Keywords: thermistor, unbalanced DC bridge, resistance temperature characteristics
1, Introduction
Thermistor is a device based on the strong temperature dependence of the conductivity of semiconductor materials, and its temperature coefficient is generally (-0.003~+0.6)℃- 1. Therefore, thermistors can generally be divided into:
ⅰ. Thermistor element with negative temperature coefficient resistance (NTC for short)
It is usually made of semiconductor metal oxides formed by some transition metal oxides (mainly copper, nickel, cobalt, cadmium and other oxides) under certain sintering conditions, and in recent years, it is also made of single crystal semiconductors and other materials. At home, it mainly refers to MF9 1~MF96 semiconductor thermistor. Because the transition metal oxides that make up this kind of thermistor are basically ionized at room temperature, that is, the carrier concentration is basically independent of temperature, the relationship between mobility and temperature is mainly considered when the resistivity of this kind of thermistor changes with temperature. With the increase of temperature, the mobility increases and the resistivity decreases. Most of them are used in temperature measurement and temperature control technology, and can also be made into flowmeter and power meter.
Ⅱ. Thermistor element with positive temperature coefficient of resistance (PTC for short)
The commonly used barium titanate material is made by adding a small amount of rare earth elements such as titanium and barium, adopting ceramic technology and firing at high temperature. The change of resistivity of this kind of thermistor with temperature mainly depends on the carrier concentration, while the change of mobility with temperature is relatively negligible. The number of carriers increases exponentially with the increase of temperature, and the more carriers, the smaller the resistivity. It is widely used, except for temperature measurement, temperature control and temperature compensation in electronic circuits, and can also be made into various heaters, such as hair dryers.
2. Experimental device and principle
Experimental device
FQJ-Ⅱ unbalanced DC bridge for teaching, experimental device for heating with FQJ unbalanced bridge (MF5 1 semiconductor thermistor (2.7kΩ) and temperature sensor for temperature control are built in the heating furnace), and several connecting wires.
Experimental principle
According to semiconductor theory, the relationship between resistivity and absolute temperature of general semiconductor materials is as follows.
( 1— 1)
Where a and b are constants of the same semiconductor material, and their values are related to the physical properties of the material. Therefore, according to the law of resistance, the resistance value of thermistor can be written as follows
( 1—2)
Where is that distance between the two electrode and the cross section of the thermistor.
For a specific resistance, and b are constants, which can be determined by experimental methods. In order to facilitate data processing, take the logarithm on both sides of the above formula, including
( 1—3)
The above formula shows that there is a linear relationship between and, as long as the values of each temperature and the corresponding resistance are measured in the experiment,
Taking the abscissa as the ordinate as the plot, the plot line obtained should be a straight line, and the values of parameters A and B can be obtained by graphic method, calculation method or least square method.
The temperature coefficient of resistance of thermistor is given by the following formula
( 1—4)
Substituting the B value obtained by the above method and the room temperature into the equation (1-4), the temperature coefficient of resistance at room temperature can be calculated.
The resistance of thermistor at different temperatures can be measured by unbalanced DC bridge. The diagram on the right shows the schematic diagram of unbalanced DC bridge. There is a load resistance between B and D. You can get the value by measuring it.
When the load resistance→, that is, the bridge output is turned on.
Road state, =0, only voltage output, represented by, when the bridge output =0, that is, the bridge is in a balanced state. For the accuracy of measurement, the bridge must be pre-balanced before measurement, so that the output voltage is only related to the resistance change of a certain arm.
If R 1, R2 and R3 are fixed, R4 is the measured resistance, and R4 = RX, then when R4→R4+△R, the voltage output due to the unbalanced bridge is:
( 1—5)
When measuring MF5 1 thermistor, the unbalanced DC bridge is a vertical bridge, and then
( 1—6)
In the formula, R and R are both pre-balanced resistance values. After measuring the voltage output, △R is obtained through the operation of the formula (1-6), thus =R4+△R is obtained.
3. Study on resistance-temperature characteristics of thermistor.
According to the resistance-temperature characteristics of MF5 1 semiconductor thermistor (2.7kΩ) in table1,the bridge circuit is studied, and the value of the resistance r sum of each arm is designed to ensure that the voltage output will not overflow (this experiment =1000.0Ω, = 4323.0Ω).
According to the type of bridge, preset the balance, turn the "function switch" to the "voltage" position, press the G and B switches, turn on the experimental heating device to raise the temperature, measure the value of 1 every 2℃, and list the measurement data (Table 2).
Table 1 MF 5 1 Resistance-temperature characteristics of semiconductor thermistor (2.7kΩ)
Temperature℃ 25 30 35 40 45 50 55 60 65
The resistance ω 2700 22251870157313411601000 868 748.
Table 2 Measurement data of MF5 1 thermistor and output form of unbalanced bridge voltage (vertical)
i 1 2 3 4 5 6 7 8 9 10
Temperature t℃10.412.414.416.418.4 20.4 22.4 24.4 26.4 28.4.
Thermodynamics t k 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 -9 1.6 - 107.8 - 126.4 - 144.4
0.0 -259.2 -529.9 -789 - 1027.2 - 124.8 - 145 1.9 - 1630. 1 - 18 15.4 - 1977.9
4323.0 4063.8 3793. 1 3534.0 3295.8 3074.9 287 1. 1 2692.9 2507.6 2345. 1
According to the data obtained in Table 2, make a chart, as shown on the right. The linear equation calculated by the least square method is the resistance-temperature characteristic of MF5 1 semiconductor thermistor (2.7kΩ), and the mathematical expression is.
4. Error of experimental results
The mathematical expression of resistance-temperature characteristics of MF5 1 semiconductor thermistor obtained through experiments is as follows. According to the obtained expression, the measured value of resistance-temperature characteristics of thermistor is calculated, which is very consistent with the reference value given in table 1, as shown in the following table:
Table 3 Comparison of experimental results
Temperature℃ 25 30 35 40 45 50 55 60 65
Reference value rt ω 2700 22251870157313411601000 868 748.
The measured value is rt ω 2720 223819001587140812321074 939 823.
The relative error is% 0.74 0.581.60 0.89 4.99 6.20 7.408.1810.00.
From the above results, it is basically within the experimental error range. However, we can clearly find that with the increase of temperature, the resistance decreases, but the relative error increases, which is mainly caused by internal thermal effect.
5, the influence of internal thermal effect
During the experiment, because there is always a certain working current when measuring the thermistor with unbalanced bridge, the thermistor has large resistance, small volume and small heat capacity, so Joule heat will quickly make the thermistor produce a stable additional internal thermal temperature rise higher than the external temperature, which is called internal thermal effect. When accurately measuring the temperature characteristics of thermistor, the influence of internal thermal effect must be considered. This experiment will not be further studied and discussed.
6. Experimental summary
It can be clearly found through experiments that the resistance of thermistor is very sensitive to the change of temperature, and its resistance decreases exponentially with the increase of temperature. Therefore, using the resistance-temperature characteristics, various sensors can be made, which can transform the tiny temperature change into resistance change and form a large signal output, especially suitable for high-precision measurement. Due to the small size of the device and the wide selection range of shapes and packaging materials, it is especially 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.