FR2497032A1 - Electromechanical band-pass filter - uses flexural resonators in cascade coupled by longitudinal vibrating half-wave resonators using direct synthesis design - Google Patents

Abstract

The electro mechanical band pass filter consists of cascaded elements, each consisting of two resonators undergoing flexural vibrations and coupled by a half wave resonator which undergoes longitudinal vibrations. The design allows lower bandpass ripple than other known methods and over a 20% bandwidth it is similar to that of the low pass prototype. The flexural vibrating rods are parallel and consist of elinvar. The filter is coupled electrically by piezoelectric ceramic plates as input and output transducers. The resonators of each element are dimensioned so that one of the relative frequency limits is related by a mathematical formula to the frequency cut off of the corresp. low pass filter. The coupling of each stage is related by a mathematical formula to the upper or lower relative frequency of the stage. A 5 stage filter using the Chebyshev approximation with a 20% bandwidth at 50kHz and 0.04dB passband ripple has been produced with the technique.

Description

ELECTROMECHANICAL VIBRANT RESONATORS
FLEXIBLE AND HALF-WAVE COUPLERS
VIBRANT LONGITUDINALLY
The present invention relates to an electromechanical filter
bandpass, that is to say a filter whose resonant elements are
metallic cylindrical bars (resonators), interconnected
by means of coupling elements (couplers) vibrating according to a
selected and possibly with bridges spanning one or
several resonators, associated with an electromechanical converter
and a reverse converter, and more particularly a filter whose
the resonators vibrate in flexion and the couplers are couplers
half-wave vibrating longitudinally. Such a filter has been the subject of
numerous publications. For example, the article published in
the review: "The electric wave", volume 58, No. 6-7, 1978, pages 482
487, entitled "Electromechanical Filters Developed in Japan", and the
French patent application No. 80 21948 filed in the name of the
Applicant on October 14, 1980.

The last document cited concerns a unit cell (and the
filter resulting from the serialization of such cells) which has the
main advantage of having a very similar bandwidth of
calculated, even when the relative bandwidth reaches
a value of several tenths of the center frequency.

The present invention relates to an electromechanical filter
bandpass made by cascading single cells, in
which the deviation of the ripple in the transmitted frequency band
is reduced with respect to the value of said corrugation obtained for
the filters calculated according to the known methods derived from the theory
electric filters. It applies advantageously to the filter
according to the aforementioned patent application and allows in this case to obtain
both the desired bandwidth, even wide, and a character
imposed on the band. Implementation
of the invention makes it possible, in fact, to obtain filters whose ripple
residual in a relative bandwidth of 20% is substantially equal to that of the low frequency prototype filter.

 The present invention relates more particularly to the choice of the bandwidth of each of the elementary cells constituting the mechanical filter.

 The disclosure of the invention assumes the different steps leading to the realization of an electromechanical filter. Many articles deal with this subject; for example, the article published by Mr. BOSC in No. 4, 1964, of the journal "Cables and Transmission", under the title "Insights on the technology of electromechanical filters". In a very schematic way, the developer, from the data (center frequency, bandwidth, out-of-band attenuation, etc.) defined by a template, synthesizes an electric filter. The results of the study of the electric filter are then transposed into the mechanical domain by applying a system of equivalence between the elements constituting the electric filter and those constituting the mechanical filter, well known to those skilled in the art.

 Without going into the details of the filter theory, it is useful to clarify the meaning of certain terms that will be used in the following. The theory of filters reduces the study of the filter of the desired type (polynomial bandpass for example) to that of a low-pass filter called a prototype low-pass filter. This prototype filter consists of a cascade of cells of the low-pass type, each being defined by a maximum limit frequency beyond which the transmission is attenuated. The basic electrical cells composing the filter having the desired characteristics are obtained from the cells of the prototype filter by a simple mathematical transformation (corresponding to a change of the variable related to the frequency). By analogy with the cell of the filter pass- Prototype low, we define the bandwidth of any filter cell as the range of frequencies transformed frequencies limiting the band of the prototype cell by the change of variable mentioned above. In the case of a complete filter obtained by cascading cells, most often of the same type, and terminated by an ohmic resistance, the response in the bandwidth is defined by the type of approximation used for the calculation of the filter (Butterworth, Chebyshev, etc.) from the imposed attenuation characteristic of the entire filter. The latter condition allows to define the template to be respected. This last condition makes it possible to define, given the type of approximation chosen, the ratio of the impedances of the branches of the cells of the prototype low-pass filter and graciated with the transformation of the variable, the ratio impedances of the branches of the cells of the corresponding electric filter (bandpass for example).

 As is well known, filter theory often leads to results whose implementation is very complex and it is customary to make approximations for the sake of simplification. These approximations result in obtaining real characteristics that may have an inadmissible deviation from the desired characteristic, especially for relatively wide bandwidths.

 The present invention consists in a direct relation between one of the limit frequencies of a mechanical filter cell and the limit frequency of the cell of the associated electric prototype low-pass filter, without recourse to the cell of the basic electric passband filter, which achieves both an improved characteristic in the transmitted band, the improvement in the amplitude of the undulations, and a precise transition characteristic between the transmitted band and the attenuated band, the precision relating to the weakening of the band. filter at frequencies far from the tuning frequency of the resonators.

où K est une constante

More specifically, each elementary cell of rank i of an electromechanical band-pass filter according to the invention, comprising two parallel bars forming resonators vibrating in bending, and a vibrating half-wave coupler longitudinally connected between the two resonators, is dimensioned such that so that one of the relative relative frequencies (b of its relative frequency band (fl1-i, Qii) is related to the limit frequency (fi4) of a cell for a low-pass electric filter corresponding to the electromechanical filter to be produced , by the relation ::

where K is a constant

Other features and advantages of the invention will become more apparent in the detailed description which follows and refers to the accompanying drawings given solely by way of example and in which:
FIG. 1 represents the template of the amplitude-frequency characteristic of an electromechanical band-pass filter to be produced according to the invention;
FIG. 2 represents the amplitude-frequency characteristic of a low-pass electric filter corresponding to the electromechanical filter to be produced;
FIG. 3 is a schematic representation of an electromechanical filter according to the invention with vibrating vibrating resonators and longitudinally vibrating couplers; and
FIGS. 4a and 4b respectively represent an example of the attenuation characteristic of a low-pass electric filter and a set of curves making it possible to compare the attenuation characteristic in the passband of the electromechanical filter according to the invention with that of a filter according to the prior art.

 FIG. 1 represents the template of the amplitude response (E) of an electromechanical bandpass filter to be produced according to the invention, which filter must transmit the frequencies between F2 and F2 with the frequency of tuning resonators, of maximum attenuation E2 (in dB), and attenuate the other frequencies, with a weakening E1 at the frequency F1 and a weakening E3 at the frequency F3.No is called the relative value 2 of the upper limit (F ' IF) of the bandwidth andQ2 the relative value of the lower limit (F2 / Fo) of the bandwidth.

 These data thus define a template shown at 3 in FIG. 1 which the attenuation characteristic of the entire electromechanical filter to be produced must fulfill. Thus, this jig 3 plays the thrust groove for the attenuation characteristic which must pass more precisely within the points A (frequency F2, attenuation E2) B (F2, E2). C (F1; E1) and D (F3; E3).

où W LP est la pulsation de la cellule du filtre passe-bas prototype,K est une constante positive, U > 2 est la pulsation de la fréquence d'accord du filtre passe-bande et W est la pulsation variable du filtre passe-bande correspondant.D'autres changements de variable permettent de passer du filtre prototype à tout autre type de filtre électrique désiré (passe-haut ou stop-bande) selon l'art antérieur.FIG. 2 represents the amplitude response (E) -frequency (f) of a low-pass filter, such as the prototype low-pass filter of the mechanical filter to be produced, corresponding to the template of FIG. 1. In the Chebyshev approximation, the upper limit frequency f 2 of the prototype low-pass filter is defined by the intersection of the attenuation characteristic and the parallel to the abscissa axis which passes through the apex of the corrugations of said curve in the band, this approximation consisting of to choose them of equal amplitude in the band. This amplitude is represented by E2 and must correspond to the attenuation at frequencies located in the bandwidth (F2 to F2) of the mechanical filter represented in FIG. 1. The definition of f2 is related to the type of approximation chosen, as well as is known to those skilled in the art. It is known, as describes the book written by TEMES and MITRA, entitled "Modern filter theory and design" on pages 23 and 24 of the 1973 edition by John WILEY, that the attenuation characteristic of a cell of the electric bandpass filter corresponding to the prototype low-pass filter (LP in the reference) is given by the same function of a new variable defined by

where W LP is the pulsation of the cell of the prototype low-pass filter, K is a positive constant, U> 2 is the pulsation of the tuning frequency of the bandpass filter and W is the variable pulsation of the bandpass filter Corresponding other changes of variable make it possible to pass from the prototype filter to any other type of desired electric filter (high-pass or stop-band) according to the prior art.

Once the characteristics of the cells of the desired electric bandpass filter had been obtained, the use of an electromechanical equivalence system made it possible to obtain the characteristic quantities of the cells of the electromechanical filter.

dans lesquellesQi et, sont respectivement les fréquences rela

On the other hand, the coupling coefficient (xi) of a unit cell consisting of two bending vibrating half-resonators and a longitudinally vibrating half-wave coupler, determined from its transfer matrix according to the theory of filters, makes it possible to directly calculate the construction coasts of the various cells whose relative frequenciesQL are known. This coupling coefficient xi obeys one of the two following conditions:

in which Qi and, respectively are the frequencies rela

où Yor est la mobilité caractéristique des résonateurs et YoC la mobilité caractéristique du coupleur. Ainsi qu'il est bien connu, la mobilité est inversement proportionnelle à la section droite de l'élément correspondant.<tb> tivesLi <SEP> upper <SEP> and <SEP> lower <SEP> of <SEP> the <SEP> band <SEP> passing <SEP> of <SEP> the <SEP> cell
<tb> unitary <SEP> i <SEP> adapted, <SEP> bM <SEP> - <SEP> ~ <SEP>) <SEP> JRr '<SEP> 31rF
<Tb>
It will be recalled that the coupling coefficient xi of a cell for an electromechanical filter is defined by the expression:

where Yor is the characteristic mobility of the resonators and YoC is the characteristic mobility of the coupler. As is well known, the mobility is inversely proportional to the cross section of the corresponding element.

soit remplie où K est une constante, fi est la fréquence limite de la cellule de rang i du filtre électrique passe-bas prototype,QLest une fréquence relative limite de la bande passante de la cellule de rang i du filtre mécanique, et la fonction (ft (#iL) est définie par::

The present invention has electromechanical band-pass filters, each of which is derived directly from a prototype lowpass electric filter constituted by a cascading of cells, the individual bandwidths of which are defined by an approximation chosen from those known in the art. those skilled in the art, in which the cells of the mechanical filter correspond to the cells of the prototype low-pass electric filter, so that the condition

where K is a constant, fi is the limit frequency of the rank i cell of the prototype low-pass electric filter, QL is a limiting relative frequency of the bandwidth of the rank i cell of the mechanical filter, and the function ( ft (#iL) is defined by ::

According to equation (4), equation (3) becomes:

comme indiqué par l'équation (1). La fréquence relative Iimite #iL peut également être la fréquence relative inférieureQi de la bande de fréquences de la cellule de rang i, et dans ce cas le coefficient de couplage de cette cellule est égal à

comme indiqué par l'équation (2).As mentioned previously, QiL is a limit relative frequency of the bandwidth of the rank i cell of the mechanical filter to be produced. This relative relative frequency may be the higher relative frequency Qi + of the frequency band of the cell of rank i, and in this case the coupling coefficient of this cell is equal to:

as indicated by equation (1). The relative frequency Iimit #iL can also be the relative lower frequency Qi of the frequency band of the cell of rank i, and in this case the coupling coefficient of this cell is equal to

as indicated by equation (2).

oùflL2= FL/Fo est une fréquence relative limite de la bande trans L mise par le filtre mécanique, F2 étant soit la fréquence supérieure F2 soit la fréquence inférieure F2 de cette bande (figure 1);
f2 est la fréquence limite de la bande transmise par le filtre électrique passe-bas prototype, tel qu'il est montré sur la figure 2;
&gamma; (#L2) est une fonction dont l'expression est donnée par l'équation (4) dans laquelle est remplacée parQ2L telle que définie ci-dessus.The value of the constant K defined above is calculated by the equation:

where FL2 = FL / Fo is a relative relative frequency of the trans L band provided by the mechanical filter, F2 being either the upper frequency F2 or the lower frequency F2 of this band (Figure 1);
f2 is the limit frequency of the band transmitted by the prototype low-pass electric filter, as shown in Figure 2;
&gamma;(# L2) is a function whose expression is given by equation (4) in which is replaced by Q2L as defined above.

 FIG. 3 diagrammatically represents an electromechanical band-pass filter comprising five parallel cylindrical bars forming resonators (6 to 10) vibrating in bending, for example of the first mode, and four cylindrical couplers (14 to 17), which vibrate longitudinally and respectively connected between two consecutive resonators. The extreme resonators 6 and 10 respectively carry reversible electromechanical transducers 20 and 21 connected to the electrical input and output terminals of the filter, not shown.

 In Figure 3, there is shown at 22 a unit cell between the dashed lines.

 Applicant has made two filters of the type shown in Fig. 3 having a relative bandwidth of 20 inches and a center frequency of 50 KHz according to the Chebyshev approximation.

 The first, whose characteristic is represented by the dashed line 30 in FIG. 4b, is an implementation of the patent application No. 80 21948 filed on October 14, 1980 in the name of the applicant. This filter is composed of five identical élinvar resonators vibrating in bending under the action of transducers consisting of piezoelectric ceramic plates. The resonators are coupled by half-wave couplers of the same material, vibrating longitudinally.

 The second, whose characteristic is represented by the strong line curve 31 of FIG. 4b, has been realized using the present invention. The transducers are identical.

The material constituting the two filters also.

 The comparison of the curves 30 and 31 shows that the maximum amplitude of the corrugations of the curve 31 is equal to 0.04 dB. As a reference, represented by the curve 32 of FIG. 4a, is the transmission characteristic of the prototype electric low-pass filter used in the design of the two compared filters. It is found that the constant amplitude of the undulations of the curve 32 is 0.04 dB, that is to say substantially equal to the maximum amplitude of the undulations of the curve 31, while those of the curve 30 reach 0 , 06 dB.

The determination of a mechanical filter according to the invention is carried out as follows:
The frequency response of the mechanical filter to be produced is defined by the data F2, F2 by the attenuation E2 in the bandwidth, and by the attenuation E1 and E3 out of the bandwidth (Figure 1). The attenuation E2 is determined by the approximation of
Chebyshev (Figure 2). If another approximation is chosen, another form of curve is obtained.

où [3 correspond par exemple à la fréquence F3 avec un affaiblissement E3 (figure 1) et 62 correspond à une limite de la bande passante (F2 à F2) de tout
2 spond (F2 2 le filtre mécanique, avec un affaiblissement E2 (figure 1).The degree d of the filter (number of cells) is calculated using a formula known to those skilled in the art, using for variable = f / K given by equation (3). This formula is:

where [3 corresponds for example to the frequency F3 with a weakening E3 (FIG. 1) and 62 corresponds to a limit of the bandwidth (F2 to F2) of any
2 spond (F2 2 the mechanical filter, with a weakening E2 (Figure 1).

 The synthesis of the prototype low-pass electric filter of degree d, ripple E2 and band f2 limit frequency is performed using known methods.

 The constant K is calculated by the formula (6).

 The formula (5) makes it possible to determine one of the relative relative frequencies. The bandwidth of each of the cells of the band-pass mechanical filter is determined from the maximum frequency f + of each of the cells of the prototype low-pass electric filter by calculation of the inverse relationship. Conditions of use of the elements constituting the elementary cells (single material, single diameter of one of the elements) result in the definition of certain parameters of the elements: couplers and resonators using the coupling coefficients x, the others are chosen by the manufacturer.

 The tuning frequencies Fo of each resonator are finally calculated with the two equations (1) and (2) for xi.

Claims (4)

 An electromechanical bandpass filter having a frequency band (F2 to F2) to be transmitted and comprising at least one cell, each cell comprising:  - two parallel bars (7, 8) forming bending vibrating resonators; and  a half-wave coupler (15) vibrating longitudinally connected between the two resonators (7, 8); characterized in that the cell of rank i is dimensioned such that one of the relative relative frequencies (Q) of its relative frequency band (Qi to fl is related to the limit frequency (f + i) of a cell for a low-pass electric filter corresponding to the electromechanical filter to be produced, by the relation:

 where K is a constant

 2.Electromechanical filter according to claim 1, characterized in that the relative limiting frequency (Q) is the higher relative frequency (Qit of the frequency band of the cell of rank i, the coupling coefficient (xi) of the cell of rank i being equal to:  3. Electromechanical filter according to claim 1, charac terized in that the relative relative frequency (Q) is the lower relative frequency (n7 of the frequency band of the cell of rank i, the coupling coefficient (xi) of the cell of rank i being equal to:

 4. Electromechanical filter according to one of the preceding claims, characterized in that it comprises electromechanical input transducers (20) and output (21) associated with the cells cascaded.