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Equation
13,13-7
can be solved for the maximum
lead length,
l,
permitted
to maintain
a
specified
error
limit.
Qombining Equations 13.3-7 and
13.3-4 and splving
for
L
gives:
1-
=
-(RoC1+
(Vln(V"A/"o)))/RoC*
[13.3-15]
where
V"
is
the measurement error limit.
EXAMPLE
I-.]EAD
LENGTH
CALCU
LATION
FOR CAMPtsELL
SCIENTIFIC
107
TEMPERATURE SENSOR
Assume
a lirhit of
O.05oC
over
a
OoC
to
+40oC
range is est4blished for the transient settling
error. This
limit
is
a reasonable choice since
it
approximatep
the polynomial error over that
range.
The
putput signalfrom the thermistor
bridge varie$ nonlinearly with
temperature (refer
to
107
Operdtor's Manual), ranging from about
2oopvfc
atlo"c to l
oopvfc
at
4ooc.
Taking
the most corfservative figure yields an error limit
of V" =
5pV.
The other
values needed to
calculate
th(
maximum lead length are
summarized
in
Table 13.3-5 and listed below:
SECTION
13.
21X MEASUREMENTS
1)
Veo
=
100mV, peak transient at
4V
excitation
2)
V"
=
SltV,
allowable measurement error
3)
t =
4501rs,
21X input settling time
4)
Ro
=
1
kohm, 107 probe
source resistance
5)
Cr
= 3.3nfd,
21X input capacitance
6)
C*=
42pld/ft., lead wire capacitance
Solving Equation 13.3-15 gives a maximum
lead length
of:
L
= 1003 ft., error
=
0.O5oC
Setting the allowable error at
0.1oC
or
approximately
1OpV,
the maximum lead length
increases to:
L
= 1085 ft.. error
= 0.1oC
Input
Range(mV)
15
150
15
500
50
500
TABLE
Sensor
Model #
Ro
Cw
(kohms)
(pfd/ft.)
1
1
1
0.1-1
1
0-5
Vx(mV)
V"o(mV)**
4000
100
3000
130
4000
0
500
0
5000
125
1000
0-90
Summary of Input Settling Data For CampbellScientific Resistive Sensors
T,*
(us)
107
207(RH)
WVU-7
227
237
o24A
8641
8771
8723
8641
8641
8771
42
41
62
42
42
41
45
44
65
5-45
45
't-222
*
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*.
13.3.4 SUMMAFY
OF
SETTLING ERRORS FOR
SCIENTIFIC RESISTIVE
SENSORS
Table 13.3-$ summarizes the data required to
estimate
thQ
effect
of lead length on settling
errors
for
sensors.
the input
Scientif
ic's resistive
the
transient level,
V"o,
to
,
one suspects that
transient
errors are
the most likely limitation for the
107
sensor. Thd sensors
in
the
WVU-7 are the
same as
in
lhe
Model 107 (the lead
wire
is
different), bqt the signal leads for the WVU-7
wet and
dry'bulbs are not subject to excitation
transients because
they are shielded
independently
f
rom the excitation.
The comparatively
smalltransient yet large
source resistance
of
the 0244 sensor indicates
that
signal rise time may be the rnost 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
13-7
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