STMicroelectronics A 200 W ripple-free input current PFC pre-regulator with the L6563S EVL6563S-200ZRC EVL6563S-200ZRC Data Sheet
Product codes
EVL6563S-200ZRC
Sensitivity of zero-ripple current condition
AN3180
10/39
Doc ID 17273 Rev 1
3
Sensitivity of zero-ripple current condition
In real-world coupled inductors it is unthinkable to reduce the ripple current in a winding to
exactly zero and produce a perfect ripple steering. There are two basic reasons for this:
exactly zero and produce a perfect ripple steering. There are two basic reasons for this:
●
Zero-ripple condition mismatch. In practice, the inductance of a winding is determined
by the number of turns and the average permeability of the associated magnetic circuit.
The turn ratio can assume only discrete values (ratio of two integer numbers) and it is
difficult to control the average permeability to achieve the exact value that allows the
meeting of the condition in
by the number of turns and the average permeability of the associated magnetic circuit.
The turn ratio can assume only discrete values (ratio of two integer numbers) and it is
difficult to control the average permeability to achieve the exact value that allows the
meeting of the condition in
or any equivalent (
). Even if this may
be obtained in occasional samples, manufacturing tolerances cause the actual value to
deviate from the target in mass production
deviate from the target in mass production
●
Impressed voltage mismatch. In real operation, there are several factors that cause the
two windings to be excited by voltages that are not exactly equal to one another, such
as the voltage drop across the winding resistance (neglected so far), or the mere
inability of the external circuit to do so. For example, in the smoothing transformer, the
finite capacitance value of CS and its ESR cause an impressed voltage mismatch even
in the case of ideal windings. To evaluate the residual ripple current it is convenient to
use the a = k n
two windings to be excited by voltages that are not exactly equal to one another, such
as the voltage drop across the winding resistance (neglected so far), or the mere
inability of the external circuit to do so. For example, in the smoothing transformer, the
finite capacitance value of CS and its ESR cause an impressed voltage mismatch even
in the case of ideal windings. To evaluate the residual ripple current it is convenient to
use the a = k n
e
, already used
(
) for deriving the zero-
ripple current condition. Based on that, it is possible to write:
Equation 8
which, after a simple algebraic manipulation, can be re-written as:
Equation 9
Although the inductance of the DC winding is theoretically irrelevant to the phenomenon
itself (the inductance could even be zero),
itself (the inductance could even be zero),
show that this inductance is
significant in practice, because it determines the actual residual ripple current resulting from
the unavoidable aforementioned mismatches. More precisely, these equations highlight the
need for a high-leakage magnetic structure, so that a low coupling coefficient k maximizes
the “residual” inductance L
the unavoidable aforementioned mismatches. More precisely, these equations highlight the
need for a high-leakage magnetic structure, so that a low coupling coefficient k maximizes
the “residual” inductance L
2
(1-k
2
).
Note that a low value for k also means that the value of n
e
that meets the zero-ripple
condition is higher: for a given primary inductance L
1
, this implies a higher value of L
2
, and
so further contributing to keeping the ripple low.
With the aim of assessing the amount of ripple attenuation in case of a non-ideal
cancellation, considering an assigned value for L
cancellation, considering an assigned value for L
1
is an important practical constraint. As
previously stated, the inductor ripple current on the cancellation winding is just determined
by its inductance L
by its inductance L
1
and this ripple is seen by the power switch of the converter. This means
that, if L
1
is unchanged, the converter circuit still operates exactly under the same conditions
even with the use of the additional coupled inductor.
(
)
2
2
k
1
L
)
t
(
k
)
t
(
dt
)
t
(
d
−
−
=
1
2
2
v
v
i
e
n
(
)
(
)
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
+
−
−
=
4
4 3
4
4 2
1
43
42
1
mismatch
condition
ripple
Zero
mismatch
voltage
pressed
Im
2
2
)
t
(
k
1
)
t
(
)
t
(
k
1
L
1
dt
)
t
(
d
1
1
2
2
v
v
v
i
e
n