Types of basic methods and technology of electrical measurements. Electrical measurements and instruments

ELECTRICAL MEASUREMENTS AND INSTRUMENTS

3.1. The role of measurements in electrical engineering

In any field of knowledge, measurements are extremely important, but they are especially important in electrical engineering.

Mechanical, thermal, light phenomena a person perceives with the help of his senses. We, although approximately, can estimate the size of objects, the speed of their movement, and the brightness of luminous bodies. For a long time this is how people studied the starry sky.

But you and I react in exactly the same way to a conductor whose current is 10 mA or 1 A(i.e. 100 times more).

We see the shape of the conductor, its color, but our senses do not allow us to assess the magnitude of the current. In the same way, we are completely indifferent to the magnetic field created by the coil, the electric field between the plates of the capacitor. Medicine has established a certain influence of electric and magnetic fields on the human body, but we do not feel this influence, and the magnitude electromagnetic field we cannot evaluate.

The only exceptions are very strong fields. But even here there is an unpleasant tingling sensation, which can be noticed when walking around high voltage line transmission will not allow us to even approximately estimate the magnitude of the electrical voltage in the line.

All this forced physicists and engineers from the first steps of research and application of electricity to use electrical measuring instruments.

Instruments are the eyes and ears of an electrical engineer. Without them he is deaf and blind and completely helpless. Millions of electrical measuring instruments are installed in factories and research laboratories. Each apartment also has a measuring device - an electric meter.

The readings (signals) of electrical measuring instruments are used to assess the operation of various electrical devices and the condition of electrical equipment, in particular the state of insulation. Electrical measuring instruments are distinguished by high sensitivity, measurement accuracy, reliability and ease of implementation.

The successes of electrical instrument making led to the fact that other industries began to use its services. Electrical methods began to be used to determine dimensions, speeds, mass, and temperature. There was even independent discipline “Electrical measurements are not electrical quantities ”.

The readings of electrical measuring instruments can be transmitted over long distances (telemetering), they can be used for direct impact on production processes(automatic regulation); with their help, the progress of controlled processes is recorded, for example by recording on tape, etc.

The use of semiconductor technology has significantly expanded the use of electrical measuring instruments.

To measure any physical quantity means to find its value experimentally using special technical means.

Bench testing of the latest equipment is unthinkable without electrical measurements. Thus, when testing a turbogenerator with a power of 1200 MW At the Elektrosila plant, measurements were taken at 1,500 points.

The development of electrical measuring instruments has led to the use of microelectronics in them, which makes it possible to measure physical quantities with an error of no more than 0.005-0.0005%.

3.2. Basic concepts, terms and definitions

results theoretical activities without experimental verification are unreliable. Measuring equipment during an experiment gives results that indicate the quality and quantity of products, the correctness of technological processes, distribution, consumption and manufacturing. At the same time, electrical measurements, due to low energy consumption, the possibility of transmitting measured values over a distance, high speed of measurements and transmission, as well as high accuracy and sensitivity, turned out to be preferable.

Electrical measurements and instruments, methods and means of ensuring their unity, methods of achieving the required accuracy - all this relates to metrology, and the principles and methods for establishing optimal norms and rules of interaction - to standardization.

IN Russian Federation standardization and metrology are combined into a single public service- State Committee of Standards. In 1963, GOST 9867-61 introduced the International System of Units (SI) based on the meter ( m), kilogram ( kg), seconds ( With), ampere ( A), kelvin ( TO) and candelas ( cd).

Issues of electrical measurements and instruments are easier to understand if the content of the terms and definitions is known.

Metrology- the science of measurements, methods and means of ensuring their unity, and methods of achieving the required accuracy.

Measurement- finding the value of a physical quantity experimentally using special technical means.

Measurement result- the value of a physical quantity found by measurement.

Measure- a measuring instrument designed to reproduce a physical quantity of a given size (for example, the unit of measurement of light - cd).

Transducer- a measuring instrument for generating a signal of measuring information in a form convenient for transmission, further conversion, processing (or storage), but not amenable to direct perception by an observer. The primary measuring transducer is a sensor.

Measuring device- a measuring instrument designed to generate a signal of measuring information in a form accessible to direct perception by an observer.

3.3. Measurement methods. Measurement error

For various measured electrical quantities there are their own measuring instruments, so-called measures. For example, normal elements serve as measures of EMF, measuring resistors serve as measures of electrical resistance, measuring inductors serve as measures of inductance, capacitors of constant capacitance serve as measures of electrical capacitance, etc.

In practice, various methods are used to measure various physical quantities. The latter, depending on the method of obtaining the result, are divided into straight And indirect. At direct measurement the value of the quantity is obtained directly from experimental data. At indirect measurement the desired value of a quantity is found by counting using a known relationship between this quantity and values obtained from direct measurements. Thus, the resistance of a section of a circuit can be determined by measuring the current flowing through it and the applied voltage, followed by calculating this resistance from Ohm’s law. The most widely used methods in electrical measuring technology are direct measurement methods, since they are usually simpler and require less time.

In electrical measuring technology they also use comparison method, which is based on a comparison of the measured value with a reproducible measure. The comparison method can be compensatory or bridge. Application example compensation method serves to measure voltage by comparing its value with the value of the EMF of a normal element. Example bridge method is to measure resistance using a four-arm bridge circuit. Measurements using the compensation and bridge methods are very accurate, but they require more sophisticated measuring equipment.

The needs of science and technology include many measurements, the means and methods of which are constantly being developed and improved. The most important role in this area belongs to measurements of electrical quantities, which find wide application in a wide variety of industries.

Concept of measurements

The measurement of any physical quantity is made by comparing it with a certain quantity of the same type of phenomenon, adopted as a unit of measurement. The result obtained from the comparison is presented numerically in appropriate units.

This operation is carried out using special means measurements - technical devices that interact with an object, certain parameters of which need to be measured. In this case, certain methods are used - techniques through which the measured value is compared with the unit of measurement.

There are several signs that serve as the basis for classifying measurements of electrical quantities by type:

Number of measurement acts. What matters here is whether they are once or twice.
Degree of accuracy. There are technical, control and verification measurements, the most accurate measurements, as well as equally accurate and non-equally accurate.
The nature of the change in the measured quantity over time. According to this criterion, measurements can be static and dynamic. By dynamic measurements we obtain instantaneous values quantities that change over time, and static ones - some constant values.
Presentation of the result. Measurements of electrical quantities can be expressed in relative terms or in terms of absolute form.
A method for obtaining the desired result. According to this criterion, measurements are divided into direct (in which the result is obtained directly) and indirect, in which quantities associated with the desired value of any one are directly measured. functional dependence. In the latter case, the desired physical quantity is calculated from the results obtained. Thus, measuring current using an ammeter is an example of direct measurement, and power is indirect.

Measuring

Devices intended for measurement must have standardized characteristics, and also retain for a certain time or reproduce the unit of the quantity for which they are intended to measure.

Instruments for measuring electrical quantities are divided into several categories depending on their purpose:

Measures. These means serve to reproduce a value of a certain specified size - such as, for example, a resistor that reproduces a certain resistance with a known error.
forming a signal in a form convenient for storage, conversion, transmission. This kind of information is not available for direct perception.
Electrical measuring instruments. These tools are designed to present information in a form accessible to the observer. They can be portable or stationary, analog or digital, recording or signaling.
Electrical measuring installations are complexes of the above mentioned means and additional devices, concentrated in one place. The installations allow for more complex measurements(For example, magnetic characteristics or resistivity), serve as verification or reference devices.
Electrical measuring systems are also a combination of various means. However, unlike installations, instruments for measuring electrical quantities and other means within the system are dispersed. Using systems, you can measure several quantities, store, process and transmit measurement information signals.

If it is necessary to solve any specific complex measurement problem, measuring and computing complexes are formed that combine a number of devices and electronic computing equipment.

Characteristics of measuring instruments

Measuring equipment devices have certain properties, important for the performance of their direct functions. These include:

such as sensitivity and its threshold, measurement range of an electrical quantity, instrument error, division value, speed, etc.
Dynamic characteristics, for example amplitude (dependence of the amplitude of the output signal of the device on the amplitude at the input) or phase (dependence phase shift depending on the signal frequency).
Performance characteristics, reflecting the degree of compliance of the device with operating requirements under certain conditions. These include properties such as reliability of readings, reliability (operability, durability and reliability of the device), maintainability, electrical safety, and efficiency.

The set of characteristics of the equipment is established by the relevant regulatory and technical documents for each type of device.

Methods used

Electrical quantities are measured using various methods, which can also be classified according to following criteria:

The type of physical phenomena on the basis of which the measurement is carried out (electrical or magnetic phenomena).
The nature of the interaction of the measuring instrument with the object. Depending on it, contact and non-contact methods measurements of electrical quantities.
Measurement mode. In accordance with it, measurements can be dynamic and static.
Both direct assessment methods have been developed, when the desired value is directly determined by a device (for example, an ammeter), and more accurate methods (zero, differential, opposition, substitution), in which it is revealed by comparison with a known value. Compensators and electrical measuring bridges of constant and constant voltage serve as comparison devices. alternating current.

Electrical measuring instruments: types and features

Measuring basic electrical quantities requires a wide variety of instruments. Depending on the physical principle, which forms the basis of their work, they are all divided into the following groups:

Electromechanical devices necessarily have a moving part in their design. To this large group measuring instruments include electrodynamic, ferrodynamic, magnetoelectric, electromagnetic, electrostatic, induction instruments. For example, the magnetoelectric principle, which is used very widely, can be used as the basis for devices such as voltmeters, ammeters, ohmmeters, and galvanometers. Electricity meters, frequency meters, etc. are based on the induction principle.
Electronic devices are distinguished by the presence of additional units: converters of physical quantities, amplifiers, converters, etc. As a rule, in devices of this type the measured quantity is converted into voltage, and their structural basis is a voltmeter. Electronic measuring instruments are used as frequency meters, capacitance, resistance, inductance meters, and oscilloscopes.
Thermoelectric devices combine in their design a magnetoelectric type measuring device and a thermal converter formed by a thermocouple and a heater through which the measured current flows. Devices of this type are used mainly for measuring high-frequency currents.
Electrochemical. The principle of their operation is based on processes that occur on the electrodes or in the medium under study in the interelectrode space. Instruments of this type are used to measure electrical conductivity, the amount of electricity and some non-electrical quantities.

By functional features differentiate the following types instruments for measuring electrical quantities:

Indicating (signaling) devices are devices that allow only direct reading of measurement information, such as wattmeters or ammeters.
Recording - instruments that allow the recording of readings, for example, electronic oscilloscopes.

Based on the type of signal, devices are divided into analog and digital. If the device produces a signal that is a continuous function of the quantity being measured, it is analog, for example a voltmeter, the readings of which are given using a dial with a pointer. In the event that the device automatically generates a signal in the form of a stream of discrete values, which is supplied to the display in numerical form, we speak of a digital measuring instrument.

Digital instruments have some disadvantages compared to analog ones: less reliability, need for a power source, more high price. However, they are also distinguished by significant advantages that, in general, make the use of digital devices more preferable: ease of use, high accuracy and noise immunity, the possibility of universalization, combination with a computer and remote signal transmission without loss of accuracy.

Errors and accuracy of instruments

The most important characteristic of an electrical measuring device - the class of electrical quantities, like any other, cannot be made without taking into account the errors of the technical device, as well as additional factors(coefficients) affecting the measurement accuracy. Limit values of given errors allowed for of this type device are called normalized and are expressed as a percentage. They determine the accuracy class of a particular device.

The standard classes that are used to mark the scales of measuring devices are as follows: 4.0; 2.5; 1.5; 1.0; 0.5; 0.2; 0.1; 0.05. In accordance with them, a division by purpose has been established: devices belonging to classes from 0.05 to 0.2 are exemplary, laboratory devices have classes 0.5 and 1.0, and, finally, devices of classes 1.5-4 ,0 are technical.

When choosing a measuring device, it is necessary that it corresponds in class to the problem being solved, while upper limit measurements should be as close as possible to the numerical value of the desired quantity. That is, the greater the deviation of the instrument needle can be achieved, the smaller the relative error of the measurement will be. If only low-class devices are available, you should choose the one that has the smallest operating range. Using these methods, measurements of electrical quantities can be carried out quite accurately. In this case, you also need to take into account the type of scale of the device (uniform or uneven, such as ohmmeter scales).

Basic electrical quantities and units of measurement

Most often, electrical measurements are associated with the following set of quantities:

Current strength (or simply current) I. This value indicates the amount of electric charge passing through the cross-section of a conductor in 1 second. The electric current is measured in amperes (A) using ammeters, avometers (testers, so-called “tseshki”), digital multimeters, and measuring transformers.
Quantity of electricity (charge) q. This value determines to what extent a particular physical body can be a source of an electromagnetic field. Electric charge is measured in coulombs (C). 1 C (ampere-second) = 1 A ∙ 1 s. The measuring instruments are electrometers or electronic charge meters (coulomb meters).
Voltage U. Expresses the potential difference (charge energy) existing between two different points electric field. For this electrical quantity, the unit of measurement is the volt (V). If, in order to move a charge of 1 coulomb from one point to another, the field does 1 joule of work (that is, the corresponding energy is expended), then the potential difference - voltage - between these points is 1 volt: 1 V = 1 J/1 Cl. Electrical voltage is measured using voltmeters, digital or analog (testers) multimeters.
Resistance R. Characterizes the ability of a conductor to prevent electric current from passing through it. The unit of resistance is ohm. 1 Ohm is the resistance of a conductor having a voltage at the ends of 1 volt to a current of 1 ampere: 1 Ohm = 1 V/1 A. Resistance is directly proportional to the cross-section and length of the conductor. To measure it, ohmmeters, avometers, and multimeters are used.
Electrical conductivity (conductivity) G is the reciprocal of resistance. Measured in siemens (Sm): 1 Sm = 1 Ohm -1.
Capacitance C is a measure of a conductor's ability to store charge, also one of the basic electrical quantities. Its unit of measurement is the farad (F). For a capacitor, this value is defined as the mutual capacitance of the plates and is equal to the ratio of the accumulated charge to the potential difference across the plates. The capacitance of a flat-plate capacitor increases with increasing area of the plates and decreasing the distance between them. If, with a charge of 1 coulomb, a voltage of 1 volt is created on the plates, then the capacitance of such a capacitor will be equal to 1 farad: 1 F = 1 C/1 V. The measurement is carried out using special devices- capacitance meters or digital multimeters.
Power P is a quantity that reflects the speed at which electrical energy is transferred (converted). As system unit power is taken as watt (W; 1 W = 1 J/s). This value can also be expressed through the product of voltage and current: 1 W = 1 V ∙ 1 A. For alternating current circuits, active (consumed) power P a is distinguished, reactive power P ra (does not take part in the operation of the current) and total power P When measuring, the following units are used: watt, var (stands for “volt-ampere reactive”) and, accordingly, volt-ampere VA. Their dimensions are the same, and they serve to distinguish between the indicated quantities. Instruments for measuring power - analog or digital wattmeters. Indirect measurements(for example, using an ammeter) are not always applicable. To determine such an important quantity as the power factor (expressed through the phase shift angle), instruments called phase meters are used.
Frequency f. This is a characteristic of alternating current, showing the number of cycles of change in its magnitude and direction (in general case) for a period of 1 second. The unit of frequency is the reciprocal second, or hertz (Hz): 1 Hz = 1 s -1. This quantity is measured using a wide class of instruments called frequency meters.

Magnetic quantities

Magnetism is closely related to electricity, since both are manifestations of a single fundamental physical process - electromagnetism. Therefore, an equally close connection is characteristic of methods and means of measuring electrical and magnetic quantities. But there are also nuances. As a rule, when determining the latter, an electrical measurement is practically carried out. The magnetic quantity is obtained indirectly from the functional relationship connecting it with the electrical quantity.

The reference quantities in this measurement area are magnetic induction, field strength and magnetic flux. They can be converted using the measuring coil of the device into EMF, which is measured, after which the required values are calculated.

Magnetic flux is measured using instruments such as webermeters (photovoltaic, magnetoelectric, analog electronic and digital) and highly sensitive ballistic galvanometers.
Induction and magnetic field strength are measured using teslameters equipped with various types of transducers.

The measurement of electrical and magnetic quantities, which are in direct relationship, allows us to solve many scientific and technical problems eg research atomic nucleus and magnetic field of the Sun, Earth and planets, study of magnetic properties various materials, quality control and others.

Non-electrical quantities

Convenience electrical methods makes it possible to successfully extend them to measurements of all kinds of physical quantities of a non-electrical nature, such as temperature, dimensions (linear and angular), deformation and many others, as well as to study chemical processes and composition of substances.

Devices for electrical measurement of non-electrical quantities are usually a complex of a sensor - a converter into some circuit parameter (voltage, resistance) and an electrical measuring device. There are many types of transducers, thanks to which you can measure the most different sizes. Here are just a few examples:

Rheostat sensors. In such converters, when exposed to the measured value (for example, when the level of a liquid or its volume changes), the rheostat slider moves, thereby changing the resistance.
Thermistors. The resistance of the sensor in devices of this type changes under the influence of temperature. Used to measure speed gas flow, temperature, to determine the composition gas mixtures.
Strain resistances make it possible to measure wire deformation.
Photosensors that convert changes in illumination, temperature, or movement into a photocurrent that is then measured.
Capacitive transducers used as sensors for the chemical composition of air, movement, humidity, pressure.
work on the principle of the occurrence of EMF in some crystalline materials when mechanical impact on them.
Induction sensors are based on converting quantities such as speed or acceleration into an induced emf.

Development of electrical measuring instruments and methods

The wide variety of means for measuring electrical quantities is due to the variety various phenomena, in which these parameters play a significant role. Electrical processes and phenomena have an extremely wide range of use in all industries - it is impossible to specify an area of human activity where they would not find application. This determines the ever-expanding range of problems of electrical measurements of physical quantities. The variety and improvement of means and methods for solving these problems is constantly growing. The area of measurement technology such as measuring non-electrical quantities using electrical methods is developing especially quickly and successfully.

Modern electrical measuring technology is developing in the direction of increasing accuracy, noise immunity and speed, as well as increasing automation of the measuring process and processing of its results. Measuring instruments have evolved from the simplest electromechanical devices to electronic and digital devices, and then to the latest measuring and computing systems using microprocessor technology. At the same time, the increasing role of the software component of measuring devices is obviously the main development trend.

ON THE TOPIC OF:

"ELECTRICAL MEASUREMENTS"

Introduction

The development of science and technology has always been closely linked with progress in the field of measurements. Great importance measurements for science have been emphasized by some scientists.

G. Galileo: “Measure everything that is accessible to measurement and make accessible everything that is inaccessible to it.”

DI. Mendeleev: “Science begins as soon as they begin to measure, exact science unthinkable without measure."

Kelvin: “Every thing is known only to the extent that it can be measured.”

Measurements are one of the main ways to understand nature, its phenomena and laws. To each new discovery in the field of natural and technical sciences preceded by a large number of different measurements. (G. Ohm - Ohm's law; P. Lebedev - light pressure).

Measurements play an important role in creating new machines, structures, and improving product quality. For example, during a bench test of the world's largest 1200 MW turbogenerator, created at the Leningrad Electrosila Association, measurements were taken at 1500 different points.

Especially important role electrical measurements of both electrical and non-electrical quantities play a role.

The world's first electrical measuring instrument "pointer electric force"was created in 1745 by academician G.V. Rokhman, colleague of M.V. Lomonosov.

It was an electrometer - a device for measuring potential differences. However, only from the second half of the 19th century, in connection with the creation of electrical energy generators, the question of developing various electrical measuring instruments became acute.

Second half of the 19th century, beginning of the 20th century - Russian electrical engineer M.O. Dolivo-volunteer developed an ammeter and voltmeter, an electromagnetic system; induction measuring mechanism; fundamentals of ferrodynamic devices.

At the same time - Russian physicist A.G. Stoletov – the law of change in magnetic permeability, its measurement.

At the same time - Academician B.S. Jacobi - instruments for measuring the resistance of an electrical circuit.

At the same time - D.I. Mendeleev - the exact theory of scales, the introduction of the metric system of measures in Russia, the organization of a department for testing electrical measuring instruments.

1927 - Leningrad built the first domestic instrument-making plant "Electropribor" (now - Vibrator production of meters).

30 years - instrument-making plants were built in Kharkov, Leningrad, Moscow, Kyiv and other cities.

From 1948 to 1967, the volume of instrument manufacturing products increased 200 times.

In the subsequent five-year plans, the development of instrument engineering proceeds at an invariably faster pace.

Main achievements:

– Analogue devices for direct assessment of improved properties;

– Narrow-profile analog signaling control devices;

– Precision semi-automatic capacitors, bridges, voltage dividers, other installations;

– Digital measuring instruments;

– Application of microprocessors;

– Measuring computer.

Modern production is unthinkable without modern means measurements. Electrical measuring technology is constantly being improved.

In instrument making, the achievements of radio electronics, computer technology, and other achievements of science and technology are widely used. Microprocessors and microcomputers are increasingly being used.

Studying the course “Electrical measurements” sets the goal:

– Study of the structure and principle of operation of electrical measuring instruments;

– Classification of measuring instruments, familiarization with symbols on instrument scales;

– Basic measurement techniques, selection of certain measuring instruments depending on the quantity being measured and measurement requirements;

– Familiarization with the main directions of modern instrument making.

1 . Basic concepts, measurement methods and errors

By measuring is called finding the values of a physical quantity experimentally using special technical means.

Measurements must be made in generally accepted units.

Electrical measuring instruments are called technical means, used in electrical measurements.

The following types of electrical measuring instruments are distinguished:

– Electrical measuring instruments;

– Measuring transducers;

– Electrical measuring installations;

– Measuring Information Systems.

Measure is a measuring instrument designed to reproduce a physical quantity of a given size.

Electrical measuring instrument is an electrical measuring instrument designed to generate measurement information signals in a form accessible to direct perception by the observer.

Measuring transducer is an electrical measuring instrument designed to generate measurement information signals in a form convenient for transmission, further conversion, storage, but not amenable to direct perception.

Electrical measuring installation consists of a number of measuring instruments and auxiliary devices. With its help, you can make more accurate and complex measurements, verification and calibration of instruments, etc.

Measurement information systems represent a set of measuring instruments and auxiliary devices. Designed to automatically receive measurement information from a number of sources, for its transmission and processing.

Classification of measurements :

A). Depending on the method of obtaining the result, direct and indirect :

Direct are called measurements, the result of which is obtained directly from experimental data (current measurement with an ammeter).

Indirect are called measurements in which the desired quantity is not directly measured, but is found as a result of calculation using known formulas. For example: P=U·I, where U and I are measured by instruments.

b). Depending on the set of techniques for using principles and measuring instruments all methods are divided into methods direct assessment and comparison methods .

Direct assessment method– the measured value is determined directly from the reading device of the measuring device direct action(current measurement with an ammeter). This method is simple, but has low accuracy.

Comparison method– the measured quantity is compared with a known one (for example: measuring resistance by comparing it with a measure of resistance - a standard resistance coil). The comparison method is divided into zero, differential and substitution .

Null– the measured and known quantity simultaneously influence the comparison device, bringing its readings to zero (for example: measuring electrical resistance with a balanced bridge).

Differential– a comparison device measures the difference between a measured and a known quantity.

Substitution method– the measured quantity is replaced in the measuring installation by a known quantity.

This method is the most accurate.

Measurement errors

The results of measuring a physical quantity provide only an approximate value due to a number of reasons. The deviation of the measurement result from the true value of the measured value is called measurement error.

Distinguish absolute and relative error.

Absolute error measurement is equal to the difference between the measurement result Ai and the true value of the measured quantity A:

Correction: dA=A–Ai

Thus, the True value of the quantity is equal to: A=Au+dA.

You can find out about the error by comparing the readings of the device with the readings of a reference device.

Relative error measurement g A is the ratio of the absolute measurement error to the true value of the measured value, expressed in%:

Example: The device shows U=9.7 V. The actual value of U=10 V is determined by DU and U:

ДU=9.7–10=–0.3 V g U =

%=3%.

Measurement errors have systematic and random components. First remain constant with repeated measurements, they are determined, and its influence on the measurement result is eliminated by introducing a correction . Second change randomly, and they cannot be identified or eliminated .

In the practice of electrical measurements, the concept is most often used given error g p:

This is the ratio of the absolute error to the nominal value of the measured value or to the last digit on the instrument scale:

Example: DU = 0.3 V. The voltmeter is designed for 100 V. g p =?

g p =0.3/100·100%=0.3%

Errors in measurements may result from :

A). Incorrect installation of the device (horizontal instead of vertical);

b). Incorrect accounting of the environment (external humidity, tє).

V). Influence of external electromagnetic fields.

G). Inaccurate readings, etc.

In the manufacture of electrical measuring instruments, certain technical means are used to ensure one or another level of accuracy.

The error due to the manufacturing quality of the device is called - main error .

In accordance with the quality of workmanship, all devices are divided into accuracy classes : 0,05; 0,1; 0,2; 0,5; 1,0; 1,5; 2,5; 4,0.

The accuracy class is indicated on the scales of measuring instruments. It denotes the Main maximum permissible reduced error of the device:

Based on the accuracy class when checking the device, it is determined whether it is suitable for further use, i.e. Does it correspond to its accuracy class?

LECTURE No. 1

Subject:ELECTRICAL INSTRUMENTS AND MEASUREMENTS OF ELECTRICAL QUANTITIES

1. General information about electro measuring instruments

Electrical measuring instruments are designed to measure various quantities and parameters of an electrical circuit: voltage, current, power, frequency, resistance, inductance, capacitance and others.

In the diagrams, electrical measuring instruments are depicted with conventional graphic symbols in accordance with GOST 2.729-68. Figure 1.1 shows the general designations of indicating and recording devices.

Rice. 1.1 Symbols of electrical measuring instruments.

To indicate the purpose of an electrical measuring device, a specific symbol established in the standards or a letter designation of the units of measurement of the device according to GOST in accordance with Table 1.1 are entered into its general designation.

Table 1.1

Name units	Symbol	Name units	Symbol
		Milliamp
		microamp
		Millivolt
		Kilowatt

Power factor

2. Electromechanical measuring instruments

According to the principle of operation, electromechanical devices are divided into devices of magnetoelectric, electromagnetic, ferrodynamic, induction, electrostatic systems. Symbols of systems are given in table. 1.2. The most widespread devices are the first three types: magnetoelectric, electromagnetic, electrodynamic.

Table 1.2

Device type	Symbol	Type of current being measured	Advantages	Flaws
electric		Constant	High accuracy, scale uniformity	Unresistant to overloads
magnetic		Variable constant	Simplicity of the device, resistant to overloads	Low accuracy, sensitive to interference
dynamic		Variable constant	High accuracy	Low sensitivity sensitive to interference
Induction		Variable	High reliability, overload resistant	Low accuracy

3. Application areas of electromechanical devices

Magnetoelectric devices: panel and laboratory ammeters and voltmeters; zero indicators when measuring in bridge and compensation circuits.

IN industrial installations low frequency alternating current, most ammeters and voltmeters are devices of the electromagnetic system. Laboratory instruments of class 0.5 and more accurately can be manufactured to measure direct and alternating currents and voltage.

Electrodynamic mechanisms are used in laboratory and model instruments for measuring direct and alternating currents, voltages and powers.

Induction devices based on induction mechanisms are used mainly as single- and three-phase AC energy meters. According to accuracy, meters are divided into classes 1.0; 2.0; 2.5. The CO meter (single-phase meter) is used to account for active energy (watt-hours) in single-phase circuits. To measure active energy in three-phase circuits, two-element inductive meters are used, the counting mechanism of which takes into account kilowatt-hours. To account for reactive energy, special inductive meters are used, which have some changes in the design of the windings or in the switching circuit.

Active and reactive meters are installed at all enterprises to pay energy supply organizations for the electricity used.

Principle of selection of measuring instruments

1. By calculating the circuit, determine the maximum values of current, voltage and power in the circuit. Often the values of the measured quantities are known in advance, for example, mains voltage or battery voltage.

2. Depending on the type of quantity being measured, direct or alternating current, the device system is selected. For technical measurements of direct and alternating current, magnetoelectric and electromagnetic systems are chosen, respectively. In laboratory and precise measurements, a magnetoelectric system is used to determine direct currents and voltages, and an electrodynamic system is used for alternating current and voltage.

3. Select the measurement limit of the device so that
the measured value was in the last, third part of the scale
device.

4. Depending on the required measurement accuracy, select a class
accuracy of the device.

4. Methods for connecting devices to a circuit

Ammeters are connected in series with the load, voltmeters are connected in parallel, wattmeters and meters, as having two windings (current and voltage), are connected in series - in parallel (Fig. 1.2.).

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Rice. 1.3. Methods for expanding the measurement limits of instruments.

The division price of multi-limit ammeters, voltmeters, and wattmeters is determined by the formula:

P" in the most significant digit) and change the polarity of the input signal when the "-" sign in the most significant digit flashes.

Measurement error of the VR-11 A multimeter.

Constant voltage: ±(0.5% Ux +4 digits).

AC voltage: ±(0.5% Ux + 10 digits),

where Ux is the instrument reading;

zn. - unit of the lowest rank.

Advantages of electronic devices: high input impedance, which allows measurements without affecting the circuit; wide measurement range, high sensitivity, wide frequency range, high measurement accuracy.

6. Errors of measurements and measuring instruments

The quality of measurement tools and results is usually characterized by indicating their errors. There are about 30 types of errors. Definitions are given in the literature on measurements. It should be borne in mind that the errors of measuring instruments and the errors of measurement results are not identical concepts. Historically, some of the names of the types of errors were assigned to the errors of measuring instruments, others to the errors of measurement results, and some are applied to both.

The methods for presenting the error are as follows.

Depending on the problems being solved, several methods of representing the error are used; absolute, relative, and reduced are most often used.

Absolute error – measured in the same units as the quantity being measured. Characterizes the magnitude of the possible deviation of the true value of the measured value from the measured value.

Relative error– the ratio of the absolute error to the value of the quantity. If we want to determine the error over the entire measurement interval, we must find the maximum value of the ratio over the interval. Measured in dimensionless units.

Accuracy class– relative error, expressed as a percentage. Typically, the accuracy class values are selected from the following range: 0.1; 0.5:1.0; 1.5; 2.0; 2.5, etc.

The concepts of absolute and relative errors apply to both measurements and measuring instruments, and the given error evaluates only the accuracy of measuring instruments.

Absolute measurement error is the difference between the measured value of x and its true value chi:

Usually the true value of the measured quantity is unknown, and instead of it in (1.1) one substitutes the value of the quantity measured by a more accurate device, that is, one that has a smaller error than the device that gives the x value. The absolute error is expressed in units of the measured value. Formula (1.1) is used when checking measuring instruments.

Relative error https://pandia.ru/text/78/613/images/image020_7.gif" width="99" height="45"> (1.2)

Based on the relative measurement error, the measurement accuracy is assessed.

The reduced error of a measuring device is defined as the ratio of the absolute error to the standard value xn and is expressed as a percentage:

(1.3)

The normalizing value is usually taken equal to the upper limit of the working part of the scale, in which the zero mark is at the edge of the scale.

The given error determines the accuracy of the measuring device, does not depend on the measured value and has a single value for a given device. From (1..gif" width="15" height="19 src="> the greater, the smaller the measured value x in relation to the measurement limit of the device xN.

Many measuring instruments differ in accuracy classes. Instrument accuracy class G is a generalized characteristic that characterizes the accuracy of the instrument, but is not a direct characteristic of the accuracy of the measurement performed using this instrument.

The accuracy class of the device is numerically equal to the greatest permissible reduced basic error, calculated as a percentage. The following accuracy classes are established for ammeters and voltmeters: 0.05; 0.1; 0.2; 0.5; 1.0; 1.5; 2.5; 4.0; 5.0. These numbers are plotted on the instrument scale. For example, class 1 characterizes the guaranteed error limits as a percentage (± 1%, for example, of the final value of 100 V, i.e. ± 1 V) in normal conditions operation.

By international classification devices with an accuracy class of 0.5 and more accurately are considered accurate or exemplary, and devices with an accuracy class of 1.0 and coarser are considered working. All devices are subject to periodic verification for compliance with metrological characteristics, including accuracy class, their passport values. In this case, the reference device must be more accurate than the one being verified through the class, namely: verification of a device with an accuracy class of 4.0 is carried out by a device with an accuracy class of 1.5, and verification of a device with an accuracy class of 1.0 is carried out by a device with an accuracy class of 0.2.

Since the instrument scale shows both the accuracy class of the instrument G and the measurement limit XN, then absolute error device is determined from formula (1.3):

https://pandia.ru/text/78/613/images/image019_7.gif" width="15 height=19" height="19"> With The accuracy class of the device G is expressed by the formula:

from which it follows that the relative measurement error is equal to the accuracy class of the device only when measuring the limiting value on the scale, i.e. when x = XN. As the measured value decreases, the relative error increases. How many times is XN > x, how many times > G. Therefore, it is recommended to select the measurement limits of the indicating device so as to take readings within the last third of the scale, closer to its end.

7. Presentation of measurement results for single measurements

The measurement result consists of an assessment of the measured value and the measurement error, which characterizes the accuracy of the measurement. According to GOST 8.011-72, the measurement result is presented in the form:

where A is the measurement result;

Absolute error of the device;

P - probability during statistical data processing.

In this case, A and https://pandia.ru/text/78/613/images/image023_5.gif" width="15" height="17"> should not have more than two significant figures.

The content of the article

ELECTRICAL MEASUREMENTS, measurement of electrical quantities such as voltage, resistance, current, power. Measurements are made using various means - measuring instruments, circuits and special devices. The type of measuring device depends on the type and size (range of values) of the measured value, as well as on the required measurement accuracy. The basic SI units used in electrical measurements are volt (V), ohm (Ω), farad (F), henry (H), ampere (A), and second (s).

STANDARDS OF UNITS OF ELECTRICAL QUANTITIES

Electrical measurement is finding ( experimental methods) the value of a physical quantity expressed in appropriate units (for example, 3 A, 4 V). The values of units of electrical quantities are determined by international agreement in accordance with the laws of physics and units of mechanical quantities. Since “maintaining” units of electrical quantities determined by international agreements is fraught with difficulties, they are presented as “practical” standards for units of electrical quantities. Such standards are supported by state metrological laboratories different countries. For example, in the United States, the National Institute of Standards and Technology bears the legal responsibility for maintaining standards for units of electrical quantities. From time to time, experiments are carried out to clarify the correspondence between the values of the standards of units of electrical quantities and the definitions of these units. In 1990, state metrological laboratories industrially developed countries signed an agreement to harmonize all practical standards of units of electrical quantities among themselves and with international definitions of the units of these quantities.

Electrical measurements are carried out in accordance with state standards of voltage and force units direct current, DC resistance, inductance and capacitance. Such standards are devices that have stable electrical characteristics, or installations in which, based on some physical phenomenon the electrical quantity calculated from known values fundamental physical constants. Watt and watt-hour standards are not supported, since it is more appropriate to calculate the values of these units using defining equations that relate them to units of other quantities.

MEASURING INSTRUMENTS

Electrical measuring instruments most often measure instantaneous values of either electrical quantities or non-electrical quantities converted into electrical ones. All devices are divided into analog and digital. The former usually show the value of the measured quantity by means of an arrow moving along a scale with divisions. The latter are equipped with a digital display that shows the measured value in the form of a number. Digital instruments are preferable for most measurements because they are more accurate, easier to take readings and generally more versatile. Digital multimeters ("multimeters") and digital voltmeters are used to measure DC resistance, as well as AC voltage and current, with medium to high accuracy. Analog devices are gradually being replaced by digital ones, although they are still used where low cost is important and high accuracy is not needed. For the most accurate measurements of resistance and impedance, there are measuring bridges and other specialized meters. To record the progress of changes in the measured value over time, recording instruments are used - strip recorders and electronic oscilloscopes, analog and digital.

DIGITAL INSTRUMENTS

All digital meters (except the simplest ones) use amplifiers and other electronic components to convert the input signal into a voltage signal, which is then converted to digital form by an analog-to-digital converter (ADC). A number expressing the measured value is displayed on a light emitting diode (LED), vacuum fluorescent or liquid crystal (LCD) indicator (display). The device usually operates under the control of a built-in microprocessor, and in simple devices the microprocessor is combined with an ADC on a single integrated circuit. Digital devices are well suited to work when connected to an external computer. In some types of measurements, such a computer switches the measuring functions of the device and gives data transmission commands for their processing.

Analog-to-digital converters.

There are three main types of ADCs: integrating, successive approximation, and parallel. An integrating ADC averages the input signal over time. Of the three types listed, this is the most accurate, although the slowest. The conversion time of the integrating ADC ranges from 0.001 to 50 s or more, the error is 0.1–0.0003%. The error of the successive approximation ADC is slightly larger (0.4–0.002%), but the conversion time is from ~10 µs to ~1 ms. Parallel ADCs are the fastest, but also the least accurate: their conversion time is about 0.25 ns, the error is from 0.4 to 2%.

Discretization methods.

The signal is sampled in time by quickly measuring it at individual points in time and holding (saving) the measured values while they are converted to digital form. The sequence of obtained discrete values can be displayed on the display in the form of a waveform; by squaring these values and summing, you can calculate the root mean square value of the signal; they can also be used to calculate rise time, maximum value, time average, frequency spectrum, etc. Time sampling can be done either over a single signal period ("real time"), or (with sequential or random sampling) over a number of repeating periods.

Digital voltmeters and multimeters.

Digital voltmeters and multimeters measure a quasi-static value of a quantity and indicate it in digital form. Voltmeters directly measure only voltage, usually DC, while multimeters can measure DC and AC voltage, current, DC resistance and sometimes temperature. These are the most common instrumentation general purpose with a measurement error of 0.2 to 0.001% can have a 3.5- or 4.5-digit digital display. A “half-integer” character (digit) is a conditional indication that the display can show numbers beyond the nominal number of characters. For example, a 3.5-digit (3.5-digit) display in the 1-2V range can show voltages up to 1.999V.

Impedance meters.

These are specialized instruments that measure and display the capacitance of a capacitor, the resistance of a resistor, the inductance of an inductor, or the total resistance (impedance) of the connection of a capacitor or inductor to a resistor. Instruments of this type are available to measure capacitance from 0.00001 pF to 99.999 µF, resistance from 0.00001 ohms to 99.999 kohms, and inductance from 0.0001 mH to 99.999 H. Measurements can be made at frequencies from 5 Hz to 100 MHz, although one device does not cover the entire frequency range. At frequencies close to 1 kHz, the error can be as small as 0.02%, but the accuracy decreases near the boundaries of the frequency ranges and measured values. Most instruments can also display derived values, such as the quality factor of a coil or the loss factor of a capacitor, calculated from the main measured values.

ANALOG DEVICES

To measure voltage, current and resistance at direct current, analog magnetoelectric devices with permanent magnet and a multi-turn moving part. Such pointer-type devices are characterized by an error of 0.5 to 5%. They are simple and inexpensive (for example, automotive instruments that indicate current and temperature), but are not used where any significant accuracy is required.

Magnetoelectric devices.

Such devices use the force of interaction between the magnetic field and the current in the turns of the winding of the moving part, which tends to turn the latter. The moment of this force is balanced by the moment created by the opposing spring, so that each current value corresponds to a certain position of the arrow on the scale. The moving part has the shape of a multi-turn wire frame with dimensions from 3-5 to 25-35 mm and is made as light as possible. The moving part, mounted on stone bearings or suspended on a metal strip, is placed between the poles of a strong permanent magnet. Two spiral springs that balance the torque also serve as conductors for the winding of the moving part.

A magnetoelectric device reacts to the current passing through the winding of its moving part, and therefore is an ammeter or, more precisely, a milliammeter (since the upper limit of the measurement range does not exceed approximately 50 mA). It can be adapted to measure higher currents by connecting a low-resistance shunt resistor in parallel with the moving part winding so that only a small fraction of the total current being measured is branched into the moving part winding. Such a device is suitable for currents measured in many thousands of amperes. If you connect an additional resistor in series with the winding, the device will turn into a voltmeter. The voltage drop across such a series connection is equal to the product of the resistance of the resistor and the current shown by the device, so its scale can be calibrated in volts. To make an ohmmeter out of a magnetoelectric milliammeter, you need to connect series-measurable resistors to it and apply serial connection constant voltage, for example from a battery. The current in such a circuit will not be proportional to the resistance, and therefore a special scale is needed to correct the nonlinearity. Then it will be possible to directly read the resistance on the scale, although not with very high accuracy.

Galvanometers.

Magnetoelectric devices also include galvanometers - highly sensitive devices for measuring extremely small currents. Galvanometers do not have bearings; their moving part is suspended on a thin ribbon or thread, a stronger magnetic field is used, and the pointer is replaced by a mirror glued to the suspension thread (Fig. 1). The mirror rotates along with the moving part, and the angle of its rotation is estimated by the displacement of the light spot it casts on a scale installed at a distance of about 1 m. The most sensitive galvanometers are capable of giving a scale deviation of 1 mm with a change in current of only 0.00001 μA.

RECORDING DEVICES

Recording instruments record the “history” of changes in the value of the measured quantity. The most common types of such instruments include strip chart recorders, which record a curve of change in value with a pen on a chart paper tape, analog electronic oscilloscopes, which display the process curve on the screen of a cathode ray tube, and digital oscilloscopes, which store single or rarely repeated signals. The main difference between these devices is the recording speed. Strip recorders, with their moving mechanical parts, are most suitable for recording signals that change over seconds, minutes, or even more slowly. Electronic oscilloscopes are capable of recording signals that change over time from millionths of a second to several seconds.

MEASURING BRIDGES

A measuring bridge is usually a four-arm electrical circuit composed of resistors, capacitors and inductors, designed to determine the ratio of the parameters of these components. A power source is connected to one pair of opposite poles of the circuit, and a null detector is connected to the other. Measuring bridges are used only in cases where the highest measurement accuracy is required. (For medium-accuracy measurements, it is better to use digital instruments because they are easier to handle.) The best AC transformer measuring bridges have an error (ratio measurement) of the order of 0.0000001%. The simplest bridge for measuring resistance is named after its inventor, Charles Wheatstone.

Double DC measuring bridge.

It is difficult to connect copper wires to a resistor without introducing contact resistance of the order of 0.0001 ohms or more. In the case of a resistance of 1 Ohm, such a current lead introduces an error of the order of only 0.01%, but for a resistance of 0.001 Ohm the error will be 10%. Double measuring bridge (Thomson bridge), the diagram of which is shown in Fig. 2, is intended for measuring the resistance of small-value reference resistors. The resistance of such four-pole reference resistors is defined as the ratio of the voltage at their potential terminals ( R 1 , R 2 resistors R s And R 3 , p 4 resistors R x in Fig. 2) to current through their current terminals ( With 1 , With 2 and With 3 , With 4). With this technique, the resistance of the connecting wires does not introduce errors into the result of measuring the desired resistance. Two additional arms m And n eliminate the influence of the connecting wire 1 between terminals With 2 and With 3. Resistance m And n these shoulders are selected so that the equality is satisfied M/m= N/n. Then, changing the resistance R s, reduce the imbalance to zero and find

R x = R s(N/M).

AC measuring bridges.

The most common AC measurement bridges are designed to measure at either line frequency 50–60 Hz or audio frequencies (usually around 1000 Hz); specialized measuring bridges operate at frequencies up to 100 MHz. As a rule, in AC measuring bridges, instead of two arms that precisely set the voltage ratio, a transformer is used. Exceptions to this rule include the Maxwell-Wien measuring bridge.

Maxwell-Wien measuring bridge.

Such a measuring bridge makes it possible to compare inductance standards ( L) with capacitance standards at an unknown operating frequency. Capacitance standards are used in high-precision measurements because they are simpler in design than precision inductance standards, more compact, easier to shield, and create virtually no external electromagnetic fields. The equilibrium conditions for this measuring bridge are: Lx = R 2 R 3 C 1 and R x = (R 2 R 3) /R 1 (Fig. 3). The bridge is balanced even in the case of an “impure” power supply (i.e. a signal source containing harmonics of the fundamental frequency), if the value Lx does not depend on frequency.

Transformer measuring bridge.

One of the advantages of AC measuring bridges is the ease of setting the exact voltage ratio using a transformer. Unlike voltage dividers built from resistors, capacitors or inductors, transformers maintain a constant voltage ratio over a long period of time and rarely require recalibration. In Fig. Figure 4 shows a diagram of a transformer measuring bridge for comparing two impedances of the same type. The disadvantages of a transformer measuring bridge include the fact that the ratio specified by the transformer depends to some extent on the frequency of the signal. This leads to the need to design transformer measuring bridges only for limited frequency ranges in which rated accuracy is guaranteed.

Grounding and shielding.

Typical null detectors.

In AC measuring bridges, two types of null detectors are most often used. The null detector of one of them is a resonant amplifier with an analog output device that shows the signal level. Another type of null detector is a phase-sensitive detector that separates the unbalance signal into active and reactive components and is useful in applications where only one of the unknown components (say, inductance) needs to be accurately balanced L, but not resistance R inductors).

MEASUREMENT OF AC SIGNALS

In the case of time-varying AC signals, it is usually necessary to measure some of their characteristics associated with the instantaneous values of the signal. Most often, it is desirable to know the RMS (rms) AC electrical values, since the heating power at 1 VDC corresponds to the heating power at 1 Vrms AC. Along with this, other quantities may be of interest, for example the maximum or average absolute value. The root mean square (effective) value of the voltage (or strength) of an alternating current is determined as the square root of the time-averaged square of the voltage (or current):

Where T– signal period Y(t). Maximum value Y max is the largest instantaneous value of the signal, and the average absolute value YAA– absolute value averaged over time. With a sinusoidal oscillation Y eff = 0.707 Y max and YAA = 0,637Y Max.

AC voltage and current measurement.

Almost all instruments for measuring AC voltage and current show a value that is proposed to be considered as the effective value of the input signal. However, cheap instruments often actually measure the average absolute or maximum value of the signal and calibrate the scale so that the reading corresponds to the equivalent effective value, assuming the input signal is a sinusoidal waveform. It should not be overlooked that the accuracy of such devices is extremely low if the signal is non-sinusoidal. Instruments capable of measuring the true rms value of AC signals can be based on one of three principles: electronic multiplication, signal sampling, or thermal conversion. Devices based on the first two principles, as a rule, respond to voltage, and thermal electrical measuring instruments – to current. When using additional and shunt resistors, all devices can measure both current and voltage.

Electronic multiplication.

Squaring and time averaging of the input signal to some approximation is carried out by electronic circuits with amplifiers and nonlinear elements to perform mathematical operations such as finding the logarithm and antilogarithm of analog signals. Devices of this type can have an error of the order of only 0.009%.

Signal sampling.

The AC signal is converted into digital form using a high-speed ADC. The sampled signal values are squared, summed, and divided by the number of sampled values in one signal period. The error of such devices is 0.01–0.1%.

Thermal electrical measuring instruments.

The highest accuracy of measuring the effective values of voltage and current is provided by thermal electrical measuring instruments. They use a thermal current converter in the form of a small evacuated glass container with a heating wire (0.5–1 cm long), to the middle part of which a thermocouple hot junction is attached with a tiny bead. The bead provides thermal contact and at the same time electrical insulation. With an increase in temperature, directly related to the effective value of the current in the heating wire, a thermo-EMF (direct current voltage) appears at the output of the thermocouple. Such converters are suitable for measuring AC current with a frequency from 20 Hz to 10 MHz.

In Fig. Figure 5 shows a schematic diagram of a thermal electrical measuring device with two thermal current converters selected according to parameters. When AC voltage is applied to the circuit input V ac at the thermocouple output of the converter TS 1 DC voltage occurs, amplifier A creates a direct current in the heating wire of the converter TS 2, in which the latter's thermocouple produces the same DC voltage, and a conventional DC meter measures the output current.

Using an additional resistor, the described current meter can be converted into a voltmeter. Since thermal electrical meters directly measure currents only from 2 to 500 mA, resistor shunts are needed to measure higher currents.

AC power and energy measurement.

The power consumed by the load in an AC circuit is equal to the time-average product of the instantaneous values of voltage and load current. If the voltage and current vary sinusoidally (as is usually the case), then the power R can be represented in the form P = EI cos j, Where E And I are the effective values of voltage and current, and j– phase angle (shift angle) of voltage and current sinusoids. If voltage is expressed in volts and current in amperes, then power will be expressed in watts. cos multiplier j, called power factor, characterizes the degree of synchronism of voltage and current fluctuations.

WITH economic point From a perspective, the most important electrical quantity is energy. Energy W is determined by the product of power and the time of its consumption. IN mathematical form it is written like this:

If time ( t 1 - t 2) measured in seconds, voltage e- in volts, and current i– in amperes, then energy W will be expressed in watt-seconds, i.e. joules (1 J = 1 Wh s). If time is measured in hours, then energy is measured in watt-hours. In practice, it is more convenient to express electricity in kilowatt-hours (1 kWh h = 1000 Wh).

Time-sharing electricity meters.

Time-sharing electricity meters use a very unique but accurate method of measuring electrical power. This device has two channels. One channel is an electronic key that allows or does not pass the input signal Y(or reversed input signal - Y) to a low pass filter. The state of the key is controlled by the output signal of the second channel with the “closed”/“open” time interval ratio proportional to its input signal. The average signal at the filter output is equal to the time average of the product of the two input signals. If one input signal is proportional to the load voltage and the other is proportional to the load current, then the output voltage is proportional to the power consumed by the load. The error of such industrial counters is 0.02% at frequencies up to 3 kHz (laboratory ones are about only 0.0001% at 60 Hz). As high-precision instruments, they are used as standard counters for checking working measuring instruments.

Sampling wattmeters and electricity meters.

Such devices are based on the principle of a digital voltmeter, but have two input channels that sample current and voltage signals in parallel. Each discrete value e(k), representing the instantaneous values of the voltage signal at the time of sampling, is multiplied by the corresponding discrete value i(k) current signal received at the same time. The time average of such products is the power in watts:

An adder that accumulates the products of discrete values over time gives the total electricity in watt-hours. The error of electricity meters can be as little as 0.01%.

Induction electricity meters.

An induction meter is nothing more than a low-power AC electric motor with two windings - a current winding and a voltage winding. A conductive disk placed between the windings rotates under the influence of a torque proportional to the power consumed. This torque is balanced by currents induced in the disk by a permanent magnet, so that the rotation speed of the disk is proportional to the power consumption. The number of revolutions of the disk for a given time is proportional to the total electricity received by the consumer during this time. The number of revolutions of the disk is counted by a mechanical counter, which shows electricity in kilowatt-hours. Devices of this type are widely used as household electricity meters. Their error is usually 0.5%; they have a long service life under any permissible levels current

Literature:

Atamalyan E.G. and etc. Instruments and methods for measuring electrical quantities. M., 1982
Malinovsky V.N. and etc. Electrical measurements. M., 1985
Avdeev B.Ya. and etc. Fundamentals of metrology and electrical measurements. L., 1987