AN441

Doc ID 3579 Rev 3

13/16

Appendix A

The winding is supplied by an alternating mains voltage “u(t)” given by Equation 5.

Equation 5

According to the laws of Lenz and Faraday, we have Equation 6, Equation 7 and Equation 8.

Equation 6

With:

●

●

B = Induction

●

N = spires number (spires number of the primary for a transformer)

●

S = section area for magnetic material

Then, induction versus time is:

Equation 7

Equation 8

We consider the case where the Triac is first triggered at mains zero voltage.

We can distinguish two cases:

Case 1

Winding is switched on whereas a remanent positive induction remains on magnetic core.

According to Equation 8, for t = 0, we have:

Equation 9

So

Equation 10

·t)

·sin(

ù

2

U

u(t)

=

dt

dB

N·S

dt

d

Ö

N

u(t)

=

=

)dt

·t

sin(

N.S

2

U

B(t)

=

N·S·

ù

2

U

B

with

0

B

)

2

ð

t

·sin(

ù

n

B

B(t)

+

−

=

r

n

0

r

0

n

B

B

B

B

B

B

B(0)

+

=

→

=

+

−

=

r

B

n

B

)

2

ð

t

·sin(

ù

n

B

B(t)

+

+

−

=

⇒