JP3106373B2 - Active filter circuit - Google Patents
Active filter circuitInfo
- Publication number
- JP3106373B2 JP3106373B2 JP03233183A JP23318391A JP3106373B2 JP 3106373 B2 JP3106373 B2 JP 3106373B2 JP 03233183 A JP03233183 A JP 03233183A JP 23318391 A JP23318391 A JP 23318391A JP 3106373 B2 JP3106373 B2 JP 3106373B2
- Authority
- JP
- Japan
- Prior art keywords
- resistor
- input
- capacitor
- operational amplifier
- filter circuit
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Description
【０００１】[0001]
【産業上の利用分野】本発明は、一次ハイパスフィルタ
と二次ノッチフィルタとを有するアクティブフィルタ回
路に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an active filter circuit having a primary high-pass filter and a secondary notch filter.
【０００２】[0002]
【従来の技術】この種の従来例のアクティブフィルタ回
路は、図２に示すように一次ハイパスフィルタ２と、二
次ノッチフィルタ４とで構成されており、それぞれはい
ずれも演算増幅器６，８を具備していた。2. Description of the Related Art A conventional active filter circuit of this kind comprises a primary high-pass filter 2 and a secondary notch filter 4, as shown in FIG. I had it.
【０００３】[0003]
【発明が解決しようとする課題】しかしながら、このよ
うに一次ハイパスフィルタ２と二次ノッチフィルタ４の
それぞれが演算増幅器６,８を具備しているために、そ
の演算増幅器６,８そのもののがコスト的に高くつくの
みならず、そこでの電力消費も大きく、しかも構成も複
雑化しているとともに、回路基板などに組み込む場合に
小型化には適していないなどの不具合があった。However, since each of the primary high-pass filter 2 and the secondary notch filter 4 includes the operational amplifiers 6 and 8 as described above, the operational amplifiers 6 and 8 themselves are costly. In addition to the high cost, the power consumption there is large and the configuration is complicated, and when incorporated in a circuit board or the like, it is not suitable for miniaturization.
【０００４】そこで、本発明は１つの演算増幅器を用い
たものにして従来と同等の特性を備えさせることで、コ
スト的に安く電力消費も少なくて済み、しかも簡単かつ
小型化可能な構成を有するアクティブフィルタ回路を提
供することを目的としている。Accordingly, the present invention uses a single operational amplifier and has the same characteristics as the conventional one, so that it has a configuration that is inexpensive, consumes less power, and can be simplified and reduced in size. It is an object to provide an active filter circuit.
【０００５】[0005]
【課題を解決するための手段】このような目的を達成す
るために、本発明のアクティブフィルタ回路において
は、入力電圧をＶｉ、出力電圧をＶｏとした場合、伝達
関数Ｖｏ／Ｖｉ〔＝Ｔ（Ｓ）〕が、In order to achieve the above object, in the active filter circuit of the present invention, when the input voltage is Vi and the output voltage is Vo, the transfer function Vo / Vi [= T ( S)],
【０００６】[0006]
【数式３】 [Equation 3]
【０００７】ただし、Ｘ1＝ωａ＋（ωｏ／Ｑ）、Ｘ2＝
ωｏ2＋（ωａωｏ／Ｑ）、Ｘ3＝ωａωｏ2 また、Ｈはフィルタの利得、Ｓはjωであらわされる角
周波数、ωａは一次ハイパスフィルタのカットオフ角周
波数、ωｏは二次ノッチフィルタのカットオフ角周波
数、ωｐは二次ノッチフィルタのノッチ角周波数、Ｑは
フィルタの尖鋭度でそれぞれあらわされる特性を実現す
るアクティブフィルタ回路であって、２入力型の演算増
幅器を有し、入力端に第１コンデンサの一端を接続し、
該第１コンデンサの他端とアースとの間に第１抵抗を接
続し、該第１コンデンサと第１抵抗との接続部と演算増
幅器の一方の入力部との間には第２抵抗を、また、該接
続部と演算増幅器の他方の入力部との間に第５抵抗をそ
れぞれ接続し、第２抵抗の両端間に第３抵抗と第２コン
デンサとを直列に接続し、第２コンデンサの両端間に第
３コンデンサと第４抵抗とを直列に接続し、第３コンデ
ンサと第４抵抗との接続部と演算増幅器の出力部とを接
続し、演算増幅器の他方の入力部とアースとの間に第６
抵抗を接続し、演算増幅器の出力部と該他方の入力部と
の間に第７抵抗を接続してなり、前記第１ないし第３コ
ンデンサの容量をそれぞれC1〜C3とし、前記第１抵抗な
いし第７抵抗のコンダクタンスをそれぞれg1〜g7とおい
た場合、当該アクティブフィルタ回路の伝達関数Ｔ(Ｓ)
は次式であらわされ、However, X 1 = ωa + (ωo / Q) and X 2 =
ωo 2 + (ωaωo / Q), X 3 = ωaωo 2 H is the gain of the filter, S is the angular frequency represented by jω, ωa is the cutoff angular frequency of the primary high-pass filter, and ωo is the cut of the secondary notch filter The off angular frequency, ωp is the notch angular frequency of the secondary notch filter, and Q is an active filter circuit that realizes characteristics represented by the sharpness of the filter. The active filter circuit has a two-input operational amplifier. Connect one end of one capacitor,
A first resistor is connected between the other end of the first capacitor and ground, and a second resistor is provided between a connection between the first capacitor and the first resistor and one input of the operational amplifier. A fifth resistor is connected between the connection and the other input of the operational amplifier, and a third resistor and a second capacitor are connected in series between both ends of the second resistor. A third capacitor and a fourth resistor are connected in series between both ends, a connection between the third capacitor and the fourth resistor is connected to the output of the operational amplifier, and the other input of the operational amplifier is connected to the ground. Sixth in between
A resistor is connected, a seventh resistor is connected between the output of the operational amplifier and the other input, and the capacitances of the first to third capacitors are C 1 to C 3 , respectively. If the conductance of the resistor to the seventh resistor placed between g 1 to g 7 respectively, the transfer function of the active filter circuit T (S)
Is represented by the following equation,
【０００８】[0008]
【数式４】 (Equation 4)
【０００９】ただし、 Ａ ＝ｃ1ｃ2ｃ3ｇ5／Ｘ Ｂ＝｛ｃ1ｃ2ｇ4ｇ5＋ｃ1ｃ3ｇ4ｇ5−ｃ1ｃ2（ｇ2＋ｇ3）（ｇ6＋ｇ7） −ｃ1ｃ3ｇ2（ｇ6＋ｇ7）｝／Ｘ Ｃ＝｛ｃ1ｇ3ｇ4ｇ5−ｃ1ｇ2ｇ3（ｇ6＋ｇ7）｝／Ｘ Ｄ＝｛ｃ1ｃ2ｇ4（ｇ5＋ｇ6）＋ｃ1ｃ3ｇ4（ｇ5＋ｇ6）＋ｃ2ｃ3ｇ1（ｇ5 ＋ｇ6）＋ｃ2ｃ3（ｇ2＋ｇ3＋ｇ5）ｇ6−ｃ1ｃ2（ｇ2＋ｇ3）ｇ7 −ｃ1ｃ3ｇ2ｇ7｝／Ｘ Ｅ＝｛ｃ1ｇ3ｇ4（ｇ5＋ｇ6）＋ｃ2ｇ1ｇ4（ｇ5＋ｇ6）＋ｃ2ｇ4ｇ6（ｇ2 ＋ｇ3＋ｇ5）＋ｃ3ｇ1ｇ4（ｇ5＋ｇ6）＋ｃ3ｇ2（ｇ3＋ｇ4）ｇ6 ＋ｃ3ｇ4ｇ6（ｇ3＋ｇ5）−ｃ1ｇ2ｇ3ｇ7−ｃ2ｇ1（ｇ2＋ｇ3）ｇ7 −ｃ3ｇ1ｇ2ｇ7｝／Ｘ Ｆ＝｛ｇ1ｇ3ｇ4（ｇ5＋ｇ6）＋ｇ3ｇ4ｇ6（ｇ2＋ｇ5）−ｇ1ｇ2ｇ3ｇ7｝／Ｘ ただし、Ｘ＝ｃ1ｃ2ｃ3（ｇ5＋ｇ6）、 そして、前記両式（１）（２）の分母および分子におけ
るＳの係数がそれぞれ等しくなるように前記容量および
コンダクタンスを選定していることを特徴としている。However, A = c 1 c 2 c 3 g 5 / X B = ｛c 1 c 2 g 4 g 5 + c 1 c 3 g 4 g 5 −c 1 c 2 (g 2 + g 3 ) (g 6 + G 7 ) −c 1 c 3 g 2 (g 6 + g 7 )} / X C = {c 1 g 3 g 4 g 5 −c 1 g 2 g 3 (g 6 + g 7 )} / X D = {c 1 c 2 g 4 (g 5 + g 6) + c 1 c 3 g 4 (g 5 + g 6) + c 2 c 3 g 1 (g 5 + g 6) + c 2 c 3 (g 2 + g 3 + g 5) g 6 - c 1 c 2 (g 2 + g 3 ) g 7 −c 1 c 3 g 2 g 7 ｝ / X E = c 1 g 3 g 4 (g 5 + g 6 ) + c 2 g 1 g 4 (g 5 + g 6 ) + C 2 g 4 g 6 (g 2 + g 3 + g 5 ) + c 3 g 1 g 4 (g 5 + g 6 ) + c 3 g 2 (g 3 + g 4 ) g 6 + c 3 g 4 g 6 (g 3 + g 5) ) -c 1 g 2 g 3 g 7 -c 2 g 1 (g 2 + g 3) g 7 -c 3 g 1 g 2 g 7} / X F = {g 1 g 3 g 4 (g 5 + 6) + g 3 g 4 g 6 (g 2 + g 5) -g 1 g 2 g 3 g 7} / X , however, X = c 1 c 2 c 3 (g 5 + g 6), and, wherein both equations (1 And (2) the capacitance and conductance are selected so that the denominator and the coefficient of S in the numerator are equal to each other.
【００１０】[0010]
【作用】上記構成によれば、演算増幅器が１個であるか
ら、使用部品の点数が削減化されている。According to the above configuration, since the number of operational amplifiers is one, the number of parts to be used is reduced.
【００１１】[0011]
【実施例】以下、本発明の実施例を図面を参照して詳細
に説明する。図１は本発明の実施例に係るアクティブフ
ィルタ回路の回路図である。Embodiments of the present invention will be described below in detail with reference to the drawings. FIG. 1 is a circuit diagram of an active filter circuit according to an embodiment of the present invention.
【００１２】まず、当該アクティブフィルタ回路の入力
端ＩＮへの入力電圧をＶi、その出力端ＯＵＴからの出
力電圧をＶoとしたときの合成伝達関数Ｖo/Ｖi＝T(S)
は、次式(1)であらわされる。First, when the input voltage to the input terminal IN of the active filter circuit is Vi and the output voltage from the output terminal OUT is Vo, the combined transfer function Vo / Vi = T (S).
Is represented by the following equation (1).
【００１３】[0013]
【数式５】 (Equation 5)
【００１４】ただし、Ｘ1＝ωａ＋（ωｏ／Ｑ）、Ｘ2＝
ωｏ2＋（ωａωｏ／Ｑ）、Ｘ3＝ωａωｏ2 また、Ｈはフィルタの利得、Ｓはjωであらわされる角
周波数、ωａは一次ハイパスフィルタのカットオフ角周
波数、ωｏは二次ノッチフィルタのカットオフ角周波
数、ωｐは二次ノッチフィルタのノッチ角周波数、Ｑは
フィルタの尖鋭度でそれぞれあらわされる。Where X 1 = ωa + (ωo / Q) and X 2 =
ωo 2 + (ωaωo / Q), X 3 = ωaωo 2 H is the gain of the filter, S is the angular frequency represented by jω, ωa is the cutoff angular frequency of the primary high-pass filter, and ωo is the cut of the secondary notch filter The off angular frequency, ωp are represented by the notch angular frequency of the secondary notch filter, and Q is represented by the sharpness of the filter.
【００１５】つぎに、本実施例のアクティブフィルタ回
路は、２入力型の演算増幅器ＡＭＰを有し、入力端ＩＮ
に第１コンデンサＣ１の一端を接続し、該第１コンデン
サＣ１の他端とアースとの間に第１抵抗Ｒ１を接続し、
該第１コンデンサＣ１と第１抵抗Ｒ１との接続部と演算
増幅器ＡＭＰの一方の入力部（−）との間には第２抵抗
Ｒ２を、また、該接続部と演算増幅器ＡＭＰの他方の入
力部（＋）との間に第５抵抗Ｒ５をそれぞれ接続し、第
２抵抗Ｒ２の両端間に第３抵抗Ｒ３と第２コンデンサＣ
２とを直列に接続し、第２コンデンサＣ２の両端間に第
３コンデンサＣ３と第４抵抗Ｒ４とを直列に接続し、第
３コンデンサＣ３と第４抵抗Ｒ４との接続部と演算増幅
器ＡＭＰの出力部とを接続し、演算増幅器ＡＭＰの他方
の入力部（＋）とアースとの間に第６抵抗Ｒ６を接続
し、演算増幅器ＡＭＰの出力部と該他方の入力部（＋）
との間に第７抵抗Ｒ７を接続してなる。そして、本実施
例のアクティブフィルタ回路は、第１ないし第３コンデ
ンサＣ１〜Ｃ３の容量をそれぞれC1〜C3とし、第１抵抗
ないし第７抵抗Ｒ１〜Ｒ７のコンダクタンスをそれぞれ
g1〜g7とおいた場合、当該アクティブフィルタ回路の伝
達関数Ｔ(Ｓ)が次式であらわされる。Next, the active filter circuit of this embodiment has a two-input operational amplifier AMP, and has an input terminal IN.
Is connected to one end of a first capacitor C1, a first resistor R1 is connected between the other end of the first capacitor C1 and ground,
A second resistor R2 is provided between a connection between the first capacitor C1 and the first resistor R1 and one input (-) of the operational amplifier AMP, and another connection between the connection and the other input of the operational amplifier AMP. A fifth resistor R5 is connected between the second resistor R2 and the third resistor R3 and the second capacitor C between both ends of the second resistor R2.
2 in series, a third capacitor C3 and a fourth resistor R4 are connected in series between both ends of the second capacitor C2, and a connection between the third capacitor C3 and the fourth resistor R4 and the operational amplifier AMP. An output section is connected, a sixth resistor R6 is connected between the other input section (+) of the operational amplifier AMP and the ground, and an output section of the operational amplifier AMP and the other input section (+) are connected.
And a seventh resistor R7 is connected between the first and second resistors. Then, the active filter circuit of this embodiment, the capacitance of the first to third capacitors C1~C3 a C 1 -C 3, respectively, the conductance of the first resistor to the seventh resistor R1~R7 respectively
If placed as g 1 to g 7, the transfer function of the active filter circuit T (S) is represented by the following equation.
【００１６】[0016]
【数式６】 (Equation 6)
【００１７】ただし、 Ａ ＝ｃ1ｃ2ｃ3ｇ5／Ｘ Ｂ＝｛ｃ1ｃ2ｇ4ｇ5＋ｃ1ｃ3ｇ4ｇ5−ｃ1ｃ2（ｇ2＋ｇ3）（ｇ6＋ｇ7） −ｃ1ｃ3ｇ2（ｇ6＋ｇ7）｝／Ｘ Ｃ＝｛ｃ1ｇ3ｇ4ｇ5−ｃ1ｇ2ｇ3（ｇ6＋ｇ7）｝／Ｘ Ｄ＝｛ｃ1ｃ2ｇ4（ｇ5＋ｇ6）＋ｃ1ｃ3ｇ4（ｇ5＋ｇ6）＋ｃ2ｃ3ｇ1（ｇ5 ＋ｇ6）＋ｃ2ｃ3（ｇ2＋ｇ3＋ｇ5）ｇ6−ｃ1ｃ2（ｇ2＋ｇ3）ｇ7 −ｃ1ｃ3ｇ2ｇ7｝／Ｘ Ｅ＝｛ｃ1ｇ3ｇ4（ｇ5＋ｇ6）＋ｃ2ｇ1ｇ4（ｇ5＋ｇ6）＋ｃ2ｇ4ｇ6（ｇ2 ＋ｇ3＋ｇ5）＋ｃ3ｇ1ｇ4（ｇ5＋ｇ6）＋ｃ3ｇ2（ｇ3＋ｇ4）ｇ6 ＋ｃ3ｇ4ｇ6（ｇ3＋ｇ5）−ｃ1ｇ2ｇ3ｇ7−ｃ2ｇ1（ｇ2＋ｇ3）ｇ7 −ｃ3ｇ1ｇ2ｇ7｝／Ｘ Ｆ＝｛ｇ1ｇ3ｇ4（ｇ5＋ｇ6）＋ｇ3ｇ4ｇ6（ｇ2＋ｇ5）−ｇ1ｇ2ｇ3ｇ7｝／Ｘ ただし、Ｘ＝ｃ1ｃ2ｃ3（ｇ5＋ｇ6）、 そして、本実施例のアクティブフィルタ回路は、前記両
式（１）（２）の分母および分子におけるＳの係数がそ
れぞれ等しくなるように前記容量およびコンダクタンス
を選定していることを特徴とするものである。A = c 1 c 2 c 3 g 5 / X B = ｛c 1 c 2 g 4 g 5 + c 1 c 3 g 4 g 5 −c 1 c 2 (g 2 + g 3 ) (g 6 + G 7 ) −c 1 c 3 g 2 (g 6 + g 7 )} / X C = {c 1 g 3 g 4 g 5 −c 1 g 2 g 3 (g 6 + g 7 )} / X D = {c 1 c 2 g 4 (g 5 + g 6) + c 1 c 3 g 4 (g 5 + g 6) + c 2 c 3 g 1 (g 5 + g 6) + c 2 c 3 (g 2 + g 3 + g 5) g 6 - c 1 c 2 (g 2 + g 3 ) g 7 −c 1 c 3 g 2 g 7 ｝ / X E = c 1 g 3 g 4 (g 5 + g 6 ) + c 2 g 1 g 4 (g 5 + g 6 ) + C 2 g 4 g 6 (g 2 + g 3 + g 5 ) + c 3 g 1 g 4 (g 5 + g 6 ) + c 3 g 2 (g 3 + g 4 ) g 6 + c 3 g 4 g 6 (g 3 + g 5) ) -c 1 g 2 g 3 g 7 -c 2 g 1 (g 2 + g 3) g 7 -c 3 g 1 g 2 g 7} / X F = {g 1 g 3 g 4 (g 5 + 6) + g 3 g 4 g 6 (g 2 + g 5) -g 1 g 2 g 3 g 7} / X , however, X = c 1 c 2 c 3 (g 5 + g 6), and the active of the present embodiment The filter circuit is characterized in that the capacitance and the conductance are selected such that the coefficients of S in the denominator and the numerator of the equations (1) and (2) are equal to each other.
【００１８】したがって、前記（１）（２）式の分母お
よび分子におけるSの係数がそれぞれ等しくなるように
各コンデンサの容量と抵抗のコンダクタンスとを選定す
ることにより、実施例のアクティブフィルタ回路は、１
個の演算増幅器でもって前記所望の合成特性を得ること
ができることになる。Therefore, by selecting the capacitance of each capacitor and the conductance of the resistance such that the coefficients of S in the denominator and the numerator of the above equations (1) and (2) are equal to each other, the active filter circuit of the embodiment can 1
The desired combination characteristic can be obtained with the operational amplifiers.
【００１９】[0019]
【発明の効果】以上説明したことから明らかなように本
発明によれば、１個の演算増幅器でもって一次ハイパス
フィルタの特性と二次ノッチフィルタの特性との両特性
が得られることから、コスト的に安く電力消費も少なく
て済み、しかも簡単かつ小型化可能な構成を有するアク
ティブフィルタ回路を提供することができる。As is apparent from the above description, according to the present invention, since both the characteristics of the primary high-pass filter and the characteristics of the secondary notch filter can be obtained with one operational amplifier, the cost is reduced. It is possible to provide an active filter circuit which is economical, consumes less power, and has a simple and compact configuration.
【図１】本発明の一実施例に係るアクティブフィルタ回
路の回路図である。FIG. 1 is a circuit diagram of an active filter circuit according to one embodiment of the present invention.
【図２】従来例のアクティブフィルタ回路の回路図であ
る。FIG. 2 is a circuit diagram of a conventional active filter circuit.
ＡＭＰ…演算増幅器 ＩＮ…入力端 Ｃ１ないしＣ３…コンデンサ Ｒ１ないしＲ７…抵抗 AMP: operational amplifier IN: input terminal C1 to C3: capacitor R1 to R7: resistor
Claims (1)
場合、伝達関数Ｖｏ／Ｖｉ〔＝Ｔ（Ｓ）〕が、 【数式１】 ただし、Ｘ1＝ωａ＋（ωｏ／Ｑ）、Ｘ2＝ωｏ2＋（ωａ
ωｏ／Ｑ）、Ｘ3＝ωａωｏ2 また、Ｈはフィルタの利得、Ｓはjωであらわされる角
周波数、ωａは一次ハイパスフィルタのカットオフ角周
波数、ωｏは二次ノッチフィルタのカットオフ角周波
数、ωｐは二次ノッチフィルタのノッチ角周波数、Ｑは
フィルタの尖鋭度でそれぞれあらわされる特性を実現す
るアクティブフィルタ回路であって、２入力型の演算増
幅器（ＡＭＰ）を有し、入力端（ＩＮ）に第１コンデン
サ（Ｃ１）の一端を接続し、該第１コンデンサ（Ｃ１）
の他端とアースとの間に第１抵抗（Ｒ１）を接続し、該
第１コンデンサ（Ｃ１）と第１抵抗（Ｒ１）との接続部
と演算増幅器（ＡＭＰ）の一方の入力部（−）との間に
は第２抵抗（Ｒ２）を、また、該接続部と演算増幅器
（ＡＭＰ）の他方の入力部（＋）との間に第５抵抗（Ｒ
５）をそれぞれ接続し、第２抵抗（Ｒ２）の両端間に第
３抵抗（Ｒ３）と第２コンデンサ（Ｃ２）とを直列に接
続し、第２コンデンサ（Ｃ２）の両端間に第３コンデン
サ（Ｃ３）と第４抵抗（Ｒ４）とを直列に接続し、第３
コンデンサ（Ｃ３）と第４抵抗（Ｒ４）との接続部と演
算増幅器（ＡＭＰ）の出力部とを接続し、演算増幅器
（ＡＭＰ）の他方の入力部（＋）とアースとの間に第６
抵抗（Ｒ６）を接続し、演算増幅器（ＡＭＰ）の出力部
と該他方の入力部（＋）との間に第７抵抗（Ｒ７）を接
続してなり、 前記第１ないし第３コンデンサ（Ｃ１〜Ｃ３）の容量を
それぞれC1〜C3とし、前記第１抵抗ないし第７抵抗（Ｒ
１〜Ｒ７）のコンダクタンスをそれぞれg1〜g7とおいた
場合、当該アクティブフィルタ回路の伝達関数Ｔ(Ｓ)は
次式であらわされ、 【数式２】 ただし、 Ａ ＝ｃ1ｃ2ｃ3ｇ5／Ｘ Ｂ＝｛ｃ1ｃ2ｇ4ｇ5＋ｃ1ｃ3ｇ4ｇ5−ｃ1ｃ2（ｇ2＋ｇ3）（ｇ6＋ｇ7） −ｃ1ｃ3ｇ2（ｇ6＋ｇ7）｝／Ｘ Ｃ＝｛ｃ1ｇ3ｇ4ｇ5−ｃ1ｇ2ｇ3（ｇ6＋ｇ7）｝／Ｘ Ｄ＝｛ｃ1ｃ2ｇ4（ｇ5＋ｇ6）＋ｃ1ｃ3ｇ4（ｇ5＋ｇ6）＋ｃ2ｃ3ｇ1（ｇ5 ＋ｇ6）＋ｃ2ｃ3（ｇ2＋ｇ3＋ｇ5）ｇ6−ｃ1ｃ2（ｇ2＋ｇ3）ｇ7 −ｃ1ｃ3ｇ2ｇ7｝／Ｘ Ｅ＝｛ｃ1ｇ3ｇ4（ｇ5＋ｇ6）＋ｃ2ｇ1ｇ4（ｇ5＋ｇ6）＋ｃ2ｇ4ｇ6（ｇ2 ＋ｇ3＋ｇ5）＋ｃ3ｇ1ｇ4（ｇ5＋ｇ6）＋ｃ3ｇ2（ｇ3＋ｇ4）ｇ6 ＋ｃ3ｇ4ｇ6（ｇ3＋ｇ5）−ｃ1ｇ2ｇ3ｇ7−ｃ2ｇ1（ｇ2＋ｇ3）ｇ7 −ｃ3ｇ1ｇ2ｇ7｝／Ｘ Ｆ＝｛ｇ1ｇ3ｇ4（ｇ5＋ｇ6）＋ｇ3ｇ4ｇ6（ｇ2＋ｇ5）−ｇ1ｇ2ｇ3ｇ7｝／Ｘ ただし、Ｘ＝ｃ1ｃ2ｃ3（ｇ5＋ｇ6）、 そして、前記両式（１）（２）の分母および分子におけ
るＳの係数がそれぞれ等しくなるように前記容量および
コンダクタンスを選定していることを特徴とするアクテ
ィブフィルタ回路。When the input voltage is Vi and the output voltage is Vo, the transfer function Vo / Vi [= T (S)] is expressed by the following equation. Here, X 1 = ωa + (ωo / Q) and X 2 = ωo 2 + (ωa
ωo / Q), X 3 = ωaωo 2 , H is the gain of the filter, S is the angular frequency represented by jω, ωa is the cutoff angular frequency of the primary high-pass filter, ωo is the cutoff angular frequency of the secondary notch filter, ωp is a notch angular frequency of a secondary notch filter, and Q is an active filter circuit for realizing characteristics represented by the sharpness of the filter. The active filter circuit has a two-input operational amplifier (AMP) and has an input terminal (IN). Is connected to one end of a first capacitor (C1).
A first resistor (R1) is connected between the other end of the first resistor and the ground, a connection between the first capacitor (C1) and the first resistor (R1), and one input (-) of the operational amplifier (AMP). ), And a fifth resistor (R2) between the connection and the other input (+) of the operational amplifier (AMP).
5), and a third resistor (R3) and a second capacitor (C2) are connected in series between both ends of the second resistor (R2), and a third capacitor is connected between both ends of the second capacitor (C2). (C3) and the fourth resistor (R4) are connected in series.
The connection between the capacitor (C3) and the fourth resistor (R4) is connected to the output of the operational amplifier (AMP), and the sixth input is connected between the other input (+) of the operational amplifier (AMP) and ground.
A resistor (R6) is connected, and a seventh resistor (R7) is connected between an output section of the operational amplifier (AMP) and the other input section (+), and the first to third capacitors (C1) are connected. capacity -C3) a C 1 -C 3, respectively, the first resistor to the seventh resistor (R
If the conductance of 1～R7) was placed and g 1 to g 7 respectively, the transfer function of the active filter circuit T (S) is expressed by the following equation, [Equation 2] Where A = c 1 c 2 c 3 g 5 / X B = ｛c 1 c 2 g 4 g 5 + c 1 c 3 g 4 g 5 −c 1 c 2 (g 2 + g 3 ) (g 6 + g 7 ) −c 1 c 3 g 2 (g 6 + g 7 )} / X C = {c 1 g 3 g 4 g 5 −c 1 g 2 g 3 (g 6 + g 7 )} / X D = {c 1 c 2 g 4 (g 5 + g 6 ) + c 1 c 3 g 4 (g 5 + g 6) + c 2 c 3 g 1 (g 5 + g 6) + c 2 c 3 (g 2 + g 3 + g 5) g 6 -c 1 c 2 (g 2 + g 3) g 7 -c 1 c 3 g 2 g 7} / X E = {c 1 g 3 g 4 (g 5 + g 6) + c 2 g 1 g 4 (g 5 + g 6) + c 2 g 4 g 6 (g 2 + g 3 + g 5 ) + c 3 g 1 g 4 (g 5 + g 6 ) + c 3 g 2 (g 3 + g 4 ) g 6 + c 3 g 4 g 6 (g 3 + g 5 ) -c 1 g 2 g 3 g 7 -c 2 g 1 (g 2 + g 3) g 7 -c 3 g 1 g 2 g 7} / X F = {g 1 g 3 g 4 (g 5 + g 6) + g 3 4 g 6 (g 2 + g 5) -g 1 g 2 g 3 g 7} / X , however, X = c 1 c 2 c 3 (g 5 + g 6), and, wherein both equations (1) and (2) An active filter circuit, wherein the capacitance and the conductance are selected such that the coefficients of S in the denominator and the numerator are equal to each other.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP03233183A JP3106373B2 (en) | 1991-09-12 | 1991-09-12 | Active filter circuit |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP03233183A JP3106373B2 (en) | 1991-09-12 | 1991-09-12 | Active filter circuit |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH0575380A JPH0575380A (en) | 1993-03-26 |
| JP3106373B2 true JP3106373B2 (en) | 2000-11-06 |
Family
ID=16951038
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP03233183A Expired - Fee Related JP3106373B2 (en) | 1991-09-12 | 1991-09-12 | Active filter circuit |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP3106373B2 (en) |
-
1991
- 1991-09-12 JP JP03233183A patent/JP3106373B2/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| JPH0575380A (en) | 1993-03-26 |
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