Design of High Precision DC Micro-resistance Tester

　　2.2.1.2 Interference noise outside the detection circuit

　　The noise in the environment where the detection circuit is located is called external interference noise. This noise is determined by the environment, not caused by the internal circuit, and belongs to external environmental noise. A certain external interference source generates noise and couples the noise to the signal detection circuit through a certain path, thereby forming external interference noise to the detection system {7]. There are many types of external interference noise, such as 50Hz AC interference from the mains, AM broadcast signals from radio stations or switching spark interference from power supplies, broadband interference caused by pulsed lasers or radar emissions, cosmic rays, lightning, and mechanical vibrations of components or parts that produce microphonic effects. Common external noises mainly include ground potential noise and power frequency noise formed by ground loops.

　　Ground potential difference noise is the noise introduced by the ground loop formed when the signal source and the measuring instrument are connected to the same ground wire. There are many grounding points on the ground wire, and different grounding points have different potentials. A small potential difference at different points can form a large current in the circuit system and produce a considerable voltage drop. This noise has a great impact on the measurement accuracy of small resistances. This external noise can be eliminated by isolating and grounding the entire measurement circuit system at the same point.

　　The influence of power frequency noise on DC signal measurement is quite obvious. Common power frequency interference sources include power frequency electric field and power frequency magnetic field generated by power lines, power frequency magnetic field generated by power lines and power transformers, harmonic interference generated by motor starters, etc. Power frequency noise has a greater impact on the measurement circuit of micro-resistance.

　　The influence of environmental interference noise on the test results is closely related to the layout and structure of the detection circuit. Its characteristics depend on the characteristics of the interference source and the characteristics of the coupling path, and have nothing to do with the quality of the components in the circuit. The power of the interference noise source is much greater than the power of the useful signal in the detection circuit. After the coupling path, the noise power is greatly weakened, but it may still be considerable relative to the weak useful signal [9]. Therefore, it is necessary to suppress the interference source of the external environment to ensure the high precision requirements of the micro-resistance tester.

　　2.2.2 Error sources in DC microresistance measurement

　　Based on the noise theory of weak DC signals, external interference noise exists in the environment and is not controlled by the detection circuit. Therefore, in DC microresistance measurement, the main research is how to reduce the impact of internal inherent noise sources on the measurement results.

　　In micro-resistance measurement, there are several sources of internal inherent noise errors. The thermal noise inside the conductor will cause thermoelectric potential errors, the contact noise between conductors will cause contact potential errors, and the combined effect of contact potential and thermoelectric potential will produce thermoelectric potential; electrochemical electromotive force errors will also be generated due to electronic polarization between the conductor and the environment; and the measurement circuit itself also has offset and temperature difference errors.

　　2.2.2.1 Thermoelectric potential

　　Thermoelectric potential is the most common source of error in weak DC voltage measurement. Thermoelectric potential includes contact potential and temperature difference potential.

　　The contact potential is caused by the diffusion movement of electrons on the contact surface due to the different electron densities inside two different conductors, and changes with temperature. In electronic measurement systems, there are many kinds of conductors, such as copper, gold, silver, tin, germanium, carbon, lead, copper oxide and other conductors, so there must be contact potential in the measurement system. The influence of the contact potential inside the measurement system amplifier circuit can be eliminated by a variety of technologies, but it is more difficult to eliminate the influence of the contact potential of the signal input circuit, so homogeneous materials should be used for connection as much as possible.

　　When the temperatures of the two ends of the same conductor are different, the electrons at the high temperature end migrate to the low temperature end, thus causing a temperature difference potential. This phenomenon is also called the Thomson effect. Obviously, there is a step-by-step uneven temperature field in the electronic measurement system: the temperature inside and outside the components is different, and the temperature in different areas of the same component is different, so there must be a temperature difference potential. Although the influence of the temperature difference potential inside the electronic measurement system can be eliminated, the influence of the contact potential of the signal input circuit is sometimes difficult to eliminate. At this time, the temperature field distribution of the measurement system should be kept as uniform as possible.

　　As mentioned previously, thermoelectric potentials are caused by the contact of conductors of different materials and the difference in temperature at the conductor junction.

　　As shown in Figure 2.2:

　　A and B are two conductors of different materials, and the temperature of the contact point between the two conductors is:

　　Among them, , is the thermoelectric potential constant when conductors of different materials are in contact, and the unit is v/℃. The following gives the values ​​of , for several metals in contact:

　　From the above, it can be seen that although the thermoelectric potential generated by copper-copper contact is very small, if the copper material is poorly connected and oxidation occurs, the influence of the thermoelectric potential on the measurement of weak DC signals is considerable.

　　2.2.2.2 Chemical electromotive force

　　Electrochemical effect is another major error source in weak DC voltage measurement. It is essentially a weak battery effect generated by the electrochemical effect between two electrodes. For example, the commonly used epoxy resin printed circuit board may produce nA error current if it is not cleaned enough and has some contamination or flux. If the temperature is high or it is contaminated, the insulation resistance of the material will be greatly reduced. High humidity can cause the material to deform or absorb moisture, and contamination may come from human body oil, salt or solder. Contamination first reduces the insulation resistance. If high humidity is added, a conductive path will be formed, and even a chemical battery with a large series resistance will be formed. This battery may produce error currents in the order of PA to nA. Like thermoelectric potential, the influence of chemical potential inside the system can be eliminated, but the influence of electrochemical potential in the signal input circuit is sometimes difficult to eliminate.
 

　　2.3 Error processing method for DC microresistance measurement

　　When the test current flows through the weak resistor, the main reason why the weak voltage signal at both ends cannot be accurately measured is the influence of the DC error source. These error sources mainly include: thermoelectric potential, electrochemical potential, offset and temperature drift of the amplifier circuit itself, etc. Under normal circumstances, the amplitude of the error signal is much larger than the voltage signal to be measured, thereby drowning it. Amplifying the signal to be measured will also amplify the error signal. Only when the error source is eliminated or reduced, the measurement is meaningful. For the thermoelectric potential error, chemical electromotive force error and offset error of the measurement circuit itself in the DC micro-resistance measurement mentioned in the previous section, first of all, it can be solved by physical means, and secondly, the current reverse three-time measurement method can be used to eliminate the error. Finally, the appropriate circuit wiring method can be selected to eliminate the interference of the error on the micro-resistance voltage value measurement to the maximum extent.

　　2.3.1 Physical means of eliminating errors

　　In order to reduce the error of thermoelectric potential, homogeneous measuring wires should be selected as much as possible when designing the circuit, and the temperature difference between the measuring end and the measuring environment should be minimized as much as possible. All nodes in the instrument circuit should be placed close to each other, and the ventilation inside the test instrument should be kept good, and the temperature of each component should be kept consistent as much as possible; the instrument should be preheated for a period of time before measurement to make the temperature inside the measuring instrument as close to the ambient temperature as possible, so as to minimize the measurement error.

　　In order to reduce the influence of chemical electromotive force, non-absorbent materials should be selected. At the same time, care should be taken to keep the insulator clean and hygienic, and not allow dirt or dust to attach to it. If dirt is found on the insulator, it should be cleaned in time. This is a physical means to eliminate and reduce the error of chemical electromotive force.

　　We can only eliminate some errors by physical means. Errors such as thermoelectric potential, electrochemical potential, and measurement circuit imbalance cannot be completely eliminated by physical means. They still exist partially. Next, we will explore the method of eliminating errors from the perspective of circuit wiring method and secondary measurement method.

　　2.3.2 Circuit wiring method design

　　There are generally four common wiring methods for resistance measurement. According to the number of feeder lines used for measurement, they can be divided into two-wire method, three-wire method and four-wire method. There is also another common wiring method for measuring resistance using the bridge method.

　　Let's look at the principles, advantages and disadvantages of the two-wire method, the three-wire method, the bridge method and the four-wire method.

　　2.3.2.1 Principle of two-wire resistance measurement

　　The circuit diagram of the two-wire method for measuring resistance is shown in Figure 2.3:

　　Among them, the resistance to be measured is 1, and the measured contact resistance and lead resistance are represented by 1 and 2 respectively. It can be seen from the figure that the resistance value of the unknown resistance 2 will be the sum of the resistance values ​​of 2, 1 and 2. Therefore, this method can only be used when the resistance to be measured is large. If the resistance to be measured is small, even smaller than the resistance of the measuring wire, then this method will produce a large error. Therefore, the two-wire method is not suitable for measuring micro-resistance with very small resistance value. It is only suitable for measuring wiring of larger resistance.

　　2.3.2.2 Principle of three-wire resistance measurement

　　The wiring for measuring resistance using the three-wire method is to connect the resistor to be measured to the ground wire. The principle is shown in Figure 2.4.

　　In the figure, one end of the resistance circuit to be measured is grounded through a wire, and the other end is connected to the op amps Al and AZ through two wires. The resistance of the three wires is required to be the same, all of which are 1. When the current I is passed through, the output voltages and K of the two op amps are: (the gains of the three op amps are all 1)

　　From the above formula, we can know that no matter what the value of the measured resistance is, the error caused by the wire resistance can be compensated. In this compensation method to measure the micro-resistance circuit, the factor to ensure the measurement accuracy is mainly whether the resistance values ​​of the three wires are consistent. Therefore, when using this method to measure a resistor with a small resistance value, special attention should be paid to the fact that the resistance values ​​of the three wires connected to the resistor to be measured must be equal to ensure the measurement accuracy.

　　This three-wire method of measuring resistance is widely used in practice. As long as the resistance values ​​of the three wires are equal, a certain accuracy requirement can be basically achieved. However, the three-wire resistance measurement method can only eliminate the influence of the equal value line resistance, but cannot eliminate the influence of the contact resistance. The lengths of the measuring wires cannot be completely equal. Therefore, the three-wire method cannot achieve the high accuracy requirements of micro-resistance measurement.