Page 176 - Mechanical Engineers' Handbook (Volume 2)

4 Thermistors 165

Table 7 Representative Thermal Dissipation Constants for
Two Different Thermistor Probe Designs
Environment 1.0-cm Disk 5.0-cm Glass Cylinder
Still air 8 (mW/ C) 1 (mW/ C)
Air at 5 m/s 35 —
Still oil 55 3.5
Still water — 5
Oil at 1 m/s 250 —

Source: Reference 39.

The transient response of thermistors is more complex than that of thermocouples, and
they are not as well suited to transient measurements. The difference arises from the thermal
response of the thermistor material itself. Thermistor materials typically have lower thermal
diffusivity than metals and hence do not equilibrate their internal temperatures as rapidly,
all other factors being the same. Thus the highest frequency at which a thermistor will yield
a first-order response is far lower than that for a thermocouple. During rapid changes, the
temperature is not uniform inside the thermistor, and the average resistance no longer de-
scribes the average temperature. Since the thermistor resistance is not a linear function of
temperature, the transient resistance cannot easily be converted to temperature.
Thermistor probes are susceptible to environmental errors (radiation, velocity, and con-
duction errors) as are all other immersion temperature sensors, and the same guidelines and
design rules apply.
Thermistor sensors can be built into complex probe designs, as can any temperature
sensor, and the structure of the probe will determine its steady-state and transient behavior.
The thermistor has relatively low thermal conductivity and is frequently encapsulated in
epoxy, glass, or vinyl, which also have low thermal conductivity. On this account, the tran-
sient response of a thermistor probe will be slower and more complex than that of a metallic
sensor.
Tagawa et al. 42 analyzed the transient response of spherical and planar thermistors and
showed that some configurations can be treated as first-order systems for slow changes in
temperature, although they display second- or third-order characteristics at higher frequen-
cies. They reported success using time constant compensation to reduce the compensated
time constant by factors as large 50.

4.5 Measuring Circuits and Peripheral Equipment
Electrical resistance is easily measured within ordinary levels of accuracy by a number of
techniques, and any method can be used with thermistors. The logarithmic variation of
resistance with temperature means that over small ranges a constant percent error in resis-
tance translates into a fixed error in temperature level. For example, with a thermistor whose
sensitivity coefficient (see Table 5) is 5%/ C, a resistance measurement accurate to 0.1%
of reading will yield a temperature measurement accurate within 0.02 C everywhere in
the range. Accuracy of this order can be achieved by two-wire and four-wire systems using
off-the-shelf instruments and thermistors.
When thermistors are used to resolve very small differences in temperature (e.g., into
the milliKelvin resolution range), special precautions must be taken to measure the resistance