JP2540843B2 - All-pass filter circuit - Google Patents

Description

The present invention relates to a filter circuit for analog signals, and more particularly to a third-order filter circuit.

B. SUMMARY OF THE INVENTION The present invention is a third-order filter circuit for analog signals, which skillfully combines resistors and capacitors, has no mutual inductance structure, and has primary and secondary filter circuits cascaded. By making the circuit configuration basically different from the conventional third-order filter circuit to be connected, it is possible to easily manufacture, and it is possible to reduce the number of elements by eliminating the need for elements for connection. It is a thing.

C. Conventional Technique For example, in a video tape recorder, a phase shift circuit (phase shift filter) is used for reducing moire so that two outputs having different phases by 90 ° can be obtained within a predetermined frequency range. This 90 ° phase shift circuit generally uses a set of all-pass filters. The circuit configuration of the all-pass filter is, for example, as shown in FIG.
1 having mutual inductance structure with coils L _A and L _B
A third-order filter circuit is known in which a next-order filter circuit 101 and a second-order filter circuit 102, which also has a mutual inductance structure of coils L _C and L _D , are connected in cascade. Further, as shown in FIG. 8, a primary filter circuit 103 including a resistor and a capacitor and a secondary filter circuit 104 also including a resistor and a capacitor are connected in series via transistors Q ₁ and Q _2. Also known is a third-order filter circuit formed by

D. Problems to be Solved by the Invention However, the filter circuit shown in FIG. 7 has a mutual inductance structure and is therefore difficult to manufacture. Further, the filter circuit shown in FIG. 8 has a problem that extra elements such as the transistors Q ₁ and Q ₂ are required and the number of elements is increased.

Therefore, the present invention has been proposed in view of the above-mentioned problems, is easy to manufacture, does not require an extra element, and is used as an all-pass filter constituting a 90 ° phase shift circuit, for example. It is an object of the present invention to provide a suitable third-order filter circuit.

E. Means for Solving the Problems The present invention proposed for solving the above problems includes a pair of input terminals to which signals each having a phase difference of 180 ° are supplied, and a first capacitor. (C ₁ ) and first
Of the first resistor (R ₁ ) connected in parallel with the second resistor (R ₂ ) in series, the third resistor (R ₃ ) and the second capacitor (C ₂ ) Series connection of the third
Second impedance circuit in which the second capacitor (C ₃ ) is connected in parallel, and a _third impedance circuit in which the fourth capacitor (C ₄ ) and the fourth resistor (R ₄ ) are connected in parallel. And an output terminal, wherein one of the input terminals is connected to the output terminal via the first impedance circuit, and the other of the input terminals is connected via the second impedance circuit. When connected to the output terminal, the output terminal is grounded via a third impedance circuit, and the transfer function of the all-pass filter is Z (s), K, α, β, and γ are filter coefficients, and the relationship between the filter coefficient and the capacitors and resistors forming the impedance circuits is as follows.

K = R ₄ / (1 + R ₄ ) α = C ₁ · R ₁ + C ₂ · R ₃ −C _{2 −} C ₃ β = C ₁ · C ₂ · R ₁ · R _{3 −} C ₁ · C ₂ · R ₁ · According to _{R 2 -C 1 · C 3 ·} R 1 · R 2 -C 2 · C 3 · R 3 γ = C 1 · C 2 · C 3 R 1 · R 2 · R 3 F. action present invention, Since it has no mutual inductance structure, it is easy to manufacture. Further, the circuit configuration is basically different from that of the conventional third-order filter circuit in which the first-order and second-order filter circuits are connected in series, and an element for connection becomes unnecessary.

G. Example Hereinafter, one example of the present invention will be described in detail with reference to the drawings.

FIG. 1 is a circuit diagram showing an embodiment of the filter circuit according to the present invention. In FIG. 1, a pair of input terminals 10
Signals having different phases are supplied to A and 10B, respectively. The phase difference between them is 180 °, for example. The first impedance circuit 1 is composed of a capacitor C ₁ and a resistor R ₁ connected in parallel, and a resistor R ₂ connected in series. Also,
The second impedance circuit 2 has a resistor R ₃ and a capacitor C ₂
And the capacitor C ₃ are connected in parallel. The third impedance circuit 3 is composed of a capacitor C ₄ and a resistor R ₄ connected in parallel. The input terminal 10A is connected to the output terminal 20A via the impedance circuit 1, and the input terminal 10B is connected to the output terminal 20A via the impedance circuit 2. The output terminal 20A is grounded via the impedance circuit 3. The filter circuit 30 of this embodiment having such a structure is a third-order filter circuit.

By the way, it is assumed that signals whose phases are different from each other by 180 ° are supplied to the input terminals 10A and 10B. The input voltage at input terminal 10A is V _IN , the input voltage at input terminal 10B is −V _IN, and the output voltage at output terminal 20A is V _IN.
OUT , impedance of impedance circuits 1, 2 and 3
When V _OUT / V _IN is represented by Z ₁ , Z ₂ and Z ₃ , the following equation is obtained.

On the other hand, the transfer function Z (s) of the third-order all-pass filter
Is generally given by

Here, K, α, β, γ are constants, and s is a complex frequency. Then, in the equation (2), K = 1 / (1+
g) and the constants a, b, c, d, e, g and τ are set as follows.

The numerator and denominator of the above equation (4) can be modified as follows.

Molecular = (1 + bs) (1 + cs) - (1 + as) (ds + es 2) = 1 + (b + c-d) s + (bc-ad-e) s 2 -aes 3 ...
(5) the denominator = (1 + bs) (1 + cs) - (1 + as) (ds + es 2) + (1 + as) (1 + cs) g (1 + τs) = 1 + (b + c + d) s + (bc + ad + e) s 2 + aes 3 + g {1+ (a + c + τ) s + (Ac + aτ + cτ) s ² +
ac τs ³ } (6) From the expressions (3), (5) and (6), b + c−d = −α (7) bc−ad−e = β (8) ae = γ (9) ) B + c + d + g (a + c + τ) = α (1 + g) (10) bc + ad + e + g (ac + aτ + cτ) = β (1 + g)
(11) ae + gacτ = γ (1 + g) (12) From the above equations (9) and (12), e = cτ (13) and erase e. Equation (8) + (11) is 2bc + g (ac + aτ + cτ) = β (2 + g) (14), and Equation (8) + (13) is bc-ad-cτ = β (15). . Also, d is erased. Equation (7) + (10) is 2 (b + c) + g (a + c + τ) = αg (16), and Equation (15) -a × (7) is bc-a (b + c) -cτ = β + aα. … (17) Also, b is erased. Formula (14) above-2 x (1
7) is g (ac + aτ + cτ) + 2a (b + c) + 2cτ = βg-2aα (18) , and the above (16) and (18) from equation (g + 2) (cτ + aα) = g (β + a 2) ... (19) above From equations (16) and (14), (g + 2) (β + c ² ) = g (aτ + cα) (20) From equations (19) and (20) above, (cτ + aα) (aτ + cα) = (β + a ² ) (β + c) ² )
(21) From equation (12), acτ = γ (22) From equations (21) and (22), (γ + a ² α) (γ + c ² α) = ac (β + a ² ) (β + c ² ) ...
(23) This equation includes two unknowns, a and c, and a is obtained as follows. Substituting τ in equation (22) into equation (19) above, we obtain g Becomes The root of the denominator = 0 in the equation (24) has, for example, three positive real roots. In such a case, the equation (24) becomes as shown in the graph of FIG. As the value of a, the value of the point p between a ₁ and a ₂ where g is the smallest is found. If the numerator is set to 0 by differentiating the above equation (24) by a, αa ⁴ − (αβ-3γ) a ² + βγ = 0 (25) The value of a at the P point is Further, when g is calculated from the above equation (20) as a function of c, When this formula (27) is differentiated by c and the numerator is set to 0, αc ⁴ − (αβ + 3γ) c ² + βγ = 0 (28) The value of c at which the above formula (27) is positive and has a minimum value is The value of g when the above equation (26) is substituted into equation (24) is g _a
Then, the value of g when the above equation (29) is substituted into the equation (27) is g _c . Now, when g _c > g _a , there are two values of a between a ₁ and a ₂ as shown in FIG. ₂ , and at that time, the value of b obtained from the above equation (16) is also It becomes positive and there are two realization circuits. From the values of a, b, c, d, e, g and τ obtained in this way, the values of each element forming the impedance circuits 1, 2 and 3 are determined.

Here, by comparing the equations (1) and (4), the impedance circuits Z ₁ , Z ₂ , and Z ₃ are respectively expressed as follows.

In the equation (30), the first term corresponds to the resistor R ₂ , and the second term corresponds to the parallel connection of the capacitor C ₁ and the resistor R ₁ . In the above equation (31), the first term corresponds to the capacitor C ₃ , and the second term is the resistor R ₃ and the capacitor C ₂
It supports serial connection of. The above equation (32) corresponds to the parallel connection of the capacitor C ₄ and the resistor R ₄ . In FIG. 1, the numerical values or symbols shown in parentheses correspond to the values of each element.

In this way, the configuration of each impedance circuit 1, 2, 3 or the filter circuit 30 is determined. In order to set the output resistance R ₄ to a unit value, the resistance may be set to a value of g times and the capacitor may be set to a value of 1 / g times.

Since the filter circuit 30 as described above does not have a mutual inductance structure by coils, it is easy to manufacture. Further, since the configuration is different from the conventional configuration in which the primary filter circuit and the secondary filter circuit are connected in series, an element for connection is not required, and the number of elements can be reduced.

By the way, the filter circuits 30 can be symmetrically combined to form a phase shift circuit as shown in FIG. 3, for example. That is, in addition to the configuration of the filter circuit 30, the phase shift circuit includes resistors R ₅ , R ₆ , R ₇ , R ₈ and capacitors C ₅ ,
It has a configuration in which C ₆ , C ₇ , and C ₈ and an output terminal 20B are added. When signals having phases different from each other by 180 ° are supplied to the input terminals 10A and 10B, signals having phases different from each other by 90 ° are output from the output terminals 20A and 20B.

Here, with the transfer function as the third order, the values of the pole and the zero that minimize the maximum error when the phase difference between the two output signals becomes 90 ° were obtained. Table 1 shows the results.

The values of the constants α, β, γ and the values of a, b, c, d, e, g, τ are calculated from the values of these poles and zeros.
As shown in the parentheses in the figure, the value of each element is determined. In Fig. 3, output resistors R ₄ and R ₈ are 1KΩ each.
Of the two circuits that can be realized, the larger one of the minimum capacitors is shown. The frequency characteristics of the phase and the phase difference in this case are shown in FIG. In FIG. 4, A indicates the phase of the signal output from the output terminal 20A,
B indicates the phase of the signal output from the output terminal 20B, and C indicates the phase difference between them. The above phase difference is Chebyshev approximation, and it is 9 in the range of 0.5MHz to 18MHz.
It is 0 ° ± 0.59 ° (equal ripple), which shows that the condition for a 90 ° phase shift circuit is satisfied.

Further, FIG. 5 shows the frequency characteristics of the group delay time and the attenuation amount for the signal output from the output terminal 20A, and the frequency characteristics of the group delay time and the attenuation amount for the signal output from the output terminal 20B are shown in FIG. Shown in the figure. The fifth of these
In FIG. 6 and FIG. 6, A indicates the group delay time, and B indicates the attenuation amount. It can be seen that the above-mentioned attenuation amount can be regarded as constant and fluctuates only in the unit of 1/100 dB in the range of 0.5 MHz to 18 MHz in any case, and satisfies the condition as an all-pass filter. .

In this way, the phase shift circuit shown in FIG.
It can operate as a 90 ° phase shift circuit in the MHz range, and is suitable for use as a phase shift circuit for reducing moire in a video tape recorder. Also, because no coil is used,
Easy to be integrated circuit (IC).

H. Effects of the Invention As is apparent from the above description of the embodiments, the filter circuit of the present invention has a circuit configuration without a mutual inductance structure, and is therefore easy to manufacture. Further, since the circuit configuration is basically different from the conventional configuration in which the primary filter circuit and the secondary filter circuit are connected in series, an element for connection becomes unnecessary and the number of elements is reduced. be able to. Therefore, it is suitable for use as an all-pass filter that constitutes a 90 ° phase shift circuit, for example.

[Brief description of drawings]

FIG. 1 is a circuit diagram showing an embodiment of the filter circuit according to the present invention, FIG. 2 is a graph showing the relationship between a and g in the equation of the transfer function, and FIG. 3 is a symmetrical view of the filter circuit of the above embodiment. FIG. 4 is a circuit diagram showing a phase shift circuit configured in combination with FIG. 4, FIG. 4 is a diagram showing each phase of each output signal of the phase shift circuit and frequency characteristics of these phase differences, and FIG. FIG. 6 is a diagram showing the frequency characteristics of the group delay time and the attenuation amount for one output signal, and FIG. 6 is a diagram showing the frequency characteristics of the group delay time and the attenuation amount for the other output signal of the phase shift circuit. FIG. 7 is a circuit diagram showing a conventional example of a filter circuit, and FIG. 8 is a circuit diagram showing another conventional example of a filter circuit. 1,2,3 ...... Impedance circuit R ₁ , R ₂ , R ₃ , R ₄ ...... Resistance C ₁ , C ₂ , C ₃ , C ₄ ...... Capacitor 10A, 10B ...... Input terminal 20A ...... Output terminal 30 ...... Filter circuit

Claims (1)

(57) [Claims] 1. A pair of input terminals to which signals whose phases are different from each other by 180 ° are respectively supplied, a parallel connection of a _first capacitor (C ₁ ) and a first resistor (R ₁ ), and a second resistor ( R ₂₎ and the first impedance circuit which are connected in series is a series connection of a third resistor and (R ₃₎ a second capacitor (C _2), the third capacitor (C ₃₎ and parallel An all-pass filter circuit including a second impedance circuit connected to the third impedance circuit, a third impedance circuit including a _fourth capacitor (C ₄ ) and a fourth resistor (R ₄ ) connected in parallel, and an output terminal. Wherein one of the input terminals is connected to the output terminal via the first impedance circuit, and the other of the input terminals is connected to the output terminal via the second impedance circuit, The terminal is the third impedance Is grounded through a road, the transfer function of the all-pass filter when the Z (s), K, α, β, γ are filter coefficients, and an all-pass filter circuit characterized in that the relationship between the filter coefficient and the capacitors and resistors forming the impedance circuits is as follows. K = R ₄ / (1 + R ₄ ) α = C ₁ · R ₁ + C ₂ · R ₃ −C _{2 −} C ₃ β = C ₁ · C ₂ · R ₁ · R _{3 −} C ₁ · C ₂ · R ₁ · _{R 2 -C 1 · C 3 ·} R 1 · R 2 -C 2 · C 3 · R 3 γ = C 1 · C 2 · C 3 R 1 · R 2 · R 3