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SECTION
13.
21X MEASUREMENTS
NOTE:
Since
the peak transient,
V"o,
causes significant error only if it
is
several
times larger than the signal,
V"o,
error
calculations made
in
this section
approximate
V'"o by V"o;
i.e.,
V'"o
=
V"o.
lf
the input settling time constant,
t,
is known,
a
quick estimation of the settling error as
a
percentage
of
the maximum error
(V.o
for rising,
V'"o
for decaying)
is
obtained by knowing how
many time
constants (Vt) are contained
in
the
450ps
21X 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
t
Time
o/o
Time
o/o
Constants
Max.
Error Constants
Max.
Error
0
100.0
5
0.7
1
36.8
7
0.'l
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,
Ro,
and lead capacitance,
C*L, is necessary.
DETERMINING SOURCE RESISTANCE
The
source resistance used to estimate the
settling time
constant
is
the resistance the 21X
input "sees" looking out
at
the
sensor.
For
our
purposes the
source resistance can
be
defined
as
the resistance from the 21X input through
all
external paths back to the
21X.
Figure 13.3-2
shows
a
typical resistive sensor, (e.9.,
a
thermistor) configured as
a half
bridge.
Figure
13.3-3
shows Figure 13.3-2 redrawn
in
terms of
the resistive paths determining the source
resistance Ro, is given
by
the parallel
resistance of Rs
and Rf, as shown in Equation
13.3-8.
F|GURE
13.3-2. Typical Resistive Half Bridge
13-4
.21X
HI
OR
LO
INPUT
FIGURE
13.3-3. Source Resistance Model
for
Half
Bridge Connected to the
21X
Ro
=
Fl.Rr/(R'+Rr)
[13.3-8]
lf
Rl
is much smaller,
equalto or
much greater
than R., the source resistance can
be
approximated
by Equations 13.3-9 through
1
3.3-1
1, respectively.
Ro
=
Rf,
RF<R,
Ro
=
R/2,
Rr=R,
Ro
= R., Rt>>B,
[13.3-e]
[13.3-10]
[13.3-1
1]
The
source resistance for several Campbell
Scientific sensors are given in column 3
of
Table 13.3-5.
DETERMINING LEAD CAPACITANCE
Wire manufacturers typically provide two
capacitance
specifications:
1)
the capacitance
between the
two leads with the shield floating,
and
2)
the
capacitance between the two leads
with the shield tied to
one
lead.
Since
the input
lead and
the shield are tied to ground
(often
through
a bridge resistor,
R)
in single-ended
measurements such
as Figure 13.3-2, the
second specification is used
in
determining
lead
capacitance. Figure 13.3-4
is
a representation
of
this capacitance, Cn, usually specified as
pfd/ft. C*
is actually
the sum
of
capacitance
between the two conductors and
the
capacitance between the top conductor and the
shield.
Capacitance for
3 Belden lead wires
used
in
Campbell Scientific sensors
is
shown
in
column
6
of
Table
13.3-2.
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