Table of Contents
Advertisement
Measurement of Small-current Signals – Measurement System Model and Physical Limitations
C
unwanted capacitance across the cell
shunt
C
current-measurement circuit's stray input capacitance
in
R
current-measurement circuit's stray input resistance
in
I
measurement circuit's input current
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
Kirchhoff's and Ohm's laws to calculate Z
Z
= E
× R
/ V
cell
S
m
Unfortunately, technology limits high-impedance measurements because:
Current measurement circuits always have non-zero input capacitance, i.e., C
Infinite R
cannot be achieved with real circuits and materials.
in
Amplifiers used in the meter have input currents, i.e., I
The cell and the potentiostat create both a non-zero C
Additionally, basic physics limits high-impedance measurements via Johnson noise, which is the inherent noise
in a resistance.
Johnson Noise in Z
cell
Johnson noise across a resistor represents a fundamental physical limitation. Resistors, regardless of
composition, demonstrate a minimum noise for both current and voltage, per the following equations:
E = (4kTR F)
1/2
I = (4kT F / R)
1/2
is infinite while C
in
is infinite and C
shunt
.
cell
is measured by the meter as V
m
:
cell
m
Figure 10-1
Equivalent Measurement Circuit
R shunt
C shunt
R in
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, use
m
Icell
C in
> 0.
in
and a finite R
shunt
74
cell
Rm
> 0.
in
.
shunt
, flows
Advertisement
Table of Contents
