University physics experiment report

Abstract: Thermistor is a kind of semiconductor resistor whose resistance is very sensitive to temperature changes. It has many unique advantages and uses. It has a wide range of applications in automatic control, wireless electronic technology, remote control technology and temperature measurement technology. In this experiment, the resistance temperature characteristics of the thermistor are studied by the bridge method, and the understanding of the resistance temperature characteristics of the thermistor is deepened.
Keywords: thermistor, unbalanced DC bridge, resistance temperature characteristics

1 Introduction

A thermistor is a device that is made according to the strong dependence of the conductivity of a semiconductor material on temperature. The temperature coefficient of resistance is generally °C-1. Therefore, thermistors can generally be divided into:
I. A thermistor element with a negative temperature coefficient of resistance is often made of a semiconductor metal oxide formed by transition metal oxide under certain sintering conditions as a basic material. In recent years, a material such as a single crystal semiconductor is also prepared. Domestically, it mainly refers to MF91~MF96 type semiconductor thermistors. Since the above transition metal oxides constituting such thermistors are substantially completely ionized in the room temperature range, that is, the carrier concentration is substantially independent of temperature, the resistivity of such thermistors mainly depends on the mobility as a function of temperature. In relation to temperature, as the temperature increases, the mobility increases and the resistivity decreases. Most of them are used for temperature measurement and temperature control technology, and can also be used as flow meters and power meters.
II. Thermistor element with positive temperature coefficient of resistance commonly used barium titanate material to increase trace amounts of titanium, tantalum, etc. or rare earth elements by ceramic process, high temperature firing. The resistivity of such a thermistors varies with temperature mainly depending on the carrier concentration, and the mobility changes with temperature are relatively negligible. The number of carriers increases exponentially with increasing temperature, and the more the number of carriers, the smaller the resistivity. Widely used, in addition to temperature measurement, temperature control, temperature compensation in electronic circuits, but also made of various types of heaters, such as hair dryers.

2. Experimental equipment and principle

【experimental device】
FQJ—II type unbalanced DC bridge for teaching, FQJ unbalanced bridge heating experimental device and temperature sensor for temperature control), several connection lines.
[Experimental principle]
According to semiconductor theory, the relationship between resistivity and absolute temperature of a typical semiconductor material is

Where a and b are constant for the same semiconductor material and their values ​​are related to the physical properties of the material. Therefore, the resistance value of the thermistor can be written according to the law of resistance.

Where is the distance between the two electrodes, which is the cross section of the thermistor.
For a particular resistor, b is constant and can be determined experimentally. In order to facilitate data processing, take the logarithm on both sides of the above formula, then

The above formula shows a linear relationship. In the experiment, as long as the temperature and the corresponding resistance are measured,
If the abscissa is plotted on the ordinate, the obtained line should be a straight line. The values ​​of parameters a and b can be obtained by graphic method, calculation algorithm or least squares method.
The temperature coefficient of resistance of the thermistor is given by

From the b value obtained by the above method and the room temperature substitution formula, the temperature coefficient of resistance at room temperature can be calculated.
The resistance of the thermistor at different temperatures can be measured by an unbalanced DC bridge. The schematic diagram of the unbalanced DC bridge is shown in the right figure. A load resistor is used between B and D. As long as it is measured, the value can be obtained.

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When the load resistance →, that is, the bridge output is in the open state, =0, only the voltage output, used to indicate, at that time, the bridge output = 0, that is, the bridge is in equilibrium. For measurement accuracy, the bridge must be pre-balanced prior to measurement so that the output voltage is only related to the change in resistance of one arm.
If R1, R2, and R3 are fixed, R4 is the resistance to be tested, and R4 = RX. When R4→R4+△R, the voltage output due to bridge imbalance is:

When measuring the MF51 type thermistor, the unbalanced DC bridge uses a vertical bridge, and,

In the formula, R and both are the resistance values ​​after pre-adjusting the balance. After the voltage output is measured, ΔR can be obtained by the formula operation, and thus = R4 + ΔR is obtained.

3. Research on resistance temperature characteristics of thermistors

According to the resistance-temperature characteristics of the MF51 type semiconductor thermistor in Table 1, the bridge circuit is studied, and the values ​​of the arm resistances R and are designed to ensure that the voltage output does not overflow.
According to the bridge type, pre-balance the balance, turn the “function conversion” switch to the “voltage” position, press the G and B switches, turn on the experimental heating device, measure 1 value every 2 °C, and list the measurement data.

Table 1 MF51 type semiconductor thermistor resistance ~ temperature characteristic temperature °C 25 30 35 40 45 50 55 60 65
Resistance Ω 2700 2225 1870 1573 1341 1160 1000 868 748

Table 2: Measurement of MF51 type thermistor by unbalanced bridge voltage output form
i 1 2 3 4 5 6 7 8 9 10
Temperature t°C 10.4 12.4 14.4 16.4 18.4 20.4 22.4 24.4 26.4 28.4
Thermodynamics TK 283.4 285.4 287.4 289.4 291.4 293.4 295.4 297.4 299.4 301.4
0.0 -12.5 -27.0 -42.5 -58.4 -74.8 -91.6 -107.8 -126.4 -144.4
0.0 -259.2 -529.9 -789 -1027.2 -124.8 -1451.9 -1630.1 -1815.4 -1977.9
4323.0 4063.8 3793.1 3534.0 3295.8 3074.9 2871.1 2692.9 2507.6 2345.1

According to the information obtained in Table 2, the map is shown as shown on the right. The linear equation calculated by the least squares method is the mathematical expression of the resistance-temperature characteristic of the MF51 type semiconductor thermistor.

4, the error of the experimental results

The mathematical expression of the resistance-temperature characteristic of the MF51 type semiconductor thermistor obtained through experiments is . According to the obtained expression, the measured value of the resistance-temperature characteristic of the thermistor is calculated, which is in good agreement with the reference value given in Table 1, as shown in the following table:
Table 3 Experimental results comparison temperature °C 25 30 35 40 45 50 55 60 65
Reference value RT Ω 2700 2225 1870 1573 1341 1160 1000 868 748
Measured value RT Ω 2720 2238 1900 1587 1408 1232 1074 939 823
Relative error % 0.74 0.58 1.60 0.89 4.99 6.20 7.40 8.18 10.00

From the above results, it is basically within the experimental error range. However, we can clearly see that as the temperature increases, the resistance value becomes smaller, but the relative error is larger, which is mainly caused by the internal heat effect.

5. The effect of internal heat effect

During the experiment, when the thermistor is measured by the unbalanced bridge, there is always a certain working current passing through. The thermistor has large resistance value, small volume and small heat capacity, so the Joule heat will quickly make the thermistor stable. An additional internal heat rise above ambient temperature, which is the so-called internal heat effect. When accurately measuring the temperature characteristics of the thermistor, the effects of the internal thermal effect must be considered. This experiment does not conduct further research and discussion.
6, the experimental summary

Through experiments, it is obvious that the resistance value of the thermistor is very sensitive to temperature changes, and as the temperature rises, its resistance value decreases exponentially. Therefore, various types of sensors can be made by using the resistance-temperature characteristics, and a small temperature change can be converted into a resistance change to form a large signal output, which is particularly suitable for high-precision measurement. Moreover, due to the small size of the components and the wide selection of shapes and packaging materials, it is particularly suitable for temperature and humidity sensors in high temperature, high humidity, vibration and thermal shock environments, and can be applied to various production operations with great development potential.

references:

[1] Yan Jiangfeng, Lu Lijuan, Lu Xiaodong. University Physics Experiment [M]
[2] Yang Shuwu, Yang Jiexin, Chen Guoying. General Physics Experiment [M] Beijing: Higher Education Press
[3] "College Physics Experiment" writing group. University Physics Experiment [M] Xiamen: Xiamen University Press
[4] Lu Shenlong, Cao Zhengdong. Experiment and teaching of resistance temperature characteristics of thermistors[J]<