Short Notes: Phase Controlled Converter | Short Notes for Electrical Engineering - Electrical Engineering (EE) PDF Download

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Form factor 
 ?
or
o
V
FF
V
 
 
or
V : rms value of output voltage. 
 
o
V : Average value of output voltage. 
 
Ripple Factor 
RF = 
2
FF 1 ? 
Distortion factor 
?
01
or
V
DF
V
 
01
V : rms value of fundamental components of 
o
V 
or
V : rms value of output voltage. 
 
Total harmonic Distortion 
??
2
1
THD 1
DF
 
Single phase half wave uncontrolled rectifier 
 R – load RL – Load L – Load 
O
V 
m
V
?
 ? ?
m
V
1 cos
2
??
?
 
0 
O
I 
m
V
R ?
 ? ?
m
V
1 cos
2R
??
?
 
?
m
V
L
 
? ? ? ? ? ? ? 2 ? 
? ?
O
I max 
2
?
 
? ?
,
2
?
? 
? 
 
? = Extinction angle, Angle at which ? 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. 
 
Page 2


 
 
 
 
 
Form factor 
 ?
or
o
V
FF
V
 
 
or
V : rms value of output voltage. 
 
o
V : Average value of output voltage. 
 
Ripple Factor 
RF = 
2
FF 1 ? 
Distortion factor 
?
01
or
V
DF
V
 
01
V : rms value of fundamental components of 
o
V 
or
V : rms value of output voltage. 
 
Total harmonic Distortion 
??
2
1
THD 1
DF
 
Single phase half wave uncontrolled rectifier 
 R – load RL – Load L – Load 
O
V 
m
V
?
 ? ?
m
V
1 cos
2
??
?
 
0 
O
I 
m
V
R ?
 ? ?
m
V
1 cos
2R
??
?
 
?
m
V
L
 
? ? ? ? ? ? ? 2 ? 
? ?
O
I max 
2
?
 
? ?
,
2
?
? 
? 
 
? = Extinction angle, Angle at which ? 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. 
 
 
 
 
 
 
 
Single phase half wave controlled rectifier 
i) R – load  
? 
? ?
? ?
? ? ?
?
m
O avg
V
V 1 cos
2
 
? 
? ?
? ?
? ? ?
?
m
O avg
V
I 1 cos
2R
 
? 
? ?
?? ?
? ? ? ? ?
??
?
??
2
m
or
V sin2
V
42
 
? Input power factor = ?
2
or or
S S S
V R V
V I V
 
                                ?
m
S
V
 V
2
 
? a = firing angle 
 
ii) R – L load 
? 
? ?
? ?
? ? ? ?
?
m
o avg
V
V cos cos
2
 
? 
? ?
? ?
? ? ? ?
?
m
o avg
V
I cos cos
2R
 
? 
? ? ? ?
? ? ? ? ? ? ? ?
?
m
or
V 1
V sin2 sin2
2
2
 
? Circuit turn off time, 
? ?
? ? ?
?
?
c
2
t 
 
Single phase full – wave rectifier 
 
                                               
                                                 
 
 
Page 3


 
 
 
 
 
Form factor 
 ?
or
o
V
FF
V
 
 
or
V : rms value of output voltage. 
 
o
V : Average value of output voltage. 
 
Ripple Factor 
RF = 
2
FF 1 ? 
Distortion factor 
?
01
or
V
DF
V
 
01
V : rms value of fundamental components of 
o
V 
or
V : rms value of output voltage. 
 
Total harmonic Distortion 
??
2
1
THD 1
DF
 
Single phase half wave uncontrolled rectifier 
 R – load RL – Load L – Load 
O
V 
m
V
?
 ? ?
m
V
1 cos
2
??
?
 
0 
O
I 
m
V
R ?
 ? ?
m
V
1 cos
2R
??
?
 
?
m
V
L
 
? ? ? ? ? ? ? 2 ? 
? ?
O
I max 
2
?
 
? ?
,
2
?
? 
? 
 
? = Extinction angle, Angle at which ? 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. 
 
 
 
 
 
 
 
Single phase half wave controlled rectifier 
i) R – load  
? 
? ?
? ?
? ? ?
?
m
O avg
V
V 1 cos
2
 
? 
? ?
? ?
? ? ?
?
m
O avg
V
I 1 cos
2R
 
? 
? ?
?? ?
? ? ? ? ?
??
?
??
2
m
or
V sin2
V
42
 
? Input power factor = ?
2
or or
S S S
V R V
V I V
 
                                ?
m
S
V
 V
2
 
? a = firing angle 
 
ii) R – L load 
? 
? ?
? ?
? ? ? ?
?
m
o avg
V
V cos cos
2
 
? 
? ?
? ?
? ? ? ?
?
m
o avg
V
I cos cos
2R
 
? 
? ? ? ?
? ? ? ? ? ? ? ?
?
m
or
V 1
V sin2 sin2
2
2
 
? Circuit turn off time, 
? ?
? ? ?
?
?
c
2
t 
 
Single phase full – wave rectifier 
 
                                               
                                                 
 
 
 
 
 
 
 
 
1 ?? 
full converter 
1 ?? 
Semi converter 
O
V 
?
?
m
2V
cos 
? ?
??
?
m
V
1 cos 
S1
I 
o
22
I
?
 
?
?
O
22
I cos
2
 
S
I 
o
I 
? ? ?
?
O
I 
DF 
22
?
 
? ?
?
? ? ? ?
22
cos
2
 
DPF ? cos ?
cos
2
 
IPF 
?
?
22
cos 
? ?
? ?
??
? ? ? ?
2
1 cos 
 
DPF: Displacement power factor = ? ?
S S1
cos angle b w V & I 
S1
I = fundamental components of 
S
I 
IPF: Input power factor 
IPF = DPF x DF 
DF: Distortion factor 
In case of continuous conductions, outgoing thyristors stop conduction before incoming 
thyristor start 
Load 
1 ?? 
Full converter 
1 ??  
Semi – converter 
       R – load 
? ?
? ? ?
?
m
o
V
V 1 cos 
? ?
? ? ?
?
m
o
V
V 1 cos 
       R – L load 
? ?
? ? ? ?
?
m
o
V
V cos cos 
? ?
? ? ?
?
m
o
V
V 1 cos 
       RLE – load  
? ? ? ?
??
? ? ? ? ? ? ? ? ? ?
??
?
??
m
o
V
V cos cos E ? ? ? ?
??
? ? ? ? ? ? ? ? ?
??
?
om
1
V V 1 cos E 
 
 
Page 4


 
 
 
 
 
Form factor 
 ?
or
o
V
FF
V
 
 
or
V : rms value of output voltage. 
 
o
V : Average value of output voltage. 
 
Ripple Factor 
RF = 
2
FF 1 ? 
Distortion factor 
?
01
or
V
DF
V
 
01
V : rms value of fundamental components of 
o
V 
or
V : rms value of output voltage. 
 
Total harmonic Distortion 
??
2
1
THD 1
DF
 
Single phase half wave uncontrolled rectifier 
 R – load RL – Load L – Load 
O
V 
m
V
?
 ? ?
m
V
1 cos
2
??
?
 
0 
O
I 
m
V
R ?
 ? ?
m
V
1 cos
2R
??
?
 
?
m
V
L
 
? ? ? ? ? ? ? 2 ? 
? ?
O
I max 
2
?
 
? ?
,
2
?
? 
? 
 
? = Extinction angle, Angle at which ? 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. 
 
 
 
 
 
 
 
Single phase half wave controlled rectifier 
i) R – load  
? 
? ?
? ?
? ? ?
?
m
O avg
V
V 1 cos
2
 
? 
? ?
? ?
? ? ?
?
m
O avg
V
I 1 cos
2R
 
? 
? ?
?? ?
? ? ? ? ?
??
?
??
2
m
or
V sin2
V
42
 
? Input power factor = ?
2
or or
S S S
V R V
V I V
 
                                ?
m
S
V
 V
2
 
? a = firing angle 
 
ii) R – L load 
? 
? ?
? ?
? ? ? ?
?
m
o avg
V
V cos cos
2
 
? 
? ?
? ?
? ? ? ?
?
m
o avg
V
I cos cos
2R
 
? 
? ? ? ?
? ? ? ? ? ? ? ?
?
m
or
V 1
V sin2 sin2
2
2
 
? Circuit turn off time, 
? ?
? ? ?
?
?
c
2
t 
 
Single phase full – wave rectifier 
 
                                               
                                                 
 
 
 
 
 
 
 
 
1 ?? 
full converter 
1 ?? 
Semi converter 
O
V 
?
?
m
2V
cos 
? ?
??
?
m
V
1 cos 
S1
I 
o
22
I
?
 
?
?
O
22
I cos
2
 
S
I 
o
I 
? ? ?
?
O
I 
DF 
22
?
 
? ?
?
? ? ? ?
22
cos
2
 
DPF ? cos ?
cos
2
 
IPF 
?
?
22
cos 
? ?
? ?
??
? ? ? ?
2
1 cos 
 
DPF: Displacement power factor = ? ?
S S1
cos angle b w V & I 
S1
I = fundamental components of 
S
I 
IPF: Input power factor 
IPF = DPF x DF 
DF: Distortion factor 
In case of continuous conductions, outgoing thyristors stop conduction before incoming 
thyristor start 
Load 
1 ?? 
Full converter 
1 ??  
Semi – converter 
       R – load 
? ?
? ? ?
?
m
o
V
V 1 cos 
? ?
? ? ?
?
m
o
V
V 1 cos 
       R – L load 
? ?
? ? ? ?
?
m
o
V
V cos cos 
? ?
? ? ?
?
m
o
V
V 1 cos 
       RLE – load  
? ? ? ?
??
? ? ? ? ? ? ? ? ? ?
??
?
??
m
o
V
V cos cos E ? ? ? ?
??
? ? ? ? ? ? ? ? ?
??
?
om
1
V V 1 cos E 
 
 
Page 5


 
 
 
 
 
Form factor 
 ?
or
o
V
FF
V
 
 
or
V : rms value of output voltage. 
 
o
V : Average value of output voltage. 
 
Ripple Factor 
RF = 
2
FF 1 ? 
Distortion factor 
?
01
or
V
DF
V
 
01
V : rms value of fundamental components of 
o
V 
or
V : rms value of output voltage. 
 
Total harmonic Distortion 
??
2
1
THD 1
DF
 
Single phase half wave uncontrolled rectifier 
 R – load RL – Load L – Load 
O
V 
m
V
?
 ? ?
m
V
1 cos
2
??
?
 
0 
O
I 
m
V
R ?
 ? ?
m
V
1 cos
2R
??
?
 
?
m
V
L
 
? ? ? ? ? ? ? 2 ? 
? ?
O
I max 
2
?
 
? ?
,
2
?
? 
? 
 
? = Extinction angle, Angle at which ? 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. 
 
 
 
 
 
 
 
Single phase half wave controlled rectifier 
i) R – load  
? 
? ?
? ?
? ? ?
?
m
O avg
V
V 1 cos
2
 
? 
? ?
? ?
? ? ?
?
m
O avg
V
I 1 cos
2R
 
? 
? ?
?? ?
? ? ? ? ?
??
?
??
2
m
or
V sin2
V
42
 
? Input power factor = ?
2
or or
S S S
V R V
V I V
 
                                ?
m
S
V
 V
2
 
? a = firing angle 
 
ii) R – L load 
? 
? ?
? ?
? ? ? ?
?
m
o avg
V
V cos cos
2
 
? 
? ?
? ?
? ? ? ?
?
m
o avg
V
I cos cos
2R
 
? 
? ? ? ?
? ? ? ? ? ? ? ?
?
m
or
V 1
V sin2 sin2
2
2
 
? Circuit turn off time, 
? ?
? ? ?
?
?
c
2
t 
 
Single phase full – wave rectifier 
 
                                               
                                                 
 
 
 
 
 
 
 
 
1 ?? 
full converter 
1 ?? 
Semi converter 
O
V 
?
?
m
2V
cos 
? ?
??
?
m
V
1 cos 
S1
I 
o
22
I
?
 
?
?
O
22
I cos
2
 
S
I 
o
I 
? ? ?
?
O
I 
DF 
22
?
 
? ?
?
? ? ? ?
22
cos
2
 
DPF ? cos ?
cos
2
 
IPF 
?
?
22
cos 
? ?
? ?
??
? ? ? ?
2
1 cos 
 
DPF: Displacement power factor = ? ?
S S1
cos angle b w V & I 
S1
I = fundamental components of 
S
I 
IPF: Input power factor 
IPF = DPF x DF 
DF: Distortion factor 
In case of continuous conductions, outgoing thyristors stop conduction before incoming 
thyristor start 
Load 
1 ?? 
Full converter 
1 ??  
Semi – converter 
       R – load 
? ?
? ? ?
?
m
o
V
V 1 cos 
? ?
? ? ?
?
m
o
V
V 1 cos 
       R – L load 
? ?
? ? ? ?
?
m
o
V
V cos cos 
? ?
? ? ?
?
m
o
V
V 1 cos 
       RLE – load  
? ? ? ?
??
? ? ? ? ? ? ? ? ? ?
??
?
??
m
o
V
V cos cos E ? ? ? ?
??
? ? ? ? ? ? ? ? ?
??
?
om
1
V V 1 cos E 
 
 
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