JPS6243605B2 - - Google Patents

Description

[Detailed description of the invention]

In the present invention, each terminal resonator is connected to an electromechanical converter that converts an electric vibration into a mechanical vibration or a mechanical vibration into an electric vibration, and the resonator vibrates longitudinally and has the same cross section over the entire length. The resonators are coupled via at least one coupler, the coupler is provided perpendicularly to the longitudinal axis of the resonator, and is coupled to the resonator at a coupling point, and the resonators are coupled in order to obtain predetermined filter passage characteristics. The present invention relates to an electromechanical filter having a plurality of torsion resonators arranged parallel to an axis and having various degrees of rotation. As is well known, electromechanical filters have become important in recent communications technology for the following reasons. In other words, electromechanical filters have a series of advantages over filters with lumped constant circuit elements in the appropriate frequency range, such as a large Q of each resonator, a small area required for the filter, and low temperature dependence. This is because it has. Various mechanical vibration modes can be used when constructing such a filter,
Among them, a combination of torsional vibration of a resonator and longitudinal vibration of a coupler is particularly performed. In this connection, the magazine “Archef der Electriquesien”
Übertlagung' (AEU¨), Volume 17, 1963
March 2013, pp. 103-107, the torsional resonators arranged parallel to each other's axes in such a filter are connected to each other via a coupler that vibrates longitudinally, and the distance between the coupling points of directly adjacent resonators is It is already known to set the wavelength to 1/4 of the wavelength generated in the coupler. When such a filter is designed using the so-called operating parameter theory, the degree of coupling between adjacent resonators must be set to various values in order to obtain a predetermined filter passage characteristic, such as a maximum flatness characteristic or a Tievisiev characteristic. This can be done by using connectors with different diameters in each section, or by making the masses of the resonators different when using connectors of the same size in each section (this can be done using the well-known filter method). (produced by providing vertical holes in several resonators). It may also be possible to couple adjacent resonators separately by means of additional couplings, as is known, for example, from DE 11 47 335 A1. However, such filter configurations require couplings with different diameters in each filter section in order to provide different degrees of coupling between each resonator and obtain a predetermined filter passage characteristic, for example a maximal flatness characteristic or a Tievisiev characteristic. or, if couplers of the same size are used, several resonators must be provided with holes with relatively precise tolerances, or if resonators with the same mass are used, This also requires additional manufacturing measures, since at least one additional connector must be provided for directly connecting adjacent connectors. Furthermore, the arithmetic symmetry of the blocking damping edges is not very good in filters with connectors of length λ/4. Also, based on the error sensitivity distribution, the influence of errors on the lower band edge cannot be ignored. Furthermore, sub-resonance in the stop band caused by torsional resonance of the coupler occurs intensively near the pass band, resulting in a sharp drop in the amount of attenuation. The basic object of the present invention is to provide various degrees of coupling between each resonator and to obtain the desired filter passage characteristics without the need for additional manufacturing measures such as those described above, and without the need for a blocking damping edge. Good arithmetic symmetry, negligible influence of errors on the lower band edge, and in addition, the sub-resonance in the stopband caused by the torsional resonance of the coupler is far away from the passband, resulting in a sharp drop in attenuation. It is an object of the present invention to provide a mechanical filter that does not cause According to the present invention, this problem is solved as follows. That is, all the intervals between the bonding points are set to be shorter than 1/4 of the wavelength λ generated in the connector between the bonding points, and the mutual magnitude relationship of the spacing between directly adjacent bonding points is such that all the spacings are equal. A magnitude relationship excluding cases where only one interval is different from the remaining intervals (hereinafter abbreviated as predetermined magnitude relationship)
, at least one of the spacings between directly adjacent coupling points is set equal to or less than 0.65 × λ/4, and the diameter of at least one resonator is set to be equal to or less than 0.65 × λ/4; The diameter of the resonator was made to be different from that of the resonator. In this way, not only can the above problems be solved, but the overall length can be significantly shortened. Incidentally, in a filter having a coupler having a length of λ/4, the length of each coupler is predefined as λ/4, so the minimum structural length is determined by the number of resonators and cannot be shortened. Due to the configuration of the present invention, unlike the case of a λ/4 length coupler, the coupler acts as an inductance between all resonators in the passband of the filter (ie at the operating frequency), as will be explained later. Furthermore, since the distance between the coupling points is shorter than in the conventional case (λ/4), a drop in the amount of attenuation can be caused at a position far away from the passband. With the configuration of the present invention, the coupling coefficient can be set variously by setting the distance between the coupling points variously. In the present invention, the desired pass characteristics of the filter and the desired allowable ripple of the attenuation curve in the pass band can be satisfactorily achieved by combining the distances between the coupling points. In other words, there is no need for the above-mentioned additional manufacturing technology measures in order to obtain various degrees of coupling between the resonators. In addition, in the present invention, the spacing between the coupling points is set to have a predetermined magnitude relationship, so that the resonance of the coupler and the drop in the attenuation are less likely to occur intensively as in the prior art. , it is also possible to always set the blocking attenuation level to a value greater than 40 dB. With the configuration of the present invention, it is possible to meet the requirement of 1/20 of the CCITT tolerance standard. Furthermore, the resonance of the coupler will occur at more distant frequency locations.
Thus, according to the invention, at least one spacing is at least 35% shorter than λ/4. In addition, in the present invention, as in the configuration, the intervals between directly adjacent connection points are divided into cases where all the intervals are equal and cases where only one interval is different from the remaining intervals (the remaining intervals are equal). Any size relationship among all size relationships except the case (for example, when there are n intervals, two intervals are equal but different from the remaining (n-2) intervals.
Alternatively, the two intervals are different and the remaining (n
-2) It is also different from the interval between the pieces. Or all the intervals are different. etc.) is set. That is, the predetermined magnitude relationship refers to all such magnitude relationships. With the configuration of the present invention, the filter length can be further shortened as described later. By setting various configurations and resonator diameters,
This is because a desired degree of coupling between the resonators can be achieved. Furthermore, by providing an additional coupler, the number of resonators can be reduced compared to a non-steepening filter. Moreover, the advantages of ~ are maintained. If the maximum spacing between the bonding points is reduced to 65% of λ/4 or less, the remaining spacing will necessarily be less than 65% of λ/4, and with known dimensioning (i.e. the bond length The total length of the filter can be further shortened compared to the case where λ/4 is selected. However, the filter must be configured so that its total length is as small as possible, and the minimum spacing (a1 in Figure 5) must be greater than the sum of the radii of both resonators to prevent contact between the two resonators. . Furthermore, the diameter of each resonator cannot be arbitrarily selected to be small. This is because this would result in undesirable disturbance-related vibrations in the filter. Fundamental Theory of Longitudinal Connectors C. Cruz, Report from VEB-RFT-Fernmeldewerk Leipzig, 1959
In 2013, Natsuhari Hitechtentechnik No. 11 describes the process of deriving the F matrix of an acoustic line. Based on this, the derivation of the F matrix of the acoustic line will be briefly explained below. In the above paper, for a mechanical longitudinal vibration line, ∂P/∂x=ρF∂V/∂t (K-3a) ∂V/∂x=α/F∂P/∂t (K-3b) The partial differential equation for is derived. However, P is force, V is velocity, ρ is the density of the material of the line, and α is 1/E (E is the elastic modulus). Further, F is the cross-sectional area of the track. Equations (K-3a) and (K-3b) are well-known equations from line transmission theory. ∂U/∂x=L'∂I/∂t (K-9a) ∂I/∂x=C'∂U/∂ t (K-9b). Of the two possible equivalent correspondences I〓P and U〓V (K-10) and U〓P and I〓V (K-11), the above paper uses the formula (K-11). ing. Note that 〓 indicates an equivalent relationship.
When using the formula (K-11), L′〓ρF (K-12) C′〓α/F (K-13), and therefore the characteristic impedance is Z=√′′〓F√ of the wave. The propagation speed is It is. By the way, λ=vo/f (K-14). Also, among the solutions of equations (K-9a) and (K-9b), when finding the solutions in the stable state after the transient phenomenon, It is. If you display this as a matrix It is. If we set 2πx/λ=b becomes. If formula (K-10) is used instead of formula (K-11), formula (K-12) and (K-13) are replaced by formula
We get (2) and (3). L′〓α/F (2) C′〓ρF (3) When formula (K-10) is used, the equivalent circuit becomes dual to the case when formula (K-11) is used. In other words, resistance becomes conductance. The characteristic impedance is It is. vo is the same as when using formula (K-11). If we follow international convention and denote the cross-sectional area by A (instead of F) and use the elastic modulus E=1/α in place of α, the characteristic impedance in equation (4) becomes Zk ^-1 = A(Eρ ) 〓 becomes. Next, substitute vo/f or 2πvo/ω in equation (K-14) into the matrix of (1), further substitute 1/√aρ or √E/ρ as vo, and replace x with length l. By using , we obtain the phase amount b b=ωl(ρ/E)〓. In this way, the F matrix of the connector get. However, A is the cross-sectional area of the connector, E is the elastic modulus, and ρ
When is the density, ZK=1/A(Eρ)〓. Also, when l is the length of the connector and ω is the angular frequency, b=ω
l(ρ/E)〓. Derivation of the F-matrix of a torsion oscillator The filter structure treated in the above paper is a cascade-connected line section in which each line section exchanges energy with an adjacent line section at both its starting and terminal ends. be. The vibration modes and vibration directions of all track sections are the same. For these reasons, the individual line sections act as a four-terminal network (in contrast, the mechanical filter of the invention consists of resonators and couplers with different vibration modes and vibration directions). Energy exchange occurs exclusively at the attachment point of the connector. Therefore, if a single continuous line coupler is provided in which the individual resonators are in contact at only one point, the resonators will act as a two-terminal network. If there is a coupler located symmetrically with respect to the vibration node of the resonator (for example, 9, 9' in Fig. 5 or the above-mentioned AEU - Fig. 1, 3
Based on the symmetry, the resonator follows the same principle and also works as a two-terminal network (Fig. 5). According to AEU¨ mentioned above, the F matrix of the resonator is It is. However, the relative detuning degree v of the frequency is v=2Δf/fo (B-3). This is a well-known approximation for small bandwidths (Δf<<fo). The exact formula is directly derived from the torsional vibration formula in the above-mentioned paper. Matrix 1 holds true not only for longitudinal waves but also for torsion. This is because it is only necessary to base the rotational motion equivalent relations instead of the translational motion equivalent relations (K-10) and (K-11). If M is a moment, r is an angular velocity, m is a mass, and Ip is a two-dimensional moment of inertia, then from page 491 of the above paper, ∂M/∂x=ρIp∂r/∂t ∂r/∂x=α/Ip2 (1+1/m) ∂M/∂t Looking at the analogy with the transmission line again, I〓M and U〓r (K-10). In the case of longitudinal vibration line, obtain L'=α/Ip・2(1+1/m) (5) C'= 〓Ip (6) in the same way as (2) and (3). From these, the characteristic impedance in the case of torsional vibration is become. Then, if we use elastic modulus E=1/α instead of α and Poisson number μ=1/m instead of m, we get Equation (8) is an equation often seen in literature. However, G
is the slip coefficient. The propagation speed vo is That is, the phase amount b is The resonator has a movable free end and therefore a moment O
It is a railway line. Resonance occurs when no moments are created at all ends (ie even at the beginning of the line).
When applied to matrix 1, this has the following meaning for the equivalent circuit; that is, when the resonator is unloaded on the output side (I ₂ = O) based on equation (K-10), its input Admittance Yo (where Yo is the rotational input admittance and Yt is the translational input admittance) It will be characterized by. The resonance condition is
Because Yo=O If the first natural resonance angular frequency (ν=1) is denoted by ωo, then Substituting equation (12) into equation (11), we get Yo=j/Ztanπω/ωo (13) For torsional resonators coupled in the tangential region (as is the case in Figure 5), the coupler is subject to forces P and A velocity V is transmitted to the resonator, and the force P and velocity V are converted into a moment M and an angular velocity r at the ends of the resonator. In this case, the lever arm is 1/2 (=D/2) of the resonator diameter. First, obtain the rotational motion input admittance Yo=M/r. Since M=pD/2 and r=V/D/2, Yo=PD/2/2V/D Therefore, Yo=P/V·D ² /4. P/V is the translational input admittance Yt. As a result, Yt=j4/ZD ² tanπω/ωo from Yo=Yt·D ² /4 equation (13). Furthermore, from equations (8) and (12) and the table in the above paper,

[Table] Yt=jD ² ρlωo/8tanπω/ωo=jmωo/
2πtanπω／ωo(14) However, m is the mass. Substituting r=ω/2π and f=fo+△ f, matrix element a ₂₁ of (B-2)
get. Yt=jωom/2πtanπ△f/fo Yt〓jωom/4・2△f/fo However, ∨〓2△f/fo, Z〓4/ωom A resonator connected to a coupler only at one end has a force/current According to the equivalence relation (K-10), since it works as a two-terminal network of parallel branch paths, the other matrix elements a ₁₁ , a ₂₂ , and a ₁₂ become a ₁₁ =a ₂₂ =1, and a ₁₂ =0.
The velocity on the left side of the connection point is equal to the velocity on the right side. On the other hand, the force of the incoming coupler is partially applied to the resonator and partially absorbed directly by the outgoing coupler. The approximation used in AEU¨ above is sufficient for the analysis of narrow filters with λ/4 length connectors. This is because the coupler is almost frequency independent. This essentially means bandpass filter/lowpass filter conversion. In the bandpass filter/lowpass filter conversion, the resonator is reduced to a parallel capacitance. In the case of more general couplers (e.g. short couplers) or wide bandwidths, the equivalent circuit of the resonator becomes a parallel circuit with the conductance YE YE=jCoω ² −ωo ² /ω. The equivalent capacitance Co is determined by matching the steepness dYE/dω of the electrical equivalent circuit to the steepness dYt/dω of the mechanical admittance during resonance. That is,

[Table] However, C ₀ 〓m/4 (15) In this way, the F matrix element is becomes. Therefore, the F matrix is becomes. Also, the F matrix of the electrical equivalent circuit is Equivalent circuit, 4-terminal matrix, and attenuation curve of a filter with a λ/4-length connector (note that a filter with a λ/4-length connector means one in which the spacing between the coupling points is all λ/4 length). , a filter with short connectors means one in which the spacing between the connecting points is all shorter than λ/4) The following will explain the above-mentioned AEU.
In the aforementioned AEU¨, the mechanical part of the filter is designed based on image parameter theory. By frequency conversion (or frequency approximation, which is the same thing after all), a low-pass filter is approximately constructed from a band-pass filter. Above mentioned AE
U¨ is limited to the design of the filter section from the first steel oscillator to the last steel oscillator. Therefore, it is almost impossible to completely understand numerically the filter described in AEU¨ above. In the above AEU¨, material values are not presented, and there is only a rough agreement between the design values and what is actually constructed, so the equivalent circuit is extremely inaccurate or cannot be overlooked. A configuration error has occurred. Especially this is the AEU mentioned above.
The minimum values of blocking attenuation in Figure 11 are 7.8Np, 7.6Np,
6.7Np, 7.7Np, the minimum values of the designed blocking attenuation shown as symmetrically distributed in Figure 8.
This becomes clear when comparing 7.2Np, 7.1Np, 7.1Np, and 7.2Np. Therefore, in terms of circuit type, center frequency, bandwidth, and blocking characteristics, we used a piezoelectric transducer, following the example of the AEU filter mentioned above, and based on the theory of operating parameters, including the operation of the piezoelectric transducer. An optimized filter design is proposed. It is assumed that the constituent elements of this filter include a resonator, a λ/4 length coupler, and a longitudinal drive vibrator. A matrix 17 is applied to the resonator. The inverter matrix of Equation (4) of the above-mentioned AEU is applied to the connector with good approximation. On the other hand, a simplified equivalent circuit is obtained for the converter as shown in FIG. 1a. As is well known, the dual force/current analogy is shown in Figure 1b.
A unit with an F matrix based on This is achieved by inserting an inverter between the static capacitance Co and the LC resonant circuit. In this case, C ₁ =L and L ₁ =C. The parallel circuit of C ₁ and L ₁ displays purely mechanical properties. When a longitudinal vibrator is used as a driving vibrator, C ₁ 〓m/2 (18). In this way, an equivalent circuit (FIG. 2) normalized by the signal source impedance and the terminal impedance is obtained. In FIG. 2, circuit parts indicated by 1 and 9 indicate drive vibrators, and 2 to 8 indicate torsional vibrators. Inverters I ₁₂ to _{I 89} represent λ/4 length connectors. Further, I ₂₅ and I ₅₈ are bridging connectors having a length of 3λ/4. C ₀ and C ₁₀ are the static capacitances of the transducer ceramic. The unit inverters I ₀ , I ₁₀ take into account the force-current analogy. To derive the 4-terminal matrix for the entire filter, the following individual matrices are required: Also, the matrix of λ/4 long combinators is as shown in −(A) below. However, in the case of a λ/4 long connector, Z _ij is 3/4λ as a positive value.
In the case of long combinators, Z _ij is assigned as a negative value. Note that in AEU¨ mentioned above, Berner assumes that all C _i and ω _i are values given a priori. Therefore, the matrix 21 has a more general shape. 2 under the bridging bond
The matrix of the two cascaded sections is obtained by multiplication of the individual matrices, as explained in the AEU section above. U = K ₂₃ * T ₃ * K ₃₄ * T ₄ * K ₄₅ and U = K ₅₆ * T ₆ * K ₆₇ * T ₇ * K ₇₈ Matrix U = However, u ₁₁ = C ₃ ω ² - ω ₃ ² / ω Z ₂₃ Z ₃₄ / Z ₄₅ U ₁₂ = N ₂₃ Z ₃₄ Z ₄₅ (C ₃ C ₄ (ω ² - ω ₃ ² ) (ω ² - ω ₄ ²⁾ )/ω ² −1/Z〓) u ₂₁ = −Z ₃₄ /Z ₂₃ Z ₄₅ u ₂₂ = C ₄ ω ² −ω ₄ ² /ω Z ₃₄ Z ₄₅ /Z ₂₃ U〓 is similar to this. The matrix of is obtained. Considering the parallel connection with the corresponding bridging connections, the following matrix is obtained. When V〓 = U〓 ‖K ₂₅ and V〓 = U〓 ‖K ₅₈ V〓 are clearly displayed in a matrix, However, V=1−Z ₂₃ Z ₄₅ /Z ₂₅ Z ₃₄ (1−C ₃ C ₄ Z ₃₄ ² (ω ² −ω ₃ ² ) (ω ² −ω ₄ ² )/ω ² ) v ₁₁ = u ₁₁ v ₁₂ = u ₁₂ v ₂₂ = u ₂₂ v ₂₁ = Z ₂₃ Z ₃₄ Z ₄₅ /Z〓(C ₃ C ₄ (ω ² −ω ₃ ² )(ω ² −ω ₄ ² )/ω ² )−1/Z 〓)+2/Z ₂₅ -Z
₃₄ /Z ₂₃ Z ₄₅ Substitute C ₃ = C ₄ ; ω ₃ = ω ₄ (because they are the same resonator) into the matrix 24, and further add v = ω ² - ω ₃ ² /ω (band pass filter/low pass filter conversion) and substitute C ₃ Z ₂₃ = K ₁₂ ^-1 , C ₃ Z ₃₄ = K ₂₃ ^-1 , C ₃ Z ₄₅ =
By substituting K ₃₄ ⁻¹ , C ₃ Z ₂₅ =−K ₁₄ ⁻¹ (normalization), equations (8) to (11) of the above AEU can be obtained. Thus, the matrix of the entire filter is A = W ₁ * K ₁₂ * T ₂ * V〓 * T ₅ * V〓 * T ₈ * K ₈₉ *
W ₉ (25) (the elements of this matrix have frequencies p=j
is a fractional rational function of ω), in general It becomes the shape of In addition It is. However, ω∞1 to ω∞4 indicate four attenuation poles formed by both bridging connectors. The values of the attenuation poles are obtained from the zeros of the denominators of the individual matrices V〓 and V〓. This is v of the matrix 24 in the case of V〓. A similar matrix exists in the individual matrix V〓. If Z ₂₅ >0, attenuation poles occur at complex frequencies. Coefficient g ⁽¹⁾ ₂ 〓, g ⁽²⁾ ₂
〓、U
⁽¹⁾ ₂ 〓, U ⁽²⁾ ₂ 〓 are linear combinations of the circuit elements of the filter. A computer is used for actual calculation. Mechanical filters are usually designed to have impedance symmetry (symmetrical matrix). In this case G ₁ = G ₂ and the characteristic function is That is, this filter has a fifth-order pole at the zero frequency position, a seventh-order pole at the infinite frequency position, and four poles at the finite frequency position. Like the AEU¨ filter mentioned above, the band edge is 196407
Hz, 199807Hz, minimum value of blocking attenuation is 62.5dB,
61.7dB, 61.7dB, 62.5dB, and if the reflection coefficient flattened by Tievisiev in the passband is 10%, the circuit constants of the circuit in Figure 2 are as follows normalized by the termination impedance and fN = 100kHz. get value

[Table] If these are converted into coupling coefficients using Equation (12) of AEU¨ mentioned above, it will be expressed as a percentage.

Obtain [table]. These values are listed above in parentheses.
It is of the same order of magnitude as the value for the AEU filter. The difference from the values for the AEU's filter shown in parentheses is that the AEU's filter design does not include the converter, and the design method relies on image parameter theory. On the other hand, the filter design method described here relies on operating parameter theory. However, since the driving oscillators, which were ignored in AEU¨ above, are indicated by 1 and 9, the index used here is the same as AE above.
1 larger than in the case of U¨. The corresponding decay curve is a _B =10log(1+|K(p)| ² ) from the characteristic function K(p), which is plotted in FIG. The length of the filter is 3λ, i.e. λ/4 (coupler length) x 8 + 2 x λ/
2 (drive vibrator). If thermo-elastomer is used as the material, the length is 70 mm. Embodiments of the present invention will be described in detail below with reference to the drawings. In FIG. 5, an electromechanical filter consisting of seven torsional resonators 1 to 7 is shown.
The torsional resonators are coupled to each other via connectors 9, 9'. In some cases only one coupling, for example coupling 9, can provide sufficient coupling between each torsional resonator, or if each coupling line is thin, two further couplings can be provided on the underside of the resonator. It is also possible to provide a completely symmetrical configuration. The coupler 9 is further led out from the termination resonator 1, 7 and connected to an electromechanical transducer 8, 8'. The transducers 8, 8' must be constructed in such a way that they can convert the electrical oscillations occurring therein into mechanical longitudinal oscillations, so that the coupling 9 undergoes longitudinal oscillations as indicated by arrow 19. Electromechanical transducers that meet these conditions are well known and can be constructed from, for example, a longitudinal resonator. This point will not be discussed in detail here as any suitable conversion element can be used. The only thing to be noted is that, for example, the electromechanical converter 8 converts electrical vibrations into mechanical longitudinal vibrations, which are converted back into electric vibrations in the electromechanical converter 8'. Each of the torsional resonators 1 to 7 is composed of a cylindrical body and arranged so that their longitudinal axes are parallel to each other. Each coupler 9, 9' is provided perpendicularly to the longitudinal axis of the resonator, and is firmly coupled to the resonator at respective coupling points 21-27 provided on the outer periphery of the resonator 1-7.
When the resonator and the coupling element are formed from metal materials, it is preferable to couple them together by welding. As is well known, in a torsional resonator, vibration nodes are formed along the central plane. That is, the resonator does not actually make any movement at this location. A support line 11 moored to the support plate 10 engages with this location. In particular, if such a support line is provided for each resonator 1 to 7, and if necessary a further support plate is provided below the filter, all resonators can be supported or suspended on both sides. It is preferable to use a filter case or a substrate as the support plate 10. It is best to keep the length of the support wire 11 as short as possible.
This allows the height of the filter to be only slightly larger than the diameter of the resonator. All that must be taken care of in this case is that the torsional resonators 1 to 7 are allowed to vibrate freely together with the coupling elements 9, 9'. When the resonator 1 is subjected to torsional vibration along the vibration direction indicated by the arrow 20 by the electromechanical transducer 8 formed as an input-side transducer, this torsional vibration causes a longitudinal vibration in the coupling elements 9, 9'. .
This longitudinal vibration similarly causes the resonators 2 to 7 to vibrate torsionally, and eventually the mechanical vibrations are converted back into electrical vibrations in the electromechanical transducer 8'. As is well known, the frequency positions of the passband of the electromechanical filter shown in FIG.
7, which is also essentially dependent on the length of each resonator. The filter passing characteristics including the bandwidth are related to the coupling strength between the resonators, and depending on the degree of coupling, arbitrary filter passing characteristics can be obtained, such as a maximum flat amplitude characteristic or a Tievishev-like damping characteristic. The coupling strength is defined on the one hand by the cross-sectional dimensions of the coupling elements 9, 9' and on the other hand by the distance b between the coupling elements 9, 9' and the vibration nodes. This is because as the distance b increases, the coupling element 9 reaches a relatively large range of vibration amplitudes, so that the coupling is increased. In addition to this method of predefining the dimensions to be constant, the bonding strength is also determined by the distance between adjacent bonding points. In FIG. 5, the distance between adjacent coupling points increases toward the center of the filter. That is, the distance a1 is set between the connecting points 21, 22 to 26, 27, the distance a2 is set between the connecting points 22, 23, 25, 26, and the connecting point 2.
The distance between 3 and 24 or between 24 and 25 is a, respectively.
It has 3. In the embodiment shown in FIG. 5, a3 is the maximum distance between adjacent resonators, and a2 and a1 are smaller than a3.
Further, a2 is larger than a1. In the present invention, at least a1 is 65% of λ/4 or shorter. As an embodiment of the present invention, not only a1 but also a2 can be made shorter than 65% of λ/4.
Furthermore, all of a1 to a3 can be made shorter than 65% of λ/4. However, it is clear from the operating parameter design theory that the minimum distance (interval a1) between two adjacent coupling points must be large enough to prevent the resonators 1 and 2 from coming into contact with each other when vibration occurs. In the present invention, the intervals a1 to a3 between all the resonators are smaller than λ/4. As mentioned above, grading the coupling strength, ie, selecting various coupling strengths of adjacent resonators, is always necessary in order to obtain predetermined filter characteristics, for example, in a filter calculated by operating parameter theory. In general, a filter characteristic with a maximal flatness characteristic or Thievishev characteristic, in which all maximum values have the same magnitude with respect to the attenuation or reflection coefficient, is particularly required. Equivalent circuit of the filter shown in Fig. 5 and 4
Terminal Matrix Here again, the explanation will be based on AEU¨ mentioned above. Fifth
The filter in the figure cannot be compared to that of the AEU¨ mentioned above. This is because the filter of AEU¨ mentioned above (see Fig. 2) is steepened by bridging connectors I ₂₅ and I ₅₈ , whereas the filter of Fig. 5 has no bridging connectors and therefore has a steep slope. This is because the attenuation rises monotonically.
Therefore, formulas (5) to (23) of AEU
It cannot be applied to the filter shown. In FIG. 6, the bridging coupler 13 connecting the resonators 3 and 7 is removed, and in addition to the bridging coupler 12 between the resonators 4 and 7, the resonators 1 and 4 are
If a bridging connector is provided between the two, the filter shown in FIG. 6 can be compared with the filter of the above AEU. However, the bridge connector 13 connecting the resonators 3 and 7 in FIG. 6 is removed, and in addition to the bridge connector 12 between the resonators 4 and 7, It is true that the filter in Figure 6 can be compared with the AEU filter mentioned above if a bridging connector is provided in is different. In fact, it can be said that the filter shown in FIG. 6 is different from the AEU filter mentioned above precisely because the above-mentioned modification has to be made. In order for the attenuation pole to occur at a finite frequency position, a phase reversal must exist. That is, both bridging connectors must be installed with the end faces of the resonator sloped, as in the case of bridging connector 12' shown in FIG. 7, for example. Therefore, first consider the filter in Figure 5,
Next, we will consider a filter that can be compared with the AEU filter mentioned above. (A) λ/4 coupler If the length of the coupler is selected so that the resonance of the coupler occurs at twice the operating frequency ωo, then or Therefore, from b=π/2 ω/ωo, the F matrix (1) takes the form of an inverter matrix or an ideal connector matrix for ω=ωo. The matrix component having a decisive meaning for the connection is jZksinπω/2ωo. (B) Short coupler If the operating frequency ωo is far below the resonant frequency corresponding to the length l, since b≪1, If this is developed into a symmetric π-shaped equivalent circuit, the series impedance is R=jZkb=jωl/AE, which exhibits the frequency characteristic of inductance (equivalent to the spring compliance l/AE). Furthermore, the two parallel admittances are as follows: G=jb/2Zk=jωm/2, and exhibit the frequency characteristic of capacitance (equivalent to 1/2 of the connector mass m=ρAl). In this way, characteristics different from those in the case of a λ/4 connector occur. The equivalent circuit of the filter in Figure 5 is L ₂₅ = L ₅₈ →∞
That is, if the bridging connector is removed, the result obtained from FIG. 3 is obtained. (19) to (21) apply to the F matrix of the drive vibrator and torsional vibrator. However, the matrix of short connectors is It is. The π-type equivalent circuit of a connector with a length shorter than λ/4 consists of two parallel capacitances Cij and one series inductance Lij, each of which is equivalent to 1/2 of the mass of the connector. Since the resonator is represented by a parallel circuit in the equivalent circuit of FIG. 3, the parallel capacitance Cij can be included in the parallel circuit capacitances Ci and Cj as shown in FIG. 4 without any loss of generality. From a physical point of view, this means adding the mass of the coupler to the effective resonator mass, i.e. considering the coupler as an inertial elastic body, yet the resonator is loaded by two halves of the mass of the coupler. It corresponds to seeing. The overall filter matrix is simpler since there are no bridging connections. A= W ₁ * K ₁₂ * T ₂ * K ₂₃ * T ₃ * K ₃₄ *...* K ₈₉ * W ₉ (29) Of the five polynomials in equation (26), only G=P is different. G ₁ , G ₂ , U ₁ , and U ₂ remain in the form of equation (26). Under the assumption of impedance symmetry G ₁ = G ₂ , the characteristic function is becomes. That is, a first-order pole exists at the zero frequency position, and a 19th-order pole exists at the infinite frequency position. Poles at finite frequencies do not exist as hypothesized. If the bandwidth and reflection coefficient are selected as described above, the optimized value, normalized by the terminating impeder, becomes: Co=C ₁₀ = 0.7966μF C ₁ …C ₉ = 25.7147μF f ₁ = f ₉ = 195236Hz f ₂ = f ₈ = 195845Hz L ₁₂ = L ₈₉ = 1.8963μH f ₃ = f ₇ = 196278Hz L ₂₃ = L ₇₈ = 2.6296μH f ₄ = f ₆ = 196359Hz L ₃₄ = L ₆₇ = 2.8170μH f ₅ = 196376Hz L ₄₅ = L ₅₆ = 2.8739μH Design example of non-steep filter Density ρ = 8g as the material for the resonator and coupler
If a cm ^-3 thermoelastomer is used, the propagation velocity of the longitudinal wave is vk 〓4.65×10 ⁵ cm/s. Furthermore, the propagation speed of the thought wave is vt = 2.85×10 ⁵ cm/s. This already defines the length of the resonator; the length of the torsional resonator is 0.726-0.728 cm. The length of the longitudinal drive oscillator is approximately 1.2 cm. The diameter of the drive oscillator can still be selected arbitrarily. To determine the remaining design values, we need electromechanical equivalent relationships for the resonator capacitance Ci and the coupler Lij. Equation (14) or (18) applies to the resonator. Also, the equivalence relationship for short vertical connectors is as described above. Longitudinal oscillator C _i 〓1/2mi Torsional oscillator Ci 〓1/4mi Short longitudinal coupler Lij〓lij/AijE (31) The equivalent inductance of the resonator is Li=1/ω _i ² C _i
According to the and resonance relational expression (12), and using the elastic coefficient E instead of the slip coefficient G for the longitudinal oscillator, it becomes as follows; Longitudinal oscillator Li〓2/π ² li/AiE (32) Torsional vibration Child Li〓4/π ²・li/AiG (33) Since equations (31) to (33) are equivalent relations and not equality, multiplying the right-hand side by an arbitrary constant q will also reduce these equivalent relations. naturally holds true. Since the constant q can be arbitrarily selected, these equivalence relational expressions can be rewritten into equations. Longitudinal oscillator Ci=1/q・mi/2 (34) Torsional oscillator Ci=1/q・mi/4 (35) Short longitudinal coupler Lij=q・lij/AijE (36) From this, q is It becomes clear that it is an electromechanical analogy coefficient. By the way, the unit of q is g/
Farad. Since at present only one electrically equivalent element corresponds in a fixed manner to one mechanical quantity, the coefficient q becomes an invariable value for all other electromechanical relationships of the filter. Assuming that the diameter of the first torsional resonator (resonator 2 in the equivalent circuit in Figure 3 or resonator 7 in Figure 5) is 0.3 cm, the mass is equal to the length of the torsional resonator.
Since it is 0.728 cm, m ₂ = 8・π/4・(0.3) ²・0.728=0.41 g. Since the ^equivalent circuit requires C ₂ = 25.71 μF (see the value _{shown at} the end of 37) Get. The mass of the driving oscillator is determined from (34), (37), and the numbers shown at the end of m ₁ = m ₉ = 2qC ₁ = 0.205g. As mentioned above, the length of the driving oscillator is determined to be l ₁ = 1.2 cm. Therefore, the cross section A ₁ =A ₉ =m ₁ /ρ·l ₁ =0.021 cm ² However, the shape of the cross section (circular, rectangular) can be arbitrarily selected. For the vertical connector, use equation (36) and E=vk ² ρ=1.73×
10 ¹² By g・cm ^-1・s ² lij/Aij=E/qLij=4.34×10 ⁸ Lijcm ^-1 (38
) holds true. If the thickness of the connector 9 is selected to be 0.019 cm, then Aij=π/4(0.019) ² =2.835×10 ⁻⁴ cm ² , and therefore lij=1.23×10 ⁵ Lij. As a result, the following lengths are obtained for each connected section. l ₁₂ = l ₈₉ = 0.233cm l ₂₃ = l ₇₈ = 0.324cm l ₃₄ = l ₆₇ = 0.347cm l ₄₅ = l ₅₆ = 0.354cm Thus, the total length of the filter including the drive vibrator is
It becomes 4.92cm. On the other hand, the total length of a filter with a connector of λ/4 length is 7 cm. This is because there is no degree of freedom in selecting the coupling length. Note that the lengths l ₂₃ to l ₄₅ correspond to the dimensions a ₁ to _{a 3} . Operational attenuation of filter design example The operational attenuation curve of the filter designed in this way is shown in FIG. Other design examples are easily derived, for example from (38). If the diameter of the connector is multiplied by the factor h, all the bond sections will be multiplied by the factor h ²
This is because there is no change in the properties of the connector. If the diameter of the vibrator is 0.3 cm, l ₁₂
≧0.15cm, and the remaining lij is lij≧0.3cm, and all
Just note that lij<λ/5=0.48cm (λ=2.4cm, so λ/4=0.6cm). Instead of one connector (for example connector 9) of 0.019 cm, a pair of connectors 9, 9' of 0.0134 cmφ can also be provided. It is also possible to multiply or reduce the diameters of all resonators and couplers by the same factor while remaining calculated as above. However, in this case, since l ₂₃ =0.324 cm, this is the upper limit value for the diameter of the torsion oscillator. All of the configuration examples described above exhibit attenuation characteristics as shown in FIG. In the filter of the invention, the arithmetic symmetry of the stop-attenuation edges is very good compared to filters with λ/4 length connectors. Note that arithmetic symmetry means that there is a relationship of ω ₀ =ω ₁ +ω ₂ /2 around the central angular frequency ω ₀ . Moreover, geometrical symmetry refers to the relationship ω ₀ ² =ω ₁ ·ω ₂ around the central angular frequency ω ₀ . Furthermore, the filter of the present invention obtains a stable lower band edge based on its error sensitivity distribution when the CCITT channel filter tolerance rules are to be satisfied. This is because, in the case of the present invention, the resonant frequency of the resonator is located near the lower band edge, so the influence of errors on the lower band edge is negligible. Furthermore, in the filter of the present invention, the width resonance in the stopband caused by the torsional resonance of the longitudinal coupler is located much further from the passband than in a filter with a λ/4 length coupler, and is dispersive. distribution, so it is easier to deal with. As described above, in a filter having a λ/4 length connector, its characteristic function has a fifth-order pole at the zero frequency position and a seventh-order pole at the infinite frequency position. Further, in the filter according to the embodiment of the present invention, the characteristic function has a first-order pole at the zero frequency position and a 19th-order pole at the infinite frequency position. That is, when a λ/4 long coupling element is used like a Berner filter, approximately the same number of poles are generated in the upper and lower stop zones. For example, if there are a total of 10 poles, 5 poles will occur in the upper stop zone and 5 poles will occur in the lower stop zone. On the other hand, when the spacing between the coupling points is shorter than λ/4 and inductive properties are exhibited as in the present invention, the number of poles is much larger in the upper stop zone than in the lower stop zone. As is clear from this, the rise in attenuation in the λ/4 long coupling filter is steeper in the lower stopband than in the filter of the present invention, and is slower in the upper stopband. Generally, in a λ/4 long coupler filter, all parallel resonances occur at the same frequency ω ₀ (center angular frequency). Therefore, frequency conversion (known as bandpass filter/lowpass filter conversion)
If you do However, ω _-c ·ω _c =ω ₀ ² , where ω _-c is the lower band edge and ω _c is the upper band edge. The characteristics of the λ/4 long coupler filter are arithmetically symmetrical around Ω=0. For the real frequency axis ω>0, Therefore, the characteristics are geometrically symmetrical about ω ₀ . The damping rise is therefore smaller in the upper stopband than in the lower stopband. However, many applications require arithmetically symmetrical rejection characteristics (particularly in the case of pulse filters, signal filters, etc.), and the filter of the present invention is suitable for these applications because of the basic tendency described above. This can be said to be extremely appropriate. As a carrier frequency channel filter, the filter of the present invention is also excellent in terms of the influence of errors (error sensitivity). In both the filter of the present invention and the λ/4 length coupler filter, a sufficiently precise adjustment of the resonant frequency is necessary and possible. Also, in both types of filters, there are manufacturing contingencies in the mechanical parts that are included in the connector. The influence of general errors in the λ/4 length connector filter is small. However, the influence is uniformly distributed in the frequency range below ω ₀ and above ω ₀ and is particularly greatest at the band edge. In contrast, the filter of the present invention is extremely stable at the lower band edge. On the other hand, at the upper band edge, a clear and larger influence appears than in the λ/4 long coupler filter. By the way, according to the CCITT standard, much stricter requirements are imposed on the error sensitivity characteristics at the lower band edge of the channel filter than at the upper band edge.
In addition to the important advantage of compact construction, the filter of the invention therefore has these advantages. The lower band edge is defined in the filter according to the invention primarily by a very precisely tuned resonator. In a Werner filter, on the other hand, the multiple poles of the lower stopband will influence the attenuation curve at the lower band edge. Since these poles are shifted to equal and exact lengths between the coupling points, i.e. exactly equal to λ/4, for example, slight manufacturing tolerances and variations have no significant effect on the attenuation curve at the lower band edge. This will have a negative effect on the situation. Next, the basis of the numerical limitation of 0.65/4λ will be explained. For the passband of carrier frequency channel filters, 1/20 of the CCITT tolerance standard is generally required. That is, aw0.11dB=0.0125Np Such an attenuation ripple corresponds to a reflection coefficient r≦15.7% based on Feltkeller's formula e ⁻² aw+|r| ² =1. As is clear from the example design of the present invention, in a non-steep filter with an electrical termination circuit and a flattened operating attenuation ripple aw according to the Tievisiev characteristic, the innermost mechanical coupling is It is the weakest and therefore has the largest distance between the bond points. The coupling between the drive oscillator and the first steel oscillator on the other hand is the strongest and therefore the shortest of all the coupling point spacings. According to the operating parameter theory, the ratio between the weakest coupling k _nio and the strongest coupling k _nax has the following relationship with respect to the reflection coefficient r;

[Table] To reduce k _nio /k _nax , k _nio should be small and k _nax should be large. for that purpose
It is necessary to increase lmax and decrease lmin. However, since lmax≦λ/4−Δ, there must be a maximum value of lmin when lmax=λ/4−Δ. By the way, when a mechanical filter is provided with a uniform coupling element, the length lik of the coupling between resonator i and resonator k is approximately sin2πlik/λ=1/Kik. However, λ is the wavelength at the center frequency of the filter, and Kik is the mechanical coupling coefficient. When scolded In the present invention, lmax<λ/4. Therefore, if we set lmax=λ/4 −△, sin2π/λlmin≦0.850×cos2π/λ△ sin2π(lmin/λ)≦0.850×cos2π/λ△ sin2π(lmin/λ)<0.850 When solving this, the following table between r and (lmin/λ) ( In particular, a value of lmin/λ=0.162) is obtained. In other words, according to the present invention, if a length slightly (△) shorter than λ/4 is associated with the weakest coupling, the following relationship between the shortest length lmin associated with λ and the reflection coefficient r can be obtained. .

[Table] Minimum length lmin/last displayed in the table above
λ is 35.2% shorter than λ/4. The value of the shortest length lmin/λ displayed last is the maximum value that can realize the strongest coupling of the 1/20-CCITT-channel filter. That is, if the minimum length is made longer than this, it is no longer possible to realize the strongest coupling of the 1/20-CCITT channel filter. In a λ/4 connector filter, the connector exhibits λ/2 characteristics at a frequency twice the band center frequency. Therefore λ/
4 The coupler itself becomes a resonator. Since all the couplers resonate at the same frequency, a deep drop in attenuation, reaching a level of less than 10 dB, occurs in the filter's rejection attenuation characteristics. Such a deep drop in attenuation always occurs at frequencies that are even multiples of the band center frequency. On the other hand, in the present invention, (1) the spacing between the coupling points is set to have a predetermined magnitude relationship, so that the resonance of the coupler occurs at frequency positions where the drop in attenuation amount is dispersed. The blocking attenuation level can also be greater than 40 dB. (2) By shortening the coupler, it is possible to cause a drop in attenuation at higher frequencies, and thus at locations farther from the passband. Incidentally, in an ideal connector with a length of zero, the amount of attenuation drops at infinite frequencies. In this way, the value of 35% prevents the concentrated occurrence of the parasitic coupler resonance as described above, generates the coupler resonance frequency at a frequency position far away from the passband, and still /20 CCITT - It can be seen that it has a meaning as a limit value to meet the request for operational attenuation. Differences between short couplers and λ/4 long couplers We will briefly discuss whether the characteristics of torsion oscillators really affect the limitations between short couplers and λ/4 couplers, and if so, to what extent. Derivation of the matrix of λ/4 long connector filters and the matrix of short connector filters, in particular the characteristic function 2 of each individual
7, 40, the difference between the two filters, that is, the difference in filter matrix or the difference in characteristic function, is due to the difference in the connector matrices 22, 28.
This is due to the difference in Incidentally, in a filter with a λ/4 length connector, the connector is a first-order approximation and is an inverter that is independent of frequency. On the other hand, short connectors exhibit the frequency characteristics of a series inductance. The fact that the difference between the two filters or their matrices or characteristic functions is related only to the difference in the couplers and does not depend on the characteristics of the resonator can be proven by the following simple example. can. That is, 2
When two identical resonators are coupled together (assuming that their frequency characteristics are G(ω)), in a λ/4 coupler filter, The short connector is In either case, the zeros of matrix element A ₂₁ give the coupler resonance. As is clear from (41), 1/Z−ZG ² (ω)=0 or G(ω)=±1/
Since Z, the coupler resonance is the oscillator resonance G(ω)=
Does not match 0. On the other hand, in the case of the short connector 42, G(ω)・(2−ωLG(ω)=0, so
The coupler resonance and the oscillator's natural resonance match. Since no assumptions were made regarding the frequency characteristic G(ω) of the resonator, the above differences are very common. In other words, the difference between the two bond formations (λ/4 long and short) is based entirely on the properties of the bond itself. Of course, in filter design, the characteristics of the resonator are included in the design formula.
For example, when two steel plates are connected to each other, they can be connected by screws or rivets, but in either case, the specific design values (i.e., thickness and length) of the connecting member are determined by the dimensions of the steel plates. However, this has no effect on the difference between a screw connection and a riveted connection. The difference in the characteristics of the connectors is stark between the short connectors and the λ/4 connectors as described above (especially equations (41) and (72)). The admittance characteristic of the torsional resonator (matrix 16) is determined by the frequency position of the bandwidth.
For filters with a small relative bandwidth (<3.4%) above 100 KHz, the electrical equivalent circuit is represented sufficiently accurately by a parallel circuit (Matrix 17). The resonant frequency of this parallel circuit corresponds to the resonant frequency of the oscillator and therefore depends only on the length of the oscillator in addition to the material constants according to equation (12). The capacitance corresponds to the mass of the resonator (formula (15)). That is, if the length of the vibrator is determined in advance, it corresponds to the cross-sectional area of the vibrator. In the general connector matrix 1, the matrix element a ₁₂ =jZsin2πx/λ is a factor that defines the connector. If we use equation (4) for x〓λ/4, we get become. By the way, for x≪1, a ₁₂ =jωx/AE (short connector). The characteristic admittance of a resonator thus includes the cross-sectional area in its molecule and the coupler reactance a ₁₂
includes the cross-sectional area in the denominator. Therefore, keeping all lengths of the filter, all cross-sectional areas (oscillator, coupler, transducer ceramic) can be reduced to (q+1).
When multiplied, all filter characteristics remain unchanged except the input admittance. The input admittance is thereby increased by a factor of (1+q). If the signal source impedance and load impedance are multiplied by 1/(q+1), the operating characteristics of the filter remain unchanged. In other words, the conclusion is that the filter characteristics are determined by the length, and the impedance level depends on the diameter. It can then be seen that for the present invention only the length of the connector is important. If it is a problem to generate so-called poles, ie complex poles or real poles, in the filter characteristics, it is possible to couple the resonators that are not directly adjacent to each other to each other by at least one additional coupler with longitudinal oscillation. be exposed. This is shown schematically in FIGS. 6 and 7, where the poles can be generated at real or complex frequencies or both. Whereas poles at real frequencies give rise to poles in the attenuation characteristic as is well known, poles at complex frequencies often similarly influence the predefined filter characteristics. FIG. 6 shows a plan view of a part of the filter including the resonators 3 to 7 of FIG. 5, and functionally the same parts are given the same reference numerals. In order to generate poles in the filter characteristic, resonators that are not directly adjacent to each other are coupled to each other by an additional coupler 12, i.e. in FIG. It is pulled out by the connector 12. It has been found that when designing a filter, the coupling between the trapped resonators must be relatively stiff in order to generate a pole in the damping characteristic; Resonators 5, 6
The distance a ₂ ' is the distance between resonators 4 and 7 directly adjacent to them.
The distance between a ₁ ′ and a 3 ′ is selected to be shorter than that between a 1 ′ and a ₃ ′. The connector 12 is in this case arranged parallel to the entire length of the connecting lines 9, 9'. Depending on the number of resonators taken in, the selection of the distance between the coupling points and the length of the additional coupling elements 12, the pole positions are formed at real or complex frequencies in the filter characteristic. Another method of providing at least one additional coupling connecting resonators that are not directly adjacent to each other is shown schematically in FIG. 7, which is a partial front view of resonators 4 to 7 in FIG. It is a diagram. In this case, the additional coupling element 12' is mounted on the front side of the resonators 5, 7, such that the fixing point is on a different side to the central plane 15 common to all resonators. The additional coupling element 12' likewise carries out mainly longitudinal oscillations. The strength of the additional coupling that defines the frequency position of the pole is determined by considering the center point M, excluding dimensions and material properties.
Adjusted by the distance of the fixed point from. In that case, in particular, the fixed point is set perpendicular to the common central plane 15 and at the center point M
It is preferable to make it lie on a line passing through . Depending on the number of resonators introduced, the selection of the distance between the coupling points and the length of the additional coupler 12', complex frequency or real frequency poles are produced in the filter characteristic. However, the correspondence is just the opposite of the correspondence in the case of Figure 6. 6 and 7, the generation of real frequency and complex frequency poles, i.e. the attenuation poles, and the adjustment of the delay characteristics are shown in FIGS. It can also be carried out by at least one other connector. Such a method is illustrated in FIG. 6, where resonators 3, 7 are coupled to coupler 1.
3 is additionally bridged. In FIGS. 6 and 7, additional connectors 12, 1
2', 13 themselves can carry any number of resonators, and additional bridging connections can also be provided between resonators 1 and 4, for example in the filter of FIG. . Generally, the diameters of the resonators are set to be the same size, but are set to be smaller than the minimum distance between adjacent coupling points. As a result, the filter has a relatively short overall length and is easy to manufacture. However, as shown in FIG. 8, when desired filter characteristics are to be obtained by adjusting the degree of coupling, it is also possible to make the diameter of at least one resonator different from the diameters of the other resonators. For example, by setting the diameter of each resonator to be different from the diameter of its adjacent resonator, a series of resonators can be provided with different degrees of coupling. This is because even if the couplers are the same and the distance between the coupling points is the same, a resonator with a smaller diameter has a smaller mass, which naturally affects the coupling strength. When welding the couplers 9, 9' and the resonators 1 to 7,
A precise welding point may not occur in the region where the coupler is tangent to the resonator. If such a weld point breaks, for example due to impact stress, the distance between the bond points and thus the degree of bond will change. To avoid this, each resonator is provided with a flat portion at least in the range of each coupling point, as shown in FIG. This results in a relatively good joint between each resonator and the coupler, and each resonator has two distinct weld points 24-27, 24'-24, respectively, as shown in FIG. 2
7', which are made to lie at the junction of the transition from the flat part to the circumference of the resonator. In addition to the precise bonding obtained in this way, the bonding distance can be further reduced. At the beginning of Steepening Filter, we explained how the filter must be constructed in order to be directly comparable to the AEU filter mentioned above.
An equivalent circuit of the filter constructed in this manner is shown in FIG. The matrix for the entire filter can be derived in the same way as for . Just use (28) instead of (22) as the connective matrix Kij. As a matrix element of the matrix 23, u ₁₁ = 1−L ₂₃ C ₃ (ω ² −ω ₃ ² )−(L ₂₃ +L ₃₄ )・C ₄ (ω ² −ω ₄ ² ) +L ₂₃ L ₃₄ C ₃ C ₄ ( ω ² −ω ₃ ² )(ω ² −ω ₄ ² ) u ₁₂ =ω{L ₂₃ +L ₃₄ +L ₄₅ −L ₂₃ (L ₃₄ +L ₄₅ )・C ₃ (ω ² −ω ₃ ² ) −L ₄₅ ( L ₂₃ +L ₃₄ )・C ₄ (ω ² −ω ₄ ² )+ L ₂₃ L ₃₄ L ₄₅ C ₃ C ₄ (ω ² −ω ₃ ² ) (ω ² −ω ₄ ² )} u ₂₁ = 1/ω {C ₃ (ω ² −ω ₃ ² )+C ₄ (ω ² −ω ₄ ² )−L ₃₄ C ₃ C ₄ (ω ² −ω ₃ ² )(ω ² −ω ₄ ² )} u ₂₂ =1− (L ₃₄ +L ₄₅ )・C ₃ (ω ² −ω ₃ ² )−L ₄₅ C ₄ (ω ² −ω ₄ ² ) +L ₃₄ L ₄₅ C ₃ C ₄ (ω ² −ω ₃ ² )(ω ² − ω ₄ ² ) However, it must be noted that in the bridging coupling, another phase inversion is inserted into the connector matrix 28. That is, The shape of Matrix K ₅₈ is also very similar to 39. The matrix elements of matrix 24 are v=ωL ₂₅ −u ₁₂ V ₁₁ = ωL ₂₅ u ₁₁ +u ₁₂ V ₁₂ = ωL ₂₅ u ₁₂ V ₂₁ = (ωL ₂₅ − u ₁₂ ) u ₂₁ − (1+u ₁₁ ) (1+ u ₂₂ ) V ₂₂ = ωL ₂₅ u ₂₂ + u ₁₂ . The attenuation pole is derived from the non-trivial zero at v=0. _{That is , V = ω _ _} ^_ _{_} ^_ _{_ _ _ _} ^_ _{_} ^_ ) −L ₂₃ L ₃₄ L ₄₅ C ₃ C ₄ (ω ² −ω ₃ ² )ω ² −ω ₄ ² )}=0 Compared with matrix 26, only the structure of polynomial G(P) is , so the characteristic function is becomes. From equation (40), it can be seen that the filter in the above example has a first-order pole at zero frequency, an eleventh-order pole at infinite frequency, and four poles at finite frequency. Therefore, compared to filter 27 of the above-mentioned AEU¨, the filter of the above example results in a steep rise in the attenuation curve in the upper stopband and a flat rise in the attenuation curve in the lower stopband. In particular, by optimizing the operating parameters according to the design criteria described under matrix 26,
The equivalent circuit normalized by the termination impedance is given as;

【table】

[Table] The mechanical design of this equivalent circuit is performed as described above. That is, the resonator length is determined by the propagation speed of the thermoelastomer. The choice of either resonator diameter defines the electromechanical analogy coefficient. The only difference to consider compared to the case already described is that the length of the bridging connector is equal to the length of the main connector li, i+1
This point is defined by the design value of . Incidentally, l ₁ =l ₉ 〓1.2 cm li = 0.727-0.730 cm, i = 2, 3-8 Note that the exact length of the drive vibrator depends on the piezoelectric ceramic used. However, this is not directly related to the present invention. If the diameter of the second resonator is chosen to be 0.25, then m ₂ =0.287g and the analogy coefficient is q = 2819g/F. If the mass of the drive vibrator is m ₁ =m ₉ =0.144 g, the cross section of the drive vibrator that can be formed into any shape is A ₁ =A ₉ =0.015 cm ² . As for the connector, it is lij/Aij6.13×10 ⁸ ×Lij. If the thickness of the connector is set to 0.016 cm, li, i+1 = 1.233×10 ⁵ ×Li, i+1 for the main connector. The result is as follows. l ₁₂ = l ₈₉ = 0.234cm l ₂₃ = 0.342cm l ₅₆ = 0.371cm l ₃₄ = 0.268cm l ₆₇ = 0.292cm l ₄₅ = 0.385cm l ₇₈ = 0.332cm The length of the longest connector l ₄₅ is also <λ /5. The length of the bridging connector is l ₂₅ = l ₂₃ + l ₃₄ + l ₄₅ = 0.995 cm l ₅₈ = l ₅₆ + l ₆₇ + l ₇₈ = 0.994 cm. The length of the bridging connector is λ/4<lij<λ/2. Its diameter must be determined based on line transmission theory. The matrix element defining the connection is jz·sin2πx/λ, as described above. Substitute l ₂₅ or l ₅₈ for x, and band center frequency fm = 198100 for λ
Substitute the wavelength in Hz. λ=vk/fm=4.65×10 ⁵ /198100=
Since 2.35cm Z=Aijρvk, we can use the analogy coefficient q to obtain 2πfmLij=q/Aijρvksin2πij/λ, so Aij=q/2πf _n ρv _k sin2πlij/λ/Lij=6.088×10 ¹⁰ sin2 .674×lij/Lij. That is, A ₂₅ = 3.33 × 10 ^-5 cm ² → φ ₂₅ = 6.51 × 10 ^-3 cm A ₅₈ = 2.17 × 10 ^-2 cm ² → φ ₅₈ = 5.26 × 10 ^-3 cm Figure 11 shows the operational attenuation of the filter. shows. The total length of this filter is 4.9 cm, which is significantly shorter than the total length of the corresponding λ/4 length connector filter. The lower the frequency (eg 100KHz), the more pronounced this advantage becomes. In the filter with a λ/4 length coupler, the design values of all lengths increase inversely proportional to the center frequency, while in the filter of the present invention, only the design value of the length of the drive oscillator increases inversely proportional to the center frequency. This is because it increases. Of course, in the filter of the present invention, the length of the torsional oscillator is also increased, but since the torsional oscillator extends transversely to the long axis of the filter, it is not related to the length of the filter. Another advantage of a short coupling filter is that it is necessary to steepen only on one side, i.e. to form an attenuation pole only on either the lower stopband or the upper stopband. Provides essential benefits. For short couplers, an attenuation pole occurs when an odd number of resonators are skipped (usually one resonator is skipped). The phase state of the bridging connector determines whether the pole occurs in the upper or lower blocking zone. This is not possible with a λ/4 coupler torsional resonator. This is because the bridging coupling has a length of λ/2 and thus becomes a resonator itself. This is also precisely reasoned in the AEU¨ mentioned above (Figures 1 and 2). Avoidance measures (which are technically more or less problematic in any case) are provided only for longitudinal wave filters in the type of filters treated in the above-mentioned paper in the AEU mentioned above, and they Not given to filters that have children. In the carrier system, the AEU filter described above requires an additional low-pass filter to cover the sharp drop in attenuation that occurs at a frequency twice the band center frequency. In the AEU¨ filter mentioned above, all the resonators vibrate in overtone, and at this frequency all the couplings have a length of λ/2 and the bridging couplings have a length of 3/2λ, so that all the coupling The child and the bridging coupler are resonators. As a result, the amount of attenuation drops by several decibels. On the other hand, the amount of attenuation is generally determined based on the request from the conveyance system.
Must be greater than 40dB. As mentioned above, although the total length of the filter according to the embodiment of the present invention can be made as small as possible by making the distance between each resonator as narrow as possible,
The desired filter characteristics can be adjusted. The additional coupler makes it possible to obtain poles of the filter characteristic if required, so that the number of resonators can be kept as low as possible. Furthermore, since each resonator is held individually, the required coupling between the resonators is
Even if, due to manufacturing tolerances, the support wire 11 does not exactly engage the vibration nodes and therefore contributes to some extent to the vibration phenomena of the resonator, there is no risk of it being nullified (the support device does not allow the resonator to be completely decoupled). ). The resulting deviations in the resonant frequency of the resonator can be easily adjusted in the resonator during tuning. Furthermore, because the support plate 10 has a greater mass than the support wire 11, vibrations that reach it are practically not transmitted, so that the initially adjusted connection is maintained.

[Brief explanation of the drawing]

Figures 1a and 1b are circuit diagrams for explaining the basic theory of longitudinal connectors, Figure 2 is an equivalent circuit diagram of a conventional mechanical filter, and Figure 3 is for explaining an embodiment of the present invention. Equivalent circuit diagram of mechanical filter, Figure 4 is equivalent circuit diagram of short connector, Figure 5~
FIG. 8 is a schematic diagram of a mechanical filter for explaining an embodiment of the present invention, FIG. 9 is a diagram of an operating attenuation curve of a conventional mechanical filter, and FIG. 10 is an operating attenuation curve of the mechanical filter of FIG. 5. FIG. 11 is a diagram of a steepened mechanical filter operating attenuation curve. 1-7... Torsional resonator, 8, 8'... Electromechanical transducer, 9, 9'... Coupler, 10... Support plate, 11...
Support line, 21-27... Connection point, 12, 12', 1
3...Additive connector.

Claims (1)

[Scope of Claims] 1. Each terminal resonator is connected to an electromechanical converter that converts electrical vibration into mechanical vibration or mechanical vibration into electrical vibration, and the resonator performs longitudinal vibration and has the same vibration over the entire length. The coupler is coupled via at least one coupler having a cross section, the coupler is provided perpendicularly to the longitudinal axis of the resonator, and is coupled to the resonator at a coupling point, and the resonator is coupled to the resonator to obtain predetermined filter passage characteristics. In electromechanical filters with various degrees of coupling between them, the entire distance between directly adjacent coupling points in the mechanical filter system existing between electromechanical transducers is equal to 1 of the wavelength λ generated in the coupling between the coupling points. /4, and make the mutual magnitude relationship of the intervals between directly adjacent bonding points into a magnitude relationship excluding cases where all the intervals are equal and cases where only one interval is different from the remaining intervals. and set at least one of the spacings between directly adjacent coupling points to be equal to or less than 0.65 x λ/4, and set the diameter of at least one resonator to be equal to or less than 0.65 x λ/4, and An electromechanical filter having a plurality of torsional resonators arranged parallel to an axis, the diameter of which is different from the diameter of the filter. 2. A plurality of resonators arranged parallel to the axis according to claim 1, characterized in that resonators that are not directly adjacent to each other are coupled to each other by at least one additional coupler 12, 12' that performs longitudinal vibration. Electromechanical filter with torsional resonators.