Operator`s manual

SECTION 13. 21X MEASUREMENTS
13-7
Equation 13.3-7 can be solved for the maximum
lead length, L, permitted to maintain a specified
error limit. Combining Equations 13.3-7 and
13.3-4 and solving for L gives:
L = -(R
o
C
f
+ (t/ln(V
e
/V
eo
)))/R
o
C
w
[13.3-15]
where V
e
is the measurement error limit.
EXAMPLE LEAD LENGTH CALCULATION
FOR CAMPBELL SCIENTIFIC 107
TEMPERATURE SENSOR
Assume a limit of 0.05
o
C over a 0
o
C to +40
o
C
range is established for the transient settling
error. This limit is a reasonable choice since it
approximates the polynomial error over that
range. The output signal from the thermistor
bridge varies nonlinearly with temperature (refer
to 107 Operator's Manual), ranging from about
200µV/
o
C at 0
o
C to 100µV/
o
C at 40
o
C. Taking
the most conservative figure yields an error limit
of V
e
= 5µV. The other values needed to
calculate the maximum lead length are
summarized in Table 13.3-5 and listed below:
1) V
eo
≈ 100mV, peak transient at 4V
excitation
2) V
e
≈ 5µV, allowable measurement error
3) t = 450µs, 21X input settling time
4) R
o
= 1kohm, 107 probe source resistance
5) C
f
= 3.3nfd, 21X input capacitance
6) C
w
= 42pfd/ft., lead wire capacitance
Solving Equation 13.3-15 gives a maximum
lead length of:
L ≈ 1003 ft., error ≈ 0.05
o
C
Setting the allowable error at 0.1
o
C or
approximately 10µV, the maximum lead length
increases to:
L ≈ 1085 ft., error ≈ 0.1
o
C
TABLE 13.3-5. Summary of Input Settling Data For Campbell Scientific Resistive Sensors
Sensor Belden Ro Cw τ
ττ
τ* Input
Model # Wire # (kohms) (pfd/ft.) (us) Range(mV) Vx(mV) V
eo
(mV)**
107 8641 1 42 45 15 4000 100
207(RH) 8771 1 41 44 150 3000 130
WVU-7 8723 1 62 65 15 4000 0
227 8641 0.1-1 42 5-45 500 500 0
237 8641 1 42 45 50 5000 125
024A 8771 0-5 41 1-222 500 1000 0-90
* Estimated time constants are for 1000 foot lead lengths and include 3.3nfd 21X input capacitance.
** Measured peak transients for 1000 foot lead lengths at corresponding excitation, V
x
.
13.3.4 SUMMARY OF SETTLING ERRORS FOR
CAMPBELL SCIENTIFIC RESISTIVE
SENSORS
Table 13.3-5 summarizes the data required to
estimate the effect of lead length on settling
errors for Campbell Scientific's resistive
sensors. Comparing the transient level, V
eo
, to
the input range, one suspects that transient
errors are the most likely limitation for the 107
sensor. The sensors in the WVU-7 are the
same as in the Model 107 (the lead wire is
different), but the signal leads for the WVU-7
wet and dry-bulbs are not subject to excitation
transients because they are shielded
independently from the excitation.
The comparatively small transient yet large
source resistance of the 024A sensor indicates
that signal rise time may be the most important
limitation. The analysis in Section 13.3.2
confirms this.
The Model 227 Soil Moisture Block has a
relatively short time constant and essentially no
transient. Lead lengths in excess of 2000 feet
produce less than a 0.1 bar (0-10 bar range)
input settling error. With this sensor, the drive
capability of the excitation channel limits the