STMicroelectronics A 200 W ripple-free input current PFC pre-regulator with the L6563S EVL6563S-200ZRC EVL6563S-200ZRC Data Sheet
Product codes
EVL6563S-200ZRC
Zero-ripple current phenomenon: theory
AN3180
6/39
Doc ID 17273 Rev 1
2
Zero-ripple current phenomenon: theory
Zero-ripple current in one of a two-winding coupled inductor, having self-inductances L1 and
L2, can be achieved if the coupling coefficient k, given by:
L2, can be achieved if the coupling coefficient k, given by:
Equation 1
(M is their mutual inductance), and the effective turns ratio n
e
defined as:
Equation 2
is such that either k n
e
= 1 or k = n
e
, provided the windings are fed by the same voltage.
To confirm this, it is convenient to consider the a = k n
e
coupled-inductor model (refer to
) with the terminals excited by proportional voltages v(t) and
αv(t) having the
same frequency and phase, shown in
. This is the only condition to be imposed on
the terminal voltages, their actual waveform is irrelevant.
Figure 4.
Coupled inductor a = k n
e
model under zero-ripple current conditions
shows that, in order for the secondary ripple current (i.e. di
2
(t)/dt) to be zero, the
voltage across the inductance L
2
(1-k
2
) must be zero, that is, the voltage on either side of it
must be the same. Thereby:
Equation 3
2
1
L
L
M
k
=
1
2
L
L
=
e
n
!-V
L
W
L
W
Y W
/
LGHDO
N Q
H
/
N
DY W
DY W
α
=
⇒
α
=
e
e
n
v
v
n
k
)
t
(
)
t
(
k