One-port surface elastic wave resonator on high permittivity substrate

Abstract

A surface elastic wave resonator comprises a piezoelectric material to propagate the surface elastic waves and a transducer inserted between a pair of reflectors comprising combs of interdigitated electrodes and having a number Nc of electrodes connected to a hot spot and an acoustic aperture W wherein the relative permittivity of the piezoelectric material is greater than about 15, a product of Nc.Math.W/fa for the transducer being greater than 100 m.Math.MHz.sup.1, where fa is the antiresonance frequency of the resonator. A circuit comprises a load impedance and a resonator according to the invention and having an electrical response manifesting as a peak in the coefficient of reflection S.sub.11 at a frequency of a minimum value of the parameter S.sub.11 that is lower than 10 dB, the antiresonance peak of the resonator being matched to the impedance of the load.

Claims

1. A measurement system having a surface elastic wave resonator circuit comprising: at least one surface elastic wave resonator; at least one load impedance; and the at least one surface elastic wave resonator configured as a one-port surface elastic wave resonator and comprising: a piezoelectric material configured to propagate surface elastic waves; and at least one transducer inserted between a pair of reflectors, said at least one transducer comprising combs of interdigitated electrodes and said at least one transducer having a number Nc of the interdigitated electrodes, the interdigitated electrodes are connected to a hot spot and the interdigitated electrodes are configured to have an acoustic aperture W, wherein a product of Nc.Math.W/fa for said at least one transducer being greater than 100 m.Math.MHz.sup.1, where fa is an antiresonance frequency of said resonator; wherein the at least one surface elastic wave resonator having an electrical response manifesting as a peak in a coefficient of reflection S.sub.11 at a frequency characterized by a minimum value of a parameter S.sub.11 that is at least lower than 10 dB with a phase rotation greater than 120; wherein the at least one surface elastic wave resonator is configured to operate in antiresonance and the at least one surface elastic wave resonator is configured such that an antiresonance peak of said resonator is matched to the at least one load impedance; and wherein the at least one surface elastic wave resonator is configured as a remotely interrogable passive sensor.

2. The measurement system having a surface elastic wave resonator circuit according to claim 1, further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the piezoelectric material comprises langasite, and wherein the product of Nc.Math.W/fa being between 100 and 1000 m.Math.MHz.sup.1.

3. The measurement system having a surface elastic wave resonator circuit according to claim 1, further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the piezoelectric material comprises zinc oxide, and wherein the product of Nc.Math.W/fa being between 400 and 2000 m.Math.MHz.sup.1.

4. The measurement system having a surface elastic wave resonator circuit according to claim 1, further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the piezoelectric material comprises aluminum nitride AlN, and wherein the product of Nc.Math.W/fa being between 400 and 2000 m.Math.MHz.sup.1.

5. The measurement system having a surface elastic wave resonator circuit according to claim 1, further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the piezoelectric material comprises lithium tantalate LiTaOz, and wherein the product of Nc.Math.W/fa being between 100 and 1000 m.Math.MHz.sup.1.

6. The measurement system having a surface elastic wave resonator circuit according to claim 1, further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the piezoelectric material comprises lithium niobate, and wherein the product of Nc.Math.W/fa being between 1400 and 3000 m.Math.MHz.sup.1.

7. The measurement system having a surface elastic wave resonator circuit according to claim 1, further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the interdigitated electrodes are based on platinum or on titanium or on tantalum, or a mixture of some of the aforementioned metals.

8. The measurement system having a surface elastic wave resonator circuit according to claim 1, comprising a passivation layer that comprises a layer of alumina (Al.sub.2O.sub.3) or of silicon oxide or of silicon nitride or of aluminum nitride.

9. The measurement system having a surface elastic wave resonator circuit according to claim 1 wherein a first one of the at least one surface elastic wave resonator is connected in series with a second one of the at lei one surface elastic wave resonator.

10. The measurement system having a surface elastic wave resonator circuit according to claim 9, wherein the first one of the at least one surface elastic wave resonator and the second one of the at least one surface elastic wave resonator are connected in series to an antenna.

11. The measurement system having a surface elastic wave resonator circuit according to claim 1 being configured as a remotely interrogable passive differential temperature sensor.

12. A measurement system for interrogating a surface elastic wave resonator circuit comprising: interrogation means operating in a band of frequencies located between all of the following frequencies: 400 MHz and 450 MHz, 900 MHz and 950 MHz, and 850 MHz and 900 MHz; and a surface elastic wave resonator circuit comprising: at least one surface elastic wave resonator; and at least one load impedance; the at least one surface elastic wave resonator configured as a one-port surface elastic wave resonator and comprising: a piezoelectric material configured to propagate surface elastic waves; and at least one transducer inserted between a pair of reflectors, said at least one transducer comprising combs of interdigitated electrodes and said at least one transducer having a number Nc of the interdigitated electrodes, the interdigitated electrodes are connected to a hot spot and the interdigitated electrodes are configured to have an acoustic aperture W, wherein a product of Nc.Math.W/fa for said at least one transducer being greater than 100 m.Math.MHz.sup.1, where fa is an antiresonance frequency of said resonator; wherein the at least one surface elastic wave resonator having an electrical response manifesting as a peak in a coefficient of reflection S.sub.11 at a frequency characterized by a minimum value of a parameter S.sub.11 that is at least lower than 10 dB with a phase rotation greater than 120.sup.0; wherein the at least one surface elastic wave resonator is configured as a remotely interrogable passive sensor; and wherein the at least one surface elastic wave resonator is configured to operate in antiresonance and the at least one surface elastic wave resonator is configured such that an antiresonance peak of said resonator is matched to the at least one load impedance.

13. The measurement system for interrogating a surface elastic wave resonator circuit according to claim 12, further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the interrogation means operates only in the band of frequencies located between 900 MHz and 950 MHz.

14. The measurement system for interrogating a surface elastic wave resonator circuit according to claim 12, further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the interrogation means operates only in the band of frequencies located between 850 MHz and 900 MHz.

15. The measurement system for interrogating a surface elastic wave resonator circuit according to claim 12, further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the interrogation means operates only in the band of frequencies located between 400 MHz and 450 MHz.

16. The measurement surface elastic wave resonator circuit according to claim 1 further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the number Nc of the interdigitated electrodes and the acoustic aperture W are configured to operate in antiresonance.

17. The measurement system for interrogating a surface elastic wave resonator circuit according to claim 12 further comprising a radio frequency antenna connected to an input of the at least one transducer, wherein the number Nc of the interdigitated electrodes and the acoustic aperture W are configured to operate in antiresonance.

18. The measurement system for interrogating a surface elastic wave resonator circuit according to claim 12, wherein: the at least one surface elastic wave resonator is configured to be remotely interrogable via a radiofrequency wireless link, and the remotely interrogable passive sensor comprises at least one of the following: a pressure sensor or a temperature sensor.

19. The measurement system having a surface elastic wave resonator circuit according to claim 1, wherein: the at least one surface elastic wave resonator is configured to be remotely interrogable via a radiofrequency wireless link, and the remotely interrogable passive sensor comprises at least one of the following: a pressure sensor or a temperature sensor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will be better understood and other advantages will become apparent on reading the following description, which is given by way of non-limiting example, and from the appended figures in which:

(2) FIGS. 1a and 1b illustrate, respectively, the responses in terms of admittance as a function of frequency and the responses in terms of S.sub.11 parameters as a function of frequency for devices developed in the context of the SAWHOT program;

(3) FIG. 2 illustrates the response, in terms of S.sub.11 coefficient, of the SEAS10 sensor, showing peaks with a dynamic range of more than 15 dB but a phase rotation of only 80 to 120.

(4) FIG. 3a illustrates a one-port elastic wave resonator used in the present invention and FIG. 3b illustrates the equivalent circuit of a one-port elastic wave resonator;

(5) FIGS. 4a to 4c illustrate the analysis of the response of resonators connected in series and in parallel for a design that is optimized at resonanceC.sub.0=0.73 pF: FIG. 4a relates to impedance (modulus), maximized for the resonators connected in series; FIG. 4b relates to a zoom-in on the match at 50, the resonators connected in series having an impedance that is always higher than 50; FIG. 4c relates to the response in terms of modulus of the coefficient of reflection S.sub.11;

(6) FIGS. 5a and 5b illustrate the analysis of the response of resonators connected in series and in parallel for a design that is optimized at antiresonanceC.sub.0=73 pF: FIG. 5a relates to impedance (modulus), minimized by the resonators connected in parallel; FIG. 5b relates to the response in terms of modulus of the coefficient of reflection S.sub.11;

(7) FIGS. 6a and 6b characterize electromechanical coupling coefficients of each contribution for the two connection configurations: FIG. 6a relates to resonators in parallel: resonance operation;

(8) FIGS. 7a and 7b illustrate, respectively, the way in which the resonators connected in parallel may be arranged when they are operated (are interrogated) at resonance (a configuration referred to as a conventional configuration) and the connection for connecting the resonators in series.

DETAILED DESCRIPTION

(9) The Applicant describes the line of reasoning that lead him to the conditions for designing and adapting surface elastic wave resonators according to the present invention in more detail below.

(10) The one-port resonator of the invention may comprise, in a conventional manner, two combs with interdigitated metalizations having fingers of width a, of period p (defining a ratio referred to as the a/p metalization ratio which is equal to the width of the electrode over the repetition pitch of the electrodes) forming a surface elastic wave transducer T that is placed between two metalized reflective gratings R1 and R2. The combs are connected so as to have different polarities. The aperture W is defined by the length of overlap between two fingers of different polarity. The number of electrodes of the transducer that are connected to a hot spot is equal to Nc. FIG. 3a thus illustrates a one-port resonator with an aperture W typically potentially of about 40, showing the transducer T between two mirrors R1 and R2 having Ne electrodes, the transducer having a total number N+ of electrodes, the relative thickness of the electrodes being equal to h/=2p.

(11) In the case of a remotely interrogable passive sensor, the transducer is connected to an antenna. Thus, the resonator/antenna assembly has in particular been studied in the context of the present invention, at the level of the impedances of the antenna and of that of the resonator.

(12) It will be recalled that one-port elastic wave resonators may be likened to an equivalent circuit having a branch, referred to as a motional branch, including, in series, an inductor L.sub.m, a capacitor C.sub.m and a resistor R.sub.m, all of which are referred to as being motional, and a capacitor, referred to as a static capacitor C.sub.0, in parallel to this branch, as shown in FIG. 3b. This equivalent circuit is known to those skilled in the art by the name Butterworth-VanDyke circuit.

(13) The circuit may be accompanied by a resistor upstream of these two branches, referred to as the series or contact resistor, representing ohmic losses due to the connection of the resonator and a leakage resistor in parallel with the static capacitor, representing current leakages in the material if the latter is not perfectly dielectric (which may be the case in the event of ionic inclusions within the crystal lattice). Such an equivalent circuit is in particular described and used in patent application VECTRON-SENGENUITY E2287584A1-WO2011/020888A1 which relates to design criteria based on the values of equivalent motional components.

(14) The Applicant describes the line of reasoning that lead him to the conditions for designing and adapting surface elastic wave resonators according to the present invention in more detail below.

(15) The analysis that has been carried out and which is presented in the present patent application consists of calculating the admittance of the circuit formed by the response of a one-port surface wave resonator (SWR) and of evaluating the value of the impedance at antiresonance in order to derive generic design laws therefrom.

(16) By assuming that the resistance of the resistor R.sub.m is zero in a rough dimensioning step, it is shown that resonance and antiresonance angular frequencies are given by the following relationships:
.sub.r=(1/L.sub.m C.sub.m).sup.1/2 and .sub.a=[(C.sub.0+C.sub.m)/L.sub.mC.sub.mC.sub.0].sup.1/2(1)

(17) If it is possible to determine the capacitance of the static capacitor C.sub.0, it is then possible to obtain the capacitance and inductance of C.sub.m and of L.sub.m using the following relationships:

(18) $\begin{array}{cc}{C}_m=C_0\left(\frac{{}_a^2-{}_r^2}{{}_r^2}\right)C_0{k}_s^2& \left(2\right)\end{array}$
where ks.sup.2 is the electromechanical coupling coefficient given by the relative difference between the resonance and antiresonance frequencies, namely 2(fafr)/fr to a first approximation, as described in the article by Royer, E. Dieulesaint, Ondes acoustiques dans les solides (Acoustic Waves in Solids), volume 1, 1998, Masson Ed.

(19) The expression for the admittance of the equivalent circuit is such that:

(20) $\begin{array}{cc}Y\left(\right)={\mathrm{jC}}_0+\frac{{\mathrm{jC}}_m}{\left(1-L_m{C}_m{}^2\right)+{\mathrm{jR}}_m{C}_m}& \left(3\right)\end{array}$

(21) The resistance R.sub.m is given by the inverse of the real part of the admittance at the resonance:
Y(r)=1/Rm+j C0r

(22) The damping coefficient A is given by the ratio: Rm/2Lm, which allows the quality coefficient Q of the resonator to be estimated as:

(23) Q=/2A or else Q=.sub.rL.sub.m/R.sub.m, which allows the resistance of the resistor to be estimated from the quality coefficient of the resonator, and thus, broadly speaking, any electrical one-port resonator to be characterized (the coupling coefficient is easily measured if the resonance is spectrally well defined by the difference between resonance and antiresonance frequencies, a low-frequency measurement providing the static capacitor capacitance). It will be noted that the coefficient Q corresponds to the quality coefficient of the resonance according to the previously established definition. It is used below in order to simplify the text but its definition remains in accordance with that given above.

(24) By rewriting the admittance on the basis of equation (3), (4) is obtained:

(25) $\begin{array}{cc}Y\left(\right)=\frac{{\mathrm{jC}}_0\left(1-L_m{C}_m{}^2\right)+{\mathrm{jC}}_m-R_m{C}_m{C}_0{}^2}{\left(1-L_m{C}_m{}^2\right)+{\mathrm{jR}}_m{C}_m}& \left(4\right)\end{array}$

(26) Seeking to rationalize, as far as possible, by using relationships (1), the following is obtained:

(27) $\begin{array}{cc}Y\left(\right)=C_0\frac{j{L}_m\left({}_a^2-{}^2\right)-R_m{}^2}{L_m\left({}_r^2-{}^2\right)+{\mathrm{jR}}_m}& \left(5\right)\end{array}$

(28) The admittance may again be expressed by the following equation:

(29) $\begin{array}{cc}Y\left(\right)=C_0\frac{jQ\left({}_{}^2-{}^2\right)-{}^2{}_r}{Q\left({}_r^2-{}^2\right)+j{}_r}& \left(6\right)\end{array}$
in which all of the elements of the motional branch have disappeared in favor of the three objectively measurable parameters, namely the resonance and antiresonance angular frequencies and the quality coefficient at resonance, which are specific to the acoustic contribution and the static capacitor.

(30) The impedance is expressed on the basis of equation (6), and the following equation (7) is obtained:

(31) $\begin{array}{cc}Z\left(\right)=\left(\frac{1}{{\mathrm{jC}}_0}\right)\frac{Q\left({}_r^2-{}^2\right)+j{}_r}{Q\left({}_a^2-{}^2\right)+j{}_r}& \left(7\right)\end{array}$

(32) Once this expression has been established, it is possible to express the impedance at resonance and at antiresonance:

(33) $\begin{array}{cc}Z\left({}_r\right)=\left(\frac{1}{C_0{}_r}\right)\frac{1}{Q\frac{{}_a^2-{}_r^2}{{}_r^2}+j}.fwdarw.Z\left({}_r\right)=\left(\frac{1}{C_0{}_r}\right)\frac{1}{{\mathrm{Qk}}_s^2+j}.fwdarw.Y\left({}_r\right)=\left({\mathrm{Qk}}_s^2+j\right)C_0{}_r& \left(8\right)\\ Z\left({}_a\right)=-\frac{1}{C_0{}_a}\left(Q\frac{\left({}_r^2-{}_a^2\right)}{{}_a{}_r}+j\right).fwdarw.Z\left({}_a\right)=\left(\frac{1}{C_0{}_r}\right)\left(Q\frac{{}_a^2-{}_r^2}{{}_a^2}+j\right).fwdarw.Z\left({}_a\right)\frac{{\mathrm{Qk}}_s^2+j}{C_0{}_r}& \left(9\right)\end{array}$

(34) In both cases, the Applicant sought to estimate the capacitance of C.sub.0 for a modulus of the impedance equal to 50 (or of the admittance equal to 20 mS) in order to determine the structure of the transducer.

(35) In the case of the resonance and the antiresonance, respectively, this yields:

(36) $\begin{array}{cc}|Y\left({}_r\right)=C_0{}_r\sqrt{(Q^2}{k}_s^2+1)\mathrm{and}\left|Z\left({}_a\right)\right|\frac{\sqrt{{\mathrm{Qk}}_s^4+1}}{C_0{}_r}& \left(10\right)\end{array}$

(37) In both cases, it will be noted that if Q.Math.k.sub.s.sup.2 is much higher than 1, expressions (10) may be simplified as follows:

(38) $\begin{array}{cc}\left|Y\left({}_r\right)\right|=C_0{}_r{\mathrm{Qk}}_s^2=\frac{1}{R_m}.fwdarw.\left|Z\left({}_r\right)\right|=R_m\mathrm{and}\left|Z\left({}_a\right)\right|\frac{{\mathrm{Qk}}_s^2}{C_0{}_r}& \left(11\right)\end{array}$

(39) The following equation is also defined (MORGAN, David. Surface acoustic wave filters: With applications to electronic communications and signal processing. Academic Press, 2010.):
Y.sub.11()=Y.sub.T()G.sub.()+j(B.sub.()+C.sub.0)(12)
where G.sub.a is the acoustic conductance, B.sub.a is the susceptance and C.sub.T is the capacitance of the transducer.

(40) The imaginary part of the admittance is naturally combined with the contribution of the capacitance of the transducer, which is defined by a dominant electrical contribution.

(41) These values are given by the equations:

(42) 0$\begin{array}{cc}{G}_a\left(\right)G_a\left({}_0\right)|\frac{\sin \left(X\right)}{X}{|}^2& \left(13\right)\\ B_a\left(\right)G_a\left({}_0\right)\frac{\sin \left(2X\right)-2x}{2X^2}& \left(14\right)\\ C_0=\mathrm{NcW}{\mathrm{.Math.}}_{}\mathrm{where}{G}_a\left({}_0\right)=2.87{}_0{\mathrm{.Math.}}_{}W{N}_c^{2}v\text{/}v\mathrm{and}{\mathrm{.Math.}}_{}=\sqrt{{\mathrm{.Math.}}_{11}{\mathrm{.Math.}}_{33}-{\mathrm{.Math.}}_{13}^2}\left(\mathrm{for}\mathrm{quartz},{\mathrm{.Math.}}_{}=5.5\mathrm{.Math.}\right).& \left(15\right)\end{array}$

(43) The Applicant firstly considered the following form, because of its simplicity and its accuracy with respect to the complete form for a synchronous transducer operating under the Bragg condition:
C.sub.0=N.sub.cW.sub. with .sub.=.sub.0+{square root over (.sub.11.sub.33.sub.13.sup.2)}(16)
and the following cases for the values of .sub., of Q and of k.sub.s.sup.2, as given in the following table:

(44) TABLE-US-00001 TABLE 1 Variation of static capacitances as a function of various usable materials, for hypothetical coupling and quality coefficients at 434 MHz Q at .sub. C.sub.0res C.sub.0antires Material 434 MHz k.sub.s.sup.2 (%) (pf/m) (pF) (pF) Quartz (AT 10000 0.1 5.5.sub.0 = 48.6 0.734 73.4 cut) AIN (C-axis 3000 0.25 10.6.sub.0 = 0.978 55 orientation) 93.7 ZnO (C-axis 2500 0.3 10.2.sub.0 = 0.978 55 orientation) 90.2 LGS (YX 1000 0.35 32.5.sub.0 = 2.09 25.7 cut) 287 LiTaO.sub.3 1000 1 42.7.sub.0 = 0.734 73.4 (YXwt 377.5 cut)/90/ 112 LiNbO.sub.3(YZ 1000 5 35.6.sub.0 = 0.147 367 cut) 315

(45) Previously, the Applicant considered that the quality coefficient mainly depended on the type of metalization and on the nature of the substrate. In fact, working at resonance or at antiresonance affects the actual quality coefficient of the device. Experimentally, Q values that are substantially higher at antiresonance than at resonance are obtained (the coefficient Q at antiresonance is then defined as the maximum resistance divided by the full width at half maximum of the antiresonance peak when considering a reference line at 0 ohms). It will nonetheless be recalled that the coefficient Q used in the relationships is given by the relationship Q=.sub.rL.sub.m/R.sub.m, namely the quality coefficient Q defined at resonance.

(46) In particular, components operating at resonance point (i.e. matched to 50 at resonance) and the coefficient .sub. of which is higher than a value of about 15 prove to be substantially more sensitive to the series resistance than components the same coefficient of which is less than or equal to this value.

(47) Additionally, Table 1 shows that as the coupling coefficient gets higher, the static capacitance at resonance gets smaller (much smaller than one pF).

(48) It may thus easily be understood that a device operating at resonance is much more sensitive to parasitic capacitive elements than a resonator making use of the antiresonance.

(49) For this reason, the Applicant proposes to favor the antiresonance over the resonance in order to minimize the sensitivity to the series resistor and the impact of parasitic capacitances on the device operating at resonance.

(50) Table 2 below recapitulates examplary static capacitance and N.sub.cW product values at resonance and antiresonance allowing devices that are much less sensitive to the effects of parasitic capacitances at antiresonance to be designed with piezoelectric materials of high relative permittivity.

(51) TABLE-US-00002 TABLE 2 Typical products of N.sub.CW at resonance and at the antiresonance for various materials, for hypothetical coupling and quality coefficients at 434 MHz C.sub.0res C.sub.0antires NcWres NcW Material .sub. (pf/m) (pF) (pF) (mm) antires (m) Quartz 5.5.sub.0 = 0.734 73.4 15.1 1.51 (AT cut) 48.6 AIN 10.6 = 0.978 55 10.4 reson (C-axis .sub.0 93.7 orientation) ZnO 10.2.sub.090.2 0.978 55 10.8 0.609 (C-axis orientation) LGS 32.5.sub.0 = 2.09 25.7 7.3 0.089 (YX cut) 287 LiTaO.sub.3 42.7.sub.0 = 0.734 73.4 1.94 0.194 (YXwt 377.5 cut)/90/ 112 LiNbO.sub.3 35.6.sub.0 = 0.147 367 0.467 1.16 (YZ cut) 315

(52) The correctness of these calculations may be demonstrated by experiment: a resonator on langasite with a crystal orientation of (YX/t)/48.5/26.7, defined according to the IEEE standard on piezoelectricity Std-176, was produced in order to have an impedance of 90 ohms at antiresonance at 455 MHz.

(53) The acoustic aperture was fixed at 700 m and the number of fingers at the hot spot at 350. 233 pf.Math.m.sup.1 is found for .sub., namely a C.sub.0 of 57.1 pF according to formula (15). The exact calculation for this configuration gives a C.sub.0 of 54.2 pF. With a Q of 900 at resonance, parameters in accordance with the predictions, and which demonstrate the efficacy of the optimization process, are obtained.

(54) The Applicant also compared design results from resonators operating at resonance and at antiresonance at neighboring frequencies, 433 MHz in this instance, always targeting a load impedance of 50 ohms and using the (YX/t)/48.5/26.7 cut. In the case of resonance operation, the Applicant determined the number of electrodes of the transducer at the hot spot to be 25 for an aperture of 160 m (N.sub.cW=4 mm) and a metalization of 155 nm of platinum. For antiresonance operation, this same thickness of metalization is retained but the acoustic aperture increases to 900 m and the number of fingers at the hot spot in the transducer increases to 350 (N.sub.cW=315 mm). The response of the resonator is calculated using the mixed matrix method. Among other initial parameters of calculation, a relative permittivity for this configuration that is equal to 28.93 was used, namely an .sub.0 value of about 265 pF/m, with a velocity of the order of 2600 m.Math.s.sup.1 (taking into account the grounding effect of the metalization).

(55) For the resonance-optimized resonator, the difference between resonance and antiresonance frequencies indicates an electromechanical coupling coefficient of 1.4 according to formula (2) and a static capacitance of 0.916 pF. For the antiresonance-optimized resonator, these characteristics go to more than 4.1 et 50.3 pF, respectively.

(56) In conclusion, the Applicant has shown that in order to guarantee the spectral purity of a single resonator, the impedance at resonance or the antiresonance must be as close as possible to that of the load circuit, in this instance of the antenna, for a remotely interrogable sensor application.

(57) For a first design pass, the Applicant considered a load impedance of 50 but the experiment shows that the design must be tailored to the particular case of the application. Simulating the variation in the impedance of the load circuit as a function of the temperature in the surrounding medium would be the best conceivable design approach, however an archetypical design for open space or confined metallic or non-metallic environments appears to be a robust approach to providing universal sensors.

(58) In particular, the tendency of the impedances of the dipole antenna and of the resonator, respectively being between 75 and 100 for the first and close to 50 for the second at room temperature, to trend toward an identical value at working temperature (for example 600 C.) explains why the energy consumption of wireless interrogation improves with temperature.

(59) By way of comparison, the relative dielectric permittivity of the Rayleigh waves on LGS varies between 20 and 30 versus 5 to 6 for quartz, thereby considerably increasing the impedance at resonance for a given configuration. This factor 5 is transferred to the size of the transducers when a transducer operating at resonance is optimized. The reduction in the size of the transducer to several tens of wavelengths, and an aperture that is smaller than about twenty wavelengths, when working with the resonance condition and with Rayleigh waves on LGS, leads to an increased sensitivity to parasitic capacitive elements, particularly as the coupling coefficient does not exceed 0.1% in this type of configuration. The optimization of such a resonator (operation in resonance) therefore requires the elimination of all sources of parasitic capacitance for the resonance mode. This mode requires a smaller number of electrodes and a smaller acoustic aperture than solutions on quartz, which actually limit the electromechanical coupling coefficient to less than 0.1 percent.

(60) Although the footprint of the corresponding chip is optimal (30 to 40% gain in size with respect to the same sensor on quartz), functional defects remain.

(61) Regarding the use of a resonator in antiresonance mode as proposed in the present patent application, it requires the use of transducers with a number of electrodes and aperture that are maximized with respect to the solutions on quartz. The improved compactness aspect, provided by the phase velocity of the surface waves on this material (10 to 20% lower than those on quartz), is therefore lost, but electromechanical coupling coefficients in line with the capacitances of the material (70 to 80% of the achievable potential, versus less than 40% for the resonance solution) are kept in return. Consequently, the static capacitance is higher than for the resonance solution and turns out actually to be substantially less sensitive to parasitic interference than the latter.

(62) Additionally, the Applicant has observed that metalizations made of Ti or of Ta/Pt are particularly well suited to the production of these resonators, easily allowing quality coefficients to be obtained that are higher for the antiresonance than for the resonance. In practice, at 434 MHz and surrounding frequencies, a minimum thickness of 100 nm of Pt may be considered in order to optimize the operation of the transducer and of the mirrors, with 150 nm being a typical value.

(63) In the case of high-temperature applications, the improvement in quality coefficient provided by the antiresonance approach may reach a factor of 2 to 3. This improvement is a highly advantageous feature of the sensors proposed by the Applicant, given the reduction in this figure of merit with temperature, potentially by a coefficient of 2 to 3 for an excursion of 600 C. for example (from room temperature to 650 C.). Langasite LGS is additionally known for its loss of conductivity, especially with increasing temperature. It is therefore necessary to avoid introducing sources of malfunction linked to a design fault in a sensor based on this material and its variants (LGT, LGN) and to guarantee, as far as possible, the impedance match over the entire range of variations in temperature.

(64) The Applicant has studied the impact of connecting resonators on the resulting electrical response.

(65) For resonators that are combined in order to produce a remotely interrogable differential sensor, the general convention is that these are connected in parallel. It is not physically impossible to connect these dipoles in another manner (in series, in a bridge, etc.) but those skilled in the art consider, as far as is currently known and practiced, that the connection of two resonators in series for the target application does not produce the desired response and cannot practically be employed.

(66) The Applicant has demonstrated that it is possible to overcome this bias by virtue of the optimization of resonators operating in antiresonance.

(67) Specifically, by postulating two resonators R.sup.(1) and R.sup.(2) that are optimized for resonance operation, it is shown that their admittance amounts to the sum of the respective admittances of each resonator. By considering the normalized form of the latter, the following is obtained:

(68) $\begin{array}{cc}Y\left(\right)=C_0^{\left(1\right)}\frac{j{Q}^{\left(1\right)}\left({}_a^{\left(1\right)2}-{}^2\right)-{}^2{}_r^{\left(1\right)}}{Q^{\left(1\right)}\left({}_r^{\left(1\right)2}-{}^2\right)+j{}_r^{\left(1\right)}}+C_0^{\left(2\right)}\frac{j{Q}^{\left(2\right)}\left({}_a^{\left(2\right)2}-{}^2\right)-{}^2{}_r^{\left(2\right)}}{Q^{\left(2\right)}\left({}_r^{\left(2\right)2}-{}^2\right)+j{}_r^{\left(2\right)}}& \left(17\right)\end{array}$

(69) It is assumed that the static capacitances and quality coefficients of the two resonators are identical in order to simplify the equations. It then becomes:

(70) $\begin{array}{cc}Y\left(\right)={\mathrm{jC}}_0\left(\frac{\left({}_a^{\left(1\right)2}-{}^2\right)+j{}_r^{\left(1\right)}}{\left({}_r^{\left(1\right)2}-{}^2\right)+j{}_r^{\left(1\right)}}+\frac{\left({}_a^{\left(2\right)2}-{}^2\right)+j{}_r^{\left(2\right)}}{\left({}_r^{\left(2\right)2}-{}^2\right)+j{}_r^{\left(2\right)}}\right)& \left(18\right)\end{array}$
where Q=.sub.r/.fwdarw.w.sub.r.sup.2/Q= .sub.r.sup.2/.sub.r= .sub.r.

(71) at resonance .sub.r.sup.(1), the equivalent circuit is written as:

(72) $\begin{array}{cc}Y\left({}_r^{\left(1\right)}\right)={\mathrm{jC}}_0{}_r^{\left(1\right)}\left(\frac{\left(w_a^{\left(1\right)2}-{}_r^{\left(1\right)2}\right)}{j{}_r^{\left(1\right)}{}_r^{\left(1\right)}}+1+\frac{\left(w_a^{\left(2\right)2}-{}_r^{\left(1\right)2}\right)+j{}_r^{\left(1\right)}{}_r^{\left(2\right)}}{\left({}_r^{\left(2\right)2}-{}_r^{\left(1\right)2}\right)+j{}_r^{\left(1\right)}{}_r^{\left(2\right)}}\right)& \left(19\right)\end{array}$

(73) The different resonance and antiresonance frequency terms are negligible for the resonator R.sup.(2), thereby allowing the following simplified form to be written:

(74) $\begin{array}{cc}Y\left({}_r^{\left(1\right)}\right)C_0\frac{{}_r^{\left(1\right)}}{{}_r^{\left(1\right)}}{}_r^{\left(1\right)}\frac{\left({}_a^{\left(1\right)2}-{}_r^{\left(1\right)2}\right)}{{}_r^{\left(1\right)2}}+2{\mathrm{jC}}_0{}_r^{\left(1\right)}=C_0{}_r^{\left(1\right)}{\mathrm{Qk}}_s^2+2{\mathrm{jC}}_0{}_r^{\left(1\right)}& \left(20\right)\end{array}$
where 1/R.sub.m is in accordance with equation (11).

(75) The parallel connection of the two resonators makes each of them appear to have a static capacitance that is double that which is naturally associated therewith. This is well known to those skilled in the art.

(76) By connecting the resonators in series, the Applicant proposes to solve the problem in terms of impedance in order to take advantage of the simple sum of the terms associated with each resonator.

(77) It thus becomes:

(78) $\begin{array}{cc}Z\left(\right)=\frac{1}{{\mathrm{jC}}_0}\left(\frac{Q\left({}_r^{\left(1\right)2}-{}^2\right)+j{}_r^{\left(1\right)}}{Q\left({}_a^{\left(1\right)2}-{}^2\right)+j{}_r^{\left(1\right)}}+\frac{Q\left({}_r^{\left(1\right)2}-{}^2\right)+j{}_r^{\left(1\right)}}{Q\left({}_a^{\left(1\right)2}-{}^2\right)+j{}_r^{\left(1\right)}}\right)& \left(21\right)\end{array}$

(79) At the antiresonance of the resonator R.sup.(1): the following form is obtained for the impedance by applying the same mechanisms as applied going from equations (18) to (20).

(80) $\begin{array}{cc}Z\left({}_a^{\left(1\right)}\right)\frac{1}{{\mathrm{jC}}_0{}_a^{\left(1\right)}}\left(\frac{Q\left({}_r^{\left(1\right)2}-{}_a^{\left(1\right)2}\right)}{j{}_a^{\left(1\right)}{}_r^{\left(1\right)}}+2\right)\frac{{\mathrm{Qk}}_s^2}{C_0{}_r^{\left(1\right)}}+\frac{2}{{\mathrm{jC}}_0{}_a^{\left(1\right)}}& \left(22\right)\end{array}$

(81) This result shows that the resonator R.sup.(1) sees a parallel capacitance divided by 2 at antiresonance.

(82) Although achievable by those skilled in the art, the calculation of the equivalent circuit of a combination of resonators in series or in parallel being trivial, this result has never been used, considering the established opinion that it is not possible for two resonators to operate in series for the wireless interrogation thereof.

(83) The main difference between the two cases dealt with here relates to the maximum impedance value that the resonators operating at resonance or at antiresonance may have. In the first case, the impedance of the resonator is 50 at resonance, but this reaches substantially higher values at antiresonance.

(84) By taking the following numerical example with the following parameters: a quality coefficient at resonance Q of 10000 and a coupling coefficient that is equal to 0.1%, the product of Q.Math.k.sub.s.sup.2 has a value of 10.

(85) For a resonance frequency of 434 MHz, the static capacitor at resonance has a capacitance of 0.73 pF for a set impedance of 50 for this frequency.

(86) The impedance at antiresonance then reaches a value of 5 k since the two conditions are separated by a factor of Q.sup.2.Math.k.sub.s.sup.4.

(87) FIGS. 4a-4c and 5a-5b then show the variation in the response of two resonators whose resonance frequency is fixed at 433.5 and 434.3 MHz, respectively.

(88) It will be noted that actually, the response in terms of coefficient of reflection S.sub.11 is maximum for resonators that are connected in parallel with a static capacitance of 0.73 pF, while it turns out to be optimized for resonators that are connected in series with C.sub.0=73 pF.

(89) It may be seen in FIGS. 4a to 4c that both configurations indeed provide responses but the dynamic range is maximum for resonators in parallel.

(90) It may be seen in FIGS. 5a and 5b that both configurations indeed provide responses but the dynamic range of the resonators connected in series is substantially more marked.

(91) Although the static capacitance seen at antiresonance by each resonator is indeed equal to C.sub.0/2, the Applicant has not observed any major differences between the electromechanical coupling coefficients calculated for the two types of circuits.

(92) It will be noted that two resonators optimized for operation at 50 at resonance do not have to be modified in terms of design, regardless of the mode of connection, as the set of FIGS. 4a-4c and 5a-5b shows.

(93) Specifically, besides its resonance and antiresonance, a single-mode dipole SAW resonator behaves as a single capacitor and hence a short circuit in RF state. From the point of view of behavior in terms of reflection, neither the short circuit nor the open circuit lead to any signal absorption (all incident energy is reflected).

(94) It is furthermore known that the presence of a resistor in series with the resonant circuit may affect the quality of resonance. Likewise, the presence of an inductor linked to the connection of the resonator adds complexity to the equivalent circuit but also provides more information on its actual response once it has been encapsulated.

(95) A complete schematic lastly includes a possible resistor in parallel to or in series with the static capacitor, representing the leakage currents in the material (langasite in particular suffers from such a defect, this being known to those skilled in the art). It is shown that antiresonance operation allows the effect of the series-connected resistance on the quality coefficient of the antiresonance peak to be minimized.

(96) This element means that for materials with particularly high electromechanical coupling coefficients (namely higher than one percent), it is also preferable to favor the antiresonance, the resonance notoriously being affected by the presence of a contact resistance of the order of 1 or more.

(97) For an exhaustive description of the results, it is noted that in series mode (resonators optimized for antiresonance), the first resonator exhibits a higher coupling coefficient than the second, the sum of the coupling coefficients being substantially equal to the coupling coefficient of each resonator taken independently (k.sub.s.sup.2 is assumed to be identical for each resonator and fixed at 0.1% for a Q of 10000, C.sub.0=73.2 pF, close to the case with quartz).

(98) FIGS. 6a and 6b characterize electromechanical coupling coefficients of each contribution for the two connection configurations: FIG. 6a represents resonators in parallel: resonance operation; FIG. 6b represents resonators in series: antiresonance operation. The curves C6a.sub.R and C6b.sub.R represent the resistance, the curves C6a.sub.c and C6b.sub.c represent the conductance.

(99) The Applicant found a coupling coefficient of 0.567 or the resonator at 433.7 MHz and 0.432 for that at 434.4 MHz.

(100) The optimized situation in terms of resonance (k.sub.s.sup.2 still fixed at 0.1% for a Q of 10000, C.sub.0=0.73 pF, close to the case with quartz) presents a highly inverted configuration.

(101) Coupling coefficients of 0.433 and 0.566 are then found for the resonance frequencies at 433.5 and 434.3 MHz. It is therefore necessary to work upstream of the resonator assembly in order to obtain a response from the circuit that is ideally optimized and balanced at the level of the contributions of each resonator.

(102) FIGS. 7a and 7b illustrate, respectively, the way in which the resonators connected in parallel may be arranged when they operate (are interrogated) in resonance (a configuration referred to as a conventional configuration) and the connection, discussed above, for connecting the resonators in series and which lends itself in particular to the case in which the resonators operate in antiresonance.

(103) These figures show the antenna allowing the sensors to be interrogated. It is shown as a quadripole connected by its radiating resistor.