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Chapter 5 -- Measurement of Small Signals -- Measurement System Model and Physical Limitations
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 equation:
E = (4 k T R δF)
I = (4 k T δF / R)
where:
k = Boltzman's constant 1.38x 10
T = temperature in
δF = noise bandwidth in Hz
R = resistance in ohms.
Figure 5-1
Equivalent Measurement Circuit
R shunt
C shunt
R in
1/2
1/2
-23
J/
o
K
o
K
5-2
Rm
C in
in
> 0
in
and a finite R
shunt
shunt
> 0
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