JPH0450655Y2 - - Google Patents

Description

[Detailed Description of the Invention] [Industrial Field of Application] This invention relates to an active filter circuit that can obtain a characteristic in which a first-order low-pass characteristic is added to a second-order band elimination characteristic.

[Conventional technology]

FIG. 2 is a diagram showing an example of a characteristic in which a first-order low-pass characteristic is added to a second-order band elimination characteristic. To obtain the above characteristics, conventionally, as shown in FIG. 3, a secondary circuit 22 and a primary circuit 21 having an operational amplifier 23 are designed separately.
Both circuits 21 and 22 are connected to an operational amplifier 2 for buffering.
This was realized by active filter circuits 2 connected in cascade via 4.

[Problem that the invention attempts to solve]

However, in the active filter circuit 2 as described above, in order to obtain the desired characteristics as described above, in addition to the operational amplifier 23, a buffer circuit is required to ensure the independence of both filter circuits 21 and 22. The operational amplifier 24 is always required, which hinders circuit miniaturization, cost reduction, and power reduction.

Therefore, the object of this invention is to provide an active filter circuit that uses a single operational amplifier and can realize the above-mentioned second-order band elimination characteristics plus a first-order low-pass characteristic. With the goal.

〔Example〕

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 the connection part and the second part of the operational amplifier 50.
A sixth resistor 76 is connected between the input parts 52, and the second
A third resistor 73 is connected between the connection between the resistor 72 and the third capacitor 63 and the ground, and a second capacitor 62 is connected between the connection and the output section 53 of the operational amplifier 50. A fourth resistor 74 and an eighth resistor 78 are connected between the output section 53 of the operational amplifier 50 and the first input section 51 and between the second input section 52, respectively, so that the first input section 51 of the operational amplifier 50
and a fifth resistor 75 and a seventh resistor 77 between the input section 52 and the ground, and between the second input section 52 and the ground, respectively.
and the output section 53 of the operational amplifier 50 is connected to the output terminal 42.

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 eighth resistors 71 to 78 are g1 to g1, respectively. g8, the transfer function of the active filter circuit
Vo/Vi is expressed by the following formula. Here, S is a frequency represented by jω.

Vo/Vi=AS ² +BS+C/DS ³ +ES ² +FS+G...(1) However, A=c2・c3・g1・g6 B=c2・g1・g4・g6+c2・g1・g5・g6+c3・
g1・g3・g6＋c3・g1・g4・g6＋c3・g1・
g5・g6−c3・g1・g2・g7−c3・g1・g2・g8 C=g1・g2・g4・g6+g1・g2・g5・g6+g1・
g3・g4・g6＋g1・g3・g5・g6 D=c1・c2・c3・g6+c1・c2・c3・g7 E=c1・c2・g4・g6+c1・c2・g4・g7+c1・
c3・g4・g6＋c1・c3・g4・g7＋c2・c3・
g1・g6＋c2・c3・g1・g7＋c2・c3・g2・g7
+c2・c3・g6・g7−c1・c2・g5・g8−c1・
c3・g2・g8−c1・c3・g3・g8−c1・c3・
g5・g8 F=c1・g3・g4・g6＋c1・g3・g4・g7＋c1・
g2・g4・g6＋c1・g2・g4・g7＋c2・g1・
g4・g6＋c2・g1・g4・g7＋c2・g2・g4・g7
＋c2・g4・g6・g7＋c3・g1・g4・g6＋c3・
g1・g4・g7＋c3・g2・g4・g7＋c3・g4・
g6・g7−c1・g2・g5・g8−c1・g3・g5・g8
−c2・g1・g5・g8−c2・g2・g5・g6−c2・
g2・g5・g8−c2・g5・g6・g8−c3・g1・
g2・g8−c3・g1・g3・g8−c3・g1・g5・g8
−c3・g2・g3・g8−c3・g2・g5・g8−c3・
g3・g6・g8−c3・g5・g6・g8 G=g1・g2・g4・g6＋g1・g2・g4・g7＋g1・
g3・g4・g6＋g1・g3・g4・g7＋g2・g3・
g4・g6＋g2・g3・g4・g7＋g2・g4・g6・g7
+g3・g4・g6・g7−g1・g2・g5・g8−g1・
g3・g5・g8−g2・g3・g5・g8−g2・g5・
g6・g8−g3・g5・g6・g8 Also, the above equation (1) can be rewritten as follows.

Vo/Vi=A/D・S ² +(B/A)S+
(C/A)/S ³ + (E/D) S ² + (F/D) S + (G/
D)...(2) On the other hand, the characteristic obtained by adding the first-order low-pass characteristic to the desired second-order band elimination characteristic as described above is expressed by the transfer function of the following equation.

Vo/Vi=H・S ² +1/S ³ +JS ² +KS+L…(3) However, H is the passband gain, I or L is a constant, and S
is the frequency expressed by jω.

Therefore, the coefficients and constants of the frequency S in the above equations (1) (or (2)) and (3) should be equal, that is, B=O, C/A=I, E/D=
By selecting the capacitances c1 to c3 and the resistance values g1 to g8 so as to satisfy J, F/D=K and G/D=L, the active filter circuit 4
The desired characteristics as mentioned above can be obtained,
The active filter circuit 4 is selected in this manner.

Furthermore, in this embodiment, the coefficients expressing the passband gain in the above equations (1) (or (2)) and (3) are made equal to each other, that is, A/D=H. . However, since the relationship between the coefficients is only related to vertically shifting the desired characteristic as described above without changing its shape (i.e., changing the gain overall), this is not necessarily the case in this example. It is not necessary to make both coefficients match.

Note that the calculation of the coefficient equality values can be performed using a well-known numerical calculation method, for example, by using a computer or the like.

[Effect of idea]

As described above, according to this invention, a characteristic in which a first-order low-pass characteristic is added to a second-order band elimination characteristic can be obtained. 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]

FIG. 1 is a circuit diagram showing an active filter circuit according to an embodiment of this invention. Figure 2 shows
FIG. 7 is a diagram showing an example of a characteristic in which a first-order low-pass characteristic is added to a second-order band elimination characteristic.
FIG. 3 is a circuit diagram showing a conventional active filter circuit that realizes the characteristics shown in FIG. 2. 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, 71-78 ……Resistor.

Claims (1)

[Claim for Utility Model Registration] When the input voltage is Vi and the output voltage is Vo, the transfer function Vi/Vo is Vo/Vi=H・S ² +I/S ³ +JS ² +KS+L where H is the passband gain , I to L are constants, S
is an active filter circuit that realizes a frequency represented by jω and a characteristic represented by
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 sixth resistor is connected between the connection and the second input section 52 of the operational amplifier 50. A third resistor 73 is connected between the connection between the second resistor 72 and the third capacitor 63 and the ground, and a second A fourth capacitor 62 is connected between the output section 53 of the operational amplifier 50 and the first input section 51 and between the second input section 52, respectively.
connect the resistor 74 and the eighth resistor 78,
A fifth resistor 75 and a seventh resistor 77 are connected between the first input section 51 of the operational amplifier 50 and the ground, and between the second input section 52 and the ground, respectively, and the output section 53 of the operational amplifier 50 is output. When the capacitances of the first to third capacitors 61 to 63 are c1 to c3, respectively, and the resistance values of the first to eighth resistors 71 to 78 are g1 to g8, respectively. , the transfer function of the active filter circuit
Vo/Vi is expressed by the following formula, Vo/Vi=AS ² +BS+C/DS ³ +ES ² +FS+G However, A=c2・c3・g1・g6 B=c2・g1・g4・g6+c2・g1・g5・g6+c3・
g1・g3・g6＋c3・g1・g4・g6＋c3・g1・
g5・g6−c3・g1・g2・g7−c3・g1・g2・g8 C=g1・g2・g4・g6+g1・g2・g5・g6+g1・
g3・g4・g6＋g1・g3・g5・g6 D=c1・c2・c3・g6+c1・c2・c3・g7 E=c1・c2・g4・g6+c1・c2・g4・g7+c1・
c3・g4・g6＋c1・c3・g4・g7＋c2・c3・
g1・g6＋c2・c3・g1・g7＋c2・c3・g2・g7
+c2・c3・g6・g7−c1・c2・g5・g8−c1・
c3・g2・g8−c1・c3・g3・g8−c1・c3・
g5・g8 F=c1・g3・g4・g6＋c1・g3・g4・g7＋c1・
g2・g4・g6＋c1・g2・g4・g7＋c2・g1・
g4・g6＋c2・g1・g4・g7＋c2・g2・g4・g7
＋c2・g4・g6・g7＋c3・g1・g4・g6＋c3・
g1・g4・g7＋c3・g2・g4・g7＋c3・g4・
g6・g7−c1・g2・g5・g8−c1・g3・g5・g8
−c2・g1・g5・g8−c2・g2・g5・g6−c2・
g2・g5・g8−c2・g5・g6・g8−c3・g1・
g2・g8−c3・g1・g3・g8−c3・g1・g5・g8
−c3・g2・g3・g8−c3・g2・g5・g8−c3・
g3・g6・g8−c3・g5・g6・g8 G=g1・g2・g4・g6＋g1・g2・g4・g7＋g1・
g3・g4・g6＋g1・g3・g4・g7＋g2・g3・
g4・g6＋g2・g3・g4・g7＋g2・g4・g6・g7
+g3・g4・g6・g7−g1・g2・g5・g8−g1・
g3・g5・g8−g2・g3・g5・g8−g2・g5・
g6・g8−g3・g5・g6・g8 And B=O, C/A=I, E/D=J,
An active filter circuit characterized in that the capacitances c1 to c3 and the resistance values g1 to g8 are selected so as to satisfy F/D=K and G/D=L.