Student
Temperature Sensing
How does the temperature sensor work
and how can it be used to control the
temperature of a refrigerator?
Contents
Initial Problem Statement 2
Narrative 3-11
Notes 12
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Temperature
Sensing
Appendix 13
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Student
Temperature Sensing
A household refrigerator is a device to keep food
products within a fixed temperature range. The
temperature should be low enough to preserve
the food as long as possible, but not too low
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that the liquids in the refrigerator freeze. To do
this the refrigerator uses a temperature sensor
to indicate when to turn on or off the cooling
system.
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How does the temperature sensor
work and how can it be used to control
the temperature of a refrigerator?
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Initial Problem Statement
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Temperature Sensing
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Student
Narrative
Introduction
Discussion
Look at the following graph of a temperature measurement made inside a
refrigerator. Describe what is happening. What temperature range would be
important for a refrigerator? How could you control the device to achieve an
appropriate temperature? How could you design the refrigerator to be as efficient
as possible?
Figure 1.
Time, t
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To prevent the cooling system turning on and off repeatedly, the control logic will usually turn off
the cooling when the lowest allowable temperature has been reached and will not turn it back on
until the highest allowable temperature has been reached. This means the temperature is controlled
within a range rather than at a single value. This method of using different control points is called
introducing hysteresis into the system and is very common in many control applications.
One possible temperature sensor is the “thermistor”. This is a device that has a resistance to the
flow of electrical current that is temperature dependent. There are two kinds of thermistor, the
positive temperature coefficient (PTC) thermistor and the negative temperature coefficient (NTC)
thermistor. The response coefficient of a device tells you whether an increase in the input leads to an
increase or decrease in the output.
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Temperature Sensing
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Temperature,T
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Look at the following two graphs. Which do you think has a positive temperature
coefficient and which has a negative temperature coefficient?
Student
Activity 1
Discussion
What do you think positive temperature coefficient and negative temperature
coefficient means?
Resistance
Resistance
graph (a)
Temperature
Temperature
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Figure 2.
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The most appropriate type of thermistor used for temperature sensing is the NTC thermistor. In all
the following text the term thermistor will specifically mean NTC thermistor.
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graph (b)
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Multimedia
Temperature Sensing
Figure 3.
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The movie Temperature Sensing Video is available to demonstrate the behaviour of a
thermistor.
The resistance of a thermistor varies with temperature as
B B 

where
You may sometimes see this
written as
B B
R = R0 exp  − 
 T T0 
is the resistance of the thermistor at the
temperature being measured
is the resistance of the thermistor at a calibration
temperature T0
is a characterising parameter published by the manufacturer
is the temperature being measured
is the calibration temperature used when measuring R0
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R
R0
B
T
T 0 − 
T T0 
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R = R0 e
B B 
 − 
 T T0 
Note, be very careful when using the expression R = R0 e
as the temperature in this expression is in Kelvin (K), not Celsius.
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Student
Thermistors are usually constructed using a semiconductor material. A typical thermistor is shown
below.
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2. The characteristics of a thermistor
See "Calibration"
on page 6.
See "The Kelvin
temperature
scale" on page 7.
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The behaviour of a device such as a thermister depends upon the materials and
construction details used in its manufacture. For a given design to be useful it must
give repeatable results which are valid over a range of temperatures. The behaviour is
characterised by calibrating the design.
Student
Calibration
For the thermistor two characterising values are used at a given calibration temperature.
The first characterising value is the resistance, R0, at a specified calibration temperature,
T0. Usually the design is such that R0 and T0 are standard. A typical value of R0 would
coincide with a standard resistor value; for example 15 kΩ, while a typical value of T0
would coincide with an expected temperature; for example 25°C.

R = R0 e
− 
T T0 
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Look at the expression that shows how the resistance of a thermistor varies with
temperature,
B B 
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What would the resistance, R, be if the measuring temperature, T, is the freezing
point of water? (Use R0 = 15 000 (Ω), T0 = 25 (°C) and B = 3500.) Is there a
problem with the device or the equation?
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Discussion
Temperature Sensing
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The second characterising value is the parameter B. This is determined by how the
resistance changes from the resistance at the calibration temperature as the temperature
changes from the calibration temperature.
After production a thermistor is found to have a characteristic resistance, R0, of
15 000 Ω at the characterising temperature, T0, of 25°C. A second calibrating
measurement is made. It is found that at a temperature, T, of 21°C the resistance, R,
is 17 793 Ω. Calculate the characterising parameter, B.
Student
Activity 2
Discussion
What are the units of B?
The Kelvin temperature scale
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The Kelvin temperature measures the so-called “absolute temperature”. The temperature
of absolute zero is defined as the point at which the motion of atoms due to thermal
energy ceases. Its value is determined to be -273.16 °C (although in this resource a value
of -273 is used). The average temperature of outer space is 2.73 K.
T (°C)
-5
T (K)
R (Ω)
Convert R to kΩ
for plotting
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Using the value of B just calculated fill in the following table and plot the results
to show how resistance varies with temperature in °C over the given range. Use
B rounded to the nearest integer, as this is the value that would published by the
manufacturer. Convert R in to kilohm to 1 d.p. Verify that the graph fits the definition
of an NTC thermistor, i.e. has a negative gradient.
5
10
15
20
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25
30
35
You could try to share the
work out in a group to
complete this table, or use a
spreadsheet.
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Activity 3
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To convert from °C to Kelvin, you just add 273 so that 0 °C is 273 K and 100 °C is 373 K
Student
Resistance, R (k Ω )
70.0
60.0
50.0
40.0
30.0
10.0
0.0
-10
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0
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20.0
25
30
35
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Activity 4
The thermistor is used in a device to measure the temperature of a room.
A resistance of 27 kΩ is recorded. Use your graph to determine the temperature to
the nearest ½ °C. Substitute your answer back into the equation
B B 
−


T T0 
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R = R0 e
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and find the corresponding value of R to check for consistency.
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Temperature Sensing
Figure 4.
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Temperature, T (°C)
Activity 5
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Figure 4.
Look at the expression relating measured resistance to the temperature:
B B 

− 
T T0 
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R = R0 e
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Rearrange this expression to make T the subject of the equation so that a measured
resistance will translate directly to a temperature.
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When using a thermistor in a practical device it is obviously not convenient for it to report the
resistance as you either have to refer that to a conversion table or a graph. Instead the resistance is
converted to a temperature which can be displayed directly or used to trigger a control mechanism.
Temperature Sensing
3. Using a thermistor in a device
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to determine what the temperature should be. Recall that for the
Use the expression R = R0 e
device you have determined that
R0 = 15
T0 = 298
( in kΩ )
( in K )
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B = 3740
Discussion
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A calibrating thermometer determines that the actual temperature is 25°C.
If the temperature given by your expression does not agree with the calibration
temperature what are the possible explanations?
Multimedia
The movie resource Temperature Sensing Video is available to demonstrate the reading of
the resistance for this experiment.
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Figure 5.
B B 
 − 
 T T0 
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You are testing a thermistor to be used in a device to measure the temperature for
control purposes. A resistance of 15.29 kΩ is recorded.
Temperature Sensing
Activity 6
Most devices are manufactured to within specified tolerances. For calibration instruments these
tolerances are usually small so that accurate readings are given. For more general devices however,
more relaxed tolerances can be used as long as the impact of these on a design are assessed as
being appropriate.
Student
4. Calculating the accuracy of the device
Activity 7
The tolerance on the thermistor being used is stated as being ±5%. This is allowed
variation of the calibration resistance, R0, at the calibration temperature, T0.
Assuming B is fixed, what is the range of temperatures that could be displayed when
the R = 15.29 kΩ?
Discussion
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Assume the calibration thermometer reading of 25.0 °C is correct. Show this value
and the expected range of variation due to the tolerance on a number line. Is the
calculated reading of 24.5 °C consistent with the accuracy of the thermistor?
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Would this device be suitable for your refrigerator control mechanism? How could
you compensate for any bias in the readings due to the manufacturing tolerance?
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Activity 8
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What is the accuracy of the thermistor you are using?
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Notes
Semiconductor resistance
Semiconductors are materials in which electrons are not usually free to
conduct electricity. As the temperature increases it give some electrons
enough energy to become available to conduct so a small current flows. Increasing the temperature
further makes more electrons available and a larger current flows. If there is a fixed potential across
the semiconductor then Ohm’s law states that the potential difference, V, the current, I, and the
resistance, R, are related as
V = IR
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As the amount of current that can flow increases with increasing temperature, it can be seen that
the resistance must fall with increasing temperature.
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Appendix
mathematical coverage
PL objectives
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Use algebra to solve engineering problems
• Be able to evaluate expressions.
• Understand and be able to work with percentages.
• Change the subject of a formula.
• Know how to check answers by substitution.
• Be able to plot data.
• Be able to draw graphs by constucting a table of values.
• Be able to construct and use conversion graphs.
• Be able to extract information from a graph.
• Solve problems using laws of logarithms.
• Solve problems involving exponential growth and decay.
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