E1C08 09/14/2010
14:53:57 Page 325
Thermistors are generally used when high sensitivity, ruggedness, or fast response times are
required (9). Thermistors are often encapsulated in glass, and thus can be used in corrosive or abrasive
environments. The resistance characteristics of the semiconductor material may change at elevated
temperatures, and some aging of a thermistor occurs at temperatures above 200
C. The high resistance
of a thermistor, compared to that of an RTD, eliminates the problems of lead wire resistance
compensation.
A commonly reported specification of a thermistor is the zero-power resistance and dissipation
constant. The zero-power resistance of a thermistor is the resistance value of the thermistor with no
flow of electric current. The zero power resistance should be measured such that a decrease in the
current flow to the thermistor results in not more than a 0.1% change in resistance. The dissipation
constant for a thermistor is defined at a given ambient temperature as
d ¼
P
T À T 1
ð8:13Þ
where
d ¼ dissipation constant
P ¼ power supplied to the thermistor
T, T 1 ¼ thermistor and ambient temperatures, respectively
Example 8.4
The output of a thermistor is highly nonlinear with temperature, and there is often a benefit to
linearizing the output through appropriate circuit, whether active or passive. In this example
we examine the output of an initially balanced bridge circuit where one of the arms contains a
thermistor. Consider a Wheatstone bridge as shown in Figure 8.8, but replace the RTD with a
thermistor having a value of R 0 ¼ 10; 000 V with b ¼ 3680 K. Here we examine the output of the
circuit over two temperature ranges: (a) 25–325
C, and (b) 25–75
C.
KNOWN A Wheatstone bridge where R 2 ¼ R 3 ¼ R 4 ¼ 10; 000 V and where R 1 is a thermistor.
FIND The output of the bridge circuit as a function of temperature.
SOLUTION The fundamental relationship between resistances in a Wheatstone bridge and the
normalized output voltage is provided in Equation 6.14:
E o
E i
¼
R 1
R 1 þ R 2
À
R 3
R 3 þ R 4
ð6:14Þ
And the resistance of the thermistor is
R ¼ R o e
bð1=TÀ1=T o Þ
Substituting in Equation 6.14 for R 1 yields
E o
E i
¼
R o e
b 1=TÀ1=T o
ð
Þ
R o e b 1=TÀ1=T o
ð
Þ þ R 2
À
R 3
R 3 þ R 4
8.4 Electrical Resistance Thermometry 325
14:53:57 Page 325
Thermistors are generally used when high sensitivity, ruggedness, or fast response times are
required (9). Thermistors are often encapsulated in glass, and thus can be used in corrosive or abrasive
environments. The resistance characteristics of the semiconductor material may change at elevated
temperatures, and some aging of a thermistor occurs at temperatures above 200
C. The high resistance
of a thermistor, compared to that of an RTD, eliminates the problems of lead wire resistance
compensation.
A commonly reported specification of a thermistor is the zero-power resistance and dissipation
constant. The zero-power resistance of a thermistor is the resistance value of the thermistor with no
flow of electric current. The zero power resistance should be measured such that a decrease in the
current flow to the thermistor results in not more than a 0.1% change in resistance. The dissipation
constant for a thermistor is defined at a given ambient temperature as
d ¼
P
T À T 1
ð8:13Þ
where
d ¼ dissipation constant
P ¼ power supplied to the thermistor
T, T 1 ¼ thermistor and ambient temperatures, respectively
Example 8.4
The output of a thermistor is highly nonlinear with temperature, and there is often a benefit to
linearizing the output through appropriate circuit, whether active or passive. In this example
we examine the output of an initially balanced bridge circuit where one of the arms contains a
thermistor. Consider a Wheatstone bridge as shown in Figure 8.8, but replace the RTD with a
thermistor having a value of R 0 ¼ 10; 000 V with b ¼ 3680 K. Here we examine the output of the
circuit over two temperature ranges: (a) 25–325
C, and (b) 25–75
C.
KNOWN A Wheatstone bridge where R 2 ¼ R 3 ¼ R 4 ¼ 10; 000 V and where R 1 is a thermistor.
FIND The output of the bridge circuit as a function of temperature.
SOLUTION The fundamental relationship between resistances in a Wheatstone bridge and the
normalized output voltage is provided in Equation 6.14:
E o
E i
¼
R 1
R 1 þ R 2
À
R 3
R 3 þ R 4
ð6:14Þ
And the resistance of the thermistor is
R ¼ R o e
bð1=TÀ1=T o Þ
Substituting in Equation 6.14 for R 1 yields
E o
E i
¼
R o e
b 1=TÀ1=T o
ð
Þ
R o e b 1=TÀ1=T o
ð
Þ þ R 2
À
R 3
R 3 þ R 4
8.4 Electrical Resistance Thermometry 325