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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. 
 
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. 
Single phase half bridge VSI 
When 
1
S is ON, 
OO
V 0, I 0 ?? 
When 
2
S is ON, 
OO
V 0, I 0 ?? 
When 
1
D is ON, ??
OO
V 0, I 0 
When 
2
D is ON, 
OO
V 0, I 0 ?? 
? The output voltage is a square wave of amplitude 
dc
V
2
 
? The fourier series of output voltage is given by  
   
? ?
?
?
??
?
? O
dc
n 1,3,5
2V
V sin n t
n
 
? rms value of fundamental components is given by 
   
??
? ? ?
??
??
??
dc
or1 dc
2V 12
VV
2
 
? rms value of output voltage ?
dc
or
V
V
2
 
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
 
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43% 
Page 2


 
 
 
 
 
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. 
 
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. 
Single phase half bridge VSI 
When 
1
S is ON, 
OO
V 0, I 0 ?? 
When 
2
S is ON, 
OO
V 0, I 0 ?? 
When 
1
D is ON, ??
OO
V 0, I 0 
When 
2
D is ON, 
OO
V 0, I 0 ?? 
? The output voltage is a square wave of amplitude 
dc
V
2
 
? The fourier series of output voltage is given by  
   
? ?
?
?
??
?
? O
dc
n 1,3,5
2V
V sin n t
n
 
? rms value of fundamental components is given by 
   
??
? ? ?
??
??
??
dc
or1 dc
2V 12
VV
2
 
? rms value of output voltage ?
dc
or
V
V
2
 
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
 
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43% 
 
 
 
 
 
 
? 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
1
S ,
2
S conduct  
OO
V 0, I 0 ?? 
When
1
D ,
2
D conduct, ??
OO
V 0, I 0 
When
3
S ,
4
S conduct, ??
OO
V 0, I 0 
When
34
D ,D conduct, 
OO
V 0, I 0 ?? 
? The output voltage is a square wave of amplitude 
dc
V 
? The fourier series of output voltage is given by  
   
? ?
?
?
??
?
? O
dc
n 1,3,5
4V
V sin n t
n
 
? rms value of fundamental components is given by 
   ?
?
or1 dc
2
VV 
? rms value of output voltage ?
or dc
VV 
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
 
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43% 
 
Three phase full bridge VSI 
 
 
 
 
 
Page 3


 
 
 
 
 
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. 
 
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. 
Single phase half bridge VSI 
When 
1
S is ON, 
OO
V 0, I 0 ?? 
When 
2
S is ON, 
OO
V 0, I 0 ?? 
When 
1
D is ON, ??
OO
V 0, I 0 
When 
2
D is ON, 
OO
V 0, I 0 ?? 
? The output voltage is a square wave of amplitude 
dc
V
2
 
? The fourier series of output voltage is given by  
   
? ?
?
?
??
?
? O
dc
n 1,3,5
2V
V sin n t
n
 
? rms value of fundamental components is given by 
   
??
? ? ?
??
??
??
dc
or1 dc
2V 12
VV
2
 
? rms value of output voltage ?
dc
or
V
V
2
 
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
 
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43% 
 
 
 
 
 
 
? 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
1
S ,
2
S conduct  
OO
V 0, I 0 ?? 
When
1
D ,
2
D conduct, ??
OO
V 0, I 0 
When
3
S ,
4
S conduct, ??
OO
V 0, I 0 
When
34
D ,D conduct, 
OO
V 0, I 0 ?? 
? The output voltage is a square wave of amplitude 
dc
V 
? The fourier series of output voltage is given by  
   
? ?
?
?
??
?
? O
dc
n 1,3,5
4V
V sin n t
n
 
? rms value of fundamental components is given by 
   ?
?
or1 dc
2
VV 
? rms value of output voltage ?
or dc
VV 
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
 
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43% 
 
Three phase full bridge VSI 
 
 
 
 
 
 
 
 
 
 
180
0
conduction mode 
In this mode, each switch will conduct for a period of 
0
180 and phase displacement between 
any two poles is 
0
120 
? Phase voltage 
? ?
?
ph dc
rms
2
VV
3
 
? ?
?
??
??
?
?
dc
RN
n 6k 1
2V
V sin n t
n
 
? ?
R1
V = rms value of fundamental component of 
RN
V 
?
?
dc
R1
2V
V 
Distortion factor, ??
?
R1
ph,rms
V 3
DF
V
 
? ? ? ?
2
1
THD 1 100 31%
DF
 
 
? Line voltage 
? ?
?
?
L L dc
rms
2
VV
3
 
? ? ? ? ? ?
?
??
??
? ? ?
?
?
dc
RY
n 6k 1
4V
n
V sin sin n t
36
n
 
? ?
RY
1
V = rms value of fundamental component of 
RY
V =
? ?
?
?
RY
1
6
V 
Distortion factor = 
3
?
 
In each phase, each switch conducts for 
0
180 out of 
0
360 
 ??
o, rms
r.rms
I
I
2
dc dc
2V V
3R 3R 2
??
?
, Where R = load resistance 
Page 4


 
 
 
 
 
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. 
 
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. 
Single phase half bridge VSI 
When 
1
S is ON, 
OO
V 0, I 0 ?? 
When 
2
S is ON, 
OO
V 0, I 0 ?? 
When 
1
D is ON, ??
OO
V 0, I 0 
When 
2
D is ON, 
OO
V 0, I 0 ?? 
? The output voltage is a square wave of amplitude 
dc
V
2
 
? The fourier series of output voltage is given by  
   
? ?
?
?
??
?
? O
dc
n 1,3,5
2V
V sin n t
n
 
? rms value of fundamental components is given by 
   
??
? ? ?
??
??
??
dc
or1 dc
2V 12
VV
2
 
? rms value of output voltage ?
dc
or
V
V
2
 
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
 
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43% 
 
 
 
 
 
 
? 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
1
S ,
2
S conduct  
OO
V 0, I 0 ?? 
When
1
D ,
2
D conduct, ??
OO
V 0, I 0 
When
3
S ,
4
S conduct, ??
OO
V 0, I 0 
When
34
D ,D conduct, 
OO
V 0, I 0 ?? 
? The output voltage is a square wave of amplitude 
dc
V 
? The fourier series of output voltage is given by  
   
? ?
?
?
??
?
? O
dc
n 1,3,5
4V
V sin n t
n
 
? rms value of fundamental components is given by 
   ?
?
or1 dc
2
VV 
? rms value of output voltage ?
or dc
VV 
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
 
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43% 
 
Three phase full bridge VSI 
 
 
 
 
 
 
 
 
 
 
180
0
conduction mode 
In this mode, each switch will conduct for a period of 
0
180 and phase displacement between 
any two poles is 
0
120 
? Phase voltage 
? ?
?
ph dc
rms
2
VV
3
 
? ?
?
??
??
?
?
dc
RN
n 6k 1
2V
V sin n t
n
 
? ?
R1
V = rms value of fundamental component of 
RN
V 
?
?
dc
R1
2V
V 
Distortion factor, ??
?
R1
ph,rms
V 3
DF
V
 
? ? ? ?
2
1
THD 1 100 31%
DF
 
 
? Line voltage 
? ?
?
?
L L dc
rms
2
VV
3
 
? ? ? ? ? ?
?
??
??
? ? ?
?
?
dc
RY
n 6k 1
4V
n
V sin sin n t
36
n
 
? ?
RY
1
V = rms value of fundamental component of 
RY
V =
? ?
?
?
RY
1
6
V 
Distortion factor = 
3
?
 
In each phase, each switch conducts for 
0
180 out of 
0
360 
 ??
o, rms
r.rms
I
I
2
dc dc
2V V
3R 3R 2
??
?
, Where R = load resistance 
 
 
 
 
 
Voltage Total RMS Fundamental RMS 
Phase 
dc
2
V
3
 
dc
2
V
?
 
Line 
dc
2
V
3
 dc
6
V
?
 
 
? This conversion from total rms to fundamental rms can be performed by multiplication of
?
?
3
DF . 
? This conversion from phase to line voltage can be performed by multiplication of 3 . 
120
0
conduction mode 
For each thyristor, conduction angle is 
0
120 & last 
0
60 for commutation. 
? Phase Voltage 
? ?
?
dc
ph
rms
V
V
6
 
? ? ? ?
?
??
??
? ? ?
?
?
dc
RN
n 6k 1
2V
V sin n sin n t n
36
n
 
?
?
R1 dc
6
VV 
Distortion factor, ?
?
3
DF 
THD = 31% 
 
? Line Voltage 
? ?
?
dc
L
RMS
V
V
2
 
? ?
? ? ? ?
?
??
?
? ? ?
?
?
dc
RY
n 6k 1
3V
V sin n t
3
n
 
? ?
?
?
RY dc
1
3
VV
2
 
Page 5


 
 
 
 
 
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. 
 
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. 
Single phase half bridge VSI 
When 
1
S is ON, 
OO
V 0, I 0 ?? 
When 
2
S is ON, 
OO
V 0, I 0 ?? 
When 
1
D is ON, ??
OO
V 0, I 0 
When 
2
D is ON, 
OO
V 0, I 0 ?? 
? The output voltage is a square wave of amplitude 
dc
V
2
 
? The fourier series of output voltage is given by  
   
? ?
?
?
??
?
? O
dc
n 1,3,5
2V
V sin n t
n
 
? rms value of fundamental components is given by 
   
??
? ? ?
??
??
??
dc
or1 dc
2V 12
VV
2
 
? rms value of output voltage ?
dc
or
V
V
2
 
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
 
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43% 
 
 
 
 
 
 
? 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
1
S ,
2
S conduct  
OO
V 0, I 0 ?? 
When
1
D ,
2
D conduct, ??
OO
V 0, I 0 
When
3
S ,
4
S conduct, ??
OO
V 0, I 0 
When
34
D ,D conduct, 
OO
V 0, I 0 ?? 
? The output voltage is a square wave of amplitude 
dc
V 
? The fourier series of output voltage is given by  
   
? ?
?
?
??
?
? O
dc
n 1,3,5
4V
V sin n t
n
 
? rms value of fundamental components is given by 
   ?
?
or1 dc
2
VV 
? rms value of output voltage ?
or dc
VV 
? Distortion Factor(DF) = ?
?
or1
or
V 22
V
 
? % Total Harmonic Distortion ??
2
1
THD 1
DF
= 48.43% 
 
Three phase full bridge VSI 
 
 
 
 
 
 
 
 
 
 
180
0
conduction mode 
In this mode, each switch will conduct for a period of 
0
180 and phase displacement between 
any two poles is 
0
120 
? Phase voltage 
? ?
?
ph dc
rms
2
VV
3
 
? ?
?
??
??
?
?
dc
RN
n 6k 1
2V
V sin n t
n
 
? ?
R1
V = rms value of fundamental component of 
RN
V 
?
?
dc
R1
2V
V 
Distortion factor, ??
?
R1
ph,rms
V 3
DF
V
 
? ? ? ?
2
1
THD 1 100 31%
DF
 
 
? Line voltage 
? ?
?
?
L L dc
rms
2
VV
3
 
? ? ? ? ? ?
?
??
??
? ? ?
?
?
dc
RY
n 6k 1
4V
n
V sin sin n t
36
n
 
? ?
RY
1
V = rms value of fundamental component of 
RY
V =
? ?
?
?
RY
1
6
V 
Distortion factor = 
3
?
 
In each phase, each switch conducts for 
0
180 out of 
0
360 
 ??
o, rms
r.rms
I
I
2
dc dc
2V V
3R 3R 2
??
?
, Where R = load resistance 
 
 
 
 
 
Voltage Total RMS Fundamental RMS 
Phase 
dc
2
V
3
 
dc
2
V
?
 
Line 
dc
2
V
3
 dc
6
V
?
 
 
? This conversion from total rms to fundamental rms can be performed by multiplication of
?
?
3
DF . 
? This conversion from phase to line voltage can be performed by multiplication of 3 . 
120
0
conduction mode 
For each thyristor, conduction angle is 
0
120 & last 
0
60 for commutation. 
? Phase Voltage 
? ?
?
dc
ph
rms
V
V
6
 
? ? ? ?
?
??
??
? ? ?
?
?
dc
RN
n 6k 1
2V
V sin n sin n t n
36
n
 
?
?
R1 dc
6
VV 
Distortion factor, ?
?
3
DF 
THD = 31% 
 
? Line Voltage 
? ?
?
dc
L
RMS
V
V
2
 
? ?
? ? ? ?
?
??
?
? ? ?
?
?
dc
RY
n 6k 1
3V
V sin n t
3
n
 
? ?
?
?
RY dc
1
3
VV
2
 
 
 
 
  
 
Distortion factor, = 
3
; THD 31% ?
?
 
In each, phase each switch conducts for 
0
120 out of 
0
360 
 
o, rms
T, rms
I
I
3
?
dc
V
2R
? 
 R = load resistance 
Voltage  Total RMS Fundamental RMS 
Phase 
dc
V
6
 
dc
6
V
?
 
Line 
dc
V
2
 
dc
3
V
2 ?
 
 
? The conversion factor remain same as in 
0
180 conduction mode. 
? In both 
00
120 & 180 conduction mode both phase & line voltages are free from even & triplen 
harmonics. 
 
Voltage control using PWM techniques 
1) Single PWM techniques 
 
In this case, width of positive & negative cycle is not ? but rather equal to 2d. 
? ?
? ? ? ?
?
?
?
??
?
? O
S
n 1,3,5
4V
V sin n sin nd sin n t
2
n
 
To eliminate n
th
 harmonics 
 Sin (nd) = 0 
 d
n
?
? 
Pulse width, 
2 4 6
2d , , ,...................
n n n
? ? ?
? 
 but 2d ?? 
To eliminate 3
rd
 harmonics 
 
2
3d ; d ; 2d
33
??
? ? ? ? 
So pulse width of 
0
120 is required.

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