RESONATOR DEVICE
20230366755 · 2023-11-16
Inventors
- Emilie Courjon (Franois, FR)
- Florent Bernad (Besançon, FR)
- Thierry LaRoche (Besançon, FR)
- Julien Garcia (Chamblay, FR)
- Alexandre Clairet (Misereux Salines, FR)
- Sylvain Ballandras (Besançon, FR)
Cpc classification
G01L1/26
PHYSICS
International classification
Abstract
A resonator device for measuring stress comprises at least two resonators, each resonator comprising an inter-digitated transducer structure arranged between two reflecting structures on or in a piezoelectric substrate, wherein the at least two resonators are arranged and positioned such that they have two different wave propagation directions, and each resonator comprises at least two parts with the area between the two parts of the at least two resonators forming a cavity, wherein the cavity is shared by the at least two resonators and wherein for at least one resonator, in particular, all resonators, the inter-digitated transducer structure comprises a first material and the reflecting structures a second material different from the first material and/or the inter-digitated transducer structure and the reflecting structures have different geometrical parameters. A differential sensing device comprises at least one resonator device as described herein.
Claims
1. A resonator device for measuring stress, comprising: at least two resonators, each resonator comprising an inter-digitated transducer structure arranged between two reflecting structures on or in a piezoelectric substrate; wherein the at least two resonators are arranged and positioned such that they have two different wave propagation directions, wherein each resonator comprises at least two parts with an area between the two parts of the at least two resonator forming a cavity, wherein the cavity is shared by the at least two resonators, and and wherein, for at least one resonator, the inter-digitated transducer structure comprises a first material and the reflecting structures comprise a second material different from the first material and/or the inter-digitated transducer structure and the reflecting structures have different geometrical parameters.
2. The resonator device of claim 1, wherein the acoustic impedance ρC.sub.ref of the second material and the acoustic impedance ρC.sub.sub of the piezoelectric substrate are matched, such that
3. The resonator devic of claim 1, wherein the first material and the second material are metals.
4. The resonator device of claim 3, wherein the reflective structure comprises a plurality of metallic strips electrically isolated from each other.
5. The resonator device of claim 4, wherein the second material and its crystal orientation and the material of the piezoelectric substrate and its crystal orientation are such that the electrical and mechanical contribution to acoustic wave reflection are out of phase.
6. The resonator device of claim 1, wherein the second material is a dielectric material.
7. The resonator device of claim 1, wherein each of the at least two parts of the at least two resonators comprises at least one reflecting structure and a part of the inter-digitated transducer structure of the corresponding resonator.
8. The resonator device of claim 1, wherein the inter-digitated transducer structure of the resonator comprises inter-digitated comb electrode, and wherein for at least one transducer structure of the at least two resonators the inter-digitated comb electrode are defined by the Bragg condition given by p = λ/2, λ being the operating acoustic wavelength of the transducer structure and p being the electrode pitch of the transducer structure.
9. The resonator device of claim 1, wherein the two different wave propagation directions form an angle Θ with each other, Θ being equal to ±90° or smaller.
10. The resonator device of claim 1, wherein the electrode of the inter-digitated transducer structure of the one resonator are electrically connected with the electrodes of the transducer structure of the other resonator in a differential way.
11. The resonator device of claim 1, wherein at least one of the resonators is arranged and positioned such that its wave propagation direction is parallel to one of the crystalline axis of the piezoelectric substrate.
12. The resonator device of claim 1, wherein at least one of the resonators is arranged and positioned such that its wave propagation direction makes an angle Ψ equal to ±45° to one of the crystalline axis of the piezoelectric substrate.
13. The resonator device of claim 1, wherein at least a part of the surface of the cavity is metalized.
14. The resonator device of claim 8, wherein the metalization of the cavity comprises at least one grating.
15. A differential sensing device comprising at least one resonator device according to claim 1.
16. The differential sensing device of claim 15, wherein the propagation direction of one of the resonators is parallel or perpendicular to a radial direction to sense a radial force, or wherein the propagation direction of one of the resonators is at an angle with respect to a radial direction to sense a tangential force.
17. The differential sensing device of claim 16, wherein the propagation direction of one of the resonators is parallel or perpendicular to a radial direction to sense a radial force, and wherein the propagation direction of one other resonator is at an angle with respect to a radial direction to sense a tangential force.
18. The differential sensing device of claim 16, wherein the at least two differential resonator devices are provided on the same piezoelectric substrate (406).
19. The differential sensing device of claim 17, wherein the at least two differential resonator devices are provided on the same piezoelectric substrate.
20. The resonator device of claim 1, wherein, for all the of the at least two resonators, the inter-digitated transducer structure comprises a first material and the reflecting structures comprise a second material different from the first material and/or the inter-digitated transducer structure and the reflecting structures have different geometrical parameters.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0040] The present disclosure may be understood by reference to the following description taken in conjunction with the accompanying figures, in which reference numerals identify features of the present disclosure.
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DETAILED DESCRIPTION
[0060] The present disclosure will now be described in more detail using advantageous embodiments in an exemplary manner and with reference to the drawings. The described embodiments are merely possible configurations and it should be kept in mind that the individual characteristics as described above can be provided independently of one another or can be omitted altogether during the implementation of the present disclosure.
[0061]
[0062] In
[0063] According to the present disclosure, the strips are made from a second material different to the material used for the IDT 208a, 208b. The second material can be another type of metal, in particular, Pt, W, Mo or Ta. According to a variant the second material can be a dielectric. According to a variant, the dielectric material can be aluminum oxide (Al.sub.2O.sub.3) or gallium nitride (GaN) or aluminum nitride (AlN) or langasite (LGS) or lithium niobate (LiNbO.sub.3) or lithium tantalate (LiTaO.sub.3) or tantalum oxide (Ta.sub.2O.sub.5) or silicon dioxide (SiO.sub.2).
[0064] Here, the reflecting structures 212, 214, 216, 218 are arranged with a gap from the inter-digitated transducer structures 208a, 208b, 210a, 210b. In a variant of the present disclosure, no gap can be present between the reflecting structures and the transducer structure, so that the reflecting structure can be considered as continuing the inter-digitated transducer periodic structure in a synchronous, i.e., with the same period and same aspect ratio, or non synchronous way. The geometrical parameters of the reflective structure can be different compared to the IDT. That is, aspect ratio a/p and/or height h or pitch p could be different between IDT and reflecting structure to optimize the behavior of the resonator.
[0065] In another variant, the at least one of the reflecting structures 212, 214, 216, 218 comprises more than one reflector, wherein the reflectors can have the same number of strips 220 or not.
[0066] In the variant of the present disclosure, when using metallic strips 220 in the reflecting structures 212, 214, 216, 218 can be connected to each other, thus shortened. This can result in an improvement of the reflection coefficient of the reflecting structures at the Bragg condition compared to electrically isolated reflecting structures. At the Bragg condition, the reflected waves due to electrical and mechanical loading are in phase so that an improved reflection coefficient of the reflector at the Bragg condition results in a better detection of the reflected waves by the corresponding transducer structure. However, situation exists in which it can be preferred to isolate the metallic strips to prevent destructive interference between the mechanical and the electric contribution to the reflectivity.
[0067] The transducer structures 208a, 208b, and the transducer structures 210a, 210b each comprise two inter-digitated comb electrodes 224a, 226a, 224b, 224b and 240a, 242a, 240b, 242b. The electrodes 224a, 226a, 224b, 224b and 240a, 242a, 240b, 242b are formed of any suitable conductive metal, for example, aluminum or aluminum alloy, as long as they are different compared to the reflecting structures. In
[0068] The transducer structures 208a, 208b and 210a, 210b are also defined by the electrode pitch p (not shown), corresponding to the edge-to-edge distance between two neighboring electrode fingers from opposite comb electrodes 224a, b and 226a, b and 240a,b and 242a,b. In a variant of the present disclosure, the electrode pitch p is defined by the Bragg condition given by p = λ/2, λ being the operating acoustic wavelength of the reflecting structures 212, 214. By operating acoustic wavelength λ, one understands λ being the acoustic wavelength following λ = V/f with f the predetermined central frequency of the resonator structure and V the phase velocity of the utilized mode. Such transducer structure, as shown in
[0069] In a variant of the present disclosure, the inter-digitated transducer structures 208, 210 can operate out of the Bragg conditions, for instance, using a 3 or 4-finger-per-wavelength excitation structure or 5 -finger-per-two-wavelength transducers or 7 or 8 finger-per-three wavelength.
[0070] The transducer structures 208a, 208b and 210a, 210b can be symmetrical, namely they have the same number of electrode fingers with the same characteristics. However, in a variant of the present disclosure, they can also be different, in particular, they can have a different number of electrode fingers and/or a different pitch p.
[0071] In a variant of the present disclosure, the inter-digitated transducer structures 208a, 208b and 210a, 210b can be tapered to reduce transverse modes.
[0072] The substrate 206 over or in which the resonators 202, 204 are provided is a piezoelectric bulk material, with crystallographic axis X, Y and Z as shown in
[0073] According to a variant of the present disclosure, the acoustic wave propagating substrate 206 on which the resonators 202, 204 and hence the transducer structures 208a, 208b and 210a, 210b and the reflecting structures 212, 214, 216, 218 are provided can be a composite substrate 206 or also called piezoelectric on insulator (POI) substrate. The composite substrate 206 comprises a layer of piezoelectric material of a certain thickness, formed on top of a base substrate. The piezoelectric layer by way of example may be lithium tantalate (LiTaO.sub.3) or lithium niobate (LiNbO.sub.3). One example of such is a LiTaO.sub.3 (YX1)/42° layer on SiO.sub.2 on a so called trap-rich polysilicon layer provided on a base substrate of Si(100). This type of substrate typically has a piezoelectric layer with thickness 600 nm, a SiO.sub.2 layer of 500 nm and a trap-rich polysilicon layer of 1 .Math.m. This POI substrate is particularly well suited for shear waves, longitudinal waves become accessible when using LiTaO.sub.3 (Yxlt)/42°/90° as top layer. A trap-rich layer can improve the isolation performance of the base substrate and may be formed by at least one of polycrystalline, amorphous, or porous materials such as, for instance, polycrystalline Silicon, amorphous Silicon, or porous Silicon. Under the term “trap-rich” one understands a layer that can absorb electrical charges without, however, forming a conductive layer.
[0074] According to the present disclosure, the resonators 202, 204 are positioned on the substrate 206 so that they have two different surface acoustic wave propagation directions but due to cross like arrangement of the two resonators 202, 204, they are sharing at least partially the same area on the substrate 206.
[0075] In this embodiment, the first resonator 202 is positioned so that its direction of propagation of acoustic wave is in the crystallographic direction X of the acoustic wave propagating substrate 206. In
[0076] In this embodiment, besides their wave propagation direction, the resonators 202, 204 have the same geometrical structure, meaning that their transducer structure 208a, 208b and 210a, 210b, respectively, and the reflecting structures 212, 214, 216, 218 have the same designs and/or dimensions. In a variant of the embodiment, they can have a different design, e.g., different dimensions and/or different geometry. For example, the reflecting structures 212, 214, 216, 218 can be different but the transducer structures 208a, 208b and 210a, 210b are the same or vice-versa or both the reflecting structures 212, 214, 216, 218 and the transducer structures 208a, 208b and 210a, 210b can be different.
[0077] In this embodiment, the resonators 202, 204 are split into two parts, each part of a resonator being separated from the other part by a certain distance d1, d2, respectively.
[0078] The cavity 222 located in between the split parts 202a, 202b and 204a, 204b of the two resonators 202, 204, with its dimensions defined by the distances d1 and d2, corresponds to an acoustic cavity 222, in particular, a resonant acoustic cavity 222. In
[0079] In this embodiment, the two split parts 202a, 202b of the resonator 202 are symmetrical in regards to the cavity 222 and identical to each other so that the cavity 222 is actually located in the center part of the resonator 202. In a variant of the embodiment, the two split parts 202a, 202b of the resonator 202 are not identical and/or symmetric in regards of the cavity 222.
[0080] In this embodiment, furthermore, the two split parts 204a, 204b of the resonator 204 are also symmetric in regards to the cavity 222 and identical to each other so that the cavity 222 is actually located in the center part of the resonator 204. Thus, in
[0081] In this embodiment, furthermore, the split parts 202a, 202b and 204a, 204b of both resonators 202, 204 are symmetric in regards to the cavity 222 and identical. In a variant of the embodiment, the split parts 202a, 202b and 204a, 204b of the resonators 202, 204 are not identical and/or symmetric in regards of the cavity 222.
[0082] The resonators 202, 204 are split in a manner so that actually, the transducer structure of the resonator is split into two parts 208a and 208b and 210a and 210b. Thus, each split part 202a, 202b, 204a, 204b of the resonators 202, 204 actually comprises a reflecting structure and a split part of the transducer structure of the respective resonator. Hence, the split part 202a of the resonator 202 comprises the reflecting structure 212 and the split part 208a of the transducer structure. The split part 202b of the resonator 202 comprises the reflecting structure 214 and the split part 208b of the transducer structure. The split part 204a of the resonator 204 comprises the reflecting structure 216 and the split part 210a of the transducer structure. The split part 204b of the resonator 204 comprises the reflecting structure 218 and the split part 210b of the transducer structure.
[0083] In a variant of the embodiment, the resonator is split in between one reflecting structure and the transducer structure. Thus, one split part of the two split parts of the resonator comprises the entire transducer structure with one reflecting structure and the other part the other reflecting structure.
[0084]
[0085] Unlike in the first embodiment, both resonators 202, 204 of the surface acoustic wave sensor 300 are now positioned at an angle Ψ to the acoustic propagation direction X of the piezoelectric substrate 306 in comparison with the surface acoustic wave device 200 of the first embodiment. This is the only difference with respect to the first embodiment.
[0086] Thus, the propagation direction of the acoustic wave for the resonator 202 is rotated by an angle Ψ compared to the crystallographic direction X of the acoustic wave propagating substrate 306.
[0087] The resonator 204 is still positioned on the acoustic propagating substrate 206 at an angle Θ = 90°. In a variant of the embodiment, another value of Θ different to 90°, for example, smaller than 90°, could be used, which would enable to correct effects such as beam steering.
[0088]
[0089] In this embodiment, the comb electrodes 224a, 242a, 226b and 240b are electrically connected by the conductive line 356 and the comb electrodes 224b, 242b, 226a and 240a are electrically connected by the conductive line 358 to form a differential arrangement. The resonators 202, 204 are here connected in parallel and the resonator device 350 operate at resonance.
[0090] In a variant of the present disclosure, the two resonators can be connected in series and the resonator device would operate at anti-resonance operation.
[0091] The resonator device 350 according to the third embodiment allows to position a test area in the central cavity shared by both resonators and to conduct a measure at the same location by the two resonators, yielding an improvement in the measurement quality and also a better immunity to parasitic stress effects compared to the state of the art device described in
[0092] In
[0093] Sensing of the change of the difference frequency Δf permits suppression of a number of common-mode interference factors and, reduce variations due to a temperature, which should cancel out in the differential sensing arrangement.
[0094]
[0095] In this embodiment, the comb electrodes 224a, 242a, 226b and 240b are electrically connected by the conductive line 376 and the comb electrodes 224b, 242b, 226a and 240a are electrically connected by the conductive line 378 to form a differential arrangement. The resonators 202, 204 are here connected in parallel and the resonator device 370 operate at resonance.
[0096] In a variant of the present disclosure, the two resonators can be connected in series and the resonator device would operate at anti-resonance operation.
[0097] The resonator device 370 according to the fourth embodiment allows to position a test area in the central cavity shared by both resonators and to conduct a measure at the same location by the two resonators, yielding an improvement in the measurement quality and also a better immunity to parasitic stress effects compared to the state of the art device described in
[0098] In
[0099] The resonators 202, 204 of the SAW device 370 are laid down on a piezoelectric substrate206 so that the surface acoustic waves propagate at an angle Ψ of ±45° relative to the crystallographic X axis of the piezoelectric substrate 206. At this angle, the contribution of temperature variations of third order elastic constants of the substrate 206 to the temperature variation of the Force sensitivity, is substantially equal and opposite to the sum total of variations in linear temperature coefficient of expansion, non-zero third order elastic constants, temperature variation of contributions caused by first order elastic constants, and temperature variations of substrate density. Thus, the resonator device 370 achieves a reduction of tangential force sensitivity variation with temperature.
[0100] The resonator device according to the present disclosure thus operates as a differential sensor in differential mode to segregate the two considered mechanical effects of radial, see
[0101]
[0102] The electrical admittance graph plots the conductance (S) and the susceptance (S) on the right and left Y axis, respectively, in function of the frequency (MHz) on the X axis. As two resonators are present, two resonance peaks are visible in the electrical admittance graph, slightly above 434 MHz and slightly above 434.3 MHZ, respectively, for both the real part of the admittance (conductance G) and the imaginary part of the admittance (susceptance B). The two resonance peaks are balanced to approach a 50 Ω matching within the 434 MHz centered ISM-band.
[0103] When a radial force is applied to the device, as in the third embodiment of the present disclosure as shown in
[0104] In contrary to the state of the art, the resonators 202 and 204 have a common cavity 222, which corresponds to the location where the measurement is made for both resonators 202, 204. Thus, both resonators will measure at the same location and a more accurate value of the applied force will be obtained, compared to the value obtained with a state of the art device as shown in
[0105] When, in addition, different materials are used for IDT and reflecting structures the size of the device can be reduced as the reflectivity can be independently optimized compared to the properties of the IDT.
[0106]
[0107] In
[0108] In the embodiment of
[0109] Both quartz dices 402, 404 are positioned on an object 406, in order to measure e.g., the stress generated by tangential and radial forces on the object 406. In
[0110] The quartz dices 402, 404 are glued onto the object 406, which comprises a steel plate at that position, with cyano-acrylate glue (M-bond 200) but any other glue or solid state attachment techniques could be used.
[0111] The resonators 202, 204 are split into two parts, as described in the third and fourth embodiment, so that the differential sensors 350 and 370 each comprises a central cavity 222, shared by the two resonators 202, 204 of each sensor 350, 370.
[0112] In this embodiment, the differential sensor 370 is configured to measure the stress on the object 406 due to the tangential forces while the other differential sensor 350 is configured to measure the stress on the object 406 due to radial forces as explained above.
[0113] Both differential sensors 350, 370 are connected to an antenna 410, to transmit the measurements. In a variant of the embodiment, each differential sensor can have its own antenna.
[0114] According to the present disclosure, the stress resulting from the forces applied to the object 406 and sensed by the sensors 350, 370 is measured at the same location at the central cavity 222 for each sensor 350, 370, yielding an improvement in the measurement quality and a better immunity to parasitic stress effects.
[0115] In a variant, the sensing device 400 can comprise more than two differential sensors according to the present disclosure.
[0116] In another variant of the present disclosure, the sensing device 400 can be applied to any other object, and not only a wheel, in order to measure concomitantly the stress due by the radial and tangential forces experienced by the object. Other physical parameters, outside of stress, can also be measured with the sensing device 400. For example, torsional effects and torque can also be measured or any other physical parameter not related to stress.
[0117] In another variant of the present disclosure, the sensing device 400 can measure the stress due by the radial and tangential forces experienced by the object at the same location. The four resonators of the sensing device would share the same resonant cavity.
[0118]
[0119] The electrical admittance graph plots the conductance (in Siemens - S) and the susceptance (in S) on the right and left Y axis, respectively, in function of the frequency (MHz) on the X axis. As two differential sensors are present, each comprising two resonators, four resonance peaks are visible in the electrical admittance graph, slightly above and below 434 MHz, for both the real part of the admittance (conductance G) and the imaginary part of the admittance (susceptance B). The resonance peaks of each resonator are balanced to approach a 50 Ω matching within the 434 MHz centered ISM-band.
[0120]
[0121] The basic structure corresponds to the one of the first embodiments and only the differences with respect to that one will be described. Thus, the features common with the first embodiment of
[0122]
[0123] The resonator device 500 as described in this variant enables to manage parasites due to directivity effects.
[0124]
[0125] The resonator device 600 as described in this variant enables to manage parasites due to directivity effects.
[0126]
[0127] Furthermore, the split parts of the resonators 702, 704 are also different and not symmetric with regards to the cavity 722, as the reflecting structures 712, 714 and 716, 718 are not identical within a resonator 702, 704, respectively. For the resonator 702, the reflecting structure 714 comprises more strips 220 as the reflecting structure 712 (same thing for the resonator 704). The strips 220 are also connected to each other. In a variant, they can also not be connected to each other.
[0128] Here, like in the second variant of the first embodiment, the split part of a resonator comprises a reflecting structure alone and the other split part of the resonator comprises the full transducer structure and the other reflecting structure adjacent the transducer structure. Again, the cavity 722 is not central within the resonators 702, 704, but is still shared by the two resonators 702, 704.
[0129] The resonator device 700 as described in this variant enables to manage parasites due to directivity effects.
[0130]
[0131] The strips 220 of the reflecting structures 712, 714 and 716, 818 are also connected to each other. In a variant, they can also not be connected to each other.
[0132] The resonator device 800 as described in this variant enables to manage parasites due to directivity effects.
[0133]
[0134] Again, the strips 220 of the reflecting structures 212, 214 and 216, 218 are also connected to each other. In a variant, they can also not be connected to each other.
[0135] The resonator device 900 as described in this variant enables to filter or select the possible modes of the structure or even allow to operate in a coupled mode configuration.
[0136]
[0137] Again, the strips 220 of the reflecting structures 212, 214 and 216, 218 are also connected to each other. In a variant, they can also not be connected to each other.
[0138] The surface acoustic wave device 1000 as described in this variant enables to filter or select the modes of the structure or even enables to operate in a coupled mode configuration.
[0139]
[0140] In this variant, the reflecting structures of the resonators 1102, 1104 comprises a plurality of reflectors, each comprising more or less strips 1120. In this variant, the resonators 1102, 1104 are SAW tag devices. SAW tag devices are sensors, which can be remotely interrogated, providing a wireless measurement of a physical quantity. Whatever this physical quantity is, it is better to put in place differential measurement to guarantee the measurement of an absolute physical quantity or to suppress correlated external perturbations affecting the sensor.
[0141] Two SAW-tags are used in a way that only the two first echoes are used to determine the stress value, the other echoes may be used as identification marks and/or as other physical effect markers (for instance, temperature).
[0142] The SAW tag device 1102 comprises a transducer structure 1108, in particular, only one transducer structure, and a set of reflectors 1114, 1116 and 1118, positioned at various delays on one side of the transducer structure 1108 in the direction of propagation X as shown in
[0143] The SAW tag device 1104 is the same as the SAW tag device 1102 but its set of reflectors 1114, 1116, 1118, positioned at various delays on one side of the transducer structure 1110 in the direction of propagation Y as shown in
[0144] The SAW tag 1102, 1104 is actually split in two parts 1102a and 1102b, 1104a and b, between the inter-digitated transducer structures 1108, 1110 and the first reflector 1116, so that one part of the split SAW tag 1102a, 1104a comprises the set of reflectors 1114, 1116, 1118 or delay line and the other part 1102b, 1104b of the SAW tag 1102, 1104 comprises only the inter-digitated transducer structure 1108, 1110.
[0145] The inter-digitated transducer structures 1108, 1110 are operating at Bragg conditions but could operate out of this condition, the reflectors 1114, 1116 and 1118 are in open circuit mode. The distances L11, L12, L13 and L21, L22 and L23 between the reflectors 1114, 1116 and 1118 and the transducer structure 1108, 1110 are chosen in such a way the corresponding echoes are not overlapping on the whole measurement range. The cavity 1122 is shared by both resonators 1102, 1104 although not being centrally located in between the two resonators 1102, 1104, since the split parts 1102a and 1102b and the split parts 1104a and 1104b of both resonators 1102, 1104 are not the same and not symmetric to each other.
[0146] In the variant shown in
[0147] In the variant in
[0148] Again, the cavity 1222 is shared by both resonators 1202, 1204 although not being centrally located in between the two resonators 1202, 1204, since the split parts 1202a and b and the split parts 1204a and b of both resonators 1202, 1204 are not the same and not symmetric to each other.
[0149] The strips 1120 of the reflectors 1118, 1116, and 1114 are also connected to each other. In a variant, they can also not be connected to each other.
[0150] The resonator device 1500 as described in this variant measures the stress at the cavity 1422, which is located within the first transducer-reflector gap of the longest SAW-tag 1202. The cavity 1422 is defined by the gap L11 and L21. In another variant, one SAW tag can share more than one cavity with the other SAW tags or resonators. This would enable to measure a distribution of stress.
[0151]
[0152] The resonator device 1400 as described in this variant enables to increase the sensor sensitivity or more generally to optimize the sensor operation.
[0153]
[0154] The resonator device 1500 as described in this variant measures the stress at the cavity 1422, which is located anywhere else on the delay line of the resonators but between the first transducer-reflector gap, defined by the distance L11 and L21,of the longest SAW-tag 1202.
[0155] A number of embodiments of the present disclosure have been described. Nevertheless, it is understood that various modifications and enhancements may be made without departing from the scope of the invention as defined by the following claims.