STMicroelectronics A 200 W ripple-free input current PFC pre-regulator with the L6563S EVL6563S-200ZRC EVL6563S-200ZRC Fiche De Données
Codes de produits
EVL6563S-200ZRC
AN3180
Sensitivity of zero-ripple current condition
Doc ID 17273 Rev 1
11/39
If the attenuation A is defined as the ratio of the residual ripple di
2
, to the ripple that would be there without the coupled inductor (di
1
(t)/dt =v
1
(t)/L
1
, equal
to the actual ripple on the cancellation winding, as L
1
is unchanged), it is possible to write for
the worst case scenario:
Equation 10
where
Δv(t) = v
2
(t)-v
1
(t) is the absolute voltage mismatch,
δ = k n
e
- 1 is the zero-ripple
condition mismatch (absolute and relative values coincide) and the factor
ρ is given by:
Equation 11
In
the attenuation A is plotted for different values of the relative voltage mismatch
Δv(t)/v
1
(t) and of the coupling coefficient k, as a function of the zero-ripple condition. From
the inspection of these plots, it is apparent that a low coupling coefficient is essential for a
good attenuation even if the zero-ripple condition is not exactly met. To achieve attenuations
always greater than 10-12 dB even with a tolerance of ±10 % on the value of
good attenuation even if the zero-ripple condition is not exactly met. To achieve attenuations
always greater than 10-12 dB even with a tolerance of ±10 % on the value of
δ and 10 %
voltage mismatch, the coupling coefficient k must be around 0.7. Lower k values would lead
to a higher insensitivity of the zero-ripple condition due to mismatches but lead to more
turns for the DC winding, which could become an issue in terms of inductor construction.
to a higher insensitivity of the zero-ripple condition due to mismatches but lead to more
turns for the DC winding, which could become an issue in terms of inductor construction.
Note that in case of under-compensation (
δ<0) the residual ripple can be higher than the
original value: this is due to a too low value of the “residual” inductance L
2
(1-k
2
).
, where the voltage
externally applied to the AC winding is affected by the voltage ripple on the capacitor C
S
(due to its finite capacitance value as well as its ESR), the voltage mismatch
Δv(t)/v
1
(t) and,
as a result, also the attenuation A, become frequency-dependent. Magnetic flux distribution
modifications with frequency, which also affect
modifications with frequency, which also affect
δ, are a second-order effect and are
neglected.
and
provide a complete analysis of the smoothing transformer frequency
behavior. Here it is convenient only to summarize the results:
1.
The smoothing transformer is capable of a third-order attenuation of current ripple, i.e.
it is equivalent to an inductor combined with an additional LC filter
it is equivalent to an inductor combined with an additional LC filter
2.
The transfer function generally includes three poles and two zeros; if the zero-ripple
condition is fulfilled (
condition is fulfilled (
δ=0), the two zeros go to infinity and the smoothing transformer
becomes a third-order all-pole filter
3.
Modeling winding resistance and capacitor ESR produces a little damping of the pole-
zero resonances but do not significantly affect the imaginary component of their
locations
zero resonances but do not significantly affect the imaginary component of their
locations
4.
The effect of the zero-ripple condition mismatch (
δ≠0) is to move the zero pair towards
the poles, therefore creating some “notch” frequencies where greater attenuation is
achieved, but degrading the overall attenuation produced at higher frequencies
achieved, but degrading the overall attenuation produced at higher frequencies
⎟
⎟
⎠
⎠
⎞
⎜
⎜
⎝
⎝
⎛
δ
+
Δ
ρ
=
=
=
)
t
(
dt
)
t
(
d
)
t
(
L
dt
)
t
(
d
dt
)
t
(
d
1
1
2
1
1
2
v
v(t)
i
v
i
i
A
(
)
2
2
2
k
1
k
1
1
−
δ
+
=
ρ