JPH0450654Y2

JPH0450654Y2 -

Info

Publication number: JPH0450654Y2
Application number: JP5030786U
Authority: JP
Priority date: 1986-04-02
Filing date: 1986-04-02
Publication date: 1992-11-30
Also published as: JPS62161423U

Description

【考案の詳細な説明】〔産業上の利用分野〕この考案は、２次バンドパス特性の高域側のロ
ールオフを急峻にしたような特性を得ることがで
きるアクテイブフイルタ回路に関する。[Detailed Description of the Invention] [Industrial Field of Application] This invention relates to an active filter circuit that can obtain characteristics such as a steep roll-off on the high frequency side of a secondary bandpass characteristic.

[Conventional technology]

第２図に、１次ローパス特性Ｅの一例、２次バ
ンドパス特性Ｆの一例および２次バンドパス特性
Ｆの高域側のロールオフを急峻にした特性Ｇの一
例を示す。この例のような１次ローパス特性Ｅは
第３図のようなフイルタ回路１で、２次バンドパ
ス特性Ｆは第４図のような演算増幅器２０を有す
るアクテイブフイルタ回路２で実現することがで
きる。 FIG. 2 shows an example of a first-order low-pass characteristic E, an example of a second-order band-pass characteristic F, and an example of a characteristic G in which the roll-off on the high frequency side of the second-order band-pass characteristic F is made steeper. The first-order low-pass characteristic E in this example can be realized by a filter circuit 1 as shown in FIG. 3, and the second-order band-pass characteristic F can be realized by an active filter circuit 2 having an operational amplifier 20 as shown in FIG. .

一方、上記例のような特性Ｇは、上記例のよう
な１次ローパス特性Ｅと２次バンドパス特性Ｆを
合成することによつて得られ、具体的には従来
は、第５図に示すように、１次ローパス特性Ｅを
実現する上記のようなフイルタ回路１と２次バン
ドパス特性Ｆを実現する上記のようなアクテイブ
フイルタ回路２とを、バツフア用の演算増幅器３
０を介して縦続接続して成るアクテイブフイルタ
回路３によつて実現していた。 On the other hand, the characteristic G as in the above example is obtained by combining the first-order low-pass characteristic E and the second-order band-pass characteristic F as in the above example. As shown in FIG.
This was realized by active filter circuits 3 connected in cascade through 0.

[Problem that the invention attempts to solve]

所が上記のようなアクテイブフイルタ回路３に
おいては、上記のような所望の合成特性を得るた
めには、演算増幅器２０に加えて、両フイルタ回
路１，２の独立性を確保するためにバツフア用の
演算増幅器３０が必ず必要であり、そのため回路
の小型化、低コスト化および低電力化が阻害され
ていた。 However, in the active filter circuit 3 as described above, in order to obtain the desired synthesis characteristics as described above, in addition to the operational amplifier 20, a buffer circuit is required to ensure the independence of both filter circuits 1 and 2. An operational amplifier 30 is always required, which hinders circuit miniaturization, cost reduction, and power reduction.

そこでこの考案は、一つの演算増幅器を用いた
もので上記のような２次バンドパス特性と１次ロ
ーパス特性の合成特性を実現することができるア
クテイブフイルタ回路を提供することを目的とす
る。 Therefore, the object of this invention is to provide an active filter circuit that can realize the composite characteristic of the above-mentioned secondary band-pass characteristic and primary low-pass characteristic using one operational amplifier.

〔Example〕

第１図は、この考案の一実施例に係るアクテイ
ブフイルタ回路を示す回路図である。このアクテ
イブフイルタ回路４は、第１入力部（即ち負側入
力部）５１、第２入力部（即ち正側入力部）５２
および出力部５３を有する演算増幅器５０を用
い、入力端４１と演算増幅器５０の第１入力部５
１間に第１の抵抗器７１、第２の抵抗器７２およ
び第３のコンデンサ６３をこの順で直列接続した
ものを接続し、第１の抵抗器７１と第２の抵抗器
７２との接続部とアース間に第１のコンデンサ６
１を接続し、第２の抵抗器７２と第３のコンデン
サ６３との接続部とアース間に第３の抵抗器７３
を接続し、当該接続部と演算増幅器５０の出力部
５３間に第２のコンデンサ６２を接続し、演算増
幅器５０の出力部５３と第１入力部５１間および
第２入力部５２間にそれぞれ第４の抵抗器７４お
よび第６の抵抗器７６を接続し、演算増幅器５０
の第２入力部５２とアース間に第５の抵抗器７５
を接続し、そして演算増幅器５０の出力部５３を
出力端４２に接続して成る。 FIG. 1 is a circuit diagram showing an active filter circuit according to an embodiment of this invention. This active filter circuit 4 includes a first input section (i.e., negative input section) 51 and a second input section (i.e., positive input section) 52.
and an operational amplifier 50 having an output section 53, an input terminal 41 and a first input section 5 of the operational amplifier 50.
A first resistor 71, a second resistor 72, and a third capacitor 63 connected in series in this order are connected between the first resistor 71 and the second resistor 72. The first capacitor 6 is connected between the
1, and a third resistor 73 between the connection between the second resistor 72 and the third capacitor 63 and the ground.
A second capacitor 62 is connected between the connection part and the output part 53 of the operational amplifier 50, and a second capacitor 62 is connected between the output part 53 of the operational amplifier 50 and the first input part 51 and the second input part 52, respectively. The fourth resistor 74 and the sixth resistor 76 are connected, and the operational amplifier 50
A fifth resistor 75 is connected between the second input section 52 of the
and the output section 53 of the operational amplifier 50 is connected to the output end 42.

そして入力電圧をVi、出力電圧をVoとし、前
記第１ないし第３のコンデンサ６１〜６３の容量
をそれぞれC₁〜C₃とし、第１ないし第６の抵抗
器７１〜７６の抵抗値をそれぞれR₁〜R₆とし、
演算増幅器５０のオープンループゲインをAdと
し、 α＝R₃／R₆ β＝正帰還率＝｛α／（１＋α）｝−１／Ad とおいた場合、当該アクテイブフイルタ回路４の
伝達関数Vo／Viは次式で表される。ここでＳは
jωで表される周波数である。 The input voltage is Vi, the output voltage is Vo, the capacitances of the first to third capacitors 61 to 63 are _C1 to _C3 , respectively, and the resistance values of the first to sixth resistors 71 to 76 are respectively R ₁ to R ₆ ,
When the open loop gain of the operational amplifier 50 is Ad, and α=R ₃ /R ₆ β=positive feedback rate={α/(1+α)}-1/Ad, the transfer function Vo/Vi of the active filter circuit 4 is is expressed by the following formula. Here S is
This is the frequency represented by jω.

Vo／Vi＝K₁Ｓ／S³＋K₂S²＋K₃Ｓ＋K₄ …(1) 但し、 K₁＝−１／１−β・１／C₁C₂R₁R₂ K₂＝１／C₁（１／R₁＋１／R₂）＋１／C₂R₄＋１／C₃R₄ −β／１−β（１／R₂＋１／R₃） K₃＝１／C₁R₄（１／C₂＋１／C₃）（１／R₁＋１／R₂）＋１／C₂C₃R₄（１／R₂＋１／R₃）−１／１−β ・１／C₁C₂（１／R₁R₂＋１／R₂R₃＋１／R₃R₁） K₄＝１／C₁C₂C₃R₄（１／R₁R₂＋１／R₂R₃ ＋１／R₃R₁）一方、前述したような所望の２次バンドパス特性
と１次ローパス特性の合成特性は次式で表され
る。 Vo/Vi=K ₁ S/S ³ +K ₂ S ² +K ₃ S+K ₄ …(1) However, K ₁ =-1/1-β・1/C ₁ C ₂ R ₁ R ₂ K ₂ = 1/C ₁ (1/R ₁ +1/R ₂ )+1/C ₂ R ₄ +1/C ₃ R ₄ −β/1−β (1/R ₂ +1/R ₃ ) K ₃ =1/C ₁ R ₄ (1 /C ₂ +1/C ₃ ) (1/R ₁ +1/R ₂ ) +1/C ₂ C ₃ R ₄ (1/R ₂ +1/R ₃ )-1/1-β ・1/C ₁ C ₂ ( 1/R ₁ R ₂ +1/R ₂ R ₃ +1/R ₃ R ₁ ) K ₄ =1/C ₁ C ₂ C ₃ R ₄ (1/R ₁ R ₂ +1/R ₂ R ₃ +1/R ₃ R ₁ ) On the other hand, the desired composite characteristic of the secondary bandpass characteristic and the primary lowpass characteristic as described above is expressed by the following equation.

Vo／Vi＝ωa・HBS／（Ｓ＋ωa）（S²＋BS＋ωo²）＝HB
ωaS／S³＋（ωa＋Ｂ）S²＋（ωo²＋Bωa）＋ωaωo²…
(2) 但し、Ｈは通過域利得、Ｂはバンド幅、ωoは
中心周波数、ωaは１次ローパスフイルタのカツ
トオフ周波数、Ｓはjωで表される周波数。Vo/Vi=ωa・HBS/(S+ωa) (S ² +BS+ωo ² )=HB
ωaS/S ³ + (ωa + B) S ² + (ωo ² + Bωa) + ωaωo ² …
(2) However, H is the passband gain, B is the bandwidth, ωo is the center frequency, ωa is the cutoff frequency of the first-order low-pass filter, and S is the frequency expressed by jω.

従つて上記(1)式と(2)式の分母における周波数Ｓ
の係数および定数がそれぞれ等しくなるように、
即ちK₂＝ωa＋Ｂ，K₃＝ωo²＋BωaおよびK₄＝
ωaωo²を満足するように上記容量C₁〜C₃および
抵抗値R₁〜R₆を選定することによつて、上記ア
クテイブフイルタ回路４で上述したような所望の
合成特性を得ることができ、当該アクテイブフイ
ルタ回路４はそのように選定している。 Therefore, the frequency S in the denominator of equations (1) and (2) above
so that the coefficients and constants of are equal,
That is, K ₂ = ωa + B, K ₃ = ωo ² + Bωa and K ₄ =
By selecting the capacitances C ₁ to C ₃ and the resistance values R ₁ to _{R 6} so as to satisfy ωaωo ² , the desired composite characteristics as described above can be obtained in the active filter circuit 4, The active filter circuit 4 is selected in this manner.

更にこの実施例においては、上記(1)式と(2)式の
分子における周波数Ｓの係数も等しくなるように
している。もつとも、当該分子間の関係は、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（即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良い。 Furthermore, in this embodiment, the coefficients of the frequency S in the numerators of the above equations (1) and (2) are also made equal. However, since the relationship between the molecules in question only involves shifting the desired synthetic property up or down in translation without changing its shape (i.e., changing the overall gain), it is not necessary to use both as in this example. It is not necessary to match the coefficients.

尚、上記係数等値の計算は、よく知られた数値
計算の手法により実行することができる。 Note that the calculation of the coefficient equality values can be performed using a well-known numerical calculation method.

〔考案の効果〕以上のようにこの考案によれば、２次バンドパ
ス特性と１次ローパス特性の合成特性が得られ、
２次バンドパス特性の高域側のロールオフを急峻
にすることができる。しかも演算増幅器が一つで
済むため、回路の小型化、低コスト化および省電
力化を図ることができる。[Effects of the invention] As described above, according to this invention, a composite characteristic of the second-order bandpass characteristic and the first-order low-pass characteristic can be obtained,
The roll-off on the high frequency side of the secondary bandpass characteristic can be made steeper. Moreover, since only one operational amplifier is required, it is possible to reduce the size, cost, and power consumption of the circuit.

[Brief explanation of the drawing]

第１図は、この考案の一実施例に係るアクテイ
ブフイルタ回路を示す回路図である。第２図は、
フイルタの諸特性の例を示す図である。第３図
は、１次ローパス特性を持つ従来のフイルタ回路
を示す回路図である。第４図は、２次バンドパス
特性を持つ従来のアクテイブフイルタ回路を示す
回路図である。第５図は、１次ローパス特性と２
次バンドパス特性の合成特性を持つ従来のアクテ
イブフイルタ回路を示す回路図である。４……実施例に係るアクテイブフイルタ回路、
４１……入力端、４２……出力端、５０……演算
増幅器、５１……第１入力部、５２……第２入力
部、５３……出力部、６１〜６３……コンデン
サ、７１〜７６……抵抗器。 FIG. 1 is a circuit diagram showing an active filter circuit according to an embodiment of this invention. Figure 2 shows
It is a figure showing an example of various characteristics of a filter. FIG. 3 is a circuit diagram showing a conventional filter circuit having first-order low-pass characteristics. FIG. 4 is a circuit diagram showing a conventional active filter circuit having second-order bandpass characteristics. Figure 5 shows the first-order low-pass characteristic and the second-order low-pass characteristic.
FIG. 2 is a circuit diagram showing a conventional active filter circuit having a composite characteristic of next-band pass characteristics. 4... Active filter circuit according to the embodiment,
41... Input end, 42... Output end, 50... Operational amplifier, 51... First input section, 52... Second input section, 53... Output section, 61-63... Capacitor, 71-76 ……Resistor.

Claims

[Scope of utility model registration claim] When the input voltage is Vi and the output voltage is Vo, the transfer function Vi/Vo is Vo/Vi=ωa・HBS/(S+ωa) (S ² +BS+ωo ² )=HBωaS/S ³ +(ωa+B)S ² +(ωo ² +Bωa)+ωaω
o ² However, H is the passband gain, B is the bandwidth, ωo is the center frequency, ωa is the cutoff frequency of the first-order low-pass filter, S is the frequency expressed by jω, and an active filter circuit that realizes the characteristics expressed as follows. Using an operational amplifier 50 having a first input section 51, a second input section 52, and an output section 53, the input terminal 41
A first resistor 71, a second resistor 72, and a third capacitor 63 connected in series in this order are connected between the first input section 51 of the operational amplifier 50, and
A first capacitor 61 is connected between the connection between the first resistor 71 and the second resistor 72 and the ground, and a first capacitor 61 is connected between the connection between the second resistor 72 and the third capacitor 63 and the ground. A third resistor 73 is connected, a second capacitor 62 is connected between the connection part and the output part 53 of the operational amplifier 50, and a second capacitor 62 is connected between the output part 53 of the operational amplifier 50 and the first input part 51 and the second input Part 52
A fourth resistor 74 and a sixth resistor 76 are respectively connected between the second input section 5 of the operational amplifier 50.
2 and ground, and the output section 53 of the operational amplifier 50 is connected to the output terminal 42, and the capacitance of the first to third capacitors 61 to 63 is set to C1 _, respectively. ~ _C3 , the resistance values of the first to sixth resistors 71 to 76 are respectively _R1 to _R6 , and the open loop gain of the operational amplifier 50 is
Ad, α=R ₅ /R ₆ β={α/(1+α)}-1/Ad, the transfer function Vo/Vi of the active filter circuit is expressed by the following equation, Vo/Vi=K ₁ S/S ³ +K ₂ S ² +K ₃ S+K _4However , K ₁ = -1/1-β・1/C ₁ C ₂ R ₁ R ₂ K ₂ = 1/C ₁ (1/R ₁ + 1/R ₂ )+1/C ₂ R ₄ +1/C ₃ R ₄ -β/1-β (1/R ₂ +1/R ₃ ) K ₃ = 1/C ₁ R ₄ (1/C ₂ +1/C ₃ ) (1 /R ₁ +1/R ₂ ) +1/C ₂ C ₃ R ₄ (1/R ₂ +1/R ₃ ) -1/1-β・1/C ₁ C ₂ (1/R ₁ R ₂ +1/R ₂ R ₃ +1
/R ₃ R ₁ ) K ₄ = 1/C ₁ C ₂ C ₃ R ₄ (1/R ₁ R ₂ + 1/R ₂ R ₃ + 1/R ₃ R ₁ ) and K ₂ = ωa + B, K ₃ = ωo ² +Bωa and
An active filter circuit characterized in that the capacitances C ₁ to C ₃ and the resistance values R ₁ to R ₆ are selected so as to satisfy K ₄ =ωaωo ² .