Lake Shore 350, User Manual

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2.5.5 Resistor Thermal Noise 23
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2.5.5 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
Vnoise = (4kTR
,
f) 1/2
where Vnoise 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 second filter is approximately 16 nV RMS or 80 nV PP.
When the resistor is cooled the thermal noise drops accordingly.
Thermal noise is normally the biggest noise source in higher value resistors being mea-
sured at room temperature.
2.5.6 Vibration Noise Noise can be generated in lead cables when they are moved or vibrated. This noise
can be related to the triboelectric effect or changes in capacitance between conduc-
tors in the cable. Cables carrying small signals should be fastened down without put-
ting strain on the connections.
2.6 Measurement
Error This section explains warm up and temperature drift, sensor installation and sensor
self-heating and thermal resistance.
2.6.1 Warm Up and
Temperature Drift When the Model 350 is first turned on, it should be allowed to warm up for at least
30 mins before use to allow its internal temperature to stabilize. Warm up is an exag-
gerated form of temperature drift because the temperature change inside the enclo-
sure is larger and faster than would be experienced in a laboratory setting.
Temperature drift, change in reading with change in ambient temperature, is small in
the Model 350 and seldom a significant factor in absolute accuracy. Measurement
repeatability is often dominated by temperature drift and temperature change
should be considered if the instrument is being installed in a rack. If possible, preci-
sion measurement instruments should not be placed in the same rack with large
power supplies or other equipment that can change the rack temperature quickly.
Instrument racks should be well ventilated to prevent the buildup of heat.
2.6.2 Sensor
Installation Installation is an important part of measurements at cryogenic temperatures. The
measured sensor must be at the temperature of its surroundings for the measure-
ment to be valid. Some installation suggestions for temperature sensors are given in
section 3.5.
2.6.3 Sensor Self-
Heating and Thermal
Resistance A sensor self-heats when the electrical power being put into the measured sensor
resistance is large enough to warm the sensor above the temperature of its surround-
ings. Electrical power gets into the sensor from both the necessary excitation current
and undesirable noise. Errors from self-heating are dangerous because they can eas-
ily go undetected. One strategy for detecting these errors is to understand the ther-
mal resistance of the sensor and predict its reaction to excitation and noise.
Self-heating (
,
T
SH
) is a product of the sensor thermal resistance (R
t
) expressed in kel-
vin per watt (K/W) and excitation power (P
s
) expressed in watts.
,
T
SH
= R
t
P
s
; P
s
can be
calculated as excitation current squared times measured resistance (R
e
) P
s
= I
2
R
e
.