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Sep 30 2019

# The Design for High Precision DC Micro Resistance Tester

## Introduction

This part mainly studies the basic theory of high precision micro resistance tester. According to its size, the resistance can be divided into high resistance (more than 100k) and medium resistance (1 to l00k.) And micro resistance (below 1). This topic main studies the resistance measurement of microohmic resistance.

Resistance measurement is usually done by applying a current to measure voltage, and micro-resistance measurement is no exception. Considering that the microelectronic resistance is very small, in addition to accurately controlling the test current and accurately measuring the weak voltage on the resistance to be tested, it is also necessary to eliminate the influence of the wire resistance on the measured value and minimize the systematic error for achieving the purpose of measuring the resistance of the micro-resistance with high precision. ## Catalog

 Introduction I Basic principle of resistance measurement II Error Analysis of DC Micro Resistance Measurement 2.1 Noise Theory for Weak DC Signal Detection 2.2 Source of Error in DC Micro-resistance Measurement III Error Processing Method for DC Micro Resistance Measurement 3.1 Physical Means of Eliminating Errors 3.2 Design of Circuit Connection Method

## I Basic principle of resistance measurement Figure 1. Basic Principle Diagram of Resistance Measurement

The basic principle of resistance measurement is very simple, that is, the volt-ampere method (figure 1) is used to measure the voltage value U of both R stages with a given current I through resistance R, and the resistance value can be obtained according to ohmic law R=u/I.

However, due to the influence of such factors as wire resistance, contact potential, temperature difference potential, and electrochemical potential in the detection circuit, when the resistance value is relatively large, these effects can be ignored. If the resistance value is extremely small, and the absolute value of the error caused by these effects may even exceed the order of magnitude of the resistance to be tested, so it is necessary to study where these errors come from, how to reduce or even eliminate them, so that the resistance value of the micro resistance can be measured with high precision.

## II Error Analysis of DC Micro Resistance Measurement

When measuring resistance with voltammetry, a DC current source is used; while the small resistance value corresponds to a weak signal. Therefore, it is necessary to first study the noise in the weak sense of DC signal detection, and then the source of the error in the DC micro-resistance measurement.

2.1 Noise Theory for Weak DC Signal Detection

Generally, the interference noise can be defined from two angles. One is from the point of view of loop, the noise expressed by the random fluctuation of the voltage or current caused by the random motion of the charge carrier is defined from the loop angle; Another is from the perspective of signal analysis, undesirable signals that contaminate or interfere with useful signals are called noise.

There are many types of interference noise, and different detection methods should be adopted for different types of interference noise signals. Before the signal detection, we should deeply analyze the essence of the signal and make clear the object of detection, so as to determine the detection principle, method and instrument, etc.

2.1.1 Intrinsic Noise Source Inside the Detection Circuit

The noise generated inside the detection circuit component is called inherent noise, which is caused by the random motion of the charge carrier.

1) Thermal noise of the conductor's own thermal noise conductor: It means that any conductor, even if it is not connected to the power supply, does not have any current passing through the conductor, and it will also exhibit noise voltage fluctuations at both ends. The thermal noise is generated by the random irregular thermal motion of the electrons inside the resistor. The magnitude of which depends on the temperature, the higher the temperature, the more intense the thermal motion of the free electrons in the conductor, and the higher the noise voltage. Once the temperature is lowered, the thermal noise will be reduced. The magnitude of the conductor is also related to the resistance value of the conductor. For large resistors, the influence of the thermal noise of the conductor is correspondingly smaller, but for the micro-resistor, the influence is large.

2) Contact noise between conductors: Acoustic contact noise, also known as 1/f noise, is caused by random fluctuations in the conductance of the contact points of the two conductors. Any device with unsatisfactory conductor contact has contact noise. The amplitude distribution of the 1/f noise current is Gaussian, and its power spectral density function is now proportional to the reciprocal of the operating frequency f. This (f) can be expressed as: Kf : Depends on the material type and geometry of the contact surface; Idc : Average DC current flowing through the contact surface.

Since Sf(f) is proportional to 1, the lower the frequency, the larger the power spectral density of such noise, and the amplitude of 1/f noise in the low frequency band may be large; An excessive noise generated by the resistance inside the resistor is also a kind of 1/f noise; The rms value of the excess noise voltage of several resistors is given below (measured in the range of 10 times per 1v voltage across the resistor):

pure carbon resistance : 0.1一3.0uv

deposited-carbon resistor : 0.05一0.3uv

metal film resistance : 0.02一0.2uv

Therefore, in order to be able to effectively measure weak signals, the measurement bandwidth should be reduced as much as possible.

3) Burst Noise: The cause of the popping noise is that impurities in the semiconductor (generally metal impurities) randomly emit or trap carriers in the PN junction. Burst noise is usually composed of a series of random current pulses of different widths and substantially the same amplitude. The pulse width is generally on the order of a few microseconds to 0.15, and the pulse amplitude is generally 0.01A to 0.001A, and the probability of occurrence is less than several hundred Hz. The burst noise depends on the manufacturing process of the conductor and the state of the impurities in the conductor material. If the burst noise is amplified and sent to the horn, you can hear a popcorn-like sound. Since the burst noise is current-type noise, the resistance of the relevant resistor in the circuit should be reduced as much as possible, and filtering measures should be taken.

2.1.2 Detecting interference noise outside the circuit

The noise present in the environment in which the detection circuit is located is called external interference noise. This noise is determined by the environment, not by the internal circuit, and belongs to the external environmental noise. An external source of interference generates noise and a certain path is used to fuse the noise to the signal detection circuit, thereby forming an external interference noise to the detection system. There are many types of external interference noise, such as 50Hz AC interference of the city, AM-amplified broadcast signals from the radio or switching sparks from the power supply, the broadband interference caused by pulsed laser or radar emissions, cosmic rays, lightning, the howling effect  caused by the mechanical vibration of the component or component. Common external noise mainly includes ground potential noise and power frequency noise formed by the ground loop.

Ground potential difference noise is the noise introduced by the ground loop formed when both the signal source and the measuring instrument are connected to the same ground. There are many contact points on the ground wire, and different potentials are present at different grounding points. A small potential difference at different points can form a large current and generate a considerable voltage drop in the circuit system. This kind of noise has a greater impact on the measurement accuracy of micro resistance. This external noise can be eliminated by isolating and grounding the entire measurement circuitry 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 line, power frequency magnetic field generated by power line and power transformer, and harmonic interference generated by motor starter. Among them, the power frequency noise has a great influence on the measurement loop of the micro resistance.

The influence of environmental interference noise on the detection result is closely related to the layout and structure of the detection circuit. Its characteristics depend on both the characteristics of the interference source and the characteristics of the coordination path, and have nothing to do with the advantages and disadvantages of the components in the circuit. The power of the interference noise source is much larger than that of the useful signal in the detection circuit. After the demarcation path, the noise power is greatly reduced, but it may still be quite significant compared to the weak useful signal. Therefore, it is necessary to suppress the interference source of the external environment, thereby ensuring the high precision requirement of the micro resistance tester.

2.2 Source of Error in DC Micro-resistance 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 the measurement of DC micro-resistance, it is mainly studied how to reduce the influence of internal internal noise sources on the measurement results.

There are several sources of internal inherent noise error in the micro-resistance measurement: The thermal noise inside the conductor will bring the temperature difference potential error, the contact noise between the conductors will bring the contact potential error, and the contact potential and the temperature difference potential will produce the thermoelectric potential. The electrochemical electromotive force error is also generated between the conductor and the environment due to electron polarization; and the measurement circuit itself also has offset and temperature difference errors.

2.2.1 Thermal Emf

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

Contact potential is caused by the diffusion of two different conductors on the contact surface due to different electron densities and changes with temperature. In the electronic measurement system, there are many kinds of conductors, such as copper, gold, silver, tin, antimony, carbon, lead, copper oxide and other conductors, and there is bound to be a contact potential in the measurement system. The influence of the contact potential inside the measuring system amplifying circuit can be eliminated by various techniques, but the influence of the contact potential of the signal input circuit is difficult to eliminate, so the homogenous material should be connected as much as possible.

When the temperature of the same conductor is different at both ends, the electrons at the high temperature end migrate toward the low temperature end to cause a temperature difference potential, which is also called the Thomson effect. Obviously, the electronic measurement system has a step-by-step unevenness of the temperature field: the temperature inside and outside the component is different, and the temperature in different regions of the same component is different, so the temperature difference potential must exist. Although the influence of the temperature difference potential inside the electronic measuring 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 measuring system is kept as uniform as possible.

As mentioned above, the thermoelectric potential is caused by the contact of conductors of different materials and the difference in junction temperature of the conductors.

As shown in figure 2: Figure 2. Electromotive Force Schematic

A, B are conductors of two different materials. T1 and T2 are the temperatures of the two conductors contacting the junction, and the thermoelectric potential generated is VAB : Among them, QAB is the thermoelectric potential constant when the conductors of different materials are in contact.

The values of the thermoelectric constants for several metal contacts are given below:

copper -- copper：<=0.2 μv/℃

copper -- silver : 0.3 μv/℃

copper -- gold : 0.3 μv/℃

copper -- tin : 1-3 μv/℃

copper -- silicon : 400 μv/℃

copper -- copper oxide : -1000 μv/℃

It can be seen from the above that although the thermoelectromotive force generated by the copper-copper contact is small, if the copper material is poorly connected and there is oxidation, the influence of the thermoelectric potential on the measurement of the weak DC signal is considerable.

2.2.2 Chemical Electromotive Force

Electrochemical effect is another major source of error in weak DC voltage measurements. It is essentially a weak battery effect caused by the electrochemical effect between two electrodes. For example, a commonly used epoxy printed circuit board may generate an error current of the order of nA when it is not clean enough to have some stains or fluxes. If the temperature is high or contaminated, the insulation resistance of the material will be greatly reduced. High humidity can cause material to deform or absorb moisture, while stains can be resulted from human body oil, salt or solder. The stains will first reduce the insulation resistance. If high humidity is added, a conductive path will be formed and even a large series resistance chemical cell will be formed, and the battery may generate an error current between PA and nA. Like the thermoelectric potential, the influence of the chemical potential inside the system can be eliminated, but the influence of the electrochemical potential of the signal input circuit is sometimes difficult to eliminate.

## III Error Processing Method for DC Micro Resistance Measurement

When the test current flows through the weak resistance, the reason why the weak voltage signal at both ends cannot be accurately measured is mainly the influence of the DC error source. These sources of error mainly include: thermoelectric potential, electrochemical potential, offset of the amplifying circuit itself and temperature drift. In general, the amplitude of the error signal is much larger than the voltage signal to be tested to flood it, and the signal to be measured is amplified while the error signal is amplified. Measurements only make sense if the amplification is eliminated or reduced. For the thermoelectric potential error, the chemical electromotive force error and the offset error of the measurement circuit itself mentioned in the previous section, the first thing can be solved by physical means. Secondly, the current reverse three 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 to the measurement of the negative value of the micro resistance to the maximum extent.

3.1 Physical Means of Eliminating Errors

In order to reduce the thermoelectric potential error, the homogenous measuring wire 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. All the nodes in the instrument circuit should be placed close to each other, and the internal ventilation of the test instrument should be kept well, keeping the temperature of each component as consistent as possible; The instrument should be warmed up for a period of time prior to measurement so that the temperature inside the measuring instrument is as close as possible to the ambient temperature and the measurement error is as small as possible.

And in order to reduce the influence of EMF, materials that do not absorb water should be selected. At the same time, care should be taken to keep the insulator clean and hygienic. And should not be attached to dirt or dust. If dirt is found on the insulator, it should be cleaned in time. Which is a physical means to eliminate and reduce the error of chemical electromotive force.

We can only eliminate some errors by physical means, such as thermoelectromotive force, electrochemical potential, measurement circuit offset and so on, which cannot be completely eliminated by physical means, but there are always some errors. Next, we discuss the elimination of errors from the circuit wiring method and the secondary measurement method.

3.2 Design of Circuit Connection Method

There are generally four commonly used methods for measuring resistance. According to the number of feeders used for measurement, the two-wire method and the three-wire method can be divided. In addition, there is a common bridge method for measuring resistance wiring.

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

1) Principle of Measuring Resistance by Two-wire Method

The schematic diagram of the circuit for measuring resistance by two-wire method, as shown in figure 3: Figure 3. Two-wire Method to Measure Resistance Schematic

Among them, the resistance to be tested is R, and the measured contact resistance and lead resistance are represented by R1 and R2, respectively. As can be seen from the figure, the resistance value measured by the unknown resistor Rx will be the sum of the resistance values of R, R1 and R2. So this method can only be used when the resistance to be tested is large. If the resistance to be measured is small, even less than the resistance of the measuring lead, the method will produce a large error. Therefore, the two-wire method is not suitable for measuring the micro-resistance with a small resistance value, and it is only suitable for the measurement wiring of a large resistance.

2) Principle of Measuring Resistance by Three-wire Method Figure 4. Three-wire Method to Measure Resistance Schematic

In the figure, one end of the resistor Rx to be tested is grounded through a wire, and the other end is connected to the operational amplifiers Al and AZ via two wires respectively, and the resistance of the three wires is required to be the same, both are R. When the current I is as shown, the output voltages of the two op amps and K are: The output voltage of A3 is: It can be seen from the above formula that regardless of the value of the measured resistance, the influence of the error caused by the resistance of the wire can be compensated. n this compensation method for measuring the micro-resistance circuit, the factor of ensuring the measurement accuracy is mainly whether the resistance values of the three wires are consistent. Therefore, when measuring the resistance with a small resistance value by this method, special attention should be paid to the equal resistance of the three wires connecting the resistance to be tested to ensure the accuracy of the measurement.

The method of measuring the resistance of the three-wire method is quite extensive in practical applications, and it is basically able to achieve a certain accuracy requirement by paying attention to the equal resistance values of the three wires. However, the three-wire resistance measurement method can only eliminate the influence of the isoline resistance, and cannot eliminate the influence of the contact resistance, so that the length of the measurement wires cannot be completely equal. Therefore, the three-wire method cannot achieve the high precision requirement of the micro resistance measurement.

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