RU2615014C1 - Apparatus for measuring parameters of multi-element rlc two-terminal networks - Google Patents

Abstract

FIELD: physics, measurement technology.

SUBSTANCE: invention relates to measurement technology and particularly to equipment for measuring parameters of objects in the form of passive two-terminal networks with lumped parameters, having a multi-element equivalent circuit. The apparatus comprises a generator of voltage test pulses, having the shape of an n-th power function, a differential current-to-voltage converter, (n + 1) variable resistors, one of the leads of the first variable resistor is connected to the output of the pulse generator, and the other is connected to the second input of the current-to-voltage converter, n analogue switches, inputs of which are connected to the leads of the second, third, …, (n+1)-th variable resistor, outputs of the switches are connected to inputs of the differential current-to-voltage converter, n-stage differentiator on differentiating RC links, the input of the first link is connected to the output of the current-to-voltage converter; (n+1) null indicators, inputs of the first, second, …, n-th null indicators are respectively connected to outputs of the n-th, (n-1)-th, …, first RC link of the differentiator, the input of the (n+1)-th null indicator is connected to the output of the differential current-to-voltage converter; the apparatus further includes a second differentiator on n series-connected differentiating RC links and n voltage followers, wherein all differentiating RC links of the second differentiator have equal RC time constants, but different resistor and capacitor values, the input of the first link of the second differentiator is connected to the output of the test pulse generator, the inputs of the voltage followers are connected to outputs of RC links of the second differentiator, and outputs of the voltage followers are connected to free leads of the second, third, …, (n+1)-th variable resistor.

EFFECT: invention provides high operating stability of the apparatus for generating reference signals and eliminates compensation errors due to delays of different components of compensation current.

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Description

The invention relates to measuring technique and, in particular, to a technique for measuring the parameters of objects in the form of passive two-terminal devices with lumped parameters having a multi-element equivalent circuit.

A known parameter meter of multi-element passive two-terminal devices (RF patent No. 2466412, G01R 17/00), in which the measured multi-element two-terminal device (MIS) is affected by voltage pulses, changing according to the law of the nth degree of time, and the two-terminal current is balanced by a compensating signal synthesized from pulses current in the form of power time functions with exponents from n to 0, and from the found amplitudes of the components of the pulses of the compensating current, the generalized conductivity parameters are calculated, and then the electron cal parameters of the two-terminal elements. The circuit for generating exemplary current pulses of the nth degree consists of a generator of rectangular voltage pulses and n series-connected integrators; to generate current pulses having the form of power functions, the output signals of the rectangular pulse generator and integrators are used, the outputs of which are connected with adjustable model resistors with discretely tunable resistance.

The disadvantage of this device is the measurement error, due, firstly, to the distortion of the shape of the test and reference current pulses, since at a finite value of the gain of the op-amp, the integrator reaction to an n-th pulse contains not only a component of the (n + 1) -th degree, but also an impulse of the (n + 2) -th degree, which creates an obstacle for a phased separate balancing, starting from a signal of a higher degree, secondly, due to the large range of amplitudes of the signals at the outputs of different stages of integrators, and secondly, a large range m amplitudes of signal components of the measured two-terminal network, and hence the reference signal (approximately a decade by one stage) and even at n = 3, the amplitude of the original rectangular pulse at the input of the first integrator is of the order of 10 mV, which is commensurate with the U bias voltage _see operational amplifiers ( OU). The integration error due to this OS parameter is transmitted along the galvanic coupling circuit from cascade to cascade.

The closest in technical essence to the proposed device is a parameter meter for multi-element RLC bipolar devices (RF patent No. 2556301, G01R 17/10, Bull. No. 19 dated 07/10/2015). The meter includes a generator of test voltage pulses, varying according to the law of the nth degree, n series differentiators on an operational amplifier each, a differential current-voltage converter, (n + 1) tunable resistor, n analog switches and (n + 1 ) equilibrium indicator. The set of output voltages of each of the differentiators is used as a set of reference signals. Serially connected differentiators are built on operational amplifiers with frequency correction in order to eliminate the instability of differentiators.

The disadvantages of the device are:

1) Conflicting requirements for the choice of frequency correction parameters for operational amplifiers, which, on the one hand, provide the stability of differentiators and, on the other hand, a sufficient bandwidth to minimize pulse shape distortions.

содержит не только первую, но и вторую, третью и т. д. производные входного напряжения. Например, при кубической форме питающего импульса напряжение на выходе первого дифференциатора содержит и квадратичный, и линейный импульсы. 2) Another disadvantage is due to the finite time delay of the signal in the stages of the differentiator. The output signal of a real differentiator with a transfer characteristic of the form $$H\left(p\right)=p\tau /\left(\mathrm{one}+p\tau \right)$$

contains not only the first, but also the second, third, etc. derivatives of the input voltage. For example, with the cubic shape of the supply pulse, the voltage at the output of the first differentiator contains both quadratic and linear pulses.

At the output of the second differentiator, a linear pulse is also generated, which is delayed relative to the same signal of the first differentiator, therefore, when regulating the linear component of the compensating current, which includes the linear voltage components of both stages of the differentiator, an error arises in determining the corresponding parameter.

The problem to which the invention is directed is to increase the stability of differentiators and eliminate the influence of delays in the chains of formation of model signals on the accuracy of balancing.

The technical result is achieved by the fact that in the parameter meter of multi-element RLC two-pole, containing a generator of test voltage pulses having the form of a function of the nth degree of time, the first (signal) output of which is connected to the first terminal for connecting the measured RLC two-pole, differential converter "current -voltage ", which consists of two series-connected operational amplifiers, the first and second resistors, respectively, the output of the first the operational amplifier is connected to the inverting input of the second operational amplifier through the third resistor, the inverting inputs of the first and second operational amplifiers form the first and second current inputs of the current-voltage converter, and the output of the second operational amplifier is the output of the converter, (n + 1) adjustable resistor, n analog switches, (n + 1) null indicator and n-cascade differentiator on differentiating RC links, the first output of the first adjustable resistor is connected to the first output of the generator pulses, the first input of the differential current-voltage converter is connected to the second terminal for connecting the measured two-terminal device, one of the terminals of the first adjustable resistor is connected to the first output of the test pulse generator, and the second output of the first adjustable resistor is connected to the second input of the current-voltage converter , one of the terminals of the second, third, etc., ..., (n + 1) -th adjustable resistor is connected to the analog input of the first, second, etc., ..., n-th analog switch, the input is first of the differentiating RC link is connected to the output of the current-voltage converter, the signal input of the first, second, etc., ..., of the nth null indicator is connected respectively to the output of the nth, (n – 1) -th and etc., ..., of the first differentiating RC link, and the signal input of the (n +1) th null indicator is connected to the output of the current-voltage converter, the first output of each analog switch is connected to the first input of the current-voltage converter ", And the second output of each analog switch is connected to the second input of the current-voltage converter e ", the output of the switching signal of the second, third, etc., ..., (n + 1) -th null indicator is connected respectively to the input of the switching signal of the first, second, etc., ..., n-th analog switch, the digital output of regulating the resistance of the first, second, etc., ..., (n + 1) -th zero indicator is connected to the digital input of the first, second, etc., ..., (n + 1) -th adjustable resistor, the inputs of the synchronization signal of all null indicators are connected to the second output of the test pulse generator, a second differentiator containing n by of differentially connected differentiating RC links, and n voltage followers, the input of the first differentiating RC link of the second differentiator is connected to the first output of the test pulse generator, the inputs of the voltage repeaters are connected to the outputs of the corresponding differentiating RC links, to the output of the first, second, etc. , ..., of the nth voltage follower, the free output of the second, third, etc., ..., (n + 1) -th adjustable resistor is connected, and all the differentiating RC links of the second differentiator have equal constant time nor RC, but different values of the resistance of the resistor and the capacitance of the resistor: the resistance of the resistor in the kth RC link is greater than in the (k – 1) th RC link, and the capacitance in the kth RC link is as many times less than in the (k – 1) th RC link.

The invention is illustrated by the example of a four-element two-terminal parameter meter.

The device diagram is shown in FIG. one.

The device contains a generator 1 of test voltage pulses (GTI), with the first (signal) output of which is connected the first terminal for connecting the measured two-terminal device, a differential current-voltage converter, built on the first and second operational amplifiers 2 and 3, in the feedback circuit of each of which resistor 4 and 5 are included, respectively, and between the output of amplifier 2 and the input of amplifier 3, resistor 6, the second terminal for connecting the measured two-terminal device is connected to the first input of the current-voltage converter and The first outputs of the switches 7, 8 and 9, the second outputs of the switches are connected to the second input of the current-voltage converter, the inputs of the switches 7, 8 and 9 are connected to adjustable resistors 10, 11, and 12. A fourth adjustable resistor 13 is connected between the first output of the generator 1 and the second input of the current-voltage converter. An input of a three-stage differentiator built on differentiating RC links is connected to the output of the current-voltage converter: capacitor 14, resistor 15, capacitor 16, resistor 17, capacitor 18, resistor 19. Output of the third differentiating RC link (capacitor 18, resistor 19 ) is connected to the input of the first zero indicator 20, the output of the second differentiating RC link (capacitor 16, resistor 17) is connected to the input of the second zero indicator 21, the output of the first differentiating RC link (capacitor 14, resistor 15) is connected to the input of the third zero indie Ator 22. Entrance fourth null indicator 23 is connected to the output of inverter "current-voltage". The inputs of the synchronization signal of all null indicators are connected to the second output (synchronization output) of the generator 1. The inputs of the digital resistance control signal of adjustable resistors 13, 10, 11 and 12 are connected to the outputs of the digital signal of the null indicator 20, 21, 22 and 23, respectively. The switching control inputs of the analog switches 7, 8, and 9 are connected to the outputs of the switching signal of the second, third, and fourth zero indicators 21, 22, and 23, respectively.

26, резистор 27, конденсатор 28, резистор 29), вход первого дифференцирующего RC-звена соединен с первым выходом генератора 1, и три повторителя напряжения на операционных усилителях 30, 31 и 32, входы которых соединены с выходами первого, второго и третьего дифференцирующих RC-звеньев соответственно. К выходам первого, второго и третьего повторителей напряжения подключены свободные выводы регулируемых резисторов 10, 11 и 12 соответственно.In the meter circuit, a second three-stage differentiator is additionally introduced on the differentiating RC links in series (capacitor 24, resistor 25, capacitor $$$$

26, resistor 27, capacitor 28, resistor 29), the input of the first differentiating RC link is connected to the first output of the generator 1, and three voltage followers on operational amplifiers 30, 31 and 32, the inputs of which are connected to the outputs of the first, second, and third differentiating RC links respectively. The outputs of the first, second and third voltage followers are connected to the free terminals of adjustable resistors 10, 11 and 12, respectively.

. После переходного процесса в МДП устанавливается импульс тока, содержащий четыре составляющих – кубичную, квадратичную, линейную и прямоугольную:The device operates as follows. Generator 1 generates cubic voltage pulses $$u_{\text{dp}}\left(t\right)=U_m{t}^3/t_{\text{and}}^3$$

. After the transition process, a current impulse is installed in the MIS containing four components - cubic, quadratic, linear and rectangular:

$$i_{\text{дп}}\left(t\right)=\frac{Y_0{U}_m{t}^3}{t_{\text{и}}^3}+\frac{3Y_1{U}_m{t}^2}{t_{\text{и}}^3}+\frac{6Y_2{U}_{m}t}{t_{\text{и}}^3}+\frac{6Y_3{U}_m}{t_{\text{и}}^3}$$

. (1) $$$$

$$i_{\text{dp}}\left(t\right)=\frac{Y_0{U}_m{t}^3}{t_{\text{and}}^3}+\frac{3Y_{\mathrm{one}}{U}_m{t}^2}{t_{\text{and}}^3}+\frac{6Y_2{U}_{m}t}{t_{\text{and}}^3}+\frac{6Y_3{U}_m}{t_{\text{and}}^3}$$

. (one)

The generalized conductivity parameters of a two-terminal network Y ₀ , Y ₁ , Y ₂ , Y _{3 are} determined by the expressions [Ivanov V.I., Titov V.S., Golubov D.A. Application of generalized parameters of a measuring circuit for identification of multi-element two-terminal devices // Sensors and Systems. 2010. No. 8. P. 43–45.]:

; $$Y_1=\frac{b_1-a_1{Y}_0}{a_0}$$

; $$Y_2=\frac{b_2-a_2{Y}_0-a_1{Y}_1}{a_0}$$

; $$Y_3=\frac{b_3-a_3{Y}_0-a_2{Y}_1-a_1{Y}_2}{a_0}$$

. (2) $$Y_0=\frac{b_0}{a_0}$$

; $$Y_{\mathrm{one}}=\frac{b_{\mathrm{one}}-a_{\mathrm{one}}{Y}_0}{a_0}$$

; $$Y_2=\frac{b_2-a_2{Y}_0-a_{\mathrm{one}}{Y}_{\mathrm{one}}}{a_0}$$

; $$Y_3=\frac{b_3-a_3{Y}_0-a_2{Y}_{\mathrm{one}}-a_{\mathrm{one}}{Y}_2}{a_0}$$

. (2)

The values a _0, a ₁ , ..., b ₀ , b ₁ , ... are the coefficients of polynomials of the denominator and numerator of the operator image of the conductivity function of a two-terminal network:

$$Y\left(p\right)=\frac{b_0+p{b}_{\mathrm{one}}+p^2{b}_2\mathrm{...}}{a_0+p{a}_{\mathrm{one}}+p^2{a}_2\mathrm{...}}$$

To implement the MIS current compensation method, it is necessary to have a set of model signals in the form of a power function: cubic, quadratic, linear and rectangular. Let us find the expressions for the pulses at the outputs of the RC links of the second differentiator. Thanks to voltage followers, which act as buffer cascades, the transfer functions at the outputs of the first, second, and third RC links are independent of the capacitances and resistances of the shunt circuits. In order to unify the formulas, we introduce autonomous designations of capacities and resistances: C ₁ - capacitance of capacitor 24, C ₂ - capacitance of capacitor 26, C ₃ - capacitance of capacitor 28, R ₁ - resistance of resistor 25, R ₂ - resistance of resistor 27, R ₃ - resistance resistor 29. Expressions for the transfer characteristics of the outputs of the first, second and third differentiating links, respectively, are bulky:

$$\begin{array}{c}{H}_{\mathrm{one}}=\frac{p{R}_{\mathrm{one}}{C}_{\mathrm{one}}\times }{\mathrm{one}+p\left(R_{\mathrm{one}}{C}_{\mathrm{one}}+R_2{C}_2+R_3{C}_3+R_{\mathrm{one}}{C}_2+R_2{C}_3\right)+p^2(R_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_2+R_{\mathrm{one}}{C}_{\mathrm{one}}{R}_3{C}_3+}\mathrm{...}\\ \frac{\times \left[\mathrm{one}+p\left(R_2{C}_2+R_3{C}_3+R_2{C}_3\right)+p^2{R}_2{C}_2{R}_3{C}_3\right]}{+R_2{C}_2{R}_3{C}_3+R_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_3+R_{\mathrm{one}}{C}_2{R}_2{C}_3+R_{\mathrm{one}}{C}_2{R}_3{C}_3)+p^3{R}_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_2{R}_3{C}_3}\end{array}$$

$$\begin{array}{c}{H}_2=\frac{p^2{R}_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_2\times }{\mathrm{one}+p\left(R_{\mathrm{one}}{C}_{\mathrm{one}}+R_2{C}_2+R_3{C}_3+R_{\mathrm{one}}{C}_2+R_2{C}_3\right)+p^2(R_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_2+R_{\mathrm{one}}{C}_{\mathrm{one}}{R}_3{C}_3+}\mathrm{...}\\ \frac{\times \left(\mathrm{one}+p{R}_3{C}_3\right)}{+R_2{C}_2{R}_3{C}_3+R_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_3+R_{\mathrm{one}}{C}_2{R}_2{C}_3+R_{\mathrm{one}}{C}_2{R}_3{C}_3)+p^3{R}_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_2{R}_3{C}_3}\end{array}$$

Для упрощения анализа результатов измерений и вычислений целесообразно установить значения постоянных времени всех каскадов одинаковыми: $$R_1{C}_1=R_2{C}_2=R_3{C}_3=\tau$$

. Если принять равными сопротивления R₁ = R₂ = R₃ и емкости С₁ = С₂ = С₃, то в этом случае и величины R₁C₂, R₁C₃ и R₂C₃ будут также равны τ, что существенно увеличит длительность переходного процесса в измерительной схеме. Для устранения этого недостатка целесообразно использовать в каждом каскаде разные значения емкости и сопротивления. Например, приняв в первом звене R₁C₁ = RC = τ, во втором звене уменьшим емкость и во столько же раз увеличим сопротивление: $$\begin{array}{c}{H}_3=\frac{p^3\times }{\mathrm{one}+p\left(R_{\mathrm{one}}{C}_{\mathrm{one}}+R_2{C}_2+R_3{C}_3+R_{\mathrm{one}}{C}_2+R_2{C}_3\right)+p^2(R_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_2+R_{\mathrm{one}}{C}_{\mathrm{one}}{R}_3{C}_3+}\mathrm{...}\\ \frac{\times R_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_2{R}_3{C}_3}{+R_2{C}_2{R}_3{C}_3+R_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_3+R_{\mathrm{one}}{C}_2{R}_2{C}_3+R_{\mathrm{one}}{C}_2{R}_3{C}_3)+p^3{R}_{\mathrm{one}}{C}_{\mathrm{one}}{R}_2{C}_2{R}_3{C}_3}\end{array}$$

To simplify the analysis of the results of measurements and calculations, it is advisable to set the values of the time constants of all cascades the same: $$R_{\mathrm{one}}{C}_{\mathrm{one}}=R_2{C}_2=R_3{C}_3=\tau$$

. If we take equal resistance R ₁ = R ₂ = R ₃ and capacitance C ₁ = C ₂ = C ₃ , then in this case the values of R ₁ C ₂ , R ₁ C ₃ and R ₂ C ₃ will also be equal to τ, which is essential will increase the duration of the transient in the measurement circuit. To eliminate this drawback, it is advisable to use different capacitance and resistance values in each cascade. For example, taking in the first link R ₁ C ₁ = RC = τ, in the second link we decrease the capacitance and increase the resistance by the same amount:

, $$C_2=mC;R_2=\frac{R}{m}$$

,

where m <1. In the third link, we again change the capacitance and resistance:

. $$C_3=m{C}_2;R_3=\frac{R_2}{m}$$

.

Then the transfer function for the output of the first stage (link C ₁ -R ₁ ) takes the form

. (3) $$H_{\mathrm{one}RC}\left(p\right)=\frac{p\tau \left(\mathrm{one}+\left(2+m\right)p\tau +p^2{\tau }^2\right)}{\mathrm{one}+\left(3+2m\right)p\tau +\left(3+2m+m^2\right)p^2{\tau }^2+p^3{\tau }^3}$$

. (3)

The generalized parameters of the function H _1RC (p) are equal

; $$H_{11}=\tau$$

; $$H_{12}=-\left(1+m\right){\tau }^2$$

; $$H_{13}=\left(1+3m+m^2\right){\tau }^3$$

, $${\mathrm{<figure-callout\; id="10"\; label="H"\; filenames="00000056.png"\; state="\{\{state\}\}">H</figure-callout>}}_{10}=0$$

; $$H_{\mathrm{eleven}}=\tau$$

; $$H_{12}=-\left(\mathrm{one}+m\right){\tau }^2$$

; $${\mathrm{<figure-callout\; id="13"\; label="H"\; filenames="00000056.png"\; state="\{\{state\}\}">H</figure-callout>}}_{13}=\left(\mathrm{one}+3m+m^2\right){\tau }^3$$

,

and the voltage at the first output of the differentiator contains not only the first, but also the second and third derivatives of the test signal:

. (4) $$u_{\mathrm{one}RC}\left(t\right)=\frac{3\tau U_{\text{m}}{t}^2}{t_{\text{and}}^3}-\frac{6\left(\mathrm{one}+m\right){\tau }^2{U}_{\text{m}}t}{t_{\text{and}}^3}+\frac{6\left(\mathrm{one}+3m+m^2\right){\tau }^3{U}_{\text{m}}}{t_{\text{and}}^3}$$

. (four)

Transfer function for the output of the second stage (link C ₂ -R ₂ )

. (5) $$H_{2RC}\left(p\right)=\frac{p^2{\tau }^2\left(\mathrm{one}+p\tau \right)}{\mathrm{one}+\left(3+2m\right)p\tau +\left(3+2m+m^2\right)p^2{\tau }^2+p^3{\tau }^3}$$

. (5)

The generalized parameters of the function H _2RC (p) are equal

; $$H_{21}=0$$

; $$H_{22}={\tau }^2$$

; $$H_{23}=-2\left(1+m\right){\tau }^3$$

$$H_{\mathrm{twenty}}=0$$

; $$H_{21}=0$$

; $${\mathrm{<figure-callout\; id="22"\; label="H"\; filenames="00000056.png"\; state="\{\{state\}\}">H</figure-callout>}}_{22}={\tau }^2$$

; $${\mathrm{<figure-callout\; id="23"\; label="H"\; filenames="00000056.png"\; state="\{\{state\}\}">H</figure-callout>}}_{23}=-2\left(\mathrm{one}+m\right){\tau }^3$$

and voltage at the second output of the differentiator

. (6) $$u_{2RC}\left(t\right)=\frac{6{\tau }^2{U}_{\text{m}}t}{t_{\text{and}}^3}-\frac{12\left(\mathrm{one}+m\right){\tau }^3{U}_{\text{m}}}{t_{\text{and}}^3}$$

. (6)

Transfer function for the output of the third stage of the differentiator

. (7) $$H_{3RC}\left(p\right)=\frac{p^3{\tau }^3}{\mathrm{one}+\left(3+2m\right)p\tau +\left(3+2m+m^2\right)p^2{\tau }^2+p^3{\tau }^3}$$

. (7)

The generalized parameters of the function H _3RC (p) are equal

; $$H_{31}=0$$

; $$H_{32}=0$$

; $$H_{33}={\tau }^3$$

$$H_{\mathrm{thirty}}=0$$

; $$H_{31}=0$$

; $${\mathrm{<figure-callout\; id="32"\; label="H"\; filenames="00000056.png"\; state="\{\{state\}\}">H</figure-callout>}}_{32}=0$$

; $${\mathrm{<figure-callout\; id="33"\; label="H"\; filenames="00000056.png"\; state="\{\{state\}\}">H</figure-callout>}}_{33}={\tau }^3$$

and the voltage at the third output of the differentiator (link C ₃ -R ₃ ) has the form

. (8) $$u_{3RC}\left(t\right)=\frac{6{\tau }^3{U}_{\text{m}}}{t_{\text{and}}^3}$$

. (8)

It follows from the formulas obtained that the two-terminal current can be compensated using the output signals of the differentiators on the RC links u _1RC (t), u _2RC (t) and u _3RC (t). The balancing of currents is carried out by adjusting the conductivity of the direct transmission G ₀ , G ₁ , G ₂ , G ₃ voltage-current converters (PNT) connected to the outputs of the differentiator. The PNT output current is proportional to the product of the code on the digital inputs and the current voltage value at the analog input. The PNT circuit can be implemented on discretely adjustable resistors or multiplying digital-to-analog converters with a current output. In the first case, the parameter G _k in each channel is equal to the conductivity of the current-setting resistor G _k = 1 / R _k , in the second it is determined by the dependence of the output current on the input values for a particular DAC circuit. Next, a circuit with adjustable resistors is considered.

At the first stage, the cubic component i _{dp 3} of the two-terminal current is balanced (1)

$$Y_0{U}_m{t}^3/t_{\text{and}}^3=U_m{t}^3/R_{13}{t}_{\text{and}}^3$$

and determine the generalized conductivity parameter Y ₀ :

. (9) $$Y_0=\frac{\mathrm{one}}{{\mathrm{<figure-callout\; id="13"\; label="R"\; filenames="00000056.png"\; state="\{\{state\}\}">R</figure-callout>}}_{13}}$$

. (9)

Then, the quadratic component of the current of the two-terminal device i _{dp 2} is compensated for by the quadratic component of the voltage pulses at the output of the first stage of the differentiator u _1RC (t) by adjusting the compensating current with the resistor R ₁₀ . From the condition of compensation of quadratic currents

$$3Y_{\mathrm{one}}{U}_m{t}^2/t_{\text{and}}^3=3\tau G_{\mathrm{one}}{U}_m{t}^2/t_{\text{and}}^3$$

find an expression for determining the conductivity parameter Y ₁ :

. (10) $$Y_{\mathrm{one}}=\frac{\mathrm{<figure-callout\; id="10"\; label="\tau \; R"\; filenames="00000056.png"\; state="\{\{state\}\}">\tau \; </figure-callout>}}{R_{}}$$

. (10)

Similarly, the linearly varying component of the MOS current i _{dp 1 is} balanced against the linear compensating current, which is formed in the circuit of the adjustable resistor R ₁₁ connected to the output of the second stage of the differentiator u _2RC (t). From the condition of compensation of the linear component of the MIS current

$$6Y_2{U}_{m}t/t_{\text{and}}^3=6{\tau }^2{U}_{m}t/R_{\mathrm{eleven}}{t}_{\text{and}}^3-6\left(\mathrm{one}+m\right){\tau }^2{U}_{m}t/R_{10}{t}_{\text{and}}^3$$

determine the conductivity parameter Y ₂ :

. (11) $$Y_2=\frac{{\tau }^2}{R_{\mathrm{eleven}}}-\frac{\left(\mathrm{one}+m\right){\tau }^2}{{\mathrm{<figure-callout\; id="10"\; label="R"\; filenames="00000056.png"\; state="\{\{state\}\}">R</figure-callout>}}_{10}}$$

. (eleven)

The process of compensating the MIS current is completed by balancing the current component i _{dp 0} with a flat top. The compensating current is set by the resistor R ₁₂ . Equilibrium occurs under the condition

, $$6Y_3{U}_m/t_{\text{and}}^3=6{\tau }^3{U}_m/R_{12}{t}_{\text{and}}^3-12\left(\mathrm{one}+m\right){\tau }^3{U}_m/R_{\mathrm{eleven}}{t}_{\text{and}}^3+6\left(\mathrm{one}+3m+m^2\right){\tau }^3{U}_m/R_{10}{t}_{\text{and}}^3$$

,

from which one can find the conductivity parameter Y ₃ :

. (12) $$Y_3=\frac{{\tau }^3}{R_{12}}-\frac{2\left(\mathrm{one}+m\right){\tau }^3}{R_{\mathrm{eleven}}}+\frac{\left(\mathrm{one}+3m+m^2\right){\tau }^3}{{\mathrm{<figure-callout\; id="10"\; label="R"\; filenames="00000056.png"\; state="\{\{state\}\}">R</figure-callout>}}_{10}}$$

. (12)

As you can see, the scheme provides separate dependent balancing. The sequence of adjustments should be as described above, namely, you should start with test pulses of the highest degree and move on to signals with a lower exponent. The balancing control of all the components of the MIS current is carried out using another three-stage differentiator on the RC links C ₁₄ -R ₁₅ C ₁₆ -R ₁₇ and C ₁₈ -R ₁₉ . The bipolar current is supplied to the first input of the current-voltage differential converter (input of the operational amplifier 2), and the compensating currents are switched using analog keys either to the second input (input of the operational amplifier 3), if the corresponding component has a plus sign, or to the summing input converter otherwise. With equal resistances of resistors 4 and 6, the voltage of the converter at the output of the operational amplifier 3 is proportional to the difference of the input currents. At the first stage of balancing, a rectangular voltage pulse is formed at the output of the third RC link C ₁₈ -R ₁₉ , the amplitude of which is proportional to the difference of cubic currents. The signal at the input of the first null indicator 20 is used to control the process of balancing cubic pulses by adjusting the resistance R _{13 of the} resistor 13. After compensating for the cubic currents, the amplitude of the rectangular pulses at the output of the third RC link takes on a zero value, and at the output of the second RC link (C ₁₆ -R ₁₇ ) a rectangular pulse is observed, the amplitude of which is proportional to the difference between the quadratic components of the MIS current and the compensating current. In the process of balancing with the help of the second zero indicator 21, the “sign” of resistance R ₁₀ and its nominal value are detected. Similarly, the balancing of the remaining components of the TIR current is carried out.

In the proposed device, the differentiators of the test pulses are built on passive circuits, and operational amplifiers are not included in the circuits with feedback elements. Therefore, there are no conditions for unstable operation. For the same reason, delays of reference signals of the same degree do not accumulate at the outputs of different stages of the differentiator, which eliminates one of the sources of current balancing errors.

 Consider an example of parameter transformations. In FIG. 2 shows an equivalent circuit of an RLC-type four-element bipolar.

The operator image of the conductivity of the two-terminal network has the form

. $$Y\left(p\right)=\frac{\mathrm{one}+p\left(R_{\mathrm{one}}+R_2\right)C_{\mathrm{one}}+p^2{L}_{\mathrm{one}}{C}_{\mathrm{one}}}{R_{\mathrm{one}}+p{R}_{\mathrm{one}}{R}_2{C}_{\mathrm{one}}+p^2{L}_{\mathrm{one}}{C}_{\mathrm{one}}}$$

.

The generalized conductivity parameters (Y-parameters) of the MIS found in accordance with formulas (2) are equal

; $$Y_1=C_1$$

; $$Y_2=-R_2{C}_1^2$$

; $$Y_3=C_1^2\left(R_2^2{C}_1-L_1\right)$$

. $$Y_0=\frac{\mathrm{one}}{R_{\mathrm{one}}}$$

; $$Y_{\mathrm{one}}=C_{\mathrm{one}}$$

; $$Y_2=-R_2{C}_{\mathrm{one}}^2$$

; $$Y_3=C_{\mathrm{one}}^2\left(R_2^2{C}_{\mathrm{one}}-L_{\mathrm{one}}\right)$$

.

In the process of balancing the currents, the resistance values of the adjustable resistors are established:

R ₁₃ = 1.6 kΩ; R ₁₀ = 3.75 kΩ; R ₁₁ = 6.6176 kΩ; R ₁₂ = 32.767 kΩ; the time constant of the RC links is τ = 15 μs. The parameter m = 0.1.

 Define the Y-parameters:

$$Y_0=\frac{\mathrm{one}}{{\mathrm{<figure-callout\; id="13"\; label="R"\; filenames="00000056.png"\; state="\{\{state\}\}">R</figure-callout>}}_{13}}=0.625m\mathrm{FROM}m$$

$$Y_{\mathrm{one}}=\frac{\mathrm{<figure-callout\; id="10"\; label="\tau \; R"\; filenames="00000056.png"\; state="\{\{state\}\}">\tau \; </figure-callout>}}{R_{}}=\frac{\mathrm{fifteen}}{3.75}=\mathrm{four}m\mathrm{FROM}m\cdot m\mathrm{to}\mathrm{from}$$

$$Y_2=\frac{{\tau }^2}{R_{\mathrm{eleven}}}-\frac{\left(\mathrm{one}+m\right){\tau }^2}{{\mathrm{<figure-callout\; id="10"\; label="R"\; filenames="00000056.png"\; state="\{\{state\}\}">R</figure-callout>}}_{10}}=\frac{225}{\mathrm{6,6176}}-\frac{\mathrm{1,1}\cdot 225}{3.75}=34-66=-32m\mathrm{FROM}m\cdot m\mathrm{to}{\mathrm{from}}^2$$

$$\begin{array}{l}{Y}_3=\frac{{\tau }^3}{R_{12}}-\frac{2\left(\mathrm{one}+m\right){\tau }^3}{R_{\mathrm{eleven}}}+\frac{\left(\mathrm{one}+3m+m^2\right){\tau }^3}{{\mathrm{<figure-callout\; id="10"\; label="R"\; filenames="00000056.png"\; state="\{\{state\}\}">R</figure-callout>}}_{10}}=\\ =\frac{3375}{\mathrm{32,767}}-\frac{2\cdot \mathrm{1,1}\cdot 3375}{\mathrm{6,6176}}+\frac{1.31\cdot 3375}{3.75}=160m\mathrm{FROM}m\cdot m\mathrm{to}{\mathrm{from}}^3\end{array}$$

At the final stage, the electrical parameters of the two-terminal components are calculated:

; $${С}_1=Y_1=4нФ$$

; $$R_2=-\frac{Y_2}{Y_1^2}=-\frac{-32}{16}=2кОм$$

; $$L_1=-\frac{Y_2^2-Y_3{Y}_1}{Y_1^3}=-\frac{{32}^2-160}{4^3}=6мГн$$

. $$R_{\mathrm{one}}=\frac{\mathrm{one}}{Y_0}=\frac{\mathrm{one}}{0.625}=\mathrm{1,6}\mathrm{to}\mathrm{ABOUT}m$$

; $${\mathrm{FROM}}_{\mathrm{one}}=Y_{\mathrm{one}}=\mathrm{four}nF$$

; $$R_2=-\frac{Y_2}{Y_{\mathrm{one}}^2}=-\frac{-32}{16}=2\mathrm{to}\mathrm{ABOUT}m$$

; $$L_{\mathrm{one}}=-\frac{Y_2^2-Y_3{Y}_{\mathrm{one}}}{Y_{\mathrm{one}}^3}=-\frac{{32}^2-160}{{\mathrm{four}}^3}=6mGn$$

.

The obtained measurement results coincide with the original data.

Claims (1)

A multi-element RLC two-terminal parameter meter containing a test voltage pulse generator having the form of a function of the nth time degree, the first (signal) output of which is connected to the first terminal for connecting the measured RLC two-pole, current-voltage differential converter, which includes two series-connected operational amplifiers, in the feedback circuit of each of them the first and second resistors are included, respectively, the output of the first operational amplifier is connected to the inverter to the input of the second operational amplifier through the third resistor, the inverting inputs of the first and second operational amplifiers form the first and second current inputs of the current-voltage converter, and the output of the second operational amplifier is the output of the converter, (n + 1) adjustable resistor, n analog switches, (n + 1) null indicator and n-cascade differentiator on differentiating RC links, the first output of the first adjustable resistor is connected to the first output of the pulse generator, the first input of the differential converter a current-voltage generator is connected to a second terminal for connecting a measured two-terminal network, one of the terminals of the first adjustable resistor is connected to the first output of the test pulse generator, and the second terminal of the first adjustable resistor is connected to the second input of the current-voltage converter, one of the terminals of the second , third, etc., ..., of the (n + 1) -th adjustable resistor is connected to the analog input of the first, second, etc., ..., of the nth analog switch, the input of the first differentiating RC link is connected to the output an ode of the current-voltage converter, the signal input of the first, second, etc., ..., of the nth null indicator is connected respectively to the output of the nth, (n – 1) of the etc., ..., the first differentiating RC link, and the signal input of the (n +1) th null indicator is connected to the output of the current-voltage converter, the first output of each analog switch is connected to the first input of the current-voltage converter, and the second output of each analog the switch is connected to the second input of the current-voltage converter, the output of the switching signal of the second, third o, etc., ..., the (n + 1) -th null indicator is connected respectively to the input of the switching signal of the first, second, etc., ..., of the n-th analog switch, the digital output of the resistance control of the first, second and etc., ..., the (n + 1) th null indicator is connected to the digital input of the first, second, etc., ..., (n + 1) th null indicators, the synchronization signal inputs of all null indicators connected to the second output of the generator of test pulses, characterized in that it additionally introduced a second differentiator containing n connected in series differentiating RC links, and n voltage repeaters, the input of the first differentiating RC link of the second differentiator is connected to the first output of the test pulse generator, the inputs of the voltage repeaters are connected to the outputs of the corresponding differentiating RC links of the second differentiator, to the output of the first, second, etc. ., ..., of the nth voltage follower, the free output of the second, third, etc., ..., (n + 1) -th adjustable resistor is connected, and all the differentiating RC-links of the second differentiator have equal time constants change RC, but different values of resistor resistance and capacitor capacitance: the resistor resistance in the kth RC link is greater than in the (k – 1) th RC link, and the capacitor capacitance in the kth RC link is as many times less than in the (k – 1) th RC link.

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