Lab 1 Calibration of a Thermistor

Pre- Lab for Calibration
of a Thermistor
A thermistor is made of a disc of semiconductor material. A semiconductor is composed of atoms that
have 4 outer electrons. The 4 outer electrons of the atoms form covalent bonds with its nearest neighbors to
form a diamond crystalline pattern. A two-dimensional representation of the crystal is shown in Fig. 1. For an
electrical current to flow in the material, the covalent bond must be broken so that the electron is free to jump
from atom to atom. In an insulator, that requires a lot of energy. In a conductor, very little energy is needed.
However, a semiconductor requires more energy that a conductor, but not as much as an insulator. An energy
level diagram can represent this (Fig. 2). The lower level is called the valence band and represents the electrons
in the atoms that are bound to the atom. The upper level is called the conduction band and represents electrons
that can move from atom to atom and can cause electrical current to flow. The distance between the valence
band and the conduction band represents the energy (E g = energy gap) needed for current to start to flow.
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Conduction Band
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E g
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Valance Band
Fig. 1
Fig. 2
Adding a tiny amount of impurities to the crystal can radically change the electrical characteristic of a
semiconductor. For example, if a few phosphorus atoms are added to the silicon crystal, then the crystal pattern
is preserved (Fig. 3). Phosphorus atoms have five outer electrons. Four of the electrons bond to its nearest
neighbors, but the fifth electron is only slightly bonded with the phosphorus atom and a small amount of energy
can cause the electron to jump from the energy level that is located in the energy gap to the conduction band
(Fig. 4). That small amount of energy can be supplied by the thermal energy of the semiconductor’s
surroundings. When the surroundings become warmer, more electrons then jump to the conduction band and
material becomes a better electrical conductor. Hence, the electrical resistant of the material will drop with a
temperature rise.
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Conduction band
E g
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Valance Band
Fig. 3
Fig. 4
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The relationship between resistance and temperature for a thermistor is given by the Steinhart-Hart equation:
1
= A + Bln(R) + Cln(R)3
T
where T is measured in Kelvin and R is the resistance in ohms. The coefficients A, B, and C are the Steinhart-
Hart coefficients and vary depending on the thermistor.
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If A = 8.267 x 10 -4 K -1 , B = 2.089 x 10 -4 K -1 , and C= 8.033 x 10 -8 K -1 , write an Excel spread sheet to complete
the following table.
Save the program on your computer for lab.
R(Ω) ln(R) 1/T
(in K -1 )
T
(in K)
T
(In C o )
T
(in F o )
269,080 12.503 0.003595 278.1 4.96 40.9
207,850
126,740
100,000
51,048
27,475
16,689
10,110
7,707
5569
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Calibration of a Thermistor
Object: Thermistors are temperature-sensitive resistive devices used in a wide range of temperature
measurement applications. In this experiment you will calibrate a thermistor over a temperature range of
0°C to 100°C and use this data to determine the coefficients of an equation relating resistance to
temperature.
Apparatus:
1. Thermistor probe
2. Digital Multimeter
3. Beaker
4. Ice
5. Hot Plate
6. Thermometer
Procedure:
1. Assemble the apparatus as demonstrated by your instructor. Beginning with ice water in the container,
take an initial reading as close to 0°C as possible. Stir the water before the reading to maintain the
thermistor and thermometer at the same steady temperature.
2. Once a good initial reading has been taken, remove the ice and begin heating the bath. Approximately
every 5 C° remove the heat and take a resistance/ temperature reading, again being certain to stir the
bath. Continue taking readings up to near 100°C.
3. When you are finished collecting data, turn off the hot plate and allow the water to cool while you
analyze the data. As the water cools, record 4 readings of temperature and resistance. These data points
will be used to check the curve fit of the data.
4. Plot the data as a scatter graph on the computer with resistance on the
x-axis and temperature along the y-axis.
5. Plot the data with inverse Kelvin temperature on the y-axis and the natural log of the resistance on the x-
axis Draw a straight line through your data points. Use the curve-fitting option in the graphing program
to make a cubic fit to your data. The formula displayed will have the approximate values of A, B, C and
D for the equation below. Use these values to check your answers in the next step.
6. The manufacture of the thermister claims the empirical equation is given by the following equation.
1
= A + Bln(R) + Cln(R)3
T
where temperature T is in degrees Kelvin and ln(R) is the natural log of the
resistance, R. How well the curve fits is given by the correlation factor R term at the end of the
equation. R
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= 1 would indicate a perfect fit. (Note: The curve fit gives a value for R and for R 2 .)
However, the Excel program does not allow the data to be fitted to any arbitrary function. Plot (1/T)
versus ln(R). Fit the graph to a polynomial of degree 3. That is, the equation we are going to use is as
following:
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1
T = A + Bln(R) + (1)
Cln(R)2 + Dln(R) 3
7. Use the graph and the equation to determine the temperatures of the water bath at those points taken
while the bath was cooling. Compare these values with those read from the mercury thermometer. The
calculations
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can be done using a calculator or an excel spreadsheet can be used.
Data: (An Excel spreadsheet can be used. Print out the spreadsheet instead of using the table below.)
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Temperature
(in C o )
Temperature
( in K)
Resistance
(in Ω)
1/T
(in K -1 )
ln(R)
Graph fitting equation:
A = _________ B = ____________ C = ____________ D = _______________
Comparison of four data points while the water is cooling.
T (Measured) R (Measured) T (From Graph) T(From Equation 1)
1
2
3
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Questions
1) How does resistance relate to temperature in your thermistor?
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