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SIMPLIFIED ANALOG INPUT ANALYSIS
V
C
= V
S
1−e
−t
c
/R
t
C
i
( )
where
R
t
= R
s
+ r
i
(1)
V
C
(1/2 LSB) = V
S
− (V
S
/2048)
(2)
V
S
−(V
S
/2048) = V
S
1−e
( )
−t
c
/R
t
C
i
and
t
c
(1/2 LSB) = R
t
× C
i
× ln(2048)
(3)
t
c
(1/2 LSB) = (R
s
+ 1 kΩ) × 60 pF × ln(2048)
(4)
R
s
r
i
V
S
V
C
1 kΩ MAX
Driving Source
†
TLC1542/3
C
i
50 pF MAX
V
I
V
I
= Input Voltage at A0−A10
V
S
= External Driving Source Voltage
R
s
= Source Resistance
r
i
= Input Resistance
C
i
= Equivalent Input Capacitance
†
Driving source requirements:
• Noise and distortion for the source must be equivalent to the
resolution of the converter.
• R
s
must be real at the input frequency.
TLC1542I , , TLC1542M , , TLC1542Q
TLC1542C , TLC1543C , TLC1543I , TLC1543Q
SLAS052G – MARCH 1992 – REVISED JANUARY 2006
APPLICATION INFORMATION (continued)
Using the equivalent circuit in Figure 17 Figure 17, the time required to charge the analog input capacitance from
0 to V
S
within 1/2 LSB can be derived as follows:
The capacitance charging voltage is given by
The final voltage to 1/2 LSB is given by
Equating equation 1 to equation 2 and solving for time t
c
gives
Therefore, with the values given the time for the analog input signal to settle is
This time must be less than the converter sample time shown in the timing diagrams.
Figure 17. Equivalent Input Circuit Including the Driving Source
19
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