JP4370463B2

JP4370463B2 - Broadband high frequency dielectric constant measurement method and apparatus

Info

Publication number: JP4370463B2
Application number: JP2003355062A
Authority: JP
Inventors: 英二田辺
Original assignee: 株式会社エーイーティー
Priority date: 2003-10-15
Filing date: 2003-10-15
Publication date: 2009-11-25
Anticipated expiration: 2023-10-15
Also published as: JP2005121422A

Description

本発明は、１GHz 以上のマイクロ波、ミリ波帯の広帯域高周波における複素誘電率を測定する方法およびその装置に関する。特に測定部のプローブの先端部を極めて微細構造にし、測定誘電体の微小部分の複素誘電率を測定し被測定誘電体の複素誘電率の分布を求めることができる方法および装置に関する。 The present invention relates to a method and apparatus for measuring a complex dielectric constant in a microwave and millimeter wave band at a frequency of 1 GHz or higher and a broadband high frequency. In particular, the present invention relates to a method and an apparatus capable of obtaining the distribution of the complex dielectric constant of the dielectric to be measured by making the tip of the probe of the measurement unit have an extremely fine structure and measuring the complex dielectric constant of a minute portion of the measurement dielectric.

従来の高周波帯域における複素誘電率測定は、共振器に被測定物を挿入する非破壊測定が一般的であり、共振周波数近傍における離散的な周波数に制約される。また、被測定物の内の空間的な誘電率の分布を測定することは困難である。 Conventional measurement of complex permittivity in a high frequency band is generally nondestructive measurement in which an object to be measured is inserted into a resonator, and is limited to discrete frequencies in the vicinity of the resonance frequency. In addition, it is difficult to measure the spatial permittivity distribution in the object to be measured.

近年のナノテクノロジー分野の発展によって、ＭＥＭＳ（Micro Electro Mechanical System）等の非常に微細なデバイスが各分野で研究開発されているなかで、高周波領域における電気的な特性としての複素誘電率の空間的な分布情報を求められるようになっている。また、ＵＷＢ（ウルトラワイドバンド）技術などの浸透により、連続的な広帯域誘電率情報が今後ますます重要となってくる。つまり所望の周波数における極めて狭い領域の誘電率情報を正確に得たいという強い要請がある。 With the recent development of the nanotechnology field, very fine devices such as MEMS (Micro Electro Mechanical System) are being researched and developed in various fields. Distribution information is required. In addition, continuous broadband dielectric constant information will become more and more important in the future due to the penetration of UWB (ultra wide band) technology and the like. That is, there is a strong demand for accurately obtaining dielectric constant information in a very narrow region at a desired frequency.

本件発明者は、後述するように測定対象である誘電体を励起する信号の波形を周知のガウス関数で定義されるパルス（GAUSSIAN PULSE) にすると信号の発生およびその後の処理に種々の利点があることに着目した。
本発明の目的は、励起パルスの波形を考慮するとともに、測定部のプローブの先端部を極めて微細構造にし、測定誘電体の微小部分の複素誘電率を測定する方法により測定誘電体の複素誘電率の分布を求めることにある。
なお、本発明において、主要な数式の理解を容易にするために時間軸の信号は信号波、周波数軸の信号は信号波形と呼ぶことにする。
そして信号波については必要に応じて（ｔ）を附し、信号波形については同様に（ω）を附することにする。以下に主要な例を示す。
入射信号波：Ｖ _i （ｔ）
反射信号波：Ｖ _r （ｔ）
入射信号波形：Ｖ _i （ω）
反射信号波形：Ｖ _r （ω） As will be described later, the present inventor has various advantages in signal generation and subsequent processing when the waveform of a signal for exciting a dielectric to be measured is changed to a pulse (GAUSSIAN PULSE) defined by a well-known Gaussian function. Focused on that.
The object of the present invention is to take into account the waveform of the excitation pulse, make the tip of the probe of the measurement unit very fine, and measure the complex dielectric constant of the minute part of the measurement dielectric. It is to obtain the distribution of.
In the present invention, in order to facilitate understanding of the main mathematical expressions, the signal on the time axis is called a signal wave, and the signal on the frequency axis is called a signal waveform.
Further, (t) is attached to the signal wave as necessary, and (ω) is similarly attached to the signal waveform. The main examples are as follows.
Incident signal wave: V _i (t)
Reflected signal wave: V _r (t)
Incident signal waveform: V _i (ω)
Reflected signal waveform: V _r (ω)

前記目的を達成するために、本発明による請求項１記載の広帯域高周波誘電率測定方法は、
同軸開放先端をもつプローブを介して試料に既知の広帯域高周波入射信号波を印加したときに、前記入射信号波Ｖ_i （ｔ），前記試料からの反射信号波Ｖ_r （ｔ）をフーリェ変換して各角周波数ωにおける入射信号波形Ｖ _i （ω），反射信号波形Ｖ _r （ω）を算出し、その結果から前記プローブの負荷である前記試料のインピーダンスＺが前記入射信号波形Ｖ _i （ω），反射信号波形Ｖ _r （ω）および前記プローブを含む供給路の特性インピーダンスＺ ₀ ，位相定数β，経路長ｄの関数として下記の式〔数１〕で与えられることを利用して、前記試料の複素誘電率ε＝ε’＋ｊε”を測定する方法であって、
前記入射信号波Ｖ_i （ｔ）として下記の式〔数３〕で与えられるガウシアン分布の電圧Ｖ_i （ｔ）を印加する入射信号波発生ステップと、
同軸端形状の先端を有するプローブの先端の導体を試料に接触させ前記試料からの反射信号波Ｖ_r （ｔ）を検出するステップと、
前記入射信号波Ｖ _i （ｔ）および前記反射信号波Ｖ _r （ｔ）をフーリェ変換して、各角周波数ωにおける入射信号波形Ｖ _i （ω），反射信号波形Ｖ _r （ω）を算出するステップと、
任意の各角周波数ωに対応する前記インピーダンスＺの虚数部からε’、実数部からε”に相当する量を演算して前記試料の複素誘電率を測定する演算ステップと、から構成されている。
記

なお、上記〔数１〕式のＶ _i ，Ｖ _r は、Ｖ _i （ω），Ｖ _r （ω）の意味で用いている。 In order to achieve the above object, a broadband high-frequency dielectric constant measuring method according to claim 1 according to the present invention comprises:
When a known broadband high-frequency incident signal wave is applied to the sample via a probe having a coaxial open tip, the incident signal wave V _i (t) and the reflected signal wave V _r (t) from the sample are Fourier transformed. Then, the incident signal waveform V _i (ω) and the reflected signal waveform V _r (ω) at each angular frequency ω are calculated, and from the result, the impedance Z of the sample, which is the load of the probe, becomes the incident signal waveform V _i (ω ), The reflected signal waveform V _r (ω) and the characteristic impedance Z _{0 of} the supply path including the probe , the phase constant β, and the function given by the following equation [Formula 1] as a function of the path length d , A method for measuring a complex dielectric constant ε = ε ′ + jε ″ of a sample,
An incident signal wave generating step of applying a voltage V _i (t) having a Gaussian distribution given by the following equation (Equation 3 ) as the incident signal wave V _i (t) ;
Detecting a reflected signal wave V _r (t) from the sample by bringing a conductor at the tip of the probe having a coaxial end shape into contact with the sample;
The incident signal wave V _i (t) and the reflected signal wave V _r (t) by Fourier transform, and calculates an incident signal waveform V _i at each angular frequency omega (omega), the reflected signal waveform V _r (ω) Steps,
A calculation step for calculating a complex dielectric constant of the sample by calculating an amount corresponding to ε ′ from the imaginary part and ε ″ from the real part of the impedance Z corresponding to each arbitrary angular frequency ω . .
Record

Note that V _i and V _r in the above [Expression 1] are used to mean V _i (ω) and V _r (ω).

本発明による請求項５記載の装置は、本発明方法の実施に用いられる装置であって、
同軸開放先端をもつプローブを介して試料に既知の広帯域高周波入射信号波を印加したときに、前記入射信号波Ｖ _i （ｔ），前記試料からの反射信号波Ｖ _r （ｔ）をフーリェ変換して各角周波数ωにおける入射信号波形Ｖ _i （ω），反射信号波形Ｖ _r （ω）を算出し、その結果から前記プローブの負荷である前記試料のインピーダンスＺが前記入射信号波形Ｖ _i （ω），反射信号波形Ｖ _r （ω）および前記プローブを含む供給路の特性インピーダンスＺ ₀ ，位相定数β，経路長ｄの関数として下記の式〔数１〕で与えられることを利用して、前記試料の複素誘電率ε＝ε’＋ｊε”を測定する方法を実施するための広帯域高周波誘電率測定装置であって、
前記入射信号波Ｖ _i （ｔ）として下記の式〔数３〕で与えられるガウシアン分布の電圧Ｖ _i （ｔ）を発生する発振器と、
前記発振器に接続された同軸ケーブルと、
前記同軸ケーブルに接続され同軸開放先端を試料に接触させて前記入射信号波Ｖ _i （ｔ）を印加し、反射信号波Ｖ _r （ｔ）を受けるプローブと、
前記入射信号波Ｖ _i （ｔ）を前記同軸ケーブルに接続し、前記反射信号波Ｖ _r （ｔ）を取り出す方向性結合器と、
前記入射信号波Ｖ _i （ｔ）と前記反射信号波Ｖ _r （ｔ）をフーリェ変換して、各角周波数ωにおける入射信号波形Ｖ _i （ω），反射信号波形Ｖ _r （ω）を算出する手段と、
任意の各角周波数ωに対応する前記インピーダンスＺの虚数部からε’、実数部からε”に相当する量を演算して前記試料の複素誘電率を測定する演算手段と、から構成されている。
記

The device according to claim 5 according to the present invention is a device used for carrying out the method of the present invention,
Through a probe having a coaxial opening tip upon application of a known wideband RF incident signal wave to the specimen, the incident signal wave V _i (t), the reflected signal wave V _r (t) from the sample and Fourier Transform Then, the incident signal waveform V _i (ω) and the reflected signal waveform V _r (ω) at each angular frequency ω are calculated, and from the result, the impedance Z of the sample, which is the load of the probe, becomes the incident signal waveform V _i (ω ), The reflected signal waveform V _r (ω) and the characteristic impedance Z _{0 of} the supply path including the probe , the phase constant β, and the function given by the following equation [Formula 1] as a function of the path length d, A broadband high-frequency dielectric constant measuring apparatus for carrying out a method for measuring a complex dielectric constant ε = ε ′ + jε ″ of a sample ,
An oscillator that generates a Gaussian-distributed voltage V _i (t) given by the following equation (Equation 3) as the incident signal wave V _i (t) :
A coaxial cable connected to the oscillator ;
A probe said coaxial open distal is connected to the coaxial cable in contact with the sample incident signal wave V _i (t) is marked pressurized, receives a reflected signal wave V _r (t),
A directional coupler for connecting the incident signal wave V _i (t) to the coaxial cable and extracting the reflected signal wave V _r (t) ;
The incident signal wave V _i (t) and the reflected signal wave V _r (t) are Fourier transformed to calculate the incident signal waveform V _i (ω) and the reflected signal waveform V _r (ω) at each angular frequency ω. Means,
And an arithmetic means for measuring the complex dielectric constant of the sample by calculating an amount corresponding to ε ′ from the imaginary part and ε ″ from the real part corresponding to each arbitrary angular frequency ω . .
Record

本発明による請求項３記載の広帯域高周波誘電率測定方法は、
同軸開放先端をもつプローブを介して未知試料に既知の広帯域高周波入射信号波Ｖ _i （ｔ）を印加したときの前記未知試料からの反射信号波がＶ _rx （ｔ）、同様に既知試料に前記広帯域高周波入射信号波Ｖ _i （ｔ）を印加したときの前記既知試料からの反射信号波がＶ _rs （ｔ）、前記既知試料のインピーダンスがＺ _s であるときに、前記反射信号波Ｖ _rs （ｔ），前記反射信号波Ｖ _rx （ｔ）をフーリェ変換して各角周波数ωにおける反射信号波形Ｖ _rs （ω），反射信号波形Ｖ _rx （ω）を算出し、その結果から前記未知試料のインピーダンスＺ _x が前記反射信号波形Ｖ _rs （ω），反射信号波形Ｖ _rx （ω），前記既知試料のインピーダンスＺ _s および前記プローブを含む供給路の特性インピーダンスＺ ₀ ，位相定数β，経路長ｄの関数として下記の式〔数２〕で与えられることを利用して、前記未知試料の複素誘電率ε＝ε’＋ｊε”を測定する方法であって、
前記入射信号波Ｖ_i （ｔ）として下記の式〔数３〕で与えられるガウシアン分布の電圧Ｖ_i （ｔ）を印加する入射信号波発生ステップと、
同軸端形状の先端を有するプローブの先端の導体を既知および未知試料に接触させて前記入射信号波Ｖ _i （ｔ）を入射させ前記それぞれの試料からの反射信号波Ｖ _rs （ｔ），Ｖ _rx （ｔ）を検出するステップと、
前記各反射信号波Ｖ _rs （ｔ），Ｖ _rx （ｔ）をフーリェ変換して、各角周波数ωにおける反射信号波形Ｖ _rs （ω），反射信号波形Ｖ _rx （ω）を算出するステップと、
任意の各角周波数ωに対応する前記インピーダンスＺ _x の虚数部からε’、実数部からε”に相当する量を演算して前記未知試料の複素誘電率を測定する演算ステップと、から構成されている。
記

なお、上記〔数２〕式のＶ _rs ，Ｖ _rx は、Ｖ _rs （ω），Ｖ _rx （ω）の意味で用いている。 The wide-band high-frequency dielectric constant measuring method according to claim 3 of the present invention is
When a known broadband high-frequency incident signal wave V _i (t) is applied to an unknown sample via a probe having a coaxial open tip, the reflected signal wave from the unknown sample is V _rx (t) , and the same is applied to the known sample. When a broadband high-frequency incident signal wave V _i (t) is applied, the reflected signal wave from the known sample is V _rs (t), and when the impedance of the known sample is Z _s , the reflected signal wave V _rs ( t), the reflected signal wave V _rx (t) is subjected to Fourier transform to calculate a reflected signal waveform V _rs (ω) and a reflected signal waveform V _rx (ω) at each angular frequency ω. The impedance Z _x is the reflected signal waveform V _rs (ω), the reflected signal waveform V _rx (ω), the impedance Z _{s of the} known sample, the characteristic impedance Z _{0 of} the supply path including the probe , the phase constant β, and the path length d. As a function of By utilizing the fact that given by expression (2), a method for measuring the complex dielectric constant of an unknown sample ε = ε '+ jε ",
The incident signal wave generating step of applying said incident signal wave V _i (t) as the voltage V _i of the Gaussian distribution given by the following equation Formula 3 (t),
The incident signal wave V _i (t) is incident by bringing the conductor at the tip of the probe having a coaxial end into contact with the known and unknown samples , and the reflected signal waves V _rs (t) and V _rx from the respective samples. Detecting (t) ;
A Fourier transform of the reflected signal waves V _rs (t) and V _rx (t ) to calculate a reflected signal waveform V _rs (ω) and a reflected signal waveform V _rx (ω) at each angular frequency ω ;
And calculating a complex dielectric constant of the unknown sample by calculating an amount corresponding to ε ′ from the imaginary part and ε ″ from the real part of the impedance Z _x corresponding to each arbitrary angular frequency ω. ing.
Record

Note that V _rs and V _{rx in the} formula [2] are used to mean V _rs (ω) and V _rx (ω).

本発明による請求項６記載の装置は、
同軸開放先端をもつプローブを介して未知試料に既知の広帯域高周波入射信号波Ｖ _i （ｔ）を印加したときの前記未知試料からの反射信号波がＶ _rx （ｔ）、同様に既知試料に前記広帯域高周波入射信号波Ｖ _i （ｔ）を印加したときの前記既知試料からの反射信号波がＶ _rs （ｔ）、前記既知試料のインピーダンスがＺ _s であるときに、前記反射信号波Ｖ _rs （ｔ），前記反射信号波Ｖ _rx （ｔ）をフーリェ変換して各角周波数ωにおける反射信号波形Ｖ _rs （ω），反射信号波形Ｖ _rx （ω）を算出し、その結果から前記未知試料のインピーダンスＺ _x が前記反射信号波形Ｖ _rs （ω），前記反射信号波形Ｖ _rx （ω），前記既知試料のインピーダンスＺ _s および前記プローブを含む供給路の特性インピーダンスＺ ₀ ，位相定数β，経路長ｄの関数として下記の式〔数２〕で与えられることを利用して、前記未知試料の複素誘電率ε＝ε’＋ｊε”を測定する方法を実施するための広帯域高周波誘電率測定装置であって、
前記試料に印加される入射信号波Ｖ _i （ｔ）として下記の式〔数３〕で与えられるガウシアン分布の電圧Ｖ_i （ｔ）を発生する発振器と、
前記発振器に接続された同軸ケーブルと、
前記同軸ケーブルに接続され同軸開放先端を既知および未知試料に接触させて前記入射信号波Ｖ _i （ｔ）を印加して各反射信号波Ｖ _rs （ｔ），Ｖ _rx （ｔ）を受けるプローブと、
前記入射信号波Ｖ _i （ｔ）を前記同軸ケーブルに接続し、前記各反射信号波Ｖ _rs （ｔ），Ｖ _rx （ｔ）を取り出す方向性結合器と、
前記方向性結合器から取り出された既知試料および未知試料からの反射信号波Ｖ _rs （ｔ），Ｖ _rx （ｔ）をフーリェ変換して、各角周波数ωにおける反射信号波形Ｖ _rs （ω），反射信号波形Ｖ _rx （ω）を算出する手段と、
任意の各角周波数ωに対応する前記インピーダンスＺ _x の虚数部からε’、実数部からε”に相当する量を演算して前記未知試料の複素誘電率を測定する演算手段と、から構成されている。
記

An apparatus according to claim 6 according to the present invention comprises:
When a known broadband high-frequency incident signal wave V _i (t) is applied to an unknown sample via a probe having a coaxial open tip, the reflected signal wave from the unknown sample is V _rx (t) , and the same is applied to the known sample. When a broadband high-frequency incident signal wave V _i (t) is applied, the reflected signal wave from the known sample is V _rs (t), and when the impedance of the known sample is Z _s , the reflected signal wave V _rs ( t), the reflected signal wave V _rx (t) is subjected to Fourier transform to calculate a reflected signal waveform V _rs (ω) and a reflected signal waveform V _rx (ω) at each angular frequency ω. The impedance Z _x is the reflected signal waveform V _rs (ω), the reflected signal waveform V _rx (ω), the impedance Z _{s of the} known sample, the characteristic impedance Z _{0 of} the supply path including the probe , the phase constant β, the path length as a function of d A of utilizing the fact that given by equation [Equation 2], a broadband high-frequency dielectric constant measuring apparatus for carrying out the method for measuring the complex dielectric constant of an unknown sample ε = ε '+ jε ",
An oscillator for generating the voltage V _i of the Gaussian distribution, given as an incident signal wave V _i (t) which is applied to the sample by the following equation Formula 3 (t),
A coaxial cable connected to the oscillator ;
A probe connected to the coaxial cable and contacting the known and unknown sample with the open end of the coaxial and applying the incident signal wave V _i (t) to receive the reflected signal waves V _rs (t) and V _rx (t) ; ,
Entering-morphism signal wave V _i (t) is connected to the coaxial cable, and a directional coupler for taking out the respective reflected signal wave V _rs (t), V _rx (t),
The reflected signal waves V _rs (t) and V _rx (t) from the known sample and the unknown sample taken out from the directional coupler are Fourier-transformed, and the reflected signal waveforms V _rs (ω), Means for calculating a reflected signal waveform V _rx (ω);
And calculating means for calculating a complex dielectric constant of the unknown sample by calculating an amount corresponding to ε ′ from the imaginary part and ε ″ from the real part of the impedance Z _x corresponding to each arbitrary angular frequency ω. ing.
Record

本発明による請求項２記載の方法は、請求項１記載の広帯域高周波誘電率測定方法において、
前記入射信号波Ｖ _i （ｔ）、前記入射信号波形Ｖ _i （ω）および前記反射信号波形Ｖ _r （ω）はそれぞれ下記の式で与えられるものとする。
記

本発明による請求項４記載の方法は、請求項３記載の広帯域高周波誘電率測定方法において、
前記反射信号波形Ｖ _rs （ω）、前記反射信号波形Ｖ _rx （ω）はそれぞれ下記の式で与えられるものとする。
記

The method according to claim 2 of the present invention is the method of measuring a broadband high-frequency dielectric constant according to claim 1,
The incident signal wave V _i (t), the incident signal waveform V _i (ω), and the reflected signal waveform V _r (ω) are respectively given by the following equations.
Record

According to a fourth aspect of the present invention, in the method for measuring a broadband high-frequency dielectric constant according to the third aspect,
The reflected signal waveform V _rs (ω) and the reflected signal waveform V _rx (ω) are respectively given by the following equations.
Record

本発明による請求項７記載の装置は、請求項５または６記載の広帯域高周波誘電率測定装置において、
前記プローブは、その外径は２ｍｍ以下、芯の外径は１ｍｍ以下で、プローブの先端に向かってテーパーを持ち、測定部の先端の芯の外径が０．２ｍｍ以下にしてある。
本発明による請求項８記載の装置は、請求項５または６記載の広帯域高周波誘電率測定装置において、
前記装置は表示手段を含み、算出したε’，ε”のスペクトル表示を行うように構成されている。 The apparatus according to claim 7 of the present invention is the broadband high-frequency dielectric constant measuring apparatus according to claim 5 or 6 ,
The probe has an outer diameter of 2 mm or less, an outer diameter of the core of 1 mm or less, has a taper toward the tip of the probe, and an outer diameter of the core at the tip of the measurement unit is 0.2 mm or less.
The device of claim 8, wherein according to the invention, in a wideband high-frequency dielectric constant measuring apparatus according to claim 5 or 6 wherein,
The apparatus includes a display unit, issued calculated epsilon ', is configured to perform a spectral display of epsilon ".

本発明による請求項９記載の装置は、請求項８記載の装置において、
前記表示手段はさらに入射信号波Ｖ_i （ｔ）と試料からの反射信号波Ｖ_r （ｔ）応答波形を同時に表示するように構成されている。
本発明による請求項１０記載の装置は、請求項８記載の装置において、
前記表示手段はさらに既知試料からの反射信号波Ｖ_rs （ｔ）と未知試料からの反射信号波Ｖ_rx （ｔ）の時間パルス応答波形を同時または別々に表示するように構成されている。
本発明による請求項１１記載の装置は、請求項８記載の装置において、
前記表示手段はさらに信号の時間パルス応答波形表示と、誘電率の周波数スペクトル表示との間に演算中を示す表示を行うように構成されている。 A device according to claim 9 according to the present invention is the device according to claim 8,
The display means is further configured to simultaneously display an incident signal wave V _i (t) and a reflected signal wave V _r (t) response waveform from the sample.
A device according to claim 10 according to the present invention is the device according to claim 8,
The display means is further configured to simultaneously or separately display the reflected signal wave V _rs (t) and the time pulse response waveform of the reflected signal wave V _rx (t) from an unknown sample from a known sample.
An apparatus according to claim 11 according to the present invention is the apparatus according to claim 8,
The display means is further configured to perform a display indicating that the calculation is being performed between the time pulse response waveform display of the signal and the frequency spectrum display of the dielectric constant.

本発明による請求項１２記載の装置は、請求項８記載の装置において、
前記表示手段はさらに信号の時間パルス応答波形表示とともに測定上限および下限の周波数のデジタル表示を行い、誘電率の周波数スペクトル表示とともに指定した特定の周波数におけるε’，ε”のデジタル表示を行うように構成されている。 A device according to claim 12 according to the present invention is the device according to claim 8,
It said display means performs a digital display of the frequency of the measurement upper and lower limits over time pulse response waveform display further signal, epsilon at a particular frequency specified with the frequency spectrum display of permittivity ', to perform the digital representation of epsilon " It is configured.

以上、説明したように本発明は、検出プローブに試料を接触するだけの簡単な操作で、１GHｚから２５GHｚの高周波マイクロ波の複素誘電率を自動的に測定できる方法および装置を提供できる。本発明のプローブの先端部は極めて細いので、測定点を沢山選べば、複素誘電率の平面的な分布を求めることができる。また、マイクロ波の近接場の効果により、接触面から極めて薄い膜の領域の誘電率を測定することができ、薄膜の誘電率も測定できる効果がある。
本発明方法は非破壊測定法であるので、誘電体を破壊しないで実際に動作する装置に設置された状態で測定でき、解析結果が動作状態を正確に表すデータが得られ、製造現場における品質管理や事故の対策に利用できる。 As described above, the present invention can provide a method and apparatus capable of automatically measuring the complex dielectric constant of a high-frequency microwave of 1 GHz to 25 GHz with a simple operation of simply contacting a sample with a detection probe. Since the tip of the probe of the present invention is extremely thin, the planar distribution of the complex dielectric constant can be obtained by selecting many measurement points. In addition, due to the effect of the near-field of the microwave, the dielectric constant of the extremely thin film region from the contact surface can be measured, and the dielectric constant of the thin film can be measured.
Since the method of the present invention is a non-destructive measurement method, it can be measured in a state where it is installed in a device that actually operates without destroying the dielectric, and data that accurately represents the operating state can be obtained as a result of analysis. It can be used for management and accident countermeasures.

また、本発明のプローブの測定端の構造はテーパー状にした先端形状であり、プローブ開口は直径０．２ｍｍ以下と、測定周波数の波長に比して十分に小さい。よって被測定物の誘電率の変化によるプローブ先端部の電場の変化は、静電場解析、つまり等価的容量への置き換えが非常によくマッチングしていることが、高周波電磁界解析および静電場解析の適用による検討から得られている。 The structure of the measurement end of the probe of the present invention has a tapered tip shape, and the probe opening is 0.2 mm or less in diameter, which is sufficiently smaller than the wavelength of the measurement frequency. Therefore, the change in the electric field at the probe tip due to the change in the dielectric constant of the object to be measured is very well matched with the electrostatic field analysis, that is, replacement with the equivalent capacitance. Obtained from application studies.

以下図面等を参照して本発明による装置の実施の形態を説明する。図１を参照して本発明による複素誘電率測定装置の基本構成を説明する。
本発明において、複素誘電率の測定周波数の範囲は、稼動する各機器の仕様によって変更することができるが、たとえば、図１の発振器１０１の発振周波数は、１GHｚから２５GHｚの高い周波数でかつ広帯域の周波数領域で動作させることができるようにしてある。
発振器１０１の出力電圧は、時間に関してガウシアン分布の電圧波になる。この電圧は方向性結合器１０２に加わる。方向性結合器１０２の出力に同軸ケーブル１０３が接続されている。この方向性結合器１０２のａ端子には同軸ケーブル１０３からの反射波が出力される。一方発振器１０１の出力電圧はサンプリングオシロスコープ１０６の第１チャンネル（１ＣＨ）に入力される。また反射波はサンプリングオシロスコープ１０６の第２チャンネル（２ＣＨ）に入力される。 Embodiments of an apparatus according to the present invention will be described below with reference to the drawings. The basic configuration of the complex dielectric constant measuring apparatus according to the present invention will be described with reference to FIG.
In the present invention, the range of the complex dielectric constant measurement frequency can be changed according to the specifications of each operating device. For example, the oscillation frequency of the oscillator 101 in FIG. 1 is a high frequency from 1 GHz to 25 GHz and a wide bandwidth. It can be operated in the frequency domain.
The output voltage of the oscillator 101 becomes a voltage wave having a Gaussian distribution with respect to time. This voltage is applied to the directional coupler 102. A coaxial cable 103 is connected to the output of the directional coupler 102. A reflected wave from the coaxial cable 103 is output to the a terminal of the directional coupler 102. On the other hand, the output voltage of the oscillator 101 is input to the first channel (1CH) of the sampling oscilloscope 106. The reflected wave is input to the second channel (2CH) of the sampling oscilloscope 106.

発振器１０１の出力電圧および同軸ケーブル１０３からの反射信号波の電圧が、サンプリングオシロスコープ１０６からディジタルデータとして、データバス１０７を介して、パソコン１０８に入力される。パソコン１０８は、このディジタルデータからフーリェ変換の演算および複素誘電率の計算を実行する。そしてパソコン１０８はその結果を表示する。さらにこの同軸ケーブル１０３の先に本発明方法および装置用に開発されたプローブ１０４が配置されている。本発明のプローブ１０４の先端部は、被測定サンプル１０５に接触している。 The output voltage of the oscillator 101 and the voltage of the reflected signal wave from the coaxial cable 103 are input as digital data from the sampling oscilloscope 106 to the personal computer 108 via the data bus 107. The personal computer 108 performs a Fourier transform operation and a complex dielectric constant calculation from the digital data. The personal computer 108 displays the result. Further, a probe 104 developed for the method and apparatus of the present invention is disposed at the end of the coaxial cable 103. The tip of the probe 104 of the present invention is in contact with the sample 105 to be measured.

次に本発明のプローブ１０４の構造について説明する。プローブ１０４は、図２に示すように、同軸状の伝送路を構成している。同軸の芯線部には内導体２０１があり、この直径は１ｍｍ程度とすることができる。内導体２０１の先の部分は、テーパーがついて、さらに細くなる。被測定サンプル１０５と接する内導体２０１の先端部の直径は、０．２ｍｍ以下になる。このテーパー角度は３０度から４５度程度にしてある。なる。内導体２０１と外導体２０３の間にテフロン（登録商標）などの低損失誘電体２０２が配置されている。このプローブ１０４の先端部までの特性インピーダンスが５０±０．５Ωを維持するように調整してある。
測定の対象である誘電体の最低必要面積は５ｍｍ角程度である。また比誘電率の測定範囲は１から２５程度まで、ｔａｎδは０．２から０．０００５程度まで測定できる。
本発明のプローブ１０４は、このように、サンプルの局部的な領域における誘電体率を測定することができるという特徴がある。 Next, the structure of the probe 104 of the present invention will be described. As shown in FIG. 2, the probe 104 forms a coaxial transmission line. An inner conductor 201 is provided in the coaxial core wire portion, and the diameter thereof can be about 1 mm. The tip portion of the inner conductor 201 is tapered and becomes thinner. The diameter of the tip of the inner conductor 201 in contact with the sample 105 to be measured is 0.2 mm or less. This taper angle is about 30 to 45 degrees. Become. A low-loss dielectric 202 such as Teflon (registered trademark) is disposed between the inner conductor 201 and the outer conductor 203. The characteristic impedance up to the tip of the probe 104 is adjusted to maintain 50 ± 0.5Ω.
The minimum required area of the dielectric to be measured is about 5 mm square. The relative dielectric constant can be measured from about 1 to about 25, and tan δ can be measured from about 0.2 to about 0.0005.
The probe 104 of the present invention is thus characterized in that it can measure the dielectric constant in a local region of the sample.

つぎに高周波マイクロ波におけるサンプルの誘電率を測定する方法の原理について説明する。今、発振器１０１の出力電圧は、時間に対して、ガウシアン分布の形の電圧波を出力する。この電圧を電圧Ｖ_i （ｔ）とする。
この波形の電圧Ｖ_i （ｔ）が測定プローブ部１０４に印加され、プローブの先端部の試料で反射された反射電圧が方向性結合器１０２のａ端子にあらわれる反射信号波をＶ_r （ｔ）とし、この反射信号波Ｖ_r （ｔ）を測定する。ガウシアン分布の電圧Ｖ_i （ｔ）およびこの波形の電圧Ｖ_i （ｔ）のフーリェ変換の関数Ｖ_i （ω）は次の１），２）式で与えられる。

１）
Ｖ_i0は時間に関して変化しない一定の振幅である。

２） Next, the principle of a method for measuring the dielectric constant of a sample in a high frequency microwave will be described. Now, the output voltage of the oscillator 101 outputs a voltage wave having a Gaussian distribution with respect to time. This voltage is defined as voltage V _i (t).
A voltage V _i (t) having this waveform is applied to the measurement probe unit 104, and a reflected signal wave in which the reflected voltage reflected by the sample at the tip of the probe appears at the a terminal of the directional coupler 102 is _expressed as V _r (t). and then, measuring the reflected signal wave V _r (t). The Fourier transform function V _i (ω) of the voltage V _i (t) of the Gaussian distribution and the voltage V _i (t) of this waveform is given by the following equations 1) and 2).

1)
V _i0 is a constant amplitude that does not change with time.

2)

一方測定された反射信号波Ｖ_r （ｔ）のフーリェ変換の関数Ｖ_r （ω）は次の３）式で与えられる。

３）
以上のとおり、それぞれの各周波数に対する反射信号波形の振幅は３）式から算出できる。 On the other hand, the Fourier transform function V _r (ω) of the measured reflected signal wave V _r (t) is given by the following equation (3).

3)
As described above, the amplitude of the reflected signal waveform for each frequency can be calculated from Equation 3).

プローブの先端に複素誘電率の既知の標準試料と測定する未知のサンプルをそれぞれ取り付けたときの入射信号波と反射信号波を測定して、このデータをフーリェ変換したＶ_i （ω）とＶ_rx（ω）ならびにＶ_rs（ω）のデータから測定サンプルの複素誘電率を求める。
ただしＶ_rx（ω）は未知の複素誘電率を測定するサンプルによる反射信号波をフーリェ変換した電圧波形を、Ｖ_rs（ω）は複素誘電率が既知である標準試料による反射信号波をフーリェ変換した電圧波形を示す。 V _i (ω) and V _rx are obtained by measuring the incident signal wave and the reflected signal wave when a standard sample having a known complex dielectric constant and an unknown sample to be measured are attached to the tip of the probe, and Fourier transforming this data. The complex dielectric constant of the measurement sample is obtained from the data of (ω) and V _rs (ω).
However, V _rx (ω) is a voltage waveform obtained by Fourier transform of a reflected signal wave from a sample for measuring an unknown complex dielectric constant, and V _rs (ω) is a Fourier transform of a reflected signal wave from a standard sample having a known complex dielectric constant. Shows the voltage waveform .

以下その算出過程について、説明する。前述したように、本発明方法のために開発されたプローブは図２に示す構造であり、同軸の先にテーパーを持ったプローブがあり、このプローブの先端部に微小な検出部が構成する構造になっている。
いま、回路を単純化し算出しやすい構成とし、理論の筋道を示す。
すなわち同軸とプローブの先端部分の回路は、回路設計の最適化によりほぼ同じ電気特性であると仮定する。この回路は一つの分布定数回路の等価回路で表わされる。詳細な解析の場合は、同軸とプローブの先端部の特性は少し異なるとして、同軸とプローブの先端部の特性の異なる回路が従属接続されているとして計算すればよい。前記の前提条件から、同軸とプローブの先端部の回路は一つの分布定数回路で表現できる。 Below we have the calculation process Nitsu be described. As described above, a probe was developed for the present invention process is a structure shown in FIG. 2, there is a probe having a tapered over coaxial Former, small detector at the tip of the probe constitutes It has a structure.
Now, we will simplify the circuit and make it easy to calculate, and show the theoretical path.
That is, it is assumed that the circuit at the tip of the coaxial and the probe has almost the same electrical characteristics by optimizing the circuit design. This circuit is I tables in the equivalent circuit of one of the distributed constant circuit. In the case of a detailed analysis, calculation may be made assuming that circuits having different characteristics between the coaxial and the tip of the probe are subtly connected, assuming that the characteristics of the coaxial and the tip of the probe are slightly different. From the above preconditions, the circuit of the coaxial and the tip of the probe can be expressed by one distributed constant circuit.

回路の微小部分（ｄｘ）のこの分布定数回路は図３に示す等価回路になる。回路の入力部では電圧が周波数ωで変化していると仮定する。ただし実際の測定回路では、発振器の出力電圧に含まれる周波数は、式２）に示す多数の周波数で励振している。しかし、各周波数に対して、回路が線形性を保つならば、それぞれの周波数について、電圧関係を解析し、分析を進めても矛盾は生じない。ここでＬはインダクタンス、Ｒは直列抵抗、Ｃは電気容量、Ｇは並列コンダクタンスでそれぞれの値は、単位長さあたりの値を示す。
位置ｘにおける電圧、電流はそれぞれＶ，Ｉとし、位置ｘ＋ｄｘにおける電圧
、電流はそれぞれＶ＋ｄＶ、Ｉ＋ｄＩとする。
これらの電圧、電流は、周波数ωで励振しているので、周波数の関数になり、Ｖ（ω）、Ｉ（ω）と明確に記載すべきところ、式の表現を簡単にし、読みやすくするために、適宜このωを記載上省略する。 This distributed constant circuit of the minute part (dx) of the circuit becomes an equivalent circuit shown in FIG. Assume that the voltage is changing at the frequency ω at the input of the circuit. However, in an actual measurement circuit, the frequency included in the output voltage of the oscillator is excited at a number of frequencies shown in Equation 2). However, if the circuit maintains linearity for each frequency, no contradiction will occur even if the voltage relationship is analyzed and the analysis is advanced for each frequency. Here, L is an inductance, R is a series resistance, C is a capacitance, G is a parallel conductance, and each value is a value per unit length.
The voltage and current at the position x are V and I, respectively, and the voltage and current at the position x + dx are V + dV and I + dI, respectively.
Since these voltages and currents are excited at the frequency ω, they become functions of the frequency and should be clearly described as V (ω) and I (ω). In order to simplify the expression and make it easier to read. In addition, this ω is appropriately omitted in the description.

図３の等価回路では、ｄＶはＬとＲの電圧降下によるもので、次の４）式が成立する。一方ｄＩは、電気容量ＣとコンダクタンスＧによる分流効果によるもので、次の５）式が成立する。

４）

５）

６）

７） In the equivalent circuit of FIG. 3, dV is due to a voltage drop between L and R, and the following equation 4) holds. On the other hand, dI is due to the shunt effect caused by the electric capacitance C and conductance G, and the following equation 5) holds.

4)

5)

6)

7)

前記６）７）式でγ＝（ＺＹ）^1/2 であり、このγは伝播定数と呼び、γ＝α＋ｊβとなりαは減衰定数、βは位相定数と呼ばれている。
６），７）式の一般解は次の８），９）式で与えられる。

８）

９）
この第一項は電源から負荷に入る進行波、第二項は負荷で反射されて、伝送回路から電源側に戻る反射波である。ここで、Ｚ₀ は（Ｚ／Ｙ）^1/2 で与えられる伝送路の特性インピーダンスである。
Ａ，Ｂはｘ＝０の進行波と反射波の電圧に等しい。これらの電圧を進行波Ｖ_i と
反射波Ｖ_r とする。ただし、Ｖ_i ＝Ｖ_i （ω）、Ｖ_r ＝Ｖ_r （ω）であるが、ωを省略する。
ｘ＝０の電圧と電流は、次の１０），１１）式で与えられる。

１０）

１１）
今伝送線とプローブの長さは十分短いとすれば、この距離の間では、伝送路の
損失はほとんど無視できる。すなわち無損失路線と仮定できるから、α＝０とすることができＶ（ｘ），Ｉ（ｘ）は１２），１３）式で与えられる。

１２）

１３） In the above 6) and 7), γ = (ZY) ^1/2 , where γ is called a propagation constant, γ = α + jβ, where α is an attenuation constant and β is a phase constant.
General solutions of equations 6) and 7) are given by the following equations 8) and 9).

8)

9)
The first term is a traveling wave that enters the load from the power source, and the second term is a reflected wave that is reflected by the load and returns from the transmission circuit to the power source side. Here, Z ₀ is the characteristic impedance of the transmission line given by (Z / Y) ^1/2 .
A and B are equal to the voltage of the traveling wave and reflected wave of x = 0. These voltages are referred to as traveling wave V _i and reflected wave V _r . However, although V _i = V _i (ω) and V _r = V _r (ω), ω is omitted.
The voltage and current at x = 0 are given by the following equations 10) and 11).

10)

11)
If the length of the transmission line and the probe is sufficiently short now, the loss of the transmission line is almost negligible between this distance. That is, since it can be assumed to be a lossless route, α = 0 can be set, and V (x) and I (x) are given by equations 12) and 13).

12)

13)

図４に示す同軸とプロ−ブで形成される等価退路の線路長をｄ（実施例では同軸の始端からプローブの先端までの線路長）とし、プローブの先端に負荷インピーダンスをＺが接続されているとする。
ｘ＝ｄ，ｘ＝０における電圧と電流は、次のようにして導かれる。

１４）

１５）
１３）式から

１６）
１５）と１６）式から逆にＶ（０），Ｉ（０）がＶ（ｄ），Ｉ（ｄ）であらわされる。

１７）

１８） The line length of the equivalent retraction formed by the coaxial and the probe shown in FIG. 4 is d (in the embodiment, the line length from the coaxial start end to the probe tip), and the load impedance Z is connected to the probe tip. Suppose that
The voltage and current at x = d, x = 0 are derived as follows.

14)

15)
13) From equation

16)
On the contrary, V (0) and I (0) are expressed as V (d) and I (d) from the equations 15) and 16).

17)

18)

いま同軸とプローブの長さは短いので、この間の損失は極めてすくないので、無損失の場合と考えられＲ＝０，Ｇ＝０として良いからγおよびβは次のようになる。
γ＝α＋ｊ（ＺＹ）^1/2 ＝〔（Ｒ＋ｊωＬ）（Ｇ＋ｊωＣ）〕^1/2
＝ｊω（ＬＣ）^1/2
からβ＝ω（ＬＣ）^1/2 となる。 Since the length of the coaxial and the probe is short now, the loss during this period is very small. Therefore, it can be considered that there is no loss, and R = 0 and G = 0 can be set, so γ and β are as follows.
γ = α + j (ZY) 1/2 = [(R + jωL) (G + jωC) ] ^1/2
= Jω (LC) ^1/2
Therefore, β = ω (LC) ^1/2 .

次に同軸伝送線の単位長当たりのインダクタンスと電気容量について求める。
等価同軸線は、内径と外径の導体の間に比誘電率ε^* を持つ誘電体で満たされていて、
また透磁率μはμ₀ にほぼ等しいとする。単位長当たりのインダクタンスは

１９）
ただしｃは真空中の光速度、
ｃ＝１／（ε₀ μ₀ ）^1/2 μ＝μ₀ ＝１／（ε₀ ｃ² ）である。
単位長さ当たりの電気容量は

２０）
したがって

２１） Next, the inductance and capacitance per unit length of the coaxial transmission line are obtained.
The equivalent coaxial line is filled with a dielectric having a relative dielectric constant ε ^* between the inner and outer conductors,
It is assumed that the magnetic permeability μ is substantially equal to μ ₀ . Inductance per unit length is

19)
Where c is the speed of light in vacuum,
c = 1 / (ε ₀ μ ₀ ) ^1/2 μ = μ ₀ = 1 / (ε ₀ c ² ).
The electric capacity per unit length is

20)
Therefore

21)

次に同軸線路の負荷側について考える。
ｘ＝０でのアドミッタンスはＹ₀ であり、ｘ＝ｄでのアドミッタンスはＹ_d とする。
１７）式と１８）式から

２２）
終端ｘ＝ｄが開放端であるとき、Ｉ（ｄ）＝０よりＹ_d ＝０になる。
２２）式から下記の２３）式、式１０）と１１）から下記の２４）式と２５式）が得られる。

２３）

２４）

２５） Next, consider the load side of the coaxial line.
The admittance at x = 0 is Y ₀ and the admittance at x = d is Y _d .
From equations 17) and 18)

22)
When the end x = d is an open end, Y _d = 0 from I (d) = 0.
From the formula 22), the following formula 23) is obtained, and from the formulas 10) and 11), the following formula 24) and formula 25 are obtained.

23)

24)

25)

いま、伝送線路の終端（プローブの先端）であるｘ＝ｄに被測定試料を設置する方法を考える。終端ｘ＝ｄの開放端に接続されるこの被測定試料の等価回路４０１を図４に示す。
本測定方法の原理を簡潔に説明するために、被測定試料の等価回路は図４に示すようにキャパシタンスＣとコンダクタンスＧで構成されていると考える。２６）式は被測定試料のインピーダンスを示す。２５）式は２７）式のように変形され、被測定試料のアドミッタンスは２８）式で表される。

２６）

なお、Ｖ _i ，Ｖ _r の変数はωである。
２７）

なお、Ｖ _i ，Ｖ _r の変数はωである。
２８）
ここでＣとＧは、被測定試料の複素誘電率の実数部と虚数部の関数として求められるので、式２８）は、複素誘電率が測定可能な入射信号波と反射信号波を用いて表現できることを示している。Ｖ_i はガウシアン分布の電圧波Ｖ_i （ｔ）をフーリェ変換した関数Ｖ_i （ω）であり、式２）で示される関数である。よって未知の試料の複素誘電率は、発振器の出力電圧（入射信号波）Ｖ_i （ｔ）と反射信号波Ｖ_r （ｔ）を測定することから求まる。 Now, consider a method of placing the sample to be measured at x = d, which is the end of the transmission line (probe tip). FIG. 4 shows an equivalent circuit 401 of this sample to be measured connected to the open end of the terminal x = d.
In order to briefly explain the principle of this measurement method, it is assumed that the equivalent circuit of the sample to be measured is composed of a capacitance C and a conductance G as shown in FIG. Equation (26) represents the impedance of the sample to be measured. Equation 25) is transformed into Equation 27), and the admittance of the sample to be measured is represented by Equation 28).

26)

Note that the variables of V _i and V _r are ω.
27)

Note that the variables of V _i and V _r are ω.
28)
Here, C and G are obtained as a function of the real part and the imaginary part of the complex dielectric constant of the sample to be measured. Therefore, Equation 28) is expressed using an incident signal wave and a reflected signal wave that can measure the complex dielectric constant. It shows what you can do. V _i is a function V _i (ω) obtained by performing a Fourier transform on the voltage wave V _i (t) having a Gaussian distribution, and is a function represented by Expression 2). Therefore, the complex permittivity of the unknown sample can be obtained by measuring the output voltage (incident signal wave) V _i (t) and the reflected signal wave V _r (t) of the oscillator.

（比較測定方法）前述した方法と異なり、複素誘電率の既知である標準サンプルで反射波のデータをもとに、未知の試料の複素誘電率を求める比較測定方法も可能である。
この比較測定方法は、入射波のデータは必要なく、標準サンプルの反射波のデータをもとに未知の試料の複素誘電率を求める方法である。この方法は測定項目が少なくなるので、測定の精度を上げることができる。２７）式において、標準サンプルの等価回路のインピーダンスをＺ_s 、未知の試料の等価回路のインピーダンスをＺ_x 、標準サンプルを測定したときの反射信号波をＶ_rs、未知試料を測定したときの反射信号波をＶ_rxとすれば、Ｚ _s は２９）式、Ｚ_x は３０）式で表される。２９）式と３０）式からＶ_i を消去して、Ｚ_x をＶ_rs ，Ｖ_rx ，Ｚ_s を用いて３１）式で表すことができる。
３１）式は、未知の試料の複素誘電率を持つ等価回路のインピーダンスＺ_x を、測定される既知の標準サンプルの複素誘電率を持つ等価回路のインピーダンスＺ_s 、標準サンプルの反射信号波形Ｖ_rs（ω）、未知の試料の反射信号波形Ｖ_rx（ω）から算出できることを示す。このように、標準サンプルの複素誘電率が解析されていて、標準サンプルの反射信号波Ｖ_rs（ｔ）と未知の試料の反射信号波Ｖ_rx（ｔ）が測定できれば、Ｖ_rs（ω）やＶ_rx（ω）が算出でき、未知の試料の複素誘電率が求まるわけである。３１）式の算出過程は付録１に示すから、適宜参照されたい。

なお、Ｖ _i ，Ｖ _rs の変数はωである。
２９）

なお、Ｖ _i ，Ｖ _rx の変数はωである。
３０）

なお、Ｖ _rs ，Ｖ _rx の変数はωである。
３１） (Comparative Measurement Method) Unlike the method described above, a comparative measurement method is also possible in which the complex dielectric constant of an unknown sample is obtained based on the reflected wave data with a standard sample with a known complex dielectric constant.
This comparative measurement method is a method for obtaining the complex dielectric constant of an unknown sample on the basis of the reflected wave data of a standard sample without the need for incident wave data. Since this method requires fewer measurement items, the accuracy of measurement can be increased. In equation (27), the impedance of the equivalent circuit of the standard sample is Z _s , the impedance of the equivalent circuit of the unknown sample is Z _x , the reflected signal wave when the standard sample is measured is V _rs , and the reflection when the unknown sample is measured Assuming that the signal wave is V _rx , Z _s can be expressed by equation 29) and Z _x can be expressed by equation 30). 29) and 30) to clear the V _i from the equation, the Z _x V _rs, V _rx, can table Succoth in by 31) below using the Z _s.
31) equation, the impedance Z _x of the equivalent circuit with a complex dielectric constant of an unknown sample, the impedance Z _s of the equivalent circuit with a complex dielectric constant of a known standard sample to be measured, reflected signal waveform V _rs of standard sample (Ω) indicates that it can be calculated from the reflected signal waveform V _rx (ω) of an unknown sample. Thus, though the complex dielectric constant of the standard sample is analyzed, if the measured reflectance signal wave V _rx (t) is the reflected signal wave V _rs (t) and the unknown sample of standard samples, Ya V _rs (omega) V _rx (ω) can be calculated, and the complex dielectric constant of an unknown sample can be obtained. The calculation process of equation (31) is shown in Appendix 1, so please refer to it appropriately.

Note that the variables of V _i and V _rs are ω.
29)

Note that the variables of V _i and V _rx are ω.
30)

Note that the variable of V _rs and V _rx is ω.
31)

請求項１記載の絶対測定方法の動作を説明する。ガウシアン分布をもつ入射信号波（Ｖ_i ）を発生する入射信号波発生ステップと、同軸端形状の先端を有するプローブの先端の導体を試料に接触させ前記試料からの反射信号波（Ｖ_r ）を検出するステップにおいて、図５Ａに示すように、入射信号波と反射信号波の進行波形図を表示する。
このとき、測定前に予め設定した測定範囲を示す上限と下限の周波数がＣＲＴの右側にデジタル表示される。図５Ｂに示すように、装置は、フーリェ変換などの演算中であることを示す表示をする。演算が終了すると図５Ｃに示すように、複素誘電率（ε＝ε’＋ｊε”）の表示をする。このとき任意の周波数（カーソルの位置）を指定して、その周波数と当該試料のε’，とε”をデジタル表示することができる。 The operation of the absolute measurement method according to claim 1 will be described. An incident signal wave generating step for generating an incident signal wave (V _i ) having a Gaussian distribution, and a conductor at the tip of a probe having a tip having a coaxial end shape are brought into contact with the sample to generate a reflected signal wave (V _r ) from the sample. In the detecting step, as shown in FIG. 5A, a progress waveform diagram of the incident signal wave and the reflected signal wave is displayed.
At this time, the upper and lower frequencies indicating the measurement range set in advance before measurement are digitally displayed on the right side of the CRT. As shown in FIG. 5B, the apparatus displays a message indicating that a computation such as a Fourier transform is being performed. When the calculation is completed, a complex dielectric constant (ε = ε ′ + jε ″) is displayed as shown in FIG. 5C. At this time, an arbitrary frequency (cursor position) is designated, and the frequency and ε ′ of the sample are displayed. , And ε ″ can be digitally displayed.

請求項３の比較測定方法の動作では、当初既知の試料に入射信号波を当てて、反射信号波を検出する。この動作は校正のステップとも言えるもので、動作および表示は前記請求項１の方法の表示と異ならない。既知試料についてガウシアン分布をもつ入射信号波（Ｖ_i ）を発生する入射信号波発生ステップと、同軸端形状の先端を有するプローブの先端の導体を試料に接触させ前記試料からの反射信号波（Ｖ_r ）を検出するステップにおいて、図５Ａに示すように、入射信号波と反射信号波の進行波形図を表示する。
このとき、測定前に予め設定した測定範囲を示す上限と下限の周波数がＣＲＴの右側にデジタル表示される。フーリェ変換などの演算中に、その状態であることを示すか他の任意の表示をすることができる（図５Ｂ）。
演算が終了すると図５Ｃに示すように、複素誘電率（ε＝ε’＋ｊε”）の表示をする。このとき任意の周波数（カーソルの位置）を指定して、その周波数と当該試料のε’，とε”をデジタル表示することができる。
続いて未知の試料にプローブを当て、このときの反射波のデータをもとにフーリェ変換を行い、未知の試料の反射信号波形Ｖ_rx（ω）を演算し、式３１に代入して演算し、Ｚ_x を演算する。その結果演算された複素誘電率ε＝ε’＋ｊε”がＣＲＴに表示される。ＣＲＴの横軸は周波数を示す。縦方向のカーソル線が横軸の周波数にあうと、そのときの周波数の値が、ＣＲＴの右側に表示される。同時にこの周波数に対するε’とε”の値も表示される。 In the operation of the comparative measurement method of claim 3, the reflected signal wave is detected by applying an incident signal wave to an initially known sample. This operation can be said to be a calibration step, and the operation and display are not different from the display of the method of claim 1. An incident signal wave generating step for generating an incident signal wave (V _i ) having a Gaussian distribution with respect to a known sample, and a conductor at the tip of a probe having a tip having a coaxial end shape is brought into contact with the sample, and a reflected signal wave (V _In the step of detecting _r ), as shown in FIG. 5A, a progress waveform diagram of the incident signal wave and the reflected signal wave is displayed.
At this time, the upper and lower frequencies indicating the measurement range set in advance before measurement are digitally displayed on the right side of the CRT . During computations such as Fourier transform, it can indicate that state or make any other display (FIG. 5B).
When the calculation is completed, a complex dielectric constant (ε = ε ′ + jε ″) is displayed as shown in FIG. 5C. At this time, an arbitrary frequency (cursor position) is designated, and the frequency and ε ′ of the sample are displayed. , And ε ″ can be digitally displayed.
Then by applying a probe to the unknown specimen performs Fourier transform the data of the reflected wave in this case is based, calculates the reflected signal waveform V _rx unknown sample (omega), calculated by substituting the formula 31 And Z _x is calculated. The calculated complex permittivity ε = ε ′ + jε ″ is displayed on the CRT. The horizontal axis of the CRT indicates the frequency. When the vertical cursor line matches the frequency of the horizontal axis, the value of the frequency at that time Are displayed on the right side of the CRT, and at the same time the values of ε ′ and ε ″ for this frequency are also displayed.

（付録１）比較測定におけるインピーダンスＺ_x を示す３１）式の算出は以下に示す。
２９）式にて（Ｖ_i −Ｖ_rs）／（Ｖ_i ＋Ｖ_rs）＝ａ，
（Ｖ_i −Ｖ_rs）／（Ｖ_i ＋Ｖ_rs）＝ｂとおき、ただしａは下記のＡ−１）式、ｂはＡ−２）式に示すとおりである。Ａ−３）式に示すＶ_i は２９）式から、Ａ−４）式に示すＶ_i は３０）式から、求めたものである。
Ａ−３）式とＡ−４）式からＶ_i を消去すると、Ａ−５）式が得られる。Ａ−５）式をｂについて解いてＡ−６）式を得る。一方ｒは、Ａ―５）式からＡ−７）式に示すように求められる。３１）式すなわちＡ−８）式は、Ａ−２），Ａ−６），Ａ−７）式から求められる。

Ａ−１）

Ａ−２）

Ａ−３）

Ａ−４）

Ａ−５）

Ａ−６）

Ａ−７）

Ａ−８） (Appendix 1) Calculation of 31) formula showing the impedance Z _x of the comparative measurement is shown below.
29) (V _i −V _rs ) / (V _i + V _rs ) = a,
(V _i −V _rs ) / (V _i + V _rs ) = b where a is the following formula A-1) and b is the formula A-2). V _i shown in the formula A-3) is obtained from the formula 29), and V _i shown in the formula A-4) is obtained from the formula 30).
If V _i is eliminated from the expressions A-3) and A-4), the expression A-5) is obtained. The A-5) equation is solved for b to obtain the A-6) equation. On the other hand, r is obtained as shown in equations A-5) to A-7). The formula 31), that is, the formula A-8) is obtained from the formulas A-2), A-6), and A-7).

A-1)

A-2)

A-3)

A-4)

A-5)

A-6)

A-7)

A-8)

本発明による広帯域高周波誘電率測定方法は、非破壊で複素誘電率を測定できるものである。したがって、誘電体の品質検査に広く利用され誘電体の製造業や、電子部品製造業で広く利用できる。また、測定装置は、計算機や計測器の分野で製造可能である。 The broadband high-frequency dielectric constant measuring method according to the present invention can measure the complex dielectric constant in a nondestructive manner. Therefore, it is widely used for dielectric quality inspection and can be widely used in the dielectric manufacturing industry and the electronic component manufacturing industry. In addition, the measuring device can be manufactured in the field of computers and measuring instruments.

本発明による高周波マイクロ波誘電率の測定回路の構成を示す略図である。1 is a schematic diagram showing the configuration of a high-frequency microwave dielectric constant measurement circuit according to the present invention. 本発明のプローブの構造を示す概略断面図である。It is a schematic sectional drawing which shows the structure of the probe of this invention. 本発明の測定回路のプローブ部を含む回路を分布定数回路として示した等価回路図である。It is the equivalent circuit diagram which showed the circuit containing the probe part of the measurement circuit of this invention as a distributed constant circuit. 同軸ケーブル，プローブ，負荷との関係を示すブロック図である。It is a block diagram which shows the relationship between a coaxial cable, a probe, and load. 入射信号波と反射信号波の進行波形図の表示状態を示す動作説明図である。It is operation | movement explanatory drawing which shows the display state of the progressive waveform figure of an incident signal wave and a reflected signal wave . 演算または校正期間中の表示の例を示す説明図である。It is explanatory drawing which shows the example of the display during a calculation or calibration period. 複素誘電率（ε＝ε’＋ｊε”）の表示状態を説明する説明図である。It is explanatory drawing explaining the display state of complex permittivity ((epsilon) = (epsilon) '+ j (epsilon) ".

Explanation of symbols

１０１ガウシアン分布の電圧波を出力する発振器
１０２方向性結合器
１０３同軸ケーブル
１０４本発明のプローブ
１０５被測定サンプル
１０６サンプリングオシロスコープ
１０７データバス
１０８パソコン
２０１内導体
２０２低損失誘電体
２０３外導体
４０１同軸ケーブルとプローブとで構成する等価回路 DESCRIPTION OF SYMBOLS 101 Oscillator which outputs voltage wave of Gaussian distribution 102 Directional coupler 103 Coaxial cable 104 Probe of this invention 105 Sample to be measured 106 Sampling oscilloscope 107 Data bus 108 Personal computer 201 Inner conductor 202 Low loss dielectric 203 Outer conductor 401 Coaxial cable and Equivalent circuit consisting of probe

Claims

When a known broadband high-frequency incident signal wave is applied to the sample via a probe having a coaxial open tip, the incident signal wave V _i (t) and the reflected signal wave V _r (t) from the sample are Fourier transformed. Then, the incident signal waveform V _i (ω) and the reflected signal waveform V _r (ω) at each angular frequency ω are calculated, and from the result, the impedance Z of the sample, which is the load of the probe, becomes the incident signal waveform V _i (ω ), The reflected signal waveform V _r (ω) and the characteristic impedance Z _{0 of} the supply path including the probe , the phase constant β, and the function given by the following equation [Formula 1] as a function of the path length d , A method for measuring a complex dielectric constant ε = ε ′ + jε ″ of a sample,
The incident signal wave generating step of applying said incident signal wave V _i (t) as the voltage V _i of the Gaussian distribution given by the following equation Formula 3 (t),
Detecting a reflected signal wave V _r (t) from the sample by bringing a conductor at the tip of the probe having a coaxial end shape into contact with the sample;
The incident signal wave V _i (t) and the reflected signal wave V _r (t) are Fourier transformed to calculate the incident signal waveform V _i (ω) and the reflected signal waveform V _r (ω) at each angular frequency ω. Steps,
A calculation step for calculating a complex dielectric constant of the sample by calculating an amount corresponding to ε ′ from the imaginary part and ε ″ from the real part of the impedance Z corresponding to each angular frequency ω ;
Broadband high frequency dielectric constant measuring method including:
Record

The wide-band high-frequency dielectric constant measuring method according to claim 1,
The incident signal wave V _i (t), the incident signal waveform V _i (ω), and the reflected signal waveform V _r (ω) are respectively given by the following formulas.
Record

When a known broadband high-frequency incident signal wave V _i (t) is applied to an unknown sample via a probe having a coaxial open tip, the reflected signal wave from the unknown sample is V _rx (t) , and the same is applied to the known sample. When a broadband high-frequency incident signal wave V _i (t) is applied, the reflected signal wave from the known sample is V _rs (t), and when the impedance of the known sample is Z _s , the reflected signal wave V _rs ( t), the reflected signal wave V _rx (t) the Fourier transform to the reflected signal waveform V _rs at each angular frequency ω (ω), calculate the reflected signal waveform V _rx (ω), the results of the unknown sample The impedance Z _x is the reflected signal waveform V _rs (ω), the reflected signal waveform V _rx (ω), the impedance Z _{s of the} known sample, the characteristic impedance Z _{0 of} the supply path including the probe , the phase constant β, and the path length d. As a function of By utilizing the fact that given by expression (2), a method for measuring the complex dielectric constant of an unknown sample ε = ε '+ jε ",
The incident signal wave generating step of applying said incident signal wave V _i (t) as the voltage V _i of the Gaussian distribution given by the following equation Formula 3 (t),
The incident signal wave V _i (t) is incident by bringing the conductor at the tip of the probe having a coaxial end into contact with the known and unknown samples , and the reflected signal waves V _rs (t) and V _rx from the respective samples. detecting a (t),
A Fourier transform of the reflected signal waves V _rs (t) and V _rx (t ) to calculate a reflected signal waveform V _rs (ω) and a reflected signal waveform V _rx (ω) at each angular frequency ω ;
A calculation step of calculating a complex dielectric constant of the unknown sample by calculating an amount corresponding to ε ′ from the imaginary part and ε ″ from the real part of the impedance Z _x corresponding to each arbitrary angular frequency ω ;
Broadband high frequency dielectric constant measuring method including:
Record

The wide-band high-frequency dielectric constant measuring method according to claim 3,
The reflected signal waveform V _rs (ω) and the reflected signal waveform V _rx (ω) are each a broadband high-frequency dielectric constant measuring method given by the following equations .
Record

Through a probe having a coaxial opening tip upon application of a known wideband RF incident signal wave to the specimen, the incident signal wave V _i (t), the reflected signal wave V _r (t) from the sample and Fourier Transform Then, the incident signal waveform V _i (ω) and the reflected signal waveform V _r (ω) at each angular frequency ω are calculated, and from the result, the impedance Z of the sample, which is the load of the probe, becomes the incident signal waveform V _i (ω ), The reflected signal waveform V _r (ω) and the characteristic impedance Z _{0 of} the supply path including the probe , the phase constant β, and the function given by the following equation [Formula 1] as a function of the path length d, A broadband high-frequency dielectric constant measuring apparatus for carrying out a method for measuring a complex dielectric constant ε = ε ′ + jε ″ of a sample ,
An oscillator that generates a Gaussian-distributed voltage V _i (t) given by the following equation (Equation 3) as the incident signal wave V _i (t) :
A coaxial cable connected to the oscillator ;
A probe said coaxial open distal is connected to the coaxial cable in contact with the sample incident signal wave V _i (t) is marked pressurized, receives a reflected signal wave V _r (t),
A directional coupler for connecting the incident signal wave V _i (t) to the coaxial cable and extracting the reflected signal wave V _r (t) ;
The incident signal wave V _i (t) and the reflected signal wave V _r (t) are Fourier transformed to calculate the incident signal waveform V _i (ω) and the reflected signal waveform V _r (ω) at each angular frequency ω. Means,
A calculation means for calculating a complex dielectric constant of the sample by calculating an amount corresponding to ε ′ from the imaginary part and ε ″ from the real part of the impedance Z corresponding to each angular frequency ω ;
Broadband high frequency dielectric constant measuring method including:
Record

When a known broadband high-frequency incident signal wave V _i (t) is applied to an unknown sample via a probe having a coaxial open tip, the reflected signal wave from the unknown sample is V _rx (t) , and the same is applied to the known sample. wideband RF reflected signal waves from the known samples of the incident signal wave V _i (t) of when the application is V _rs (t), when the impedance of the known sample is a Z _s, the reflected signal wave V _rs ( t), the reflected signal wave V _rx (t) is subjected to Fourier transform to calculate a reflected signal waveform V _rs (ω) and a reflected signal waveform V _rx (ω) at each angular frequency ω. The impedance Z _x is the reflected signal waveform V _rs (ω), the reflected signal waveform V _rx (ω), the impedance Z _{s of the} known sample, the characteristic impedance Z _{0 of} the supply path including the probe , the phase constant β, the path length as a function of d A of utilizing the fact that given by equation [Equation 2], a broadband high-frequency dielectric constant measuring apparatus for carrying out the method for measuring the complex dielectric constant of an unknown sample ε = ε '+ jε ",
An oscillator for generating the voltage V _i of the Gaussian distribution, given as an incident signal wave V _i (t) which is applied to the sample by the following equation Formula 3 (t),
A coaxial cable connected to the oscillator ;
A probe connected to the coaxial cable and contacting the known and unknown sample with the open end of the coaxial and applying the incident signal wave V _i (t) to receive the reflected signal waves V _rs (t) and V _rx (t) ; ,
Entering-morphism signal wave V _i (t) is connected to the coaxial cable, and a directional coupler for taking out the respective reflected signal wave V _rs (t), V _rx (t),
The reflected signal waves V _rs (t) and V _rx (t) from the known sample and the unknown sample taken out from the directional coupler are Fourier-transformed, and the reflected signal waveforms V _rs (ω), It means for calculating a reflected signal waveform V _rx (ω),
A calculation means for calculating a complex dielectric constant of the unknown sample by calculating an amount corresponding to ε ′ from the imaginary part and ε ″ from the real part of the impedance Z _x corresponding to each arbitrary angular frequency ω ;
Broadband high frequency dielectric constant measuring method including:
Record

The wide-band high-frequency dielectric constant measuring apparatus according to claim 5 or 6,
The probe has an outer diameter of 2 mm or less, an outer diameter of the core of 1 mm or less, a taper toward the tip of the probe, and an outer diameter of the core at the tip of the measurement unit of 0.2 mm or less. measuring device.

The wide-band high-frequency dielectric constant measuring apparatus according to claim 5 or 6,
The apparatus includes a display means, and a broadband high-frequency dielectric constant measuring apparatus configured to display a spectrum of calculated ε ′, ε ″.

9. The broadband high-frequency dielectric constant measuring apparatus according to claim 8, wherein the display means further displays an incident signal wave V _i (t) and a reflected signal wave V _r (t) response waveform from the sample simultaneously.

9. The apparatus according to claim 8, wherein the display means further displays the time pulse response waveforms of the reflected signal wave V _rs (t) from the known sample and the reflected signal wave V _rx (t) from the unknown sample simultaneously or separately. Broadband high-frequency dielectric constant measuring device.

9. The wide-band high-frequency dielectric constant measuring apparatus according to claim 8, wherein the display means further performs a display indicating that a calculation is being performed between a time pulse response waveform display of a signal and a frequency spectrum display of a dielectric constant.

9. The apparatus according to claim 8, wherein said display means further performs digital display of the upper and lower frequencies of measurement together with the time pulse response waveform display of the signal, and ε ′, ε at a specified frequency together with a frequency spectrum display of dielectric constant. Wide-band high-frequency dielectric constant measuring device that performs digital display.