US 12,455,262 B2
Method and device for characterising the response of resonant sensors
Román Fernández Díaz, Picanya (ES); Maria Calero Alcarria, Castellón de la Plana (ES); José Vicente García Narbón, Burjassot (ES); Yolanda Jimenez Jimenez, Valencia (ES); and Antonio Arnau Vives, Valencia (ES)
Assigned to UNIVERSIDAD POLITECNICA DE VALENCIA, Valencia (ES); and ADVANCED WAVE SENSORS, S.L., Paterna (ES)
Appl. No. 18/007,330
Filed by UNIVERSIDAD POLITECNICA DE VALENCIA, Valencia (ES); and ADVANCED WAVE SENSORS, S.L., Paterna (ES)
PCT Filed Jul. 14, 2021, PCT No. PCT/ES2021/070518
§ 371(c)(1), (2) Date Jan. 30, 2023,
PCT Pub. No. WO2022/023598, PCT Pub. Date Feb. 3, 2022.
Claims priority of application No. ES202030810 (ES), filed on Jul. 30, 2020.
Prior Publication US 2023/0296565 A1, Sep. 21, 2023
Int. Cl. G01N 29/036 (2006.01); G01N 29/44 (2006.01)
CPC G01N 29/036 (2013.01) [G01N 29/4418 (2013.01)] 10 Claims
OG exemplary drawing
 
1. A method for measuring variations in a resonance frequency and a dissipation factor of a piezoelectric resonator used as a sensor, the resonator being modeled by a Butterworth-Van Dyke (BVD) equivalent circuit and a behavior of the resonator is approximated by the Small Load Approximation (SLA), the method comprising:
(a) measuring an initial complex admittance spectrum of the sensor as a function of frequency, in a vicinity of a resonance frequency of a selected vibration mode of the resonator;
b) fitting, by non-linear numerical methods, the initial complex admittance spectrum of the sensor obtained in step (a) to a Lorentzian model, according to the equations (10) and (11):

OG Complex Work Unit Math
to extract six parameters that characterize the initial response: where,
fr: a dynamic series resonance frequency,
Gmax: the maximum conductance,
Goff: a conductance offset level,
Boff: an offset level of the susceptance,
Γ: the half bandwidth of the resonance curve (this parameter is inversely related to the dissipation factor in the sensor),
ϕ: an angle accounting for the smalls slopes in the resonance curve in the complex plane,
G(f): experimental conductance as a function of frequency, and
B(f): experimental conductance as a function of frequency;
c) determining the values of the BVD equivalent circuit parameters Rm, Lm, Cm, and C0, from the fitted value fr, Gmax, Goff, Boff, Γ, and ϕ be obtained in step (b) and from the following equations:
Rm=1/Gmax,  (12)
Lm=Rm/4πΓ,  (13)
Cm=¼π2fr2Lm,  (14)
C0=Boff/2πfr,  (15)
where,
Rm: electrical resistance modelling viscous losses,
Lm: inductive parameter proportional to surface mass density,
Cm: capacitive parameter proportional to elastic energy stored in the sensor, and
C0: static capacitance of the sensor;
d) selecting a test signal frequency substantially equal to a dynamic series resonance frequency, fr, of the resonator in the initial state of the sensor obtained in step (b), and considering the values of Cm and C0 obtained in step (c) and associated with electrical artifacts outside the sensor itself as invariant during the subsequent experimental characterization;
e) measuring complex admittance values of the sensor at the test signal frequency obtained in step (d);
f) calculating updated values of the dynamic series resonance frequency and the dissipation factor of the sensor from the complex admittance measured in step (e), using the equivalent model parameters obtained in step (c) and the proposed equations (6), (7), (8), and (9):
Rm=1/[G(ωt)[1+(ωtC0−B(ωt)2/G(ωt)2]]  (6)
Lm=(Rm/ωt)[(ωtC0−B(ωt))/G(ωt)]+1/(ωtCm)  (7)
fr=1/(2π√LmCm)  (8)
D=1/Q=Rm/(2πfrLm)  (9)
and
f) updating the test frequency to the dynamic series resonance frequency obtained in step (f).