WO2022153490A1 - Dielectric constant measurement method - Google Patents

Abstract

One embodiment of the present invention is a dielectric constant measurement method having: a step for performing calibration; a step for calculating a theoretical error component of an admittance yi, with respect to the actual value of the admittance yi; a step for measuring, with a measurement device, the dielectric constant of a substance being measured; a step for calculating, on the basis of the measurement result for the dielectric constant of the substance being measured, the actual value of the admittance ym of the end surface of a probe of the measurement device; a step for correcting the actual value of the admittance ym of the end surface of the probe by using the error component; and a step for calculating the dielectric constant of the substance being measured by substituting the corrected actual value of the admittance ym for the theoretical value of admittance ym in a model formula that expresses the relationship between the theoretical admittance ym and the dielectric constant of the substance being measured.

Description

Permittivity measurement method

The present invention relates to a method for measuring a dielectric constant.

Aging is progressing, and dealing with adult diseases has become a major issue. Testing such as blood glucose level is a heavy burden on the patient because it requires blood sampling. Therefore, a non-invasive component concentration measuring device that does not collect blood is drawing attention.

As a non-invasive component concentration measuring device, electromagnetic waves in the microwave-millimeter wave band are less scattered in the living body than optical methods such as near-infrared light, and the energy of one photon is low. A method using is proposed.

For example, there is a method using the resonance structure shown in Non-Patent Document 1. In this method, a device having a high Q value such as an antenna or a resonator is brought into contact with the measurement sample, and the frequency characteristics around the resonance frequency are measured. Since the resonance frequency is determined by the complex permittivity around the device, the component concentration is estimated from the shift amount of the resonance frequency by predicting the correlation between the shift amount of the resonance frequency and the component concentration in advance.

As another method using electromagnetic waves in the microwave-millimeter wave band, the dielectric spectroscopy shown in Patent Document 1 has been proposed. In dielectric spectroscopy, an electromagnetic wave is irradiated into the skin, the electromagnetic wave is absorbed according to the interaction between a blood component to be measured, for example, a glucose molecule and water, and the amplitude and phase of the electromagnetic wave are observed. The dielectric relaxation spectrum is calculated from the amplitude and phase of the observed electromagnetic wave with respect to the frequency. The dielectric relaxation spectrum is generally expressed as a linear combination of relaxation curves based on the Core-Cole equation, and the complex permittivity is calculated. In the measurement of biological components, for example, the complex permittivity has a correlation with the amount of blood components such as glucose and cholesterol contained in blood, and is measured as an electric signal (amplitude, phase) corresponding to the change. A calibration model is constructed by measuring the correlation between the change in the complex permittivity and the component concentration in advance, and the component concentration is calibrated from the measured change in the dielectric relaxation spectrum. Regardless of which method is used, it is important to measure the change in permittivity in advance by wideband dielectric spectroscopy because the measurement sensitivity can be expected to improve by selecting a frequency band that has a strong correlation with the target component. Is.

Among the dielectric spectroscopy, the method using a coaxial probe (Open-end coaxial probe or Open-end coaxial line) as shown in Non-Patent Documents 2 and 3 is a sample in which water or the like is easily available for calibrating the measuring instrument. In addition, since it is possible to measure the dielectric constant of the measurement sample by bringing the sample to be measured into contact with the probe end face without the need for special processing of the material, it is possible to measure living organisms, fruits, soil, etc. It is suitable for measuring samples for which electrical characteristics are to be evaluated while avoiding processing.

Japanese Unexamined Patent Publication No. 2013-32933

M. Hofmann, G. Fischer, R. Weigel, and D. Kissinger, “Microwave-Based Noninvasive Concentration Measurements for Biomedical Applications”, IEEE Trans. Microwave Theory and Techniques, Vol.61, No.5, pp.219 , 2013 JP Grant, R N. Clarke, G T. SYymm and N M. Spyrou, “A critical study of the open-ended coaxial line sensor techniques for RF and microwave complex permittivity measurements”, J. Physci. Instrum, Vol.22, pp. 757-770, 1989 T.P. Marsland, and S. Evans “Dielectric measurements with an open-ended coaxial probe”, IEE Proceedings, Vol. 134, No. 4, 1987

However, measurement using a conventional coaxial probe is based on the premise that the substance to be measured has a sufficient thickness, and for thin-layer samples and multilayer materials, the thickness of the material and the dielectric constant of a part of the material are known. Otherwise, there is a problem that the dielectric constant of the layered material cannot be measured.

In view of the above circumstances, it is an object of the present invention to provide a method for measuring the dielectric constant capable of accurately measuring the dielectric constant of a MUT having an arbitrary shape.

The uniformity according to the present invention is the step of calibrating the measuring device using the standard sample and the measured value of the admittance _yi of the probe end face of the measuring device calculated based on the measurement result of the dielectric constant of the standard sample. And the theoretical value of the admitance y _i of the probe end face when the object to be measured is the standard sample, and the error component of the theoretical value of the admitance y _i with respect to the measured value of the admitance y _i is calculated. A step of measuring the dielectric constant of the substance to be measured with the measuring device, and a step of calculating the measured value of the admittance _ym of the probe end face of the measuring device based on the measurement result of the dielectric constant of the substance to be measured. The step of correcting the measured value of the admittance _ym of the probe end face using the error component, and the model formula expressing the relationship between the theoretical value of the admittance _ym and the dielectric constant of the substance to be measured are described above. This is a method for measuring the dielectric constant, which comprises a step of calculating the dielectric constant of the substance to be measured by substituting the measured value of the admittance _ym corrected as the theoretical value of the admittance _ym .

According to the present invention, it is possible to provide a method for measuring the dielectric constant capable of accurately measuring the dielectric constant of a MUT having an arbitrary shape.

It is a schematic diagram of the measuring method of the dielectric constant of this embodiment. It is a schematic diagram between a measuring device and a coaxial probe. It is a flowchart of the measuring method of the dielectric constant of this embodiment. It is a schematic diagram of the equivalent circuit of the coaxial probe end face of the dielectric constant measurement method of this embodiment. It is a schematic diagram of the equivalent circuit of the antenna admittance of the dielectric constant measurement method of this embodiment. It is a graph which shows the difference of admittance between a model formula and the measured value. It is a graph which shows the comparison between the model formula of the conventional method and this embodiment, and the measured value. It is the flowchart of the dielectric constant measurement method of the conventional method, and the schematic diagram of the equivalent circuit of the coaxial probe end face.

In the dielectric constant analysis method according to the present embodiment, the admittance of the probe end face is calculated using the interface between the coaxial probe and the substance to be measured as the calibration end face using three types of calibration standards as in the conventional coaxial method. It is represented by an equivalent circuit model consisting of capacitance and radiation admittance. The parasitic element component is identified in advance using the measurement result of the calibration standard, and the admittance using the parasitic element component is corrected so that the admittance is equivalent to the analytical formula. Perform an inverse problem analysis on the admittance measurements corrected using the admittance model formula for any single or layered material.

With the above configuration, it is possible to measure the complex permittivity in consideration of the material shape and the influence of the radiated electromagnetic field. Furthermore, it can be expected that the complex permittivity of the MUT can be measured accurately even when measuring a layered material or when measuring a high frequency band such as a millimeter wave or a THz wave.

The dielectric constant analysis method according to the embodiment of the present invention has the following steps. (Step a) Calibrate the measuring device with a standard sample. (Step b) The measured value of the admittance yi of the probe end face of the measuring device calculated based on the measurement result of the dielectric constant of the standard sample, and the theoretical value of the admittance yi of the probe end face when the object to be measured is the standard sample. And, are used to calculate the error component of the theoretical value of admittance yi with respect to the measured value of admittance yi. (Step c) The dielectric constant of the substance to be measured is measured with a measuring device. (Step d) The measured value of the admittance ym of the probe end face of the measuring instrument is calculated based on the measurement result of the dielectric constant of the substance to be measured. (Step e) The measured value of the admittance ym of the probe end face is corrected by using the error component. (Step f) Substituting the measured value of admittance ym corrected as the theoretical value of admittance ym into a model formula expressing the relationship between the theoretical value of admittance ym and the permittivity of the substance to be measured, the dielectric constant of the substance to be measured. Calculate the rate.

FIG. 1 shows a schematic diagram of the dielectric constant measuring method according to the present embodiment. As shown in FIG. 1, the measuring instruments include a display that displays the calculation result of the permittivity, a calculator that calculates the permittivity from the measurement results obtained by the measuring instrument, and a measuring instrument for measuring high frequency characteristics. And a coaxial probe which is an interface for contacting the MUT. The display may be, for example, a display such as a measuring instrument or a PC. The arithmetic unit may be a device capable of digital data processing such as a PC and a microcomputer. As the measuring instrument, for example, a device capable of measuring high-frequency S-parameters and impedance such as a vector network analyzer or an impedance analyzer, or an IC chip capable of measuring its reflection characteristics by transmitting and receiving high frequencies may be used. In the method for measuring the dielectric constant according to the present embodiment, a known measuring device may be used.

(A) and (b) of FIG. 2 show a schematic diagram when a general-purpose measuring instrument is used as a measuring instrument and when an IC for measurement is used. The measuring instrument and the coaxial probe are connected using a high-frequency cable, a transmission line formed on a high-frequency substrate, and a high-frequency connector. A coaxial line may be used for the high-frequency cable, and a microstrip line, a coplanar line, a coplanar strip, or the like may be used for the transmission line. As the high frequency connector, a coaxial type connector such as SMA, SMK, SMV, 1 mm connector, a push-on type connector such as SMP, SMPM, or the like may be used.

FIG. 8 is a flowchart of a method for measuring the dielectric constant in the conventional method. When measuring the admittance of MUT, calibration is generally performed to eliminate the influence of high frequency characteristics such as cables and connectors. At that time, by using the coaxial type calibration standard, the calibration end face becomes the AA'plane in FIG. At this time, the relationship between the linear mapping between the reflectance coefficient ρ and admittance y when air, metal (metal for shorting), water and MUT used as standard samples is installed is expressed by the following equations (1) and (2). expressed.

　非特許文献３に記載の通り、誘電率εの媒質のアンテナの放射アドミタンスＧには（４）式の関係がある。（３）式及び（４）式により、（２）式の右辺の第２項のＧ_０とεの２．５乗に比例関係が導かれる。

At this time, the subscripts 1 to 3 correspond to the standard sample, and m corresponds to the MUT. Further, the equivalent circuit of admittance on the end face of the coaxial probe, that is, the BB'plane of FIG. 2 is represented by FIG. 8 (b-2). At this time, C ₀ is a capacitance component that spreads from the probe end face into the vacuum in the vacuum. G ₀ is the radiation conductance from the coaxial probe end face to the vacuum. The relational expression of Eq. (3) is derived by regarding the element components other than the capacitance component and the radiation conductance as minute dipoles.

As described in Non-Patent Document 3, the radiation admittance G of the antenna of the medium having a dielectric constant ε has the relation of the equation (4). From equations (3) and (4), a proportional relationship is derived from G ₀ and ε to the 2.5th power of the second term on the right side of equation (2).

Since the radiation from the coaxial probe end face is smaller than the capacitance component of the probe end face, ωC ₀ >> G ₀ . Therefore, G ₀ can be approximated to 0. At this time, the equivalent circuit is as shown in FIG. 8 (b-1). Further, when the metal is calibrated and standardized, the coaxial probe is in a short-circuited state, so that y _{i = short} can be approximated to infinity. As a result, the equations (1) and (2) can be transformed into the following equations (5) and (6).

a, s and w refer to calibration standard air, metal and water. By substituting Eq. (6) into Eq. (5), Eq. (8) is derived, and the permittivity of MUT is derived.

In the conventional method, the permittivity is calculated from the ratio of the equivalent circuit assuming that the MUT is a uniform dielectric material. Therefore, when measuring a material such as a layered material whose dielectric constant distribution in the depth direction is not uniform, Since the effective permittivity up to the penetration depth of the probe is measured, the measurement result may differ depending on the measurement probe. For the same reason, even when the thickness of the MUT is less than or equal to the penetration depth of the probe, the dielectric constant of the mechanism for fixing the material such as the microchannel and the sample setting table may affect the measurement result. In addition, in the conventional method, the radiated electromagnetic field from the end face of the coaxial probe is ignored as sufficiently small, or is represented by a model approximated as a minute dipole. Therefore, there is a problem that the measurement accuracy may decrease in the frequency band above the GHz band. Further, as the measurement frequency becomes higher, the influence of the radiation conductance of the coaxial probe increases, which may cause an error factor used in the approximation of the conventional method.

FIG. 3 shows a flowchart of the dielectric spectroscopy method of the present embodiment. First, calibration is performed by the same method as the conventional method. In this embodiment, the calibration of FIG. 3 is step a.

Next, the dielectric constant ε _wc and the admittance wc when the MUT is water are calculated using the measured values of air, metal, and water. That is, the equations in equations (5) and (8) with m = wc are created. When the water is measured only once, the calculation is performed with the subscripts i = wc = w in the equations (5) and (8). At the time of calibration, the reflectance coefficient of water may be measured twice, and one of them may be calculated as i = w and the other as i = wc. In the present embodiment, the step of calculating the correction element parameter of FIG. 3 is step b.

　ここでε_ｃは同軸線路の絶縁体の誘電率、ｋｍは測定周波数におけるＭＵＴを伝搬時の波数、ε_ｍ及びγ_ｍはＭＵＴの誘電率およびＭＵＴ伝搬時の電磁波の伝搬定数、Ｊ_０（ｘ）は０次ベッセル関数である。また、変数ζはＨａｎｋｅｌ変換に伴い生じる変数である。アドミタンスの理論式は同軸プローブのアドミタンスの数式表現は、同軸プローブ端面からＭＵＴの間を伝搬定数の結合で表現したＴｒａｎｓｍｉｓｓｉｏｎ　ｌｉｎｅ　Ｍｏｄｅｌなどを用いてもよい。本実施形態において、図３のアドミタンスモデルに基づく影響の補正が、工程ｅである。 In the dielectric spectroscopy method of the present embodiment, the admittance theoretical formula of the coaxial probe end face at the time of MUT installation is constructed with the variable as the permittivity of the MUT, and the dielectric constant of the MUT is analyzed so as to satisfy the measured value. Is calculated. The theoretical formula of admittance is the mathematical expression of the admittance of the coaxial probe. For example, the integral-admittance model shown in the formula (9) may be used. In the present embodiment, the step of measuring the reflectance coefficient of the MUT in FIG. 3 is step c. Further, the calculation of the admittance Ymeas in FIG. 3 is the step d.

Here, ε _c is the permittivity of the insulator of the coaxial line, km is the number of waves when propagating the MUT at the measurement frequency, ε _m and γ _m are the permittivity of the MUT and the propagation constant of the electromagnetic wave when propagating the MUT, J ₀ (x). ) Is a 0th order Vessel function. The variable ζ is a variable generated by the Hankel transform. The theoretical formula of admittance The mathematical expression of admittance of the coaxial probe may use a Transmission line model or the like in which the distance between the end face of the coaxial probe and the MUT is expressed by the coupling of propagation constants. In the present embodiment, the correction of the influence based on the admittance model of FIG. 3 is step e.

The electromagnetic wave on the coaxial end face is composed of a reflected wave returning from the MUT to the measuring instrument and a radiated wave radiated into space when the coaxial probe is regarded as a minute antenna. Therefore, in the present embodiment, the admittance model of the coaxial probe is represented by the equivalent circuit shown in FIG. In FIG. 4, both C _fcal and C _f indicate the fringe capacitance of the electric field generated in the coaxial probe internal insulator. C _fcal indicates the capacitance component deembed by the probe end face according to the equation (5) or (8). C ₀ indicates the capacitance component extending from the probe end face into the vacuum in vacuum, and Yant indicates radiative admittance.

In the conventional method, the radiated admittance is modeled as the radiated conductance of a minute dipole as shown in FIG. 8 (b-2). On the other hand, in the present embodiment, as shown in FIG. 5, the radiated admittance is expressed by using a series resonance or a parallel resonance circuit. In addition to the circuit shown in FIG. 5, circuit elements may be added to model the radiated admittance as a circuit having more complicated resonance characteristics. The calibration used in Eq. (5) or (8) deembeds the error component assuming that the metal is a short circuit, the air is an open circuit, and the water is an arbitrary load. Therefore, the circuit components included in the calibration end face BB'in FIG. 2 are only C _f and ε C ₀ in FIG. 4, and there is a possibility that a discrepancy with the circuit components of the theoretical model may occur.

　ここでＹ_{ｍｅａｓｕｒｅｄ}（ε_ｗｃ）は（５）式を用いて算出したＭＵＴを水とした際の同軸プローブのアドミタンスである。 In this embodiment, it is assumed that the component of the fringe capacitance inside the coaxial probe that is removed by the deembed is sufficiently small, and the error between the theoretical formula of admittance of the coaxial probe end face and the measured value in the conventional method is the radiation term Yant. It is assumed that it is caused by. Here, when the error between the theoretical value of admittance when measuring water and the measured value is calculated, the error component Yant (ε _wc ) when measuring water having a dielectric constant ε _wc can be expressed by Eq. (11). ..

Here, Y _measured (ε _wc ) is the admittance of the coaxial probe when MUT is water, which is calculated by using Eq. (5).

（１１）及び（１２）式から、Ｙａｎｔ（ε_ｗｃ）は真空中の放射アドミタンスＹａｎｔ（ε_０）を用いて、（１３）式と表現できる。

（１３）式を満たすように回路素子パラメータＹａｎｔ（ε_０、ω）を同定することにより、ディエンベッドにより除去された放射素子成分を抽出する。（１１）式と（１３）式との関係から、実効誘電率ε_ｅｆｆの材料をＭＵＴとした場合の同軸プローブのモデル式は（１４）式となる。

Yant (ε _wc ) has the waveform shown in FIG. Therefore, Yant (ε _wc ) can be expressed by, for example, an RLC series resonant circuit. Here, assuming that Yant (ε _wc ) is the antenna radiation term, there is a relationship represented by Eq. (12) between the radiation admittance in vacuum and the radiation admittance in the medium having a permittivity ε _r .

From equations (11) and (12), Yant (ε _wc ) can be expressed as equation (13) using the radiation admittance Yant (ε ₀ ) in vacuum.

By identifying the circuit element parameter Yant (ε ₀ , ω) so as to satisfy the equation (13), the radiating element component removed by the deembed is extracted. From the relationship between the equations (11) and (13), the model equation of the coaxial probe when the material having an effective dielectric constant ε _eff is MUT is the equation (14).

In the subsequent analysis, the admittance and the permittivity ε _r are measured at the time of MUT measurement, and the measured value Y _measured (ε _r ) of the admittance is corrected by using the equation (14) to reduce the error from the model equation. In the present embodiment, the calculation of the complex permittivity by the inverse problem analysis of FIG. 3 is step f.

　Ｙ_{ｃｏｒｒｅｃｔｅｄ}は（１４）式により補正したアドミタンス、Ｙ_{ｍｏｄｅｌ}（ε_ｒ）は例えば（９）式である。ＭＵＴが一様な材料ではなく、その形状が既知である場合はＭＵＴの形状を含めたモデルをＹ_{ｍｏｄｅｌ}として用いてよい。例えばＭＵＴが２層からなる層状材料である場合は（１６）式のように示す。

ここで添え字の１、２は層状材料の第一層、第二層であり、プローブ端面と接する側を第一層とする。また、変数ｄ１は第一層の層厚を示す。 FIG. 7 shows a comparison between the measured values of admittance before and after the correction and the model formula. It can be seen that the error between the measured value and the model formula is reduced by the proposed method, and the admittance model can be corrected so as to match the model formula. Then, ε _r that satisfies Eq. (15) is calculated by inverse problem analysis.

Y oriented is the admittance _corrected by the equation (14), and Y _model (ε _r ) is, for example, the equation (9). If the MUT is not a uniform material and its shape is known, a model including the shape of the MUT may be used as the Y _model . For example, when the MUT is a layered material composed of two layers, it is shown as in Eq. (16).

Here, the subscripts 1 and 2 are the first layer and the second layer of the layered material, and the side in contact with the probe end face is the first layer. Further, the variable d1 indicates the layer thickness of the first layer.

Regarding the inverse problem analysis of Eq. (13), if the layer thickness d1 of the first layer and the permittivity ε ₂ of the second layer are known, they are used as constants, and if they are unknown, they are added as variables and the inverse problem analysis is performed. You may. Further, the theoretical formula Y _model may be used as an analysis formula based on electromagnetism for the admittance of the coaxial probe end face at the time of MUT measurement for any shape of MUT such as a multilayer material. This makes it possible to analyze the inverse problem for any shape. Since equations (9) and (16) are generally non-linear functions, the inverse problem represented by equation (15) is an optimization method represented by, for example, the simplex method, the steepest descent method, or particle swarm optimization. , May be calculated using a numerical calculation method such as a neural network. As described above, the influence of radiation admittance is suppressed, and highly accurate dielectric spectroscopy for MUTs of arbitrary shapes becomes possible.

As described above, in this embodiment, after the measurement using the coaxial probe is performed, the measured admittance is corrected by using the correction formula, and the permittivity is measured by the inverse problem analysis of the correction value and the theoretical model of admittance. By carrying out the above, the influence of the radiation term and the influence of the shape of the MUT can be suppressed. Therefore, it can be applied not only to a uniform MUT but also to a layered or thin layer MUT. As a result, it becomes possible to measure the dielectric constant in a higher frequency band.
Further, the dielectric constant analysis method according to the present embodiment does not require the addition of a measurement procedure from the conventional method. In addition, the influence of parasitic components is corrected for the admittance measurement value of the coaxial probe at the time of sample measurement, and the inverse problem analysis of the admittance model formula of a single or layered material based on the electromagnetic field theory is performed. As a result, the complex permittivity of the substance to be measured (MUT: Material Under the Test) can be measured with higher accuracy.

According to the present invention, since it can be applied to a permittivity measuring device for a solution existing in a human or an animal and a permittivity measuring device for a solution collected from a human or an animal, it has high industrial utility value.

Claims (3)

The process of calibrating measuring equipment using standard samples and
The measured value of the admittance y _i of the probe end face of the measuring device calculated based on the measurement result of the dielectric constant of the standard sample, and the admittance y _i of the probe end face when the object to be measured is the standard sample. A step of calculating an error component of the theoretical value of the admittance y _i with respect to the measured value of the admittance y _i using the theoretical value and
The process of measuring the dielectric constant of the substance to be measured with the measuring device,
A step of calculating an actually measured value of admittance _ym of the probe end face of the measuring device based on the measurement result of the dielectric constant of the substance to be measured, and
A step of correcting the measured value of the admittance _ym of the probe end face using the error component, and a step of correcting the measured value.
The measured value of the _{admittance ym} corrected as the theoretical value of the admittance _ym is substituted into the model formula expressing the relationship between the theoretical value of the admittance ym and the permittivity of the substance to be measured. And the process of calculating the permittance of
A method for measuring the permittivity. The method for measuring a permittivity according to claim 1, wherein the admittance of the probe end face is represented by an equivalent circuit including capacitance and radiated admittance, and the error component is represented by the element parameter of the radiated admittance. The method for measuring a permittivity according to claim 2, wherein the radiation admittance is represented by a parallel resonance circuit or a series resonance circuit.

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