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Because of the charging of C
exponential curve shown in Figure 2-26B. At the end of one
time constant (R
C
), the voltage will reach approximately
S
IN
63% of its final value. At the end of two time constants
(2R
C
), the voltage will reach about 86% of its final value,
S
IN
and so on. Generally, at least five time constants should be al-
lowed for better than 1% accuracy.
The amount of time that must be allowed will, of course, de-
pend on the relative values of R
when measuring a voltage with a source resistance of 10GΩ
with an input capacitance of 100pF, a time constant of one
second results. Thus, at least five seconds must be allowed to
achieve a better than 1% accuracy figure. Table 2-9 summa-
rizes voltage values and percentage error values for ten dif-
ferent time constants (τ = R
Table 2-9
Voltage and percent error for various time constants
Time
constant*
V
M
τ
0.632E
2τ
0.86E
3τ
0.95E
4τ
0.982E
5τ
0.993E
6τ
0.9975E
7τ
0.999E
*τ = R
C
S
IN
The most obvious method to minimize the slowing effects of
input capacitance is to minimize the amount of capacitance
in the circuit. Using low-capacitance cable and keeping the
cable as short as possible are two ways to do so. However,
there is a limit to the amount of capacitance reduction that
can be achieved. In those cases, especially where high im-
pedance levels are involved, guarded operation (see para-
graph 2.7.4) may be necessary.
While input capacitance does increase rise-time, it can help
to filter out some noise present at the input by effectively re-
ducing electrometer bandwidth. If we assume that all input
capacitance is lumped into a single element, the half-power
(-3dB) point of the circuit in Figure 2-26A will be:
f
3dB
–
, the electrometer follows the
IN
and C
. For example,
S
IN
C
).
S
IN
%Error
37%
S
14%
S
5%
S
1.8%
S
0.674%
S
0.25%
S
0.09%
S
1
=
------------------------- -
2πR
C
S
IN
Thus, if R
has a value of 10MΩ, and C
S
100pF, the half-power point will be 159Hz.
2.13.7 Source resistance
As shown in Table 2-10, a minimum value of source resis-
tance is recommended for each AMPS range. The reason for
this limitation can be understood by examining Figure 2-27.
C
and C
do not affect low-frequency noise and drift and
S
F
can be ignored for the purposes of this discussion.
C S
E S
Figure 2-27
Simplified model for source resistance and source capaci-
tance
Table 2-10
Minimum source resistance
Range
All pA
All nA
All µA
All mA
Input amplifier noise (E
NOISE
the output can be calculated as follows:
OutputE
=
NOISE
Thus, it is clear that, as long as R
put E
. However, as R
NOISE
Output E
increases. When R
NOISE
× Input E
, and the same relationship applies for E
NOISE
Operation
has a value of
IN
C F
R F
TO RANGING
AMPLIFIER
E OS
E NOISE
Minimum source
resistance
100GΩ
100MΩ
100kΩ
100Ω
) and offset (E
) appearing at
OS
R
F
×
InputE
1
+
------ -
NOISE
R
S
>> R
, Output E
S
F
NOISE
decreases in value relative to R
S
= R
, Output E
F
S
NOISE
= In-
,
F
= 2
.
OS
2-33
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