PXD20 Datasheet, PDF (94/130 Pages) Freescale Semiconductor, Inc – PXD20 Microcontroller

Electrical characteristics
₁  RSW + RAD  CS « TS
Eqn. 7
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 Equation 8:
VA1  CS + CP1 + CP2 = VA  CP1 + CP2
Eqn. 8
• A second charge transfer involves also C_F (that is typically bigger than the on-chip capacitance) 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:
₂  RL  CS + CP1 + CP2
Eqn. 9
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:
10  ₂ = 10  RL  CS + CP1 + CP2  TS
Eqn. 10
Of course, R_L shall 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. Equation 11 must be respected (charge
balance assuming now C_S already charged at V_A1):
VA2  CS + CP1 + CP2 + CF = VA CF + VA1 CP1 + CP2 + CS
Eqn. 11
The two transients above are not influenced by the voltage source that, due to the presence of the R_FC_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_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
T_C 2 R_FC_F (Conversion Rate vs. Filter Pole)
f_F  f₀ (Anti-aliasing Filtering Condition)
2 f₀ f_C (Nyquist)
f₀
f
Anti-Aliasing Filter (f_F = RC Filter pole)
Sampled Signal Spectrum (f_C = conversion Rate)
f_F
f
f₀
f_C
f
Figure 17. Spectral representation of input signal
PXD20 Microcontroller Data Sheet, Rev. 2
94
Preliminary—Subject to Change Without Notice
Freescale Semiconductor