JPH0114725B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention provides that each terminal resonator is connected to an electromechanical converter that converts electrical vibration into mechanical vibration or mechanical vibration into electrical vibration, and all torsional resonators perform longitudinal vibration. and directly adjacent torsional resonators that are connected to each other via coupling lines (coupler) configured as through lines with the same cross section over their entire length or that are present in individual filter subsections and are directly adjacent to each other are connected to each other in each section. are coupled to each other via associated section coupling lines (coupler) which carry out longitudinal oscillation and have the same cross section over their entire length, and the coupling lines or section coupling lines are arranged perpendicularly to the longitudinal axis of the resonator. The resonators are connected to each other at each coupling point, and the effective masses of the resonators are substantially equal, and the degrees of coupling between each resonator are selected in various ways in order to obtain predetermined filter passage characteristics. The present invention relates to a mechanical filter having a plurality of torsional resonators arranged in a mechanical filter. 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 is a well-known method). (In a filter, this is produced by providing vertical holes in several resonators)
achieved. In some cases, adjacent resonators may be
A separate connection with additional connectors is also possible, as is known, for example, from DE 11 47 335 A1. However, such a filter configuration has various diameters in each filter section in order to provide various degrees of coupling between each resonator and obtain a predetermined filter passage characteristic, for example, a maximum flatness characteristic is a Thievishev characteristic. If couplings are provided, or if couplings of the same size are used, several resonators must be provided with perforations with relatively precise tolerances, or if resonators with the same mass are used. Since at least one additional connector must be provided for directly connecting adjacent connectors, additional manufacturing measures are required. 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. The symmetry is good, the effect of errors on the lower band edge is negligible, and in addition, the subresonance in the stopband caused by the torsional resonance of the coupler is kept far from the passband, thereby eliminating the drawbacks of the prior art. The purpose of the present invention is to provide a mechanical filter that eliminates the According to the present invention, this problem is solved as follows. That is, the spacing between adjacent coupling points between each resonator gradually increases from both end resonators provided on both sides of the filter toward the center of the filter, and in this case, the spacing between the adjacent coupling points The maximum spacing is less than 1/4 of the wavelength λ in the driven state, and the minimum spacing is at least less than 1/4 of the wavelength λ in the driven state.
This is solved by setting it shorter by 35%. In the present invention, the spacing between adjacent coupling points between each resonator is gradually increased from both end resonators provided on both sides of the filter toward the center of the filter, that is, a symmetrical filter. For the first time, additional manufacturing technology measures such as those described above are not required in order to provide various degrees of coupling between each resonator and achieve a predetermined filter pass characteristic, that is, a good flat characteristic in the pass band of the filter. Moreover, the symmetry of the stop-attenuation edge is good, so that the influence of errors on the lower band edge can be ignored, and in addition, the sub-resonance in the stop band caused by the torsional resonance of the coupler is far away from the pass band. The remarkable effect of eliminating the drawbacks of the prior art can be achieved. In other words, in a non-steep mechanical filter, in order to achieve good flatness characteristics in the passband of the filter, the degree of coupling must be strongest at both ends of the filter, and the degree of coupling must be weakest at the center of the filter. This is achieved by the specific features specified in the claims of the invention, namely by the symmetrical filter specific to the invention. Thus, the introduction of symmetry provides significant advantages for any symmetrical arrangement of filters. In other words, in the case of a mechanical filter, exactly the same number of resonators and couplers is required, but the inherent symmetry also depends on the theoretical filter design, i.e. on the characteristic function of the filter. The specific symmetrical configuration of the electromechanical filter according to the invention therefore allows the above-mentioned special effects to be achieved. With the configuration of the present invention, not only the above problems can be solved, but also the overall length can be significantly shortened. By the way, in a filter with a coupler having a length of λ/4, the length of each coupler is predefined as λ/4, so the minimum configuration length is determined by the number of resonators.
It 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 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, since the spacing between the coupling points is different, the resonance of the coupler and therefore the drop in attenuation does not occur concentratedly as in the prior art. It is also possible to set it to a larger value. Due to the configuration of the present invention, the tolerance standard of CCITT is 1/20
can respond to the requests of Moreover, the resonance of the coupler will occur at more distant frequency locations. Also, in the present invention, the minimum spacing is set to be at least 35% shorter than λ/4. 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 connector length The total length of the filter can be further shortened compared to the case where λ/4 is selected. However, the filter should be configured so that its overall length is as small as possible, and the minimum spacing (see Figure 5a)
1) must be made larger than the sum of the radii of both resonators to prevent contact between the two resonators. Also,
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 Leipzig, 1959.
Natsuharichten Technique 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, δ _P / δ _x = ρFδ _V / δ _t (K-3a) δ _V / δ _x = α/F δ _P / δ _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. Formula (K-3a), (K-3b)
is compared with the equations δ _U /δ _x =L′δ _I /δ _t (K-9a) and δ _I /δ _x = C′δ _U /δ _t (K-9b), which are well known from line transmission theory. Of the two possible and equivalent correspondences I∧ = P and U∧ = V (K-10) and U∧ = P and I∧ = V (K-11), the above paper deals with (K-11). using the formula. 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 √ The wave 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 solution in the stable state after the transient phenomenon, U ₁ = U ₂ cos2π _x /λ+I ₂ Zj sin2π _x /λ I ₁ = U ₂ / Zj sin2π _x /λ+I ₂ cos2π _x /λ. If you display this as a matrix It is. If we set 2π _x /λ=b becomes. If formula (K-10) is used instead of formula (K-11), formula (K-12) and (K-13) can be replaced by formula
We obtain (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 ^1/2 . Next, add the formula (K-14) to the matrix of (1).
By substituting vo/f or 2π _vp /ω, further substituting [Formula] or [Formula] as vo, and using length l instead of x, the phase amount b b = ωl (ρ/E) ^1/ Get ² . 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(E〓) ^1/2 . Also, when l is the length of the connector and ω is the angular frequency, b=
ωl(ρ/E) ^1/2 . 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 of the frequency is =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 I _p is a two-dimensional moment of inertia, then from page 491 of the above paper, δ _M / δ _x = ρI _p δ _r / δ _t δ _r / δ _x = δ /I _p 2 (1+1/m) δ _M /δ _t Looking at the analogy with the transmission line again, I∧ = M and U∧ = r (K-10). In the case of a longitudinal vibration line, use the same procedure as (2) and (3) to obtain L'=α/I _p・2 (1+1/m) (5) C'=ρI _p (6). From these, the characteristic impedance in the case of torsional vibration is become. Then, if we use elastic coefficient 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 a slip coefficient. The propagation speed vo is That is, the phase amount b is The resonator has a movable free end and is therefore a line of moment O. If there is no moment at all ends (ie even at the beginning of the line), resonance will occur. Applied to matrix (1), this has the following implications for the equivalent circuit; i.e., the equation (K−
10), when the resonator is unloaded on the output side (I ₂ =O), its input admittance Yo (where Yo is the rotational input admittance and Yt is the translational input admittance). It is characterized by: The resonance condition is
Because Yo=O If we denote the first natural resonance frequency (ν=1) by ωo, then Substituting equation (12) into equation (11), Yo=j/Ztanπω/ωo (13) For torsional resonators that are coupled in the connection region (as is the case in the embodiment of Fig. 5), the coupler is A force P and velocity V are 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, Yo=Yt・D ² /4 From equation (13), Yt=j4/ZD ² tanπω/ωo. Furthermore, from equations (8), (12) and the table in the above paper, Yt=jD ² ρlω _p /8tanπω/ω _p = jmω _p /2πtanπω/ω _p (14) D ² ρlω _p =D ² ρπ √G/ρ... According to equation (12). =D ² π√ =D ² π/Z・I _p ... According to formula (8). =32/D ⁴ π・D ² π/Z=32/ZD ² ... According to the table above. However, m is the mass. Substituting f=ω/2π and f=f _p +△ f gives the matrix element of (B-2)
get a21. Yt＝jω _pn /2πtanπ△f/fo Ytjω _pn /4・2△f/fo However, ∧ =2△f/fo, Z∧ =4/ω _pnThe resonator connected to the coupler only at one end has a force -According to the current equivalence relationship (K-10), since it works as a two-terminal network of parallel branch paths, the other matrix elements a11, a22, a12 become a11=a22=1, a12=O. The velocities to the left of the connection point are equal. 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, j・C _p ω ² +ω ² _p /ω ² |〓 ₌ 〓 _p ∧ = j・m/2 (1+tan ² πω/ω _p ) |〓 ₌ 〓 _pHowever , C _p ∧ = m/4 (15) This In this way, the F matrix element becomes a ₁₁ =1 a ₁₂ =O a ₂₁ =j·ω _p ·m/2π·tanπ·Δf/f _p a ₂₂ =1. Therefore, the F matrix is becomes. Also, the F matrix of the electrical equivalent circuit is However, C _p ∧ = m/4 The equivalent circuit of a filter with a λ/4-length connector, a 4-terminal matrix, and an attenuation curve (note that in a filter with a λ/4-length connector, the spacing between the coupling points is all λ /4 length, and a filter with short connectors means one in which the spacing between the connecting points is all shorter than λ/4.) Below, the explanation will be based on the above-mentioned AEU.
In the AEU mentioned above, the mechanical part of the filter is designed using image parameter theory. Through the 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
AEU¨ 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-mentioned 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. In particular, this
AEU¨Minimum value of blocking attenuation in Fig. 11 7.8Np,
This becomes clear by comparing 7.6Np, 6.7Np, 7.7p with the design minimum values 7.2Np, 7.1Np, 7.1Np, 7.2Np, which are shown as symmetrically distributed in Figure 8. It is. Therefore, in terms of circuit type, center frequency, bandwidth, and blocking characteristics, this filter is not similar to the above-mentioned AEU¨. Using a piezoelectric transducer, we propose an optimized filter design based on operating parameter theory, including the operation of the piezoelectric transducer. It is assumed that the constituent elements of this filter include a resonator, a λ/4 length coupler, and a longitudinal drive vibrator. The matrix (17) is applied to the resonator. The inverter matrix of Equation (4) of AEU described above 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. The dual force/current analogy is, as is well known, the first
F matrix based on figure b A unit inverter with static capacitance Co
This is achieved by inserting it between the LC resonant circuit and the LC resonant circuit. In this case, C ₁ =L, L ₁ =C. C ₁ and
The parallel circuit of L ₁ displays purely mechanical properties.
When using a longitudinal vibrator 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. Co and C ₁₀ are the static capacitances of the transducer ceramic. The unit inverters I _p , 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. In addition, the matrix of λ/4 long combinators is However, in the case of a λ/4 length connector, Zij is assigned as a positive value, and in the case of a 3/4 length connector, Zij is assigned as a negative value. In AEU¨ mentioned above, Berner assumes that all Ci and ωi are values given a priori. Therefore matrix (21)
is becoming more common. The matrix of the two cascaded sections under the bridging connection is as shown above.
As explained in AEU¨, it is obtained by multiplication of individual matrices. 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 ² / ₃ / ω Z ₂₃ Z ₃₄ / Z ₄₅ u ₁₂ = Z ₂₃ Z ₃₄ Z ₄₅ (C ₃ C ₄ (ω ₂ − ^{ω 2} / ₃ ) / ω ² −1 A matrix similar to this can be obtained for /Z ² / ₃₄ u ₂₁ = −Z ₂₃ /Z ₂₃ Z ₄₅ u ₂₂ = C ₄ ω ₂ −ω ² / ₄ /ω Z ₃₄ Z ₄₅ /Z ₂₃ U〓 . Considering the parallel connection with the corresponding bridging coupling, the following matrix is obtained. When V〓 = U〓 ‖ K ₂₅ and V〓 = U〓 ‖ K ₅₈ V〓 are expressed in a matrix, However, v=1−Z ₂₃ Z ₄₅ /Z ₂₅ Z ₃₄ (1−C ₃ C ₄ Z ² ₃₄ (ω ² −ω ² / ₃ ) (ω ² −ω ² / ₄ )/
ω ² v ₁₁ = u ₁₁ v ₁₂ = u 12 v 22 = u _{22 v 21} = Z ₂₃ Z _{34 Z 45 /} Z ² / ₂₅ (C ₃ C ₄ (ω ² −ω ² / ₃ ) (ω ² − ω ^2/4 ) _/ ^ω2-1
/Z ² / ₃₄ ) +2 / Z ₂₅ −Z ₃₄ /Z ₃₃ Substitute C ₃ = C ₄ , ω ₃ = ω ₄ (because they are the same resonator) into the Z ₄₅ matrix (24), and further calculate V = ω ₂ − Substituting ω ² / ₃ ) / ω (band pass filter/low pass filter conversion), C ₃ Z ₂₃ = K ^-1 ₁₂ , C ₃ Z ₃₄ = K ^-1 ₂₃ , C ₃ Z ₄₅ = K ^{- 1} ₃₄ , C ₃ ,
By substituting Z ₂₅ =−K ⁻¹ ₁₄ (normalization), equations (8) to (11) of AEU¨ above are 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 are the frequencies P=jω
), in general It becomes the shape of In addition It is. However, ω _∞ 1 to ω _∞ 4 indicate four attenuation poles formed by both bridge connectors. The values of the attenuation poles are obtained from the zeros of the individual matrices V〓 and the denominator of V〓 . In the case of V〓, this is the v of matrix (24)
It is. A similar matrix exists in the individual matrix V〓 . If Z ₂₅ >O, attenuation poles occur at complex frequencies. Coefficient g2ν ⁽¹⁾ , g2ν ⁽²⁾ , U2ν ⁽¹⁾
，
U2ν ⁽²⁾ is the linear combination of the filter's circuit elements. A computer is used for actual calculation. Mechanical filters are usually designed with source 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, the following [Table] is obtained as a percentage. 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 numerical values for the AEU¨ filter listed above in parentheses is that in the AEU¨ listed above, the converter is not included when designing the filter, 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 drive vibration operation, which was ignored in AEU¨ above, is indicated by 1 and 9, the index used here is the same as AEU¨ above.
1 larger than in the case of . The corresponding decay curve is aB=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 the embodiment of FIG. 5, there are seven torsional resonators 1 to 7.
An electromechanical filter is shown, each torsional resonator being coupled to one another via a coupler 9, 9'. In some cases, only one coupling, for example coupling 9, is sufficient to provide a sufficient coupling between each torsional resonator, or if each coupling line is thin, two further couplings are provided below the resonators. 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'. converter 8,
8' must be constructed in such a way that the electrical vibrations occurring therein can be converted into mechanical longitudinal vibrations, so that the connector 9 undergoes longitudinal vibrations as indicated by arrow 19. Electromechanical transducers that meet these conditions are 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. In this case, care must be taken to ensure that the torsional resonators 1 to 7 can vibrate freely together with the couplers 9, 9'. In this embodiment, when the resonator 1 is made torsionally vibrate along the vibration direction indicated by the arrow 20 by the electromechanical transducer 8 formed as an input side transducer, this torsional vibration is caused vertically in the couplers 9, 9'. Causes vibration. 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 position of the passband of the electromechanical filter of FIG. It depends on the 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. On the one hand, the coupling strength is
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 dimensions to be constant, the bonding strength is also defined by the distance between adjacent bonding points. In the embodiment shown 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 and 22 to 26 and 27, the distance a2 is set between the connecting points 22 and 23 and 25 and 26, and the distance a2 is set between the connecting points 23 and 24 and 24 and 25.
There is a distance a3 between each. 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 shorter than 65% of λ/4. 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, in terms of operating parameter design theory, it is clear that the minimum distance between two adjacent coupling points (distance a1 in the example) must be large enough to prevent resonators 1 and 2 from coming into contact with each other when vibration occurs. It is. 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. Particularly required is a filter characteristic with a maximum flatness characteristic or a Tievisiev characteristic, in which all maxima generally have the same magnitude with respect to the attenuation or reflection coefficient. Equivalent circuit and 4-terminal matrix of the filter of the embodiment shown in FIG. Fifth
The filter of the illustrated embodiment cannot be compared with that of the AEU described 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 the embodiment shown in Fig. 5 does not have bridging connectors. This is because the attenuation rises monotonically. Therefore, formulas (5) to (23) of AEU¨ above
cannot be directly applied to the filter in Figure 5. Therefore, first we will consider the filter of the embodiment shown in FIG. 5, and then we will discuss embodiments of the filter that can be compared with the filter of the above-mentioned AEU. (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 ω _p , then or Therefore, from b=π/2 ω/ω _p , the F matrix (1) takes the form of an inverter matrix or an ideal connector matrix for ω=ω _p . The matrix component that has a decisive meaning for the connection is jZk sinπω/2ω _p . (B) Short coupler If the operating frequency ω _p is far below the resonant frequency corresponding to the length l, then b << 1, so sin bb cos b1−b ₂ /2 This can be converted into a symmetric π-shaped equivalent circuit. When expanded, the arrayed impedance is R=jZkb=jωl/AE, and exhibits the frequency characteristic of impedance (equivalent to the spring compliance l/AE). Moreover, the two parallel admittances are G=jb/2Zk=jω _n /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 the mass of the connector. Since the resonator is represented by a parallel circuit in the equivalent circuit of Fig. 3, without any loss of generality, the parallel capacitance Cij can be expressed as the parallel circuit capacitance Ci, Cj as shown in Fig. 4.
can be included in 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 looking at it. 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) Among 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 termination impedance, becomes: [Table] Design example of a non-steep filter according to the present invention If thermoelastomer with a density of ρ8 g cm _-3 is used as the material for the resonator and coupler, the propagation velocity of longitudinal waves can be reduced.
vk4.65×10 ⁵ cm/s. Further, the propagation speed of the torsion wave is vt2.85×10 ⁵ cm/s. This already defines the length of the resonator; the length of the torsional resonator is 0.726-0.728 cm. The vertical drive vibrator is approximately 1.2
The length is cm. The diameter of the drive oscillator can still be chosen 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 Ci∧ = 1/2mi Torsional oscillator Ci∧ = 1/4mi Short longitudinal coupler Lij∧ =lij/AijE (31) The equivalent inductance of the resonator is Li=1/ωi ² Ci and the resonance relational expression According to (12), and using the elastic coefficient E instead of the slip coefficient G for the longitudinal oscillator, we have the following; Longitudinal oscillator Li∧ = 2/π ²・li/AiE (32) Torsional oscillator Li ∧ = 4/π ²・li/AiG (33) Equations (31) to (33) are equivalent relations, not equality, so even if you multiply the right-hand side by an arbitrary constant q, these equivalent relations become Naturally it will be established. 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. Incidentally, 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 0.728cm, m ₂ =8.π/4・(0.3) ² 0.728=0.41g. Since the ^equivalent circuit requires C ₂ = 25.71 μF (see the value _{shown at} the end of 37). 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. The length of the driving oscillator as described above is determined to be l ₁ = 1.2 cm. Therefore, the cross section A ₁ =A ₉ =m ₁ /ρ・l ₁ =0.021cm ² However, the shape of the cross section (circular, rectangular) can be arbitrarily selected. Equation (36) and E=vk ² ρ=1.73×10 ¹² are used for the vertical connector.
By g・cm ⁻¹・s ² lij/Aij=E/qLij=4.34×10 ⁸ Lijcm ⁻¹ (38) holds. If the thickness of the connector 9 is selected to be 0.019 cm, then Aij=λ/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. In addition, length L ₂₃ ~ _{L 45}
corresponds to dimensions a ₁ to a ₃ . Operational attenuation of the filter design example according to the present invention The operational attenuation curve of the filter thus designed is shown in FIG. Other design examples are easily derived, for example from (38). This is because if the diameter of the connector is multiplied by the coefficient h, all the connected sections are multiplied by the coefficient ^h2 , and the characteristics of the connector remain unchanged. If the diameter of the vibrator is 0.3cm, l ₁₂ ≧
0.15cm, the remaining lij are lij≧0.3cm, and all lij<
Just note that λ/5=0.48cm (λ=2.4cm, so λ/4=0.6cm). Instead of one connector (for example connector 9) with a diameter of 0.019 cm, a pair of connectors 9, 9' with a diameter of 0.013 cm 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 with the central angular frequency ω ₀ as the center. Also, geometric symmetry is
It means that there is a relationship of ω ² ₀ ] = ω ₁ · ω ₂ with the central angular frequency ω ₀ as the center. 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. In addition, in the filter of the present invention, the sub-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)
Then, Ω=ω−ω ² /〓 _/0 /ω _c −ω ² / ₀ /ω _c =ω− ² / ₆ /
ω/B where ω _−c ·ω _c =ω ² ₀ , 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 symmetric around 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, sufficiently accurate tuning of the resonant frequency is necessary and possible. In both types of filters, the connectors also include manufacturing contingencies of mechanical parts.
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. However, according to the CCITT standard, much stricter requirements are imposed on the error sensitivity characteristics at the lower band edge of a channel filter than at the upper band edge. In addition to these advantages, such advantages can also be recognized. 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 depend on equal and precise lengths between the coupling points, e.g. exactly equal to λ/4, slight manufacturing tolerances and variations will not have a significant effect on the attenuation curve at the lower band edge. This will have a negative effect on the situation. Next, the basis for limiting the value to 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, a _W 0.11dB=0.0125Np Such an attenuation ripple corresponds to the reflection relationship r≦15.7% based on Feltkeller's formula e ^2aW +|r| ² =1. As is clear from the design example of the present invention, in a non-steep filter with an electrical termination circuit and a flattened operational attenuation ripple a _W according to the Tievisiev characteristic, the innermost mechanical coupling 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 coupling point spacings. According to the operating parameter theory, the weakest coupling
The ratio between kmin and the strongest coupling kmax is the reflection coefficient r
The relationship is as follows; [Table] To reduce kmin/kmax, kmin should be small and kmax should be large. To achieve this, 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, if a uniform coupling element is provided in which the effective masses of all the resonators of a mechanical filter are at least substantially equal to each other, the length lik of the coupler between resonators i and k is approximately Then 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 kmin/kmax=sin2π lmin/λ/sin2π lmin/λ≦
0.850 In the present invention, lmax<λ/4. Therefore, if we set lmax = λ/4-△, sin2π/λlmin/sin2π/λ (λ/4-△)≦0.850 sin2π/λlmin/sin (π/2-2π/λ△)≦0.850 sin2λ/λlmin≦ 0.850×cos2π/λ△ sin2π(lmin/λ)≦0.850×cos2π/λ△ sin2π(lmin/λ)<0.850 When solving this, the table below (especially lmin/λ) between r and (lmin/λ) = 0.162). In other words, according to the present invention, if a length slightly (△) shorter than λ/4 is associated with the weakest bond, the shortest length associated with λ
The following relationship between lmin and reflection coefficient r is obtained. [Table] Minimum length displayed last in the table above
lmin/λ is 55.2% shorter than λ/4. The value of the shortest length lmin/λ displayed last is the maximum value that can realize the strongest combination of 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, the λ/4 coupler itself becomes a resonator. And since all the connectors resonate at the same frequency,
A deep drop in attenuation occurs in the filter's rejection characteristic, reaching a level of less than 10 dB.
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) Since the spacing between the coupling points is different, the resonance of the coupler and therefore the drop in the attenuation amount occurs at dispersed frequency positions. For example, set the blocking attenuation level to 40dB.
It can also be set to a larger value. (2) By shortening the coupler, a drop in attenuation can be caused at higher frequencies, and therefore farther from the passband. Incidentally, in an ideal connector with a length of zero, the amount of attenuation drops at an infinite frequency. In this way, the value of 35% prevents the concentrated generation of parasitic coupler resonances as described below, and also causes the coupler resonance frequency to occur at a frequency position far away from the passband. /20-CCITT - It can be seen that it has a meaning as a limit value to meet the request for operational attenuation. The coupling coefficient between resonator n and resonator n-1 is obtained by dividing a predetermined function by the square root of the product of mass Mn of resonator n and mass Mn-1 of resonator n-1. When the distance between the resonators is shorter than λ/4 as in the present invention, the mass of the resonators does not affect the coupling coefficient much. For example, even if the masses of both resonators are made to differ by 10%, the coupling coefficient will only be affected by a value on the order of 1/100. Thus, in the present invention, it is sufficient that the effective masses of the resonators are at least approximately equal. Furthermore, it is possible to finely adjust the coupling coefficient by varying the spacing between the coupling points and adjusting the resonator diameter or mass in order to achieve desired filter passage characteristics. Since the resonator mass does not significantly affect the coupling coefficient, this fine adjustment can be easily performed. 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. As is clear from the derivation of the matrix of the λ/4 long connector filter and the matrix of the short connector filter, especially from the respective characteristic functions (27) and (40), the difference between the two filters, that is, the difference in the filter matrix or The difference in characteristic functions is due to the combination of connector matrices (22),
This is due to the difference in (28). 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. In other words, when two identical resonators are coupled together (however, their frequency characteristics are expressed as G(ω)
), and for a λ/4 connector filter, The short connector is In either case, the zeros of matrix element A ₂₁ give the coupler resonance. As is clear from (41), since 1/Z−ZG ² (ω)=O or G(ω)=±1/Z, the coupler resonance is the oscillator resonance G(ω)=O
does not match. On the other hand, in the case of a short coupler (42), since G(ω)·(2−ωLG(ω))=O, the coupling resonance and the natural resonance of the vibrator 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 types (λ/4 long and short) is based entirely on the characteristics of the connector 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. As described above, the differences in the characteristics of the connectors are stark between the short connectors and the λ/4 connectors (especially equations (41) and (42)). The amidotance characteristic (matrix (16)) of a torsional resonator 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 circuit 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 =jZ sin2π _x /λ is a factor that defines the connector. If we use equation (4) for xλ/4, we get become. By the way, for x≪1, a ₁₂ =jω _x /AE (short connector). The characteristic admittance of a resonator thus contains a 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. Steepening Filters According to Embodiments of the Invention At the outset, it was explained how the filters of the invention must be constructed in order to be directly comparable with the filters of the above-mentioned AEU. An equivalent circuit of the filter of the present invention 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) with the connective matrix Kij . As a matrix element of matrix (23), u ₁₁ = 1−L ₂₃ C ₃ (ω ² −ω ² ₃ )−(L ₂₃ +L ₃₄ )・C ₄ (
ω ² −ω ² ₄ ) +L ₂₃ L ₃₄ C ₃ C ₄ (ω ² −ω ² ₃ ) (ω ² −ω ² ₄ ) u ₁₂ = ω｛L ₂₃ +L ₃₄ +L ₄₅ −L ₂₃ (L ₃₄ +L ₄₅ )・C ₃ (ω ²
−ω ² ₃ )−L ₄₅ (L ₂₃ +L ₃₄ ) ・C ₄ (ω ² −ω ² ₄ )+L ₂₃ L ₃₄ L ₄₅ C ₃ C ₄ (ω ² −ω ² ₃ )(ω ²
−ω ² ₄ )} u ₂₁ = 1/ω{C ₃ (ω ² −ω ² ₃ )+C ₄ (ω ² −ω ² ₄ )−L ₃₄
C ₃ C ₄ (ω ² −ω ² ₃ ) (ω ² −ω ² ₄ )} u ₂₂ =1−(L ₃₄ +L ₄₅ )・C ₃ (ω ² −ω ² ₃ )−L ₄₅ C ₄ (
ω ² −ω ² ₄ )+L ₃₄ L ₄₅ C ₃ C ₄ (ω ² −ω ² ₃ )(ω ² −ω ² ₄ ) However, in the bridging coupling, there is another phase inversion with respect to the connector matrix (28). It must be noted that the is inserted. That is, The shape of matrix K ₅₈ is also very similar to (30).
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 ₂₅ −L ₂₃ −L ₃₄ −L ₄₅ +L ₂₃ C ₃ (L ₃₄ +L ₄₅ )(
ω ² −ω ² ₃ ) +L ₄₅ C ₄ (L ₂₃ +L ₃₄ ) (ω ² −ω ² ₄ )−L ₂₃ L ₃₄ L ₄₅ C ₃ C
₄ (ω ² −ω ² ₃ )(ω ² −ω ² ₄ )}=0 Compared with matrix (26), the polynomial G(p)
Only the structure of , so the characteristic function is becomes. From equation (40), it can be seen that the filter of the above embodiment of the present invention has a first-order pole at zero frequency and an 11-order pole at infinite frequency.
It can be seen that it has the following poles and has four poles at finite frequencies. Therefore, compared to (27) of the AEU filter mentioned above, the filter of the above embodiment of the present invention exhibits a steep rise in the attenuation curve in the upper stop band and a flat rise in the attenuation curve in the lower stop band. result. In particular, by the method of optimizing the operating parameters according to the design criteria explained for matrix (26), the equivalent circuit normalized by the terminal impedance is given as follows; The design is carried out 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 longer than that 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 to 0.730 cm, i = 2, 3 to 8.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 . For the connector, lij/Aij=6.13×10 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·sin2π _x /λ, as described above. Substitute l ₂₅ or l ₅₈ for x, and band center frequency _n = λ
Substitute the wavelength at 198100Hz. λ=vk/ _n =4.65×10 ⁵ /198100=2.35cm Since Z=Aijρvk, we can use analogy coefficient q to set 2π _n Lij = q/Aijρvksin2πlij/λ, so Aij=q/2π _n ρv _k sin2πlij/λ/L _ij =6.088×10 ¹⁰ sin2.674×lij/L _ij . That is, A ₂₅ = 3.33×10 ^-5 cm ² →φ ₂₅ = 6.51×10 ⁻³ cm A ₅₈ = 2.17×10 ⁻⁵ cm ² →φ ₅₈ = 5.26×10 ⁻³ cm Figure 8 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, the length of the torsional oscillator is also increased in the filter of the present invention, 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. In short couplers, the odd-numbered resonators are skipped and bridge-coupled. An attenuation pole occurs when the resonator is bridge-coupled (usually by skipping one resonator).
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 is λ/2 and therefore becomes a resonator itself. This is also precisely reasoned in the AEU¨ mentioned above (Figures 1 and 2). Avoidance measures (which are more or less technically problematic in any case) are provided only for longitudinal wave filters in the type of filters dealt with in the above-mentioned AEU paper, and are not limited to twisting. It is not provided for filters with vibrators. 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 twice the band center frequency. In the AEU¨ filter mentioned above, all the resonators vibrate with an 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 the resonators are held individually, the necessary coupling between the resonators may occur if, due to manufacturing tolerances, the support wires 11 do not engage exactly in the vibration nodes and therefore contribute slightly to the vibration phenomena of the resonators. However, there is no risk of it being disabled (the support device can support the resonator in a fully decoupled state). The resulting deviation of the resonant frequency of the resonator of the resonator can be easily adjusted in the resonator during adjustment. 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 drawings]

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. An equivalent circuit diagram of a mechanical filter, FIG. 4 is an equivalent circuit diagram of a short connector, FIG. 5 is a schematic diagram of a mechanical filter according to an embodiment of the present invention, and FIG. 6 is a diagram of an operating attenuation curve of a conventional mechanical filter. , FIG. 7 is a diagram of the operational attenuation curve of the mechanical filter of the present invention,
FIG. 8 is a diagram of a steepened operational attenuation curve of the mechanical filter of the present invention. 1 to 7... Torsional resonator, 8, 8'... Electromechanical transducer, 9, 9'... Coupler, 10... Support plate,
11...Support line, 21-27...Connection point, 12,
12', 13...Additional connectors.

Claims (1)

[Claims] 1 Each end resonator is connected to an electromechanical transducer that converts electrical vibrations into mechanical vibrations or mechanical vibrations into electrical vibrations, and all torsional resonators vibrate longitudinally and have the same cross section over their entire length. Torsional resonators that are connected to each other via coupling lines (coupler) configured as through lines or that are present in individual filter subsections and are directly adjacent to each other perform longitudinal vibration in each section and extend over the entire length. and are connected to each other via associated section coupling lines (coupler) having the same cross section, which coupling lines or section coupling lines are arranged perpendicularly to the longitudinal axis of the resonator and at each resonator and each coupling point. A plurality of torsional resonances arranged parallel to each other's axes are coupled together, the effective masses of the resonators are substantially equal, and the degree of coupling between each resonator is variously selected to obtain predetermined filter passage characteristics. In an electromechanical filter having a
The distance between adjacent coupling points between each resonator is
It gradually increases from both end resonators provided on both sides of the filter toward the center of the filter, and in this case, the maximum distance between the adjacent coupling points is shorter than 1/4 of the wavelength λ in the driving state. Thus, an electromechanical filter having a plurality of torsional resonators arranged parallel to the axis, wherein the minimum interval is set to be at least 35% shorter than 1/4 of the wavelength λ in the driven state.