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Publication numberUS3376521 A
Publication typeGrant
Publication dateApr 2, 1968
Filing dateMay 19, 1964
Priority dateMay 21, 1963
Also published asDE1277463B, DE1277463C2, DE1616526A1, DE1616526B2
Publication numberUS 3376521 A, US 3376521A, US-A-3376521, US3376521 A, US3376521A
InventorsKarl Traub
Original AssigneeSiemens Ag
Export CitationBiBTeX, EndNote, RefMan
External Links: USPTO, USPTO Assignment, Espacenet
Mechanical vibrator with electrostrictive excitation
US 3376521 A
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Description  (OCR text may contain errors)

April 2, 1968 K. TRAUB 3,376,521

MECHANICAL VIBRATOR WITH ELECTROSTRiCTIVE EXCITATION Filed May 19. 1964 5 Sheets-Sheet 1 L l F|g.1

Fig.3

IN A 5 v V X F lg.

April 2, 1968 K. TRAUB MECHANICAL VIBRATOR WITH ELECTROSTRICTIVE EXCITATION Filed May 19. 1964 5 Sheets-Sheet 2 United States Patent ABSTRACT OF THE DISCLOSURE An electromechanical filter having blocks of electrostrictive material along the length of an elongated metallic vibrator, the blocks being arranged with their planes extending perpendicular to the longitudinal axis of the metallic resonator and polarized in the direction of the longitudinal axis of the resonator whereby the harmonics of the vibrations may be filtered.

The invention relates to a mechanical vibrator which is formed by small plates or blocks of electrostrictive material for the transition from electrical oscillations to mechanical bending or longitudinal vibrations and vice versa, and is preferably provided as an end vibrator of a multipart mechanical filter, in which the blocks of electrostrictive material are specifically arranged within an area limited by two vibration nodes with plane of the block extending perpendicular to the longitudinal axis of the vibrator.

Mechanical resonators, due to stability and their high quality, can be used to advantage in oscillator circuits and filter circuits in which the requirements with respect to frequency precision or steepness of the filter flanks can be fulfilled, only with difiiculty, with lumped circuit elements. A mechanical resonator has, as a rule, the form of an acoustic conduction line in which there holds for it only in a relatively narrow frequency range the electric equivalent circuit diagram representing a resonant circuit. If a mechanical resonator is to be utilized for a large frequency range, its input resistance, in contrast to a resonant circuit from lumped circuit elements, shows continuously repeating null and pole points which are evoked by the so-called harmonics of the resonator. For this reason, for example, in a band pass filter utilizing mechanical vibrators, in addition to the desired pass range other interfering pass ranges occur, which then have to be eliminated by an additional expenditure in coils and condensers. If a mechanical resonator is operated on a harmonic rather than on the fundamental, in order with productionally feasible dimensions to achieve higher resonance frequencies, the relative distance to the next harmonic is diminished. The nearer the first harmonic lies to the desired pass range, and the greater the demands on the blocking attenuation, the more narrow banded must be the electrical resonant circuits utilized for the suppression of the undesired pass ranges, which situation, however, has as a consequence an increase of the pass attenuation in the pass range. Similar difiiculties exist when a mechanical resonator is to be used in an oscillator circuit which has no other clement. In this case, the oscillator, under some circumstances, can swing to an undesired over wave of higher frequency of the resonator. In slender longitudinal vibrators such overwave frequencies occur, as is well known, harmonically, that is at whole multiples of the fundamental, while in bending vibrators with free ends, they are not disposed harmonically to the fundamental.

It is the object of the invention to eliminate the above described difficulties in a relatively simple manner. Among their high frequency other things, it is to be achieved, that in electrostrictively excited vibrators, through a suitable arrangement of the excitation systems a series of harmonics is rendered un objectionable.

Proceeding from a mechanical vibrator which is formed by small plates or blocks of electrostrictive material for the transition from electric vibrations to mechanical bending or longitudinal vibrations and vice versa and is preferably provided as an end vibrator of a multi-part mechanical filter, and in which the blocks of electrostrictive material are arranged predominantly substantially within the space extending between two vibration nodes, with the block plane lying perpendicular to the longitudinal axis of the vibrator, such problem is solved according to the invention, by an arrangement such that the plates or blocks of electrostrictive material are located at points of the vibrator at which no deformation occurs in the harmonic to be suppressed and/ or that several blocks are so located at different points of the vibrator that the forces effective in the vibration excitation very nearly completely cancel each other out for the harmonics to be suppressed.

It is advantageous if the blocks of electrostrictive material are arranged in the central portion of the vibrator, or if such blocks are arranged symmetrically to the center of the vibrator.

Advantageous forms of construction can further be achieved if the blocks of electrostrictive material are arranged symmetrically to the center of the vibrator in vibration nodes of odd numbered harmonics, or if the blocks of electrostrictive material are mounted at least approximately symmetrically to vibration nodes of harmonics of higher order.

For the excitation of bending vibrations it is favorable if the blocks of electrostrictive material are interrupted adjacent the neutral axis with respect to bending vibrations, and if the blocks disposed on both sides of the neutral point are oppositely polarized, or if the blocks of electrostrictive material are subdivided by a metal coating, preferably a silver coating, which runs parallel to the limit surfaces established through length and width of the blocks and if these conducting layers are provided with connecting wires.

In the drawings, wherein like reference characters indicate like or corresponding parts:

FIGS. 1 to 5 are graphs of deformation vibrations in a bending vibrating bar for a fundamental frequency and certain harmonics;

FIG. 6 illustrates a mechanical bending vibrator constructed in accordance with the invention;

FIGS. 7 and 8 illustrate additional embodiments of the invention;

FIG. 9 illustrates the electrical equivalent circuit of the construction illustrated in FIG. 6;

FIG. 10 illustrates an additional modification of the invention;

FIG. 11 illustrates an electrical equivalent circuit for the construction illustrated in FIG. 10;

FIGS. 12 and 13 illustrate additional embodiments of the invention in bending vibrators;

FIG. 14 is a graph, similar to FIGS. 1-5, of deformation vibrations in a longitudinally vibrating bar for a fundamental frequency and certain harmonics; and

FIG. 15 illustrates a mechanical longitudinal vibrator constructed in accordance with the invention.

From the differential equation of a bending vibrator, free at both ends, there can be computed, through consideration of the suitable initial conditions, the resonance frequencies of such a bending vibrator according to the following approximation formula:

E here signifies the elasticity modulus of the vibrator material, I the moment of inertia of the bar in the vibrational direction, m the mass per unit of length, l the length of the bar and n the order number of the resonance frequency (n: 1,2,3 In FIGS. 1 to 5, the deformation and the position of the vibration nodes are plotted in dependence on a coordinate x/l, with x signifying an arbitrary point on the bar. These results can be derived from the same differential equation as the resonance condition. FIG. 1 illustrates the deformation and the position of the vibration nodes for the fundamental, FIG. 2 for the second harmonic, etc., and in FIG. 5 the corresponding deformation and position of the vibration nodes for the fifth harmonic. (The order number 1 is allocated to the fundamentalso that fundamental and first harmonic are identical.) It will be noted from FIGS. 1 to 5 that there occurs in all even numbered overwaves in the middle of the bar (x/l=0.5) a vibration on node at which the bending moment is zero. At two places symmetrical to the middle of the bar there occur equally large, but oppositely directed deformations. In the fundamental and the odd numbered overwaves there is a maximum of deformation in the middle of the bar and at two places symmetrical to the middle of the bar there occur equal sized and like directed deformations.

FIG. 6 illustrates a mechanical bending vibrator, which is constructed, as to the manner of excitation of the mechanical bending vibrations, in a known manner by means of electrostrictive ceramic blocks. A steel bar 5 is provided, at both sides of the point which is neutral with respect to bending vibrations, with electrostrictively active blocks 6 and '7. As electrostrictively active material lead ceramic (lead zirconate) is used, such as is known, for example, under the trade name PZT 6 of the Clevite firm. The ceramic blocks are provided on the sides facing the steel portions with a silver coating and are firmly soldered to such steel portions. The polarization of the ceramic plates is indicated by the arrows 8 and 9 and is so selected that the block 6, disposed above the neutral axis, is oppositely polarized to the block 7 lying below the neutral axis. In the vibration nodes 10 and 11 of the fundamental, metal lead wires 12 and 13 are attached, which extend to corresponding connecting terminals 1 and 2. The lead wires 12 and 13, if of corresponding thick structure, can also be utilized for supporting the vibrator in a casing (not illustrated).

On applying an alternating potential to terminals 1 and 2, for example, the polarization direction of the ceramic block 6 is opposed to the electric field direction, while the polarization direction of block 7 corresponds with the direction of the electric field. Corresponding to this condition, the one block expands itself under the influence of the electric field, while the other block contracts, whereby the vibrator is bent to one side, If the polarity of the applied alternating potential is reversed, then correspondingly the vibrator is bent to the other side, so that it executes pronounced bending vibrations if the frequency of the applied alternating potential agrees at least approximately with its own characteristic frequency. In FIG. 6 the ceramic blocks are mounted in the middle of the bar (that is, at 0.5.1).

In the example of the invention illustrated in FIG. 7, the electrostrictively active systems are arranged symmetrical to the center of the bar and to the portions of the steel vibrator 5 there are soldered ceramic blocks 15, 16, 17 and 18. In the vibration nodes 10 and 11 for the fundamental there are attached lead wires 12 and 12', which extend to a common connecting terminal 1. In the middle portion of the steel bar there is attached an additional lead wire 19, which extends to a connecting terminal 2. The polarization of the ceramic blocks is indicated by the arrows 20, 21, 22 and23, and again is so selected that the blocks lying above the neutral axis are polarized oppositely to the blocks lying below the neutral axis, with the polarization directions of the two systems being opposed to each other. In this embodiment the vibrator executes mechanical bending vibrations when an electric alternating potential is applied to the terminals 1 and 2, whose frequency agrees with its resonance frequency.

In FIG. 9 there is depicted the electrical equivalent circuit diagram of such bending vibrators. The fundamental can be represented by a series resonance circuit including inductance LI, the capacity C and a loss resistance R with a capacitance C being connected in parallel with such series circuit. For agreement with the mechanical vibrators, the connecting terminals are designated 1 and 2,,. For the possible harmonics occurring on the mechanical vibrators there are indicated, in broken lines, in the equivalent circuit diagram additional series vibration circuits with the circuit elements L C and R to L C and R In the embodiments of the invention illustrated in FIGS. 6 and 7 none of the even numbered harmonics is excited, as will be apparent from a comparison with FIGS. 2 and 4. Since all the even numbered harmonics have vibration nodes in the middle of the bar according to FIG. 6 (x/l=0.5). In an excitation according to FIG. 7, by reason of the polarization indicated by arrows 20 to 23,

' the forces for the fundamental are promoted. If in the example of execution of FIG. 7 the distance a of the electrostrictive block from the end of the bar is so selected that the exciting blocks 15 and 16 or 17 and 18 lie in the vibration nodes of an odd numbered harmonic, this too is then suppressed. For a==0/ 356.1 there results therefore a suppression of the third and of all even numbered harmonics, whereby after the fundamental, the fifth harmonic will be the next that can be excited. It is thereby possible to achieve the next harmonic by a frequency separa tion generally sufficient for practical purposes. In the equivalent circuit diagram of FIG. 9, therefore, there are eliminated the circuit elements L C and R as well as all the even numbered circuit elements.

T he embodiment illustrated in FIG. 8 corresponds in its construction to that of FIG. 7, the only difference being in the selection of polarization direction for the individual electrostrictively active blocks 15, 16, 17 and 18. The polarization is indicated by arrows 2t)", 21', 22. and 23' and is so selected that the blocks lying above the neutral axis are polarized oppositely to the blocks lying below the neutral axis. However, for both systems the blocks lying above and below the neutral axis are polarized in the same direction. Upon application of an alternating potential to the terminals 1 and 2 the electrostrictively active blocks are subjected to expansions and contractions, so that the vibrator executes bending vibrations in reference to the polarization direction. As is apparent from a comparison with FIGS. 1 to 5, the exciting forces cancel each other out, as a result of the symmetry of the system, for all odd numbered harmonics and for the fundamental, so that these are not excited. If the distance a is so selected that the ceramic blocks are disposed in vibration nodes of an even numbered harmonic, this likewise is not excited. If, for example, a is selected so that the ceramic blocks are disposed in the vibration nodes of the fourth harmonic (a =0.277 1, see FIG. 4), the resonator then vibrates on the second harmonic and the next vibration does not occur until the sixth harmonic. In the equivalent circuit diagram of FIG. 9, therefore, the circuit elements L C and R; as well as all the circuit elements with odd numbers are eliminated.

In FIG. 10 a mechanical bending vibrator is represented, whose excitation takes place over electrostrictively active blocks of calcium-barium-titanate, whose Curie temperature, as is Well known, is lower than the requisite soldering temperature. For this reason the electrostrictively acting blocks 30, 31, 32, 33, 34, 35, 36 and 3 7 are correspondingly subdivided by silver layers 38, 39, 4t) and 41. By applying a direct potential to corresponding silver layers and parts the vibrator 5 it is possible then to impress on the ceramic blocks, according to the soldering process, the polarization suited for the particular purpose in use. In the vibration nodes and 11 of the fundamental, lead wires 42 and 43 are attached, which, if suitably proportioned as to thickness, can also serve for the supporting of the vibrator in a casing (not illustrated), and which lead wires are then connected by means of a suitable connecting line to a common conecting terminal 1. Leading from the middle portion of the vibrator 5 is a connecting wire 44, which extends to a connecting terminal 2, and leading from the silver layers 38 to 41 and connecting wires 4'5, 46, 47 and 48 which extend to a common connecting terminal 3. The polarization direction of the individual ceramic blocks is indicated by the arrows 49 to 56 is made such that the blocks located above the neutral axis are polarized oppositely to the blocks located below the neutral axis. If there is applied to the connecting terminals 1 and 3 an input alternating voltage U whose frequency roughly corresponds with the frequency of the bending vibrator, the latter will execute bending vibrations in the rhythm of the applied alternating voltage, since the blocks .32 and 37, for example, lying above the neutral axisexpand, while the blocks and lying below the neutral axis contract. If the polarity of the applied alternating voltage is reversed, the blocks lying above the neutral axis contract, while the blocks lying below the neutral axis expand. Through the bending vibration the blocks 31, .33, 34 and 36 are also subjected to expansions and contractions; so that between the silver layers 38 to 41 and the middle portion of the vibrator 5 a voltage appears, which can be obtained as an output alternating voltage U across the terminals 2 and 3.

The electrical equivalent circuit diagram of a vibrator according to FIG. 10 is depicted in FIG. 11. It consists, for the fundamental, of a circuit in-whose longitudinal branch there is a loss-loaded series resonant circuit with the inductance L' the capacitance (1' and the nonreactive resistance R' and in which at the input and output there are approximately equal shunt capacitance C and CO disposed. In order to take into account a possibly unsymmetrical arrangement, a difference in thickness of the electrostrictive blocks, or a difference in their polarization, there is inserted in the output circuit, ahead of the output cross capacity C an ideal transformer U with the transformation ratio 1:U. For-agreement with the designation of the mechanical vibrators, the connecting terminals, are designated with 1' 2',, and 3',,. In order to take into consideration the harmonics, there are connected in parallel with the series resonant circuit lying in the longitudinal branch, additional series circuits L C' R' to L and R,,, indicated in 'brokenlines, with the series resonance circuits corresponding to the order numbers 3 to n-l being indicated merely by a broken line.

If, in the embodiment of FIG. 10, there is applied to the terminals 1 and 3 an input alternating potential U, the exciting forces for the fundamental are then supported, while as a result of the symmetrical arrangement and the selected polarization, even number harmonics very nearly completely cancel each other (see FIGS. 1 to 5). If the distance a of the ceramic blocks from the vibrator ends is so selected that the ceramic blocks are disposed in the vibration nodes of an odd numbered harmonic, it is not excited. If, for example, there is selected a'=0-.3561, the ceramic blocks are disposed in vibration nodes of the third harmonic, which therefore is not excited. In the equivalent circuit diagram of FIG. 11, all the circuit elements designated with even numbers as well as the series vibratory circuits L' C' R are then eliminated. A vibrator constructed according to FIG. 10, whose fundamental resonance frequency lies at about 7 kc., delivers at approximately between 9 and 65 kc. a blocking attenuation on the order of magnitude of 8 nepers and presents the next attenuation break only at about '72 kc., which corresponds to the fifth harmonic. It can thereby be achieved that the attenuation break following the fundamental occurs only at a tenfold distance from the fundamental frequency.

The embodiment illustrated in FIG. 10 can also be operated, in analogy with the equivalent circuit diagram of FIG. 9, in the manner of a bipole, if the terminals 1 and 2 are connected with each other and the exciting voltage is applied to the terminals 3 and the connecting line between terminals 1 and 2. In this case there results, for example, for the operation of a multi-part filter, an end vibrator in which the third and all even numbered harmonics are not excited. Thereby there is eliminated in the equivalent circuit diagram of FIG. 9 all of the circuit elements with even numbers as well as the series resonance circuit consisting of L C and R In FIG. 12 a mechanical bending vibrator is illustrated, whose excitation systems consist of a lead ceramic. In the middle of vibrator 5 there is disposed ceramic blocks 6% and 61, which are oppositely polarized, as indicated by the arrows 64 and 65. The ceramic blocks 62 and 63 are likewise oppositely polarized, corresponding to the arrow directions 66 and 67, and are positioned in a vibration node for the third harmonic. From the steel parts of vibrator 5, insulated from each other by the ceramic blocks there extend connecting wires 68, 69 and '70 corresponding terminals 1, 2 and 3. This vibrator can likewise be considered with respect to the equivalent circuit of FIG. 11. If an alternating potential is applied to terminals 1 and 3, none of the even numbered harmonics will be excited, since the exciting blocks 60 and 61 are located in the middle of the bar (x/l 0.5). Between terminals 2 and 3 an output alternating potential can be obtained which does not contain the voltages corresponding to the third harmonic. In this example of the invention, therefore, the third and all even-numbered harmonics are suppressed.

In FIG. 13, in further development of the concept of the invention, there is represented a mechanical bending vibrator operated as a quadrupole, in which the third and fifth harmonics as well as all the even numbered harmonics are suppressed. The steel portions of the vibrator 5 are here connected with each other over respective pairs of blocks and 76, 77, 79 and 80, 81 and 82 of a lead ceramic, the polarization of the individual blocks being indicated .by the arrows 83 to and so selected that in each case the blocks located above the neutral axis are polarized oppositely to the blocks located below the neutral axis, and moreover, the blocks located in the left hand half of the bar are polarized oppositely to the blocks located in the right hand half of the bar. The blocks 75 and 76 and also the blocks 81 and 82 are so arranged that they are positioned in vibration nodes of the third harmonic (b 0.3561) Blocks 77, 78, 79 and 80 lie in vibration nodes of the fifth harmonic (x/l 0.409). From the individual steel portions of the vibrator extend connecting wires 91 and 92 to a terminal 1, a connecting wire 93 to a terminal 2 and connecting wires 94 and 95 to a terminal 3.

The equivalent circuit diagram of this vibrator likewise can be considered with respect to FIG. 11. If there is applied between terminals 1 and 3 an input alternating potential U, by reason of the excitation system. consisting of the blocks 75, 76, 81 and 82, the vibrator then executes bending vibrations, through which the blocks 77 and 78, as well as the blocks 79 and 80 are expanded and contracted. It is possible, therefore, to obtain between terminals 2 and 3 an output alternating voltage U,,. Since the blocks forming the excitation system are located in the vibration nodes of the third harmonic, the latter is not excited, and as the output voltage is derived over ceramic blocks which are positioned in vibration nodes of the fifth harmonic, frequencies corresponding to this harmonic are not contained in the output voltage. Moreover, as a result of the symmetry of the arrangement, no even numbered harmonics are even initially excite-d.

If, in the embodiment of FIG. 13, the distance b of the blocks 75 and 76 and of the blocks 81 and 82 from the respective vibrator ends are so selected that these blocks are arranged in vibration nodes of the fifth harmonic (b 0.227 l), the electrostriotively active systems are disposed symmetrically to the center of the vibrator and at least approximately symmetrically to the vibration nodes of the third harmonic. The longitudinal symmetry occurring with reference to the vibration of the third harmonic can be compensated with respect to the electrical operation, by suitable selection of the thickness of the plates 75 and 76 and 81 and 82 whereby they differ from the thickness of plates 77 and 78, and 79 and 80, respectively. Furthermore, if the terminals 1 and 2 are connected and the exciting voltage is applied to terminal 3 and the connecting line of terminals 1 and 2, an end vibration is produced for the operation of a 'multi-part filter, in which no excitation takes place of the third, fifth and all even numbered harmonics. The suppression of the even numbered harmonics is achieved by the symmetry with respect to the bar center; the suppression of the third harmonic results from the symmetry of the blocks with respect to the vibration nodes of the third harmonic, while the fifth harmonic is not excited, since the blocks are disposed in its vibration nodes. In the equivalent circuit diagram of FIG. 9 there are then eliminated all the elements with even numbers and the series resonance circuits representing the third and fifth harmonics.

In the bending vibrators illustrated in FIGS. 6- to 13, moreover, as a result of the symmetry to the neutral axis and the opposite polarization directions in each case, no longitudinal vibrations can be excited.

In FIG. 14 the deformation and the position of the vibration nodes of a longitudinal vibrator are plotted in dependence on a running coordinate x/l, when x is an arbitrary point and l signifies the bar length. The bar length is as a rule so selected that it amounts, at the fundamental, to about a half wave length (l= \/2, where A=wave length). The curve 100 represents the deformation for the fundamental, the curve 101 the deformation for the second harmonic and curve 102 the deformation for the third harmonic. As already mentioned, in longitudinal vibrations the higher frequencies occur harmonically to the fundamental, as is apparent also from the diagram of FIG. 14.

In FIG. 15 a longitudinal vibrator is depicted which consists of a steel portion 105, into which electrostrictively active blocks 106 and 107 are soldered in known manner, the polarization of these blocks being indicated by the arrows 108 and 109. From the steel portions insulated from one another by the ceramic blocks connecting wires 110, 111 and 112 extend to respective terminals 1, 2 and 3. The electrical equivalent circuit diagram of such a longitudinal vibrator can be considered with respect to FIG. 11. If an input alternating voltage U is applied between terminals 1 and 3, the vibrator executes longitudinal vibrations, since the exciting ceramic block 108 extends across the entire cross section of the vibrator, and since the excitation system lies in a vibration node of the third harmonic, this is not excited. If the frequency of the exciting voltage corresponds, for example, with the resonant frequency of the vibrator, an output alternating voltage can be obtained between terminals 2 and 3, in which no voltages of even numbered harmonics are contained, since the system realized through ceramic plate 107 is arranged in the center of the vibrator (x/l=0.5), that is in such a plate at which for all even numbered harmonics node points of the deformation occur. Accordingly, in a longitudinal vibrator constructed in this manner, the third as well as all even numbered harmonics are suppressed.

From a comparison of the examples of construction illustrated in FIGS. 12 and 15, the analogy between iongitudinal and bending vibrators will be readily apparent. The suppression of undesired harmonics in longitudinal vibrators can therefore also be achieved by the analogous application of the rules herein set forth in connection with bending vibrators illustrated in FIGS. 6 to 13.

Changes may be made within the scope and spirit of the appended claim which define what is believed to be new and desired to have protected by Letters Patent.

I claim:

1. An electromechanical filter having an elongated metallic vibrator for the transition of electrical oscillations to longitudinal vibrations, and blocks of electrostrictive material disposed along the length of the metallic vibrator, said blocks of electrostrictive material extending perpendicular to the longitudinal axis of said vibrator and polarized in the direction of the longitudinal axis, wherein the improvement comprises at least one block at the mid point of the metallic vibrator and a second block at a vibration node of an odd-numbered harmonic.

References Cited UNITED STATES PATENTS 3,015,789 l/1962 Honda et al 3337l 3,028,564 4/1962 Tanaka et a1 33371 3,293,575 12/ 1966 Albsmeier 33372 3,311,760 3/1967 Durgin et al 3l08.2

ROY LAKE, Primary Examiner.

DARWIN R. HOSTETTER, Examiner.

Patent Citations
Cited PatentFiling datePublication dateApplicantTitle
US3015789 *Apr 16, 1957Jan 2, 1962Toyotsushinki Kabushiki KaishaMechanical filter
US3028564 *Jun 14, 1960Apr 3, 1962Kokusai Electric Co LtdMechanical filter
US3293575 *Aug 27, 1962Dec 20, 1966Siemens AgElectromechanical filter having means to reduce harmonic transmission
US3311760 *Nov 21, 1963Mar 28, 1967Westinghouse Electric CorpHigh q resonator
Referenced by
Citing PatentFiling datePublication dateApplicantTitle
US3686593 *Feb 11, 1970Aug 22, 1972Int Standard Electric CorpElectromechanical resonator
US3842294 *Nov 7, 1973Oct 15, 1974Nippon Electric CoElectromechanical transducer comprising a pair of antiparallel poled rectangular piezoelectric ceramic pieces
US4281298 *Nov 13, 1979Jul 28, 1981Fujitsu LimitedFlexural transducer
US5006824 *Apr 7, 1986Apr 9, 1991Rockwell International CorporationThird mode torsional F-M resonator
US5773912 *Dec 13, 1996Jun 30, 1998Murata Manufacturing Co., Ltd.Piezoelectric resonator including oscillation buffer materials
Classifications
U.S. Classification333/186, 968/488, 310/321, 331/155
International ClassificationH03H9/56, H03H9/24, H03H9/00, H04M, H03H9/17, H03H, H03H9/54
Cooperative ClassificationH03H9/56, H03H9/17
European ClassificationH03H9/56, H03H9/17