STMicroelectronics A 200 W ripple-free input current PFC pre-regulator with the L6563S EVL6563S-200ZRC EVL6563S-200ZRC Data Sheet
Product codes
EVL6563S-200ZRC
Electrical equivalent circuit models of coupled inductors and transformers
AN3180
32/39
Doc ID 17273 Rev 1
inductance L
b
is associated to the secondary leakage flux, the flux generated by the
secondary winding and not completely linked to itself nor to the primary winding: it is called
secondary leakage inductance and is designated by L
secondary leakage inductance and is designated by L
l2
.
This choice of a is perhaps the most logical one, and is also very useful because it provides
a clear physical meaning to each element of the equivalent circuit, shown in
a clear physical meaning to each element of the equivalent circuit, shown in
, but it
is not the only one that makes sense.
Figure 25.
Model of coupled inductors with a = n (a=n model)
Another possible choice, which leads to always positive values for L
a
and L
b
, is a =
.
This quantity, usually indicated with n
e
, is termed “equivalent turn ratio” and is conceptually
and numerically different from the physical turn ratio n:
Equation 27
which coincides with n if and only if L
l2
= n
2
L
l1
, that is in case of symmetrical magnetic
coupling (k
1
= k
2
= k).
This choice is particularly useful when the physical turn ratio n is unknown, so that it is
possible to complete the model computing n
possible to complete the model computing n
e
from L
1
and L
2
, which are easily measurable.
In this case,
, considering
, takes the form:
Equation 28
It is worth noting that L
b
, reflected back to the primary side, equals L
a
, as pointed out by the
third
. Note that this property is often erroneously attributed to the primary and
secondary leakage inductances L
l1
and L
l2
. It is worth stating once more that k represents
an average coupling between the windings and that the coupling k
1
of the primary winding
to the secondary one is generally different from the coupling k
2
of the secondary winding to
the primary one, and so L
l2
≠ n2 L
l1
. It is L
l2
= n2 L
l1
only in the special case of a winding
geometry symmetrical in such a way that the reluctance of the leakage flux path is the same
for both windings, resulting in symmetrical coupling between windings (k
for both windings, resulting in symmetrical coupling between windings (k
1
= k
2
= k).
!-V
L
W
L
W
Q
Y
W
Y
W
/
0
/
O
/
O
L
0
W
LGHDO
L
2
L
1
⁄
M
1
M
2
2
1
2
L
L
L
L
L
L
+
+
=
=
l
l
n
n
e
(
)
(
)
⎪
⎩
⎪
⎨
⎧
=
−
=
=
−
=
μ
a
2
2
b
1
1
a
L
L
k
1
L
L
k
L
L
k
1
L
e
n