Campbell Scientific CR510 Basic Datalogger - Manual (Page 148)

SECTION 13. CR510 MEASUREMENTS
13-4
FIGURE 13.3-1. Input Voltage Rise and Transient Decay
13.3.1 THE INPUT SETTLING TIME CONSTANT
The rate at which an input voltage rises to its full
value or that a transient decays to the correct
input level are both determined by the input
settling time constant. In both cases the
waveform is an exponential. Figure 13.3-1
shows both a rising and decaying waveform
settling to the signal level, Vso. The rising input
voltage is described by Equation 13.3-1 and the
decaying input voltage by Equation 13.3-2.
V
s
= V
so
(1-e-t/R o C T ), rise [13.3-1]
V
s
= V
so
+ (V
eo
-V
so
) e-t/R o C T , decay [13.3-2]
where V
s
is the input voltage, V
so
the true signal
voltage, V
eo
the peak transient voltage, t is time
in seconds, R
o
the source resistance in ohms,
and C
T
is the total capacitance between the
signal lead and ground (or some other fixed
reference value) in farads.
The settling time constant,
τ
in seconds, and the
capacitance relationships are given in
Equations 13.3-3 through 13.3-5,
τ
= R
o
C
T
[13.3-3]
C
T
= C
f
+ C
w
L [13.3-4]
C
f
= 3.3 nfd [13.3-5]
where C
f
is the fixed CR510 input capacitance
in farads, C
w
is the wire capacitance in
farads/foot, and L is the wire length in feet.
Equations 13.3-1 and 13.3-2 can be used to
estimate the input settling error, V
e
, directly.
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 CR510 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.