Chapter 9: Measurement Of Small Signals; Overview; Measurement System Model And Physical Limitations - Gamry Instruments Interface 1010 Operator's Manual

Chapter 9: Measurement of Small Signals

Overview

The Interface 1010 is a very sensitive scientific instrument. It can theoretically resolve current changes as small
as 333 femtoamperes (333 x 10
2 000 000 electrons per second!
The small currents measured by the Interface 1010 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. We offer hints on cell and
system design. The emphasis is on EIS (Electrochemical Impedance Spectroscopy), a highly demanding
application for the Interface 1010.

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 9-1. We are attempting to measure the cell impedance given by Z
This model is valid for analysis purposes even though the real Interface 1010 circuit topology differs
significantly.
In Figure 9-1:
E is an ideal signal source
s
Z is the unknown cell impedance
cell
is the "real" cell current
I
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
is the measurement circuit's input current
I
in
In the ideal current-measurement circuit R
through R .
m
With an ideal cell and voltage source, R
measurement circuit comes from Z
The voltage developed across R
use Kirchhoff's and Ohm's law to calculate Z
Z = E × R / V
cell s m
Measurement of Small Signals – Overview
A). To place this current in perspective, 333 fA represents the flow of about
−15
is infinite while C
in
is infinite and C
shunt
.
cell
is measured by the meter as V
m
:
cell
m
and I are zero. All of the cell current, I
in in
is zero. All the current flowing into the current
shunt
. Given the idealities discussed above, you can
m
59
.
cell
, flows
cell