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SECTION 13. CR510 MEASUREMENTS
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.
(1-e -t/R
C
o
V
= V
s
so
V
= V
+ (V
-V
s
so
eo
so
where V
is the input voltage, V
s
voltage, V
the peak transient voltage, t is time
eo
in seconds, R
the source resistance in ohms,
o
and C
is the total capacitance between the
T
signal lead and ground (or some other fixed
reference value) in farads.
The settling time constant, in seconds, and the
capacitance relationships are given in
Equations 13.3-3 through 13.3-5,
C
= R
o
T
C
= C
+ C
L
T
f
w
C
= 3.3 nfd
f
where C
is the fixed CR510 input capacitance
f
in farads, C
is the wire capacitance in
w
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
For the rising case, V
the decaying transient, V
Substituting these relationships for V
13-4
FIGURE 13.3-1. Input Voltage Rise and Transient Decay
T
), rise
[13.3-1]
) e -t/R
C
o
T
, decay
[13.3-2]
the true signal
so
[13.3-3]
[13.3-4]
[13.3-5]
, directly.
e
= V
-V
, whereas for
s
so
e
= V
+V
.
s
so
e
in
s
Equations 13.3-1 and 13.3-2, respectively,
yields expressions in V
e
e -t/R
C
o
T
V
= V
, rise
e
so
e -t/R
C
o
T
V
= V
, decay
e
e'o
Where V
= V
-V
, the difference between
e'o
eo
so
the peak transient voltage and the true signal
voltage.
NOTE: Since the peak transient, V
causes significant error only if it is several
times larger than the signal, V
calculations made in this section
approximate V
by V
e'o
If the input settling time constant, , is known, a
quick estimation of the settling error as a
percentage of the maximum error (V
rising, V
for decaying) is obtained by knowing
e'o
how many time constants (t/ ) 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
Time
%
Constants Max. Error Constants
0
100.0
1
36.8
3
5.0
Before proceeding with examples of the effect
of long lead lengths on the measurement, a
discussion on obtaining the source resistance,
R
, and lead capacitance, C
o
, the input settling error:
[13.3-6]
[13.3-7]
,
eo
, error
so
; i.e., V
= V
-V
eo
eo
eo
so
for
so
Time
%
Max. Error
5
0.7
7
0.1
10
0.004
L, is necessary.
w
.
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