JP2008089561A - DETECTION METHOD OF INSULATOR DIELECTRIC LOSS ANGLE (CALLED AS tandelta) IN APPARATUS DURING OPERATION - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a mathematical processing method capable of calculating tanδ which is an index of the deterioration degree, though tanδ which is a dielectric loss angle to a high insulator cannot be measured hitherto, and to provide a method for detecting tanδ to an electric workpiece during charging or an object being moved on an operation line of a product. <P>SOLUTION: A circuit impedance and a phase are measured in each frequency by applying a variable frequency in a high frequency domain to a test object, and a least-squares method or a vector locus of a complex relative dielectric constant is used in correspondence with an attenuation constant of Maxwell electromagnetic equation and a phase constant, and a calculation procedure of tanδ can be provided from the dielectric constant corresponding to a phase extreme value point. Furthermore, a current is made to flow through a stray capacitance between a test object being moved on a manufacture line or the like and a support instrument, and tanδ of a moving object is detected, and a system capable of performing quality control can be organized. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

The present invention relates to a method for calculating tan δ from the relative permittivity of an insulator portion of an electric workpiece and a tan δ detection method for evaluating the in-device insulation function quality during operation of an electric device.

With a high-insulation material with a high insulation level, the conventional tan δ meter has a very small detection current, is difficult to detect, and cannot be measured.

Tan δ of the target equipment connected to the operation circuit by charging or applied voltage, insulation quality of the outer enamel part of the conductor core wire of the running enamel wire during the wire manufacturing process, cleaning liquid management of the semiconductor manufacturing process, semiconductor device doving The tan δ measurement for evaluating the dielectric loss from the level inspection and quality control of the fluid dielectric material or the like has not been applied.

Problems to be solved by the invention

It was necessary to measure tan δ in order to evaluate the insulation level of the high insulator.

A method based on tan δ is necessary for evaluating the quality of equipment insulation during charging and for quality control of articles during the manufacturing process.

In view of the above problems, the present invention provides a measurement system that establishes a method for calculating tan δ that can be used for insulation diagnosis of an electric workpiece being charged and for quality control of a product during operation of a production line. .

Means for solving the problem

The calculation method of tan δ according to the present invention is such that a continuously variable high frequency of about 200 KHZ to about 600 KHZ is applied to an insulator with a small current of 100 A to 1 A, which can overcome noise with a non-destructive voltage of about 10 V to 1000 V. Is measured by a circuit of, an impedance Z curve and a phase curve θ are drawn by a network analyzer, and Zm [Ω] and θm [degrees] at an extreme point fm [HZ] where the θ curve is distorted are formed. From the root X of the propagation equation, a complex relative dielectric constant ε * is calculated, and tan δ is derived. As shown in FIG. 9, the imaginary part j · er2 of the complex relative permittivity ε * has a maximum point in the frequency range of a general insulator. From FIG. 5, the frequency fm of the extreme point varies slightly depending on the type of insulator as shown in FIG.

数値０．２部分をＮＭ、 べき乗指数−１２部分をＦＫＭｆｍで示す。
Ｚ＝１０００Ωの時

同様にして、
ＮＭ１＝０．６ ＦＫＭｆｍ１＝−９
Ｚ＝５００Ωの時

同様にして、
ＮＭ２＝０．４ 、 ＦＫＭｆｍ３＝−６
ＮＭは０から、１．０まで変動する。それに対して、１０のＦＫＭｆｍ乗は、１０（−１２乗）から、１０（−６乗）と、大きく変動する。この小幅変動部をＮＭｆｍとし、大幅変動部をΔＮＭｆｍ
で示すと、（６０）式のＹ（Ｘ）＝ＮＭｆｍ ＋ ΔＮＭｆｍ
となり、Ｘ（ε＊）＝ＮＭｆｍ ＋ ΔＮＭｆｍ
のように対応させる。そして、複素比誘電率ｅｒ１、虚部のｅｒ２らの周波数による値は、コール・コールの半円軌跡に近似出来るので、（４１）式と図１０から、（５５）式のε＊とＦＫＭｆｍとの関係を最小自乗法から、（５６）、（５７）式を作成、そして、小幅変動部ＮＭ部も最小自乗法から、ε＊との関係式を作成する。これらから、インピーダンスＺ曲線の内、位相曲線θ角の極値点から、根Ｘとε＊の軌跡点との関係（６３）式によって、物体の比誘電率ε＊を算出するものである。
この手法が、本発明のポイントである。
この対象物体のキャパシタンスＸＣＢは、
ＸＣＢ＝Ｋ・（ＮＭ・ＦＫＭｆｍ）・（ＮＭ・ＦＫＭｆｍ）
Ｋ：形状係数、 位相極値点ｆｍ［ＨＺ］点のリアクタンをｈｘｃＲ［Ω］
この点のインピーダンスをＺｍ、位相θｍとすると物体の抵抗部
Ｒｓｉｓは、 Ｒｓｉｓ＝Ｚｍ・ＣｏｓΘｍ となり、物体の沿面の漏洩抵抗を含めた損失角ｔａｎδは、次式で、示せる。
ｔａｎδ［％］＝１００／（Ｒｓｉｓ・ＸＣＢ・ωｍ）As a point of invention,
Corresponding measurement impedance Zm [Ω], attenuation constant α [neper / m], phase angle θm [degree], and phase constant β [rad / m], the frequency having the extreme value of the phase curve is the impedance at fm point. If the root X is solved from the electromagnetic propagation equation (31) and can be derived from the phase angle, and α = Zm and β = θm in (31) are substituted, the root X in (33) is as follows: FKMfm varies from -12 to -6: Take the first root with a power exponent. On the other hand, the absolute value of the complex dielectric constant ε * from the Cole-Cole diagram moves on a locus that is almost a semicircle. Since the correlation between the ε * and the value of X is larger at the first root, it is one of the points of the present invention to adopt this. From this correlation, each coefficient is calculated by the method of least squares, and ε * is determined from X. Thus, fm [KHZ] of the phase inflection point is high frequency, and in particular, the imaginary part of the relative permittivity comes out, and the εR2 part that becomes the expression (7) from the expression (5) becomes the fm point. Therefore, the extreme value θm appears in the phase curve θ. The method of calculating the absolute value of ε * from the impedance Zm and θm at this point is original. Details are shown in [0021] to [0023]. For example, when Z is 9000Ω (fm point)

The numerical value 0.2 part is indicated by NM, and the power exponent -12 part is indicated by FKMfm.
When Z = 1000Ω

Similarly,
NM1 = 0.6 FKMfm1 = -9
When Z = 500Ω

Similarly,
NM2 = 0.4, FKMfm3 = -6
NM varies from 0 to 1.0. On the other hand, the 10th power of FKMfm varies greatly from 10 (-12th power) to 10 (-6th power). This small fluctuation part is defined as NMfm, and the large fluctuation part is defined as ΔNMfm.
, Y (X) in equation (60) = NMfm + ΔNMfm
X (ε *) = NMfm + ΔNMfm
It corresponds as follows. Since the values of the complex dielectric constant er1 and the frequency of er2 of the imaginary part can be approximated to the Cole-Cole semicircular locus, from Equation (41) and FIG. 10, ε * and FKMfm in Equation (55) (56) and (57) are created from the least square method, and the small fluctuation part NM is also created from ε * by the least square method. From these, the relative dielectric constant ε * of the object is calculated from the extreme value point of the phase curve θ angle in the impedance Z curve by the equation (63) between the root X and the locus point of ε *.
This technique is the point of the present invention.
The capacitance XCB of this target object is
XCB = K ・ (NM ・ FKMfm) ・ (NM ・ FKMfm)
K: shape factor, reactance of phase extreme point fm [HZ] point hxcR [Ω]
When the impedance at this point is Zm and the phase θm, the resistance portion Rsis of the object becomes Rsis = Zm · CosΘm, and the loss angle tan δ including the leakage resistance along the creepage of the object can be expressed by the following equation.
tan δ [%] = 100 / (Rsis · XCB · ωm)

Read about the tan δ measurement system for insulation diagnosis of charged workpieces and product management of production lines.
As shown in FIG. 1, the insulation diagnosis of the charged electric workpiece is performed from 10V in the range of 200 KHZ to 600 KHZ as a variable frequency for the charged workpiece with a capacitor of 40 [PF] to 40 [nF]. From 100V, 100mA to 1A, an impedance curve and a phase curve for each frequency are drawn from this current and the voltage at both ends applied to the workpiece. Then, tan δ is calculated as described above, where fm is the extreme point of the phase distortion point.
For quality control of articles during the manufacturing process, for example, the thickness fluctuation of the enamel part of the enamel wire in the electric wire production line is captured as capacitance fluctuation, and this occurs in parallel with the capacitance between the electric wire core and enamel. The detected leakage resistance is detected as tan δ, and the thickness of the enamel portion is monitored during operation. As shown in Fig. 2, from the first of the two metal or conductive roller pieces supporting the wire, the above variable frequency is applied, the wire enamel is passed through the capacitance to the core wire, and the separated high frequency current A circuit that returns to the variable frequency oscillator is configured as a current return pole from the second roller coma on the return path. Because of the high frequency, in the gap between the rotating portion and the support portion, the current returns to the returning roller piece through the core wire through the floating capacitance formed therebetween.

電束密度Ｄも変化し、その定常振動は、

のように、印加電場Ｅに対して、電束密度Ｄの方は、位相がδだけ遅れる。このときの比誘電率をε＊とすると、複素数でなければならないので、以後ε＊を複素比誘電率と呼称する。
Ｄ＝ε０・ε＊・Ｅ・・・・（６）
ε＊＝ε１−ｊ・ε２・・・・（７）
ε１：実部比誘電率 ε２：虚部比誘電率
ε１＝Ｄ０・Ｃｏｓδ／ε０・Ｅ０・・・・（８）
ε２＝Ｄ０・Ｓｉｎδ／ε０・Ｅ０・・・・（９）
ＭＴｔａｎδ＝１００・ε１／ε２＝１００／Ｒ・Ｃ・ω・・・・（１０）
ＭＴｔａｎδ＝１００・ＩＲ／ＩＣ ・・・・（１１）
この誘電体損ＭＴｔａｎδは、印加した絶縁物体内の物性に寄る誘電体損失を表している。 これは、図３のＲｐ部分での有効電力損失、ジュール熱となるＩＲｘＩＲｘＲｐの積で示せる消費電力である。
ε２への寄与は、σ／（ε０・ω） ただし、σは、導電率
誘電分散には、大別して、緩和型分散と共鳴型分散とであり、緩和型は、配向分極の示す緩和現象である。高周波の場合電場印加に対して、配向分極は、直ちに追従できないので誘電損失が起きる。このように高周波を印加すると、位相変化δが発生し、図−４のように位相曲線に極値が観測できる。
一方、高周波は、絶縁物中の平面電磁波として進行するので絶縁物中の導電率がσ、誘電率をε、透磁率をμとすると

電界が Ｘ 方向、波が、Ｚ 方向に進行するとき

（２１）式の両辺を２乗して実部と虚部とが等しいと置くと

（２３）、（２４）式からβを消去して、

αは減衰定数、βは位相定数、 高周波を印加したときは、σ／ω・εが１より、充分小さいので、（２６）、（２７）式は、次式となる。

（２８）。（２９）式より、σ^２ を消去して、（３０）式となり、ε＞０から、εで割り算して、（３１）式となる。The calculation principle for carrying out the invention is shown.
When a low frequency is applied to the insulator, when the dielectric constant εr of the insulator is P, the magnitude of polarization is proportional to the strength of the electric field felt by the dielectric, so that P = ε0 · χ · E ... (1)
When the electric flux density is represented by D, D = εr · ε0 · E (2)
D = ε0 (1 + χ) E = ε0 · E + P (3)
Here, when the applied frequency is increased, the polarization P cannot follow the time change of the electric field. A phenomenon in which the dielectric constant depends on the frequency is called dielectric dispersion. Applied electric field E

The electric flux density D also changes, and its steady state vibration is

As described above, the phase of the electric flux density D is delayed by δ with respect to the applied electric field E. If the relative permittivity at this time is ε *, it must be a complex number, and hence ε * is hereinafter referred to as a complex relative permittivity.
D = ε0 · ε * · E (6)
ε * = ε1-j · ε2 (7)
ε1: Real part relative permittivity ε2: Imaginary part relative permittivity ε1 = D0 · Cosδ / ε0 · E0 (8)
ε2 = D0 · Sinδ / ε0 · E0 (9)
MTtan δ = 100 · ε1 / ε2 = 100 / R · C · ω (10)
MT tan δ = 100 · IR / IC (11)
This dielectric loss MT tan δ represents the dielectric loss due to the physical properties in the applied insulating object. This is the power consumption that can be represented by the product of IRxIRxRp, which is the effective power loss and Joule heat in the Rp portion of FIG.
The contribution to ε2 is σ / (ε0 · ω) where σ is roughly divided into conductivity-type dielectric dispersion, relaxation-type dispersion and resonance-type dispersion, and relaxation-type is a relaxation phenomenon indicated by orientation polarization. is there. In the case of high frequency, the dielectric polarization occurs because the orientation polarization cannot immediately follow the applied electric field. When a high frequency is applied in this way, a phase change δ occurs, and an extreme value can be observed on the phase curve as shown in FIG.
On the other hand, since the high frequency wave travels as a plane electromagnetic wave in the insulator, the conductivity in the insulator is σ, the dielectric constant is ε, and the magnetic permeability is μ.

When the electric field travels in the X direction and the wave travels in the Z direction

If both sides of equation (21) are squared and the real part and the imaginary part are equal,

Eliminating β from the equations (23) and (24),

α is an attenuation constant, β is a phase constant, and σ / ω · ε is sufficiently smaller than 1 when a high frequency is applied, so Equations (26) and (27) become the following equations.

(28). From equation (29), σ ² is eliminated to obtain equation (30), and from ε> 0, division by ε yields equation (31).

Mathematical development part for invention application

Invention term: Solving the root from the electromagnetic equation and calculating the relative permittivity.

ε＊：高周波になると比誘電率は複素数で表す
εｒ１：比誘電率の実数部
εｒ２：非誘電率の虚数部
ＮＭ：解の実根の数値部分
ＦＫＭ：根の数値の階乗部分の浮動指数
ＦＫＭｆｍ：位相の極値周波数点ｆｍでの階乗指数（右肩上の上付き数字）
ｆｍ：位相曲線上の極値を有する点の周波数 図４参照
Ｘ＝ＮＭ・ＦＫＭｆｍ ・・・・（３５）
（３２）式より
ε＊（ｆｍ）＝Ｘ・Ｘ／ε０ ・・・・（３６）
＝（εｒ１ − ｊ・εｒ２）

Numerical part NM and exponent exponent FKM of calculation root X to be applied for invention

ε *: The relative permittivity is expressed as a complex number at a high frequency εr1: Real part of relative permittivity εr2: Imaginary part of non-permittivity NM: Real root numerical part FKM: Floating exponent FKMfm of root numerical factorial part : Factorial exponent at the extreme frequency point fm of the phase (superscript on the right shoulder)
fm: frequency of a point having an extreme value on the phase curve See FIG. 4 X = NM · FKMfm (35)
From equation (32), ε * (fm) = X · X / ε0 (36)
= (Εr1−j · εr2)

誘電分散に関するデバイの理論から緩和型分散の場合次式が成立する。
図９の位相曲線の極値は、ωｍ・τ付近に現れ、図１０の曲線から実部誘電率ε１（ω）、虚部誘電率ε２（ω）の合成から、それぞれの絶縁物によって図５から、図８までの様相が変化する。

τ：緩和時間 （３８）、（３９）式から、図９が描かれる。
多分散の度合いＱによって、（４０）式に表現できる。

（３８）、（３９）式から、ω・τを消去して、（４１）式を得る。
（４１）式を作図すると図１０の半円となり、これをｃｏｌｅ−ｃｏｌｅｐｌｏｔ という。
位相曲線の極値点の周波数をｆｍとして、図９から、
２・ε２（ｆｍ）＝ε１（０） ・・・・（４２）
複素比誘電率ε＊の絶対値は、コール・コールプロットの半径であることから

ε１（０）＝ ε１（ｆｍ） ｘ ２ ・・・・（４４）
６０ＨＺの周波数のとき、ε１（６０）は、
ε１（６０）＝ ε１（ｆｍ）ｘ ｆｍ／６０ ・・・・（４５）

先の緩和型分散に対して、絶縁物に寄っては、共鳴型分散と言われている様相を呈する（位相曲線の極値が顕著に出てくる）場合がある。これは、電子分極やイオン分極により、電場を印加したとき、電荷の重心の運動は、減衰を伴う弾性振動の系と見なせる場合があり、質量Ｍ，固有振動数ω０，正負電荷量ｑの相対変位Ｘのとき、

減衰項を含む運動方程式は、

ε２（ω）は、ω＝ω０点で、最大となり、ε１（ω）は、０となる。
「が０であれば、実部誘電率ε１（ω）しか存在しない。虚部のε２（ω）＝０である。この模様は、図１１に示す。
（３２）式の根から実部誘電率ε１（ｆｍ）を算出する場合、Ｘの数値部分ＮＭは、次式で求める。

Method for calculating relative permittivity of object from root X of invention

From the Debye theory on dielectric dispersion, the following equation holds for relaxed dispersion.
The extreme value of the phase curve in FIG. 9 appears in the vicinity of ωm · τ. From the synthesis of the real part dielectric constant ε1 (ω) and the imaginary part dielectric constant ε2 (ω) from the curve in FIG. To FIG. 8 changes.

τ: Relaxation time FIG. 9 is drawn from the equations (38) and (39).
Depending on the degree Q of polydispersity, it can be expressed as equation (40).

From equations (38) and (39), ω · τ is eliminated to obtain equation (41).
When formula (41) is drawn, it becomes a semicircle in FIG. 10, which is referred to as “colle-collelot”.
From FIG. 9, assuming that fm is the frequency of the extreme point of the phase curve,
2 · ε2 (fm) = ε1 (0) (42)
Because the absolute value of the complex dielectric constant ε * is the radius of the Cole-Cole plot

ε1 (0) = ε1 (fm) x 2 (44)
At a frequency of 60 Hz, ε1 (60) is
ε1 (60) = ε1 (fm) × fm / 60 (45)

In contrast to the above-described relaxation type dispersion, there is a case where the insulator is in a state called resonance type dispersion (the extreme value of the phase curve appears remarkably). This is because when the electric field is applied due to electronic polarization or ionic polarization, the motion of the center of gravity of the charge may be regarded as a system of elastic vibration accompanied by damping, and the relative mass of M, natural frequency ω0, and positive and negative charge quantity q For displacement X,

The equation of motion including the damping term is

ε2 (ω) is maximum at ω = ω0 point, and ε1 (ω) is 0.
If “is 0, only the real part dielectric constant ε1 (ω) exists. The imaginary part ε2 (ω) = 0. This pattern is shown in FIG.
When calculating the real part dielectric constant ε1 (fm) from the root of the equation (32), the numerical value portion NM of X is obtained by the following equation.

根Ｘのベキ乗指数部分をＦＫＭｆｍで示すと

周波数ｆが、４００ＫＨＺ点＝ｆｕ点で、
インピーダンスＺ（ｆｕ）＝３０００Ωを基準にして、位相曲線上で極値となるｆｍ点の解Ｘのベキ乗指数部分を次の（５４）式でＬＸＸを定義する。
ｆｍは、多数の極値が現れる場合、一番周波数の低い極値点とする。Invention term: In order to match tan δ which has been generally adopted from the past, when the impedance at the point fm of the distortion extreme point of the phase curve of this method is 1500Ω, −10 is taken as a power exponent.

The power exponent part of root X is shown by FKMfm

The frequency f is 400 KHZ point = fu point,
With reference to impedance Z (fu) = 3000Ω, LXX is defined by the following equation (54) for the power exponent part of the solution X at the fm point that is an extreme value on the phase curve.
When a large number of extreme values appear, fm is an extreme point having the lowest frequency.

図６ と（４７）式から、複素比誘電率ε＊の絶対値を（５５）式で表現できる。

ｃｏｌｅ−ｃｏｌｅ ｐｌｏｔの半円からｆｍ点のε＊の絶対値とＸの

（６０）式となる。
Ｘのベキ乗指数からのε＊の数値部分をＮＭｆｍで示し、
Ｘの数値ＮＭにより変動する数値部分をΔＮＭｆｍで示すとInvention term: Similarly, in order to match tan δ which has been generally adopted, an exponent of -12 to 3000Ω is good.

From FIG. 6 and equation (47), the absolute value of the complex relative dielectric constant ε * can be expressed by equation (55).

The absolute value of ε * at the fm point from the semi-circle of the colle-cole plot

(60).
The numerical part of ε * from the power exponent of X is indicated by NMfm,
When the numerical value portion that varies depending on the numerical value NM of X is indicated by ΔNMfm

式で示すと
最小自乗法で、Ａ，Ｂ，Ｃの定数が決まる。As an invention term, there is a method of associating the absolute value of ε *, which is the root of the square of ε1 and ε2 in the Cole-Cole diagram, which is the frequency characteristic of the relative permittivity, with ε * calculated from X by the least square method. It is the point of creation.

In terms of formula
Constants of A, B, and C are determined by the method of least squares.

ただし、

Ｙ（Ｘ）＝ＮＭｆｍ ＋ΔＮＭｆｍ ・・・・（６０）
Ｘ（ε）＝Ｙ（Ｘ） ・・・・（６１）
ｆｍ点から得た複素比誘電率の絶対値［ε＊（ｆｍ）］は、

絶縁物の等価な平行平板に置き換えて、その平板面積をＳ、板間距離をｄとすると、絶縁物のキャパシタンスをＸＣＢとして、

Ｋ：形状係数
ｆｍ ［ＨＺ］点のリアクタンスをｈｘｃＲ［Ω］とすると
ｈｘｃＲ＝１／（ωｍ・ＸＣＢ） ・・・（６４）
固有抵抗をＲｓｉｓ［Ω］とすると
Ｒｓｉｓ＝Ｚｍ・Ｃｏｓθｍ ・・・・（６５）
ただし、Ｚｍ：ｆｍ点のインピーダンス
θｍ：ｆｍ点の位相角［度］
ｆｍ点の絶縁物の沿面の漏洩抵抗を含めた損失角をｔａｎδｍ［％］とするとInvention term: The numerical part NM of X and the FKMfm of the power part are divided into LXX and LHX, and ε * is associated with each other by the method of least squares.

However,

Y (X) = NMfm + ΔNMfm (60)
X (ε) = Y (X) (61)
The absolute value [ε * (fm)] of the complex dielectric constant obtained from the fm point is

Substituting an equivalent parallel flat plate of an insulator, assuming that the flat plate area is S and the distance between the plates is d, the capacitance of the insulator is XCB,

K: When the reactance of the shape factor fm [HZ] point is hxcR [Ω], hxcR = 1 / (ωm · XCB) (64)
When the specific resistance is Rsis [Ω], Rsis = Zm · Cosθm (65)
However, Zm: impedance at fm point θm: phase angle at fm point [degree]
When the loss angle including the leakage resistance along the creepage of the insulator at the fm point is tan δm [%]

６０［ＨＺ］点の絶縁物の沿面の漏洩抵抗を含めた損失角をｔａｎδ［％］とすると
ｔａｎδ［％］＝ｔａｎδｍ［％］・ｆｍ／６０ ・・・・（６７）Invention term: tan δm at the fmHZ point and tan δ at the 60HZ point are calculated from the phase θm and the impedance Zm at the fm point.
This tan δ is a loss angle including the leakage resistance along the creeping surface of the insulator.

Tan δ [%] = tan δm [%] · fm / 60 (67) where the loss angle including the leakage resistance along the creepage of the insulator at the point of 60 [HZ] is tan δ [%].

Tan δ calculated from the effective relative permittivity ε1 in the object and the invalid (imaginary axis) relative permittivity ε2 is expressed by the following equations (10) and (11).

In mathematical processing, if there is an extreme value on the phase curve at the frequency fm [KHZ], the root X of the equation (33) is solved from the impedance Zm [Ω] at that point, and as shown in Table 1, FKMfm of the exponential exponent part of the values of relative permittivity ε *, εr1, X, logarithm display KNN, and tan δ obtained as a calculation result. Enter the remaining life [years] that can be calculated.

As an example of the results obtained by calculating from the root X of the equation (33), three cases of A, B, and C are shown.

An example of a calculation program is shown. Of the two roots X, the power having the smaller absolute value but the larger fluctuation range is adopted. This is because the correlation with the fluctuation range of the complex dielectric constant ε * due to high frequency is larger.

Application circuit to a charged electrical workpiece Measuring circuit used for quality control of objects moving on the manufacturing process line Equivalent circuit in an insulating object Extreme point appearing in phase curve Extreme point of εr2 for an object with a time constant of 0.3μS Extreme point on an object with a time constant of 0.5μS Extreme point on an object with a time constant of 0.05μS Extremity point of εr1, εr2 synthesis on an object with time constant of 0.3μS Debye's relaxation curve Circle diagram of Cole Cole and others Relationship between dielectric constant and frequency of resonant dispersion

Claims (4)

A network analyzer with a high frequency variable frequency of 200 KHZ or higher, or an impedance Z [Ω] and a phase θ [degree] obtained by approaching a certain fixed frequency f [KHZ] suitable for an object among the high frequencies, and a phase curve at a variable frequency Is a phase distortion extreme value point frequency fm [KHZ] that is caused by the maximum point of the complex relative dielectric constant, and the impedance Zm [Ω] at this point is expressed by an attenuation constant α [neper / m] and a phase θm [degree]. Corresponding to the phase constant β [rad / m] and substituting it into the electromagnetic propagation equation, and calculating the complex relative dielectric constant of the two roots (hereinafter referred to as the first root) whose numerical value is the power of the analysis root X Use for. Although there are differences depending on the material, in the high frequency band, the complex relative permittivity ε * forms a Cole-Cole semicircle, and the first root of X for each frequency fm is correlated with ε *. Using the least square method, formulate the degree of relationship and calculate the complex relative permittivity from the previous f, fm, Z, Zm, and θ and θm using the solution of the electromagnetic propagation formula how to When the Zm varies greatly from 9000 Ω to 10 Ω, the power portion varies from −12 to −6 to the power. On the other hand, a method of formulating a relationship in which ε * fluctuates from about 80 to about 2 and adapting it to a solution of an electromagnetic propagation formula established from an attenuation constant α and a phase constant β was created. This makes it possible to calculate tan δ which is a dielectric loss angle of a high insulator. A high-impedance capacitor is used to measure the insulation of charged workpieces, as well as from rotating, parallel-moving liquids, solids, conductors that support moving objects, and semiconductor structures. Apply tan δ measurement system as product quality control from the impedance and phase of the circuit including moving objects

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