RU2374633C1 - Method and device for determining moisture using current-voltage characteristics of materials - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: in the method of determining moisture according to the invention, voltage is applied across a measurement cell which consists of series-connected wet material and standard resistance. The linear current-voltage characteristic of the analysed material is determined using an excess amplification coefficient. Diffusion conductance is determined from the angle of inclination of the linear current-voltage characteristics of the analysed material, as a ratio of the current measured on the standard resistance to the voltage applied across the sample of wet material, and moisture is determined from a calibration curve. The device for determining moisture according to the invention consists of a measurement cell, made from series-connected wet material and standard resistance. The device also includes an operational amplifier, in the negative circuit of which is connected the measurement cell, analysed sample of material and standard resistance, connected to the input and output of the device, respectively.

EFFECT: increased metrological efficiency, specifically accuracy of measurement, due to elimination of non-linearity.

3 cl, 6 dwg, 1 tbl

Description

The present invention relates to measuring technique, in particular to measuring the moisture content of capillary-porous materials.

There is a method of measuring the humidity of capillary-porous materials [A. Lapshin Electric moisture meters. - M .: Gosenergoizdat, 1960, pp. 15-20], where the differential electrical resistance of the material sample is used as the parameter by which humidity is determined. The method consists in determining the electrical resistance of a sample of material at a constant current at one fixed voltage, and the device contains a measuring probe in the form of a voltage divider.

The disadvantages of this method and device are: low measurement accuracy due to the dependence of the electrical resistance of the sample material on the applied voltage, high voltage to go to a linear, steeper section of the characteristic and the narrowness of the measurement range due to voltage fixation.

The known method [Berliner MA Moisture measurement. - M .: Energia, 1973, p.52-54], which consists in making contact with the sample using four electrodes located along the line at a fixed distance from each other. A direct current is passed through the external electrodes, and the voltage is measured between the internal electrodes, which determine the specific volume resistance of the material and humidity. The device is made in the form of a four-probe voltage divider.

The disadvantage of the data of the method and device is the low accuracy of the measurements due to the dependence of the electrical resistance of the material sample on the transmitted current, the electrodes must be removed from all surfaces of the material, except the test one, the medium must be semi-infinite.

For the prototype adopted the method [see RF patent No. 2187098, G01N 27/04, 2002, Bull. No. 22], which consists in measuring the diffusion conductivity by the current-voltage characteristic (CVC). To do this, measure the electrical characteristics of the sample material in the range of 10-29% at a voltage of 5-10 V. The device contains a measuring cell, consisting of series-connected wet material and a reference resistance.

The disadvantage of the prototypes is low accuracy due to the methodological error due to the nonlinearity of the current-voltage characteristics of the measuring probe with a passive voltage divider.

The technical task of the method and device is to eliminate methodological errors by eliminating non-linearity.

The technical task is achieved as follows.

1. In the method for determining humidity by the current-voltage characteristic of materials, which consists in contacting the sample using two electrodes located along a line perpendicular to the sample fibers at a fixed distance from each other, a voltage is applied to the measuring cell, consisting of series-connected wet material and reference resistance, measure the current due to the voltage drop across the reference resistance and determine the humidity by diffusion conductivity, in contrast to and of the known solutions, they organize the linear current-voltage characteristic of the test sample due to the excess gain, determine the diffusion conductivity by the angle of inclination of the linear current-voltage characteristic of the test material as the ratio of the current measured on the reference resistance to the applied voltage on the sample of the wet material, and humidity is determined by the calibration addictions.

2. In the method according to claim 1, in contrast to the prototype, the function of diffusion conductivity of the structure of dry material with a given constant of normalized humidity serves as a calibration characteristic, the calibration function is determined in the process of measuring diffusion conductivities on two standards corresponding to the lower and upper boundaries of the measured humidity range.

3. In the device for determining humidity by the current-voltage characteristic of materials, consisting of a measuring cell, organized from series-connected wet material and a reference resistance, in contrast to the prototype, an operational amplifier is introduced, in the negative connection of which a measuring cell, an investigated sample of material and the reference resistance of which is connected respectively to the input and output of the device.

The essence of the proposed method and device is illustrated in figures 1-4.

The proposed method includes 2 stages:

1) Measurement of diffusion conductivity.

2) Determination of humidity by diffusion conductivity.

1. The moisture content of the materials is determined by measuring the diffusion conductivity. To do this, make contact with the sample using two electrodes located along a line perpendicular to the fibers of the sample at a fixed distance from each other. Apply voltage U _i to the measuring cell, consisting of series-connected wet material 1 with differential conductivity Y _d and reference resistance 2 with known conductivity Y (Fig. 1). Measure the current I _i (figa) due to the voltage drop U at the reference resistance 2 by the known conductivity Y:

Humidity is determined by the diffusion conductivity Y _{0 of} sample 1, which is found due to the gain redundancy β (Fig. 1) by the slope of the linear volt-ampere characteristic (CVC) (Fig. 2a) of the material under study 1. In this case, the ratio of measured on the reference resistance 2 currents I _i (1) to the applied voltage U _i per sample of wet material 1:

The I – V characteristic linearity is organized by including a measuring cell in the negative feedback circuit of the operational amplifier 3 with an excess gain β (Fig. 1a). To do this, the test sample 1 is connected between the input of the device with the voltage potential U _i and the inverse e_ input of the amplifier 3, and between it and the output of the device (output of the operational amplifier 3) include a reference resistance 2.

Let us prove the linearity of measuring the I – V characteristic of the device (Fig. 1, a) according to its equivalent circuit in the signal graphs (Fig. 1, b). According to the graph-scheme (Fig. 1, b), according to I and II Kirchhoff rules, the system of equations for nodes with potentials e_ and U:

We express from the second equation of system (3) the inverse potential e_ with redundancy of the gain β

and substitute its values in the first equation, whence we get:

.

.

We find the linear CVC of the proposed device (figure 1), taking into account the current I _i (1):

where the minus sign reflects the inversion of the signal by amplifier 3.

, то после разделения переменных

запишем интегральное уравнение:Since differential conductivity

then after separation of variables

we write the integral equation:

.

.

As a result of integration and logarithm, we obtain a linear CVC:

from which follows the measurement algorithm (2) and the identity Y _d = Y ₀ corresponding to the product of the diffusion parameters I ₀ = U ₀ Y ₀ (see Fig. 1, a).

It should be noted that the linearity of the CVC (5) and (6) is achieved by condition (4): gain redundancy and zero potential e_ of the inverse input of the amplifier (3). This corresponds to a zero-measure virtual ground galvanically decoupling the input U _i and output U voltage of the measuring cell. Due to the virtual ground of conditions (4), the input voltage U _i as the potential difference U _i -e_ = U _{i is} distributed only on the sample of wet material 1, and the output voltage U as the potential difference U-e_ = U is applied only to the reference resistance 2 with the known conductivity. This eliminates the nonlinearity of the I – V characteristic of the measuring cell, in contrast to the known solutions for passive switching on of the studied cell according to the voltage divider circuit.

For a passive voltage divider without conditions (4), the first equation of system (3) has the form:

because the voltage U _i applied to the cell is divided by the voltage U of the reference resistance 2 relative to the zero potential and the voltage drop U _i -U on the test sample 1.

The passive divider corresponds to the conditions Y _d = dI / dU and U _i = U ₀ , UY = I ₀ and UY _d = I, after substituting which into expression (7) we obtain a first-order differential equation:

The solution of equation (8) is the exponential CVC in an implicit form:

the investigated material 1 due to the voltage drop U _i -U on it, and the current (9) is measured on the reference resistance 2 in known solutions.

We estimate the nonlinearity η BAX (9) with respect to the linear equivalent (6) of the proposed solution, for this we multiply and divide expression (9) by the voltages U _i and U ₀ and, taking into account (6), write:

where the nonlinearity has the form

From expression (10) we determine the methodological error ε of the known solutions:

which is absent in the proposed solutions due to the unit constant η = 1, and for the prototype it is a non-linear function (11) with an implicit dependence of the measured voltage U. In real conditions, U _i = U ₀ m, and U = U _i / 2 at a matched load reference resistance 2 and sample 1, then nonlinearity (11) can be represented as

.The dependences η (m) and ε (m) by formulas (13) and (12) are tabulated for

.

m one 2 3 four 5 6 7 8 9 10 twenty η 0.65 0.86 1.16 1,60 2.24 3.18 4,59 6.7 9.9 14.7 1101 ε,% 35 fourteen -16 -60 -124 -218 -359 -570 -890 -1370 1,110 ⁵

From the table it follows that η = 1 at m = 2.5, which is possible only with excessive gain. At m = 5, nonlinearity is twice the norm, and at m = 10 it is 14.7 times higher than the regulation. In practice, m> 10; therefore, the methodical error ε of the probe on the passive divider exceeds the norm by 5 orders of magnitude, which leads to measurement uncertainty of both diffusion conductivity and sample humidity during linearization of the I – V characteristics of known solutions.

материала выглядит следующим образом:2. By analogy with (9), the humidity characteristic

material is as follows:

является произвольной константой влажности (см. фиг.3, 4), а Y_Si - функция диффузионной проводимости структуры сухого материала (фиг.3, 2), компенсирующая неопределенность константы.where is the parameter

is an arbitrary humidity constant (see Figs. 3, 4), and Y _Si is a function of the diffusion conductivity of the structure of the dry material (Figs. 3, 2), which compensates for the constant uncertainty.

As

тогда диффузионная проводимость образца имеет вид

Из данного соотношения получим влажностную характеристику материала (14).Where

then the diffusion conductivity of the sample has the form

From this ratio we obtain the moisture content of the material (14).

The reference function Y _Si0 (Fig. 3, 1) can be found by comparing formula (14) with the equivalent of Y _{0 of the} humidity characteristic with the informative parameters W ₀ and Y _S.

From equation (14), the experimental dependence Y _Si (Figs. 3, 2) can be expressed in terms of informative parameters W ₀ and Y _{S is} equivalent to (15), provided that Y _i = Y _{0 is} equivalent:

Calibration on the standards of the range boundaries is used to calculate the informative parameters W ₀ (Figs. 3, 4) and Y _S (Figs. 3, 5) to optimize the experimental static (16) characteristics of Y _Si (Figs. 3, 2) relative to the reference humidity dependence Y _Si0 (Fig. 3, 1).

When calibrating, measure the values of the conductivity function Y _Si in the lower and Y _{Si + 1} in the upper boundaries of the normalized humidity range on standard materials with known humidity W _i0 and W _{i + 10} (Fig. 3). The algorithm for calculating the informative parameters W ₀ and Y _{S is} found by formula (16) from a system of two equations for the first (i) th and second (i + 1) th measurements.

Solving the system of equations (16), we find the values of the informative parameters: diffusion conductivity Y _{S of} dry material

and normalized humidity W ₀

In expressions for calculating informative parameters (17, 18), the abbreviation

,

,

moreover, W _i and W _{i + 1} - the measured values of the humidity of the reference samples with known moisture content W _i0 and W _{i + 10} .

.The obtained parameters W ₀ and Y _S uniquely determine the function (16) of the diffusion conductivity Y _{Si0 of the} structure (Fig. 3, 1), therefore, they are taken as informative parameters (Fig. 3, 5) and a calibration curve is constructed (Fig. 3, 3) the functions

.

в нормированном диапазоне калибровки W_i,0 W_i,0+1 (фиг.4).The moisture content W _{j0 is} determined in the (j) -th experiment when measuring the diffusion conductivity Y _{Si of the} test material 1 by the calibration function (16) of the structure conductivity

in the normalized calibration range W _{i, 0} W _{i, 0 + 1} (figure 4).

In Fig. 5, the errors of measuring the diffusion conductivity of Y _Si by humidity were made before calibration Δ1 (Fig. 5, 1) and after Δ2 (Fig. 5, 2):

,

.

,

.

From the analysis of the graphs it follows that calibration reduces the deviation from the reference function by at least four times. This makes it possible to determine humidity from the diffusion conductivity in a given range with a normalized control accuracy determined by the error of the reference materials at the boundaries of the adaptive range.

Let us prove the effectiveness of ψ in the accuracy of the proposed method relative to the prototype in assessing their methodological error.

предлагаемых решений (2), получим:By differentiating equivalent conductivity

proposed solutions (2), we obtain:

The methodological error σ ₁ (6, 1) of the proposed solutions for the mean-square estimate of the derivative (19) has the form:

We estimate the nonlinear conductivity of the prototype Y _d = Y _e η, where the nonlinearity

Differentiating the expression (21), we obtain the methodological error of the prototype σ _η (Fig.6, 2):

The efficiency ψ (6, 3) in accuracy is determined by the ratio of the methodological errors of the prototype (22) to the proposed solution (20):

ψ = σ _η / σ ₁ .

From the analysis of the graphs (Fig.6) it follows that the methodological error of the prototype (Fig.6, 2) is determined by the nonlinearity of the algorithm of the known method, which reduces the accuracy by an order of magnitude in the voltage range below 0.15 V. At 0.25 V voltage, the error of the proposed solutions ( 6, 1) 3 times lower than the known ones, and for the regulated error σ = 2, the range expands towards low amplitudes from 0.23 V to 0.07 V or 3 times and by an order of magnitude at σ = 10. This is due to linear conversion due to excessive gain.

Thus, the proposed method and device, in contrast to the known solutions, reduce the methodological error by at least 3 times due to linear transformations according to the I – V characteristics of the materials under study, which makes it possible to determine humidity in the adaptive range with a given accuracy of exemplary measures.

Claims (3)

1. The method of determining humidity by the current-voltage characteristic of the materials, which consists in the fact that they make contact with the sample using two electrodes located along a line perpendicular to the sample fibers at a fixed distance from each other, apply a voltage to the measuring cell, consisting of in series included wet material and reference resistance, measure the current due to the voltage drop across the reference resistance and determine the humidity by diffusion conductivity, different m, which organize the linear volt-ampere characteristic of the sample under study due to gain redundancy, determine the diffusion conductivity by the angle of inclination of the linear volt-ampere characteristic as the ratio of the current measured on the reference resistance to the applied voltage on the sample of wet material, and humidity is determined by the calibration characteristic. 2. The method according to claim 1, characterized in that the calibration characteristic is a function of the diffusion conductivity of the structure of the dry material with a unit constant of normalized humidity, which is determined in the process of measuring diffusion conductivities on two standards that correspond to the lower and upper boundaries of the measured humidity range. 3. A device for determining humidity by the current-voltage characteristic of materials, consisting of a measuring cell, organized from series-connected wet material and a reference resistance, characterized in that an operational amplifier is additionally introduced, in the negative connection of which a measuring cell, an investigated sample of material and a reference are included the resistance of which is connected respectively to the input and output of the device.

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