Datasheet

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 Figure 5, 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
1
(1-k
2
) must be zero, that is, the voltage on either side of it must be
the same:
Equation 4
If in Equation 3 and 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:
● 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
Figure 4 and 5,
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.
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:
Equation 5
which, consistent with the terminology used for the smoothing transformer of Figure 3, is
termed DC winding, while the primary winding is termed AC or cancellation winding.
Equation 5, considering Equation 1 and 2 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
ee
n
n
v
n
v =α⇒=α⇒α= k1
k
)t(
k
)t(
1k =
e
n
e
n=k
1k
=
e
n