Campbell Scientific CR7 Measurement and Control System - Manual (Page 131)

SECTION 13. CR7 MEASUREMENTS
13-7
EXAMPLE LEAD LENGTH CALCULATION
FOR CAMPBELL SCIENTIFIC 107
TEMPERATURE SENSOR
Assume a limit of 0.05oC over a 0oC to +40oC
range is established for the transient settling
error. This limit is a reasonable choice since it
approximates the linearization error over that
range. The output signal from the thermistor
bridge varies non-linearly with temperature
(refer to 107 Operator's Manual), ranging from
about 200 µV/oC at 0oC to 100 µV/oC at 40oC.
Taking the most conservative figure yields an
error limit of Ve = 5 µV. The other values
needed to calculate the maximum lead length
are summarized in Table 13.3-5 and listed
below:
1) Veo ≈ 100mV, peak transient at 4V excitation
2) Ve ≈ 5µV, allowable measurement error
3) t = 500µs, CR7 input settling time
4) Ro = 1kohm, 107 probe source resistance
5) Cf = 0.01nfd, CR7 input capacitance
6) Cw = 42pfd/ft., lead wire capacitance
Solving Equation 13.3-15 gives a maximum
lead length of:
L
≈ 965 ft., error ≈ 0.05oC
Setting the allowable error at 0.1oC or
approximately 10µV, the maximum lead length
increases to:
L
≈ 1050 ft., error ≈ 0.1oC
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, Veo, 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
lead length. If the capacitive load exceeds 0.1
ufd and the resistive load is negligible, Vx will
oscillate about it's control point. If the capacitive
load is 0.1 ufd or less, Vx will settle to within
0.1% of its correct value in 150µs. A lead
length of 2000 feet is permitted for the Model
227 before approaching the drive limitation.
TABLE 13.3-5. Summary of Input Settling Data for Campbell Scientific Resistive Sensors
Sensor Belden Ro Cw
τ*
Input
Model # Wire # (kohms) (pfd/ft.) (us) Range(mV) Vx(mV) Veo(mV)**
107 8641 1 42 52 15 4000 100
207(RH) 8771 1 41 51 150 3000 130
WVU-7 8723 1 62 72 15 4000 0
227 8641 0.1-1 42 5-52 500 500 0
237 8641 1 42 52 50 5000 125
024A 8771 0-5 41 1-255 500 1000 0-90
* Estimated time constants are for 1000 foot lead lengths and include 0.01nfd CR7 input capacitance.
** Measured peak transients for 1000 foot lead lengths at corresponding excitation, Vx.