PXD10 Datasheet, PDF (99/130 Pages) Lumins Inc. – 4” Dia.X 6” extruded aluminum step poles

Electrical characteristics
source V_A; the time constant R_FC_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.
Analog source bandwidth (V_A)
Noise
f₀
f
Anti-aliasing filter (f_F = RC filter pole)
T_C 2 R_FC_F (conversion rate vs. filter pole)
f_F  f₀ (anti-aliasing filtering condition)
2 f₀ f_C (Nyquist)
Sampled signal spectrum (f_C = conversion rate)
f_F
f
f₀
f_C
f
Figure 21. Spectral representation of input signal
Calling f₀ the bandwidth of the source signal (and as a consequence the cut-off frequency of the
anti-aliasing filter, f_F), according to the Nyquist theorem the conversion rate f_C must be at least 2f₀; 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_FC_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.
The considerations above lead to impose new constraints on the external circuit, to reduce the accuracy
error due to the voltage drop on C_S; from the two charge balance equations above, it is simple to derive
Equation 14 between the ideal and real sampled voltage on C_S:
--V-----A---- = --------C----P---1-----+-----C----P----2----+-----C----F---------
VA2 CP1 + CP2 + CF + CS
Eqn. 14
From this formula, in the worst case (when V_A is maximum, that is for instance 5V), assuming to accept a
maximum error of half a count, a constraint is evident on C_F value:
CF  2048  CS
Eqn. 15
PXD10 Microcontroller Data Sheet, Rev. 1
Freescale Semiconductor
99