RU2137144C1 - Process measuring electric resistance - Google Patents

Abstract

FIELD: electrical engineering. SUBSTANCE: process measuring electric resistance consists in transmission of electric current through measured resistance. First measurements of current and drop of voltage across measured resistance are taken and their values are used to find first value of resistance. After first measurement of current and drop of voltage current through measured resistance is changed by way of connection of additional resistance in series with measured one. Second measurement of current and drop of voltage across measured resistance are taken and their values are used to determine second value of resistance. Measured resistance is found by given formula with account of values of internal resistance of measuring device without additional resistance. EFFECT: widened functional capabilities. 1 dwg

Description

 The invention relates to the field of measuring technology, in particular to measuring electrical resistance, mainly in the microohm range, for example, the contact resistance of switching devices.

 Known bridge method (see, for example, the book. Fundamentals of metrology and electrical measurements. Edited by E. M. Dushin. 6th ed. L .: Energoatomizdat. Leningrad. Otd.-niye, 1987, p. 422), based on the inclusion of the measured resistance in the bridge circuit, balancing this circuit and determining the unknown resistance according to the balance condition of the bridge circuit. The disadvantages of this method, limiting the scope of its application, is that when measuring very small resistances (in the microohm range), to ensure the necessary sensitivity of the bridge, it is necessary to pass very large currents through the measured resistance — tens or even hundreds of amperes, and when measuring large resistances (in the megaohm range) - increase the voltage at the studied object to hundreds or even thousands of volts.

 There is also known a method of measuring electrical resistance, which is based on measuring the voltage drop across an unknown resistance included in an electrical circuit. The value of the measured resistance is determined by the voltage drop across this resistance. Examples of the implementation of this method are electronic and magnetoelectric ohmmeters (see ibid., Pp. 421-422). However, they are notable for low accuracy (accuracy class 1.0 - 1.5) and uneven scale. In addition, the measurement range of such devices is limited below by resistance values of about 1 Ohm, which does not allow them to be used, for example, when measuring the contact resistances of switching devices.

 Closest to the claimed is a method of measuring electrical resistance (the method of an ammeter and voltmeter), which is based on measuring the voltage drop at an unknown resistance included in the electrical circuit, and the current in this circuit. The value of the measured resistance is defined as the ratio of the voltage drop across it to the flowing current / cm. ibid., p. 423 /. The disadvantage of this prototype method is the low accuracy of the measurements due to the influence on the result of measurement errors of current and voltage. In particular, additive constant systematic errors appear (see, for example, book: Aliev T.M., Ter-Khachaturov A.A. Measuring equipment. Textbook for technical universities. - M.: Higher school, 1991, pp. 26-27, Fig. 3.2). The reasons for such errors are, for example, the inaccuracy of the “zero” setting of the used ammeter and voltmeter, the bias voltage of the input amplifiers of the electronic measuring transducers of current and voltage, and the thermal and contact emfs in measuring chains.

 The objective of the invention is to reduce the additive constant systematic error in the measurement of electrical resistance and the expansion of the measurement range in the direction of low resistances.

где R₀ - сумма внутреннего сопротивления источника питания и сопротивления измерителя тока; R_д - дополнительное сопротивление; r₁ и r₂ - первое и второе значения сопротивления при первом и втором измерениях соответственно.The solution to the problem is achieved by the fact that in the method of measuring electrical resistance, which consists in the fact that an electric current is passed through the measured resistance, a first measurement of the current and voltage drop across the measured resistance is performed and the first resistance value is determined from their values, additionally after the first measurement of current and drop voltage measure the current through the measured resistance by switching in series with the measured additional resistance, perform a second current measurement and the drop of the voltage across the resistance being measured and their values define the second resistance value and the measured resistance is determined by the formula

where R ₀ is the sum of the internal resistance of the power source and the resistance of the current meter; R _d - additional resistance; r ₁ and r ₂ are the first and second resistance values in the first and second measurements, respectively.

где R₀ - внутреннее сопротивление устройства измерения сопротивления без дополнительного сопротивления; R_д - дополнительное сопротивление; r₁ и r₂ - первое и второе значения измеряемого сопротивления при первом и втором измерениях соответственно.The claimed technical solution differs from the prototype in that after the first measurement of the current and voltage drop, the current is changed through the measured resistance by switching on additional resistance, the second measurement of current and voltage drop at the measured resistance is performed and the second resistance value is determined from their values, and the measured resistance is determined by the formula

where R ₀ is the internal resistance of the resistance measurement device without additional resistance; R _d - additional resistance; r ₁ and r ₂ - the first and second values of the measured resistance in the first and second measurements, respectively.

 Comparison of the claimed technical solution with the prototype allows us to establish compliance with its criterion of "novelty."

 Signs that distinguish the claimed technical solution from the prototype, are not identified in other technical solutions in the study of this and related areas of technology and, therefore, provide the claimed solution with the criterion of "significant differences".

The drawing shows a structural diagram of an electronic ohmmeter - a device illustrating the implementation of the proposed method on the example of measuring the active resistance. The device contains a series-connected limiting 1 (R _ogre ), additional 2 (R _d ) resistors, a measuring shunt 3 (R _W ) and a measured resistance 4 (R _x ) connected to a supply voltage source 5 (IP) and forming a measuring circuit. Resistor 1 limits the current of the measuring circuit to a predetermined maximum value. The key 6 is connected in parallel with the additional resistor 2. The inputs of the differential amplifiers 7 and 8 (ДУ1 and ДУ2), the outputs of which are connected to the inputs of the division device 9 (УД), are connected to the shunt 3 and the resistance 4, respectively. At the outputs of amplifiers 7 and 8, voltages U _w ^* and U _x ^{* are formed} , and at the output of dividing device 9, an output signal r is proportional to the quotient of dividing the voltage drop U _x ^* at the measured resistance 4 by the voltage drop U _w ^* at shunt 3. Thus, the signal r is proportional to the measured resistance 4.

When measuring the current with determining its value by the voltage drop on the shunt 3, you can write:
U _W = R _W • I,
where U _W - voltage drop on the shunt 3; I is the current flowing through the measuring circuit.

The voltage drop U _x at the measured resistance 4 is
U _x = R _x • I.

Погрешности измерения падений напряжения U_x и U_ш, возникающие из-за влияния аддитивных погрешностей измерителей этих падений напряжений, приводят к погрешности определения сопротивления R_x. Причем, с уменьшением измеряемых сопротивлений, а следовательно, и значений U_x погрешность резко возрастает.Solving these equations for R _x , we find that the measured resistance can be determined by the formula:

Errors in measuring voltage drops U _x and U _W , arising due to the influence of the additive errors of the meters of these voltage drops, lead to errors in determining the resistance R _x . Moreover, with a decrease in the measured resistances, and hence the values of U _{x, the} error increases sharply.

In accordance with the proposed method, the measurement of the unknown resistance 4 is carried out by the method of an ammeter-voltmeter and is performed in two stages, during which two preliminary values of r ₁ and r _{2 of} resistance 4 are obtained with errors due to imperfect channels for measuring current and voltage drop across the measured resistance, and then specify the value of the measured resistance by mathematical processing of the obtained preliminary values.

где E - напряжение источника 5; R_ш - сопротивление шунта 3; R_огр - сопротивление ограничительного резистора 1; R_вн - внутреннее сопротивление источника 5; R_x ^* - истинное значение измеряемого сопротивления 4; R₀ = R_ш + R_огр + R_вн - внутреннее сопротивление устройства для измерения сопротивлений.At the first stage, the measurement is performed with the key 6. closed. In this case, the true value of the current I ₁ ^* flowing in the measuring circuit is

where E is the voltage of the source 5; R _W - the resistance of the shunt 3; R _ogre - resistance of the limiting resistor 1; R _vn is the internal resistance of source 5; R _x ^* is the true value of the measured resistance 4; R ₀ = R _W + R _ogre + R _int - internal resistance of the device for measuring resistances.

When the current I ₁ ^* flows on the shunt 3 and the measured resistance 4, voltage drops are created equal to, respectively, I ₁ ^* • R _w and I ₁ ^* • R _x ^* . With the help of differential amplifiers 7 and 8, current and voltage drop are measured at the measured resistance 4. In this case, due to the non-ideal amplifiers 7 and 8 or other devices used to measure current and voltage drop, an additive component determined by the bias voltage of amplifiers 7 is added to the useful signals and 8, as well as the input circuits of the division device 9. The device 9 performs the division of the signal U _x ^* by the signal U _W ^* , which in the first stage are respectively equal
U _x1 ^* = (I ₁ ^* • R _x ^* + U _cm2 ) • K ₂ ;
U _W1 ^* = (I ₁ ^* • R _W + U _cm1 ) • K ₁ ,
where U _cm1 and U _cm2 are the bias voltages of the differential amplifiers 7 and 8 and the corresponding inputs of the division device 9, reduced to the inputs of the respective amplifiers; K ₁ and K ₂ are the amplification factors of amplifiers 7 and 8, respectively.

When measuring resistances and mikroomnom millimeter ranges, when the voltage drop across the resistor 4 is a few millivolts and the proportion, in the composition of the voltage U _cm2 constitute a substantial part of the contact and also the thermo emf in the circuit of the input circuit of the amplifier 8 (resistor 4, connecting wires and the input amplifier leads 8).

где K₃ - передаточный коэффициент устройства деления 9.In accordance with the above, at the output of the division device 9, a signal r ₁ is generated - the result of measuring the resistance at the first stage - the first value of the measured resistance, which, in accordance with (1), is

where K ₃ - gear ratio of the division device 9.

To simplify further transformations, we take into account the coefficient K ₃ in one of the coefficients K ₁ or K ₂ , which allows us to further consider K ₃ = 1.

Подставляя в (3) значение I₁ ^* из (2) после преобразования получаем:

Для наглядности пояснений перепишем выражение (6) в виде:

где γ = (R₀ + R_x ^*)•U_см2/(R_x ^*•E) - составляющая относительной погрешности измерения падения напряжения на сопротивлении 4, определяемая постоянной систематической аддитивной погрешностью измерения падения напряжения; β = (R₀ + R_x ^*)•U_см1/(R_ш•E) - составляющая относительной погрешности измерения тока, определяемая постоянной систематической аддитивной погрешностью измерения тока.The fractional coefficient K ₁ / K ₂ indicates that in order to express the value of r ₁ in ohms, the voltage U _x1 ^* must be divided by the gain K ₂ , and the voltage U _w1 ^* - by K ₁ . In accordance with this, the measured values of the voltage drop U _x1 on the resistance 4 and current I ₁ are equal
U _x1 = I ₁ ^* • R _x ^* + U _cm2 = U _x1 ^* / K ₂ ; (4)

Substituting in (3) the value of I ₁ ^* from (2) after the conversion, we obtain:

For clarity of explanation, we rewrite expression (6) in the form:

where γ = (R ₀ + R _x ^* ) • U _cm2 / (R _x ^* • E) is the component of the relative error in measuring the voltage drop at resistance 4, determined by the constant systematic additive error in measuring the voltage drop; β = (R ₀ + R _x ^* ) • U _cm1 / (R _W • E) - component of the relative error of current measurement, determined by the constant systematic additive error of current measurement.

The resistance of the shunt 3 is determined during the design of the measuring device, then this resistance can always be chosen so that the voltage drop across the shunt 3 is much greater than the voltage U _cm1 . Therefore, the coefficient β ≪ 1 and, according to approximate calculation methods, the ratio (1 + γ) / (1 + β) can be replaced by the product (1 + γ) • (1-β) (see, for example, Prince Vygodsky M.Ya. Handbook of Higher Mathematics. Fifth Edition, Moscow: State Publishing House of Physics and Mathematics, 1961, p. 308).

где R_x = приближенное значение измеряемого сопротивления 4.Performing the indicated replacement, we obtain:
r ₁ ≈ R $\genfrac{}{}{0ex}{}{\text{*}}{\text{x}}$ • (1 + γ) • (1-β) = R $\genfrac{}{}{0ex}{}{\text{*}}{\text{x}}$ • (1 + γ-β-γ • β).
Since the coefficients γ and β are small in comparison with unity, their product can also be neglected and it can be assumed that
r ₁ ≈ R $\genfrac{}{}{0ex}{}{\text{*}}{\text{x}}$ • (1 + γ-β).
Performing such a substitution in expression (6), we obtain:

where R _x = approximate value of the measured resistance 4.

где R_д - сопротивление дополнительного резистора 4.When the operating current is changed by turning on the additional resistor 2 (R _d ) at the second stage of measurement, the key 6 opens and this resistor is introduced into the measuring circuit. The current in the measuring circuit takes an I ₂ ^* value equal to

where R _d is the resistance of the additional resistor 4.

Вычитаем выражение (7) из выражения (9):

Решаем полученное равенство относительно выражения в скобках:

и подставляем в формулу (7):

Решив последнее выражение относительно R_x, окончательно получаем, что приближенное значение измеряемого сопротивления 4 можно определить по формуле:

Устройство, реализующее предложенный способ, работает следующим образом.Performing transformations similar to those used in the derivation of expression (7), we obtain the value of the output signal r _{2 of} the division device 9 at the second measurement stage:

Subtract expression (7) from expression (9):

We solve the resulting equality with respect to the expression in parentheses:

and substitute in the formula (7):

Having solved the last expression with respect to R _x , we finally obtain that the approximate value of the measured resistance 4 can be determined by the formula:

A device that implements the proposed method works as follows.

At the first measurement stage, with the switch 6 closed, the operating current is passed through the measured resistance 4 from the source 5, which creates a voltage drop at the measured resistance 4 and the measuring shunt 3. Differential amplifiers 7 and 8 generate signals U _x1 ^* and U _ш1 ^* , proportional to the voltage drop on the measured resistance and the current flowing through it. After dividing these signals at the output of the division device 9, a signal r _{1 is formed} , which is the first approximate value of the measured resistance. This value is remembered. Then, at the second measurement stage, the key 6 is opened and an additional resistor 2 is included in the measuring circuit, which reduces the operating current of the measuring circuit. Converters 7 and 8 give new values of the signals U _x2 ^* and U _W2 ^* , when dividing which the division device generates a second approximate value of the signal r ₂ . Knowing the internal resistance of the measuring circuit of the ohmmeter R ₀ and the resistance of the additional resistor R _d , from the obtained values of r ₁ and r ₂ using formula (11) we find the updated resistance R _x .

 The proposed method for measuring resistances when using an alternating voltage generator as source 5 can be used to measure not only active resistances, but also total (complex) resistances. In this case, the amplitude or current values of the current and voltage drop are measured. When using a phase-sensitive detector in the channel for measuring the voltage drop, it is possible to measure the active and reactive components of the impedance of a series equivalent circuit. When using a phase-sensitive detector in the current measurement channel, it is possible to measure the active and reactive components of the impedance of a parallel equivalent circuit. When the connection of the inputs of the division device 9 is changed and the measured current value is divided by the measured voltage drop value, the electrical conductivity of the resistance 4 is measured.

 Improving the measurement accuracy occurs when using in the measuring circuit not only active, but also reactance.

To assess the effect achieved by the implementation of the proposed method, we consider specific examples, given the resistance of the connecting wires as part of the limiting resistor:
Example 1
Assume that the circuit of FIG. 1 has the following parameters:
E = 1 V;
R _int = 5 ohms;
R _ogre = 95 ohms;
R _W = 100 Ohms;
R _d = 100 Ohms;
R _x ^* = 100 ohms;
U _cm1 = -50 mV;
U _cm2 = +50 mV.

At the first stage of measurement, the true value of the current in the measuring circuit is I ₁ ^* = 3.333333 mA. In this case, the measured value of the voltage drop across the resistance R _x is I ₁ ^* • R _x + U _cm2 = 283.33 mV (i.e., it is determined with a relative error of 15% compared to the true value I ₁ ^* • R _x = 333, 33 mV), and the measured current value in the measuring circuit is I ₁ = (I ₁ ^* • R _w + U _cm1 ) / R _w = 3.8333 mA (determined with a relative error of 15%). As a result of the division, we obtain r ₁ = 73.91 Ohms. With a true resistance of the resistor R _x = 100 Ohms, the relative error in determining the resistance R _x is 26%.

In the second measurement step, the true value of the current in the measuring circuit is I ₂ ^* = 2.5 mA. The measured values of the voltage and current drops are 200 mV and 3.0 mA, respectively, and as a result of the division we get r ₂ = 66.67 Ohms with a relative error of more than 30%. After converting the preliminary values of r ₁ and r ₂ according to the formula (11), we obtain the calculated R _x = 95.29 Ohms. As a result, the relative error instead of 26% became equal to 4.3%, i.e. decreased by 6 times.

Example 2
Assume that the circuit of FIG. 1 has the following parameters:
E = 10 V;
R _int = 5 ohms;
R _ogre = 95 ohms;
R _W = 100 Ohms;
R _d = 100 Ohms;
R _x ^* = 0.01 Ohms;
U _cm1 = +1 mV;
U _cm2 = -100 μV.

At the first stage of measurement, the true value of the current in the measuring circuit is I ₁ ^* = 0.04999750 A. The measured value of the voltage drop across the resistance R _x is I ₁ ^* • R _x ^* + U _cm2 = 399.9750 μV (i.e. defined with a relative error of about 20% compared with the true value of I ₁ ^* • R _x ^* = 499.9750 μV), and the measured current value taking into account the resistance of the shunt 3 is (I ₁ ^* • R _w + U _cm1 ) / R _w = 0.05000750 mA (determined with a relative error of about 0.015% compared to the true value of I ₁ ^* ). As a result of the division by the formula (11), we obtain r ₁ = 0.007998300 Ohms. With a true resistor resistance of R _x = 0.01 Ohms, the relative error exceeds 20%.

At the second stage of the measurement, the true value of the current in the measuring circuit is I ₂ ^* = 0.03333222 A. The measured values of the voltage drop and current are 233.3222 μV and 0.03334222 A, respectively, and as a result of division we get r ₂ = 0.006997825 Ohms s relative error of more than 30%. After converting the preliminary values of r ₁ and r ₂ according to the formula (11), we obtain the calculated R _x = 0.009999429 Ohm. Thus, as a result of the implementation of the proposed method, the relative error instead of 20% (when implementing the prototype method) became less than 0.006%, i.e. decreased by more than 3,000 times.

It should be noted that the use of the proposed method significantly reduces the constant systematic additive errors of both the voltage drop measurement channel and the current measurement channel. Moreover, the greatest effectiveness of the application of the method gives when measuring small resistances (R _x ^* << R ₀ ).

 The proposed method can be applied not only in electronic ohmmeters, but also in measuring current and voltage drop with the help of separate instruments - an ammeter (milliammeter) and a voltmeter (millivoltmeter). Moreover, the calculation by the formula (11) can be performed, for example, using a calculator. In this case, there is a decrease in the zero adjustment errors of these devices.

 The proposed method can significantly reduce the constant systematic additive error in the measurement of active, reactive and total resistances of elements and sections of electrical circuits, and therefore the total measurement error. For microohmmeters, the use of this method allows accurate measurements with reduced values of the voltage drop across the measured resistances, i.e. at lower values of current in the measuring circuit, which will increase the efficiency of microohmmeters and reduce their weight and overall dimensions. By reducing the sensitivity threshold by reducing the additive error, the lower limit of the measurement of microohmmeters can be reduced by several orders of magnitude without increasing the operating current.

Claims (1)

The method of measuring electrical resistance, which consists in the fact that an electric current is passed through the measured resistance, the first measurement of the current and voltage drop across the measured resistance is performed, and the first resistance value is determined from their values, characterized in that after the first measurement of the current and voltage drop, the current is changed through measured resistance by switching in series with the measured additional resistance, perform the first measurement of current and voltage drop across the measured s rebellion against their values and determining a second resistance value and the measured resistance is determined by the formula

where R _o is the internal resistance of the resistance measuring device without additional resistance;
R _d - additional resistance;
r ₁ and r ₂ - the first and second values of the measured resistance in the first and second measurements, respectively.