Chapter 9 -- Measurement of Small Current Signals--Measurement System Model and Physical Limitations
9 - 4
f
RC
= 1/ 6.28 (1x10
7
)(2x10
-12
)
≈ 8000 Hz
In general, one should stay two decades below f
RC
to keep phase shift below one degree. The uncorrected
upper frequency limit on a 6 nA range is therefore around 80 Hz.
One can measure higher frequencies using the higher current ranges (i.e. lower impedance ranges) but this
would reduce the total available signal below the resolution limits of the "voltmeter". This then forms one basis
of statement that high frequency and high impedance measurements are mutually exclusive.
Software correction of the measured response can also be used to improve the useable bandwidth, but not by
more than an order of magnitude in frequency.
Leakage Currents and Input Impedance
In Figure 9-1, both R
in
and I
in
affect the accuracy of current measurements. The magnitude error due to R
in
is
calculated by:
Error = 1- R
in
/(R
m
+R
in
)
For an R
m
of 10
7
ohms, an error < 1% demands that R
in
must be greater than 10
9
ohms. PC board leakage,
relay leakage, and measurement device characteristics lower R
in
below the desired value of infinity.
A similar problem is the finite input leakage current I
in
into the voltage measuring circuit. It can be leakage
directly into the input of the voltage meter, or leakage from a voltage source (such as a power supply) through
an insulation resistance into the input. If an insulator connected to the input has a 10
12
ohm resistance
between +15 volts and the input, the leakage current is 15 pA. Fortunately, most sources of leakage current
are DC and can be tuned out in impedance measurements. As a rule of thumb, the DC leakage should not
exceed the measured AC signal by more than a factor of 10.
The Reference 3000 uses an input amplifier with an input current of around 5 pA. Other circuit components
may also contribute leakage currents. You therefore cannot make absolute current measurements of very low
pA currents with the Reference 3000. In practice, the input current is approximately constant, so current
differences or AC current levels of less than one pA can usually be measured.
Voltage Noise and DC Measurements
Often the current signal measured by a potentiostat shows noise that is not the fault of the current
measurement circuits. This is especially true when you are making DC measurements. The cause of the
current noise is noise in the voltage applied to the cell.
Assume that you have a working electrode with a capacitance of 40 µF. This could represent a 1 cm
2
polished
noble metal immersed in an electrolyte solution. You can roughly estimate the capacitance of the electrical
double layer formed by a metal/electrolyte interface as 20 µF/cm
2
. The area is the microscopic area of the
surface, which is larger than the geometric area, because even a polished surface is rough. The impedance of
this 40 µF electrode, assuming ideal capacitive behavior, is given by:
Z = 1/ωC
At sixty Hertz, the impedance magnitude is about 66 Ω.
Apply an ideal DC potential across this ideal capacitor and you get no DC current.
Unfortunately, all potentiostats have noise in the applied voltage. This noise comes from the instrument itself
and from external sources. In many cases, the predominant noise frequency is the AC power line frequency.
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