US 12,455,262 B2 · Method and device for characterising the response of resonant sensors

Abstract

A method and device for characterizing the response of resonant sensors. The method is based on an analytic algorithm that establishes a relationship between the complex admittance G of the sensor, measured at a single test frequency, the variations in resonance frequency and the losses, such as the quality factor at the acoustic resonator. The device includes at least one piezoelectric resonator on whose surface is deposited a thin layer of material, a fluid medium in contact therewith, a stable signal source, a frequency synthesis subsystem, a multiplex subsystem that enables the excitation/interrogation of a particular resonator, a signal conditioning and acquisition subsystem, a control subsystem based on the use of digital integrated circuits enabling the coordinated control of the different subsystems that make up the device.

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):
G
⁡
(
f
)
=
G
max
(
f
2
(
2
⁢
Γ
)
2
(
f
r
2
-
f
2
)
2
+
f
2
(
2
⁢
Γ
)
2
⁢
cos
⁢
ϕ
-
f
⁡
(
2
⁢
Γ
)
⁢
(
f
r
2
-
f
2
)
(
f
r
2
-
f
2
)
2
+
f
2
(
2
⁢
Γ
)
2
⁢
sin
⁢
ϕ
)
+
G
off
(
10
)
B
⁡
(
f
)
=
G
max
(
f
2
(
2
⁢
Γ
)
2
(
f
r
2
-
f
2
)
2
+
f
2
(
2
⁢
Γ
)
2
⁢
sin
⁢
ϕ
+
f
⁡
(
2
⁢
Γ
)
⁢
(
f
r
2
-
f
2
)
(
f
r
2
-
f
2
)
2
+
f
2
(
2
⁢
Γ
)
2
⁢
cos
⁢
ϕ
)
+
B
off
(
11
)
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√{square root over (LmCm)}) (8)
D=1/Q=Rm/(2πfrLm) (9)
and
f) updating the test frequency to the dynamic series resonance frequency obtained in step (f).

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Method and device for characterising the response of resonant sensors

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Method and device for characterising the response of resonant sensors

Life of this patent

Abstract

Claims10