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Chapter 5 -- Measurement of Small Signals
Overview
The PCI4 is a sensitive scientific instrument. It can resolve current changes as small as 0.01 picoamps (10
amps). To place this current in perspective, 0.01 pA represents the flow of about 60,000 electrons per second!
The small currents measured by the PCI4 place demands on the instrument, the cell, the cables and the
experimenter. Many of the techniques used in higher current electrochemistry must be modified when used to
measure pA currents. In many cases, the basic physics of the measurement must be considered.
This chapter will discuss the limiting factors controlling low current measurements. It will include hints on cell
and system design. The emphasis will be on EIS (Electrochemical Impedance Spectroscopy), a highly
demanding application for the PCI4.
Measurement System Model and Physical Limitations
To get a feel for the physical limits implied by picoamp measurements, consider the equivalent circuit shown in
Figure 5-1. We are attempting to measure a cell impedance given by Z
This model is valid for analysis purposes even though the real PCI4 circuit topology differs significantly.
In Figure 5-1:
E
Is an ideal signal source
s
Z
Is the unknown cell impedance
cell
R
Is the current measurement circuit's current measurement resistance
m
R
Is an unwanted resistance across the cell
shunt
C
Is an unwanted capacitance across the cell
shunt
C
Is the current measurement circuit's stray input capacitance
in
R
Is the current measurement circuit's stray input resistance
in
I
Is the measurement circuit's input current
in
In the ideal current measurement circuit R
through R
.
m
With an ideal cell and voltage source, R
current measurement circuit is due to Z
The voltage developed across R
can use Kirchoff's and Ohms law to calculate Z
Z
= E
cell
Chapter 5 -- Measurement of Small Signals -- Overview
is infinite while C
in
is infinite and C
shunt
.
cell
is measured by the meter as V
m
:
cell
* R
/ V
s
m
m
.
cell
and I
are zero. All the cell current, I
in
in
is zero. All the current flowing into the
shunt
. Given the idealities discussed above, one
m
5-1
-14
, flows
cell
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