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

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 ⋅

⋅

=ω

with u

d

(

ω

t) = 0V

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 ⋅

⋅

∫

∫

−

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

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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