STMicroelectronics A 200 W ripple-free input current PFC pre-regulator with the L6563S EVL6563S-200ZRC EVL6563S-200ZRC Data Sheet

Product codes
EVL6563S-200ZRC
Page of 39
   
   
   
Electrical equivalent circuit models of coupled inductors and transformers
AN3180
34/39
 Doc ID 17273 Rev 1
Figure 28.
Model of coupled inductors with a = k n
e
 (a = k n
e
 model)
Other possible choices of a are a = M/L
1
 = k n
e
, which nulls L
a
 and puts all the elements 
related (logically, not physically) to the leakage flux on the secondary side (see
 
and a = L
2
 /M = n
e
/k, which nulls L
b
 and puts all the elements related to the leakage flux on 
the primary side (see 
From inspection of 
 and 
 it is apparent that the quantity L
2
 (1-k
2
) is the 
inductance of the secondary winding measured with a shorted primary winding and that L
1
 
(1-k
2
) is the inductance of the primary winding with the secondary shorted out.
Figure 29.
Model of coupled inductors with a = n
e
/k (a = n
e
/k model)
The usefulness of having different models available, dependent on the value attributed to a, 
is that it is possible to choose the one that best fits the specific problem under consideration, 
leading to a simpler solution or minimum mathematical manipulations.
An important assumption underlying the modeling techniques so far described, is that the 
behavior of the magnetic circuit, represented by an equivalent linear electric circuit, is also 
linear; that is, the magnetic flux is proportional to the magneto-motive forces that excite the 
windings. This is true only if the flux density inside the core is well below the saturation limit 
of the material.
The models can give useful information also on what happens in case the magnetic core 
saturates. With reference to the “physical model” of 
, the leakage inductances L
l1
 
and L
l2
 are relevant to magnetic flux that is located mostly in air and so they do not saturate 
and their value can be considered constant; the non linear element of the circuit is L
M
, which 
!-V
L

W
L

W
Y

W
Y

W
/

LGHDO
Q
H
/

N 

!-V
/

N 

L

W
L

W
Y

W
Y

W
LGHDO
/


 Q
H
N