JPH0744421B2 - Active filter circuit - Google Patents

Active filter circuit

Info

Publication number
JPH0744421B2
JPH0744421B2 JP1034504A JP3450489A JPH0744421B2 JP H0744421 B2 JPH0744421 B2 JP H0744421B2 JP 1034504 A JP1034504 A JP 1034504A JP 3450489 A JP3450489 A JP 3450489A JP H0744421 B2 JPH0744421 B2 JP H0744421B2
Authority
JP
Japan
Prior art keywords
resistor
capacitor
active filter
filter circuit
ground
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
Application number
JP1034504A
Other languages
Japanese (ja)
Other versions
JPH02214210A (en
Inventor
直人 吉岡
昭一 藤田
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Murata Manufacturing Co Ltd
Original Assignee
Murata Manufacturing Co Ltd
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Murata Manufacturing Co Ltd filed Critical Murata Manufacturing Co Ltd
Priority to JP1034504A priority Critical patent/JPH0744421B2/en
Publication of JPH02214210A publication Critical patent/JPH02214210A/en
Publication of JPH0744421B2 publication Critical patent/JPH0744421B2/en
Anticipated expiration legal-status Critical
Expired - Fee Related legal-status Critical Current

Links

Landscapes

  • Networks Using Active Elements (AREA)

Description

【発明の詳細な説明】 （産業上の利用分野） 本発明は、１次ローパスフィルタおよび２次ローパスフ
ィルタからなる３次ローパスフィルタと２次ローパスフ
ィルタとの両フィルタ特性を合わせ持つアクティブフィ
ルタ回路に関する。The present invention relates to an active filter circuit having both filter characteristics of a third-order low-pass filter composed of a first-order low-pass filter and a second-order low-pass filter and a second-order low-pass filter. .

（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、第２図に
示すように３次ローパスフィルタ２と、２次ローパスフ
ィルタ４とで構成されており、いずれのフィルタ2,4も
演算増幅器6,8を具備していた。(Prior Art) An active filter circuit of a conventional example of this type is composed of a third-order low-pass filter 2 and a second-order low-pass filter 4 as shown in FIG. It was equipped with amplifiers 6 and 8.

（発明が解決しようとする問題点） しかしながら、このようにそれぞれのフィルタ2,4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。(Problems to be Solved by the Invention) However, since the respective filters 2 and 4 are provided with the operational amplifiers 6 and 8 as described above, the operational amplifiers 6 and 8 are not provided.
Not only is it expensive in terms of cost, but it also consumes a large amount of power and has a complicated structure, and it is not suitable for miniaturization when incorporated into a circuit board or the like.

そこで、本発明は１つの演算増幅器を用いたもので３次
ローパスフィルタと２次ローパスフィルタとの両フィル
タ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。Therefore, the present invention uses one operational amplifier and is provided with both filter characteristics of a third-order low-pass filter and a second-order low-pass filter, so that the cost is low, the power consumption is low, and the size is simple and compact. It is an object to provide an active filter circuit having a possible configuration.

（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。第１図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。(Example) Hereinafter, an example of the present invention will be described 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.

まず、３次ローパスフィルタと２次ローパスフィルタと
からなるアクティブフィルタ回路への入力電圧をVi、出
力電圧をVoとしたときの合成伝達関数Ｔ（Ｓ）＝Vo/Vi
は、 ただし、 X1＝ω0＋ω1/Q1＋ω2/Q2、 X2＝ω1 2＋ω2 2＋ω1ω0/Q1＋ω2ω0/Q2＋ω1ω2/Q
1Q2、 X3＝（ω0＋ω2/Q2）ω1 2＋（ω0＋ω1/Q1）ω2 2＋ω0
ω1ω2/Q1Q2 X4＝ω0ω1ω2（ω2/Q1＋ω1/Q2）＋ω1 2ω2 2 X5＝ω0ω1 2ω2 2であり、 また、Ｈはフィルタの通過域利得、Ｓはｊωであらわさ
れる角周波数、Q1,Q2は２次ローパスフィルタの尖鋭
度、ω0は１次ローパスフィルタのカットオフ角周波
数、ω1，ω2は２次ローパスフィルタのカットオフ角周
波数、でそれぞれあらわされる。First, when the input voltage to the active filter circuit including the third-order low-pass filter and the second-order low-pass filter is Vi and the output voltage is Vo, the combined transfer function T (S) = Vo / Vi
Is However, X 1 = ω 0 + ω 1 / Q 1 + ω 2 / Q 2 , X 2 = ω 1 2 + ω 2 2 + ω 1 ω 0 / Q 1 + ω 2 ω 0 / Q 2 + ω 1 ω 2 / Q
1 Q 2 , X 3 = (ω 0 + ω 2 / Q 2 ) ω 1 2 + (ω 0 + ω 1 / Q 1 ) ω 2 2 + ω 0
ω 1 ω 2 / Q 1 Q 2 X 4 = ω 0 ω 1 ω 2 (ω 2 / Q 1 + ω 1 / Q 2 ) + ω 1 2 ω 2 2 X 5 = ω 0 ω 1 2 ω 2 2 Further, H is the pass band gain of the filter, S is the angular frequency represented by jω, Q 1 and Q 2 are the sharpness of the secondary low-pass filter, ω 0 is the cutoff angular frequency of the primary low-pass filter, and ω 1 and ω 2 is the cutoff angular frequency of the second-order low-pass filter.

つぎに、本発明のアクティブフィルタ回路10は、利得Ｋ
の演算増幅器12を用い、入力端14から演算増幅器12の入
力部16までの間に第１、第２、第３、第４および第５の
抵抗R1ないしR5をこの順序で直列接続してなる抵抗直列
回路を挿入し、第１抵抗R1および第２抵抗R2の接続部18
とアース20との間に第６抵抗R6と第１コンデンサC1とを
それぞれ挿入接続し、また第２抵抗R2および第３抵抗R3
の接続部22と演算増幅器の出力部24との間に第２コンデ
ンサC2、第３抵抗R3および第４抵抗R4の接続部26とアー
ス18との間に第３コンデンサC3、第４抵抗R4および第５
抵抗R5の接続部28と演算増幅器12の出力部24との間に第
４コンデンサC4、第５抵抗R5および演算増幅器12の入力
部16の接続部30とアース18との間に第５コンデンサC5を
それぞれ接続してなり、第１ないし第５コンデンサC1な
いしC5の容量をそれぞれC1〜C5とし、前記第１抵抗ない
し第６抵抗R1ないしR6の抵抗値をそれぞれr1〜r6とおい
た場合、当該アクティブフィルタ回路の伝達関数Vo/Vi
は次式であらわされ、 ただし、 Ａ＝A1/P、Ｂ＝B1/P、Ｃ＝C1/P、Ｄ＝D1/P、Ｅ＝1/P、
Ｈ＝Ｋ・r6/(r1+r6)、ｒ＝r1r6/(r1+r6)で、かつ、 A1＝rr2r3r4{(1-K)C1C2C3C4+C1C2C3C5}+rr2r3r5{C1C2C3
C5+C1C2C4C5}+rr2r4r5{C1C2C4C5+C1C3C4C5}+rr3r4r5{C1
C3C4C5+C2C3C4C5}+r2r3r4r5C2C3C4C5、 B1＝〔rr2r3{C1C2C3+(1-K)C1C2C4+C1C2C5}+rr2r4{C1C2C
5+(1-K)C1C2C4+(1-K)C1C3C4+C1C3C5}+rr2r5{C1C3C5+C1C
4C5+C1C2C5}+rr3r4{(1-K)C1C3C4+C1C3C5+(1-K)C2C3C4+C
2C3C5}+rr3r5{C1C3C5+C1C4C5+C2C3C5+C2C4C5}+rr4r5{C1
C4C5+C2C4C5+C3C4C5}+r2r3r4{(1-K)C2C3C4+C2C3C5}+r2r
3r5{C2C3C5+C2C4C5}+r2r4r5{C2C4C5+C3C4C5}+r3r4r5C3C
4C5〕 C1＝[rr2{(1-K)C1C2+C1C3+(1-K)C1C4+C1C5}+rr3{C1C3+
(1-K)C1C4+C1C5+C2C3+(1-K)C2C4+C2C5}+rr4{(1-K)C1C4+
C1C5+(1-K)C2C4+C2C5+(1-K)C3C4+C3C5}+rr5{C1C5+C2C5+
C3C5+C4C5}+r2r3{C2C3+(1-K)C2C4+C2C5}+r2r4{(1-K)C2C
4+C2C5+(1-K)C3C4+C3C5}+r2r5{C2C5+C3C5+C4C5}+r3r
4{(1-K)C3C4+C3C5}+r3r5{C3C5+C4C5}+r4r5C4C5] D1＝r{C1+(1-K)C2+C3+(1-K)C4+C5}+r2{(1-K)C2+C3+(1-
K)C4+C5}+r3{C3+(1-K)C4+C5}+r4{(1-K)C4+C5}+r5C5 Ｐ＝C1C2C3C4C5rr2r3r4r5 である。Next, the active filter circuit 10 of the present invention has a gain K
The operational amplifier 12 is used to connect the first, second, third, fourth and fifth resistors R 1 to R 5 in series between the input terminal 14 and the input section 16 of the operational amplifier 12 in this order. A resistor series circuit formed by connecting the first resistor R 1 and the second resistor R 2 to each other.
The sixth resistor R 6 and the first capacitor C 1 are respectively connected between the ground and the ground 20, and the second resistor R 2 and the third resistor R 3 are connected.
The second capacitor C 2 between the connection 22 and the output 24 of the operational amplifier, the third capacitor C 3 between the connection 26 of the third resistor R 3 and the fourth resistor R 4 and the ground 18, 4 resistors R 4 and 5
A fourth capacitor C 4 is provided between the connecting portion 28 of the resistor R 5 and the output portion 24 of the operational amplifier 12, a fifth resistor R 5 is provided between the connecting portion 30 of the input portion 16 of the operational amplifier 12, and the ground 18. 5 will be capacitor C 5 was connected, first through to fifth capacitor C 1 to a C 1 -C 5, respectively the capacitance of C 5, wherein the first resistor to to sixth no resistor R 1 and the resistance value of R 6 When r 1 to r 6 are respectively set, the transfer function Vo / Vi of the active filter circuit is
Is expressed as However, A = A 1 / P, B = B 1 / P, C = C 1 / P, D = D 1 / P, E = 1 / P,
H = K · r 6 / (r 1 + r 6 ), r = r 1 r 6 / (r 1 + r 6 ), and A 1 = rr 2 r 3 r 4 {(1-K) C 1 C 2 C 3 C 4 + C 1 C 2 C 3 C 5 } + rr 2 r 3 r 5 {C 1 C 2 C 3
C 5 + C 1 C 2 C 4 C 5 } + rr 2 r 4 r 5 {C 1 C 2 C 4 C 5 + C 1 C 3 C 4 C 5 } + rr 3 r 4 r 5 {C 1
C 3 C 4 C 5 + C 2 C 3 C 4 C 5 } + r 2 r 3 r 4 r 5 C 2 C 3 C 4 C 5 , B 1 = (rr 2 r 3 {C 1 C 2 C 3 + (1-K) C 1 C 2 C 4 + C 1 C 2 C 5 } + rr 2 r 4 {C 1 C 2 C
5 + (1-K) C 1 C 2 C 4 + (1-K) C 1 C 3 C 4 + C 1 C 3 C 5 } + rr 2 r 5 {C 1 C 3 C 5 + C 1 C
4 C 5 + C 1 C 2 C 5 } + rr 3 r 4 {(1-K) C 1 C 3 C 4 + C 1 C 3 C 5 + (1-K) C 2 C 3 C 4 + C
2 C 3 C 5 } + rr 3 r 5 {C 1 C 3 C 5 + C 1 C 4 C 5 + C 2 C 3 C 5 + C 2 C 4 C 5 } + rr 4 r 5 {C 1
C 4 C 5 + C 2 C 4 C 5 + C 3 C 4 C 5 } + r 2 r 3 r 4 {(1-K) C 2 C 3 C 4 + C 2 C 3 C 5 } + r 2 r
3 r 5 {C 2 C 3 C 5 + C 2 C 4 C 5 } + r 2 r 4 r 5 {C 2 C 4 C 5 + C 3 C 4 C 5 } + r 3 r 4 r 5 C 3 C
4 C 5 ] C 1 = [rr 2 {(1-K) C 1 C 2 + C 1 C 3 + (1-K) C 1 C 4 + C 1 C 5 } + rr 3 {C 1 C 3 +
(1-K) C 1 C 4 + C 1 C 5 + C 2 C 3 + (1-K) C 2 C 4 + C 2 C 5 } + rr 4 {(1-K) C 1 C 4 +
C 1 C 5 + (1-K) C 2 C 4 + C 2 C 5 + (1-K) C 3 C 4 + C 3 C 5 } + rr 5 {C 1 C 5 + C 2 C 5 +
C 3 C 5 + C 4 C 5 } + r 2 r 3 {C 2 C 3 + (1-K) C 2 C 4 + C 2 C 5 } + r 2 r 4 {(1-K) C 2 C
4 + C 2 C 5 + (1-K) C 3 C 4 + C 3 C 5 } + r 2 r 5 {C 2 C 5 + C 3 C 5 + C 4 C 5 } + r 3 r
4 {(1-K) C 3 C 4 + C 3 C 5 } + r 3 r 5 {C 3 C 5 + C 4 C 5 } + r 4 r 5 C 4 C 5 ] D 1 = r {C 1 + (1-K) C 2 + C 3 + (1-K) C 4 + C 5 } + r 2 {(1-K) C 2 + C 3 + (1-
K) C 4 + C 5 } + r 3 {C 3 + (1-K) C 4 + C 5 } + r 4 {(1-K) C 4 + C 5 } + r 5 C 5 P = C 1 C 2 C 3 C 4 C 5 rr 2 r 3 r 4 r 5

したがって、前記（１）（２）式の分母における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
抗の抵抗値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12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 resistance value of the resistor so that the coefficients of S in the denominators of the above equations (1) and (2) are equal, the active filter circuit of the embodiment performs one calculation. With the amplifier 12, the desired combined characteristic can be obtained.

なお、この実施例では上記（１）（２）の分子における
Ｓの係数も等しくなるようにしている。もっとも、この
分子間の関係は所望の合成特性をその形を変えずに上下
に平行移動させる、すなわち利得を全体的に変えるのに
関係するだけであるため、必ずしもこの例のように両係
数を一致させなくてもよい。In this embodiment, the coefficients of S in the numerator of (1) and (2) are made equal. However, since the relationship between the molecules is only related to the translation of desired synthetic characteristics up and down without changing its shape, that is, to the overall change of gain, both coefficients are not necessarily changed as in this example. It does not have to match.

第２図は本発明の他の実施例に係るアクティブフィルタ
回路の回路図であり、第１図と対応する部分には同一の
符号を付すとともに、その同一の符号に係る部分につい
ての説明は省略する。FIG. 2 is a circuit diagram of an active filter circuit according to another embodiment of the present invention. The portions corresponding to those in FIG. 1 are designated by the same reference numerals, and the description of the portions associated with the same reference numerals is omitted. To do.

第２図の実施例のアクティブフィルタ回路において特徴
とする構成は、第１図のアクティブフィルタ回路31にお
ける第１抵抗R1から第５抵抗R5からなる前記抵抗直列回
路において、第１抵抗R1と第２抵抗R2との間に第７抵抗
R7を挿入接続するとともに、第１抵抗R1と第７抵抗R7と
の接続部32とアース20との間に第６抵抗R6、第７抵抗R7
と第２抵抗R2との接続部34とアース20との間に第１コン
デンサC1をそれぞれ接続し、かつ、前記ｒ＝r1r6/(r1+r
6)の式をｒ＝(r1+r6+r6r7+r7r1)/(r1+r6)としたことで
あり、その他の構成および作用は第１図のそれと同様で
あるからその説明は省略する。Configuration, wherein in the active filter circuit of the embodiment of FIG. 2, in the resistor series circuit from the first resistor R 1 in the active filter circuit 31 of FIG. 1 consists of a fifth resistor R 5, the first resistor R 1 And a second resistor R 2 between the seventh resistor
R 7 is inserted and connected, and the sixth resistor R 6 and the seventh resistor R 7 are connected between the connection portion 32 between the first resistor R 1 and the seventh resistor R 7 and the ground 20.
The first capacitor C 1 is connected between the connecting portion 34 between the second resistor R 2 and the ground 20 and the above-mentioned r = r 1 r 6 / (r 1 + r
6 ) is defined as r = (r 1 + r 6 + r 6 r 7 + r 7 r 1 ) / (r 1 + r 6 ), and other configurations and actions are the same as those in FIG. Therefore, the description thereof is omitted.

（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３次ローパスフィルタの特性
と２次ローパスフィルタの特性との合成特性が得られる
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。(Effect) As is apparent from the above description, according to the present invention,
A single operational amplifier can provide a combined characteristic of the characteristics of the third-order low-pass filter and the characteristics of the second-order low-pass filter, so that the cost is low, the power consumption is low, and the configuration is simple and compact. An active filter circuit having the same can be provided.

【図面の簡単な説明】[Brief description of drawings]

第１図は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、第２図は本発明の他の実施例に係るアクテ
ィブフィルタ回路の回路図、第３図は従来例のアクティ
ブフィルタ回路の回路図である。 12……演算増幅器、14……入力端、16……演算増幅器の
入力部、24……演算増幅器の出力部、C1ないしC5……コ
ンデンサ、R1ないしR7……抵抗。FIG. 1 is a circuit diagram of an active filter circuit according to one embodiment of the present invention, FIG. 2 is a circuit diagram of an active filter circuit according to another embodiment of the present invention, and FIG. 3 is a conventional active filter circuit. It is a circuit diagram. 12 ... Operational amplifier, 14 ... Input end, 16 ... Operational amplifier input section, 24 ... Operational amplifier output section, C 1 to C 5 ... Capacitor, R 1 to R 7 ... Resistance.

Claims (2)

【特許請求の範囲】[Claims] 【請求項１】入力電圧をVi、出力電圧をVoとした場合、
伝達関数Vo/Viが、 ただし、 X1＝ω0＋ω1/Q1＋ω2/Q2、 X2＝ω1 2＋ω2 2＋ω1ω0/Q1＋ω2ω0/Q2＋ω1ω2/Q
1Q2、 X3＝（ω0＋ω2/Q2）ω1 2＋（ω0＋ω1/Q1）ω2 2＋ω0
ω1ω2/Q1Q2 X4＝ω0ω1ω2（ω2/Q1＋ω1/Q2）＋ω1 2ω2 2 X5＝ω0ω1 2ω2 2であり、 また、Ｈはフィルタの通過域利得、Ｓはｊωであらわさ
れる角周波数、Q1,Q2は２次ローパスフィルタの尖鋭
度、ω0は１次ローパスフィルタのカットオフ角周波
数、ω1，ω2は２次ローパスフィルタのカットオフ角周
波数、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、 利得Ｋの演算増幅器を用い、入力端から演算増幅器の入
力部までの間に第１、第２、第３、第４および第５の抵
抗をこの順序で直列接続してなる抵抗直列回路を挿入
し、第１抵抗および第２抵抗の接続部とアースとの間に
第１コンデンサおよび第６抵抗をそれぞれ接続し、また
第２抵抗および第３抵抗の接続部と演算増幅器の出力部
との間に第２コンデンサ、第３抵抗および第４抵抗の接
続部とアースとの間に第３コンデンサ、第４抵抗および
第５抵抗の接続部と演算増幅器の出力部との間に第４コ
ンデンサ、第５抵抗および演算増幅器の入力部の接続部
とアースとの間に第５コンデンサをそれぞれ接続してな
り、 前記第１ないし第５コンデンサの容量をそれぞれC1〜C5
とし、前記第１抵抗ないし第６抵抗の抵抗値をそれぞれ
r1〜r6とおいた場合、当該アクティブフィルタ回路の伝
達関数Vo/Viは次式であらわされ、 ただし、 Ａ＝A1/P、Ｂ＝B1/P、Ｃ＝C1/P、Ｄ＝D1/P、Ｅ＝1/P、
Ｈ＝Ｋ・r6/(r1+r6)、ｒ＝r1r6/(r1+r6)で、かつ、 A1＝rr2r3r4{(1-K)C1C2C3C4+C1C2C3C5}+rr2r3r5{C1C2C3
C5+C1C2C4C5}+rr2r4r5{C1C2C4C5+C1C3C4C5}+rr3r4r5{C1
C3C4C5+C2C3C4C5}+r2r3r4r5C2C3C4C5、 B1＝〔rr2r3{C1C2C3+(1-K)C1C2C4+C1C2C5}+rr2r4{C1C2C
5+(1-K)C1C2C4+(1-K)C1C3C4+C1C3C5}+rr2r5{C1C3C5+C1C
4C5+C1C2C5}+rr3r4{(1-K)C1C3C4+C1C3C5+(1-K)C2C3C4+C
2C3C5}+rr3r5{C1C3C5+C1C4C5+C2C3C5+C2C4C5}+rr4r5{C1
C4C5+C2C4C5+C3C4C5}+r2r3r4{(1-K)C2C3C4+C2C3C5}+r2r
3r5{C2C3C5+C2C4C5}+r2r4r5{C2C4C5+C3C4C5}+r3r4r5C3C
4C5〕 C1＝[rr2{(1-K)C1C2+C1C3+(1-K)C1C4+C1C5}+rr3{C1C3+
(1-K)C1C4+C1C5+C2C3+(1-K)C2C4+C2C5}+rr4{(1-K)C1C4+
C1C5+(1-K)C2C4+C2C5+(1-K)C3C4+C3C5}+rr5{C1C5+C2C5+
C3C5+C4C5}+r2r3{C2C3+(1-K)C2C4+C2C5}+r2r4{(1-K)C2C
4+C2C5+(1-K)C3C4+C3C5}+r2r5{C2C5+C3C5+C4C5}+r3r
4{(1-K)C3C4+C3C5}+r3r5{C3C5+C4C5}+r4r5C4C5] D1＝r{C1+(1-K)C2+C3+(1-K)C4+C5}+r2{(1-K)C2+(1-K)C4
+C5}+r3{C3+(1-K)C4+C5}+r4{(1-K)C4+C5}+r5C5 Ｐ＝C1C2C3C4C5rr2r3r4r5 そして、前記両式（１）（２）の少なくとも分母におけ
るＳの係数を満足するように前記容量および抵抗値を選
定していることを特徴とするアクティブフィルタ回路。1. When the input voltage is Vi and the output voltage is Vo,
Transfer function Vo / Vi is However, X 1 = ω 0 + ω 1 / Q 1 + ω 2 / Q 2 , X 2 = ω 1 2 + ω 2 2 + ω 1 ω 0 / Q 1 + ω 2 ω 0 / Q 2 + ω 1 ω 2 / Q
1 Q 2 , X 3 = (ω 0 + ω 2 / Q 2 ) ω 1 2 + (ω 0 + ω 1 / Q 1 ) ω 2 2 + ω 0
ω 1 ω 2 / Q 1 Q 2 X 4 = ω 0 ω 1 ω 2 (ω 2 / Q 1 + ω 1 / Q 2 ) + ω 1 2 ω 2 2 X 5 = ω 0 ω 1 2 ω 2 2 Further, H is the passband gain of the filter, S is the angular frequency represented by jω, Q 1 and Q 2 are the sharpness of the secondary lowpass filter, ω 0 is the cutoff angular frequency of the primary lowpass filter, and ω 1 and ω Reference numeral 2 is an active filter circuit that realizes the characteristics respectively expressed by the cutoff angular frequency of the second-order low-pass filter, which uses an operational amplifier with a gain of K. A resistor series circuit is formed by connecting the second, third, fourth and fifth resistors in series in this order, and the first capacitor and the first capacitor and the first resistor are connected between the connection portion of the first resistor and the second resistor and the ground. 6 resistors are connected to each other, and the second resistor is connected between the connecting portion of the second resistor and the third resistor and the output portion of the operational amplifier. Sensor, a third capacitor between the connection of the third resistor and the fourth resistor and the ground, and a fourth capacitor between the connection of the fourth resistor and the fifth resistor and the output of the operational amplifier, the fifth resistor and constituted by connecting respective fifth capacitor between the input portion of the connecting portion and the ground of the operational amplifier, respectively the capacity of the first through fifth capacitors C 1 -C 5
And the resistance values of the first resistor to the sixth resistor are respectively
When r 1 to r 6 are set, the transfer function Vo / Vi of the active filter circuit is expressed by the following equation, However, A = A 1 / P, B = B 1 / P, C = C 1 / P, D = D 1 / P, E = 1 / P,
H = K · r 6 / (r 1 + r 6 ), r = r 1 r 6 / (r 1 + r 6 ), and A 1 = rr 2 r 3 r 4 {(1-K) C 1 C 2 C 3 C 4 + C 1 C 2 C 3 C 5 } + rr 2 r 3 r 5 {C 1 C 2 C 3
C 5 + C 1 C 2 C 4 C 5 } + rr 2 r 4 r 5 {C 1 C 2 C 4 C 5 + C 1 C 3 C 4 C 5 } + rr 3 r 4 r 5 {C 1
C 3 C 4 C 5 + C 2 C 3 C 4 C 5 } + r 2 r 3 r 4 r 5 C 2 C 3 C 4 C 5 , B 1 = (rr 2 r 3 {C 1 C 2 C 3 + (1-K) C 1 C 2 C 4 + C 1 C 2 C 5 } + rr 2 r 4 {C 1 C 2 C
5 + (1-K) C 1 C 2 C 4 + (1-K) C 1 C 3 C 4 + C 1 C 3 C 5 } + rr 2 r 5 {C 1 C 3 C 5 + C 1 C
4 C 5 + C 1 C 2 C 5 } + rr 3 r 4 {(1-K) C 1 C 3 C 4 + C 1 C 3 C 5 + (1-K) C 2 C 3 C 4 + C
2 C 3 C 5 } + rr 3 r 5 {C 1 C 3 C 5 + C 1 C 4 C 5 + C 2 C 3 C 5 + C 2 C 4 C 5 } + rr 4 r 5 {C 1
C 4 C 5 + C 2 C 4 C 5 + C 3 C 4 C 5 } + r 2 r 3 r 4 {(1-K) C 2 C 3 C 4 + C 2 C 3 C 5 } + r 2 r
3 r 5 {C 2 C 3 C 5 + C 2 C 4 C 5 } + r 2 r 4 r 5 {C 2 C 4 C 5 + C 3 C 4 C 5 } + r 3 r 4 r 5 C 3 C
4 C 5 ] C 1 = [rr 2 {(1-K) C 1 C 2 + C 1 C 3 + (1-K) C 1 C 4 + C 1 C 5 } + rr 3 {C 1 C 3 +
(1-K) C 1 C 4 + C 1 C 5 + C 2 C 3 + (1-K) C 2 C 4 + C 2 C 5 } + rr 4 {(1-K) C 1 C 4 +
C 1 C 5 + (1-K) C 2 C 4 + C 2 C 5 + (1-K) C 3 C 4 + C 3 C 5 } + rr 5 {C 1 C 5 + C 2 C 5 +
C 3 C 5 + C 4 C 5 } + r 2 r 3 {C 2 C 3 + (1-K) C 2 C 4 + C 2 C 5 } + r 2 r 4 {(1-K) C 2 C
4 + C 2 C 5 + (1-K) C 3 C 4 + C 3 C 5 } + r 2 r 5 {C 2 C 5 + C 3 C 5 + C 4 C 5 } + r 3 r
4 {(1-K) C 3 C 4 + C 3 C 5 } + r 3 r 5 {C 3 C 5 + C 4 C 5 } + r 4 r 5 C 4 C 5 ] D 1 = r {C 1 + (1-K) C 2 + C 3 + (1-K) C 4 + C 5 } + r 2 {(1-K) C 2 + (1-K) C 4
+ C 5 } + r 3 {C 3 + (1-K) C 4 + C 5 } + r 4 {(1-K) C 4 + C 5 } + r 5 C 5 P = C 1 C 2 C 3 C 4 C 5 rr 2 r 3 r 4 r 5 And, the capacitance and resistance values are selected so as to satisfy the coefficient of S in at least the denominator of the above equations (1) and (2). Active filter circuit. 【請求項２】前記請求項第１項のアクティブフィルタ回
路において、 前記抵抗直列回路における第１抵抗と第２抵抗との間に
第７抵抗を挿入接続するとともに、第１抵抗と前記第７
抵抗との接続部とアースとの間に前記第６抵抗、前記第
７抵抗と前記第２抵抗との接続部とアースとの間に前記
第１コンデンサをそれぞれ接続してなり、 前記ｒ＝r1r6/(r1+r6)の式をｒ＝(r1r6+r6r7+r7r1)/(r1
+r6)としたことを特徴とするアクティブフィルタ回路。2. The active filter circuit according to claim 1, wherein a seventh resistor is inserted and connected between the first resistor and the second resistor in the resistor series circuit, and the first resistor and the seventh resistor are connected.
The sixth resistor is connected between a connection portion with a resistor and the ground, and the first capacitor is connected between a connection portion between the seventh resistor and the second resistor and the ground, and r = r The equation of 1 r 6 / (r 1 + r 6 ) is r = (r 1 r 6 + r 6 r 7 + r 7 r 1 ) / (r 1
+ r 6 ) An active filter circuit characterized by the above.
JP1034504A 1989-02-14 1989-02-14 Active filter circuit Expired - Fee Related JPH0744421B2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP1034504A JPH0744421B2 (en) 1989-02-14 1989-02-14 Active filter circuit

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP1034504A JPH0744421B2 (en) 1989-02-14 1989-02-14 Active filter circuit

Publications (2)

Publication Number Publication Date
JPH02214210A JPH02214210A (en) 1990-08-27
JPH0744421B2 true JPH0744421B2 (en) 1995-05-15

Family

ID=12416086

Family Applications (1)

Application Number Title Priority Date Filing Date
JP1034504A Expired - Fee Related JPH0744421B2 (en) 1989-02-14 1989-02-14 Active filter circuit

Country Status (1)

Country Link
JP (1) JPH0744421B2 (en)

Also Published As

Publication number Publication date
JPH02214210A (en) 1990-08-27

Similar Documents

Publication Publication Date Title
JP3181588B2 (en) Universal filter
US5424675A (en) Full differential type analog circuit having parallel oppositely connected capacitors to eliminate unbalanced parasitic capacitances
US20080204129A1 (en) Simplified Sallen-Key Low-Pass Filter Circuit
JPS6362133B2 (en)
JPH0744420B2 (en) Active filter circuit
JPH0744421B2 (en) Active filter circuit
JPH0614508Y2 (en) Active filter circuit
JP3106373B2 (en) Active filter circuit
JP3170796B2 (en) Active filter circuit
JPS6117369B2 (en)
JPH0641387Y2 (en) Active filter circuit
JPH0641388Y2 (en) Active filter circuit
JPH0450654Y2 (en)
JPH0614507Y2 (en) Active filter circuit
JPH0614506Y2 (en) Active filter circuit
JPS6351576B2 (en)
JP3225260B2 (en) Filter circuit
JPH0450655Y2 (en)
JPS6138278Y2 (en)
JP2666860B2 (en) Negative impedance circuit
JPH0619216Y2 (en) Active filter circuit
JPS6342745Y2 (en)
JPS6438825U (en)
JPS6347284B2 (en)
JPS6438826U (en)

Legal Events

Date Code Title Description
LAPS Cancellation because of no payment of annual fees