Design diagram of high-precision thermal resistance measurement circuit based on three-wire system
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Thermistor sensor is a temperature sensor whose resistance value changes with the ambient temperature. Among them, thermistor made of metal platinum is widely used because of its good stability, high accuracy, and wide temperature measurement range. Thermistor thermometers for measuring temperature are mainly composed of thermometer sensors, measuring display instruments, and connecting wires. Since the temperature sensitivity of the thermometer sensor itself is low, the line resistance of the connecting wire has an influence on the measurement result that cannot be ignored. In order to eliminate the influence of the wire resistance, the thermometer widely uses the balanced bridge three-wire connection method. This method can compensate the temperature error to a certain extent, but the influence of the line resistance still exists. A three-wire wire resistance compensation method based on constant voltage and voltage divider is proposed. The circuit is simple and easy to implement, and the influence of the wire resistance can be completely eliminated. Compared with the wire resistance compensation method proposed in the literature that uses more hardware circuits for wire resistance compensation, this method has a simpler wire resistance compensation circuit.
1 Analysis of commonly used thermometer measurement methods
For Pt100 platinum thermometer, the relationship between its resistance and temperature is given in the international temperature scale BS-90 as shown in formula (1).
In the formula, Rt is the resistance of the thermal resistor at a temperature of t℃, R0 is the resistance of the thermal resistor at a temperature of 0℃, R0=100Ω, A=3.96847×10-3℃-1, B=-5.847x10-7℃-2, C=-4.22x10-12℃-3 are coefficients related to the sensor itself.
From formula (1), it can be seen that the sensitivity of the Pt100 thermal resistor is about 0.38Ω/℃. In order to reduce the influence of the line resistance of the connecting wire on the measurement result, the three-wire bridge method is generally used for measurement. VR=1 V. The circuit principle is shown in Figure 1. Rt is the temperature measuring resistor, r is the connecting wire resistance, R1, R2, R3 are fixed bridge arms, R1=R2=1 000Ω, R3=100Ω, VR is the reference voltage, and G is the measuring instrument. In this circuit, three wires are connected to the sensor bridge arm, the resistor bridge arm and the output end respectively. This method can easily measure the resistance Rt to be measured. However, in actual use, there is often a certain distance between the temperature sensor and the temperature measurement circuit, and the resistivity of the connecting wire is about 0.1~0.5 Ω/m. The measurement error caused by the connecting wire resistance r cannot be ignored.
As shown in Figure 1, when the line resistance r is not considered, the output of the bridge is:, when the line resistance is considered, the bridge output Vc=VR(Rt+r)／(R1+Rt+r)-VR(R3+r)／(R2+R3+r), assuming that the bridge is balanced when Rt=Rx, that is, R2Rx=R1R3, and the bridge arm resistance R1=R2=R3=Rx=R, when Rt changes by △R, that is, Rt=R+△R, the error caused by the existence of the line resistance r can be calculated as:
It can be seen that the wire resistance r affects the measurement result of Rt, and it cannot be completely eliminated by the zeroing circuit. Based on the above analysis, a constant voltage divider three-wire high-precision preamplifier circuit that can completely eliminate wire errors is proposed.
2 Constant voltage divider three-wire measurement circuit
2.1 Measurement principle
The constant voltage divider three-wire method used here to measure resistance can eliminate the interference of wire resistance. Its equivalent schematic diagram is shown in Figure 2. Where Rt is the thermal resistor. r is the equivalent resistance of the wire. VR is the reference voltage, VAD is the reference voltage of the A/D converter, and β is the voltage magnification factor.
The basic relationship can be obtained from Ohm's law:
From formula (3), it can be seen that when RV and VR are known, to obtain Rt, only V2 and V1 need to be measured, and it has nothing to do with the wire resistance r. And the measurement accuracy only depends on the accuracy of RV and the measurement accuracy of V1 and V2. The wire resistance that cannot be eliminated in the bridge method is completely eliminated in the constant voltage divider three-wire method.
Since the temperature of the thermal resistor will rise when current passes through it, its own self-heating error must be considered, that is, the temperature rise error caused by the current flowing through the thermal resistor must be considered. The commonly used Pt100 thermal resistor drive current is about 1 mA. At 0℃, it is equivalent to a self-heating power of about 0.1 mW. When measuring with high precision, the self-heating power should be further reduced to reduce the self-heating error. Here, VR=2.5V and RV=10kΩ are set, and the self-heating power is about 0.006 mW.
2.2 Measures to improve measurement accuracy
Similar to the three-wire balanced bridge method, the output voltages V1 and V2 of the circuit shown in Figure 2 are small in value, and a first-level voltage amplification should be added before A/D conversion. The reference voltage VR is generally provided by a precision constant voltage source to provide a stable voltage signal. In addition, when the microcontroller software selects an appropriate algorithm and word length in mathematical calculations, the calculation error can also be ignored. However, the amplification factor β and RV of the amplifier circuit will vary from component to component, especially in mass production, the accuracy of components is difficult to ensure uniformity. Therefore, for a specific input circuit, the error caused by β and RV must also be considered.
In order to eliminate the error caused by β and RV, the calibration method can be used to automatically calibrate and calculate the actual circuit β and RV values during instrument production. These two parameters are then recorded in the non-volatile memory of the instrument. When the instrument measures temperature, the parameters are read and calculated according to formula (1) to obtain the accurate measured temperature.
If the long wire in Figure 2 is replaced by the shortest wire possible (i.e. r=0), and the thermal resistor Rt is replaced by a precision resistor R, VAD is the reference voltage of the A/D converter, β is the voltage magnification factor, and the rest remain unchanged, then:
In formula (4), R is a precision resistor with a known resistance value; D is the result of the A/D conversion, which can be easily read from the instrument display device; VR and VAD are reference voltages, which are constants; β is the total magnification factor of the circuit; K is the proportional factor of the A/D conversion, such as K=214 for a 14-bit A/D converter. Then there are only two unknowns RV and β in formula (2). For a specific input circuit, if two precision resistors R1 and R2 with known resistance values are connected to the circuit shown in Figure 2 for calibration (when calibrating, try to make r=0), a set of two-variable linear equations can be obtained. Thus, for a specific input circuit, β and RV can be solved from the equations, and the results are as follows:
The above calibration method can be summarized as follows: two precision standard resistors R1 and R2 with known resistance values are connected to the input terminals of the instrument respectively, and the resistance of the connecting wire is minimized as much as possible. At this time, the instrument readings D1 and D2 are recorded, and the unknown parameters β and RV of the calibrated instrument can be calculated by substituting them into formula (5). In use, it is recommended to use the same reference source for VR and VAD, so that the calculation of β in formula (5) is independent of the accuracy of the reference voltage. This method reduces the differences between different reference sources, especially the influence of time drift and temperature drift of different references.
2.3 Measurement circuit
Figure 3 is the front input circuit of the high-precision Pt100 temperature measurement system, in which the Pt100 reference voltage and the reference voltage of the A/D converter ICL7135 are the same voltage reference source. The two measurement input signals V1 and V2 of Pt100 are amplified by the same operational amplifier (1+R3/R4) times and then enter the A/D converter. The micro relay K1 is used for channel selection. This method shares the operational amplifier, A/D converter, and reference voltage source, reducing the impact of differences between different devices on the measurement results. The A/D conversion result of ICL7135 is connected to the microcontroller in serial mode, which can greatly save the IO port of the microcontroller. When calibrating the circuit, standard resistors 100Ω and 300Ω are used for calibration, and the calibration results β and RV are stored in the EEPROM of the microcontroller system. In actual measurement, the microcontroller system takes out β and RV as known values, and calculates the resistance Rt value by formula (3).
2.4 Analysis of measurement circuit test
Compared with the three-wire balanced bridge method, the detection results of this circuit have been greatly improved. Table 1 is a comparison of the standard resistance values measured by two different methods. Among them, r is the line resistance.
It can be seen from Table 1 that the theoretical measurement results of the three-wire balanced bridge method have large errors, and the error caused by the increase of the line resistance r is larger. As the resistance value of the thermal resistor to be measured increases, the absolute error also increases. In Table 1, the absolute error is 2.57% when the measured resistance Rt=300 Ω and the line resistance r=20 Ω. The actual measurement results of the improved three-wire method used in this paper have an absolute error of only 0.3 Ω and a relative error of ±0.1% within the measured data range. The A/D converter used in the circuit is only equivalent to 14-bit A/D conversion accuracy. If a higher-precision A/D converter is used, higher measurement accuracy can be achieved. In the actual thermal resistor sensor temperature measuring instrument, it is also necessary to add a related program that converts the measured resistance into the corresponding temperature. That is, after Rt is measured, the actual temperature value can be accurately solved by formula (1).
3 Conclusion
The three-wire balanced bridge method is widely used in thermal resistor measurement, but there is a problem that the measurement error caused by the sensor lead resistance cannot be eliminated. This paper analyzes the problems existing in the balanced bridge method for measuring thermal resistors, proposes a constant voltage divider three-wire measurement method, analyzes the causes and influencing factors of the measurement circuit error, derives and establishes the influencing parameters and formulas of the resistance to be measured, and designs a complete measurement circuit, including a signal amplifier and an A/D converter as well as an interface circuit with a single-chip microcomputer. Finally, the test accuracy of the designed circuit is tested and determined. The test shows that when the three-wire balanced bridge method measures the standard resistance value of 100~300Ω and the line resistance is 0~20Ω, the **** measurement error reaches 2.57%, while the balanced three-wire measurement error is only ±0.1%. Thus, a high-precision three-wire thermal resistor measurement circuit is obtained.
