RU2209440C2 - Method measuring parameters of input impedance and device for its realization - Google Patents

Abstract

FIELD: electrical engineering, determination of values of parameters of electric circuits. SUBSTANCE: in compliance with method active and reactive components of input impedance of both channels of digital phasometer are measured in advance, corresponding components of input impedance of channels are balanced and true values of components of admittance of measured impedance are found in accordance with following expressions:

,

where α and β are measured values of angles between voltage drops across reference resistor, measured impedance and voltage of generator of sinusoidal form; r_crr,g_ic,b_cis are correspondingly conductance of reference resistor, input conductance and input susceptance of phasometer. Device for realization of given method is inserted with double two- position switch, additional resistor and capacitor. Common point of connection of reference resistor and measured impedance is directly connected to potential input of measurement channel of digital phasometer. In upper position of switch digital phasometer measures angle contained between voltage of generator of sinusoidal voltage and voltage drop across reference resistor, in lower position it measures angle between voltage of mentioned generator and voltage drop across measured impedance. Additional resistor and capacitor balancing channels of digital phasometer are connected to proper input terminals of those channels whose resistance or reactance have greater value. EFFECT: increased measurement precision and widened range of measured impedance. 2 cl, 4 dwg

Description

 The invention relates to electrical engineering, in particular to measuring the parameters of complex values of alternating current.

 Known AC bridges for measuring complex resistances [1]. Bridge measurement methods provide the highest measurement accuracy (they do not have a methodological error, since when the bridge measuring circuit is in equilibrium, its input resistance is theoretically equal to infinity). At the same time, AC bridges have a number of significant drawbacks. This is the mutual influence of the measurement channels of the active and reactive components of the complex resistance, the need to use exemplary reactive elements (capacitors and inductors, the adjustment error of which is much larger than for active resistances), the complexity of manufacturing and, accordingly, the high cost. This led to the search for new ways to determine the parameters of complex resistances based on the use of a personal computer.

и

где U_R0 и U_X - амплитуды комплексных напряжений

и

φ₀ и φ_x - фазовые углы векторов

и

относительно вектора

которые обозначены через α и β (фиг.2). Комплексное сопротивление

Здесь R_o - сопротивление образцового резистора. Модуль комплексного сопротивления и его фазовый угол будут равны соответственно: R_oU_x(U_R0)^-1, γ = φ_x-φ_o = α+β, как внешний для углов α и β. Так как по теореме синусов U_X(U_RO)^-1 = sinα(sinβ)^-1, то модуль комплексного сопротивления

Недостатком данного способа является невысокая точность измерения из-за использования приборов прямого преобразования (фазометров) в сравнении с мостами переменного тока. Это объясняется тем, что в процессе измерения не учитывается влияния активных и реактивных составляющих входных сопротивлений измерительных приборов, что особенно существенно на пределах измерений свыше 10-100 кОм. Учет их приводит к замене трехэлементной эквивалентной электрической измерительной цепи

- к семиэлементной (фиг.3). Здесь R_фA, Х_фA и R_фB, Х_фB - соответственно активные и реактивные составляющие комплексных входных сопротивлений измерительного (А) и опорного (В) каналов цифрового фазометра.The closest in technical essence to the proposed method and the device that implements it is the method of indirect aggregate measurements of the complex resistance parameters based on the phase method for determining two angles of a triangle by phase meters for the selected value of the reference resistor of the measuring circuit and the device that implements it [2]. Its functional diagram is shown in figure 1. It contains a power source (sinusoidal voltage generator) 1, the output of which is connected in series to an exemplary resistor 2 and the measured complex resistance 3. To the resistance 3 and resistor 2 are connected the signal inputs of the first 4 and second 5 converters - digital phase meters. The reference inputs of the transducers 4 and 5 are connected to the output of the source 1. The outputs of the transducers 4 and 5 are connected to the inputs of the computing device 6. When the measuring circuit is powered by a sinusoidal voltage generator with an amplitude E _p on the model resistor 2 and the measured complex resistance 3 there will be voltage drops, respectively

and

where U _R0 and U _X are the amplitudes of the complex stresses

and

φ ₀ and φ _x are the phase angles of the vectors

and

relative to the vector

which are denoted by α and β (figure 2). Complex resistance

Here R _o is the resistance of the reference resistor. The complex resistance modulus and its phase angle will be equal respectively: R _o U _x (U _R0 ) ^-1 , γ = φ _x -φ _o = α + β, as external for angles α and β. Since, by the sine theorem, U _X (U _RO ) ^-1 = sinα (sinβ) ^-1 , the modulus of complex resistance

The disadvantage of this method is the low measurement accuracy due to the use of direct conversion devices (phase meters) in comparison with AC bridges. This is because the measurement process does not take into account the influence of the active and reactive components of the input resistances of the measuring devices, which is especially significant for measurements over 10-100 kΩ. Accounting for them leads to the replacement of a three-element equivalent electrical measuring circuit

- to the seven-element (figure 3). Here R _fA , X _fA and R _fB , X _fB are respectively the active and reactive components of the complex input resistances of the measuring (A) and reference (B) channels of the digital phase meter.

 Moreover, the error in determining the parameters of bipolar elements can be made commensurate with the error in AC bridges by measuring the input resistance of the phase meter and taking it into account in the calculation process.

 The present invention is aimed at improving the accuracy of measurement and expanding the measuring range of the parameters of complex resistances.

где α и β - измеренные значения углов между падениями напряжения на образцовом резисторе, измеряемом комплексном сопротивлении и напряжением генератора синусоидальной формы;
g₀ - активная проводимость образцового резистора,
g_ф и b_ф - соответственно активные и реактивные входные проводимости отдельных каналов цифрового фазометра после симметрирования.This is achieved by the fact that in the method for measuring the parameters of the complex resistances, based on the measurement by the digital phase meter of the angles between the voltage drops on the reference resistor, the measured complex resistance and the output voltage of a sinusoidal generator, according to the invention, the active and reactive components of the complex input resistances of the measured and reference channels of a digital phase meter; the corresponding components of the complex input resistances of these channels are balanced and the true values of the components of the total conductivity of the measured complex resistance are determined in accordance with:

where α and β are the measured values of the angles between the voltage drops across the model resistor, the measured complex resistance and the voltage of the sine wave generator;
g ₀ - active conductivity of the reference resistor,
g _f and b _f - respectively, the active and reactive input conductivities of the individual channels of the digital phase meter after balancing.

генератора 1 и падением напряжения

на образцовом резисторе 2, а для нижнего положения переключателя 4, наоборот, потенциальный вход опорного канала В подключен к выходной клемме генератора синусоидального напряжения 1, связанной с образцовым резистором 2, а общая шина обоих каналов цифрового фазометра 5 в нижнем положении переключателя 4 связана к выходной клеммой генератора синусоидального напряжения 1, соединенной с измеряемым комплексным сопротивлением 3, и поэтому цифровой фазометр измеряет угол между напряжением генератора

синусоидального напряжения 1 и падением напряжения

на измеряемом комплексном сопротивлении 3.A device for measuring the parameters of the complex resistances is illustrated in the drawing. Figure 4 shows a block diagram of a device. It contains a sinusoidal voltage generator 1, an exemplary resistor 2, a measured impedance 3, a dual switch to two positions 4, a digital phase meter 5, a PC 6. A sinusoidal voltage generator 1, an exemplary resistor 2 and a measured impedance 3 form a series-connected measuring circuit, and the common connection point of the reference resistor 2 and the measured complex resistance 3 is connected directly to the potential input of the measuring channel of the digital phase meter 5, and the potential input of its reference channel for the upper position of the dual switch 4 is connected to the output terminal of the sinusoidal voltage generator 1, connected to the measured impedance 3, and the common bus of the digital phase meter 5 through the second channel of the switch 4 in the upper position is connected to the terminal of the sinusoidal voltage generator 1, connected with an exemplary resistor 2, and since the digital phase meter 5 determines the relative position of the voltage vectors of the channels A and B relative to the common bus, it measures angle between voltage

generator 1 and voltage drop

on the model resistor 2, and for the lower position of the switch 4, on the contrary, the potential input of the reference channel B is connected to the output terminal of the sinusoidal voltage generator 1, connected to the model resistor 2, and the common bus of both channels of the digital phase meter 5 in the lower position of the switch 4 is connected to the output terminal of the sinusoidal voltage generator 1, connected to the measured complex resistance 3, and therefore the digital phase meter measures the angle between the voltage of the generator

sinusoidal voltage 1 and voltage drop

on the measured complex resistance 3.

относительно вектора напряжения питания

(фиг.2) указывает на емкостной характеркомплексного сопротивления, а отставание

относительно

- на индуктивный его характер.Depending on the upper or lower position of the dual switch, the digital phase meter 5 measures the phase angle α between the voltage vectors of the sinusoidal voltage generator 1 and the reference resistor 2 or the angle β between the voltage vectors of the sinusoidal voltage generator 1 and the measured complex resistance 3 (Fig. 2). The nature of the measured bipolar is determined by the polarity of the angle of the phase shift. Stress vector advance

relative to the supply voltage vector

(figure 2) indicates the capacitive nature of the complex resistance, and the lag

regarding

- on its inductive character.

To the input terminals of the channels, the input active or reactance of which is of greater importance, for example channel A (Fig. 4), additional reference resistor R _add -7 and capacitor C _add -8 are connected in parallel.

If R _fA , C _fA and R _fV , C _fV are the input resistances and capacitance of the measured A and reference B channels of the digital phasemeter 5, respectively, then to exclude the methodological measurement error from the bypass of the measuring circuit, the input resistances of the individual channels are pre-measured and balanced. To the input terminals of the channel of the phase meter, the input active or reactance of which has large values, for example, channel A, an additional reference resistor and capacitor are connected in parallel, the parameters of which are equal to:
R _ext = R R _{fB fA} (R _fA -R _vWF) ^-1 and C = C _ext C. _{fA fB (fA} C -C _vWF) ^-1.

Therefore now
R ' _fA = R _fB = R _f ; C ' _fA = C _fB = C _f .

на образцовом резисторе 2, а в нижнем положении переключателя 4 - угол β между напряжением генератора 1 и падением напряжения

на измеряемом двухполюснике 3. Значения углов α, β и γ = α+β вместе со значениями величины образцового резистора 2-R_O, активных и реактивных составляющих входных сопротивлений цифрового фазометра 5 R'_фА=R_фB=R_ф; С'_фА=С_фB=С_ф и частоты ω напряжения генератора 1 заносятся в память ПЭВМ 6. Расчет параметров измеряемого комплексного сопротивления удобно провести через проводимости. Векторная диаграмма эквивалентной измерительной цепи, построенная по результатам измерений, соответствует фиг.2. Так как образцовый резистор R_o и измеряемое комплексное сопротивление Z_x зашунтированы входными импедансами опорного и измеряемого каналов фазометра, то:

и для данной цепи имеем:

Откуда:

Используя теорему синусов из векторной диаграммы (фиг.2) комплекс,

можно представить в виде:

Обозначим комплекс

где A = sinβ (sinα)^-1cosγ; B = sinβ (sinα)^-1sinγ, а γ = α+β.
Приравняв правые части уравнений (3) и (4), получим:

Из данного уравнения после ряда преобразований найдем выражения для активной g_x и реактивной b_х составляющих общей комплексной проводимости измеряемого комплексного сопротивления
g_x = sinβ(sinα)^-1[(g₀+g_ф)cosγ-b_фsinγ]-g_ф (7)
b_x = sinβ(sinα)^-1[(g₀+g_ф)sinγ+b_фcosγ]-b_ф. (8)
Используя данные выражения, нетрудно вычислить значения параметров комплексного сопротивления:
Для последовательного соединения элементов
R_x=g_x(g_x ²+b_x ²)^-1, (9)
X=g_x(g_x ²+b_x ²)^-1. (10)
Для параллельного соединения

В соответствии с выражениями (1), (7), (8), а затем (9), (10) или (11), (12) ПЭВМ 6 вычислит значения параметров R_x, Х с последовательным или параллельным соединением элементов. В результате этих действий повышается точность измерения параметров комплексных сопротивлений.Using the device of the claimed method is implemented as follows. In the up position of switch 4, the digital phase meter 5 measures the angle α between the voltage of the sine wave generator 1 and the voltage drop

on the model resistor 2, and in the lower position of the switch 4 - the angle β between the voltage of the generator 1 and the voltage drop

on the measured two-terminal network 3. The values of the angles α, β, and γ = α + β together with the values of the reference resistor 2-R _O , active and reactive components of the input resistances of the digital phase meter 5 R ' _fA = R _fB = R _f ; With ' _fA = C _fB = C _f and frequency ω the voltage of the generator 1 is stored in the memory of the personal computer 6. It is convenient to calculate the parameters of the measured complex resistance through conductivity. The vector diagram of the equivalent measuring circuit, constructed according to the measurement results, corresponds to figure 2. Since the reference resistor R _o and the measured complex resistance Z _{x are} shunted by the input impedances of the reference and measured channels of the phase meter, then:

and for this circuit we have:

From:

Using the sine theorem from the vector diagram (figure 2) complex,

can be represented as:

Denote the complex

where A = sinβ (sinα) ^-1 cosγ; B = sinβ (sinα) ^-1 sinγ, and γ = α + β.
Equating the right sides of equations (3) and (4), we obtain:

From this equation, after a series of transformations, we find the expressions for the active g _x and reactive b _x components of the total complex conductivity of the measured complex resistance
g _x = sinβ (sinα) ^-1 [(g ₀ + g _f ) cosγ-b _f sinγ] -g _f (7)
b _x = sinβ (sinα) ^-1 [(g ₀ + g _f ) sinγ + b _f cosγ] -b _f . (8)
Using these expressions, it is easy to calculate the values of the complex resistance parameters:
For series connection of elements
R _x = g _x (g _x ² + b _x ² ) ^-1 , (9)
X = g _x (g _x ² + b _x ² ) ^-1 . (10)
For parallel connection

In accordance with the expressions (1), (7), (8), and then (9), (10) or (11), (12), the PC 6 will calculate the values of the parameters R _x , X with serial or parallel connection of elements. As a result of these actions, the accuracy of measuring the parameters of complex resistances is increased.

Sources of information
1. Kneller V. Yu. Automatic measurement of the components of complex resistance. - M.-L.: Energy, 1967, p. 40, Fig. 2-13.

 2. Copyright certificate of the USSR 1167530, MKI G 01 R 27/02, BI 26, 1985. Measuring instrument of complex resistance parameters.

Claims (2)

1. A method for measuring the parameters of complex resistances, based on a digital phase meter measuring two angles between voltage drops on a sample resistor, measured complex resistance and voltage of a sinusoidal generator, characterized in that the active and reactive components of the complex input resistances of the measuring and reference channels of the digital phase meter are pre-measured , the corresponding components of the complex input resistances of both channels symmetry and the true values of nent total conductivity measured complex impedance is determined in accordance with the following expressions:

where α and β are the measured values of the angles between the voltage drops across the model resistor, the measured complex resistance and the voltage of the sine wave generator;
g ₀ is the active conductivity of the reference resistor;
g _f - active input conductivity of individual channels of the digital phase meter;
b _f - reactive input conductivity of individual channels of the digital phase meter.  2. A device for measuring the parameters of complex resistances, containing a sinusoidal voltage generator connected in series, an exemplary resistor and a measured impedance, a digital phase meter, the output of which is connected to a PC input, characterized in that a double switch into two positions, an additional exemplary resistor and capacitor, and the common connection point of the reference resistor and the measured complex resistance is connected directly to the potential input the measuring channel of the digital phase meter, the other inputs of the phase meter are connected to the output of the sinusoidal voltage generator through the dual switch, and in the upper position of the switch, the digital phase meter measures the angle between the voltage of the sinusoidal voltage generator and the voltage drop across the reference resistor, and in the lower position of the switch - between the voltage of the sinusoidal voltage generator and voltage drop across the measured complex resistance, and additional reference resistor and capacitor for balancing the channels of the digital phase meter are connected to the input terminals of those channels, the input active or reactive resistances of which are of greater importance.

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