Chapter 8: Measurement Of Small Signals; Overview; Measurement System Model And Physical Limitations - Gamry Instruments Interface 1000 Operator's Manual

Chapter 8: Measurement of Small Signals

Overview

The Interface 1000 is a very sensitive scientific instrument. It can theoretically resolve current changes as
small as 333 femtoamperes (333 x 10
of about 2 000 000 electrons per second!
The small currents measured by the Interface 1000 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 1000.

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
This model is valid for analysis purposes even though the real Interface 1000 circuit topology differs
significantly.
In Figure 8-1:
E is an ideal signal source
s
Z is the unknown cell impedance
cell
I is the "real" cell current
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
flows through R .
m
With an ideal cell and voltage source, R
current measurement circuit comes from Z
The voltage developed across R
can use Kirchoff's and Ohm's law to calculate Z
Z = E
cell
Chapter 8: Measurement of Small Signals--Overview
A). To place this current in perspective, 333 fA represents the flow
−15
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
and I are zero. All of the cell current, I
in in
is zero. All the current flowing into the
shunt
. Given the idealities discussed above, you
m
:
8 - 1
.
cell
,
cell