JP5082386B2 - Insulator dielectric loss angle (referred to as tan δ) during operation - Google Patents

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.

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), which can be derived from the phase angle, and α = 1 / Zm and β = θm in (31) are substituted, the root X in (33) is FKMfm varies from −12 to −6 as follows: The first root having a power exponent is adopted.

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）
ｔａｎδ＝１００・ε２／ε１＝１００／Ｒ・Ｃ・ω・・・・（１０）
ｔａｎδ＝１００・ＩＲ／ＩＣ ・・・・（１１）
この誘電体損ｔａｎδ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。
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
Ｉ＝σＥ Δ^ＸＥ＝−ｊωμＨ
・・・・（１２） ・・・・（１３）
Δ^ＸＨ＝（σ＋ｉωε）Ｅ ・・・・（１４）
Δ^ＸΔ^ＸＥ＝−Δ^２Ｅ＝（−ｉωｕ）（σ＋ｉωε）Ｅ
・・・・（１５）

電界が Ｘ 方向、波が、Ｚ 方向に進行するとき

Ｚ＝ｊω μ／γ ・・・・（２０）

（２１）式の両辺を２乗して実部と虚部とが等しいと置くと
−ω^２εｕ＋ｉωｕσ＝α^２−β^２＋ｉ２αβ
α^２−β^２＝−ω^２εｕ・・・・（２２）
・・・・（２３）
２αβ＝ ω ｕ σ ・・・・（２４）
（２３）、（２４）式からβを消去して、
４α^２＋４ω^２εｕα^２−ω^２σ^２ｕ^２＝０・・・・（２５）

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σ^２り、 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)
tan δ = 100 · ε2 / ε1 = 100 / R · C · ω (10)
tan δ = 100 · IR / IC (11)
This dielectric loss tan δ represents the dielectric loss due to the physical properties in the applied insulating object.
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, if the conductivity in the insulator is σ, the dielectric constant is ε, and the magnetic permeability is μ, I = σE Δ ^X E = −jωμH
(12) (12)
Δ ^X H = (σ + iωε) E (14)
^{Δ X Δ X E = -Δ 2} E = (- iωu) (σ + iωε) E
.... (15)

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

Z = jω μ / γ (20)

If both sides of equation (21) are squared and the real part and the imaginary part are equal, -ω ² εu + iωuσ = α ² −β ² + i2αβ
α ² −β ² = −ω ² εu (22)
.... (23)
2αβ = ω u σ (24)
Eliminating β from the equations (23) and (24),
4α ² + 4ω ² εuα ² −ω ² σ ² u ² = 0 (25)

Since 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, equations (26) and (27) are as follows.

(28). By eliminating σ ^{2 according to} equation (29), equation (30) is obtained,
Dividing from ε> 0 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^２／ε０ ・・・・（３６）
＝（εｒ１−ｊ・εｒ２）

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

ε *: relative permittivity is expressed by complex number at high frequency εr1: real part of relative permittivity εr2: imaginary part of non-permittivity NM: numerical part of real root of solution FKM: floating exponent FKMfm of factorial part of numerical value of root : Factorial exponent at the extreme frequency point fm of the phase (superscript on the right shoulder)
fm: frequency of the point having the extreme value on the phase curve See FIG. 4 X = NM · FKMfm (35)
From equation (32) ε * (fm) = X ² / 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−ｃｏｌｅ ｐｌｏｔという。
デバイの式の固有振動ω０は、本案の測定では２πｆｍに当たり
位相曲線の極値点の周波数をｆｍとして、図９から、半径＝｜ε＊｜＝ε２（ｆｍ）であり、ε１（０）は直径に当たり、（４２）式が成立する。
実用するには、近似的に周波数が∞の時ε１（∞）≒０となり、６０ＨＺの時は、ε１（６０）≒ε１（０）と置ける。そして、
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半径

図１０から、半径｜ε^＊｜＝ε２（ｆｍ）が等しいことから、この円弧則から
ε１（０）≒ε１（６０）＝２・ε２（ｆｍ）＝２・｜ε＊（ｆｍ）｜・・・・（４３）
ε１（０）＝ ε２（ｆｍ） ｘ ２ ・・・・（４４）
ε１（６０）＝εｒ１（６０）≒ε１（０） ・・・・（４５）
ε２（ｆｍ）＝ ｜ε^＊｜ から・・・・・（４６）

円弧則を用いると
ε１（０）＝２×ε２（ｆｍ） ・・・・（４８）
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（ω０）は、０となる。
ωが０であれば、実部誘電率ε１（０）しか存在しない。虚部のε２（０）＝０である。この模様は、図１０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。
Ｘ＝１．２３ｘ １０^−１０ 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 of polydispersity Q, it can be expressed as (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-coll plot”.
The natural vibration ω0 in the Debye equation corresponds to 2πfm in the measurement of the present plan, and the frequency of the extreme point of the phase curve is fm, and from FIG. 9, radius = | ε * | = ε2 (fm), and ε1 (0) corresponds to the diameter, and formula (42) is established.
In practical use, when the frequency is approximately ∞, ε1 (∞) ≈0, and when the frequency is 60 Hz, ε1 (60) ≈ε1 (0). And
2 · ε2 (fm) = ε1 (0) (42)
The absolute value of the complex dielectric constant ε * is the radius of the Cole-Cole plot.

From FIG. 10, since the radius | ε ^* | = ε2 (fm) is equal,
ε1 (0) ≈ε1 (60) = 2 · ε2 (fm) = 2 · | ε * (fm) | (43)
ε1 (0) = ε2 (fm) x 2 (44)
ε1 (60) = εr1 (60) ≈ε1 (0) (45)
From ε2 (fm) = | ε ^* | (46)

Using the arc rule, ε1 (0) = 2 × ε2 (fm) (48)
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 When the displacement is X,

The equation of motion including the damping term is

ε2 (ω) is maximum at ω = ω0 point, and ε1 (ω0) is 0.
If ω is 0, only the real part dielectric constant ε1 (0) exists. The imaginary part ε2 (0) = 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.
X = 1.23 × 10 ⁻¹⁰

根Ｘのベキ乗指数部分をＦＫＭｆｍで示すと
ＦＫＭｆｍ＝ １０^−１０ ・・・・（５３）
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堝含、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.

When the power exponent part of the root X is represented by FKMfm, FKMfm = 10 ⁻¹⁰ (53)
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.
fm is the extreme point with the lowest frequency, including the crucible where many extreme values appear.

図６ と
（４７）式から、

ｃｏｌｅ−ｃｏｌｅ ｐｌｏｔの半円からｆｍ点のε＊の絶対値Ｘの１０^−１２を基準としたベキ乗指数部分ＬＸＸとの相関は、（５６）式で示せる。相関曲線は、最小自乗法で、ａ，ｂ，ｃの定数を決める。絶対値
｜ε^＊（ｆｍ）｜とＬＸＸとの関連を最小自乗法で関係式Ｙ（Ｘ）を作成すると
（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 that has been generally adopted, an exponent of -12 to 3000Ω is good

From FIG. 6 and equation (47),

The correlation with the power exponent portion LXX based on 10 ⁻¹² of the absolute value X of ε * at the fm point from the semicircle of the core-coll plot can be expressed by the equation (56). The correlation curve determines the constants a, b, and c by the method of least squares. When the relational expression Y (X) is created by the least square method for the relationship between the absolute value | ε ^* (fm) | and LXX, the expression (60) is obtained.
The numerical part of ε * from the power exponent of X is indicated by NMfm, and the numerical part that varies depending on the numerical value NM of X is indicated by ΔNMfm.

１０^−１１を基準としたベキ乗指数部分ＬＨＸ｛（５９）式｝との相関を、（５７）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, 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, and | ε * | The method is the point of creating this proposal.

When the correlation with the power exponent portion LHX {Equation (59)} on the basis of 10 ⁻¹¹ is represented by Equation (57), the constants of A, B, and C are determined by the method of least squares.

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ｆｍ点のキャパシタスをＸＣＢとして、

ＸＣＢは、ε＊が周波数によって非線形変動するので、低周波の６０ＨＺへの換算は、コール・コールの円弧則から比誘電率ε１（６０）を出し、（６９）式、（７０）式で、６０ＨＺでのリアクタンスＸＣＲ［Ω］を算出する。
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.

Substituting an equivalent parallel flat plate of an insulator, where the flat plate area is S and the distance between the plates is d, the capacitor at the fm point of the insulator is XCB,

In XCB, since ε * fluctuates nonlinearly depending on the frequency, the conversion to low frequency 60HZ is based on Cole-Cole's arc law, giving the relative permittivity ε1 (60), and the equations (69) and (70) The reactance XCR [Ω] at 60 Hz is calculated.
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

高絶縁物は、低周波では電流が通過せず、測定が不可能である。そこで、当発明項のように高周波を印加して、測定可能とし、抵抗のｆｍから６０ＨＺへの換算は次式とする。

ＸＣＢ［Ｆ］＝ε０・ εｒ１（６０）・Ｓ／ｄ （６９）
ＸＣＲ［Ω］＝１／（３７７・ＣＢ） （７０）ただし、Ｓ［ｍ^２］は絶縁物の面積、ｄ［ｍ］は、絶縁物の厚さである。このように、高周波ｆｍ印加により、高絶縁物の誘電体損失角ｔａｎδｍ［％］を得て、６０ＨＺのｔａｎδ［％］を算出する。
ｆｍ点では、Ｒｓｉｓ＝Ｚｍ・Ｃｏｓθｍであり、リアクタンスｈｘｃＲ＝１／（ωｍ・ＸＣＢ）であり、６０ＨＺへの換算は、抵抗が（６８）式でＲとし、ＸＣＢの比誘電率εｒ１（６０）は、円弧則で換算し、６０ＨＺでのリアクタンスＸＣＲを出して、（６７）式でｔａｎδを算出する。tan δm at the fmHZ point is calculated by the equation (66), and tan δ at the 60 HZ point is calculated from the equation (67).
From the phase θm at the fm point and the impedance Zm , | ε * |
The relative dielectric constant ε1 (60) = εr1 (60) is calculated from the arc rule, and tan δ is calculated. This tan δ is a loss angle including the leakage resistance along the creeping surface of the insulator.

When the loss angle including the leakage resistance along the creepage of the insulator at 60 [HZ] is tan δ [%]

High insulators do not pass current at low frequencies and cannot be measured. Therefore, it is possible to measure by applying a high frequency as in the present invention, and the conversion of resistance from fm to 60 Hz is as follows.

XCB [F] = ε0 · εr1 (60) · S / d (69)
XCR [Ω] = 1 / (377 · CB) (70) where S [m ² ] is the area of the insulator and d [m] is the thickness of the insulator. In this way, the dielectric loss angle tan δm [%] of the high insulator is obtained by applying the high frequency fm , and the tan δ [%] of 60 Hz is calculated.
At the fm point, Rsis = Zm · Cos θm, reactance hxcR = 1 / (ωm · XCB), and conversion to 60HZ is that the resistance is R in the equation (68), and the relative permittivity εr1 (60) of XCB Is converted by the arc law, reactance XCR at 60 HZ is obtained, and tan δ is calculated by equation (67).

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).
tan δ = 100 · ε2 / ε1 = 100 / R · C · ω (10)
tan δ = 100 · IR / IC (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. From this, the lifetime correlation from the result of each substance is obtained from the least square method. 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 (1)

Using a network analyzer that outputs a signal with a high-frequency variable frequency of 200 KHZ or higher, measure the frequency characteristics of impedance Z [Ω] and phase θ [degrees] of the insulator to be measured. The frequency fm [KHZ] of the corresponding phase distortion extreme point, the impedance Zm [Ω] and the phase θm [degree] of this point are obtained, and the impedance Zm [Ω] is determined as the attenuation constant α [Neper / m] and the phase. θm [degree] is made to correspond to the phase constant β [rad / m], and α = 1 / Zm is substituted into the electromagnetic propagation equation. A method for calculating a complex dielectric constant of a measured insulator,
The calculation of the complex dielectric constant from the electromagnetic propagation equation uses the equation (1):

Method of calculating complex relative permittivity of calculating absolute value | ε * (fm) | of complex relative permittivity from formula (2) from X1 which is the smaller of two roots X1 and X2 from quadratic formula of X .
ε0 = dielectric constant in vacuum

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