JP4164274B2 - Automatic balancing circuit for impedance measurement - Google Patents

Description

【数４】

【００１６】
上記（５）において、位相角θｂａｌ１もしくはθｂａｌ２での電圧値ＶθｂａｌＡと平均値Ｖａｖｅとを比較する場合、別の態様として、平均値Ｖａｖｅに代えて、上記電圧Ｖｘ，Ｖｙ，Ｖｚの中間値Ｖｍｉｄを採用してもよい。また、上記（５）での不等式ＶθｂａｌＡ＞Ｖａｖｅ，ＶθｂａｌＡ＜Ｖａｖｅのいずれか一方に等号を持たせてもよい。
【００１７】
【発明の実施の形態】
図１に本発明に係る自動平衡回路１００のブロック図を示す。ハード的に構成は上記先願発明と同じであるが、本発明の実施形態を先願発明と対比しながら説明する。
【００１８】
上記先願発明と同じく、この自動平衡回路１００は、第１発振器１０１と第２発振器１０６の２つの発振器を備え、第１発振器１０１側のＨ端子点（信号印加側端子点）と第２発振器１０６側のＬ端子点（電流検出側端子点）との間に被測定試料１０２が装着される。
【００１９】
第１発振器１０１から所定周波数の正弦波信号が被測定試料１０２に与えられる。第２発振器１０６からも上記測定用正弦波信号と同一周波数の正弦波信号が出力されるが、第２発振器１０６とＬ端子点との間には、検出素子としての検出抵抗１０５が接続されている。なお、検出抵抗１０５に代えて、インピーダンスが正確に分かっていることを条件として、コンデンサ（Ｃ）やコイル（Ｌ）を用いてもよい。
【００２０】
また、この自動平衡回路１００は、Ｌ端子点の電圧を検出する電圧検出器１０７およびその検出電圧をディジタル信号に変換するＡ／Ｄ変換器１０８と、同Ａ／Ｄ変換器１０８からの検出電圧データに基づいて第２発振器１０６の振幅および位相角を制御するとともに、被測定試料１０２のインピーダンスおよび位相角などを算出する機能を有する制御手段としてのＣＰＵ１０９とを備えている。
【００２１】
本発明においても上記先願発明と同様に、ＣＰＵ１０９により２つの発振器の内の例えば第２発振器１０６に対して、その振幅を任意の振幅Ｂａとした状態で、３つの異なる位相角θｘ，θｙおよびθｚを順次設定して、その各位相角ごとに被測定試料１０２のＬ端子点側に現れる電圧Ｖｘ，ＶｙおよびＶｚを測定することにより、下記の式（Ａ１），（Ａ２）により算出される位相角θｂａｌ１，θｂａｌ２のいずれか一方を平衡状態の第１成立要因としての平衡位相角θｍｉｎとすることができる。
【００２２】
【数５】

【数６】

【００２３】
また、上記先願発明においては、第２発振器１０６の位相角を上記位相角θｍｉｎに調整した後、振幅を２つの異なる振幅Ｂａ，Ｂｂ（好ましくは同一レンジ内）に順次設定して、その各振幅ごとにＬ端子点側に現れる電圧Ｖａ，Ｖｂを測定することにより、下記の式（Ｂ１），（Ｂ２）により算出されるいずれか一方の振幅を平衡状態の第２成立要因としての平衡振幅Ｂｍｉｎとしている。なお、平衡状態とはＬ端子が最小電圧（好ましくは０Ｖ）となる状態を言う。
【００２４】
【数７】

【数８】

【００２５】
ここで、上記各式の導出過程を手短に説明する（詳しくは、上記先願発明を参照されたい）。第１発振器１０１の振幅をＡ，その位相角をθａ、第２発振器１０６の振幅をＢ，その位相角をθｂ，検出抵抗１０５のインピーダンスをＺｆ，その位相角をθｆ，Ｌ端子に発生する入力容量ＣのインピーダンスをＺｉ，その位相角をθｉ，そして被測定試料１０２のインピーダンスをＺｍ，その位相角をθｍとする。なお、第１発振器１０１と第２発振器１０６の周波数はともに同一でωとする。
【００２６】
Ｌ端子点の電圧をＶＬとして、キルヒホッフの法則によりＬ端子点に流れ込む電流の総和は０になるため、次式（１）が成立する。
【数９】

【００２７】
この式（１）を展開すると、Ｌ端子点の電圧ＶＬの振幅は次式（２），位相は次式（３）となる。
【数１０】

【数１１】

ただし、式（２）中のＹｔは次式（４）である。
【数１２】

【００２８】
平衡状態ではＬ端子点の電圧ＶＬが０Ｖ（最小）になる。まず、平衡位相角θｍｉｎを求めるため、第２発振器１０６に３つの異なる位相角を順次設定して、その各々のＬ端子点の電圧ＶＬを測定して、上記式（Ａ１），（Ａ２）により平衡位相角候補としての２つの位相角θｂａｌ１，θｂａｌ２を算出するが、上記式（Ａ１），（Ａ２）での計算を容易にするため、３つの異なる位相角を９０゜，１８０゜，２７０゜とする。
【００２９】
振幅はいずれの場合もＢａとして、位相を９０゜としたときにＬ端子点で測定される電圧をＶ_９０，位相を１８０゜としたときにＬ端子点で測定される電圧をＶ_１８０，位相を２７０゜としたときにＬ端子点で測定される電圧をＶ_２７０とすると、上記式（Ａ１），（Ａ２）より、一方の位相角θｂａｌ１は次式（５）で表され、他方の位相角θｂａｌ２は次式（６）で表される。
【数１３】

【数１４】

【００３０】
この式（５），（６）の根拠について説明する。Ｌ端子点の振幅は上記式（２）であるから、これを自乗すると次式（７）が得られる。
【数１５】

【００３１】
式（７）中、変数は第２発振器１０６の位相角θｂのみであるから、ここでα，β，γを定数として式（７）を次式（８）に置き換える。
ＶＬ^２＝α＋βｃｏｓ（γ＋θｂ）……（８）
【００３２】
上記のように、第２発振器１０６の位相を９０゜に設定し、そのときの電圧をＶ_９０とすると式（８）より、
Ｖ_９０ ^２＝α＋βｃｏｓ（γ＋９０）＝α−βｓｉｎγ……（９）
同じく式（８）より、第２発振器１０６の位相を１８０゜に設定し、そのときの電圧をＶ_１８０とすると、
Ｖ_１８０ ^２＝α＋βｃｏｓ（γ＋１８０）＝α−βｃｏｓγ……（１０）
同じく式（８）より、第２発振器１０６の位相を２７０゜に設定し、そのときの電圧をＶ_２７０とすると、
Ｖ_２７０ ^２＝α＋βｃｏｓ（γ＋２７０）＝α＋βｓｉｎγ……（１１）
【００３３】
上記式（９），（１１）より、
Ｖ_９０ ^２＋Ｖ_２７０ ^２＝２α……（１２）
上記式（１０），（１２）より、
Ｖ_１８０ ^２＝（Ｖ_９０ ^２＋Ｖ_２７０ ^２）／２−βｃｏｓγ
したがって、βｃｏｓγ＝（Ｖ_９０ ^２＋Ｖ_２７０ ^２）／２−Ｖ_１８０ ^２……（１３）
上記式（９），（１２）より、
Ｖ_９０ ^２＝（Ｖ_９０ ^２＋Ｖ_２７０ ^２）／２−βｓｉｎγ
したがって、βｓｉｎγ＝（Ｖ_２７０ ^２−Ｖ_９０ ^２）／２……（１４）
【００３４】
上記式（１３），（１４）より、
ｔａｎγ＝（（Ｖ_２７０ ^２−Ｖ_９０ ^２）／２）／（（Ｖ_９０ ^２＋Ｖ_２７０ ^２）／２−Ｖ_１８０ ^２）
＝（Ｖ_２７０ ^２−Ｖ_９０ ^２）／（Ｖ_９０ ^２＋Ｖ_２７０ ^２−２Ｖ_１８０ ^２）
よって、
γ＝ｔａｎ^−１（（Ｖ_２７０ ^２−Ｖ_９０ ^２）／（Ｖ_９０ ^２＋Ｖ_２７０ ^２−２Ｖ_１８０ ^２））…（１５）
【００３５】
平衡状態では上記式（８）中のｃｏｓ（γ＋θｂ）＝−１となるため、
γ＋θｍｉｎ＝１８０……（１６）
上記式（１５），（１６）より、平衡位相θｍｉｎは、
θｍｉｎ＝１８０−γ、
したがってθｍｉｎ＝１８０−ｔａｎ^−１（（Ｖ_２７０ ^２−Ｖ_９０ ^２）／（Ｖ_９０ ^２＋Ｖ_２７０ ^２−２Ｖ_１８０ ^２））……（１７）
【００３６】
上記のアルゴリズムで算出される位相角θｍｉｎは、測定対象がコンデンサ，抵抗，コイルなどであるとして±９０゜（９０゜〜２７０゜）の範囲を想定してのものであるが、測定回路で使用されているオペアンプやフィルタなどで生ずる位相誤差や検出抵抗１０５の位相角θｆによって位相角θｍｉｎが±９０゜の範囲外になる場合がある。
【００３７】
一例として、コンデンサを測定した場合、被測定試料１０２の位相角θｍは−９０゜となるが、検出抵抗１０５の位相角θｆが２０゜であると仮定した場合、θｍｉｎ＝２９０゜（−７０゜）となる。
【００３８】
そこで、位相角θｍｉｎが±１８０゜の範囲に存在する場合、上記式（１５）は、
ｔａｎ^−１（（Ｖ_２７０ ^２−Ｖ_９０ ^２）／（Ｖ_９０ ^２＋Ｖ_２７０ ^２−２Ｖ_１８０ ^２））＝γまたは１８０＋γ……（１８）
となり、上記式（１６），（１８）により、
θｍｉｎ（θｂａｌ１）＝１８０−ｔａｎ^−１（（Ｖ_２７０ ^２−Ｖ_９０ ^２）／（Ｖ_９０ ^２＋Ｖ_２７０ ^２−２Ｖ_１８０ ^２））……（１９）
または
θｍｉｎ（θｂａｌ２）＝−ｔａｎ^−１（（Ｖ_２７０ ^２−Ｖ_９０ ^２）／（Ｖ_９０ ^２＋Ｖ_２７０ ^２−２Ｖ_１８０ ^２））……（２０）
となる。
【００３９】
次に、平衡振幅Ｂｍｉｎを算出する上記式（Ｂ１），（Ｂ２）の根拠について説明する。第２発振器１０６の位相をθｍｉｎ，振幅をＢａに設定したときのＬ端子点で測定される電圧をＶａとする。また、第２発振器１０６の位相をθｍｉｎ，振幅をＢｂに設定したときのＬ端子点で測定される電圧をＶｂとする。
【００４０】
Ｌ端子点の振幅は上記式（２）で表されるため、位相をθｍｉｎにしたときの式（２）は次式（２１）または次式（２２）のようになる。
ＶＬ＝（Ａ・Ｚｆ−Ｂ・Ｚｍ）／Ｚｆ・Ｚｍ・Ｙｔ……（２１）
ＶＬ＝−（Ａ・Ｚｆ−Ｂ・Ｚｍ）／Ｚｆ・Ｚｍ・Ｙｔ……（２２）
【００４１】
これらの式（２１），（２２）に、振幅をＢａに設定して上記Ｌ端子点で測定された電圧Ｖａをあてはめると、
Ｖａ＝（Ａ・Ｚｆ−Ｂａ・Ｚｍ）／Ｚｆ・Ｚｍ・Ｙｔから、
Ｚｆ・Ｚｍ・Ｙｔ＝（Ａ・Ｚｆ−Ｂａ・Ｚｍ）／Ｖａ ……（２３）
または、
Ｖａ＝（−Ａ・Ｚｆ＋Ｂａ・Ｚｍ）／Ｚｆ・Ｚｍ・Ｙｔから、
Ｚｆ・Ｚｍ・Ｙｔ＝（−Ａ・Ｚｆ＋Ｂａ・Ｚｍ）／Ｖａ ……（２４）
【００４２】
また、上記式（２１），（２２）に、振幅をＢｂに設定して上記Ｌ端子点で測定された電圧Ｖｂをあてはめると、
Ｖｂ＝（Ａ・Ｚｆ−Ｂｂ・Ｚｍ）／Ｚｆ・Ｚｍ・Ｙｔから、
Ｚｆ・Ｚｍ・Ｙｔ＝（Ａ・Ｚｆ−Ｂｂ・Ｚｍ）／Ｖｂ ……（２５）
または、
Ｖｂ＝（−Ａ・Ｚｆ＋Ｂｂ・Ｚｍ）／Ｚｆ・Ｚｍ・Ｙｔから、
Ｚｆ・Ｚｍ・Ｙｔ＝（−Ａ・Ｚｆ＋Ｂｂ・Ｚｍ）／Ｖｂ ……（２６）
【００４３】
上記式（２３），（２５）から、
（Ａ・Ｚｆ−Ｂａ・Ｚｍ）／Ｖａ＝（Ａ・Ｚｆ−Ｂｂ・Ｚｍ）／Ｖｂ
したがって、
Ｚｍ＝（Ｖｂ−Ｖａ）Ａ・Ｚｆ／（Ｂａ・Ｖｂ−Ｂｂ・Ｖａ）……（２７）
また、上記式（２３），（２６）から、
（Ａ・Ｚｆ−Ｂａ・Ｚｍ）／Ｖａ＝（−Ａ・Ｚｆ＋Ｂｂ・Ｚｍ）／Ｖｂ
したがって、
Ｚｍ＝（Ｖｂ＋Ｖａ）Ａ・Ｚｆ／（Ｂａ・Ｖｂ＋Ｂｂ・Ｖａ）……（２８）
【００４４】
また、平衡状態では次式（２９）が成立する。
Ａ・Ｚｆ＝Ｂｍｉｎ・Ｚｍから、
Ｂｍｉｎ＝Ａ・Ｚｆ／Ｚｍ……（２９）
上記式（２７），（２９）から、
Ｂｍｉｎ＝（Ｂａ・Ｖｂ−Ｂｂ・Ｖａ）／（Ｖｂ−Ｖａ）……（３０）
上記式（２８），（２９）から、
Ｂｍｉｎ＝（Ｂａ・Ｖｂ＋Ｂｂ・Ｖａ）／（Ｖｂ＋Ｖａ）……（３１）
このようにして、上記式（Ｂ１）のＢｍｉｎ１と上記式（Ｂ２）のＢｍｉｎ２とが導き出される。
【００４５】
上記先願発明によると、Ｌ端子点を平衡状態とする要因としての位相条件および振幅条件のいずれにおいても解が２つ存在する。すなわち、位相についてはθｂａｌ１，θｂａｌ２、振幅についてはＢｍｉｎ１，Ｂｍｉｎ２が存在するため、最適な方を選択する必要がある。この選択手順を含めて、上記先願発明の一連の動作を図２のフローチャートに沿って説明する。
【００４６】
まず、ステップＳＴ２１〜ＳＴ２３で、第２発振器１０６の振幅をＢａに設定した状態で、位相を９０゜，１８０゜，２７０゜に順次設定して、その各々のＬ端子点電圧Ｖ_９０，Ｖ_１８０，Ｖ_２７０を測定する。そして、ステップＳＴ２４で、これらの測定電圧の平均値Ｖａｖｅを算出する。
【００４７】
次に、ステップＳＴ２５として、電圧Ｖ_９０，Ｖ_１８０，Ｖ_２７０を上記式（５），（６）に代入して、平衡位相候補θｂａｌ１，θｂａｌ２を算出する。しかる後、ステップＳＴ２６で、第２発振器１０６の振幅をＢａにしたまま、位相に例えば一方の平衡位相候補θｂａｌ１を設定してＬ端子点電圧ＶθｂａｌＡを測定する。
【００４８】
ステップＳＴ２７で、平均値Ｖａｖｅと電圧ＶθｂａｌＡとを比較する。ＶθｂａｌＡ＜Ｖａｖｅであれば、ステップＳＴ２８ａで位相変数θｍｉｎをθｂａｌ１とし、電圧変数ＶａをＶθｂａｌＡとしてステップＳＴ２９に至る。
【００４９】
これに対して、Ｖａｖｅ＜ＶθｂａｌＡのときには、ステップＳＴ２８ｂを実行する。すなわち、第２発振器１０６の振幅をＢａとして、こんどは位相に他方の平衡位相候補θｂａｌ２を設定してＬ端子点電圧ＶθｂａｌＢを測定し、ステップＳＴ２８ｃで平衡位相変数θｍｉｎをθｂａｌ２とし、電圧変数ＶａをＶθｂａｌＢとした上でステップＳＴ２９に至る。
【００５０】
ステップＳＴ２９では、第２発振器１０６の振幅をＢａとは異なる値のＢｂとし、また、位相に上記ステップで求めた平衡位相変数θｍｉｎを設定して、Ｌ端子点電圧Ｖｂを測定する。そして、ステップＳＴ３０において、電圧変数Ｖａと電圧Ｖｂとを上記式（Ｂ１），（Ｂ２）に代入して、平衡電圧Ｂｍｉｎ１，Ｂｍｉｎ２を算出した後、ステップＳＴ３１で電圧ＶａとＶｂの平均値Ｖａｖｅを算出する。
【００５１】
ステップＳＴ３２では、第２発振器１０６の振幅を例えば一方の平衡電圧Ｂｍｉｎ１とし、位相に平衡位相変数θｍｉｎを設定してＬ端子点電圧Ｖｍｉｎ１を測定する。
【００５２】
ステップＳＴ３３で、平均値Ｖａｖｅと電圧Ｖｍｉｎ１を比較し、Ｖｍｉｎ１＜Ｖａｖｅであれば、ステップＳＴ３４ａを実行して、平衡電圧変数ＢｍｉｎにＢｍｉｎ１を置く。これに対して、Ｖｍｉｎ１＞Ｖａｖｅのときには、ステップＳＴ３４ｂで平衡電圧変数ＢｍｉｎにＢｍｉｎ２を置く。
【００５３】
上記のようにして、最適平衡位相角θｍｉｎと最適平衡振幅Ｂｍｉｎを選択した後、最終ステップＳＴ３５において、
Ｚｍ＝Ｚｆ×Ａ／Ｂ
のＢにＢｍｉｎを代入し、また、
θｍ＝θｆ＋θａ−θｂ−１８０゜
のθｂにθｍｉｎを代入して、被測定試料１０２のインピーダンスＺｍと位相θｍとをそれぞれ算出する。
【００５４】
上記先願発明によれば、先の図７で説明したアナログ的に平衡をとる自動平衡ブリッジに比べて、回路構成が簡単であり、装置の小型化および低コスト化を実現できるとともに、ディジタルおよびソフト的に平衡をとるため、回路が安定である。また、上記の自動平衡ブリッジの場合、高周波数では位相の検出がきわめて難しいが、上記先願発明のアルゴリズムにしたがえば位相を検出する必要もない、などの利点がある。
【００５５】
しかしながら、上記先願発明では、例えば第２発振器１０６の位相および振幅条件を変えながらＬ端子点（平衡点）の電圧を測定し、平衡条件を求めているため、その分、測定時間が遅くなる。ちなみに、測定回数は最小で６回（ステップＳＴ２１，２２，２３，２６，２９，３２）、最大で７回（さらにステップＳＴ２８ｂが加わるため。）行う必要がある。
【００５６】
また、平衡振幅Ｂｍｉｎを求めるときに次の問題がある。すなわち、平衡振幅Ｂｍｉｎを求めるにあたって、第２発振器１０６の位相をθｍｉｎとして、振幅に任意の異なる２つの振幅Ｂａ，Ｂｂを設定し、それぞれのＬ端子点電圧Ｖａ，Ｖｂを測定するようにしている。
【００５７】
ところで、設定する振幅Ｂａ（またはＢｂ）がたまたま平衡振幅Ｂｍｉｎの近傍の値である場合、Ｌ端子点電圧Ｖａ（またはＶｂ）が約０〔Ｖ〕となる。しかしながら、０〔Ｖ〕近辺の電圧はノイズに埋もれやすく正確に検出することが困難でしばしば測定誤差を伴うため、これが平衡振幅Ｂｍｉｎ（Ｂｍｉｎ１，Ｂｍｉｎ２）の算出誤差として表れることになる。
【００５８】
本発明によれば、上記先願発明よりも測定回数が少なくて済み、また、平衡振幅Ｂｍｉｎをより正確に求めることができる。すなわち、本発明では、平衡振幅Ｂｍｉｎを求めるにあたって、第２発振器１０６の位相をθｍｉｎではなくθｍａｘとして平衡振幅Ｂｍｉｎを求める。
【００５９】
これにより、平衡振幅Ｂｍｉｎを求める過程で０〔Ｖ〕付近を検出することがなくなり、上記先願発明で問題とされたノイズによる測定誤差を解消することができる。また、上記先願発明では平衡振幅Ｂｍｉｎの解が２つ（Ｂｍｉｎ１，Ｂｍｉｎ２）存在していたが、第２発振器１０６の位相をθｍａｘとすることにより、Ｖａ，Ｖｂから算出される平衡振幅Ｂｍｉｎの解が一つになる。
【００６０】
先にも説明したように、Ｌ端子点の電圧は次式（７）によって表される。
【数１６】

【００６１】
第２発振器１０６の位相をθｍａｘに設定した場合、上記式（７）中の（θｆ−θｍ−θｂ）＝０でｃｏｓ（θｆ−θｍ−θｂ）＝１となることを意味するから、上記式（７）は次式（３２）となる。
【数１７】

したがって、式（３２）を解くと、次式（３３），（３４）が得られる。
【数１８】

【数１９】

【００６２】
図３に、第２発振器１０６の位相をθｍａｘとした場合において、第２発振器１０６に設定される任意の異なる２つの振幅Ｂａ，ＢｂとＬ端子点電圧ＶＬ（平衡点電圧）との関係を示す。この図から分かるように、Ｂａ，Ｂｂ設定時のＬ端子点電圧ＶＬは上記式（３３）上になるため、そのときの測定電圧Ｖａ，Ｖｂから算出されるＢｍｉｎの結果が一つになる。
【００６３】
これに対して、上記先願発明の場合（第２発振器１０６の位相をθｍｉｎとした場合）には、図４に示すように、測定電圧Ｖａ，Ｖｂが上記式（３３），（３４）のいずれの上にあるか不明なため、平衡振幅Ｂｍｉｎの解が２つ存在することになる。
【００６４】
次に、本発明の一連の動作を図５のフローチャートに沿って説明する。ステップＳＴ２１〜ＳＴ２６までは、上記先願発明と同じである。すなわち、第２発振器１０６の振幅をＢａとして、位相を９０゜，１８０゜，２７０゜に順次設定してＬ端子点の電圧を測定し、平均値Ｖａｖｅを求めるとともに、θｂａｌ１，θｂａｌ２を算出する。そして、第２発振器１０６の振幅をＢａとし、位相にθｂａｌ１を設定して、そのときのＬ端子点の電圧ＶθｂａｌＡを測定する。
【００６５】
しかる後、ステップＳＴ２７で、平均値Ｖａｖｅと電圧ＶθｂａｌＡとを比較するのであるが、本発明においては、Ｖａｖｅ＜ＶθｂａｌＡであれば、ステップＳＴ２８ａ’で位相変数θｍａｘをθｂａｌ１，位相変数θｍｉｎをθｂａｌ２，電圧変数ＶａｍａｘをＶθｂａｌＡとしてステップＳＴ２９’に至る。
【００６６】
これに対して、ＶθｂａｌＡ＜Ｖａｖｅのときには、ステップＳＴ２８ｂを実行する。すなわち、第２発振器１０６の振幅をＢａとして、こんどは位相に他方の平衡位相θｂａｌ２を設定してＬ端子点電圧ＶθｂａｌＢを測定した後、ステップＳＴ２８ｃ’で位相変数θｍａｘをθｂａｌ２，位相変数θｍｉｎをθｂａｌ１，電圧変数ＶａｍａｘをＶθｂａｌＢとしてステップＳＴ２９’に至る。
【００６７】
なお、上記ステップＳＴ２７で比較基準値としてＶａｖｅを採用しているが、別の態様として、平均値Ｖａｖｅに代えて、上記電圧Ｖｘ，Ｖｙ，Ｖｚの中間値Ｖｍｉｄを採用してもよい。また、上記ステップＳＴ２７における判定式ＶθｂａｌＡ＞Ｖａｖｅ，ＶθｂａｌＡ＜Ｖａｖｅのいずれか一方に等号を持たせてもよい。
【００６８】
ステップＳＴ２９’では、第２発振器１０６の振幅をＢａとは異なる別の値Ｂｂとし、また、位相に上記ステップで求めた位相変数θｍａｘを設定して、Ｌ端子点電圧Ｖｂｍａｘを測定する。
【００６９】
そして、ステップＳＴ３０’において、次式（３５）により平衡振幅Ｂｍｉｎを算出する。
Ｂｍｉｎ＝（Ｂａ・Ｖｂｍａｘ−Ｂｂ・Ｖａｍａｘ）／（Ｖａｍａｘ−Ｖｂｍａｘ）……（３５）
【００７０】
そして、最終ステップＳＴ３１’において、上記ステップＳＴ３０’で求めた平衡振幅Ｂｍｉｎを、
Ｚｍ＝Ｚｆ×Ａ／Ｂ
のＢに代入し、また、
上記ステップＳＴ２８ａ’もしくは上記ステップＳＴ２８ｃ’で設定した位相変数θｍｉｎを、
θｍ＝θｆ＋θａ−θｂ−１８０゜
のθｂに代入して、被測定試料１０２のインピーダンスＺｍと位相θｍとをそれぞれ算出する。
【００７１】
本発明によれば、測定回数は最小で５回（ステップＳＴ２１，２２，２３，２６，２９’）、最大で６回（さらにステップＳＴ２８ｂが加わるため。）となり、場合によっては、測定回数を上記先願発明よりも２回減らすことができる。また、平衡振幅Ｂｍｉｎを求める過程で０〔Ｖ〕付近を検出することがなくなるため、ノイズによるＢｍｉｎの測定誤差を排除することが可能となる。
【００７２】
なお、上記実施形態では、第２発振器１０６の振幅と位相を操作するようにしているが、第２発振器１０６の振幅と位相を固定とし、第１発振器１０１側の振幅と位相を操作するようにしてもよい。
【００７３】
【発明の効果】
以上説明したように、本発明によれば、被測定試料に対して同一周波数の正弦波信号を印加する２つの発振器を備え、そのいずれか一方の発振器に異なる３つの位相角を設定することにより平衡位相角が求められ、また、その平衡位相角のもとで異なる２つの振幅値を設定することにより平衡振幅値が得られるのであるが、さらに平衡条件をより速く、しかも正確に求めることが可能となる。
【図面の簡単な説明】
【図１】本発明によるインピーダンス測定用自動平衡回路の概略的なブロック図。
【図２】先願発明の動作フローチャート。
【図３】第２発振器の位相をθｍａｘとした場合における任意の異なる２つの振幅とＬ端子点電圧との関係を示す本発明例のグラフ。
【図４】第２発振器の位相をθｍｉｎとした場合における任意の異なる２つの振幅とＬ端子点電圧との関係を示す上記先願発明例のグラフ。
【図５】本発明の動作フローチャート。
【図６】インピーダンス測定用自動平衡回路の第１従来例を示すブロック図。
【図７】インピーダンス測定用自動平衡回路の第２従来例を示すブロック図。
【符号の説明】
１００ 自動平衡回路
１０１ 第１発振器
１０２ 被測定試料
１０５ 検出素子
１０６ 第２発振器
１０７ 電圧検出器
１０８ Ａ／Ｄ変換器
１０９ ＣＰＵ[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an automatic balance circuit for impedance measurement applied to LCR meters, impedance analyzers, and the like. More specifically, a balanced state can be obtained even in a high frequency band, and the impedance and phase angle of a sample to be measured can be measured with high accuracy. It is related to the technology.
[0002]
[Prior art]
First, a basic configuration of an automatic balancing circuit used in an impedance measuring instrument such as an LCR meter or an impedance analyzer is shown in FIG. 6 and will be described. The automatic balancing circuit 300 is connected to an oscillator 301 for applying a sine wave signal having a predetermined frequency from the H terminal on the signal input side to the sample 304 to be measured, and to the other terminal side of the sample 304 to be measured via the L terminal. And a signal detection unit.
[0003]
In this case, the signal detection unit has an operational amplifier 306 as a current-voltage converter, the detection signal from the L terminal is input to the (−) input terminal side, and the (+) input terminal is grounded. A detection resistor 305 is connected to a feedback system between the output terminal and the (−) input terminal of the operational amplifier 306.
[0004]
When the gain of the operational amplifier 306 is sufficiently large, the voltage at the L terminal becomes 0 V (equilibrium state) due to an imaginary short, so that the amplitude of the oscillator 301 is A, the phase angle is θa, and the operational amplifier 306 outputs the voltage. Assuming that the amplitude of the output signal is B, the phase angle is θb, the impedance of the detection resistor 305 is Zf, and the phase angle is θf, the impedance Zm and the phase angle θm of the sample 304 to be measured are obtained by the following equations.
[0005]
Zm = Zf × A / B
θm = θf + θa−θb−180 °
[0006]
Although the automatic balancing circuit 300 has a simple configuration, when the frequency of the measurement sine wave signal given from the oscillator 301 to the sample 304 to be measured is increased, the gain of the operational amplifier 306 is decreased, so that an imaginary short circuit is not established. A voltage is generated at the L terminal. As a result, a current flows through the input capacitance C existing between the L terminal and the ground (GND), resulting in a measurement error.
[0007]
In order to maintain the L terminal at 0 V up to the high frequency band, an automatic balancing loop called a null loop method has been proposed. FIG. 7 shows a circuit configuration in which the null loop method is adopted for the automatic balancing circuit of FIG.
[0008]
In this null loop method, the current of the sample 302 to be measured flowing into the L terminal is converted and amplified to a voltage by a null detection circuit 401 composed of an inverting operational amplifier, and input to the subsequent multipliers 402 and 403. One multiplier 402 is supplied with the sine wave signal of the oscillator 301 as a reference signal, and the other multiplier 403 is supplied with the sine wave signal of the oscillator 301 through the 90 ° phase shifter 404 as a cosine wave signal. Thus, vector detection is performed.
[0009]
Subsequently, the outputs of the multipliers 402 and 403 are integrated and smoothed by the integrating circuits 405 and 406, respectively. The smoothed vector detection signal is supplied to multipliers 407 and 408. In one multiplier 407, the sine wave component vector-detected by the multiplier 402 is multiplied by the sine wave signal from the oscillator 301, and in the other multiplier 408, the cosine wave component vector-detected by the multiplier 403 is multiplied by 90. The cosine wave signal from the phase shifter 404 is multiplied.
[0010]
These multiplication results are added by the adder 409 and fed back to the null detection circuit 401 via the detection resistor 305. According to this null loop method, the current fed back to the null detection circuit 401 via the detection resistor 305 has the same value as the current flowing through the sample to be measured. That is, since the feedback current by the detection resistor 305 changes so that the voltage output from the null detection circuit 401 is always 0 V, an automatic balancing loop is configured.
[0011]
According to the null loop method, even when the frequency of the measurement sine wave is high, it is possible to maintain the voltage at the L terminal at 0 V. Therefore, the influence of the input capacitance existing between the L terminal and the ground (GND) can be reduced. Although accurate impedance measurement can be performed without receiving it, the following problems have been pointed out.
[0012]
That is, many circuit parts are required, the configuration is complicated, the apparatus becomes large, and the cost must be increased. In addition, the circuit tends to become unstable because it is balanced in an analog manner. Furthermore, it is difficult to obtain a complete equilibrium state due to the DC offset of the multiplier and integrator for synchronous detection.
[0013]
[Problems to be solved by the invention]
In order to solve this problem, the applicant of the present invention has specified an automatic balance circuit for impedance measurement that has a simple circuit configuration, is stable in operation, and can easily obtain a balanced state by digital control. The application has already been filed as Japanese Patent Application No. 2001-46598 and Japanese Patent Application No. 2001-328655 (hereinafter referred to as the prior invention).
[0014]
The invention of the prior application includes two oscillators that apply a sine wave signal of the same frequency to the sample to be measured, and the balanced phase angle is obtained by setting three different phase angles to one of the oscillators. In addition, the balanced amplitude value can be obtained by setting two different amplitude values under the balanced phase angle. The present invention relates to the improvement of the above-mentioned prior application, and the problem is that the balanced condition is The goal is to be faster and more accurate.
[0015]
[Means for Solving the Problems]
In order to solve the above problems, the present invention provides a first oscillator that applies a sine wave signal having a predetermined frequency to one terminal of a sample to be measured, and a predetermined detection element on the other terminal side of the sample to be measured. A second oscillator that outputs a sine wave signal having the same frequency as the sine wave signal of the first oscillator, a voltage detector that detects the voltage on the other terminal side of the sample to be measured, and the detected voltage as digital voltage data An A / D converter for conversion, and control means for controlling the amplitude and phase angle of the first oscillator or the second oscillator based on the voltage data, and the other terminal of the sample to be measured by the control means The sample to be measured is obtained from the amplitude and phase angle of the first oscillator, the amplitude and phase angle of the second oscillator, and the impedance and phase angle of the detection resistor under an equilibrium state where the side voltage is the minimum voltage. An automatic balancing circuit for impedance measurement to calculate the impedance and phase angle, the control means, to the one of the oscillator of the first oscillator or the second oscillator,
(1) Arbitrary three different phase angles θx, θy, and θz are sequentially set in a state where the amplitude is an arbitrary first amplitude value Ba, and the other terminal of the sample to be measured is set for each phase angle. Measuring the voltages Vx, Vy and Vz appearing on the side;
(2) obtaining an average value Vave of the voltages Vx, Vy and Vz;
(3) From the phase angles θx, θy and θz and the voltages Vx, Vy and Vz, the phase angles θbal1, θbal2 as the first establishment factor candidates of the equilibrium state based on the following formulas (A1), (A2) Calculating steps,
(4) With the amplitude set to the first amplitude value Ba, one of the phase angles θbal1 and θbal2 is set as the first phase angle, and appears on the other terminal side of the sample to be measured. Measuring a voltage VθbalA;
(5) Compare the voltage VθbalA with the average value Vave,
If VθbalA> Vave, one of the first phase angles set in (4) is set as a variable θmax, the other second phase angle is set as a variable θmin, and VθbalA is set as a variable Vamax.
If VθbalA <Vave, the voltage VθbalB appearing on the other terminal side of the measured sample is measured by setting the second phase angle as the phase angle in the state where the amplitude is the first amplitude value Ba, Setting the second phase angle as a variable θmax, the first phase angle as a variable θmin, and VθbalB as a variable Vamax;
(6) measuring the voltage Vbmax appearing on the other terminal side of the sample to be measured by setting the amplitude θmax as the second amplitude value Bb different from the first amplitude value Ba and setting the variable θmax as the phase angle; ,
(7) From the first amplitude value Ba, the second amplitude value Bb, the variable Vamax, and the voltage Vbmax, an amplitude Bmin as a second establishment factor of the equilibrium state is obtained.
Bmin = (Ba · Vbmax−Bb · Vamax) / (Vamax−Vbmax)
And calculating the impedance and phase angle of the sample to be measured based on the amplitude Bmin and the variable θmin.
[Equation 3]

[Expression 4]

[0016]
In the above (5), when the voltage value VθbalA at the phase angle θbal1 or θbal2 and the average value Vave are compared, as another aspect, instead of the average value Vave, an intermediate value Vmid of the voltages Vx, Vy, Vz is used. It may be adopted. Further, an equal sign may be given to any one of the inequalities VθbalA> Vave and VθbalA <Vave in the above (5).
[0017]
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 shows a block diagram of an automatic balancing circuit 100 according to the present invention. Although the hardware configuration is the same as that of the prior application invention, the embodiment of the present invention will be described in comparison with the prior application invention.
[0018]
Similar to the prior application invention, the automatic balancing circuit 100 includes two oscillators, a first oscillator 101 and a second oscillator 106, and an H terminal point (signal application side terminal point) on the first oscillator 101 side and a second oscillator. The sample to be measured 102 is mounted between the L terminal point on the 106 side (current detection side terminal point).
[0019]
A sine wave signal having a predetermined frequency is supplied from the first oscillator 101 to the sample 102 to be measured. The second oscillator 106 also outputs a sine wave signal having the same frequency as that of the measurement sine wave signal, and a detection resistor 105 as a detection element is connected between the second oscillator 106 and the L terminal point. Yes. In place of the detection resistor 105, a capacitor (C) or a coil (L) may be used on condition that the impedance is accurately known.
[0020]
The automatic balancing circuit 100 includes a voltage detector 107 that detects the voltage at the L terminal, an A / D converter 108 that converts the detected voltage into a digital signal, and a detection voltage from the A / D converter 108. A CPU 109 is provided as a control unit that controls the amplitude and phase angle of the second oscillator 106 based on the data and has a function of calculating the impedance and phase angle of the sample 102 to be measured.
[0021]
Also in the present invention, as in the above-mentioned prior application, the CPU 109 controls, for example, the second oscillator 106 out of the two oscillators with three different phase angles θx, θy and By sequentially setting θz and measuring the voltages Vx, Vy, and Vz appearing on the L terminal point side of the sample to be measured 102 for each phase angle, they are calculated by the following equations (A1) and (A2). Any one of the phase angles θbal1 and θbal2 can be set as the equilibrium phase angle θmin as the first establishment factor of the equilibrium state.
[0022]
[Equation 5]

[Formula 6]

[0023]
In the prior invention, after adjusting the phase angle of the second oscillator 106 to the phase angle θmin, the amplitudes are sequentially set to two different amplitudes Ba and Bb (preferably within the same range). By measuring the voltages Va and Vb appearing on the L terminal point side for each amplitude, one of the amplitudes calculated by the following equations (B1) and (B2) is used as an equilibrium amplitude as a second establishment factor of the equilibrium state. Bmin. The equilibrium state means a state where the L terminal is at the minimum voltage (preferably 0 V).
[0024]
[Expression 7]

[Equation 8]

[0025]
Here, the derivation process of the above equations will be briefly described (for details, refer to the above-mentioned prior invention). The amplitude of the first oscillator 101 is A, the phase angle is θa, the amplitude of the second oscillator 106 is B, the phase angle is θb, the impedance of the detection resistor 105 is Zf, and the phase angle is generated at the θf and L terminals. The impedance of the capacitor C is Zi, its phase angle is θi, the impedance of the sample 102 to be measured is Zm, and its phase angle is θm. The frequencies of the first oscillator 101 and the second oscillator 106 are the same and are ω.
[0026]
Assuming that the voltage at the L terminal point is VL and the sum of the currents flowing into the L terminal point is 0 according to Kirchhoff's law, the following equation (1) is established.
[Equation 9]

[0027]
When this expression (1) is developed, the amplitude of the voltage VL at the L terminal point is expressed by the following expression (2), and the phase is expressed by the following expression (3).
[Expression 10]

[Expression 11]

However, Yt in Formula (2) is following Formula (4).
[Expression 12]

[0028]
In the equilibrium state, the voltage VL at the L terminal is 0 V (minimum). First, in order to obtain the balanced phase angle θmin, three different phase angles are sequentially set in the second oscillator 106, the voltage VL at each L terminal point is measured, and the above equations (A1) and (A2) are used. Two phase angles θbal1 and θbal2 are calculated as equilibrium phase angle candidates, but three different phase angles are set to 90 °, 180 °, and 270 ° in order to facilitate the calculation using the equations (A1) and (A2). And
[0029]
In all cases, the amplitude is Ba, and the voltage measured at the L terminal point when the phase is 90 ° is V₉₀, The voltage measured at the L terminal when the phase is 180 °, V₁₈₀, The voltage measured at the L terminal when the phase is 270 ° is V₂₇₀Then, from the above formulas (A1) and (A2), one phase angle θbal1 is represented by the following formula (5), and the other phase angle θbal2 is represented by the following formula (6).
[Formula 13]

[Expression 14]

[0030]
The basis of these formulas (5) and (6) will be described. Since the amplitude of the L terminal point is the above equation (2), when this is squared, the following equation (7) is obtained.
[Expression 15]

[0031]
In Expression (7), since the variable is only the phase angle θb of the second oscillator 106, Expression (7) is replaced with the following Expression (8) with α, β, and γ as constants.
VL²= Α + βcos (γ + θb) (8)
[0032]
As described above, the phase of the second oscillator 106 is set to 90 °, and the voltage at that time is set to V₉₀Then, from equation (8),
V₉₀ ²= Α + βcos (γ + 90) = α−βsinγ (9)
Similarly, from the equation (8), the phase of the second oscillator 106 is set to 180 °, and the voltage at that time is set to V₁₈₀Then,
V₁₈₀ ²= Α + βcos (γ + 180) = α−βcosγ (10)
Similarly, from the equation (8), the phase of the second oscillator 106 is set to 270 °, and the voltage at that time is set to V₂₇₀Then,
V₂₇₀ ²= Α + βcos (γ + 270) = α + βsinγ (11)
[0033]
From the above formulas (9) and (11),
V₉₀ ²+ V₂₇₀ ²= 2α …… (12)
From the above formulas (10) and (12),
V₁₈₀ ²= (V₉₀ ²+ V₂₇₀ ²) / 2-βcosγ
Therefore, βcosγ = (V₉₀ ²+ V₂₇₀ ²) / 2-V₁₈₀ ²(13)
From the above formulas (9) and (12),
V₉₀ ²= (V₉₀ ²+ V₂₇₀ ²) / 2-βsinγ
Therefore, βsinγ = (V₂₇₀ ²-V₉₀ ²) / 2 …… (14)
[0034]
From the above equations (13) and (14),
tanγ = ((V₂₇₀ ²-V₉₀ ²) / 2) / ((V₉₀ ²+ V₂₇₀ ²) / 2-V₁₈₀ ²)
= (V₂₇₀ ²-V₉₀ ²) / (V₉₀ ²+ V₂₇₀ ²-2V₁₈₀ ²)
Therefore,
γ = tan^-1((V₂₇₀ ²-V₉₀ ²) / (V₉₀ ²+ V₂₇₀ ²-2V₁₈₀ ²)) ... (15)
[0035]
Since cos (γ + θb) = − 1 in the above equation (8) in the equilibrium state,
γ + θmin = 180 (16)
From the above equations (15) and (16), the equilibrium phase θmin is
θmin = 180−γ,
Therefore, θmin = 180−tan^-1((V₂₇₀ ²-V₉₀ ²) / (V₉₀ ²+ V₂₇₀ ²-2V₁₈₀ ²)) …… (17)
[0036]
The phase angle θmin calculated by the above algorithm is assumed to be in the range of ± 90 ° (90 ° to 270 °) assuming that the object to be measured is a capacitor, resistor, coil, etc. In some cases, the phase angle θmin falls outside the range of ± 90 ° due to a phase error caused by an operational amplifier or a filter, or the phase angle θf of the detection resistor 105.
[0037]
As an example, when a capacitor is measured, the phase angle θm of the sample 102 to be measured is −90 °, but when it is assumed that the phase angle θf of the detection resistor 105 is 20 °, θmin = 290 ° (−70 °). )
[0038]
Therefore, when the phase angle θmin is in the range of ± 180 °, the above equation (15) is
tan^-1((V₂₇₀ ²-V₉₀ ²) / (V₉₀ ²+ V₂₇₀ ²-2V₁₈₀ ²)) = Γ or 180 + γ …… (18)
From the above equations (16) and (18),
θmin (θbal1) = 180−tan^-1((V₂₇₀ ²-V₉₀ ²) / (V₉₀ ²+ V₂₇₀ ²-2V₁₈₀ ²)) …… (19)
Or
θmin (θbal2) = − tan^-1((V₂₇₀ ²-V₉₀ ²) / (V₉₀ ²+ V₂₇₀ ²-2V₁₈₀ ²)) …… (20)
It becomes.
[0039]
Next, the basis of the above formulas (B1) and (B2) for calculating the equilibrium amplitude Bmin will be described. The voltage measured at the L terminal point when the phase of the second oscillator 106 is set to θmin and the amplitude is set to Ba is Va. The voltage measured at the L terminal point when the phase of the second oscillator 106 is set to θmin and the amplitude is set to Bb is Vb.
[0040]
Since the amplitude of the L terminal point is expressed by the above formula (2), the formula (2) when the phase is θmin is expressed by the following formula (21) or the following formula (22).
VL = (A · Zf−B · Zm) / Zf · Zm · Yt (21)
VL = − (A · Zf−B · Zm) / Zf · Zm · Yt (22)
[0041]
When the voltage Va measured at the L terminal point with the amplitude set to Ba is applied to these equations (21) and (22),
From Va = (A · Zf−Ba · Zm) / Zf · Zm · Yt,
Zf.Zm.Yt = (A.Zf-Ba.Zm) / Va (23)
Or
From Va = (− A · Zf + Ba · Zm) / Zf · Zm · Yt,
Zf · Zm · Yt = (− A · Zf + Ba · Zm) / Va (24)
[0042]
Further, when the voltage Vb measured at the L terminal point with the amplitude set to Bb is applied to the equations (21) and (22),
From Vb = (A · Zf−Bb · Zm) / Zf · Zm · Yt,
Zf.Zm.Yt = (A.Zf-Bb.Zm) / Vb (25)
Or
From Vb = (− A · Zf + Bb · Zm) / Zf · Zm · Yt,
Zf · Zm · Yt = (− A · Zf + Bb · Zm) / Vb (26)
[0043]
From the above equations (23) and (25),
(A · Zf−Ba · Zm) / Va = (A · Zf−Bb · Zm) / Vb
Therefore,
Zm = (Vb−Va) A · Zf / (Ba · Vb−Bb · Va) (27)
From the above equations (23) and (26),
(A · Zf−Ba · Zm) / Va = (− A · Zf + Bb · Zm) / Vb
Therefore,
Zm = (Vb + Va) A.Zf / (Ba.Vb + Bb.Va) (28)
[0044]
In the equilibrium state, the following equation (29) is established.
From A · Zf = Bmin · Zm,
Bmin = A · Zf / Zm (29)
From the above equations (27) and (29),
Bmin = (Ba · Vb−Bb · Va) / (Vb−Va) (30)
From the above equations (28) and (29),
Bmin = (Ba · Vb + Bb · Va) / (Vb + Va) (31)
In this way, Bmin1 of the above formula (B1) and Bmin2 of the above formula (B2) are derived.
[0045]
According to the invention of the prior application, there are two solutions for both the phase condition and the amplitude condition as factors for bringing the L terminal point into an equilibrium state. That is, θbal1 and θbal2 exist for the phase, and Bmin1 and Bmin2 exist for the amplitude. Therefore, it is necessary to select the optimum one. A series of operations of the invention of the prior application including this selection procedure will be described with reference to the flowchart of FIG.
[0046]
First, in steps ST21 to ST23, with the amplitude of the second oscillator 106 set to Ba, the phases are sequentially set to 90 °, 180 °, and 270 °, and the respective L terminal point voltages V are set.₉₀, V₁₈₀, V₂₇₀Measure. In step ST24, an average value Vave of these measurement voltages is calculated.
[0047]
  Next, as step ST25, the voltage V₉₀, V₁₈₀, V₂₇₀Is substituted into the above formulas (5) and (6) to calculate balanced phase candidates θbal1 and θbal2. Thereafter, in step ST26, while the amplitude of the second oscillator 106 is set to Ba, for example, one balanced phase candidate θbal1 is set as the phase, and the L terminal point voltage VθbalAMeasure.
[0048]
  In step ST27, average value Vave and voltage VθbalAAnd compare. VθbalAIf <Vave, the phase variable θmin is set to θbal1 in step ST28a, and the voltage variable Va is set to VθbalATo step ST29.
[0049]
  In contrast, Vave <VθbalAIn the case of step ST28b is executed. That is, assuming that the amplitude of the second oscillator 106 is Ba, the other balanced phase candidate θbal2 is set as the phase, and the L terminal voltage VθbalBIn step ST28c, the equilibrium phase variable θmin is set to θbal2, and the voltage variable Va is set to VθbalBThen, the process proceeds to step ST29.
[0050]
In step ST29, the amplitude of the second oscillator 106 is set to Bb having a value different from Ba, and the balanced phase variable θmin obtained in the above step is set to the phase, and the L terminal voltage Vb is measured. In step ST30, the voltage variables Va and Vb are substituted into the above formulas (B1) and (B2) to calculate the balanced voltages Bmin1 and Bmin2. Then, in step ST31, the average value Vave of the voltages Va and Vb is calculated. calculate.
[0051]
In step ST32, the amplitude of the second oscillator 106 is set to one balanced voltage Bmin1, for example, the balanced phase variable θmin is set as the phase, and the L terminal point voltage Vmin1 is measured.
[0052]
In step ST33, the average value Vave and the voltage Vmin1 are compared. If Vmin1 <Vave, step ST34a is executed to place Bmin1 in the balanced voltage variable Bmin. On the other hand, when Vmin1> Vave, Bmin2 is set in the equilibrium voltage variable Bmin in step ST34b.
[0053]
After selecting the optimal equilibrium phase angle θmin and the optimal equilibrium amplitude Bmin as described above, in the final step ST35,
Zm = Zf × A / B
Substitute Bmin for B, and
θm = θf + θa−θb−180 °
The impedance Zm and the phase θm of the sample to be measured 102 are respectively calculated by substituting θmin for θb.
[0054]
According to the above-mentioned prior application, the circuit configuration is simple and the apparatus can be reduced in size and cost as compared with the analog balanced automatic balancing bridge described in FIG. The circuit is stable because it is balanced in terms of software. In the case of the above automatic balancing bridge, it is very difficult to detect the phase at a high frequency, but there is an advantage that it is not necessary to detect the phase according to the algorithm of the prior invention.
[0055]
However, in the above-mentioned prior invention, for example, the voltage at the L terminal point (equilibrium point) is measured while changing the phase and amplitude conditions of the second oscillator 106, and the equilibrium condition is obtained. . Incidentally, the number of measurements needs to be performed at a minimum of 6 times (steps ST21, 22, 23, 26, 29, and 32) and a maximum of 7 times (because step ST28b is added).
[0056]
Further, there are the following problems when obtaining the balanced amplitude Bmin. That is, when obtaining the balanced amplitude Bmin, the phase of the second oscillator 106 is set to θmin, two different amplitudes Ba and Bb are set as the amplitude, and the respective L terminal point voltages Va and Vb are measured. .
[0057]
By the way, when the set amplitude Ba (or Bb) happens to be a value near the balanced amplitude Bmin, the L terminal voltage Va (or Vb) becomes about 0 [V]. However, since the voltage near 0 [V] is easily buried in noise and difficult to detect accurately, and often involves measurement errors, this appears as a calculation error of the balanced amplitude Bmin (Bmin1, Bmin2).
[0058]
According to the present invention, the number of times of measurement is less than that of the prior invention, and the equilibrium amplitude Bmin can be determined more accurately. That is, in the present invention, when obtaining the balanced amplitude Bmin, the balanced amplitude Bmin is obtained by setting the phase of the second oscillator 106 to θmax instead of θmin.
[0059]
As a result, the vicinity of 0 [V] is not detected in the process of obtaining the balanced amplitude Bmin, and the measurement error due to noise, which is a problem in the prior application invention, can be eliminated. In the above-mentioned prior invention, there are two solutions (Bmin1, Bmin2) of the balanced amplitude Bmin. By setting the phase of the second oscillator 106 to θmax, the balanced amplitude Bmin calculated from Va, Vb The solution becomes one.
[0060]
As described above, the voltage at the L terminal point is expressed by the following equation (7).
[Expression 16]

[0061]
When the phase of the second oscillator 106 is set to θmax, it means that (θf−θm−θb) = 0 in the above equation (7) and cos (θf−θm−θb) = 1, so that (7) becomes the following equation (32).
[Expression 17]

Therefore, when the equation (32) is solved, the following equations (33) and (34) are obtained.
[Expression 18]

[Equation 19]

[0062]
  Figure3The relationship between any two different amplitudes Ba and Bb set in the second oscillator 106 and the L terminal point voltage VL (equilibrium point voltage) when the phase of the second oscillator 106 is θmax is shown. As can be seen from this figure, since the L terminal point voltage VL at the time of setting Ba and Bb is on the above equation (33), the result of Bmin calculated from the measured voltages Va and Vb at that time is one.
[0063]
  On the other hand, in the case of the above-mentioned invention (when the phase of the second oscillator 106 is θmin),4As shown in FIG. 2, since it is unknown whether the measured voltages Va and Vb are above the above equations (33) and (34), there are two solutions of the balanced amplitude Bmin.
[0064]
  Next, a series of operations of the present invention will be described along the flowchart of FIG. Steps ST21 to ST26 are the same as the prior invention. That is, assuming that the amplitude of the second oscillator 106 is Ba, the phase is sequentially set to 90 °, 180 °, and 270 °, the voltage at the L terminal point is measured, the average value Vave is obtained, and θbal1 and θbal2 are calculated. Then, the amplitude of the second oscillator 106 is set to Ba, the phase is set to θbal1, and the voltage V at the L terminal point at that time is set.θbalAMeasure.
[0065]
  Thereafter, in step ST27, the average value Vave and the voltage VθbalAIn the present invention, Vave <VθbalAIn step ST28a ', the phase variable θmax is set to θbal1, the phase variable θmin is set to θbal2, and the voltage variable Vamax is set to VθbalAAs a result, step ST29 'is reached.
[0066]
  In contrast, VθbalAIf <Vave, step ST28b is executed. That is, assuming that the amplitude of the second oscillator 106 is Ba, and this time, the other balanced phase θbal2 is set as the phase, and the L terminal voltage VθbalBIn step ST28c ', the phase variable θmax is set to θbal2, the phase variable θmin is set to θbal1, and the voltage variable Vamax is set to V.θbalBAs a result, step ST29 'is reached.
[0067]
  Although Vave is adopted as the comparison reference value in step ST27, as another aspect, an intermediate value Vmid of the voltages Vx, Vy, Vz may be adopted instead of the average value Vave. Also, aboveIn step ST27Either one of the determination formulas VθbalA> Vave and VθbalA <Vave may have an equal sign.
[0068]
In step ST29 ', the amplitude of the second oscillator 106 is set to another value Bb different from Ba, and the phase variable θmax obtained in the above step is set to the phase, and the L terminal voltage Vbmax is measured.
[0069]
In step ST30 ', the equilibrium amplitude Bmin is calculated by the following equation (35).
Bmin = (Ba · Vbmax−Bb · Vamax) / (Vamax−Vbmax) (35)
[0070]
In the final step ST31 ', the equilibrium amplitude Bmin obtained in step ST30' is
Zm = Zf × A / B
Substituting for B, and
The phase variable θmin set in step ST28a ′ or step ST28c ′ is
θm = θf + θa−θb−180 °
The impedance Zm and the phase θm of the sample 102 to be measured are calculated respectively.
[0071]
According to the present invention, the minimum number of measurements is 5 (steps ST21, 22, 23, 26, 29 ') and the maximum is 6 (because step ST28b is added). This can be reduced twice compared to the prior invention. Further, since it is no longer possible to detect the vicinity of 0 [V] in the process of obtaining the balanced amplitude Bmin, it is possible to eliminate the measurement error of Bmin due to noise.
[0072]
In the above embodiment, the amplitude and phase of the second oscillator 106 are manipulated. However, the amplitude and phase of the second oscillator 106 are fixed, and the amplitude and phase of the first oscillator 101 are manipulated. May be.
[0073]
【The invention's effect】
As described above, according to the present invention, two oscillators for applying a sine wave signal of the same frequency to a sample to be measured are provided, and three different phase angles are set for one of the oscillators. An equilibrium phase angle is obtained, and by setting two different amplitude values under the equilibrium phase angle, an equilibrium amplitude value can be obtained. However, it is possible to obtain an equilibrium condition faster and more accurately. It becomes possible.
[Brief description of the drawings]
FIG. 1 is a schematic block diagram of an automatic balancing circuit for impedance measurement according to the present invention.
FIG. 2 is an operation flowchart of the prior invention.
FIG. 3 is a graph of an example of the present invention showing the relationship between any two different amplitudes and the L terminal point voltage when the phase of the second oscillator is θmax.
FIG. 4 is a graph of the prior invention example showing the relationship between any two different amplitudes and the L terminal point voltage when the phase of the second oscillator is θmin.
FIG. 5 is an operation flowchart of the present invention.
FIG. 6 is a block diagram showing a first conventional example of an impedance measuring automatic balancing circuit.
FIG. 7 is a block diagram illustrating a second conventional example of an automatic balancing circuit for impedance measurement.
[Explanation of symbols]
100 automatic balancing circuit
101 First oscillator
102 Sample to be measured
105 Detection element
106 Second oscillator
107 Voltage detector
108 A / D converter
109 CPU

Claims (3)

A first oscillator that applies a sine wave signal of a predetermined frequency to one terminal of the sample to be measured, and the same frequency as the sine wave signal of the first oscillator via a predetermined detection element on the other terminal side of the sample to be measured A second oscillator that outputs a sine wave signal, a voltage detector that detects a voltage on the other terminal side of the sample to be measured, an A / D converter that converts the detected voltage into digital voltage data, and the voltage Control means for controlling the amplitude and the phase angle of the first oscillator or the second oscillator based on the data, and the control means is in an equilibrium state with the voltage on the other terminal side of the measured sample as the minimum voltage. Below, the impedance and phase angle of the sample to be measured are calculated from the amplitude and phase angle of the first oscillator, the amplitude and phase angle of the second oscillator, and the impedance and phase angle of the detection resistor. An automatic balancing circuit for that impedance measurement,
The control means is for either one of the first oscillator and the second oscillator.
(1) Arbitrary three different phase angles θx, θy, and θz are sequentially set in a state where the amplitude is an arbitrary first amplitude value Ba, and the other terminal of the sample to be measured is set for each phase angle. Measuring the voltages Vx, Vy and Vz appearing on the side;
(2) obtaining an average value Vave of the voltages Vx, Vy and Vz;
(3) From the phase angles θx, θy and θz and the voltages Vx, Vy and Vz, the phase angles θbal1, θbal2 as the first establishment factor candidates of the equilibrium state based on the following equations (A1), (A2) Calculating steps,
(4) With the amplitude set to the first amplitude value Ba, one of the phase angles θbal1 and θbal2 is set as the first phase angle, and appears on the other terminal side of the sample to be measured. Measuring a voltage VθbalA;
(5) Compare the voltage VθbalA with the average value Vave,
If VθbalA> Vave, one of the first phase angles set in (4) is set as a variable θmax, the other second phase angle is set as a variable θmin, and VθbalA is set as a variable Vamax.
If VθbalA <Vave, the voltage VθbalB appearing on the other terminal side of the sample to be measured is measured by setting the second phase angle as the phase angle in the state where the amplitude is the first amplitude value Ba, and Setting the second phase angle as a variable θmax, the first phase angle as a variable θmin, and VθbalB as a variable Vamax;
(6) measuring the voltage Vbmax appearing on the other terminal side of the sample to be measured by setting the amplitude θmax as the second amplitude value Bb different from the first amplitude value Ba and setting the variable θmax as the phase angle; ,
(7) From the first amplitude value Ba, the second amplitude value Bb, the variable Vamax, and the voltage Vbmax, an amplitude Bmin as a second establishment factor of the equilibrium state is obtained.
Bmin = (Ba · Vbmax−Bb · Vamax) / (Vamax−Vbmax)
And calculating the impedance and the phase angle of the sample to be measured based on the amplitude Bmin and the variable θmin.

  The automatic balancing circuit for impedance measurement according to claim 1, wherein an intermediate value Vmid of the voltages Vx, Vy, Vz is adopted instead of the average value Vave of (2).   The automatic balancing circuit for impedance measurement according to claim 1 or 2, wherein an equal sign is given to one of the inequalities VθbalA> Vave and VθbalA <Vave in (5).

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