JP5428085B2

JP5428085B2 - Measuring method of electromagnetic characteristics

Info

Publication number: JP5428085B2
Application number: JP2007082678A
Authority: JP
Inventors: 敏秀北澤
Original assignee: Ritsumeikan Trust
Current assignee: Ritsumeikan Trust
Priority date: 2007-03-27
Filing date: 2007-03-27
Publication date: 2014-02-26
Anticipated expiration: 2027-03-27
Also published as: JP2008241468A

Description

本発明は、電磁気特性の測定方法、特に同軸線路を用いて広帯域における複素誘電率、さらには複素透磁率を高精度に測定することが可能な電磁気特性の測定方法に関する。 The present invention relates to a method for measuring electromagnetic characteristics, and more particularly to a method for measuring electromagnetic characteristics capable of measuring a complex permittivity and a complex permeability in a wide band with high accuracy using a coaxial line.

連続的な周波数帯域における電気特性を矩形導波管や同軸線路を用いて測定する方法がある。この方法は、被測定試料を充填した矩形導波管や同軸線路に電磁波を入射して複素反射係数や複素透過係数を測定し、電磁界解析を用いて測定した値に基き複素誘電率や複素透磁率を求めるものである。しかしながら、空隙が存在する、あるいは被測定試料が変形すると、測定誤差となるため、被測定試料を断面全面に隙間なく充填する必要があり、被測定試料の作成時に高い寸法精度が求められていた。特に、誘電率や透磁率が大きい場合には、空隙の影響が顕著であった。また、電磁波吸収体のような高損失材料を被測定試料とする場合、断面全面に充填するため、透過波が微弱となり、測定精度が低下した。さらに、複素誘電率および複素透磁率を測定するには、寸法の異なる複数の被測定試料を用いるか、複素反射係数と複素透過係数の両者を測定する必要があった。複数の被測定試料を用いる場合、被測定試料間のばらつきが問題となった。複素反射係数の測定は、測定基準面を設定する校正が困難であるため、複素透過係数の測定に比べ困難であり、測定精度が劣化した。 There is a method of measuring electrical characteristics in a continuous frequency band using a rectangular waveguide or a coaxial line. In this method, electromagnetic waves are incident on a rectangular waveguide or coaxial line filled with the sample to be measured, and the complex reflection coefficient and complex transmission coefficient are measured. Based on the values measured using electromagnetic field analysis, the complex dielectric constant and complex The permeability is obtained. However, if there is a gap or the sample to be measured is deformed, a measurement error occurs. Therefore, it is necessary to fill the sample with the entire cross section without any gaps, and high dimensional accuracy is required when creating the sample to be measured. . In particular, when the dielectric constant and the magnetic permeability are large, the influence of the air gap is significant. Further, when a high-loss material such as an electromagnetic wave absorber is used as the sample to be measured, the entire cross section is filled, so that the transmitted wave is weak and the measurement accuracy is lowered. Furthermore, in order to measure the complex permittivity and the complex permeability, it is necessary to use a plurality of samples to be measured having different dimensions or to measure both the complex reflection coefficient and the complex transmission coefficient. In the case of using a plurality of samples to be measured, variation between the samples to be measured has become a problem. The measurement of the complex reflection coefficient is difficult compared with the measurement of the complex transmission coefficient because the calibration for setting the measurement reference plane is difficult, and the measurement accuracy is deteriorated.

なお、矩形導波管を用いた方法では、矩形導波管に被測定試料を部分装荷し、拡張スペクトル領域法をモードマッチング法と組み合わせたハイブリッド電磁界解析法（ＥＳＤＭＭ）による高精度かつ高効率な電磁界解析を用いて、複素誘電率や複素透磁率を求めることが提案されている（非特許文献１および非特許文献２参照。）。
Ｔ．Ｓｈｉｒａｉｓｈｉ，Ｔ．Ｎｉｓｈｉｋａｗａ，Ｋ．ＷａｋｉｎｏａｎｄＴ．Ｋｉｔａｚａｗａ，ＩＥＩＣＥＴｒａｎｓ．Ｅｌｅｃｔｒｏｎ．，Ｖｏｌ．Ｅ８６−Ｃ、Ｎｏ．１１，Ｎｏｖｅｍｂｅｒ２００３，ｐｐ．２１８４−２１９０電子情報通信学会論文誌、ＣＶｏｌ．Ｊ８９−Ｃ、Ｎｏ．１２、（２００６）、ｐｐ．１０４７−１０５３ In the method using the rectangular waveguide, the sample to be measured is partially loaded in the rectangular waveguide, and the hybrid electromagnetic field analysis method (ESDMM) combining the extended spectrum region method with the mode matching method is highly accurate and highly efficient. It has been proposed to obtain a complex dielectric constant and a complex magnetic permeability using simple electromagnetic field analysis (see Non-Patent Document 1 and Non-Patent Document 2).
T. T. et al. Shirai, T .; Nishikawa, K .; Wakino and T.W. Kitazawa, IEICE Trans. Electron. , Vol. E86-C, no. 11, November 2003, pp. 2184-2190 IEICE Transactions, C Vol. J89-C, No. 12, (2006), pp. 1047-1053

光ファイバやＣＡＴＶなどの浸透により、ブロードバンドにも対応可能な広周波数帯域において連続的に複素誘電率や複素透磁率を高精度に測定することが重要視されている。しかしながら、非特許文献１および非特許文献２にて提案されている測定方法は矩形導波管を用いているので、無線ＬＡＮ等に対応する狭い周波数帯域しか測定することができない。また、従来の同軸線路を用いる測定方法は、上記した問題がある。 Due to the penetration of optical fibers and CATV, it is important to measure complex permittivity and complex permeability with high accuracy continuously in a wide frequency band that can be used for broadband. However, since the measurement methods proposed in Non-Patent Document 1 and Non-Patent Document 2 use rectangular waveguides, only a narrow frequency band corresponding to a wireless LAN or the like can be measured. Moreover, the conventional measuring method using a coaxial line has the above-mentioned problems.

本発明は、かかる課題に鑑みてなされたものであり、広帯域において複素誘電率や複素透磁率を高精度に測定することが可能な電磁気特性の測定方法を提供することを目的とする。 The present invention has been made in view of such a problem, and an object of the present invention is to provide a method for measuring electromagnetic characteristics capable of measuring complex permittivity and complex permeability with high accuracy in a wide band.

上記目的を達成するために、本発明の電磁気特性の測定方法は、軸方向直交断面に空隙を設けて被測定試料を装荷した同軸線路に電磁波を入射し、複素透過係数を測定するステップと、前記同軸線路内の空間を複数の均質な領域に分割し、前記領域の境界面において電磁界の連続条件が満たされるよう、前記測定した複素透過係数から、前記被測定試料の複素誘電率を求めるステップと、を備えることを特徴としている。 In order to achieve the above object, the method for measuring electromagnetic characteristics according to the present invention includes a step of measuring a complex transmission coefficient by injecting electromagnetic waves into a coaxial line loaded with a sample to be measured by providing a gap in an axially orthogonal cross section, and The space in the coaxial line is divided into a plurality of homogeneous regions, and the complex permittivity of the sample to be measured is obtained from the measured complex transmission coefficient so that the continuous condition of the electromagnetic field is satisfied at the boundary surface of the region. And a step.

請求項１に記載の電磁気特性の測定方法は、軸方向直交断面に空隙を設けて被測定試料を装荷した同軸線路に電磁波を入射し、複素透過係数を測定するステップと、電磁気特性が既知の試料を追加して装荷した同軸線路に電磁波を入射し、複素透過係数を測定するステップと、前記同軸線路内の空間を複数の均質な領域に分割し、前記領域の境界面において電磁界の連続条件が満たされるよう、前記測定した２つの複素透過係数から、前記被測定試料の複素透磁率、または複素誘電率および複素透磁率を求めるステップと、を備えることを特徴としている。 According to a first aspect of the present invention, there is provided a method for measuring electromagnetic transmission characteristics, wherein electromagnetic waves are incident on a coaxial line provided with a sample to be measured by providing a gap in a cross section orthogonal to the axial direction, and the electromagnetic transmission characteristics are known. Injecting electromagnetic waves into a coaxial line loaded with a sample and measuring the complex transmission coefficient, dividing the space in the coaxial line into a plurality of homogeneous regions, and continuing the electromagnetic field at the boundary surface of the region Obtaining a complex magnetic permeability of the sample to be measured, or a complex dielectric constant and a complex magnetic permeability, from the two measured complex transmission coefficients so that the condition is satisfied.

本発明の電磁気特性の測定方法は、軸方向直交断面に空隙を設けて被測定試料を装荷し、軸方向一端を短絡した同軸線路に軸方向他端から電磁波を入射し、複素反射係数を測定するステップと、前記被測定試料の軸方向の装荷位置を変更した同軸線路に前記軸方向他端から電磁波を入射し、複素反射係数を測定するステップと、前記同軸線路内の空間を複数の均質な領域に分割し、前記領域の境界面において電磁界の連続条件が満たされるよう、前記測定した２つの複素反射係数から、前記被測定試料の複素透磁率、または複素誘電率および複素透磁率を求めるステップと、を備えることを特徴としている。 In the method for measuring electromagnetic characteristics of the present invention, a sample to be measured is provided with a gap in an axially orthogonal cross section, an electromagnetic wave is incident from the other axial end to a coaxial line whose one axial end is short-circuited, and a complex reflection coefficient is measured. Measuring the complex reflection coefficient by injecting electromagnetic waves from the other axial end to the coaxial line whose axial loading position of the sample to be measured has been changed, and a plurality of homogeneous spaces in the coaxial line. From the two measured complex reflection coefficients, the complex permeability of the sample to be measured, or the complex dielectric constant and the complex permeability are calculated so that the electromagnetic field continuity condition is satisfied at the boundary surface of the area. And a step for obtaining.

本発明の電磁気特性の測定方法によれば、軸方向直交断面に空隙を設けて被測定試料を装荷した同軸線路に電磁波を入射し、複素透過係数を測定する。そのため、被測定試料を断面全面に隙間なく充填する必要がないので、被測定試料の作成時に高い寸法精度が求められない。また、電磁波吸収体のような高損失材料を被測定試料とする場合であっても、断面全面に充填する場合に比べて透過波が微弱とならないので、高精度に測定することが可能となる。同軸線路を用いるため、広周波数帯域（ブロードバンド）において連続的に複素誘電率を高精度に測定することが可能となる。同軸線路内の空間を複数の均質な領域に分割し、領域の境界面において電磁界の連続条件が満たされるよう、測定した複素透過係数から、被測定試料の複素誘電率を求める。このため、電磁界解析は高精度かつ効率的なものとなり、複素誘電率をオンサイトで高精度に測定することが可能となる。 According to the method for measuring electromagnetic characteristics of the present invention, electromagnetic waves are incident on a coaxial line loaded with a sample to be measured by providing a gap in a cross section orthogonal to the axial direction, and the complex transmission coefficient is measured. For this reason, since it is not necessary to fill the entire surface of the sample with no gaps, high dimensional accuracy is not required when the sample to be measured is created. In addition, even when a high-loss material such as an electromagnetic wave absorber is used as a sample to be measured, the transmitted wave does not become weak compared to the case where the entire cross-section is filled, so that measurement can be performed with high accuracy. . Since the coaxial line is used, the complex permittivity can be continuously measured with high accuracy in a wide frequency band (broadband). The space in the coaxial line is divided into a plurality of homogeneous regions, and the complex dielectric constant of the sample to be measured is obtained from the measured complex transmission coefficient so that the continuity condition of the electromagnetic field is satisfied at the boundary surface of the region. For this reason, electromagnetic field analysis becomes highly accurate and efficient, and the complex permittivity can be measured on-site with high accuracy.

請求項１に記載の電磁気特性の測定方法によれば、軸方向直交断面に空隙を設けて被測定試料を装荷した同軸線路に電磁波を入射し、複素透過係数を測定する。そして、電磁気特性が既知の試料を追加して装荷した同軸線路に電磁波を入射し、複素透過係数を測定する。そのため、被測定試料を断面全面に隙間なく充填する必要がないので、被測定試料の作成時に高い寸法精度が求められない。また、電磁波吸収体のような高損失材料を被測定試料とする場合であっても、断面全面に充填する場合に比べて透過波が微弱とならないので、高精度に測定することが可能となる。また、被測定試料は１つしか必要としないので、被測定試料間のばらつきが問題とならず、高精度に測定することが可能となる。また、複素透過係数のみを測定するので、校正が困難な複素反射係数を測定する必要がなく、高精度に測定することが可能となる。同軸線路を用いるため、広周波数帯域（ブロードバンド）において連続的に複素誘電率や複素透磁率を高精度に測定することが可能となる。同軸線路内の空間を複数の均質な領域に分割し、領域の境界面において電磁界の連続条件が満たされるよう、測定した２つの複素透過係数から、被測定試料の複素誘電率や複素透磁率を求める。このため、電磁界解析は高精度かつ効率的なものとなり、複素誘電率や複素透磁率をオンサイトで高精度に測定することが可能となる。 According to the method for measuring electromagnetic characteristics described in claim 1 , electromagnetic waves are incident on a coaxial line loaded with a sample to be measured by providing a gap in an axially orthogonal cross section, and the complex transmission coefficient is measured. Then, an electromagnetic wave is incident on a coaxial line loaded with a sample having a known electromagnetic characteristic, and the complex transmission coefficient is measured. For this reason, since it is not necessary to fill the entire surface of the sample with no gaps, high dimensional accuracy is not required when the sample to be measured is created. In addition, even when a high-loss material such as an electromagnetic wave absorber is used as a sample to be measured, the transmitted wave does not become weak compared to the case where the entire cross-section is filled, so that measurement can be performed with high accuracy. . In addition, since only one sample to be measured is required, variations between the samples to be measured do not pose a problem, and measurement can be performed with high accuracy. Further, since only the complex transmission coefficient is measured, it is not necessary to measure a complex reflection coefficient that is difficult to calibrate, and it is possible to measure with high accuracy. Since the coaxial line is used, the complex permittivity and the complex permeability can be continuously measured with high accuracy in a wide frequency band (broadband). Divide the space in the coaxial line into multiple homogeneous regions, and measure the complex permittivity and complex permeability of the sample to be measured from the two measured complex transmission coefficients so that the electromagnetic field continuity condition is satisfied at the boundary surface of the region. Ask for. For this reason, the electromagnetic field analysis becomes highly accurate and efficient, and the complex permittivity and the complex permeability can be measured on-site with high accuracy.

本発明の電磁気特性の測定方法によれば、軸方向直交断面に空隙を設けて被測定試料を装荷し、軸方向一端を短絡した同軸線路に軸方向他端から電磁波を入射し、複素反射係数を測定する。そして、被測定試料の軸方向の装荷位置を変更した同軸線路に軸方向他端から電磁波を入射し、複素反射係数を測定する。そのため、被測定試料を断面全面に隙間なく充填する必要がないので、被測定試料の作成時に高い寸法精度が求められない。また、被測定試料は１つしか必要としないので、被測定試料間のばらつきが問題とならず、高精度に測定することが可能となる。また、同軸線路の軸方向一端が短絡されているので、複素反射係数の校正を容易に行うことができ、高精度に測定することが可能となる。同軸線路を用いるため、広周波数帯域（ブロードバンド）において連続的に複素誘電率や複素透磁率を高精度に測定することが可能となる。同軸線路内の空間を複数の均質な領域に分割し、領域の境界面において電磁界の連続条件が満たされるよう、測定した２つの複素反射係数から、被測定試料の複素透磁率、または複素誘電率および複素透磁率を求める。このため、電磁界解析は高精度かつ効率的なものとなり、複素誘電率や複素透磁率をオンサイトで高精度に測定することが可能となる。 According to the method for measuring electromagnetic characteristics of the present invention, a sample to be measured is provided with a gap in an axially orthogonal cross section, an electromagnetic wave is incident from the other axial end to a coaxial line whose one axial end is short-circuited, and a complex reflection coefficient. Measure. Then, an electromagnetic wave is incident from the other axial end on the coaxial line whose axial loading position of the sample to be measured is changed, and the complex reflection coefficient is measured. For this reason, since it is not necessary to fill the entire surface of the sample with no gaps, high dimensional accuracy is not required when the sample to be measured is created. In addition, since only one sample to be measured is required, variations between the samples to be measured do not pose a problem, and measurement can be performed with high accuracy. In addition, since one axial end of the coaxial line is short-circuited, the complex reflection coefficient can be easily calibrated, and measurement can be performed with high accuracy. Since the coaxial line is used, the complex permittivity and the complex permeability can be continuously measured with high accuracy in a wide frequency band (broadband). The space in the coaxial line is divided into a plurality of homogeneous regions, and the complex permeability or complex dielectric of the sample to be measured is calculated from the two measured complex reflection coefficients so that the continuity condition of the electromagnetic field is satisfied at the boundary surface of the region. Find the rate and complex permeability. For this reason, the electromagnetic field analysis becomes highly accurate and efficient, and the complex permittivity and the complex permeability can be measured on-site with high accuracy.

以下、本発明に係る電磁気特性の測定方法について、図面に基づき説明する。本測定方法は、軸方向直交断面に空隙を設けて被測定試料を装荷した同軸線路に電磁波を入射し、複素透過係数を測定し、同軸線路内の空間を複数の均質な領域に分割し、領域の境界面において電磁界の連続条件が満たされるよう、測定した複素透過係数から、被測定試料の電磁気特性を求めるものである。電磁界解析には、拡張スペクトル領域法をモードマッチング法と組み合わせたハイブリッド電磁界解析法であるＥＳＤＭＭ（Extended Spectral Domain Mode Matching Method）を用いる。 Hereinafter, a method for measuring electromagnetic characteristics according to the present invention will be described with reference to the drawings. In this measurement method, an electromagnetic wave is incident on a coaxial line loaded with a sample to be measured with a gap in an axially orthogonal cross section, a complex transmission coefficient is measured, and a space in the coaxial line is divided into a plurality of homogeneous regions. The electromagnetic characteristics of the sample to be measured are obtained from the measured complex transmission coefficient so that the continuous condition of the electromagnetic field is satisfied at the boundary surface of the region. The electromagnetic field analysis uses an extended spectral domain mode matching method (ESDMM), which is a hybrid electromagnetic field analysis method in which the extended spectral domain method is combined with the mode matching method.

図１（ａ）および図１（ｂ）に示すように、同軸線路１０に被測定試料２０を部分装荷する。同軸線路１０は、ｚ軸方向の軸線を同一とする内導体１１および外導体１２から構成される。内導体１１は半径ａの丸棒状であり、外導体１２は内半径ｂの円筒状であり、内導体１１と外導体１２との間に空気領域が形成される。内導体１１および外導体１２は、金属、特に導電率が高い金属、例えば、銀、銅、金などからなる。被測定試料２０は、半径ａの貫通孔を中央に備え、外半径ａ＋ｃ（ただし、ａ＋ｃ＜ｂ）、ｚ軸方向厚さｔのドーナツ形状であり、ｚ軸対称に形成される。被測定試料２０は、その貫通孔が内導体１１に挿通され、不図示のホルダに固定されることにより同軸線路１０に装荷される。被測定試料２０の外半径ａ＋ｃは外導体１２の内半径ｂより小さく、軸線であるｚ軸方向に直交する断面（軸方向直交断面）、すなわち半径方向であるρ方向に空隙を設けて、被測定試料２０が同軸線路１０に装荷される。また、被測定試料２０の厚さｔが同軸線路のｚ軸方向の長さよりも短く、軸線の一部にのみ被測定試料２０が同軸線路１０に装荷される。なお、被測定試料２０厚さｔは、入射される電磁波ＨINCの波長等に関わらず、適宜定めればよい。 As shown in FIGS. 1A and 1B, the sample 20 to be measured is partially loaded on the coaxial line 10. The coaxial line 10 includes an inner conductor 11 and an outer conductor 12 having the same z-axis direction axis. The inner conductor 11 has a round bar shape with a radius a, and the outer conductor 12 has a cylindrical shape with an inner radius b, and an air region is formed between the inner conductor 11 and the outer conductor 12. The inner conductor 11 and the outer conductor 12 are made of a metal, particularly a metal having high conductivity, such as silver, copper, or gold. The sample 20 to be measured has a through-hole having a radius a in the center, has an outer radius a + c (where a + c <b), a donut shape having a thickness t in the z-axis direction, and is formed symmetrically with the z-axis. The sample 20 to be measured is loaded on the coaxial line 10 by inserting the through hole into the inner conductor 11 and fixing it to a holder (not shown). The outer radius a + c of the sample 20 to be measured is smaller than the inner radius b of the outer conductor 12, and a gap is provided in a section perpendicular to the z-axis direction that is the axis (axis-direction orthogonal section), that is, in the ρ direction that is the radial direction. A measurement sample 20 is loaded on the coaxial line 10. Further, the thickness t of the sample 20 to be measured is shorter than the length of the coaxial line in the z-axis direction, and the sample 20 to be measured is loaded on the coaxial line 10 only at a part of the axis. The thickness t of the sample 20 to be measured may be determined as appropriate regardless of the wavelength of the incident electromagnetic wave HINC.

次に、被測定試料２０が部分装荷された同軸線路１０に対するＥＳＤＭＭに関して説明する。まず、図２に示すように、同軸線路１０内の全領域を３つの領域Ｓ１、Ｓ２、Ｓ３に分割する。領域Ｓ１は、ｚ＜０の領域であり、被測定試料２０より入力側の均質な空気領域である。領域Ｓ２は、０＜ｚ＜ｔの領域であり、その断面の一部に被測定試料２０が存在する非均質な領域である。領域Ｓ３は、ｚ＞ｔの領域であり、被測定試料２０より出力側の均質な空気領域である。そして、領域Ｓ１と領域Ｓ２との境界面ｚ＝０、すなわち被測定試料２０の前面（電磁波ＨINCが入射される面に近い側面）を含む面に間隙電界ｅａ（ρ）を、領域Ｓ２と領域Ｓ３との境界面ｚ＝ｔ、すなわち被測定試料２０の後面（前面と反対側の面）を含む面に間隙電界ｅｂ（ρ）を、それぞれ導入する。電磁界の等価定理より、各領域Ｓ１、Ｓ２、Ｓ３は独立に取り扱うことができる。領域Ｓ１、Ｓ３においては、均質であるので、位相φ変分のない基本波（ＴＥ波）ＨINCが入射される場合、図３（ａ）に概念的に示されるように、電磁界Φｍ（ρ）はρの三角関数による固有関数により級数展開することができる。 Next, the EDDM for the coaxial line 10 in which the sample 20 to be measured is partially loaded will be described. First, as shown in FIG. 2, the entire region in the coaxial line 10 is divided into three regions S1, S2, and S3. The region S <b> 1 is a region where z <0, and is a homogeneous air region on the input side from the sample 20 to be measured. The region S2 is a region of 0 <z <t, and is a non-homogeneous region where the sample 20 to be measured exists in a part of the cross section. The region S3 is a region where z> t, and is a homogeneous air region on the output side from the sample 20 to be measured. The gap electric field ea (ρ) is applied to the boundary surface z = 0 between the region S1 and the region S2, that is, the surface including the front surface of the sample 20 to be measured (the side surface close to the surface on which the electromagnetic wave HINC is incident). A gap electric field eb (ρ) is introduced into the boundary surface z = t with S3, that is, the surface including the rear surface (surface opposite to the front surface) of the sample 20 to be measured. From the electromagnetic field equivalent theorem, each region S1, S2, S3 can be handled independently. Since the regions S1 and S3 are homogeneous, when the fundamental wave (TE wave) HINC having no phase φ variation is incident, as shown conceptually in FIG. 3A, the electromagnetic field Φm (ρ ) Can be expanded in series by the eigenfunction of trigonometric function of ρ

一方、領域Ｓ２は、非均質であり、電磁界Φ_ｍ（ρ）が異なる媒体に渡って存在するので、三角関数等の単純な固有関数では級数展開することができない。そこで、領域Ｓ２を更に均質な複数の小領域Ｓａ、Ｓｂに分割する。小領域Ｓａは被測定試料２０が全体に渡って存在する均質な領域であり、小領域Ｓｂは被測定試料２０が存在しない均質な空気領域である。小領域Ｓａ、Ｓｂにおける電磁界をそれぞれ表す異なる固有関数Φ_ｍ ^（ａ）（ρ）、Φ_ｍ ^（ｂ）（ρ）を導入する。

ここで、Ａ_ｍ、Ｂ_ｍは規格化係数、ｋ_ｍは未知の固有値である。これらの固有関数Φ_ｍ ^（ａ）（ρ）、Φ_ｍ ^（ｂ）（ρ）は、小領域Ｓａと小領域Ｓｂとの境界面における連続条件を満たすよう、モードマッチング法により求めることができる。固有値方程式を数値的に解くことにより、図３（ｂ）に概念的に示されるような固有関数Φ_ｍ ^（ａ）（ρ）、Φ_ｍ ^（ｂ）（ρ）が定められる。 On the other hand, since the region S2 is inhomogeneous and the electromagnetic field Φ _m (ρ) exists across different media, the series cannot be expanded with a simple eigenfunction such as a trigonometric function. Therefore, the region S2 is further divided into a plurality of smaller subregions Sa and Sb. The small area Sa is a homogeneous area where the sample 20 to be measured exists throughout, and the small area Sb is a homogeneous air area where the sample 20 to be measured does not exist. Different eigenfunctions Φ _m ^(a) (ρ) and Φ _m ^(b) (ρ) representing the electromagnetic fields in the small regions Sa and Sb are introduced.

_Here, A _{_m, B} m the normalized coefficient, _{k m} is the unknown eigenvalues. These eigenfunctions Φ _m ^(a) (ρ) and Φ _m ^(b) (ρ) can be obtained by the mode matching method so as to satisfy the continuous condition at the boundary surface between the small region Sa and the small region Sb. By solving the eigenvalue equation numerically, eigenfunctions Φ _m ^(a) (ρ) and Φ _m ^(b) (ρ) as conceptually shown in FIG. 3B are determined.

これらの固有関数Φ_ｍ ^（ａ）（ρ）、Φ_ｍ ^（ｂ）（ρ）は非均質な領域である領域Ｓ２全体に渡り次に示す双直交条件を満足する。

ここで、ε_ｒ２ａ、ε_ｒ２ｂはそれぞれ小領域Ｓａ、Ｓｂの比誘電率であり、δ_ｍｎはクロネッカのデルタを表す。この双直交条件を用いることにより、非均質領域Ｓ２の電磁界Φ_ｍ（ρ）も、領域Ｓ１、Ｓ３における電磁界Φ_ｍ（ρ）と同様に級数展開（スペクトル表示）することができる。スペクトル領域では、グリーン関数Ｔ^（１）、Ｔ^（２）、Ｔ^（３）を容易に求めることができる。各領域Ｓ１、Ｓ２、Ｓ３のρ方向の磁界Ｈ^（１）、Ｈ^（２）、Ｈ^（３）は、間隙電界ｅ_ａ（ρ）、間隙電界ｅ_ｂ（ρ）に関連付けられて表される。

ここで、Ｈ^ｉｎｃは入射する基本波の磁界である。 These eigenfunctions Φ _m ^(a) (ρ) and Φ _m ^(b) (ρ) satisfy the following bi-orthogonal condition over the entire region S2, which is a non-homogeneous region.

Here, ε _r2a and ε _r2b are the relative dielectric constants of the small regions Sa and Sb, respectively, and δ _mn represents the Kronecker delta. By using the bi-orthogonal conditions, an electromagnetic field [Phi _m of heterogeneous region S2 _([rho) may also be electromagnetic field [Phi _{m ([rho)} and likewise series expansion (spectral representation) in the area S1, S3. In the spectral region, the Green functions T ⁽¹⁾ , T ⁽²⁾ , T ⁽³⁾ can be easily obtained. The magnetic fields H ⁽¹⁾ , H ⁽²⁾ , H ⁽³⁾ in the ρ direction of each region S1, S2, S3 are expressed in association with the gap electric field e _a (ρ) and the gap electric field e _b (ρ). .

Here, H ^inc is the magnetic field of the incident fundamental wave.

残りの境界面における境界条件を適用することにより、間隙電界ｅ_ａ（ρ）、ｅ_ｂ（ρ）に関する積分方程式が得られる。ここでは、積分方程式の数値計算にガレルキン法を用いる。未知の間隙電界ｅ_ａ（ρ）、ｅ_ｂ（ρ）は適切な基底関数ｆ_ｋ（ρ）によって次のように表される。

ここで、ａ_ｋ、ｂ_ｋは未知の係数である。これらを式（２）から式（４）に代入する。間隙電界ｅ_ａ（ρ）、ｅ_ｂ（ρ）は境界条件の連続性から得られる。次に、基底電界ｆ_ｋ（ρ）と固有関数Φ_ｍ ^（ａ）（ρ）の内積をとり、数値積分にて計算し、Ｓパラメータ（散乱パラメータともいい、複素反射係数Ｓ_１１および複素透過係数Ｓ_２１からなる。）を求める。 By applying boundary conditions at the remaining boundary surfaces, an integral equation for the gap electric fields e _a (ρ), e _b (ρ) is obtained. Here, the Galerkin method is used for the numerical calculation of the integral equation. The unknown gap electric fields e _a (ρ), e _b (ρ) are expressed by the appropriate basis function f _k (ρ) as follows:

Here, a _k and b _k are unknown coefficients. These are substituted into equations (2) to (4). The gap electric fields e _a (ρ) and e _b (ρ) are obtained from the continuity of the boundary conditions. Next, the inner product of the base electric field f _k (ρ) and the eigenfunction Φ _m ^(a) (ρ) is taken, calculated by numerical integration, and the S parameter (also called scattering parameter, complex reflection coefficient S ₁₁ and complex transmission coefficient) consisting of S _21.) seek.

多様な無損失、高損失材料からなる被測定試料の電磁気特性を評価するため、小領域Ｓａ、Ｓｂの開口面に汎用な基底関数ｆ_ｋ（ρ）、例えば、ルーフトップ関数を用いて間隙電界ｅ_ａ（ρ）、ｅ_ｂ（ρ）を表す。

ここで、Ｗ_ｊ、Ｎ_ｊはそれぞれ各小領域Ｓａ、Ｓｂの開口幅、基底関数の数である。本法による行列サイズは、基底関数ｆ_ｋ（ρ）の数と同じ次数であり、行列サイズが固有関数（モード関数）の数の次数である従来のモードマッチング法よりも遥かに小さい。以上のように、高精度な電磁界解析を用いるので、Ｓパラメータを高精度に測定することが可能となる。 In order to evaluate the electromagnetic characteristics of a sample to be measured made of various lossless and high-loss materials, a gap field is generated using a general basis function f _k (ρ), for example, a rooftop function, on the opening surfaces of the small regions Sa and Sb. e _a (ρ) and e _b (ρ) are represented.

Here, W _j and N _j are the opening width and the number of basis functions of the small regions Sa and Sb, respectively. The matrix size by this method is the same order as the number of basis functions f _k (ρ), and is much smaller than the conventional mode matching method in which the matrix size is the order of the number of eigenfunctions (mode functions). As described above, since highly accurate electromagnetic field analysis is used, the S parameter can be measured with high accuracy.

図４（ａ）および図４（ｂ）は、同軸線路１０に部分装荷された被測定試料２０のＳパラメータの比誘電率依存性を示すグラフである。複素誘電率ε_rの実部ε´_rを横軸にとり、本発明に係る数値計算法による計算値を実線で、有限要素解析法（ＦＥＭ）による計算値を丸点にて示した。ここで、同軸線路１０の内導体１１の半径ａを１．５２ｍｍ、外導体１２の内半径ｂを３．５ｍｍとし、被測定試料２０の外半径と内半径の差ｃを１．４８ｍｍ、厚さｔを５．０ｍｍ、複素誘電率ε_rの虚部ε″_rを０、複素透磁率μ_rの実部μ´_rを１、虚部μ″_rを０とした。本発明に係る数値計算法による計算値と有限要素解析法による数値とは、振幅（実部Ｓ´_１１、Ｓ´_２１）│Ｓ_１１│、│Ｓ_２１│、位相（虚部Ｓ″_１１、Ｓ″_２１）∠Ｓ_１１、∠Ｓ_２１ともに広い範囲に渡って良く一致しており、本発明に係る数値計算法の妥当性が示されている。 FIGS. 4A and 4B are graphs showing the relative permittivity dependence of the S parameter of the sample 20 to be measured partially loaded on the coaxial line 10. The real part Ipushiron' _r of the complex dielectric constant epsilon _r horizontal axis, the calculated value by the numerical calculation method according to the present invention with a solid line, shown finite element analysis calculated values by (FEM) in a round point. Here, the radius a of the inner conductor 11 of the coaxial line 10 is 1.52 mm, the inner radius b of the outer conductor 12 is 3.5 mm, the difference c between the outer radius and the inner radius of the sample 20 to be measured is 1.48 mm, the thickness is 5.0mm the t, "0 and _r, 1 the real part _μ'r of the complex permeability μ _r, the imaginary part μ" imaginary part ε of the complex dielectric constant ε _r was 0 _r. The calculated value by the numerical calculation method and the numerical value by the finite element analysis method according to the present invention are the amplitude (real part S ′ ₁₁ , S ′ ₂₁ ) | S ₁₁ |, | S ₂₁ |, phase (imaginary part S ″ ₁₁ , S ″ ₂₁ ) ∠S ₁₁ and ∠S ₂₁ are in good agreement over a wide range, indicating the validity of the numerical calculation method according to the present invention.

以下、本発明の第１の実施の形態に係る電磁気特性の測定方法について、図面に基づき説明する。この測定方法は、図１（ａ）および図１（ｂ）に示すように、まず、ｚ軸方向直交断面に空隙を設けて被測定試料２０を同軸線路１０に部分装荷する。被測定試料２０を断面全面に隙間なく充填する必要がないので、被測定試料２０の作成時に高い寸法精度が求められない。そして、不図示のベクトル・ネットワーク・アナライザ等の透過特性測定装置を用いて、同軸線路１０のｚ軸方向端面側から基本波Ｈ^INCを入射し、複素透過係数Ｓ_２１（実部Ｓ_２１´と虚部Ｓ_２１″）を計測する。被測定試料２０が電磁波吸収体のような高損失材料であっても、断面全面に充填する場合に比べて透過波が微弱とならないので、複素透過係数Ｓ_２１を高精度に測定することができる。 Hereinafter, a method for measuring electromagnetic characteristics according to a first embodiment of the present invention will be described with reference to the drawings. In this measurement method, as shown in FIGS. 1A and 1B, first, a gap is provided in a cross section orthogonal to the z-axis direction, and the sample 20 to be measured is partially loaded on the coaxial line 10. Since it is not necessary to fill the entire surface of the measurement object 20 with no gap, high dimensional accuracy is not required when the measurement object 20 is created. Then, using a transmission characteristic measuring device such as a vector network analyzer (not shown), the fundamental wave H ^INC is incident from the end surface side of the coaxial line 10 in the z-axis direction, and the complex transmission coefficient S ₂₁ (real part S ₂₁ ′ and The imaginary part S ₂₁ ″) is measured. Even if the sample 20 to be measured is a high-loss material such as an electromagnetic wave absorber, the transmitted wave does not become weak compared to the case where the entire cross section is filled. ₂₁ can be measured with high accuracy.

次に、同軸線路１０内の空間を複数の均質な領域に分割し、領域の境界面において電磁界の連続条件が満たされるよう、測定した複素透過係数Ｓ_２１から、被測定試料２０の複素誘電率ε_rを求める。具体的には、被測定試料２０の複素誘電率ε_rの実部ε´_rと虚部ε″_rの初期値としてε´_r ^(０) _、ε″_r ^（０）を適宜定めて、計測した複素透過係数Ｓ_２１との差が所定の許容値未満となるまで、繰り返し複素透過係数Ｓ_２１を算出し、被測定試料２０の複素誘電率ε_rを求める。同軸線路１０を用いるため、広周波数帯域において連続的に複素誘電率ε_rを高精度に測定することが可能となる。また、高精度な電磁界解析を用いるので、複素誘電率ε_rを高精度に測定することができる。 Next, divide the space of the coaxial line 10 into a plurality of homogeneous areas, so that the continuous condition of the electromagnetic field is met at the interface region, the complex transmission coefficient S ₂₁ measured, the complex dielectric of the measured sample 20 The rate ε _r is obtained. Specifically, ε ′ _r ⁽⁰⁾ _and ε ″ _r ⁽⁰⁾ are appropriately determined as the initial values of the real part ε ′ _r and the imaginary part ε ″ _r of the complex dielectric constant ε _r of the sample 20 to be measured. The complex transmission coefficient S ₂₁ is repeatedly calculated until the difference from the measured complex transmission coefficient S ₂₁ is less than a predetermined allowable value, and the complex dielectric constant ε _r of the sample 20 to be measured is obtained. Since the coaxial line 10 is used, the complex permittivity ε _r can be continuously measured with high accuracy in a wide frequency band. In addition, since the electromagnetic field analysis with high accuracy is used, the complex dielectric constant ε _r can be measured with high accuracy.

図５は、同軸線路１０に部分装荷された被測定試料２０の複素誘電率ε_rの周波数依存性を示すグラフである。ここで、同軸線路１０の内導体１１の半径ａは１．５２ｍｍ、外導体１２の内半径ｂは３．５ｍｍであった。被測定試料２０は、タケチ工業製の市販のマイクロ波吸収シートであり、ゴムと粉末カーボンからなる。被測定試料２０は、同軸線路１０の不図示の試料ホルダに載置し、内導体１１の外周表面との間には間隙が無い。被測定試料２０の外半径と内半径の差ｃは１．４８ｍｍ、ｚ軸方向の厚さｔは４．９６ｍｍであった。被測定試料２０と外導体１２との隙間は０．１３ｍｍであった。ＶＮＡ（ＡｇｉｌｅｎｔＴｅｃｈｎｏｌｏｇｉｅｓＩｎｃ．８７１９ＥＴ伝送／反射ベクトル・ネットワーク・アナライザ）を用いて３〜１２ＧＨｚの周波数帯域に渡って複素透過係数Ｓ_２１を測定した。図５において、本実施形態に係る測定方法による計算値を実線で、タケチ工業による被測定試料２０に係るデータシートの記載値を丸点にて示した。計算値とデータシートの記載値とは、実部ε´_r、虚部ε″_rともに広い周波数範囲に渡って良く一致しており、本測定方法の妥当性が示されている。インテル社のペンティアム４（登録商標、動作周波数２ＧＨｚ）搭載のパーソナルコンピュータを用いて数秒以内の短時間で複素誘電率ε_rを求めることができた。 FIG. 5 is a graph showing the frequency dependence of the complex dielectric constant ε _r of the sample 20 to be measured partially loaded on the coaxial line 10. Here, the radius a of the inner conductor 11 of the coaxial line 10 was 1.52 mm, and the inner radius b of the outer conductor 12 was 3.5 mm. The sample 20 to be measured is a commercially available microwave absorbing sheet manufactured by Takechi Kogyo, and is made of rubber and powdered carbon. The sample 20 to be measured is placed on a sample holder (not shown) of the coaxial line 10, and there is no gap between the outer peripheral surface of the inner conductor 11. The difference c between the outer radius and the inner radius of the sample 20 to be measured was 1.48 mm, and the thickness t in the z-axis direction was 4.96 mm. The gap between the sample 20 to be measured and the outer conductor 12 was 0.13 mm. VNA was measured complex transmission coefficient _{S 21} over the frequency band of 3~12GHz using (Agilent Technologies Inc.8719ET transmission / reflection vector network analyzer). In FIG. 5, the calculated value by the measuring method according to the present embodiment is indicated by a solid line, and the described value of the data sheet relating to the sample 20 to be measured by Takechi Industry is indicated by a circle. The calculated value and the value described in the data sheet are in good agreement over a wide frequency range for both the real part ε ′ _r and the imaginary part ε ″ _r, indicating the validity of this measurement method. Using a personal computer equipped with Pentium 4 (registered trademark, operating frequency 2 GHz), the complex permittivity ε _r could be obtained in a short time within several seconds.

以下、本発明の第２の実施の形態に係る電磁気特性の測定方法について、図面に基づき説明する。この測定方法は、図１（ａ）および図１（ｂ）に示すように、まず、軸方向直交断面に空隙を設けて被測定試料２０を同軸線路１０に部分装荷する。被測定試料２０を断面全面に隙間なく充填する必要がないので、被測定試料２０の作成時に高い寸法精度が求められない。そして、不図示のベクトル・ネットワーク・アナライザ等の透過特性測定装置を用いて、同軸線路１０のｚ軸方向端面側から基本波Ｈ^INCを入射し、複素透過係数Ｓ_{２１（１）}（実部Ｓ´_{２１（１）}と虚部Ｓ″_{２１（１）}）を計測する。被測定試料２０が電磁波吸収体のような高損失材料であっても、断面全面に充填する場合に比べて透過波が微弱とならないので、複素透過係数Ｓ_{２１（１）}を高精度に測定することができる。 Hereinafter, a method of measuring electromagnetic characteristics according to the second embodiment of the present invention will be described with reference to the drawings. In this measurement method, as shown in FIGS. 1A and 1B, first, a gap is provided in the cross section orthogonal to the axial direction, and the sample 20 to be measured is partially loaded on the coaxial line 10. Since it is not necessary to fill the entire surface of the measurement object 20 with no gap, high dimensional accuracy is not required when the measurement object 20 is created. Then, using a transmission characteristic measuring device such as a vector network analyzer (not shown), the fundamental wave H ^INC is incident from the end face side of the coaxial line 10 in the z-axis direction, and the complex transmission coefficient S _{21 (1)} (real part S ′ _{21 (1)} and imaginary part S ″ _{21 (1)} ). Even if the sample 20 to be measured is a high-loss material such as an electromagnetic wave absorber, a transmitted wave is generated as compared with the case where the entire cross section is filled. Since it does not become weak, the complex transmission coefficient S21 ₍₁₎ can be measured with high accuracy.

次に、図６に示すように、電磁気特性が既知の試料２１を追加して装荷する。被測定試料２０は１つしか必要としないので、被測定試料２０間のばらつきが問題とならない。なお、既知の試料２１の装荷位置は任意でよい。そして、上記透過特性測定装置を用いて、同軸線路１０のｚ軸方向端面側から基本波Ｈ^INCを入射し、複素透過係数Ｓ_{２１（２）}（実部Ｓ´_{２１（２）}と虚部Ｓ″_{２１（２）}）を計測する。複素透過係数Ｓ_{２１（１）}、Ｓ_{２１（２）}のみを測定しており、校正が困難な複素反射係数Ｓ_１１を測定する必要がない。 Next, as shown in FIG. 6, a sample 21 with known electromagnetic characteristics is added and loaded. Since only one sample 20 to be measured is required, variations between the samples 20 to be measured do not matter. In addition, the loading position of the known sample 21 may be arbitrary. Then, using the transmission characteristic measuring device, the fundamental wave H ^INC is incident from the end face side of the coaxial line 10 in the z-axis direction, and the complex transmission coefficient S _{21 (2)} (real part S ′ _{21 (2)} and imaginary part S ″ _{21 (2)} ). Only the complex transmission coefficients S _{21 (1)} and S _{21 (2)} are measured, and it is not necessary to measure the complex reflection coefficient S ₁₁ that is difficult to calibrate.

次に、同軸線路１０内の空間を複数の均質な領域に分割し、領域の境界面において電磁界の連続条件が満たされるよう、測定した２つの複素透過係数Ｓ_{２１（１）}、Ｓ_{２１（２）}から、被測定試料２０の複素誘電率ε_rおよび複素透磁率μ_rを求める。具体的には、被測定試料２０の複素誘電率ε_rの実部ε´_rと虚部ε″_rの初期値としてε´_r ^(０) _、ε″_r ^（０）および複素誘電率μ_rの実部μ´_rと虚部μ″_rの初期値としてμ´_r ^(０) _、μ″_r ^（０）を適宜定めて、計測した複素透過係数Ｓ_{２１（１）、}Ｓ_{２１（２）}との差がともに所定の許容値未満となるまで、繰り返し複素透過係数Ｓ_{２１（１）、}Ｓ_{２１（２）}を算出し、被測定試料２０の複素誘電率ε_rおよび複素透磁率μ_rを求める。同軸線路１０を用いるため、広周波数帯域において連続的に複素誘電率ε_rおよび複素誘電率μ_rを高精度に測定することができる。また、高精度な電磁界解析を用いるので、複素誘電率ε_rおよび複素誘電率μ_rを高精度に測定することができる。 Next, the space in the coaxial line 10 is divided into a plurality of homogeneous regions, and the measured two complex transmission coefficients S _{21 (1)} and S _{21 ( From 2)} , the complex permittivity ε _r and complex permeability μ _r of the sample 20 to be measured are obtained. Specifically, ε ′ _r ⁽⁰⁾ _, ε ″ _r ⁽⁰⁾ and complex dielectric constant μ _r as initial values of real part ε ′ _r and imaginary part ε ″ _r of complex dielectric constant ε _r of sample 20 to be measured. real Myu' _r and the imaginary part μ "μ'as an initial value of _{_r r} ^_(0), μ" of _r ⁽⁰⁾ the suitably determined, complex transmission coefficient _{S 21} measured _{(1), S 21 (2} ) The complex transmission coefficients S _{21 (1) and} S _{21 (2)} are calculated repeatedly until the difference between the two values is less than the predetermined allowable value, and the complex permittivity ε _r and the complex permeability μ _r of the sample 20 to be measured are calculated. Ask. Since the coaxial line 10 is used, the complex dielectric constant ε _r and the complex dielectric constant μ _r can be continuously measured with high accuracy in a wide frequency band. In addition, since highly accurate electromagnetic field analysis is used, the complex dielectric constant ε _r and the complex dielectric constant μ _r can be measured with high accuracy.

以下、本発明の第３の実施の形態に係る電磁気特性の測定方法について、図面に基づき説明する。この測定方法は、図７（ａ）に示すように、内導体１１と外導体１２とを短絡する短絡板１３をｚ軸方向端部に設けた同軸線路１０を用いる。まず、軸方向直交断面に空隙を設けて被測定試料２０を同軸線路１０に部分装荷する。被測定試料２０を断面全面に隙間なく充填する必要がないので、被測定試料２０の作成時に高い寸法精度が求められない。そして、不図示のベクトル・ネットワーク・アナライザ等の透過特性測定装置を用いて、同軸線路１０の短絡板１３を設けた側とは反対側のｚ軸方向端面側から基本波Ｈ^INCを入射し、複素反射係数Ｓ_{１１（１）}（実部Ｓ´_{１１（１）}と虚部Ｓ″_{１１（１）}）を計測する。同軸線路１０の軸方向一端が短絡されているので、校正を容易に行うことができ、複素反射係数Ｓ_{１１（１）}を高精度に測定することが可能となる。 Hereinafter, a method for measuring electromagnetic characteristics according to a third embodiment of the present invention will be described with reference to the drawings. As shown in FIG. 7A, this measurement method uses a coaxial line 10 in which a short-circuit plate 13 for short-circuiting the inner conductor 11 and the outer conductor 12 is provided at the end in the z-axis direction. First, a gap is provided in the cross section orthogonal to the axial direction, and the sample 20 to be measured is partially loaded on the coaxial line 10. Since it is not necessary to fill the entire surface of the measurement object 20 with no gap, high dimensional accuracy is not required when the measurement object 20 is created. Then, using a transmission characteristic measuring device such as a vector network analyzer (not shown), the fundamental wave H ^INC is incident from the z-axis direction end face side opposite to the side where the short-circuit plate 13 of the coaxial line 10 is provided, The complex reflection coefficient S _{11 (1)} (real part S ′ _{11 (1)} and imaginary part S ″ _{11 (1)} ) is measured. Since one end of the coaxial line 10 in the axial direction is short-circuited, calibration is easily performed. Thus, the complex reflection coefficient S _{11 (1)} can be measured with high accuracy.

次に、図７（ｂ）に示すように、被測定試料２０のｚ軸方向の装荷位置を変更する。被測定試料２０は１つしか必要としないので、被測定試料２０間のばらつきが問題とならない。なお、被測定試料２０の変更後の装荷位置は任意でよい。そして、上記透過特性測定装置を用いて、同軸線路１０のｚ軸方向端面側から基本波Ｈ^INCを入射し、複素反射係数Ｓ_{１１（２）}（実部Ｓ´_{１１（２）}と虚部Ｓ″_{１１（２）}）を計測する。 Next, as shown in FIG. 7B, the loading position of the sample 20 to be measured in the z-axis direction is changed. Since only one sample 20 to be measured is required, variations between the samples 20 to be measured do not matter. In addition, the loading position after the change of the sample 20 to be measured may be arbitrary. Then, using the transmission characteristic measuring apparatus, the fundamental wave H ^INC is incident from the end face side of the coaxial line 10 in the z-axis direction, and the complex reflection coefficient S _{11 (2)} (real part S ′ _{11 (2)} and imaginary part S ″ _{11 (2)} ) is measured.

次に、同軸線路１０内の空間を複数の均質な領域に分割し、領域の境界面において電磁界の連続条件が満たされるよう、測定した２つの複素反射係数Ｓ_{１１（１）、}Ｓ_{１１（２）}から、被測定試料２０の複素誘電率ε_rおよび複素透磁率μ_rを求める。具体的には、被測定試料２０の複素誘電率ε_rの実部ε´_rと虚部ε″_rの初期値としてε´_r ^(０) _、ε″_r ^（０）および複素誘電率μ_rの実部μ´_rと虚部μ″_rの初期値としてμ´_r ^(０) _、μ″_r ^（０）を適宜定めて、計測した複素反射係数Ｓ_{１１（１）、}Ｓ_{１１（２）}との差がともに所定の許容値未満となるまで、繰り返し複素反射係数Ｓ_{１１（１）、}Ｓ_{１１（２）}を算出し、被測定試料２０の複素誘電率ε_rおよび複素透磁率μ_rを求める。同軸線路１０を用いるため、広周波数帯域において連続的に複素誘電率ε_rおよび複素誘電率μ_rを高精度に測定することができる。また、高精度な電磁界解析を用いるので、複素誘電率ε_rおよび複素誘電率μ_rを高精度に測定することができる。 Next, the space in the coaxial line 10 is divided into a plurality of homogeneous regions, and the measured two complex reflection coefficients S _{11 (1),} S _{11 ( From 2)} , the complex permittivity ε _r and complex permeability μ _r of the sample 20 to be measured are obtained. Specifically, ε ′ _r ⁽⁰⁾ _, ε ″ _r ⁽⁰⁾ and complex dielectric constant μ _r as initial values of real part ε ′ _r and imaginary part ε ″ _r of complex dielectric constant ε _r of sample 20 to be measured. real Myu' _r and the imaginary part μ "μ'as an initial value of _{_r r} ^_(0), μ" of _r ⁽⁰⁾ the determined appropriate, the complex reflection coefficient _{S 11} measured _{(1), S 11 (2} ) The complex reflection coefficients S _{11 (1) and} S _{11 (2)} are calculated repeatedly until the difference between the _two and the sample is less than the predetermined tolerance, and the complex permittivity ε _r and the complex permeability μ _r of the sample 20 to be measured are calculated. Ask. Since the coaxial line 10 is used, the complex dielectric constant ε _r and the complex dielectric constant μ _r can be continuously measured with high accuracy in a wide frequency band. In addition, since highly accurate electromagnetic field analysis is used, the complex dielectric constant ε _r and the complex dielectric constant μ _r can be measured with high accuracy.

なお、本発明は上記実施の形態に限定されるものではなく、本発明の要旨の範囲内で種々の変形実施が可能である。例えば、同軸線路１０に被測定試料２０を部分装荷する位置や態様は限定されない。また、被測定試料２０のｚ軸方向の装荷位置の変更し、かつ電磁気特性が既知の試料２１を追加して装荷する測定方法であってもよい。また、同軸線路１０内の領域の分割方法についても限定されない。また、数値計算にガレルキン法を用い基底関数ｆ_ｋ（ρ）をルーフトップ関数としたが、これに限定されるものでもない。 The present invention is not limited to the above embodiment, and various modifications can be made within the scope of the gist of the present invention. For example, the position and aspect in which the sample 20 to be measured is partially loaded on the coaxial line 10 is not limited. Further, the measurement method may be such that the loading position in the z-axis direction of the sample 20 to be measured is changed and the sample 21 having a known electromagnetic characteristic is added and loaded. Further, the method for dividing the region in the coaxial line 10 is not limited. Moreover, although the Galerkin method was used for the numerical calculation and the basis function f _k (ρ) was the rooftop function, it is not limited to this.

本発明の実施形態に係る電磁気特性の測定方法において、被測定試料を同軸線路に部分装荷した状態を模式的に示し、（ａ）は斜視図、（ｂ）は断面図である。In the electromagnetic characteristic measuring method according to the embodiment of the present invention, a state in which a sample to be measured is partially loaded on a coaxial line is schematically shown, (a) is a perspective view, and (b) is a cross-sectional view. 被測定試料を部分装荷した同軸線路内の分割した領域を概念的に説明する部分断面図である。It is a fragmentary sectional view which illustrates notionally the divided field in the coaxial line which carried the sample part partially loaded. 固有関数を概念的に示すグラフであり、（ａ）は均質な領域における固有関数を、（ｂ）は不均質な領域における固有関数をそれぞれ示す。It is a graph which shows an eigenfunction conceptually, (a) shows the eigenfunction in a homogeneous area | region, (b) shows the eigenfunction in an inhomogeneous area | region, respectively. 同軸線路に部分装荷された被測定試料のＳパラメータの比誘電率依存性を示すグラフであり、（ａ）は振幅を、（ｂ）は位相をそれぞれ示す。It is a graph which shows the dielectric constant dependence of the S parameter of the to-be-measured sample partially loaded on the coaxial line, (a) shows an amplitude, (b) shows a phase, respectively. 本発明の第１の実施形態に係る電磁気特性の測定方法において、同軸線路に部分装荷された被測定試料の複素誘電率ε_rの周波数依存性を求めたグラフである。5 is a graph showing the frequency dependence of the complex dielectric constant ε _r of a sample to be measured partially loaded on a coaxial line in the electromagnetic characteristic measurement method according to the first embodiment of the present invention. 本発明の第２の実施形態に係る電磁気特性の測定方法において、電磁気特性が既知の試料２１を追加して装荷した状態を概念的に示す断面図である。It is sectional drawing which shows notionally the state which added and loaded the sample 21 with a known electromagnetic characteristic in the measuring method of the electromagnetic characteristic which concerns on the 2nd Embodiment of this invention. 本発明の第３の実施形態に係る電磁気特性の測定方法において、（ａ）は被測定試料２０を最初に装荷した状態を概念的に示す断面図であり、（ｂ）は被測定試料２０の装荷位置を変更した状態を概念的に示す断面図である。In the electromagnetic characteristic measuring method according to the third embodiment of the present invention, (a) is a cross-sectional view conceptually showing a state in which the sample 20 to be measured is initially loaded, and (b) is a diagram of the sample 20 to be measured. It is sectional drawing which shows notionally the state which changed the loading position.

符号の説明Explanation of symbols

１０同軸線路
１１内導体
１２外導体
１３短絡板
２０被測定試料
２１電磁気特性が既知の試料 10 Coaxial line 11 Inner conductor 12 Outer conductor 13 Short-circuit plate 20 Sample to be measured 21 Sample with known electromagnetic characteristics

Claims

軸方向直交断面に空隙を設けて被測定試料を装荷した同軸線路に電磁波を入射し、複素透過係数を測定するステップと、
電磁気特性が既知の試料を追加して装荷した同軸線路に電磁波を入射し、複素透過係数を測定するステップと、
前記同軸線路内の空間を複数の均質な領域に分割し、前記領域の境界面において電磁界の連続条件が満たされるよう、前記測定した２つの複素透過係数から、前記被測定試料の複素透磁率、または複素誘電率および複素透磁率を求めるステップと、を備えることを特徴とする電磁気特性の測定方法。 An electromagnetic wave is incident on a coaxial line loaded with a sample to be measured by providing a gap in an axially orthogonal cross section, and measuring a complex transmission coefficient;
Injecting an electromagnetic wave into a coaxial line loaded with a sample having a known electromagnetic property and measuring a complex transmission coefficient;
The space in the coaxial line is divided into a plurality of homogeneous regions, and the complex permeability of the sample to be measured is calculated from the measured two complex transmission coefficients so that the electromagnetic field continuity condition is satisfied at the boundary surface of the region. Or a step of obtaining a complex permittivity and a complex permeability, and a method for measuring electromagnetic characteristics.