GT6108 race bridge comprehensive experimental instrument manual
(Measure the DC resistance by comparison method)
I. Overview
Resistance is a common component in electromagnetic experimental work. In the history of electromagnetics, the bridge resistance has played an important role. The balance comparison method used by the bridge is a special case when the difference of the differential comparison method is zero; The differential method is one of the comparative methods.
In today's rapid development of measurement technology, how to use digital technology to measure resistance is a subject worth studying. This experiment uses a digital voltmeter to adopt a more intuitive comparison measurement method than the general bridge method (voltage ratio is equal to the resistance ratio). , can measure the resistance more simply and more accurately.
Second, the purpose of the experiment
1. Measure the measured resistance by voltammetry and study the effect of the internal resistance of the meter on the measurement accuracy;
2. Measure the unknown resistance with a Wheatstone bridge (single bridge) and a double bridge to calculate the uncertainty;
3. Calculate the uncertainty by using a direct comparison method (resistance ratio equal to the voltage ratio) to measure different unknown resistances;
4. Measuring the electrical resistivity of the wire at room temperature;
*5. Using a DC constant current source instead of a non-balanced bridge to measure continuously changing non-electricity;
*6. Attachment: Research experiments, distribution of errors and nonlinear residuals of four-and-a-half digital voltmeters
Third, the experimental instrument
1, GT6108 race bridge comprehensive experimental instrument
2, four and a half digital multimeter (optional)
3, QJ23a DC single arm bridge (optional)
4, ZX21a DC resistance box (optional)
5, QJ44 dual-arm bridge (with other)
6, spiral micrometer and vernier caliper (>200mm) (optional)
Fourth, the experimental principle
(1) Principle of measuring resistance by voltammetry
1. Comparison and selection of experimental lines
When the internal resistance of the ammeter is 0 and the internal resistance of the voltmeter is infinite, the measurement uncertainty of the following two test circuits is the same.
Figure 1 The current meter external measurement circuit Figure 2 The current meter internal measurement circuit
Measured resistance
The actual ammeter has a certain internal resistance, which is recorded as RI; the voltmeter also has a certain internal resistance, which is recorded as RV. Because of the existence of RI and RV, if simply used
Formula calculation
The resistor resistance value inevitably leads to additional measurement errors. To reduce this additional error, the measurement circuit can be roughly selected as follows:
Compare the size of lg(R/RI) and lg(RV/R). When comparing, take the rough value or the known approximate value. If the former is large, select the current meter in-line method, and the latter select the current meter external method ( Choice principle 1).
If you want to get the measured value, you must press the 1 and 2 formulas to correct it.
That is, when the ammeter is connected to the measurement
(1) When the ammeter is connected to the external measurement
(2)
In the above two formulas: R—resistance of the measured resistance, Ω; V—the reading of the voltmeter, V; I—the reading of the ammeter, A; RI—the internal resistance of the ammeter, Ω; RV—the internal resistance of the voltmeter, Ω .
2. Basic error limits and uncertainty
When the range and accuracy level of the digital voltmeter and ammeter used in the experiment are fixed, the UV and UI can be estimated, and the simplified formula can be used.
Relative uncertainty in calculation
(3)
Where UR represents the uncertainty of measuring R, not the voltage value of R.
It can be seen that in order to make the measurement accuracy high, the parameters of the line should be selected so that the reading of the digital meter is as close as possible to the full scale (selection principle 2), because the V and I values ​​are large at this time, and the UR/R will be smaller.
When the internal resistance value RV, RI of the digital voltmeter and the ammeter and its uncertainty magnitude URI and URV are known, the values ​​of R can be obtained more accurately by the formulas (1) and (2), and the relative uncertainty is determined by Formula:
When the ammeter is connected:
(4)
When the ammeter is connected externally:
(5)
It is known that when the resistance value R is obtained by the formulas (1) and (2), the line scheme and parameters should be selected to minimize the UR/R (choose principle 3).
(2) The principle of measuring the unknown resistance of Wheatstone bridge (single bridge) and double bridge
In modern metrology, DC bridges are gradually being replaced by digital meters. In the past, bridges played an important role in resistance measurement.
Wheatstone, s bridge has been used for nearly two hundred years. It was first proposed by Cheistie in 1833 and later named after Wheatstone. Measuring resistance with Wheatstone bridge is also a large and middle school physics experiment. Common Topics. The background of the bridge is:
1) In the period before the development of digital meters, if the resistance R=V/I was measured by voltammetry, it was necessary to accurately measure the voltage V and the current I at the same time. At that time, the manufacturing cost and price of the 0.2-stage analog meter were significantly higher than the accuracy. Approximately 0.05% 6-bit keyed resistance box.
2) The requirements for measurement by voltammetry are relatively high. For example, the requirements for the use and verification of the 0.2-level electric meter are higher, and the stability requirements for the power supply are also high.
3) The bridge adopts the comparative measurement method, only the balance of the zero gauge is high enough (no accuracy is required), and the requirements for the power stability index are also low. The accurate resistor is easy to manufacture, and the accuracy of the analog meter is poor. The general power supply stability difference is the material background generated by the Wheatstone bridge. The clever comparative measurement idea is the theoretical reason for the long-term use of the bridge for teaching experiments.
1. The principle of Wheatstone bridge (single bridge)
The schematic diagram of the bridge is shown in Figure 3. The resistance values ​​of the standard resistors R1, R2 and the variable resistor R are known. They are connected to the measured resistance RX in a quadrilateral shape, and each side is called an arm of the bridge. Diagonal A Connect power supply E to and from C; galvanometer G is connected between diagonals B and D. It is like a bridge. If R is adjusted so that the current in the galvanometer is zero, the B and D points are equipotential, and the bridge is balanced.
(6)
If the ammeter is sensitive enough, equation (6) can be fairly well established, and the measured resistance value Rx can be obtained from only the values ​​of the three standard resistors, independent of the supply voltage. This process is equivalent to Rx and standard. The resistance is compared, so the accuracy is high. In the instrument, R2/R1 is made into a ratio of C, then Rx is
Figure 3 Schematic diagram of the bridge
(7)
2. Basic error limits and uncertainty
Under certain reference conditions (near 20 °C, the power supply voltage deviates from the rated value by no more than 10%, the insulation resistance meets certain requirements, the relative humidity is 40-60%, etc.), the allowable basic error of the DC bridge (basic error limit) EIim is
(8)
Where c is the ratio value, the first term α%cR=α%Rx is proportional to the measured resistance. The second term α%(cRN/10) is a constant term, which we agree on for the QJ23a/24 type bridge of the laboratory. RN=5000, which is the simplified processing in teaching (RN=10000 given by the general manufacturer). The grade index α mainly reflects the accuracy of each standard resistance in the bridge. The index α of the certain measurement range and the power supply voltage and current detection The indicators are related. In use, you need to refer to the bridge manual or the labeling parameters of the instrument nameplate. In the teaching, the absolute value of EIim is generally used as the uncertainty of the resistance measurement result.
(9)
Where URx represents the uncertainty of RX, not the voltage of RX, the same below.
3, the sensitive threshold of the bridge
When the power supply and galvanometer indicators do not meet the corresponding requirements of the measurement range, after the bridge is balanced, the RX galvanometer may not be deflected, indicating that the bridge is not sensitive enough. The RX of the current meter sensitivity threshold (0.2 grid) is corresponding. The amount of change ΔS is defined as the bridge sensitivity threshold. The RX change ΔS can be equivalent to: make RX unchanged and only change R to ΔS/c. Then the step of measuring ΔS is: after the balance, the measurement disk R is adjusted to (R+ ΔR), the galvanometer is deflected by Δd (2 or 1 grid), approximately
(10)
The bridge sensitivity threshold ΔS reflects the error effect of the balance judgment. It is related to the parameters of the power supply and the galvanometer, and is also related to the ratios of the ratio c and RX. The larger the ΔS, the less sensitive the bridge. To reduce the ΔS, it can be appropriately increased. Supply voltage or externally sensitive galvanometer. When the power supply and galvanometer indicators meet the requirements of the specification, the influence of ΔS is already included in EIim-; if not, ΔS and EIim should be combined to obtain the uncertainty. URX. For example, a three-resistance box can be used as a bridge arm self-assembled bridge:
(11)
In the middle
Indicates the relative uncertainty of RX, not the voltage on RX divided by RX, similar
Also indicates the relative uncertainty of R1, the same below.
4, double bridge measurement low value resistance
The low value resistor cannot be used with Wheatstone bridge (single bridge), and double bridge can be used. The double bridge measures the low value resistor using four-terminal connection method, as shown in Figure 4. The current terminal is C1, C2, voltage terminal For the P1 and P2 terminals. The voltage measurement takes almost no current. The additional voltage on the lead resistance of AP1 and BP2 is negligible. The voltage of the current I on the leads C1A, BC2 and the contact potential difference on the contacts C1 and C2 are also excluded. Outside the measuring branch P1ABP2. If the measured resistance is a uniform wire, the length of the measured wire is the distance between two points of AB. The principle and usage of the double bridge are not discussed. You can refer to the relevant information. You can read the instrument manual before use. .
Under certain reference conditions (near 20 °C, the power supply voltage deviates from the rated value by no more than 10%, the insulation resistance meets certain requirements, the relative humidity is 40-60%, etc.), the allowable basic error of the double-arm bridge (basic error limit) EIim is
Figure 4 Schematic diagram of the four-terminal method
(12)
Where c is the ratio arm value and R is the measured disk value. The first term α%cR=α%Rx is proportional to the measured resistance. The second term α%(cRN/10) is a constant term, for example, for the experiment The common QJ44 type bridge in the room, we agreed to take RN=0.1Ω in the teaching. The grade index α mainly reflects the accuracy of each standard resistance in the bridge. The index α of a certain measurement range is related to the power supply voltage and the galvanometer index. Contact, in the use of the need to refer to the bridge manual or the instrument nameplate marking parameters.
5, wire resistance and conductivity measurement
The relationship between the resistance RX of the uniform wire and the diameter D, the length l, and the specific resistance Ï is
(13)
In the experiment, the conductivity of the stainless steel wire is measured as a function of temperature. At room temperature, it is on the order of 10 x Ω·m, so the resistance RX of the stainless steel wire is very small. When measuring the low value resistance, a large current is used, and it is necessary to reduce the lead wire ( Connection wire) The influence of resistance and contact point resistance on the measurement, because the lead resistance and contact resistance are often not negligible compared with the measured low value resistance. The diameter of the stainless steel wire can be measured more than five times with a spiral micrometer. ; measure the effective length with a vernier caliper.
(3) Comparison method to measure resistance
1. Principle of measuring resistance by comparison method
With the development of modern digital technology, a more straightforward direct (direct reading) comparison measurement method can be adopted. The schematic diagram of the circuit principle is shown in Fig. 5. In the figure, E is a regulated power supply with an electromotive force E, and the power supply is equivalent. The internal resistance is rE (the lead resistance of the external circuit is included in rE); the object to be measured is Rx; the standard resistance for comparison measurement is RN; the digital voltmeter V with equivalent internal resistance is rV can measure RN and Rx respectively through the switch Voltage VN and VX. rV→∽ are available
Figure 5
(14)
When the internal resistance of the voltmeter is small, the upper formula does not seem to hold, but in fact, when the rE is ignored, the above formula is an identity. Interested students can prove it by themselves.
Under the premise of ignoring the principle error of (14), the relative uncertainty of Rx is
(15)
Where URN is the uncertainty of the standard resistance RN. Because it is a comparative measurement in a short time interval, UVN and UVX do not need to be calculated according to the uncertainty when directly measured by the digital meter, but can be replaced by the nonlinear residual limit Uinl ,min, or directly use Urel, inl as the relative uncertainty value in (15). The advantage of this is that the nonlinear residual limit of the digital table is significantly less than the uncertainty (see the conclusion of the appendix experiment). When the accuracy of the standard resistance is high, that is, when the URN/RN is small, the accuracy of the measurement result of Rx is also high.
In addition, this measurement method does not affect the voltage ratio even if the voltage unit is read incorrectly; even if the uncertainty of the voltmeter is large, the measurement result is still accurate as long as the nonlinear (relative) residual error is small.
2, the implementation
The measuring equipment used in this experiment consists of the following parts:
1) 1~19V ultra-low quasi-static internal resistance adjustable DC regulated power supply, with two multi-turn potentiometers for coarse adjustment and fine adjustment, output current >10mA, can be used as resistance measurement of several tens of ohms or more
power supply;
2) 0~1V voltage source, the maximum current is 5A, used for measuring low-value resistance below tens of ohms;
3) 0 to 10 mA output current source, open circuit voltage 19V, can be used to measure various types of resistance response sensors, or replace the unbalanced bridge for the corresponding experiment;
4) Comparison measurement circuit, including standard resistance RN and transfer switch. RN consists of 11 high-accuracy standard resistors with a nominal value of 10K. For low value resistors, median resistors and high values
Three different objects to be measured, the standard resistance RN uses different values, as shown in Table 1. The switch uses strict four-terminal connection method when measuring low-value resistance, and the experimental device is on the panel.
There are different terminal buttons on the voltage terminal and current terminal.
Table 1
Range of measured resistance
Low value resistor
Median resistance
High value resistor
Similar bridge instrument
QJ44
QJ23
QJ36
RN (Ω)
10-2
10-1
100
101
102
103
104
105
106
107
Measuring range
method 1
0.199RN~1.99RN
Method 2
0.316RN~3.16RN ( )
Power supply selection
Low voltage, 0.02~1 V
1.0 to 19 V continuously adjustable
High current, 0~5 A
Not more than 30 mA
Voltmeter range (V)
0.19999
1. 9999
Voltmeter
Attribute
Range (V)
0.19999
1.9999 (parallel rpar and then serial rser)
Total equivalent internal resistance rv (kΩ)
30
300
3000
5) Multi-range digital voltmeter. It consists of digital voltmeter, parallel anti-bleeding resistor rpar, series fixed-value resistor rser, etc. There are 4 ranges: 0.2V (>10MΩ), 0.2V (30kΩ),
2V (300kΩ), 2V (3MΩ), can be used to measure voltage, and can study the effect of internal resistance on measurement.
6) The measured low value resistor consists of a uniform wire and terminal knob.
3, the specific measurement method
The following two forms can be used as needed:
1) "Direct reading" measurement step with voltage adjustment to make VN the rated value
For "direct reading" measurements, the measurement is equal to the reading value multiplied by 10K. The method is as follows
1 Adjust the power supply voltage so that the VN is rated at 0.10000V, 1.0000 V, etc.
2 After VX is directly read, according to formula (14), RX=VX×10K, where the index K is an integer related to the range.
2) "Full-scale" measurement steps calculated with RX=RNVX/VN
In order to reduce the uncertainty URX of RX, after knowing the approximate value of RX, the measurement range is selected according to the formula of 0.316RN≤RX≤3.16RN. The method is as follows:
1 Adjust the power supply voltage so that the voltage on a resistor with a large resistance value in RX and RN is close to full scale;
2 Then measure the voltage on another smaller resistor, and finally get RX=RNVX/VN.
The measurement results of such operation steps are calculated by calculation, which is not as convenient as the above method. However, since both VX and VN are relatively large, the denominator in the root of equation (15) can be increased to reduce the uncertainty.
* (4) Using a DC constant current source instead of a non-balanced bridge to measure the continuously varying resistance
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