Campbell Scientific CR23X Micrologger - Manual (Page 205)

SECTION 13. CR23X MEASUREMENTS
13-5
For the rising case, V
s
= V
so
-V
e
, whereas for
the decaying transient, V
s
= V
so
+V
e
.
Substituting these relationships for V
s
in
Equations 13.3-1 and 13.3-2, respectively,
yields expressions in V
e
, the input settling error:
V
e
= V
so
e-t/R o C T , rise [13.3-6]
V
e
= V
e'o
e-t/R o C T , decay [13.3-7]
Where V
e'o
= V
eo
-V
so
, the difference between
the peak transient voltage and the true signal
voltage.
NOTE: Since the peak transient, V
eo
,
causes significant error only if it is several
times larger than the signal, V
so
, error
calculations made in this section
approximate V
e'o
by V
eo
; i.e., V
eo
= V
eo
-V
so
.
If the input settling time constant,
τ
, is known, a
quick estimation of the settling error as a
percentage of the maximum error (V
so
for
rising, V
e'o
for decaying) is obtained by knowing
how many time constants (t/
τ
) are contained in
the 450 µs CR23X input settling interval (t).
The familiar exponential decay relationship is
given in Table 13.3-1 for reference.
TABLE 13.3-1. Exponential Decay, Percent
of Maximum Error vs. Time in Units of
τ
Time % Time %
Constants Max. Error Constants Max. Error
0 100.0 5 0.7
1 36.8 7 0.1
3 5.0 10 0.004
Before proceeding with examples of the effect
of long lead lengths on the measurement, a
discussion on obtaining the source resistance,
R
o
, and lead capacitance, C
w
L, is necessary.
CR23X
FIGURE 13.3-2. Typical Resistive Half Bridge
CR23X
HI OR LO
INPUT
FIGURE 13.3-3. Source Resistance Model for Half Bridge Connected to the CR23X