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2.6.3 Analog Circuit Noise 35
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noise by breaking the loop or circuit. The Model 372 has a well-designed power sup-
ply and uses galvanic isolation between the instrument chassis and measurement
circuits. Careful installation is necessary to take advantage of the isolation. Ground
loop noise can be kept as low as a few microvolts and usually appears as line fre-
quency or one of its low harmonics.
2.6.3 Analog Circuit
Noise The current source and amplifiers inside the Model 372 make a contribution to mea-
surement noise. Circuits were carefully chosen to maintain good noise performance
over a wide resistance range without generating high leakage currents that could self
heat resistors. Leakage current limits the practical current excitation range of the
Model 372 to a few picoamps. Most analog circuit noise is distributed over a broad
frequency band. It is often referred to as 1/f noise because there is equal noise power
in each decade of frequency. Instrument noise, specified in Table 1-1, is dominated by
amplifier noise for low resistances and by resistor thermal noise for high resistances.
Noise from both sources can be further reduced with longer filter settling time.
2.6.4 Digital Circuit
Noise All digitally controlled instruments emit some high-frequency noise both through the
air and on their leads. Emission from a Model 372 is very low and will not affect resis-
tance measurements or heat measured resistors if the instrument is installed prop-
erly. The high frequency noise can interfere with very sensitive measurements being
made in the same Dewar. Interference can be minimized by separating the instru-
ments and their leads outside the Dewar and placing ferrite beads on the Model 372
measurement leads, near the Dewar, to stop the noise from getting inside. Wrapping
leads through the large beads more than one time improves their attenuation of
unwanted signals. A more common source of digital noise than the instrument itself
is digital computers used for data acquisition. Computers with their high clock seeds
generate a wide spectrum of noise and transmit it through line cords and interface
cables. Isolation in the Model 372 separates the measurement circuits from interface
circuits but computers must still be treated carefully during installation of a system.
2.6.5 Resistor Thermal
Noise Thermal noise or Johnson noise is the most common noise associated with resistors.
This noise is present in all resistors, is independent of excitation, and has a flat fre-
quency spectrum. The equation for Johnson noise is often expressed as:
V
noise
= (4kTR
,
f)
q
, where V
noise
is the RMS noise voltage, k is Boltzmann's constant
(1.38 × 10 -23 J/K), T is temperature in Kelvin and
,
f is the noise bandwidth in Hz.
Some considerations when using the equation: peak-to-peak noise will be within 5
times RMS noise more than 99% of the time, f can be calculated several ways and a
common method is (
'
/2) f
3db
where f
3db
is the 3 dB bandwidth of the dominant low-
pass filter in the measuring circuit. As a practical example, the noise voltage of a
100 k
)
resistor at room temperature using a 1 s filter is approximately 16 nV RMS or
80 nV PP which is 8% of a measurement made at 1 µV. This must be kept in mind
when trying to characterize the measurement noise of the Model 372. The published
noise specifications in Chapter 1 assume the resistive load is at room temperature.
When the resistor is cooled, the thermal noise drops accordingly.
Please note that thermal noise is normally the biggest noise source in resistors being
measured but not the only one. Metallic conductors approach the theoretical limit for
thermal noise, but other materials have additional noise, sometimes referred to as
flicker noise, that has a 1/f spectrum. Flicker noise is different for every material, is
proportional to current and can change with construction techniques including lead
attachment. Shot noise, which is a product of the discrete nature of electron flowing
through resistive materials, is insignificant in most measurement, but can become
measurable when current drops into the picoamp range.