STMicroelectronics A 200 W ripple-free input current PFC pre-regulator with the L6563S EVL6563S-200ZRC EVL6563S-200ZRC Data Sheet
Product codes
EVL6563S-200ZRC
AN3180
Electrical equivalent circuit models of coupled inductors and transformers
Doc ID 17273 Rev 1
31/39
Figure 24.
Electrical equivalent circuit of coupled inductors
The branch-constitutive equations of the circuit are the following:
Equation 25
By comparing
it is possible to find the following relationships:
Equation 26
It is important to notice that the model (
) and the resulting relationships
(
) use four parameters (L
µ
, L
a
, L
b
, a), but equations (
) show that
three parameters only (L
1
, L
2
, M) are needed to completely define the two-port circuit. This
means that one of the four parameters in
) - a is the obvious choice - can be
arbitrarily fixed, therefore leading to an infinite number of models
(
) equivalent to
(
A good criterion for choosing a is that both L
a
and L
b
have a positive value: should they
result otherwise, the terminal equations would still be represented correctly but a negative
inductance does not make physical sense and leads to wrong results as far as energy
considerations are concerned.
inductance does not make physical sense and leads to wrong results as far as energy
considerations are concerned.
It is possible to show that, if a equals the secondary-to-primary turns ratio n=N
2
/N
1
, L
a
and
L
b
are always positive. Moreover, it is possible to prove that this choice leads to the same
model as the reluctance model approach; and so the model with a = n is the physical model
of a coupled inductor.
of a coupled inductor.
L
µ
is associated to the mutual flux that links the primary and secondary winding mostly
through the magnetic core, it is called primary magnetizing inductance and is designated by
L
L
M
; L
a
is associated to the flux generated by the primary winding and not completely linked
to itself or to the secondary winding, that is the primary leakage flux: L
a
is therefore called
primary leakage inductance and is designated by L
l1
. Similarly, on the secondary side the
!-V
L
W
L
W
0
/
/
Y
W
Y
W
L
L
W
W
D
Y
W
Y
W
/
/
D
/
E
LGHDO
L
W
Y
W
Y
W
L
W
L
W
(t)
(t)
dt
d
L
L
L
L
L
L
(t)
(t)
b
2
a
2
1
2
1
i
i
v
v
+
+
=
μ
μ
μ
μ
a
a
a
⎪
⎪
⎪
⎩
⎪⎪
⎪
⎨
⎧
⎪
⎪
⎪
⎩
⎪⎪
⎪
⎨
⎧
−
=
=
−
=
⇒
−
=
=
−
=
⇒
⎪
⎩
⎪
⎨
⎧
+
=
=
+
=
μ
μ
μ
μ
μ
μ
μ
M
L
L
M
L
M
L
L
L
L
L
M
L
L
L
L
L
L
L
L
M
L
L
L
2
b
1
a
2
2
b
1
a
b
2
2
a
1
a
a
a
a
a
a
a