Gamry Reference 600+ - Chapter 8: Measurement of Small Signals; Overview; Measurement System Model and Physical Limitations

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Chapter 8: Measurement of Small Signals
Overview
The Reference 600+ is a very sensitive scientific instrument. It can theoretically resolve current changes as
small as 1 femtoampere (1 × 10
–15
A). To place this current in perspective, 1 fA represents the flow of
about 6000 electrons per second!
The small currents measured by the Reference 600+ 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 discusses the limiting factors controlling low-current measurements. It includes hints on cell
and system design. The emphasis is on EIS (Electrochemical Impedance Spectroscopy), a highly demanding
application for the Reference 600+.
Measurement System Model and Physical Limitations
To get a feel for the physical limits implied by very sensitive current measurements, consider the equivalent
circuit shown in Figure 8-1. We are attempting to measure the cell impedance given by Z
cell
.
This model is valid for analysis purposes even though the real Reference 600+ circuit topology differs
significantly.
In Figure 8-1:
E
S
ideal signal source
Z
cell
unknown cell impedance
I
cell
“real” cell current
R
m
current measurement circuit’s current-measurement resistance
R
shunt
unwanted resistance across the cell
C
shunt
unwanted capacitance across the cell
C
in
current-measurement circuit’s stray input capacitance
R
in
current-measurement circuit’s stray input resistance
I
in
measurement circuit’s input current
In the ideal current-measurement circuit, R
in
is infinite while C
in
and I
in
are zero. All of the cell current, I
cel
,
flows through R
m
.
With an ideal cell and voltage source, R
shunt
is infinite and C
shunt
is zero. All the current flowing into the
current measurement circuit is due to Z
cell
.
The voltage developed across R
m
is measured by the meter as V
m
. Given the idealities discussed above, use
Kirchoff’s and Ohm’s laws to calculate Z
cell
:
Z
cell
= E
S
× R
m
/ V
m