US3437850A - Composite tuning fork filters - Google Patents
Composite tuning fork filters Download PDFInfo
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- US3437850A US3437850A US303060A US3437850DA US3437850A US 3437850 A US3437850 A US 3437850A US 303060 A US303060 A US 303060A US 3437850D A US3437850D A US 3437850DA US 3437850 A US3437850 A US 3437850A
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10H—ELECTROPHONIC MUSICAL INSTRUMENTS; INSTRUMENTS IN WHICH THE TONES ARE GENERATED BY ELECTROMECHANICAL MEANS OR ELECTRONIC GENERATORS, OR IN WHICH THE TONES ARE SYNTHESISED FROM A DATA STORE
- G10H3/00—Instruments in which the tones are generated by electromechanical means
- G10H3/12—Instruments in which the tones are generated by electromechanical means using mechanical resonant generators, e.g. strings or percussive instruments, the tones of which are picked up by electromechanical transducers, the electrical signals being further manipulated or amplified and subsequently converted to sound by a loudspeaker or equivalent instrument
- G10H3/14—Instruments in which the tones are generated by electromechanical means using mechanical resonant generators, e.g. strings or percussive instruments, the tones of which are picked up by electromechanical transducers, the electrical signals being further manipulated or amplified and subsequently converted to sound by a loudspeaker or equivalent instrument using mechanically actuated vibrators with pick-up means
- G10H3/20—Instruments in which the tones are generated by electromechanical means using mechanical resonant generators, e.g. strings or percussive instruments, the tones of which are picked up by electromechanical transducers, the electrical signals being further manipulated or amplified and subsequently converted to sound by a loudspeaker or equivalent instrument using mechanically actuated vibrators with pick-up means using a tuning fork, rod or tube
Definitions
- This invention relates generally to electro-mechanical resonators and more particularly to organ tone generating systems employing such resonators.
- the present invention is related in subject matter to an application for U.S. patent filed in the name of Wayne, Ser. No. 46,704 filed Aug. 1, 1960, and entitled Electric Organ, and assigned to the assignee of the present application, and which concerns an organ system in which harmonic rich generators apply their output to a series of semitone filters, which individually select the semitones into separate channels.
- the signal content of the separate channels is then processed and combined to produce a tone having a desired frequency spectrum.
- the filters employed to separate the semitones may have desirable characteristics apart from the stated function, i.e., they may have sufiiciently high Q to impart a relatively long build up time or onset, and a relatively long decay, to the individual tone components. Furthermore, they may be slightly detuned with respect to their driving signals,
- Chiff components may be introduced into an organ tone in response to transient excitation of certain of the resonators, which may not be driven in steady state for the particular tone, more specifically, a chitf resonator may be transiently excited in response to and during onset of excitation of another resonator which is to be excited in steady state.
- a chitf resonator may be transiently excited in response to and during onset of excitation of another resonator which is to be excited in steady state.
- electromechanical resonators may be employed instead.
- the resonators of the present invention are further useful in an organ tone generating system disclosed in a I copending application for U.S. patent, in the name of Cunningham, filed Aug. 19, 1963, entitled Chiff and Tone Generator, and assigned to the assignee of the present application.
- a square wave or sine wave generator system is employed, and for each tone an electrical resonant filter or resonator is employed, tuned to the fundamental of the tone, and having a Q selected to insert an appropriate rise and decay time into the wave envelope of the response of the resonant filter to the generator output.
- the filters may also be detuned with respect to the generator fundamental frequency in order to impart a variation of frequency during tone onset and decay, due to the combination of steady state response of the resonator with its transient response, these occurring at the driving frequency and at the filter resonant frequency, respectively.
- the response of the filter is applied to a harmonic generator, the output of which con stitutes a frequency spectrum appropriate for tone generation and the tone may be further formed, as required, by means of tone forming filters, the latter operating in a manner generally well understood in the art of organ tone production.
- chiff is introduced into certain of the organ tones.
- chiff is commonly found in the flute tones of pipe organs.
- the serious musician desires an electronic organ to simulate the tones of pipe organs and accordingly desires particularly to insert chiff into flute tone outputs of the electronic organ.
- Some difference of opinion appears to exist among musicians in respect to precise definitions of chiff.
- flute tones it is agreed that chiif consists of a transient, gradually rising and gradually decaying frequency component equal to about 5.5 times the fundamental frequency of the flute tone, and which occurs only during the build up of the flute tone.
- the chiff may be at a subharmonic frequency.
- transient frequency components which occur during onset only, and which may correspond with a harmonic or subharmonic, or any partial, of the fundamental frequency of a given tone, as distinguished from-an unharmonic or subharmonic frequency may properly be denominated chiff.
- any of these transient frequencies having a suitable transient wave shape, and which serve to simulate the onset quality of any tones of a pipe organ more closely than would be the case otherwise are denominated chifi.
- chiff is produced by shock exciting a resonator especially selected for the purpose.
- chili is produced by applying, to an oscillator, a gating wave which keys on the oscillator at the onset of a tone, and which modulates the amplitude of the oscillator during the onset of the tone in such a way as to generate or simulate chiff.
- the electromechanical resonators of the present invention have been found valuable for the purpose of producing chitf effects, in organs of both the Wayne and the Cunningham types,
- Still another object of the invention resides in the provision of an electromechanical resonator in which the tines are piezoelectric elements.
- a further object of the invention resides in the provision of a tuning fork employing tines having piezoelectric drivers, or consisting of piezoelectric elements, in which the location of the electrodes on the tines is selected to reduce the amplitudes of certain modes of vibration of the tuning fork.
- Electromechanical resonators employing piezoelectric drivers or in which the piezoelectric element constitutes the resonating component of the resonator are found to have responses or modes of vibration, which may be undesirable.
- modes introduce undesired tonal components, which must be eliminated by filtering.
- a mode of vibration occurs at 6.3 times the fundamental mode of the resonator, and many additional modes may occur, these several modes being of relatively high amplitudes, sometimes approaching that of the fundamental. Accordingly, in resonators intended to be employed in tone generating systems, it is essential that the undesired modes be re prised in amplitude as far as possible, although for some purposes one or more of the modes may be musically useful.
- electromechanical resonators be electrostatically driven because such resonators may be expected to be fabricated at reduced cost.
- the use of coils for driving resonators inevitably becomes expensive.
- piezoelectric crystals employed as resonators are not feasible because impedances involved are extremely high and because it is difficult to fabricate such crystals in required shapes for audio applications, i.e., as elongated rods. For example, a length of approximately 2" may be required for about a 100 c.p.s. resonator, and the length and thickness may be measured in a few hundredths of an inch.
- Resonators of very many different lengths and different operating frequencies are required for application to a single organ, and the use of crystals for so many different frequencies would be prohibitively expensive.
- ceramic piezoelectric resonators because of their reasonable cost, ease of design for audio frequency operation, and their excellent mechanical properties.
- Ceramic piezoelectric material varies in Youngs modulus over a considerable range of values in accordance with stress. This means that when the material is used as a resonator the resonant frequency of the resonator becomes a function of the driving voltage. Moreover, when the resonator is utilized because of its slow response property, in forming the envelopes of tones, frequency may vary as the tone builds up, with a corresponding build up of mechanical vibration amplitudes. This efiect may involve a variation of frequency of more than 1%, which is audibly obtrusive.
- spring steel for example, for a large portion of the length of the tine and piezoelectric material for the remainder of the tine, or by building the tines entirely of spring steel having cemented thereto piezoelectric driving elements, the tonal frequency shift with amplitude of vibration may be radically reduced, since spring steel has a Youngs modulus which does not appreciably vary with deflection. While spring steel has been suggested as a suitable tine material, this is not requisite. Other materials may be selected which have the required resilience to form resonators having desired Q values, and spring steel has been found to represent merely one example of a suitable material.
- a further broad object of the invention resides in modes of inclusion of electromechanical resonators in electronic organ tone generators, to take advantage of the properties of such resonators which are not available in purely electrical resonators.
- FIGURE 1 is a block diagram of an organ tone generator according to the invention.
- FIGURE 2 is a view in elevation of a tuning fork resonator according to the invention, useful in the system of FIGURE 1;
- FIGURE 3 is a view in plan of a modification of the resonator of FIGURE 2;
- FIGURES 4a, 4b and 5 are waveforms useful in ex plaining the invention of FIGURES 1-3;
- FIGURE 6 is a sketch of a functional equivalent of a tuning fork resonator
- FIGURE 7 is a view in plan of a modification of the resonator of FIGURES 2 and 3;
- FIGURES 8, 9, l0 and 11 are block diagrams of modifications of the system of FIGURE 1.
- the reference numeral 10 denotes an oscillator, which may be a sine wave oscillator for the purposes of the present invention but which preferably is a square wave oscillator since such oscillators may be fabricated more cheaply than sinusoidal oscillators in the audio frequency range.
- a source of D.C. voltage 11 may be provided in series with the oscillator 10.
- the source of D.C. voltage 11 is not necessary, but is advisable, when a square wave generator is employed, but is necessary when a sinusoidal generator is employed.
- a mechanically resonant filter 12 is connected to the generator 10 via a key switch 13, operated by a key of an electronic organ.
- Mechanically resonant filter 12 has a fundamental response frequency equal to the fundamental frequency of the generator 10. Further the mechanically resonant filter 12 has a transient response frequency in a second mode, equal to about 6.3 times the fundamental frequency of the generator
- the Q of the resonator 12 is assumed to be approximately 50. Assuming that the generator 10' has a fundamental frequency of about 100 'c.p.s., an appropriate rise time will be available in the resonator 12 to provide simulation of the rise times of certain organ tones. For other organ tones a different rise time may be desirable and accordingly the Q of the resonator 12 may be adjusted to suit the application, in a manner to be described hereinbelow.
- Resonator 12 has a second mode transient response at 6.3 times the fundamental response, as has been above explained. This frequency approaches with reasonable closeness to a chiff frequency suitable for the fundamental frequency, although perfect chiff frequency should, according to some writers on the subject, be 5.5 times the fundamental frequency.
- the output of the resonator 12 is applied in parallel to two low Q band-pass filters.
- One of the filters, 14, which may be a band-pass filter having sufiicient width that it does not modify appreciably the response of the resonator 12, selects the fundamental response of the filter for further application in the tone generating system.
- the other filter, 15, selects the chiff component of the filter response
- the output of the filter 14 alone is applied to a harmonic generator 16, various examples of which are disclosed in the above mentioned Cunningham application.
- the spectrum generated by the harmonic generator 16 may be applied to a tone forming filter 17.
- the generator 16 and the filter 17 together form a tone simulating one or another of the tone types appropriate to electronic organs.
- the output of the tone filter 17 is applied to suitable amplification system 18, and is radiated acoustically by a loudspeaker or other analogous device 19.
- the output of the chili filter is applied to the input of the amplifier 18, so that the chiff plus the fundamental tone may be combined.
- Chiff is a tone component which is required to occur only at the onset of a tone and not at its decay and furthermore is a component which requires a relatively slow buildup and slow decay during the onset time of the main tone and does not occur during the steady state of the main tone. Accordingly, the resonator 12, in order to produce a chiff component of a generated tone is required to have peculiar characteristics, not normally found in resonators. Appropriate characteristics are inherent in resonators fabricated according to the present invention, and illustrated in FIGURES 2, 3 and 4 of the present invention.
- FIGURE 2 of the drawings there is illustrated a tuning fork configuration 20 having two tines 21 and 22 joined by a bridging element 23 at one end of the tines, the remaining ends of the tines being free to vibrate in the fiexural mode. While such a tuning fork may have many modes of vibration, at the center point 24 of the bridging element 23 all these modes of vibration have zero amplitude. Accordingly center point 24 is utilized as a mounting point for the tuning fork 20. Point 24 is suspended from a helical spring 25 which may extend vertically, in a mounted and operating tuning fork, and spring 25 may extend from the central point of a horizontally extending helical spring 26, the ends of which are secured to mounting posts 27, 28. Each tine is composed of a spring steel rod 29 which constitutes an extension of the piezoelectric rod 30, and is cemented thereto at point 31 for that purpose.
- Signal may be applied at terminal 33, and abstracted at terminal 39.
- the bridging element 23, when fabricated of metal may be utilized as a ground or common point for the system.
- tines of purely piezoelectric ceramic have a considerable variation of frequency with driving amplitude or driving voltage applied to terminal 33. This occurs because Youngs modulus for the material involved varies with strain. This is 1 an extremely undersirable property from the point of view of a music instrument. In order to reduce the impact of this property steel is used as a major portion of the tines.
- the piezoelectric element may have a length of 1.6. The remainder of the length being made up of spring steel.
- the length of the piezoelectric element may be reduced to .6" for example so that the major part of the time is spring steel.
- the total length of piezoelectric element employed is a function of the voltage sensitivity desired for the system, and the total length of piezoelectric element cannot be reduced indefinitely without seriously reducing the output of the system for a given signal input. A compromise value must be reached, for which variation of resonance frequency is acceptable. Where variation of resonant frequency of the order of 1 /2 is acceptable the entire tine may be fabricated of piezoelectric material, as in FIG- URE 3, where the tines 40 and 41 are no longer composite tines but are totally piezoelectric.
- the electrodes 42, 43 for the time 40* and 44, 45 for the tine 41 do not extend over the entire piezoelectric body. Accordingly, while the entire tine is made of piezoelectric material, and has a length resonant to the frequency involved, the entire tine is not electrically active.
- the theory on which is based the effectiveness of reduced electrical length for a piezoelectric vibrator is that for all modes above the first the crystal has both positive and negative curvature. The phase of the output voltage generated by the crystal is dependent upon the sign of the curvature. Thus there is a point along the crystal at which the voltage caused by the positive curvature of the crystal cancels the voltage caused by the negative curvature of the crystal.
- any given mode can be reduced by a factor of over 30 db, and for some electrode lengths a great many of the higher modes may be radically reduced simultaneously.
- the third mode can be reduced over db the 4th mode over db, the 5th mode over 50 db, while the first mode is attenuated only about 7 or 8 db and the second mode only about 20 db.
- the second mode is often desirable but the remaining modes are undesirable. Accordingly, the fact that the second mode cannot be radically reduced is not of serious import. However, if it were desired to highly attenuate the second mode also this might be possible by appropriately selecting the electrode length for one of the tines so as to minimize the second mode and for the other tine so as to minimize the remaining modes.
- FIGURE 3 wherein are shown loads 50 in the form of masses positioned so as to vary frequency.
- Each of the modes has a point at which vibration is a maximum.
- vibration amplitude is a maximum at the free end of the tine.
- the other modes it occurs at other points.
- FIGURE 2 is shown the utilization of mass loads 50 at the ends of the tine. This varies the frequency of the resonator in the fundamental or first mode.
- the total mass of the bridging element 23 is important because as this mass is varied the coupling between the tines is varied. Eventually a point is reached at which the coupling between the tines is sufliciently great that the two tines constitute critically coupled circuit. Such circuits, in their transient response, are quite dilferent than singly coupled circuits, under coupled circuits or overcoupled circuits.
- FIGURE 4a of the accompanying drawings is illustrated the transient response of an essentially singly resonant tube circuit to which has been applied a step voltage of the type illustrated in FIGURE 5.
- the oscillations rapidly attain a very high or maximum amplitude, when the step function commences, and decays as a function of time according to the Q of the resonator.
- Such a response is not suitable for the tonal characteristic known as chiff.
- the latter requires a gradually built up transient followed by a gradually decaying transient rather than a transient which builds up very suddenly and then decays.
- the transient response of a critically doubly tuned circuit which is illustrated in FIGURE 4b does approximate the envelope characteristic of cá, and accordingly the resonators of FIGURES 2 and 3 may be designed to provide appropriate transient characteristics for utilization in chiff generators by suitably coupling the tines. This may be best accomplished by suitably reducing or increasing the mass of the bridging element 23, on an empirical basis.
- One of the important characteristics of the resonators of FIGURES 2 and 3 is the transient response of these filters in the second mode. This is a mode which is particularly, tough not exclusively, useful for production of chiff. The production of chitf requires a transient at onset on the main tone, but must not occur at decay of the main tone.
- a resonator of the type of FIGURE 2 has the requisite onset transient for the fundamental tone, but not for its decay relates to the character of the resonator.
- a transient occurs when the driving signal is removed, as well as when it is applied, assuming that the fundamenal frequency of the resonator is equal to or substantially equal to the driving frequency. If the driving frequency is not equal to the resonant frequency of the resonator, then as the driving frequency is switched on, the resonator is shock excited by the driving frequency, but is also driven by the driving frequency.
- the two frequencies initially exist together, causing a peculiar beating effect which is musically very pleasant.
- FIGURE 6 of the accompanying drawings represents a mechanical equivalent of a tuning fork.
- a step function i.e., may be applied a DC steady state voltage on closure of the switch 61.
- the driving tine of the resonator is exemplified by a resonator 62 having electrodes 63, 64.
- Mechanical coupling between the tines is exemplified by the line 65 and the driven tine is represented by the crystal 66, the output terminal being 67.
- the switch 61 is closed a voltage appears across the electrodes 63, 64, which is applied to the element 62.
- the resonator 62 is then shock excited and vibrates in its various modes, transiently.
- the coupling between the resonators 62 and 66 is so slight that the circuit looks like the singly coupled circuit to the driving step function.
- the piezoelectric elements of FIGURES 2 and 3 are flexural elements, which implies that each element is composed of two differently polarized ceramic layers in a sandwich.
- a ceramic piezoelectric device which operates in the longitudinal mode.
- This single layer, as at 70 in FIGURE 7 may be cemented to a tine 71 of a steel tuning fork 72 and may have a single electrode plated thereon as 73, the tine itself constituting another electrode, if desired, or two electrodes may be provided on the ceramic, as is commonly the case when the ceramics are purchased commercially.
- the ceramic is operated in the longitudinal mode, i.e., it has a length determined by the voltage applied thereto.
- FIG. 8 the output of the resonator 12, including its second overtone at approximately 6.3 times the fundamental, are applied in toto to the harmonic generator 16.
- the system being otherwise the same as in FIGURE 1.
- the harmonic generator 16 then generates harmonics of the cat frequency as well as harmonics of the steady state frequency and the chiff now is a relatively complex chiff instead of being essentially a single frequency chiff.
- the advantage of the system of FIGURE 8 over the system of FIGURE 1 is that two filters are eliminated from the system of FIGURE 1 and the disadvantage is that the chitf component is not a pure tone, which it preferably should be.
- Chiff is normally employed with pure flue tones, although various forms of chitf may also occur with other tones.
- For the pure flute tone very few harmonic tones are required, and accordingly any harmonics provided by the harmonic generators may be of very low amplitude, or may be nonexistent. Accordingly, for flute tones in particular, the requirement for separate fundamental and chiff filters becomes nonexistent and the system of FIGURE 8 becomes entirely practical.
- Resonator 12a is designed to have a minimum second mode as well as minimum 3rd, 4th, 5th mode, etc.
- Resonator 12b is tuned to about 5.5 times the fundamental frequency and also is designed to minimize all modes other than the fundamental mode.
- the resonator 12b is then shock excited, when switch 13 is closed, since the driving frequency provided by the oscillator contains no component at 5.5 times the fundamental.
- the resonator 12a is driven in the fundamental mode.
- the resonator 12b provides a transient at 5.5 times the fundamental frequency on onset of the tone, i.e., when the key switch 13 is closed, but, because of the considerations explained by reference to FIGURE 6 of the drawings, there is no terminating transient.
- two resonators are employed, identified by the reference numerals 12c and 12d. These are designed to have the same fundamental frequency. However the resonator 120 is designed to minimize the second mode, while the resonator 12d is designed to provide a substantial second mode oscillation.
- the resonator 12d is not excited by the generator 10 in the system of FIGURE 10 but is excited by a DC source 60 which is connected to the resonator 12d by means of a key switch 61 ganged to the key switch 13.
- the resonator 12d is an overcoupled tuning fork which is designed to produce an envelope of transient response appropriate to chifl production.
- the transient response of the resonator 12d then is composite, i.e., there is a transient response at the fundamental and there is a transient response in the second mode, but there is no steady state response.
- the resonator 12c produces only a fundamental response, or produces other than fundamental mode responses which are greatly reduced in amplitude, and produces its own transient onset and decay for the fundamentals.
- the resonator 12d provides no transient on decay but only at onset, i.e., any transient on decay is so slow as to be audibly ineffective.
- the advantage of the system of FIG- URE 10 is that the two resonators may be similar in many of their constructional features, which simplifies fabrication.
- a further advantage is that two different fundamental transient responses occur, at onset, which enhances the transient response of the finally generated tone. This system also enables easy selection of a desired chifi frequency.
- FIGURE 11 is similar to FIGURE 10 except in that the resonator He is operated in its second mode, i.e., is resonant in its fundamental mode to 5.5 times the frequency of generator 10.
- the output of resonator 12e is a transient, since it is excited only by a chiff function.
- FIG- URES 2, 3 and 7 Various other applications of the resonators of FIG- URES 2, 3 and 7 may be envisaged, particularly by reference to the Wayne and the Cunningham application-s, wherein are disclosed various forms of tone generating systems employing resonators.
- a mechanically resonant band-pass high Q filter comprising a tuning fork including a first tine, a second tine, a metallic bridging element joining adjacent first ends of said tines, each of said tines comprising a ceramic piezoelectric rod, said bridging element mechanically coupling said rods, each of said piezoelectric rods including a pair of electrodes, terminals for applying driving signal connected only to one of said pairs of electrodes, and
- terminals for acquiring output signal connected only to the other of said pairs of electrodes.
- a mechanically resonant band-pass high Q filter comprising a tuning fork including a first tine, a second tine, a metallic bridging element joining adjacent first ends of said tines, each of said tines comprising a ceramic piezoelectric rod, said bridging element mechanically coupling said rods, each of said piezoelectric rods including a pair of electrodes, terminals for applying driving signal connected only to one of said pairs of electrodes, and terminals for acquiring output signal connected only to the other of said pair of electrodes, wherein said electrodes extend for less than the total lengths of said rods commencing at said bridging elements, each of said tines including a length of piezoelectric material having electrodes and a substantial length of piezoelectric material having no electrodes, the length of said electrodes with respect to the lengths of said rods being selected to selectively eliminate the magnitudes of preselected vibratory mode responses of said rods.
- a mechanically resonant band-pass high Q filter comprising a tuning fork including a first tine, a second tine, a metallic bridging element joining adjacent first ends of said tines, each of said tines comprising a ceramic piezoelectric rod, said bridging element mechanically coupling said rods, each of said piezoelectric rods including a pair of electrodes, terminals for applying driving signal connected only to one of said pairs of electrodes, and terminals for acquiring output signal connected only to the other of said pairs of electrodes, wherein a length of further metallic rod is secured as an extension to each of said piezoelectric rods, the relative lengths of said further metallic rods and said piezoelectric rods being selected to eliminate undesired vibratory modes, to control the Q of said filters, and to reduce the variation of Q with amplitude of driving signal which is characteristic of ceramic piezoelectric rod.
- a mechanical resonator system comprising a ceramic piezoelectric tuning fork having a fundamental steady state response and a transient response at approximately 5 .5 times the frequency of said fundamental when excited by a signal devoid of a steady state alternating current component at approximately 5.5 times the frequency of said fundamental, wherein said tuning fork includes a direct current capacitive drive circuit, and means for generating said transient response only on direct current energization of said driver and not on steady state deenergization thereof, said last means including a slow resistive discharge circuit for said capacitive drive circuit.
- a tuning fork filter including tines each at least including ceramic piezoelectric elements having electrodes,
- said bridging element being metallic
- the total mass of said bridging element being selected to provide critical coupling between said tines, whereby the tuning fork filter possesses the electrical characteristics of a critically double tuned circuit.
- a piezoelectric tuning fork comprising two tines
- each of said tines being a piezoelectric rod having two electrodes located respectively on opposite sides thereof, and
- each of said piezoelectric rods being constituted of a spring steel rod secured to said piezoelectric rod.
- a piezoelectric chiff generator for an electric organ comprising a two tined piezoelectric tuning fork having critical mechanical coupling between the tines of said tuning fork,
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Description
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
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US30306063A | 1963-08-19 | 1963-08-19 |
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US3437850A true US3437850A (en) | 1969-04-08 |
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US303060A Expired - Lifetime US3437850A (en) | 1963-08-19 | 1963-08-19 | Composite tuning fork filters |
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Cited By (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US3683213A (en) * | 1971-03-09 | 1972-08-08 | Statek Corp | Microresonator of tuning fork configuration |
US4773493A (en) * | 1986-07-01 | 1988-09-27 | Sensor International | Vibration type measuring apparatus |
US6507141B2 (en) * | 1999-09-15 | 2003-01-14 | Bei Technologies, Inc. | Inertial rate sensor tuning fork |
US20150101404A1 (en) * | 2012-08-28 | 2015-04-16 | Dingding Chen | Sensor characterization apparatus, methods, and systems |
US9514725B1 (en) * | 2015-07-31 | 2016-12-06 | Joseph A. Brandstetter | Musical instrument |
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US3354413A (en) * | 1961-11-13 | 1967-11-21 | Kokusai Electric Co Ltd | Electromechanical filter for low frequencies |
US3141100A (en) * | 1962-06-21 | 1964-07-14 | Avco Corp | Piezoelectric resonance device |
US3336529A (en) * | 1962-12-03 | 1967-08-15 | Lockheed Aircraft Corp | Vibrating reed frequency responsive device |
US3345588A (en) * | 1964-11-12 | 1967-10-03 | Gen Instrument Corp | Annular piezoelectric filter with arcuate electrodes |
Cited By (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US3683213A (en) * | 1971-03-09 | 1972-08-08 | Statek Corp | Microresonator of tuning fork configuration |
US4773493A (en) * | 1986-07-01 | 1988-09-27 | Sensor International | Vibration type measuring apparatus |
US6507141B2 (en) * | 1999-09-15 | 2003-01-14 | Bei Technologies, Inc. | Inertial rate sensor tuning fork |
US20150101404A1 (en) * | 2012-08-28 | 2015-04-16 | Dingding Chen | Sensor characterization apparatus, methods, and systems |
US9857279B2 (en) * | 2012-08-28 | 2018-01-02 | Halliburton Energy Services, Inc. | Sensor characterization apparatus, methods, and systems |
US9514725B1 (en) * | 2015-07-31 | 2016-12-06 | Joseph A. Brandstetter | Musical instrument |
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