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
Zero-ripple current phenomenon: theory
Doc ID 17273 Rev 1
7/39
Figure 5.
Coupled inductor a = n
e
/k model under zero-ripple current conditions
Similarly, considering the model of
, again excited by proportional voltages v(t) and
αv(t), it is equally apparent that, in order for the primary ripple current to be zero the voltage
across the inductance L
across the inductance L
1
(1-k
2
) must be zero, that is, the voltage on either side of it must be
the same:
Equation 4
α=1, which means that equal voltages are impressed on either side of
the coupled inductor, we find the above mentioned assertion. As
α=1 is the most common
condition found in switching converters, from now on this is the only case that is taken into
consideration, therefore:
consideration, therefore:
●
condition for zero-ripple secondary current
●
condition for zero-ripple primary current
Note that, as k < 1, to obtain a zero-ripple secondary current it must be n
e
> 1, that is L
2
>
L
1
, while to obtain a zero-ripple primary current it must be n
e
< 1, that is L
1
> L
2
; and so
ripple current cannot be reduced to zero in both windings simultaneously. In
and
note also that the inductance of the winding, where zero-ripple current is achieved, is
irrelevant, since there is no ripple current flowing (only DC current can flow). As a
consequence, the zero-ripple current winding reflects an open circuit to the other one, so
that the inductance seen at the terminals of that winding equals exactly its self-inductance.
irrelevant, since there is no ripple current flowing (only DC current can flow). As a
consequence, the zero-ripple current winding reflects an open circuit to the other one, so
that the inductance seen at the terminals of that winding equals exactly its self-inductance.
The designation of which winding is the primary or the secondary is purely conventional.
Therefore, we consider only one zero-ripple current condition and arbitrarily assume the
condition to be assigned to the secondary winding:
Therefore, we consider only one zero-ripple current condition and arbitrarily assume the
condition to be assigned to the secondary winding:
Equation 5
which, consistent with the terminology used for the smoothing transformer of
termed DC winding, while the primary winding is termed AC or cancellation winding.
, considering
and
can be written in different equivalent ways:
!-V
/
N
L
W
Y W
N /
L
W
LGHDO
Q
H
N
D
Y W
D
Y W
N
Q
H
e
e
e
n
n
v
n
v
=
α
⇒
=
α
⇒
α
=
k
1
k
)
t
(
k
)
t
(
1
k
=
e
n
e
n
=
k
1
k
=
e
n