JP2004294124A

JP2004294124A - Electrical physical property value measurement method and measuring tool

Info

Publication number: JP2004294124A
Application number: JP2003083761A
Authority: JP
Inventors: Hiromichi Yoshikawa; 博道吉川; Akira Nakayama; 明中山
Original assignee: Kyocera Corp
Current assignee: Kyocera Corp
Priority date: 2003-03-25
Filing date: 2003-03-25
Publication date: 2004-10-21
Anticipated expiration: 2023-03-25
Also published as: JP4726395B2

Abstract

<P>PROBLEM TO BE SOLVED: To provide an electrical physical property value measurement method and a measuring tool for measuring the electrical physical property value of a dielectric substrate having a high dielectric constant and a thick dielectric substrate at a frequency band to be measured, and for greatly improving the measurement precision of the physical property value of the dielectric substrate. <P>SOLUTION: A dielectric substrate 31 is arranged between a pair of closed-end cylindrical conductors 32a, 32b having different depths so that it faces each opening to compose a cylindrical cavity resonator, the resonance frequency and unloaded Q of the TE mode of the cylindrical cavity resonator are measured, and the electrical physical propert values of the dielectric substrate 31 are measured from the resonance frequency and the unloaded Q. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

【０００１】
【発明の属する技術分野】
本発明は電気的物性値測定法及び測定用冶具に関するものであり、特にミリ波領域で電子部品又は回路基板として使用する誘電体材料の誘電定数又は抵抗率を測定するための電気的物性値測定法及び測定用冶具に関するものである。
【０００２】
【従来技術】
従来から、３０ＧＨｚ以上のミリ波帯における誘電体基板の誘電定数測定法としてはファブリぺロ共振器法が知られている。しかしながら、このファブリぺロ共振器法では１辺７５ｍｍ以上の角板、或いは直径７５ｍｍ以上の円板形状の大型の試料が望ましいため、セラミックス等の誘電体基板にこの方法を適用することは困難であった。
【０００３】
これに対して、近年、３０ＧＨｚ以上のミリ波帯における誘電体基板の誘電定数測定法として、遮断円筒導波管法が提案されている（非特許文献１参照）。
【０００４】
この方法は、２個の円筒導波管の間に誘電体基板を配置して共振器構造を構成し、ＴＥ_０ｍ１（ｍ＝１、２・・・）モードの共振周波数と無負荷Ｑを測定し、該共振周波数と無負荷Ｑから誘電体基板の比誘電率と誘電正接を計算する方法である。
【０００５】
又、誘電正接の計算のために必要な遮断円筒内壁の導電率測定は、試料を挟まない状態で行われ、遮断円筒の両端に短絡導体板を配置して構成した空洞共振器のＴＥ_０ｍ１（ｍ＝１、２・・・）モードの共振周波数と無負荷Ｑの測定から決定される。通常、空洞共振器の共振周波数が測定したい周波数帯になるように共振器寸法を設計する。
【０００６】
このような遮断円筒導波管法では、比較的作製容易な１辺３０ｍｍ以下の角板、或いは直径３０ｍｍ以下の円板形状の試料を用いて測定できるため、ミリ波帯における誘電定数測定法として有効である。
【０００７】
【非特許文献１】
「電子情報通信学会、信学技法ＭＷ２００１−１３７（２００１−１２）、「遮断円筒導波管法によるミリ波複素誘電率の測定結果に関する検討」
【０００８】
【発明が解決しようとする課題】
しかしながら、遮断円筒導波管法では、測定試料である誘電体基板の比誘電率や厚さによって、ＴＥ_０ｍ１（ｍ＝１、２・・・）モードの共振周波数が試料を挟まないときの空洞共振器の共振周波数に対して大きく変化する。その結果、測定したい周波数で測定を行うためには比誘電率が高いほど試料の厚さを薄くする必要があり、ある程度の厚みを持った試料では所望の周波数で誘電定数を測定することが困難になるという問題があった。
【０００９】
又、誘電正接の解析するときに用いる円筒内壁の導電率は、試料を挟まない状態で測定される。この測定周波数と試料を挟んだときの周波数の差があまりに大きいと導電率の値に不確かさが生じる。これはミリ波帯では微小ながらも導電率に周波数依存性があるためである。その結果、誘電体基板の誘電定数測定の測定精度に不確かさが生じることも課題である。
【００１０】
例えば、非特許文献１では、内径７．０ｍｍ、長さ２６．１ｍｍを有する遮断円筒の導電率測定の周波数は５３ＧＨｚであるのに対し、比誘電率が２．１と低い場合では、厚さ０．２ｍｍのテフロン（Ｒ）試料の測定周波数は５２ＧＨｚであり、両周波数は近いため、テフロン（Ｒ）試料の誘電正接の測定精度は良好である。同じ遮断円筒を用いて比誘電率が９．４と高いサファイア試料では、テフロン（Ｒ）と同じ厚さ０．２ｍｍの場合、測定周波数は４２ＧＨｚ、厚さ０．５ｍｍの場合、測定周波数は３２ＧＨｚとなり、サファイアの厚みにより測定周波数は大きく低下する。このように比誘電率が高く試料が厚い場合では、測定したい周波数帯で測定できない。更に、試料の測定周波数と遮断円筒の導電率測定の周波数（５３ＧＨｚ）は大きく異なり、サファイア試料の誘電正接の測定精度は誤差が大きくなるという問題があった。
【００１１】
本発明は、比誘電率の高い誘電体基板や厚い誘電体基板の電気的物性値を、測定したい周波数帯で測定できるとともに、誘電体基板の物性値の測定精度を大きく向上できる電気的物性値測定法及び測定用冶具を提供することを目的とする。
【００１２】
【課題を解決するための手段】
本発明者等は上記課題に対して検討を重ねた結果、深さの異なる一対の有底筒状導体間、もしくは有底筒状導体と導体板間に、誘電体基板を配置して円筒空洞共振器を構成し、該円筒空洞共振器のＴＥモード、特にＴＥ_０１１モードの共振周波数と無負荷Ｑを測定し、該共振周波数と無負荷Ｑから、誘電体基板の電気的物性値を求めること、つまり、共振器の構造において電界強度が弱い場所に試料を配置することにより、誘電体基板への電界の集中を緩和し共振周波数の低下を防ぎ、この結果、誘電体基板の電気的物性値を所望の測定周波数で測定するに際して、測定周波数が誘電体基板の比誘電率と厚さに大きく依存しないようにすることにより、測定周波数が３０ＧＨｚ以上のミリ波帯における比誘電率や誘電損失等の電気的物性値を測定できることを見出し、本発明に至った。
【００１３】
即ち、本発明の電気的物性値測定法は、深さの異なる一対の有底筒状導体間に、それぞれの開口部に面するように誘電体基板を配置して円筒空洞共振器を構成し、該円筒空洞共振器のＴＥモードの共振周波数と無負荷Ｑを測定し、該共振周波数と無負荷Ｑから、前記誘電体基板の電気的物性値を求めることを特徴とする。
【００１４】
また、本発明の電気的物性値測定法は、導体板上に誘電体基板を配置し、該誘電体基板上に、開口部が前記誘電体基板側となるように有底筒状導体を載置して円筒空洞共振器を構成し、該円筒空洞共振器のＴＥモードの共振周波数と無負荷Ｑを測定し、該共振周波数と無負荷Ｑから、前記誘電体基板の電気的物性値を求めることを特徴とする。
【００１５】
本発明の誘電定数測定法によって、誘電体基板の比誘電率と厚さに測定周波数を大きく依存させずに、３０ＧＨｚ以上のミリ波帯における誘電定数を測定できる理由を説明する。図５は円筒空洞共振器のＴＥ_０１１モードの電界強度の分布を示すもので、この円筒空洞共振器のＴＥ_０１１モードの電界強度は空洞共振器の高さ方向の中心面で最大になり、両端でゼロになる。１０ＧＨｚ前後で誘電体基板の誘電定数を測定する場合、図６に示すように、空洞共振器の中央に誘電体基板１を配置する方法がＪＩＳＲ１６４１：２００２として規定されている。
【００１６】
しかしながら、この方法を３０ＧＨｚ以上のミリ波帯域に拡張した場合、図７に示すように、空洞共振器の寸法が周波数に比例して小型になるのに対して誘電体基板１の厚さは割れないような厚さまでしか薄くできない。この結果、マイクロ波に比べて共振器の寸法に対する基板の厚みが相対的に大きくなるため、誘電体基板１に蓄積されるＴＥ_０１１モードの電界エネルギーが大きくなる。この状態では、試料を挿入していない状態の空洞共振器のＴＥ_０１１モードの共振周波数に対して、誘電定数の測定周波数が大きく低下する。つまり、上記円筒空洞共振器の測定周波数は、誘電体基板１の比誘電率と厚さに大きく依存するようになる。尚、図５〜７において、符号２ａ、２ｂは遮断円筒を示している。
【００１７】
非特許文献１の誘電定数測定法は、図８（ａ）に示すように両端の導体を除去した円筒空洞、もしくは図８（ｂ）に示すように両端に電波吸収体３ａ、３ｂを配置した遮断円筒とするものであるが、測定周波数が誘電体基板１の比誘電率と厚さに大きく依存する傾向は図７の場合と同じである。
【００１８】
これに対して、本発明の電気的物性値測定法では、図３に示すように、誘電体基板３１を空洞共振器の高さ方向の中心面から外れた面に設置するか、図４に示すように、端面の導体板３６に接して配置するため、円筒空洞共振器本来のＴＥ_０１１モード電界強度の小さな位置に誘電体基板３１を配置することになる。この結果、誘電体基板３１の中に蓄積される電界エネルギーが制限され、ＴＥ_０１１モードの共振周波数の低下、即ち誘電定数の測定周波数の低下が緩和される。
【００１９】
又、本発明の電気的物性値測定法によって得た誘電体基板の比誘電率と誘電正接より、誘電体基板の抵抗率を計算することができるので、本発明は誘電体基板の抵抗率測定法としても機能する。
【００２０】
さらに、本発明の電気的物性値測定法は、円筒空洞共振器の温度を変化させ、該円筒空洞共振器の共振周波数と無負荷Ｑの温度依存性を測定し、誘電体基板の電気的物性値の温度依存性を求めることを特徴とする。このような電気的物性値測定法では、より簡単に誘電体基板の電気的物性値の温度依存性を求めることができる。
【００２１】
また、本発明の測定用冶具は、誘電体基板が載置される導体板と、前記導体板側が開口する有底筒状導体とを具備することを特徴とする。このような測定冶具を用いることにより、より簡単に誘電体基板の電気的物性値を求めることができる。
【００２２】
【発明の実施の形態】
図１は円筒空洞共振器に測定試料である誘電体基板を配置した状態を示す縦断面図である。この図１において円筒空洞共振器は高さ方向中央から外れた面で２分割され、誘電体基板３１が分割面で挟持されている。即ち、円筒空洞共振器３２は、開口部を有し且つ深さの異なる一対の金属製の有底筒状導体３２ａ、３２ｂ間に、それぞれの開口部に面するように誘電体基板３１を介装して構成されている。
【００２３】
有底筒状導体３２ａの側壁には貫通孔が形成され、外部から内部に向けて同軸ケーブル３４ａ、３４ｂが挿通しており、その内部側の先端にはループアンテナ３５ａ、３５ｂが形成されている。ループアンテナ３５ａ、３５ｂの空洞共振器への挿入深さＬはＴＥ_０１１モードの共振周波数における挿入損失が３０ｄＢ程度になるように調整される。
【００２４】
発信器、例えばシンセサイズドスイーパーから周波数が掃引された信号を片方の同軸ケーブルからループアンテナを通して空洞共振器に注入し、ＴＥ_０１１モードの共振電磁界が励振される。他方のループアンテナから同軸ケーブルを通して、空洞共振器の透過信号がネットワークアナライザー等の測定機器に入力され、空洞共振器の共振周波数、無負荷Ｑが測定される。
【００２５】
図２は本発明の電気的物性値測定法の他の形態を示す縦断面図である。この図２において円筒空洞共振器３２は、開口部を有した有底筒状導体３２ａと、導体板３６の間に、開口部に面するように（導体板３６上に）誘電体基板３１を配置して構成される。
【００２６】
円筒空洞共振器のＴＥモード電界強度の小さな位置に誘電体基板３１を配置し、誘電体基板３１の中に蓄積される電界エネルギーを抑制するという点から、図２に示す空洞共振器を用いて測定することが望ましい。
【００２７】
測定用冶具は、図１の場合には、一対の金属製の有底筒状導体３２ａ、３２ｂ、図２の場合には、有底筒状導体３２ａと、導体板３６となる。
【００２８】
この図２の場合、比誘電率は次式から計算される。
【００２９】
【数１】

【００３０】
ここで、ｆ_０は共振周波数、ε_１は比誘電率、ｔ_１は誘電体試料の厚み、Ｌ_１は空洞長さ、Ｒは空洞半径を示す。ただしｄｅｔＨは行列Ｈの行列式であり、Ｈは次式で与えられる。
【００３１】
【数２】

【００３２】
ここで、β_１ｐ、β_２ｐはそれぞれ誘電体領域および空気領域の伝搬定数を示す。又、誘電正接ｔａｎδは次式から計算される。
【００３３】
【数３】

【００３４】
ここで、Ｑｕは無負荷Ｑ、Ｑｄは誘電体損によるＱ、Ｑｃは導体損によるＱである。
【００３５】
【数４】

【００３６】
ここで、Ｗは共振器に蓄えられる全蓄積エネルギー、Ｐ_ｄ１は誘電体で失われる損失エネルギーである。
【００３７】
【数５】

【００３８】
ここで、Ｗは共振器に蓄えられる全蓄積エネルギー、Ｐ_ｃ１は誘電体領域で失われる導体損失エネルギー、Ｐ_ｃ２は空気領域で失われる導体損失エネルギーである。
【００３９】
【数６】

【００４０】
ここで、Ｗ１は誘電体に蓄えられる蓄積エネルギーとＷ２は空気に蓄えられる蓄積エネルギーの和である。
【００４１】
【数７】

【００４２】
ここで、誘電正接ｔａｎδとＰ_ｄ１は次式の関係となっている。
【００４３】
【数８】

【００４４】
ここで、Ｗ１は電界の積分より次式から求められる。
【００４５】
【数９】

【００４６】
ここで、Ｗ２は電界の積分より次式から求められる。
【００４７】
【数１０】

【００４８】
ここで、Ｐ_ｃ１は磁界の積分より次式から求められる。
【００４９】
【数１１】

【００５０】
ここで、Ｐ_ｃ２は磁界の積分より次式から求められる。
【００５１】
比誘電率は共振周波数の測定値より求められ、行列式である式（１）を０にするような比誘電率を求める。また誘電正接は、無負荷Ｑの測定値より式（３）を用いて求める。ここで、誘電正接は式（３）のＱｄに式（７）、（４）を代入することで求められる。又、Ｑｃも式（５）、（１０）、（１１）を式（３）へ代入することで求まる。
【００５２】
また、図１の場合は、シミュレータやモード整合法等の電磁界解析を用いて新たに共振周波数と比誘電率の関係、無負荷Ｑと誘電正接の関係を求めることが必要である。比誘電率は共振周波数の測定値から求めることができる。また誘電正接も同様に、無負荷Ｑの測定値から式（３）の関係を用いて求めることができる。
【００５３】
本発明の電気的物性値測定法は、特にミリ波帯において最も効果があり、有機系材料および無機系誘電体基板の測定に好適に用いることができ、特に比誘電率が２〜２０の誘電体基板の測定に好適である。
【００５４】
また、本発明では、誘電体基板の厚みを厚くしても、共振周波数が殆ど変化しないため、測定試料である誘電体基板の破損を防止でき、より高周波での測定が可能となる。
【００５５】
【実施例】
誘電体基板を挿入する前に、まず、測定で使用する空洞共振器の評価をする必要がある。この評価方法はすでにＪＩＳＲ１６４１：２００２で確立されており、その方法に従った。空洞共振器は、予めモードチャートにより空洞の寸法設計を行っており、測定されるＴＥ_０１１モードの共振ピークが３８ＧＨｚ付近になるように、又、他のモードから妨害されないようになっている。ＴＥ_０１１モードと縮退してるＴＭ_１１１モードは空洞の端板に溝を入れることで分離している。測定に使用する空洞共振器の寸法およびＴＥ_０１１モードのＱｕより測定した比導電率を表１に示す。また、使用した空洞共振器を図２に示す。
【００５６】
【表１】

【００５７】
次に、測定された空洞共振器を用いて誘電体基板の比誘電率、誘電正接の測定を行う。本測定に用いた誘電体基板（試料）は、厚さが０．５ｍｍから０．７ｍｍ程度、直径２０ｍｍのＣ面サファイア基板である。
【００５８】
空洞共振器にサファイア基板を挿入したときの共振周波数も予め計算しておき、横軸比誘電率、縦軸共振周波数のモードチャートを作成し、共振器の設計を行っておく必要がある。具体的には、測定に用いる共振器の寸法が、サファイア基板の厚みが０．５ｍｍから０．８ｍｍ程度、比誘電率が１から１０までの間で、ＴＥ_０１１モードが他のモードと交差することのないように、つまり妨害されることのないように設計されている。
【００５９】
さらにモードチャートから予想されるＴＥ_０１１モードの近くのモードの抑制を行った。測定に用いた寸法の場合では、ＴＥ_３１１モードの抑制のため、直径に対して励振孔を対称関係から３０度ずらした位置に設けている。
【００６０】
更に、ＴＥ_１１２モードの抑制のため励振孔を共振器の長さに対して、サファイア基板側から長さの０．４倍の位置に設けている。ネットワークアナライザを用いて共振周波数および無負荷Ｑの測定を行い、サファイア基板の比誘電率、誘電正接を計算した結果を表２に示す。
【００６１】
【表２】

【００６２】
表１、２より、本発明の電気的物性値測定法においては、空洞共振器本来のＴＥ_０１１モードの共振周波数と、サファイア基板を空洞共振器内に配置した後の共振周波数の変化が少なく、さらにサファイア基板の厚さの増加による共振周波数の低下幅も小さいことが判る。
【００６３】
又、Ｃ軸に垂直なサファイア基板の比誘電率は１０ＧＨｚ前後において９．４〜９．５であることが知られており、本測定結果はこれらと良く一致する。また、サファイア基板の誘電正接は周波数／誘電正接＝１×１０^６ＧＨｚであることが報告されているが、これによると今回の３５ＧＨｚ付近の誘電正接は０．００００３５となり、表２の誘電正接はこれに近い値になっていることが判る。
【００６４】
【発明の効果】
本発明によれば、３０ＧＨｚ以上のミリ波帯においても、空洞共振器の本来のＴＥ_０１１モードの共振周波数と、誘電体基板挿入後の共振周波数の変化が小さいため、所望の周波数で誘電定数等の電気的物性値を測定できる。さらに、空洞共振器の実効導電率の測定周波数と誘電定数の測定周波数が近いため、誘電正接の測定精度を高くすることができる。
【図面の簡単な説明】
【図１】本発明の電気的物性値測定法に用いられる円筒空洞共振器の励振方法の一例を示す説明図である。
【図２】本発明の他の電気的物性値測定法に用いられる円筒空洞共振器の励振方法の一例を示す説明図である。
【図３】図１の電気的物性値測定法に用いられる円筒空洞共振器の構造（ａ）、及び電界強度分布（ｂ）を示すものである。
【図４】図２の電気的物性値測定法に用いられる円筒空洞共振器の構造（ａ）、及び電界強度分布（ｂ）を示すものである。
【図５】従来の円筒空洞共振器の構造（ａ）、及びＴＥ_０１１モードの電界強度分布（ｂ）（ｃ）
【図６】中央に誘電体基板を配置した従来の円筒空洞共振器の構造（ａ）、及び電界強度分布（ｂ）である。
【図７】中央に誘電体基板を配置した従来の円筒空洞共振器の構造（ａ）、及びミリ波帯における電界強度分布（ｂ）である。
【図８】中央に誘電体基板を配置した従来の遮断円筒導波管共振器の構造を示す説明図である。
【符号の説明】
３１・・・誘電体基板（試料）
３２ａ、３２ｂ・・・有底筒状導体
３６・・・導体板[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a method for measuring electrical properties and a jig for measurement, and in particular, to measuring electrical properties for measuring a dielectric constant or resistivity of a dielectric material used as an electronic component or a circuit board in a millimeter wave region. The present invention relates to a method and a measuring jig.
[0002]
[Prior art]
Conventionally, a Fabry-Perot resonator method has been known as a method for measuring the dielectric constant of a dielectric substrate in a millimeter wave band of 30 GHz or more. However, it is difficult to apply this method to a dielectric substrate such as a ceramic because a large sample of a square plate having a side of 75 mm or more or a disk having a diameter of 75 mm or more is desirable in the Fabry-Perot resonator method. there were.
[0003]
On the other hand, in recent years, a cut-off cylindrical waveguide method has been proposed as a method for measuring the dielectric constant of a dielectric substrate in a millimeter wave band of 30 GHz or more (see Non-Patent Document 1).
[0004]
In this method, a dielectric substrate is arranged between two cylindrical waveguides to form a resonator structure, and the resonance frequency and unloaded Q of TE _0m1 (m = 1, 2,...) Mode are measured. In this method, the relative dielectric constant and the dielectric loss tangent of the dielectric substrate are calculated from the resonance frequency and the no-load Q.
[0005]
Further, the conductivity measurement of the inner wall of the cut-off cylinder necessary for calculation of the dielectric loss tangent is performed without sandwiching the sample, and TE _0m1 (TE _0m1 ( m = 1, 2,...) mode and the no-load Q measurement. Usually, the dimensions of the cavity are designed so that the resonance frequency of the cavity is in a frequency band to be measured.
[0006]
Such a cut-off cylindrical waveguide method can be measured using a square plate having a side of 30 mm or less or a disk-shaped sample having a diameter of 30 mm or less, which is relatively easy to manufacture. It is valid.
[0007]
[Non-patent document 1]
"IEICE, IEICE Techniques MW 2001-137 (2001-12)," Study on Measurement Results of Millimeter-Wave Complex Permittivity by Blocked Cylindrical Waveguide Method "
[0008]
[Problems to be solved by the invention]
However, in the cut-off cylindrical waveguide method, the cavity when the resonance frequency of the _TE0m1 (m = 1, 2,...) Mode does not sandwich the sample is _determined by the relative permittivity and the thickness of the dielectric substrate as the measurement sample. It changes greatly with the resonance frequency of the resonator. As a result, in order to perform measurement at the frequency to be measured, it is necessary to reduce the thickness of the sample as the relative dielectric constant increases, and it is difficult to measure the dielectric constant at a desired frequency with a sample having a certain thickness. Was a problem.
[0009]
Further, the conductivity of the inner wall of the cylinder used when analyzing the dielectric loss tangent is measured without a sample interposed therebetween. If the difference between the measurement frequency and the frequency when the sample is sandwiched is too large, uncertainty will occur in the conductivity value. This is because in the millimeter-wave band, conductivity is frequency-dependent, albeit very small. As a result, there is also a problem that the measurement accuracy of the dielectric constant measurement of the dielectric substrate becomes uncertain.
[0010]
For example, in Non-Patent Document 1, while the frequency of conductivity measurement of a blocking cylinder having an inner diameter of 7.0 mm and a length of 26.1 mm is 53 GHz, when the relative dielectric constant is as low as 2.1, the thickness is reduced. The measurement frequency of the 0.2 mm Teflon (R) sample is 52 GHz, and the two frequencies are close to each other. Therefore, the measurement accuracy of the dielectric loss tangent of the Teflon (R) sample is good. In the case of a sapphire sample having a relative dielectric constant as high as 9.4 using the same insulating cylinder, the measurement frequency is 42 GHz when the thickness is 0.2 mm, which is the same as that of Teflon (R), and the measurement frequency is 32 GHz when the thickness is 0.5 mm. And the measurement frequency is greatly reduced by the thickness of the sapphire. When the sample has a high relative dielectric constant and a large thickness, measurement cannot be performed in a desired frequency band. Further, the measurement frequency of the sample and the frequency (53 GHz) of the conductivity measurement of the cut-off cylinder are greatly different, and there is a problem that the measurement accuracy of the dielectric loss tangent of the sapphire sample becomes large.
[0011]
The present invention can measure the electrical properties of a dielectric substrate having a high relative permittivity or a thick dielectric substrate in a frequency band to be measured, and can greatly improve the measurement accuracy of the physical properties of the dielectric substrate. An object of the present invention is to provide a measuring method and a measuring jig.
[0012]
[Means for Solving the Problems]
As a result of repeated studies on the above problems, the present inventors found that a dielectric substrate was disposed between a pair of bottomed cylindrical conductors having different depths or between a bottomed cylindrical conductor and a conductor plate to form a cylindrical cavity. Forming a resonator, measuring a resonance frequency and a no-load Q of a TE mode of the cylindrical cavity resonator, particularly a TE ₀₁₁ mode, and obtaining an electrical property value of the dielectric substrate from the resonance frequency and the no-load Q; In other words, by arranging the sample in a place where the electric field strength is weak in the structure of the resonator, the concentration of the electric field on the dielectric substrate is reduced, and the resonance frequency is prevented from lowering. As a result, the electrical properties of the dielectric substrate are reduced. When measuring at a desired measurement frequency, the measurement frequency does not largely depend on the relative permittivity and the thickness of the dielectric substrate, so that the relative permittivity and dielectric loss in a millimeter wave band of 30 GHz or more are measured. Electrical properties of The inventors have found that measurement can be performed, and have reached the present invention.
[0013]
That is, the method for measuring electrical properties of the present invention comprises the steps of: forming a cylindrical cavity resonator by disposing a dielectric substrate between a pair of bottomed cylindrical conductors having different depths so as to face respective openings. And measuring a resonance frequency and a no-load Q of the TE mode of the cylindrical cavity resonator, and calculating an electrical property value of the dielectric substrate from the resonance frequency and the no-load Q.
[0014]
Further, in the method for measuring electrical properties of the present invention, a dielectric substrate is disposed on a conductor plate, and a bottomed cylindrical conductor is placed on the dielectric substrate such that an opening is on the dielectric substrate side. To form a cylindrical cavity resonator, measure the TE mode resonance frequency and the no-load Q of the cylindrical cavity resonator, and determine the electrical properties of the dielectric substrate from the resonance frequency and the no-load Q. It is characterized by the following.
[0015]
The reason why the dielectric constant measurement method of the present invention can measure the dielectric constant in the millimeter wave band of 30 GHz or more without largely depending on the relative permittivity and the thickness of the dielectric substrate and the measurement frequency will be described. Figure 5 shows the distribution of the electric field strength of the TE ₀₁₁ mode cylindrical cavity resonator, the electric field strength of the TE ₀₁₁ mode of the cylindrical cavity resonator is maximized at the center plane in the height direction of the cavity resonator, both ends And becomes zero. When measuring the dielectric constant of the dielectric substrate at around 10 GHz, as shown in FIG. 6, a method of arranging the dielectric substrate 1 at the center of the cavity resonator is specified in JIS R 1641: 2002.
[0016]
However, when this method is extended to a millimeter wave band of 30 GHz or more, as shown in FIG. 7, while the size of the cavity resonator becomes smaller in proportion to the frequency, the thickness of the dielectric substrate 1 becomes smaller. It can only be thinned to a thickness that does not exist. As a result, the thickness of the substrate relative to the size of the resonator becomes larger than that of the microwave, so that the TE ₀₁₁ mode electric field energy stored in the dielectric substrate 1 increases. In this state, the measured frequency of the dielectric constant is significantly lower than the resonance frequency of the TE ₀₁₁ mode of the cavity resonator in which no sample is inserted. That is, the measurement frequency of the cylindrical cavity resonator greatly depends on the relative permittivity and the thickness of the dielectric substrate 1. 5 to 7,

reference numerals

2a and 2b indicate blocking cylinders.
[0017]
According to the dielectric constant measurement method of Non-Patent Document 1, a cylindrical cavity in which conductors at both ends are removed as shown in FIG. 8A, or radio wave absorbers 3a and 3b are arranged at both ends as shown in FIG. 8B. Although a cut-off cylinder is used, the tendency that the measurement frequency greatly depends on the relative permittivity and the thickness of the dielectric substrate 1 is the same as in the case of FIG.
[0018]
On the other hand, in the method for measuring electrical properties according to the present invention, as shown in FIG. 3, the dielectric substrate 31 is placed on a plane deviated from the center plane in the height direction of the cavity resonator, or as shown in FIG. As shown in the _figure , the dielectric substrate 31 is disposed at a position where the TE ₀₁₁ mode electric field strength inherent in the cylindrical cavity resonator is small, since the dielectric substrate 31 is disposed in contact with the conductor plate 36 on the end face. As a result, the electric field energy stored in the dielectric substrate 31 is limited, and the decrease in the resonance frequency of the TE ₀₁₁ mode, that is, the decrease in the measurement frequency of the dielectric constant is alleviated.
[0019]
Further, the resistivity of the dielectric substrate can be calculated from the relative permittivity and the dielectric loss tangent of the dielectric substrate obtained by the method for measuring electrical properties of the present invention. It also works as a law.
[0020]
Further, the electrical property measurement method of the present invention changes the temperature of the cylindrical resonator, measures the resonance frequency of the cylindrical resonator and the temperature dependence of the no-load Q, and determines the electrical property of the dielectric substrate. It is characterized in that the temperature dependence of the value is obtained. In such an electrical property value measuring method, the temperature dependence of the electrical property value of the dielectric substrate can be obtained more easily.
[0021]
Further, the measuring jig of the present invention is characterized by comprising a conductor plate on which a dielectric substrate is mounted, and a bottomed cylindrical conductor having an opening on the conductor plate side. By using such a measuring jig, the electrical properties of the dielectric substrate can be obtained more easily.
[0022]
BEST MODE FOR CARRYING OUT THE INVENTION
FIG. 1 is a longitudinal sectional view showing a state in which a dielectric substrate as a measurement sample is arranged in a cylindrical cavity resonator. In FIG. 1, the cylindrical cavity resonator is divided into two parts at a plane deviated from the center in the height direction, and a dielectric substrate 31 is sandwiched between the divided planes. That is, the cylindrical cavity resonator 32 has the opening and is disposed between the pair of metal bottomed

cylindrical conductors

32a and 32b having different depths via the dielectric substrate 31 so as to face the respective openings. It is configured by mounting.
[0023]
A through-hole is formed in the side wall of the bottomed cylindrical conductor 32a, and

coaxial cables

34a and 34b are inserted from the outside to the inside, and

loop antennas

35a and 35b are formed at the inner end thereof. . The insertion depth L of the

loop antennas

35a and 35b into the cavity resonator is adjusted so that the insertion loss at the resonance frequency of the TE ₀₁₁ mode is about 30 dB.
[0024]
A signal whose frequency is swept from a transmitter, for example, a synthesized sweeper, is injected from one coaxial cable through a loop antenna into a cavity resonator, and a _TE011 mode resonant electromagnetic field is excited. The transmission signal of the cavity resonator is input from the other loop antenna through a coaxial cable to a measurement device such as a network analyzer, and the resonance frequency and the no-load Q of the cavity resonator are measured.
[0025]
FIG. 2 is a longitudinal sectional view showing another embodiment of the method for measuring electrical properties according to the present invention. In FIG. 2, a cylindrical cavity resonator 32 includes a dielectric substrate 31 between a bottomed tubular conductor 32 a having an opening and a conductor plate 36 so as to face the opening (on the conductor plate 36). It is arranged and configured.
[0026]
The dielectric substrate 31 is disposed at a position where the TE mode electric field strength of the cylindrical cavity resonator is small, and the electric field energy accumulated in the dielectric substrate 31 is suppressed. It is desirable to measure.
[0027]
In FIG. 1, the jig for measurement is a pair of metal-made bottomed

tubular conductors

32a and 32b, and in FIG. 2, a bottomed tubular conductor 32a and a conductor plate 36.
[0028]
In the case of FIG. 2, the relative permittivity is calculated from the following equation.
[0029]
(Equation 1)

[0030]
Here, f ₀ is the resonance frequency, ε ₁ is the relative permittivity, t ₁ is the thickness of the dielectric sample, L ₁ is the cavity length, and R is the cavity radius. Where detH is the determinant of the matrix H, and H is given by the following equation.
[0031]
(Equation 2)

[0032]
Here, β _1p and β _2p indicate propagation constants in the dielectric region and the air region, respectively. The dielectric loss tangent tan δ is calculated from the following equation.
[0033]
[Equation 3]

[0034]
Here, Qu is unloaded Q, Qd is Q due to dielectric loss, and Qc is Q due to conductor loss.
[0035]
(Equation 4)

[0036]
Here, W is the total stored energy stored in the resonator, and P _d1 is the loss energy lost by the dielectric.
[0037]
(Equation 5)

[0038]
Here, W is the total stored energy stored in the resonator, P _c1 is the conductor loss energy lost in the dielectric region, and P _c2 is the conductor loss energy lost in the air region.
[0039]
(Equation 6)

[0040]
Here, W1 is the sum of the stored energy stored in the dielectric and W2 is the sum of the stored energy stored in the air.
[0041]
(Equation 7)

[0042]
Here, the dielectric loss tangent tan δ and P _d1 have the following relationship.
[0043]
(Equation 8)

[0044]
Here, W1 is obtained from the following equation from the integral of the electric field.
[0045]
(Equation 9)

[0046]
Here, W2 is obtained from the following equation based on the integral of the electric field.
[0047]
(Equation 10)

[0048]
Here, P _c1 is obtained from the following equation from the integral of the magnetic field.
[0049]
[Equation 11]

[0050]
Here, _Pc2 is obtained from the following equation from the integration of the magnetic field.
[0051]
The relative permittivity is obtained from the measured value of the resonance frequency, and the relative permittivity that makes the determinant (1) zero is obtained. The dielectric loss tangent is obtained from the measured value of the no-load Q using Expression (3). Here, the dielectric loss tangent is obtained by substituting equations (7) and (4) for Qd in equation (3). Qc can also be obtained by substituting equations (5), (10) and (11) into equation (3).
[0052]
In the case of FIG. 1, it is necessary to newly obtain the relationship between the resonance frequency and the relative dielectric constant and the relationship between the no-load Q and the dielectric loss tangent by using an electromagnetic field analysis such as a simulator or a mode matching method. The relative permittivity can be obtained from the measured value of the resonance frequency. Similarly, the dielectric loss tangent can be determined from the measured value of the no-load Q using the relationship of Expression (3).
[0053]
The method for measuring electrical properties of the present invention is most effective especially in the millimeter wave band, and can be suitably used for measurement of organic materials and inorganic dielectric substrates. It is suitable for measurement of a body substrate.
[0054]
Further, in the present invention, even if the thickness of the dielectric substrate is increased, the resonance frequency hardly changes, so that the dielectric substrate, which is a measurement sample, can be prevented from being damaged, and measurement at a higher frequency can be performed.
[0055]
【Example】
Before inserting the dielectric substrate, it is necessary to first evaluate the cavity used in the measurement. This evaluation method has already been established in JIS R 1641: 2002, and was followed. The cavity size of the cavity is designed in advance using a mode chart, so that the measured TE ₀₁₁ mode resonance peak is around 38 GHz and is not disturbed by other modes. The TE ₀₁₁ mode and the degenerated TM ₁₁₁ mode are separated by making a groove in the end plate of the cavity. Table 1 shows the dimensions of the cavity resonator used for measurement and the specific conductivity measured from Qu in the TE ₀₁₁ mode. FIG. 2 shows the used cavity resonator.
[0056]
[Table 1]

[0057]
Next, the relative permittivity and the dielectric loss tangent of the dielectric substrate are measured using the measured cavity resonator. The dielectric substrate (sample) used in this measurement is a C-plane sapphire substrate having a thickness of about 0.5 mm to 0.7 mm and a diameter of 20 mm.
[0058]
It is necessary to calculate the resonance frequency when the sapphire substrate is inserted into the cavity resonator in advance, create a mode chart of the relative dielectric constant on the horizontal axis and the resonance frequency on the vertical axis, and design the resonator. Specifically, when the dimensions of the resonator used for the measurement are such that the thickness of the sapphire substrate is about 0.5 mm to 0.8 mm and the relative dielectric constant is 1 to 10, the TE ₀₁₁ mode intersects the other modes. It is designed to be unobtrusive, that is, unobstructed.
[0059]
Further, a mode near the TE ₀₁₁ mode expected from the mode chart was suppressed. In the case of the dimensions used for the measurement, in order to suppress the TE ₃₁₁ mode, the excitation holes are provided at positions shifted by 30 degrees from the symmetric relation with respect to the diameter.
[0060]
Further, an excitation hole is provided at a position 0.4 times the length from the sapphire substrate side to the length of the resonator to suppress the TE ₁₁₂ mode. Table 2 shows the results obtained by measuring the resonance frequency and the no-load Q using a network analyzer and calculating the relative permittivity and the dielectric loss tangent of the sapphire substrate.
[0061]
[Table 2]

[0062]
From Tables 1 and 2, it can be seen that, in the method for measuring electrical properties of the present invention, the change in the resonance frequency of the TE ₀₁₁ mode inherent in the cavity resonator and the resonance frequency after the sapphire substrate is disposed in the cavity resonator are small. Further, it can be seen that the decrease in the resonance frequency due to the increase in the thickness of the sapphire substrate is small.
[0063]
It is known that the relative permittivity of the sapphire substrate perpendicular to the C axis is 9.4 to 9.5 at around 10 GHz, and the present measurement results agree well with these. It is also reported that the dielectric loss tangent of the sapphire substrate is frequency / dielectric tangent = 1 × 10 ⁶ GHz. According to this, the dielectric loss tangent around 35 GHz this time is 0.000035, and the dielectric loss tangent in Table 2 is It can be seen that the value is close to this.
[0064]
【The invention's effect】
According to the present invention, even in the millimeter wave band of 30 GHz or more, since the change in the resonance frequency of the original TE ₀₁₁ mode of the cavity resonator and the resonance frequency after inserting the dielectric substrate is small, the dielectric constant and the like at a desired frequency are reduced. Can be measured for electrical properties. Further, since the measurement frequency of the effective conductivity of the cavity resonator is close to the measurement frequency of the dielectric constant, the measurement accuracy of the dielectric loss tangent can be increased.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram showing an example of a method of exciting a cylindrical cavity resonator used in a method for measuring electrical properties of the present invention.
FIG. 2 is an explanatory diagram showing an example of a method of exciting a cylindrical cavity resonator used in another method for measuring electrical properties of the present invention.
FIG. 3 shows a structure (a) of a cylindrical cavity resonator used in the method for measuring electrical properties shown in FIG. 1 and an electric field intensity distribution (b).
4 shows a structure (a) and an electric field intensity distribution (b) of a cylindrical cavity resonator used in the method for measuring electrical properties shown in FIG.
FIG. 5 shows the structure of a conventional cylindrical cavity resonator (a), and the electric field intensity distribution in the TE ₀₁₁ mode (b) (c).
FIG. 6 shows a structure (a) of a conventional cylindrical cavity resonator having a dielectric substrate disposed at the center, and an electric field intensity distribution (b).
FIGS. 7A and 7B show a structure of a conventional cylindrical cavity resonator having a dielectric substrate disposed at the center (a) and an electric field intensity distribution in a millimeter wave band (b).
FIG. 8 is an explanatory diagram showing the structure of a conventional blocking cylindrical waveguide resonator having a dielectric substrate disposed at the center.
[Explanation of symbols]
31 ... Dielectric substrate (sample)
32a, 32b: tubular conductor with bottom 36: conductor plate

Claims

Between a pair of bottomed tubular conductors having different depths, a dielectric substrate is arranged so as to face each opening to form a cylindrical cavity resonator, and the resonance frequency of the TE mode of the cylindrical cavity resonator and A method for measuring an electrical property value, comprising measuring an unloaded Q and obtaining an electrical property value of the dielectric substrate from the resonance frequency and the unloaded Q.

A dielectric substrate is placed on a conductor plate, and a bottomed tubular conductor is placed on the dielectric substrate so that an opening is on the dielectric substrate side to form a cylindrical cavity resonator. A method for measuring an electrical property value, comprising measuring a resonance frequency and a no-load Q of a TE mode of a cavity resonator, and obtaining an electrical property value of the dielectric substrate from the resonance frequency and the no-load Q.

3. The electrical property measurement according to claim 1, wherein the resonance frequency and the no-load Q of the TE ₀₁₁ mode are measured, and the electrical property of the dielectric substrate is obtained from the resonance frequency and the no-load Q. Law.

Changing the temperature of the cylindrical resonator, measuring the temperature dependence of the resonance frequency and the no-load Q of the cylindrical resonator, and determining the temperature dependence of the electrical properties of the dielectric substrate. Item 4. The method for measuring electrical properties according to any one of Items 1 to 3.

A measuring jig comprising: a conductor plate on which a dielectric substrate is mounted; and a bottomed cylindrical conductor having an opening on the conductor plate side.