Vo
Vor
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3
3
Full converter
3Vml
cos 

Semi converter
3Vml
1  cos  
2
Expression varies for   600 &   600
Vml
IS1
1 3 3

cos 2
2 4
For   600 , it becomes 3-pulse converter.
 
6
IO

6
I cos 
2
 O
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IS
2
IO
3
DF
3

DPF
cosα
IPF
3
cos 

IO


6
cos 
2
   
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cos 
2
6
cos2 
2
   x
IS1 : Fundamental rms value of source current
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IS : rms value of source current
Effect of source inductance
Assuming source inductance equal to L S .
Due to source inductance, there is an overlap b/w incoming and outgoing thyristor, given by
overlap angle    .
For 2-pulse converter
VO 
L
2Vm
cos   S IO


VO 
Vm
cos   cos      

 
Displacement power factor = cos     
2

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For 6 – pulse converter
VO 
3LS
3Vm
cos  
I

 O
VO 
3Vm
cos   cos      

2 
Displacement power factor = cos     
2

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Chopper
Buck Converter
When CH is ON  o  t  DT 
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Voltage across inductor VL   VS  VO 
When CH is OFF (DT < t < T)
Voltage across inductor VL  VO
Applying volt-sec balance across inductor
 VS  VO   DT   VO   T  DT  0
 VS  VO  D  VO 1  D   0
VO  DVS
D = duty cycle =
TON
T
Where T = switching period = 1
f
f = switching frequency
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
Average output voltage = DVS

rms output voltage =

Average source current = DIO

Average current of FD = 1  D  IO
DVS
Ripple in output current
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When CH is ON  0  t  DT 
VL  VS  VO  1  D  VS
During this period, since voltage is positive current increase from minimum value to maximum
value.
i  Imax  Imin
t  DT  0  DT
L
 i  
DT
i 

1  D  V
S
D 1  D  VS
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This formula gives approximate value of output ripple current for maximum ripple, D = 0.5
 imax 
VS
4fL
IL
2
I
 IO  L
2

Imax  IO 

Imin
Critical Inductance (LC)
Value of inductance at which inductor voltage waveform is just discontinuous.
Lc 
1  D  R
2f
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Critical Capacitance (CC)
Value of capacitance at which capacitor voltage waveform is just discontinuous.
CC 
1
8fR
Step-up chopper (Boost converter)
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when CH is ON  0  t  DT  ,
VL  VS
when CH is OFF DT  t  T  ,
VL   VS  VO 
Applying volt-sec balance across inductor
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VS DT    VS  VO  1  D  T  0
VS
VO 
1  D 

Since D < 1, VO  VS

when CH is ON  0  t  DT  ,
IC  IO
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when CH is OFF DT  t  T  , IC  IL  IO
Applying Ampere  sec balance across capacitor
IO DT    IL  IO 1  D  T  0
IL 
IO
1  D 
Ripple in inductor current
When CH is ON  0  t  DT  , current increase from Imin to Imax
L
VS DT  DVS
iL
 VS  iL 

DT
L
fL
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Ripple in output voltage
when CH is ON , IC  IO
C.
VC
 I O
DT
VO  VC 
IO DT 
C
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-ve sign indicates voltage decrease
 VO 
IO DT 
C
Critical Inductance (Lc)
I
IL  L
2
LC 
D 1  D  R
2f
Critical Capacitance (Cc)
VO 
VO
2
CC 
D
2fR
asy
En
gin
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If inductor also has an internal resistance, then
 1  D  

VO  VS 
2
 r  1  D  
 R

r = internal resistance of inductor
R = load resistance
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Buck-Boost Converter
When CH is ON (O < t < DT)
VL  VS
I C  I O
When CH is OFF (DT < t < T)
VL  VO
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IC    IL  IO 
Applying volt-sec balance across inductor
VS DT   VO 1  D  T  0
VO 
asy
En
gin
ee
DVS
1  D 
Applying Ampere-sec balance across inductor
IO DT    IL  IO  1  D  T  0
IL 
IL 
I O
1  D 
 VO
R 1  D 

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DVS
R 1  D 
2
Ripple in inductor current
When CH is ON (O < t < DT)
Inductor current increase from Imin to Imax
L
IL
 VS
DT
IL 
DVS
fL
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Ripple in output voltage
When CH is ON (O < t < DT)
Capacitor discharge & voltage decrease from Vmax to Vmin
CVO
 I O
DT
VO 
DIO
fC
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Critical inductance (Lc)
IL 
IL
2
LC 
R 1  D 
2
2f
Critical capacitance (Cc)
VO
VO 
2
CC 
asy
En
gin
ee
rin
g.n
et
I O 1  D  T
2VS
If internal resistance (r) of inductor is also considered then
 D 1  D  
 VS
VO  
2
 r  1  D  
 R

R = load resistance
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Inverters
Inverters circuits will convert DC power to AC power at required voltage & required frequency.
Classification
1) Voltage source Inverter
 Input source is a voltage source.

Switching device is bidirectional & unipolar.

Load voltage depends on source voltage & load current depends on load parameters.
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2) Current source Inverters
 Input source is a current source.

Switching device is bidirectional & bipolar

Load voltage depends on source current & load voltage on load parameters.
asy
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ee
Single phase half bridge VSI
When S1 is ON, VO  0, IO  0
When S2 is ON, VO  0, IO  0
When D1 is ON, VO  0, IO  0
When D 2 is ON, VO  0, IO  0


V
The output voltage is a square wave of amplitude dc
2
The fourier series of output voltage is given by
VO 



n1,3,5
2Vdc
sin nt 
n
rin
g.n
et
rms value of fundamental components is given by
 2V  1
2
Vor1   dc  

V
 dc
2
  
Vor 
Vdc

rms value of output voltage

Distortion Factor(DF) =

% Total Harmonic Distortion THD 
Vor1
Vor

2
2 2

1
 1 = 48.43%
DF2
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
If load power factor is lagging, then it requires forced commutation.

If load power factor is leading, then natural commutation occurs.
Single phase Full Bridge VSI
When S1 , S2 conduct VO  0, IO  0
When D1 , D 2 conduct, VO  0, IO  0
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When S3 , S 4 conduct, VO  0, IO  0
When D3 ,D 4 conduct, VO  0, IO  0

The output voltage is a square wave of amplitude Vdc

The fourier series of output voltage is given by
VO 

asy
En
gin
ee


n1,3,5
4Vdc
sin nt 
n
rms value of fundamental components is given by
Vor1 
2
V
 dc
Vor  Vdc

rms value of output voltage

Distortion Factor(DF) =

% Total Harmonic Distortion THD 
Vor1
Vor

2 2

1
 1 = 48.43%
DF2
Three phase full bridge VSI
rin
g.n
et
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1800conduction mode
In this mode, each switch will conduct for a period of 1800 and phase displacement between
any two poles is 1200

Phase voltage
V 

2
V
3 dc
VRN 

n6k 1

2Vdc
ph rms
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n
sin nt 
 VR1  = rms value of fundamental component of V
2Vdc
VR1 


1
 1  100  31%
DF2
Line voltage
 VL L rms 
VRY 


n6k 1
asy
En
gin
ee
VR1
3

Vph,rms 
Distortion factor, DF 
THD 
RN
rin
g.n
et
2
V
3 dc
4Vdc
n
 3  sinn  t   6 
sin n
 VRY 1 = rms value of fundamental component of V
RY
Distortion factor = 3
=  VRY  
1
6


In each phase, each switch conducts for 1800 out of 3600
 Ir.rms 
Io, rms
2

2Vdc
3R  2

Vdc
, Where R = load resistance
3R
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Voltage
Phase
Total RMS
2
Vdc
3
2
Vdc
3
Line

Fundamental RMS
2
Vdc

6 V
 dc
This conversion from total rms to fundamental rms can be performed by multiplication of
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3  DF .


This conversion from phase to line voltage can be performed by multiplication of
3.
1200conduction mode
asy
En
g
ine
 

e
For each thyristor, conduction angle is 1200 & last 60 0 for commutation.

Phase Voltage
V 
ph rms
VRN 
VR1 

Vdc
6


n6k 1
2Vdc
n

sin n 
3
6
V
 dc
Distortion factor, DF  3
sin nt  n 
6
rin
g.n
et

THD = 31%

Line Voltage
 VL RMS 
Vdc
2

 VRY   
n6k 1
 VRY 1 
3
2
3Vdc
n

sin n t  
3

Vdc
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Distortion factor, = 3 ; THD  31%

In each, phase each switch conducts for 1200 out of 3600
I T , rms 
Io, rms
3

Vdc
2R
R = load resistance
Voltage
Phase
Total RMS
Vdc
Line
6
Vdc
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Fundamental RMS
6
Vdc

3
Vdc
2
2
asy
En
gin
ee

The conversion factor remain same as in 1800 conduction mode.

In both 1200 & 1800 conduction mode both phase & line voltages are free from even & triplen
harmonics.
Voltage control using PWM techniques
1) Single PWM techniques
rin
g.n
et
In this case, width of positive & negative cycle is not  but rather equal to 2d.
VO 
S
sin n   sin nd sin nt 

2
n

n1,3,5

4V
To eliminate nth harmonics
Sin (nd) = 0
d  n
Pulse width, 2d  2 n , 4 n , 6 n ,...................
but 2d  
To eliminate 3rd harmonics
3d   ; d   3 ; 2d  2 3
So pulse width of 1200 is required.
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2) Multiple PWM techniques
Here a single pulse of ‘2d’ width is divided into ‘n’ pulses each of width
n
2d
.
n
fc
2fr
fc = carrier signal frequency
fr = reference signal frequency
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AC - AC Converters
These circuits control AC power. They are of 2 types:
1) AC voltage regulator
2) Cyclo-converter
AC voltage regulator
asy
En
gin
ee
These transfer AC power from 1 circuit to another by controlling output voltage & fixed
frequency.
rin
g.n
et
Single phase half wave ACVR

VO avg 
Vm
 cos   1
2
IO avg 
Vm
 cos   1
2R
1


V 
2
1
VOrms  m  2     sin2 
2
2 

Vor
1
2
1 
1
pf 

 2     sin2 
Vsr
2
2 

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Single phase fully controlled ACVR
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
Vo avg  0


asy
En
gin
ee
1


V 
2
1
Vo rms  m       sin2 
 
2
2 

If R – L load is used, then in steady state I O lags VO by an angle 
 wL 
  tan1 

 R 
rin
g.n
et

If r   , then above formulas remain valid & output voltage is controllable by controlling α.

If r   , output voltage is not controllable & Vor  Vsr
So, range of firing angle is     1800
Integral cycle control (ON/OFF) control
If in fully controlled ACVR, thyristors conduct for m cycle & are OFF for n cycle then
1
 VO rms
 m 2
 Vsr 

mn
1
V
 m 2
For R – load, pf  or  

Vsr  m  n 
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I T1 avg 


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Vm  m 


R  m  n 
1
V  m 2
I T1 rms  m 
  2R  m  n 
R = load resistance ; Vm is maximum value of VS
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asy
En
gin
ee
rin
g.n
et
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asy
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