E1C08 09/14/2010
14:53:57 Page 323
are reduced from 0.25 to 0.025, yielding
u RTD ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 Â 0:025
ð
Þ
2 þ 1 Â À0:025
ð
Þ
2 þ 1 Â 0:025
ð
Þ
2
q
¼ 0:0433 V
and the resulting 95% uncertainty interval in temperature is Æ0.44
C, which satisfies the design
constraint.
COMMENT This result provides confidence that the effect of the resistors’ uncertainties will not
cause the uncertainty in temperature to exceed the target value. However, the uncertainty in temperature
also depends on other aspects of the measurement system. The design-stage uncertainty analysis
performed in this example may be viewed as ensuring that the factors considered do not produce a
higher than acceptable uncertainty level.
Practical Considerations
The transient thermal response of typical commercial RTDs is generally quite slow compared with other
temperature sensors, and for transient measurements bridge circuits must be operated in a deflection
mode or use expensive auto-balancing circuits. For these reasons, RTDs are not generally chosen for
transient temperature measurements. A notable exception is the use of very small platinum wires and
films for temperature measurements in noncorrosive flowing gases. In this application, wires having
diameters on the order of 10 mm can have frequency responses higher than any other temperature sensor,
because of their extremely low thermal capacitance. Obviously, the smallest impact would destroy this
sensor. Other resistance sensors in the form of thin metallic films provide fast transient response
temperature measurements, often in conjunction with anemometry or heat flux measurements. Such
metallic films are constructed by depositing a film, commonly of platinum, onto a substrate and coating
the film with a ceramic glass for mechanical protection (7). Typical film thickness ranges from 1 to 2 mm,
with a 10-mm protective coating. Continuous exposure at temperatures of 600
C is possible with this
construction. Some practical uses for film sensors include temperature control circuits for heating
systems and cooking devices and surface temperature monitoring on electronic components subject to
overheating. Uncertainty levels range from about Æ0.1 to 2
C.
Thermistors
Thermistors (from thermally sensitive resistors) are ceramic-like semiconductor devices. The
most common thermistors are NTC, and the resistance of these thermistors decreases rapidly
with temperature, which is in contrast to the small increases of resistance with temperature for
RTDs.
Equation 8.2 is too simple to accurately describe resistance changes over practical temperature
ranges; a more accurate functional relationship between resistance and temperature for a thermistor
is generally assumed to be of the form
R ¼ R 0 e
b 1=TÀ1=T 0
ð
Þ
ð8:12Þ
The parameter b ranges from 3500 to 4600 K, depending on the material, temperature, and
individual construction for each sensor, and therefore must be determined for each thermistor.
Figure 8.9 shows the variation of resistance with temperature for two common thermistor materials;
8.4 Electrical Resistance Thermometry 323
14:53:57 Page 323
are reduced from 0.25 to 0.025, yielding
u RTD ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 Â 0:025
ð
Þ
2 þ 1 Â À0:025
ð
Þ
2 þ 1 Â 0:025
ð
Þ
2
q
¼ 0:0433 V
and the resulting 95% uncertainty interval in temperature is Æ0.44
C, which satisfies the design
constraint.
COMMENT This result provides confidence that the effect of the resistors’ uncertainties will not
cause the uncertainty in temperature to exceed the target value. However, the uncertainty in temperature
also depends on other aspects of the measurement system. The design-stage uncertainty analysis
performed in this example may be viewed as ensuring that the factors considered do not produce a
higher than acceptable uncertainty level.
Practical Considerations
The transient thermal response of typical commercial RTDs is generally quite slow compared with other
temperature sensors, and for transient measurements bridge circuits must be operated in a deflection
mode or use expensive auto-balancing circuits. For these reasons, RTDs are not generally chosen for
transient temperature measurements. A notable exception is the use of very small platinum wires and
films for temperature measurements in noncorrosive flowing gases. In this application, wires having
diameters on the order of 10 mm can have frequency responses higher than any other temperature sensor,
because of their extremely low thermal capacitance. Obviously, the smallest impact would destroy this
sensor. Other resistance sensors in the form of thin metallic films provide fast transient response
temperature measurements, often in conjunction with anemometry or heat flux measurements. Such
metallic films are constructed by depositing a film, commonly of platinum, onto a substrate and coating
the film with a ceramic glass for mechanical protection (7). Typical film thickness ranges from 1 to 2 mm,
with a 10-mm protective coating. Continuous exposure at temperatures of 600
C is possible with this
construction. Some practical uses for film sensors include temperature control circuits for heating
systems and cooking devices and surface temperature monitoring on electronic components subject to
overheating. Uncertainty levels range from about Æ0.1 to 2
C.
Thermistors
Thermistors (from thermally sensitive resistors) are ceramic-like semiconductor devices. The
most common thermistors are NTC, and the resistance of these thermistors decreases rapidly
with temperature, which is in contrast to the small increases of resistance with temperature for
RTDs.
Equation 8.2 is too simple to accurately describe resistance changes over practical temperature
ranges; a more accurate functional relationship between resistance and temperature for a thermistor
is generally assumed to be of the form
R ¼ R 0 e
b 1=TÀ1=T 0
ð
Þ
ð8:12Þ
The parameter b ranges from 3500 to 4600 K, depending on the material, temperature, and
individual construction for each sensor, and therefore must be determined for each thermistor.
Figure 8.9 shows the variation of resistance with temperature for two common thermistor materials;
8.4 Electrical Resistance Thermometry 323