JP3148458B2 - Active filter - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a BEF (Band E
More specifically, the present invention relates to an active filter that can increase the sharpness Q of the filter.

[0002]

2. Description of the Related Art A secondary BEF as shown in FIG. 2 is known. 2, the input signal V _in from the input terminal (1) is divided by the voltage dividing resistors (2) and (3), via a buffer (4), first differential amplifier of the current output type (5), a second capacitor (6), a resistor (7),
It is applied to the LPF (10) consisting of (8) and (9).

[0003] Also, the input signal V _in is applied to the output terminal A of the buffer (11) and the first through the condenser (12) current output of the second differential amplifier (13). The first capacitor (12) and the second differential amplifier (13) form an HPF (14) as viewed from the input terminal (1). LPF (1
Since the output of (0) is applied to the input of the HPF (14), the signal passing through the LPF (10) and the HPF (14) is obtained at the output terminal of the buffer (15). The output signal generated at the output terminal is fed back to the negative input terminals (-) of the first and second differential amplifiers (5) and (13) and the positive input terminal (-) of the second differential amplifier (13). +) Via the third capacitor (16) and comprehensively determines the Q of the BEF.

In FIG. 2, the resistance values of resistors (2) and (3) are R ₁ and R ₂ , (R ₂ / (R ₁ + R ₂ ) = K), resistors (7), (8) and The resistance value of (9) is R ₃ ,
R _X and R ₃ , (2R ₃ + R _X = a), resistance (1
7), (18) and (19) are represented by R ₄ , R _Y and R
₄ , (2R ₄ + R _Y = b), the conductances of the first and second differential amplifiers (5) and (13) are gm ₁ and gm
m ₂ , the first to third capacitors (12), (6), (1
Assuming that the capacitance value of 6) is C _{1 to} C ₃ and jw = S,

[0005]

(Equation 1)

[0006] From equation (1), the break point (cutoff) frequency W _O , the zero point (center) frequency W _N and Q
Is

[0007]

(Equation 2)

[0008]

(Equation 3)

[0009]

(Equation 4)

## EQU1 ## FIG. 3 shows the corner frequency W _O.
Shows the relationship between the zero-point frequency W _N. Therefore, it is clear that the circuit of FIG.

[0011]

However, a sufficient Q could not be obtained with the circuit of FIG. The third capacitor (16) was arranged to increase Q, but this was not sufficient.

[0012]

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned point, and an output current of a first differential amplifier to which an input signal from an input terminal is applied to one input terminal is supplied to a second input terminal. An LPF to be supplied to a capacitor, and a second output terminal to which an output signal of the LPF is applied to one input terminal and an input signal from the input terminal is applied to an output terminal of the first input terminal via a first capacitor.
An active filter including an HPF configured by the differential amplifier of the above, and a buffer that feeds back an output signal of the HPF to the other input terminal of the first and second differential amplifiers. A resistor connected between one input terminal of the second differential amplifier and the other input terminal; a third capacitor connected between one input terminal of the second differential amplifier and a reference potential point; And a fourth capacitor connected between the other input terminal of the differential amplifier and the reference potential point.

[0013]

According to the present invention, since the capacitors are provided at the two input terminals of the second differential amplifier functioning as the HPF, the Q of the BEF can be increased.

[0014]

FIG. 1 is a circuit diagram showing an embodiment of the present invention.
(20) is a fourth capacitor having a capacitance C connected between the connection point between the resistors (17) and (18) and the ground, and (21) is a connection between the resistors (18) and (19). The fifth capacitor having the capacitance C connected between the point and the ground.

In FIG. 1, the same circuit elements as those in FIG. 2 are denoted by the same reference numerals, and description thereof will be omitted. The voltage at terminal P in FIG. 1 is the output voltage of buffer (22) and the resistance (1
7) It is determined according to the voltage from the side. The voltage _Vout1 at the input terminal of the buffer (22) is the output voltage of the first differential amplifier (5) and the output voltage _Vout is the second and third capacitors (6).
And the voltage that is fed back via (16) is added and determined. Therefore, the voltage V _out1 is

[0016]

(Equation 5)

## EQU1 ## The resistors (17) and (1) in FIG.
8), resistor (19), fourth and fifth capacitors (20)
And (21) are extracted and shown in FIG. The circuit of FIG. 4 is shown in FIG. 5 by Δ-Y conversion. The impedances Z _{1 to} Z _{3 in} FIG.

[0018]

(Equation 6)

[0019]

(Equation 7)

## EQU2 ## The voltage V _out1 of the terminal P in FIG.
Is the current flowing through the terminal P and the terminal Q as i ₁ and i ₂ respectively.

[0021]

(Equation 8)

And the voltage V generated at the terminal Q
_out is

[0023]

(Equation 9)

## EQU1 ## Therefore, since equation (5) and equation (8) can be set equal,

[0025]

(Equation 10)

## EQU2 ## Further, the voltage V _{2 at} the terminal P _{1 in} FIG.

[0027]

[Equation 11]

Where the voltage V ₃ at the terminal Q ₁ is

[0029]

(Equation 12)

## EQU2 ## Therefore, when the left side of Expression (10) is set to X and Expression (10) and Expression (9) are added,

[0031]

(Equation 13)

## EQU1 ## Also, when equation (9) is subtracted from equation (10),

[0033]

[Equation 14]

## EQU1 ## From equation (13)

[0035]

(Equation 15)

## EQU1 ## Also, from equation (14)

[0037]

(Equation 16)

## EQU4 ## Therefore, Expression (15) and Expression (16)
And the current i ₁ becomes

[0039]

[Equation 17]

## EQU4 ## Similarly, when the equations (15) and (16) are subtracted, the current i ₂ becomes

[0041]

(Equation 18)

Is as follows. By substituting equation (17) into equations (11) and (12), the voltage V ₂ becomes

[0043]

[Equation 19]

[0044]

(Equation 20)

When subtracting equation (20) from equation (19),

[0046]

(Equation 21)

Is as follows. On the other hand, the output voltage V _out of FIG.

[0048]

(Equation 22)

Equation (21) is replaced by Equation (2)
Substituting into 2), the output voltage V _out becomes

[0050]

(Equation 23)

Is as follows. Therefore, rearranging equation (23), the transfer function (V _out / V _in ) is

[0052]

(Equation 24)

Is as follows. From the equation (24), it is clear that the active filter in FIG. 1 is a second-order BEF. From equation (24), the zero point frequency W _N , the break point frequencies W _O and Q of the BEF are

[0054]

(Equation 25)

[0055]

(Equation 26)

[0056]

[Equation 27]

Is as follows. Therefore, Z ₁ of the equation (6) is changed to the equation (2)
Substituting into 7), Q is

[0058]

[Equation 28]

Is as follows. Here, (Q / Q ′) is obtained by assuming that Q in equation (4) is Q ′.

[0060]

(Equation 29)

Is obtained. In the equation (29), b is larger than R _Y. However, in a region where the input signal frequency is high, the S term is sufficiently large, and (Q / Q ') is sufficiently larger than 1 as a whole. Therefore, according to the circuit of FIG. 1, a second-order BEF having a high Q can be configured. As is clear from the comparison of the equations (2), (3), (25) and (26), the values of W _O and W _N change, but by selecting the resistance value, in practice, It can be a change without problems.

FIG. 6 shows a specific example of the first and second differential amplifiers (5) and (13) of FIG.
If 2) is connected to the reference voltage point and an input signal is applied from the terminal (23), an LPF output is obtained at the terminal (24).
The terminal (23) is connected to the reference voltage point, and the terminal (22)
, An HPF output is obtained at the terminal (24).

[0063]

As described above, according to the present invention, a second-order BEF having a high Q can be obtained only by adding two capacitors.

[Brief description of the drawings]

FIG. 1 is a circuit diagram showing a BEF of the present invention.

FIG. 2 is a circuit diagram showing a conventional BEF.

FIG. 3 is a frequency characteristic diagram of the BEF of FIG. 1;

FIG. 4 is a circuit diagram for explaining FIG. 1;

FIG. 5 is a circuit diagram for explaining FIG. 1;

FIG. 6 is a specific circuit diagram of the differential amplifier of FIG. 1;

[Explanation of symbols]

 (5) First differential amplifier (10) LPF (12) First capacitor (13) Second differential amplifier (14) HPF (18) Resistance (20) Fourth capacitor (21) Fifth capacitor

Claims (2)

(57) [Claims] An LPF for supplying an output current of a first differential amplifier, to which an input signal from an input terminal is applied to one input terminal, to a second capacitor, and an output signal of the LPF being applied to one input terminal. An HPF constituted by a second differential amplifier which is applied and an input signal from the input terminal is applied to an output terminal of the HPF via a first capacitor; and outputs the output signal of the HPF to the first and second An active filter having a buffer for feeding back to the other input terminal of the differential amplifier, comprising: a resistor connected between one input terminal and the other input terminal of the second differential amplifier; A third capacitor connected between one input terminal of the differential amplifier and a reference potential point, and a fourth capacitor connected between the other input terminal of the second differential amplifier and a reference potential point And Active filter according to claim. 2. The active filter according to claim 1, further comprising a fifth capacitor between the buffer and one input terminal of the second differential amplifier.