# IGBT Modules - Technologies, Driver and Application (Second Edition) - page 386

374
( )
( ) ( )
( )
( )
( )
t
i
I t
i
t
i
t
i
t
i
t
i
k d
2D
3D
k
4D
1D
ω− =ω =ω
ω=ω =ω
Eq. 11.3
During this interval, all four diodes are conducting and the resulting output voltage is 0V
(assuming ideal diodes). Correspondingly, a reduced value will occur as open circuit
voltage, which can be derivedas follows.
For the voltage across themains impedance:
( )
( )
dt
di
L t
sin U2 t
u
k
N
N
L
N
=ω ⋅
with u
d
(
ω
t) = 0V
Eq. 11.4
ay nowbe expandedwith
ω
and transposed to:
( ) ( )
( ) ( )
(
)
d
N
N
d N
N
I
I
k N
t
0
N
k N
N
I
V2
L 21u cos
I L 2 u cos 1 U2
di
L
t d t
sin U2
di
L t d t
sin U2
d
d
u
⋅ω⋅
−=
⋅ω⋅ =
− ⋅
⋅ω=ω ⋅ω ⋅
⋅ω=ω ⋅ω ⋅
Eq. 11.5
For the open circuit voltageU
d (B2)
therefore a value reduced by the commutation interval
will result:
( )
( )
( )
( )
d
N
N
u
0
N
0
N
u
N
2Bd
I L 2 U90.0
dt t
sin U2 1 dt t
sin U2 1
dt t
sin U2 1
U
π
⋅ω⋅
− ⋅
=
ω ⋅
π
− ω ⋅
π
=
ω ⋅
π
=
π
π
Eq. 11.6
For L
N
=0H
erges int
In the next step, the B2 rectifier is studied with the smoothing capacitor C
1
and a
resistive load. The capacitor can be taken as a voltage source. As a result, the diodes
D
1
and D
4
or D
3
and D
2
will only conduct when their voltage is above the capacitor
voltage. Accordingly, a distortion and phase shift
ϕ
occurs in the mains current.
hows a simulation of the voltage and current characteristics of a B2 bridge
rectifier.
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