STMicroelectronics A 200 W ripple-free input current PFC pre-regulator with the L6563S EVL6563S-200ZRC EVL6563S-200ZRC Fiche De Données

   

   

   

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 Doc ID 17273 Rev 1

The mutual inductance M cannot be assigned arbitrarily but must fulfill the inequality:

The case 

 is that of perfectly coupled inductors, that is when the magnetic flux 

generated by either winding is totally linked to the other. However, in real-world systems 
there is always some flux linking one winding but not the other or not completely linking the 
winding itself, e.g. because it “leaks” into the surrounding air; and so it is possible to write:

k, which lies in the range -1 k 1 is the so-called coupling coefficient and is a measure of the 
degree of magnetic coupling between the windings. For simplicity, from now on winding 
polarity is neglected and assume M>0 (and 0 k 1) always, the extension to the case M<0 
being obvious.

It is possible to prove that k is the geometric mean of the portion k1 of flux generated by the 
first winding that links the second one, and the portion k2 of flux generated by the second 
winding that links the first one:

Note that, in general, k

1

 

≠ k

2

: fluxes do not necessarily link windings symmetrically one to 

another.

It is often useful to represent a system of coupled inductors with an equivalent circuit 
including an ideal transformer, that is a circuit element with a transfer function v

2

'(t) / v

1

'(t)=a 

for voltages and i

2

'(t) / i

1

'(t)= 1/a for currents. This equivalent circuit is shown in 

.

!-V

2

1

L

L

M

≤

2

1

L

L

M

=

2

1

L

L

k

M

=

2

1

k

k

k

=