Analog / digital converter UM0404
388/564 DocID13284 Rev 2
designed to be robust also in the very worst case: the sampling time T
S
is always much
longer than the internal time constant:
• The charge of C
P1
and C
P2
is redistributed also on C
S
, determining a new value of the
voltage V
A1
on the capacitance according to the following equation:
• A second charge transfer involves also C
F
(that is typically bigger than the on-chip
capacitances) through the resistance R
L
: again considering the worst case in which
C
P2
and C
S
were in parallel to C
P1
(since the time constant in reality would be faster),
the time constant is:
• In this case, the time constant depends on the external circuit: in particular imposing
that the transient is completed well before the end of sampling time T
S
, a constraints on
R
L
sizing is obtained:
• Of course, R
L
should be sized also according to the current limitation constraints, in
combination with R
S
(source impedance) and R
F
(filter resistance). Being C
F
definitively bigger than C
P1
, C
P2
and C
S
, then the final voltage V
A2
(at the end of the
charge transfer transient) will be much higher than V
A1
. The following equation must be
respected (charge balance assuming now C
S
already charged at V
A1
):
The two transients above are not influenced by the voltage source that, due to the presence
of the R
F
C
F
filter, is not able to provide the extra charge to compensate the voltage drop on
C
S
with respect to the ideal source V
A
; the time constant R
F
C
F
of the filter is very high with
respect to the sampling time (T
S
). The filter is typically designed to act as anti-aliasing (see
Figure 167).
Calling f
0
the bandwidth of the source signal (and as a consequence the cut-off frequency of
the anti-aliasing filter, f
F
), according to Nyquist theorem the conversion rate f
C
must be at
least 2f
0
; it means that the constant time of the filter is greater than or at least equal to twice
the conversion period (T
C
). Again the conversion period T
C
is longer than the sampling time
T
S
, which is just a portion of it, even when fixed channel continuous conversion mode is
selected (fastest conversion rate at a specific channel): in conclusion it is evident that the
time constant of the filter R
F
C
F
is definitively much higher than the sampling time T
S
, so the
charge level on C
S
cannot be modified by the analog signal source during the time in which
the sampling switch is closed.
V
A1
C
S
C
P1
C
P2
++()⋅ V
A
C
P1
C
P2
+()⋅=
10 τ
2
⋅ 10 R⋅
L
= C
S
C
P1
C
P2
++()
T
S
≤⋅
V
A2
C
S
C
P1
C
P2
C
F
+++()⋅ V
A
C
F
⋅ V
A1
+ C
P1
C
P2
+C
S
+()⋅=
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