JP2007051905A - Auto-balance circuit for measuring impedance - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To quickly and accurately attain a balanced state by specified algorithm. <P>SOLUTION: This auto-balance circuit is provided with the first and second oscillators 101, 106 for applying sine waves of the same frequency to a measured sample 102. In the circuit, three different phase angles θx, θy, θz are sequentially set, for example, to the second oscillator 106, from a CPU 109, the optimum phase angle θmin of bringing the balanced state is found on the basis of voltages Vx, Vy, Vz in an L-terminal point measured at the respective phase angles, constants α, β are found using the expression V<SB>L</SB><SP>2</SP>=α+βcosäγ-(θa or θb)} (α, β, γ are constants) as an amplitude value in the L-terminal point, based on the voltages Vx, Vy, Vz and the optimum phase angle θmin, and the optimum amplitude Bmin of bringing the balanced state is obtained on the basis of the calculated constants α, β. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to an automatic balance circuit for impedance measurement applied to an LCR meter, an impedance analyzer, and the like. More specifically, the balanced state is reliably obtained even in a high frequency band, and the impedance and phase angle of a sample to be measured can be reduced in a short time. The present invention relates to a technique that enables measurement with high accuracy.

  First, a basic configuration of an automatic balancing circuit used in an impedance measuring instrument such as an LCR meter or an impedance analyzer is shown in FIG. 3 and will be described. The automatic balancing circuit 300 is connected to an oscillator 301 for applying a sine wave signal having a predetermined frequency from the H terminal on the signal input side to the sample 304 to be measured, and to the other terminal side of the sample 304 to be measured via the L terminal. And a signal detection unit. The H terminal is a contact portion of the source side probe pin, and the L terminal is a contact portion of the sense side probe pin.

  In this case, the signal detection unit has an operational amplifier 306 as a current-voltage converter, the detection signal from the L terminal is input to the (−) input terminal side, and the (+) input terminal is grounded. A detection resistor 305 is connected to a feedback system between the output terminal and the (−) input terminal of the operational amplifier 306.

  When the gain of the operational amplifier 306 is sufficiently large, the voltage at the L terminal becomes 0 V (equilibrium) due to an imaginary short, so that the amplitude of the oscillator 301 is A, the phase angle is θa, and the operational amplifier 306 outputs the voltage. Assuming that the amplitude of the output signal is B, the phase angle is θb, the impedance of the detection resistor 305 is Zf, and the phase angle is θf, the impedance Zm and the phase angle θm of the sample 304 to be measured are obtained by the following equations.

Zm = Zf × A / B
θm = θf + θa−θb−180 °

  Although the automatic balancing circuit 300 has a simple configuration, when the frequency of the measurement sine wave signal supplied from the oscillator 301 to the sample 304 to be measured is increased, the gain of the operational amplifier 306 is decreased, so that an imaginary short circuit is not established. A voltage is generated at the L terminal. As a result, a current flows through the input capacitance C existing between the L terminal and the ground (GND), resulting in a measurement error.

  In order to maintain the L terminal at 0 V up to the high frequency band, an automatic balance loop called a null loop method has been proposed. FIG. 4 shows a circuit configuration in which the null loop method is adopted for the automatic balance circuit of FIG.

  In this null loop method, the current of the sample 302 to be measured flowing into the L terminal is converted and amplified to a voltage by a null detection circuit 401 composed of an inverting operational amplifier, and input to the subsequent multipliers 402 and 403. One multiplier 402 is supplied with the sine wave signal of the oscillator 301 as a reference signal, and the other multiplier 403 is supplied with the sine wave signal of the oscillator 301 through the 90 ° phase shifter 404 as a cosine wave signal. Thus, vector detection is performed.

  Subsequently, the outputs of the multipliers 402 and 403 are integrated and smoothed by the integrating circuits 405 and 406, respectively. The smoothed vector detection signal is supplied to multipliers 407 and 408. In one multiplier 407, the sine wave component vector-detected by the multiplier 402 is multiplied by the sine wave signal from the oscillator 301, and in the other multiplier 408, the cosine wave component vector-detected by the multiplier 403 is multiplied by 90. The cosine wave signal from the phase shifter 404 is multiplied.

  These multiplication results are added by the adder 409 and fed back to the null detection circuit 401 via the detection resistor 305. According to this null loop method, the current fed back to the null detection circuit 401 via the detection resistor 305 has the same value as the current flowing through the sample to be measured. That is, since the feedback current by the detection resistor 305 changes so that the voltage output from the null detection circuit 401 is always 0 V, an automatic balancing loop is configured.

  According to the null loop method, even when the frequency of the measurement sine wave is high, it is possible to maintain the voltage at the L terminal at 0 V. Therefore, the influence of the input capacitance existing between the L terminal and the ground (GND) can be reduced. Although accurate impedance measurement can be performed without receiving it, the following problems have been pointed out.

  That is, many circuit parts are required, the configuration is complicated, the apparatus becomes large, and the cost must be increased. In addition, the circuit tends to become unstable because it is balanced in an analog manner. Furthermore, it is difficult to obtain a complete equilibrium state due to the DC offset of the multiplier and integrator for synchronous detection.

  In order to solve this point, the present applicant has disclosed, for example, Patent Document 1 as an impedance measurement in which the circuit configuration is simple, the operation is stable, and an equilibrium state can be easily obtained by digital control. An automatic balancing circuit has been proposed.

  According to this, it is provided with two oscillators (a first oscillator on the H terminal side and a second oscillator on the L terminal side) that apply a sine wave signal of the same frequency to the sample to be measured, and one of the oscillators, For example, the balanced phase angle can be obtained by setting three different phase angles in the second oscillator, and the balanced amplitude value can be obtained by setting two different amplitude values under the balanced phase angle. .

JP 2003-279607 A

  However, in the invention described in Patent Document 1, it is necessary to change, for example, the setting of the second oscillator as follows in order to obtain the equilibrium condition. Referring to the flowchart of FIG. 5 of Patent Document 1, first, for example, 90 °, 180 °, and 270 ° are set as three different phase angles θx, θy, and θz in the second oscillator (DDS2) (step ST21). ~ ST23). Next, the amplitude Ba and the phase angle θmin1 are set in the second oscillator (step ST26). Thereafter, the amplitude Bb and the phase angle θmax are set in the second oscillator.

As described above, in the invention described in Patent Document 1, it is necessary to change the setting of the second oscillator five times in order to obtain the equilibrium condition, and accordingly, the measurement takes time. Depending on the voltage measured in step ST26, it is necessary to set the amplitude Ba and the phase angle θmin2 in the second oscillator (step ST28b), and the time is further prolonged.
As

  Therefore, an object of the present invention is to reduce the number of times the oscillator is set so that the equilibrium condition can be obtained more quickly and accurately.

In order to solve the above problems, the present invention provides a first oscillator that applies a sine wave signal having a predetermined frequency to one H terminal of a sample to be measured, and a predetermined detection element to the other L terminal of the sample to be measured. A second oscillator for outputting a sine wave signal having the same frequency as the sine wave signal of the first oscillator, a voltage detector for detecting the voltage on the L terminal side of the sample to be measured, and the detected voltage as digital voltage data. An A / D converter for conversion, and control means for controlling the amplitude and phase angle of the first oscillator or the second oscillator based on the voltage data, and the control means controls the L terminal side of the sample to be measured. From the amplitude A and phase angle θa of the first oscillator, the amplitude B and phase angle θb of the second oscillator, the impedance Zf of the detection resistor, and the phase angle θf, Serial The automatic balancing circuit for impedance measurement to calculate the sample to be measured impedance Zm and phase angle .theta.m,
The control means is for either one of the first oscillator and the second oscillator.
In a state where the amplitude is an arbitrary amplitude value, arbitrary three different phase angles θx, θy, θz are sequentially set, and the voltage Vx, which appears on the other terminal side of the measured sample for each phase angle. A first step of measuring Vy, Vz;
From the phase angles θx, θy, θz and the voltages Vx, Vy, Vz, the phase angle θmin1, as the first establishment factor candidate of the equilibrium state based on the following equations (1-1), (1-2): a second step of calculating θmin2 and setting either one of the phase angles to the optimum phase angle θmin for achieving the equilibrium state;
The voltage amplitude value at the L terminal point is V _L ² = α + βcos {γ− (θa or θb)} (α, β, γ are constants), and the above equation is obtained from the voltages Vx, Vy, Vz and the optimum phase angle θmin. After calculating the constants α and β, the amplitudes Bmin1 and Bmin2 as the second establishment factor candidates in the equilibrium state are obtained by the following formulas (2-1) and (2-2), and either one of the amplitudes is calculated. The third step of setting the optimum amplitude Bmin to be in the equilibrium state is performed.

  In the present invention, in the second step, when the phase angle at which the measured voltages Vx, Vy, Vz have the minimum value among the phase angles θx, θy, θz is θL, and | θmin1-θL | <90 ° The phase angle θmin1 is set to the optimum phase angle θmin to be in the equilibrium state, and in other cases, the phase angle θmin2 is set to the optimum phase angle θmin.

  In the third step, A · Zf <B · Zm (A is the amplitude of the first oscillator, B is the amplitude of the second oscillator, Zf is the impedance of the detection resistor, and Zm is the impedance of the sample to be measured) If it is known that A · Zf> B · Zm, the optimum amplitude Bmin to be in the equilibrium state is set to the optimum amplitude Bmin to be in the equilibrium state. An amplitude Bmin1 is employed.

  When the magnitude relationship between A · Zf and B · Zm is unknown, after the third step, as the fourth step, either the first oscillator or the second oscillator has the optimum phase angle θmin and the amplitude. Bmin1 is set and the voltage Vmin at the L terminal point is measured. When the voltage Vmin is 0 V (equilibrium state), the amplitude Bmin1 is set to the optimum amplitude Bmin, and otherwise, the amplitude A Let Bmin2 be the optimum amplitude Bmin.

  According to the present invention, when determining the equilibrium condition, when the magnitude relationship of A · Zf <B · Zm or A · Zf> B · Zm is known in advance, a sine wave of the same frequency with respect to the sample to be measured. Of the two oscillators to which signals are applied (the first oscillator on the H terminal side and the second oscillator on the L terminal side), for example, three different phase angles may be set on the second oscillator side.

  That is, the amplitude A of the first oscillator, the amplitude B of the second oscillator, and the impedance Zf of the detection resistor so that the magnitude relationship of A · Zf <B · Zm or A · Zf> B · Zm is established within the measurable range. By selecting this value, the set number of times for the second oscillator can be reduced to three.

  Further, even when the magnitude relationship between A · Zf and B · Zm is unknown, the optimum phase angle θmin and the amplitude Bmin1 may be additionally set in the second oscillator as the fourth step. The set number of times can be limited to four.

  Next, an embodiment of the present invention will be described with reference to FIGS. 1 and 2, but the present invention is not limited to this.

  As shown in the block diagram of FIG. 1, the automatic balancing circuit 100 includes two oscillators, a first oscillator 101 and a second oscillator 106, and an H terminal point on the first oscillator 101 side (a source terminal point on the signal application side). ) And the L terminal point on the second oscillator 106 side (sense terminal point on the current detection side), the measured sample 102 is mounted.

  A sine wave signal having a predetermined frequency is supplied from the first oscillator 101 to the sample 102 as a measurement signal. The second oscillator 106 also outputs a sine wave signal having the same frequency as the measurement sine wave signal, and a detection resistor 105 as a detection element is connected between the second oscillator 106 and the L terminal point. Is done. In place of the detection resistor 105, a capacitor (C) or a coil (L) may be used on condition that the impedance is accurately known.

  The automatic balancing circuit 100 includes a voltage detector (NULL detector) 107 that detects the voltage at the L terminal point, an A / D converter 108 that converts the detected voltage into a digital signal, and an A / D converter. A CPU 109 is provided as a control means for controlling the amplitude and the phase angle of the second oscillator 106 based on the detected voltage data from 108 and calculating the impedance and the phase angle of the sample 102 to be measured.

  According to the present invention, the CPU 109 sequentially sets three different phase angles θx, θy, θz with the amplitude set to an arbitrary amplitude, for example, the second oscillator 106 of the two oscillators. By measuring the voltages Vx, Vy and Vz appearing on the L terminal point side of the sample to be measured 102 for each phase angle, the phase angle θmin1, calculated by the following equations (1-1) and (1-2) Any one of θmin2 can be set as the equilibrium phase angle θmin as the first establishment factor of the equilibrium state. The equilibrium state means a state where the L terminal is at the minimum voltage (preferably 0 V).

  Here, the derivation process of the above equations will be briefly described. The amplitude of the first oscillator 101 is A, the phase angle is θa, the amplitude of the second oscillator 106 is B, the phase angle is θb, the impedance of the detection resistor 105 is Zf, the phase angle is θf, and the input is generated at the L terminal. The impedance of the capacitor C is Zi, its phase angle is θi, the impedance of the sample 102 to be measured is Zm, and its phase angle is θm. The frequencies of the first oscillator 101 and the second oscillator 106 are the same and are ω.

Assuming that the voltage at the L terminal point is V _{L and} the sum of the currents flowing into the L terminal point is 0 according to Kirchhoff's law, the following equation (3) is established.

ただし、式（４）中のＹｔは次式（６）で表される。

When this expression (3) is developed, the amplitude of the voltage V _{L at} the L terminal point is expressed by the following expression (4), and the phase is expressed by the following expression (5).

However, Yt in Formula (4) is represented by following Formula (6).

In the equilibrium state, the voltage V _L at the L terminal is 0 V (minimum). In order to obtain the balanced phase angle θmin, three different phase angles are sequentially set in the second oscillator 106, the voltage V _L at each L terminal point is measured, and the above equations (1-1), (1- 2), two phase angles θmin1 and θmin2 as equilibrium phase angle candidates are calculated, but three different phase angles are set to 90 in order to facilitate the calculations in the above equations (1-1) and (1-2). °, 180 °, and 270 °.

When the phase is 90 °, the voltage measured at the L terminal point is V ₉₀ , when the phase is 180 °, the voltage measured at the L terminal point is V ₁₈₀ , and when the phase is 270 °, the L terminal If the voltage measured at the point and _{V 270,} the equation (1-1), (1-2) from, one of the phase angle θmin1 is expressed by the following equation (7), the other phase angle θmin2 the following formula It is represented by (8).

The basis of these formulas (7) and (8) will be described. Since the amplitude of the L terminal point is the above equation (4), when this is squared, the following equation (9) is obtained.

この式（１０）において、α，β，γは次式（１０−１），（１０−２），（１０−３）である。

In Expression (9), since the variable is only the phase angle θb of the second oscillator 106, Expression (9) is replaced with the following Expression (10) with α, β, and γ as constants.

In this equation (10), α, β, and γ are the following equations (10-1), (10-2), and (10-3).

第２発振器１０６の位相を１８０゜に設定し、そのときの電圧をＶ_１８０とすると、同じく式（１０）より、

第２発振器１０６の位相を２７０゜に設定し、そのときの電圧をＶ_２７０とすると、同じく式（１０）より、

As described above, when the phase of the second oscillator 106 is set to 90 ° and the voltage at that time is set to V ₉₀ , from the equation (10),

Assuming that the phase of the second oscillator 106 is set to 180 ° and the voltage at that time is V ₁₈₀ , the following equation (10)

The phase of the second oscillator 106 is set 270 °, when the voltage at that time and _{V 270,} also from the equation (10),

上記式（１１−２），（１２）より、

上記式（１１−１），（１２）より、

From the above formulas (11-1) and (11-3),

From the above formulas (11-2) and (12),

From the above formulas (11-1) and (12),

From the above equations (13) and (14),

Since cos (γ−θb) = − 1 in the above formula (10) in the equilibrium state,
γ−θmin = 180 (16)
Holds. Accordingly, the balanced phase θmin is θmin = γ−180, and the following equation (17) is obtained from the above equations (15) and (16).

  The phase angle θmin calculated by the above algorithm is assumed to be within a range of ± 90 ° (90 ° to 270 °) assuming that the object to be measured is a capacitor, resistor, coil, etc. The phase angle θmin may be outside the range of ± 90 ° due to a phase error caused by an operational amplifier or a filter used or the phase angle θf of the detection resistor 105.

  For example, when measuring a capacitor, the phase angle θm of the sample 102 to be measured is −90 °, but assuming that the phase angle θf of the detection resistor 105 is 20 °, θmin = 290 ° (−70 °). It becomes.

Therefore, when the phase angle θmin is within a range of ± 180 °, the above equation (15) becomes the following equation (18).

  Accordingly, from the above equations (16) and (18), two solutions (θmin1 and θmin2) represented by the above equations (7) and (8) are derived as the balanced phase θmin. Then, one of them is set as the optimum phase angle θmin.

That is, among the voltages V ₉₀ , V ₁₈₀ , and V ₂₇₀ measured when the phase angle of the second oscillator 106 is set to 90 °, 180 °, and 270 ° as described above, the phase angle indicating the minimum value is set. As θL, when | θmin1−θL | <90 °, one phase angle θmin1 represented by the above formula (7) is set as the optimum phase angle θmin to be in an equilibrium state, and otherwise, the optimum phase angle θmin1 is set. The other phase angle θmin2 expressed by the above equation (8) is set as the angle θmin.

Next, how to determine the equilibrium amplitude Bmin will be described. For this purpose, the coefficients α, β and γ are calculated from the values of the measurement voltages V ₉₀ , V ₁₈₀ and V ₂₇₀ and the optimum phase angle θmin. Α is expressed by the above equation (12).
α = (V ₉₀ ² + V ₂₇₀ ² ) / 2 (19)
β is obtained by the above equations (14) and (13).
β = | (V ₉₀ ² −V ₂₇₀ ² ) / 2sin γ | (20a)
β = | {(V ₉₀ ² + V ₂₇₀ ² ) / 2−V ₁₈₀ ² } / cos γ | (20b)
γ is expressed by the above equation (16),
γ = θmin + 180 (21)
As required. For β, the above equation (20b) is used when γ = 0 ° and 180 °, and the above equation (20a) is used otherwise.

Here, assuming that the maximum voltage of the voltage V _L at the L terminal point is Vmax and the minimum voltage is Vmin, Vmax is expressed by the following equation (22), and Vmin is expressed by the following equations (23a) and (23b). .

  Since Vmin ≧ 0, when A · Zf> B · Zm, the above equation (23a) is used, the equilibrium amplitude obtained at this time is Bmin1, and the impedance of the sample 102 to be measured is Zm1. Further, in the case of A · Zf <B · Zm, the equation (23b) is used, the equilibrium amplitude obtained at this time is Bmin2, and the impedance of the sample 102 to be measured is Zm2.

In the case of A · Zf> B · Zm, the following equation (24) is established from the above equations (22) and (23a), and the following equations (24-1), (24-2) and The impedance Zm1 of the sample 102 to be measured is obtained by the following equation (25).

この式（２６）は、上記式（２−１）に書き直すことができる。 In the equilibrium state, A · Zf = Bmin1 · Zm1, and therefore, the equilibrium amplitude Bmin1 at this time is calculated by the following equation (26).

This equation (26) can be rewritten into the above equation (2-1).

Next, in the case of A · Zf <B · Zm, the following equation (27) is established from the above equations (22) and (23b), and the following equations (27-1) and (27− 2), the impedance Zm2 of the sample 102 to be measured is obtained by the following equation (28).

この式（２９）は、上記式（２−２）に書き直すことができる。 In the equilibrium state, A · Zf = Bmin2 · Zm2, so the equilibrium amplitude Bmin2 at this time is calculated by the following equation (29).

This equation (29) can be rewritten into the above equation (2-2).

  Thus, according to the present invention, if it is known in advance whether A · Zf> B · Zm or A · Zf <B · Zm, that is, within a measurable range, A · Zf <B By selecting the values of the amplitude A of the first oscillator, the amplitude B of the second oscillator, and the impedance Zf of the detection resistor so that the magnitude relationship of Zm or A · Zf> B · Zm is established, the balanced amplitudes Bmin1, Bmin2 Can be set to the optimum balanced amplitude Bmin.

  Therefore, by substituting the values of α and β calculated by the above formula (19) and the above formula (20a) or (20b) into the above formulas (2-1) and (2-2), the balanced amplitude Bmin1 , Bmin2 can be calculated.

  When it is not certain whether A · Zf> B · Zm or A · Zf <B · Zm, the phase of the second oscillator 106 is set to the balanced phase θmin obtained as described above, and the amplitude is set as described above. One of the obtained amplitudes Bmin1 is set, and the voltage Vmin at the L terminal point is measured.

  As a result, if the voltage Vmin at the L terminal point is 0 V (equilibrium state), it is assumed that the amplitude Bmin1 is the optimum balanced amplitude Bmin and the impedance of the sample 102 to be measured is Zm1. Otherwise, it is assumed that the amplitude Bmin2 is the optimum equilibrium amplitude Bmin and the impedance of the sample 102 to be measured is Zm2. FIG. 2 shows a schematic operation flowchart of the present invention as a summary.

After selecting the optimal equilibrium phase angle θmin and the optimal equilibrium amplitude Bmin as described above, finally,
Zm = Zf × A / B
Substitute Bmin for B, and
Substituting θmin into θb of θm = θf + θa−θb−180 °, the impedance Zm and the phase θm of the sample 102 to be measured are respectively calculated.

  According to the present invention, the circuit configuration is simple and the apparatus can be reduced in size and cost as compared with the analog-balanced automatic balancing bridge described with reference to FIG. The circuit is stable. In the case of the conventional automatic balancing bridge, it is extremely difficult to detect the phase at a high frequency, but there is an advantage that it is not necessary to detect the phase according to the algorithm of the present invention.

  Further, according to the present invention, when the equilibrium condition is obtained, if the magnitude relationship of A · Zf <B · Zm or A · Zf> B · Zm is known in advance, the same frequency with respect to the sample to be measured is obtained. Of the two oscillators to which the sine wave signal is applied (the first oscillator on the H terminal side and the second oscillator on the L terminal side), for example, three different phase angles may be set on the second oscillator side.

  That is, the amplitude A of the first oscillator, the amplitude B of the second oscillator, and the impedance Zf of the detection resistor so that the magnitude relationship of A · Zf <B · Zm or A · Zf> B · Zm is established within the measurable range. By selecting this value, the set number of times for the second oscillator can be completed three times (steps ST21 to ST23 in the operation flowchart of FIG. 2).

  Even when the magnitude relationship between A · Zf and B · Zm is unknown, the optimum phase angle θmin and the amplitude Bmin1 may be additionally set in the second oscillator (step ST26 in the operation flowchart of FIG. 2). Even in this case, the set number of times for the second oscillator can be reduced to four.

  In the above embodiment, the amplitude and phase of the second oscillator 106 are manipulated. However, the amplitude and phase of the second oscillator 106 are fixed, and the amplitude and phase of the first oscillator 101 are manipulated. May be.

1 is a schematic block diagram of an automatic balancing circuit for impedance measurement according to the present invention. The operation | movement flowchart of this invention. The block diagram which shows the 1st prior art example of the automatic balance circuit for impedance measurements. The block diagram which shows the 2nd prior art example of the automatic balance circuit for impedance measurements.

Explanation of symbols

DESCRIPTION OF SYMBOLS 100 Automatic balance circuit 101 1st oscillator 102 Sample to be measured 105 Detection element 106 2nd oscillator 107 Voltage detector 108 A / D converter 109 CPU

Claims (4)

A first oscillator that applies a sine wave signal of a predetermined frequency to one H terminal of the sample to be measured, and the same as the sine wave signal of the first oscillator via a predetermined detection element to the other L terminal of the sample to be measured. A second oscillator that outputs a sine wave signal of a frequency, a voltage detector that detects a voltage on the L terminal side of the sample to be measured, an A / D converter that converts the detected voltage into digital voltage data, and the voltage Control means for controlling the amplitude and phase angle of the first oscillator or the second oscillator based on the data, and under the equilibrium state where the voltage on the L terminal side of the sample to be measured is the minimum voltage by the control means. From the amplitude A and phase angle θa of the first oscillator, the amplitude B and phase angle θb of the second oscillator, the impedance Zf and phase angle θf of the detection resistor, the impedance Zm of the sample to be measured In impedance measurement auto-balancing circuit for calculating a phase angle θm and,
The control means is for either one of the first oscillator and the second oscillator.
In a state where the amplitude is an arbitrary amplitude value, arbitrary three different phase angles θx, θy, θz are sequentially set, and the voltage Vx, which appears on the other terminal side of the measured sample for each phase angle. A first step of measuring Vy, Vz;
From the phase angles θx, θy, θz and the voltages Vx, Vy, Vz, the phase angle θmin1, as the first establishment factor candidate of the equilibrium state based on the following equations (1-1), (1-2): a second step of calculating θmin2 and setting either one of the phase angles to the optimum phase angle θmin for achieving the equilibrium state;
The voltage amplitude value at the L terminal point is V _L ² = α + βcos {γ− (θa or θb)} (α, β, γ are constants), and the above equation is obtained from the voltages Vx, Vy, Vz and the optimum phase angle θmin. After calculating the constants α and β, the amplitudes Bmin1 and Bmin2 as the second establishment factor candidates in the equilibrium state are obtained by the following formulas (2-1) and (2-2), and either one of the amplitudes is calculated. And a third step of setting the optimum amplitude Bmin to be in the balanced state.

  In the second step, when the phase angle at which the measured voltages Vx, Vy, Vz show the minimum value among the phase angles θx, θy, θz is θL, and | θmin1-θL | <90 °, the equilibrium state 2. The automatic impedance measurement impedance measurement device according to claim 1, wherein the phase angle θmin1 is set to the optimum phase angle θmin, and the phase angle θmin2 is set to the optimum phase angle θmin otherwise. Balanced circuit.   In the third step, A · Zf <B · Zm (A is the amplitude of the first oscillator, B is the amplitude of the second oscillator, Zf is the impedance of the detection resistor, and Zm is the impedance of the sample to be measured) When it is known that the amplitude Bmin2 is adopted as the optimum amplitude Bmin to be in the equilibrium state, and when A · Zf> B · Zm is known, the amplitude Bmin1 is set to the optimum amplitude Bmin to be in the equilibrium state. The automatic balancing circuit for impedance measurement according to claim 1 or 2, wherein:   After the third step, as the fourth step, the optimum phase angle θmin and the amplitude Bmin1 are set in either the first oscillator or the second oscillator, and the voltage Vmin at the L terminal point is measured. 2. When the voltage Vmin is 0 V (equilibrium state), the amplitude Bmin1 is set as the optimum amplitude Bmin; otherwise, the amplitude Bmin2 is set as the optimum amplitude Bmin. Or the automatic balance circuit for impedance measurement of 2.

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