Piezoelectric resonators and oscillator circuit based on higher-order out-of-plane modes for density-viscosity measurements of liquids

Toledo, J.; Manzaneque, Tomás; Ruiz-Díez, Víctor; Kučera, Martin; Pfusterschmied, Georg; Wistrela, E.; Schmid, U.; Sánchez‐Rojas, J. L.

doi:10.1088/0960-1317/26/8/084012

Cited by 20 publications

(25 citation statements)

References 34 publications

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“…The determination of the fluid parameters from the fluid loaded resonator is difficult, as

and

appear also in the arguments of two Bessel functions. The fluid models presented in this work, are based on an expansion the hydrodynamic function in Equation ( 2 ) into a power series around

, yielding

For the reduced order models [ 22 , 23 , 24 , 25 , 26 ], the approximation of the fluid force in Equation ( 7 ) is added to the equation of motion of the resonator (see Section 2.3 ), yielding models for the resonance parameters of the fluid loaded resonator shown in Equation ( 12 ). A consequence of the agreement between Equation ( 7 ) and Equation ( 2 ) being best for large

is that the model approximation is more accurate for thicker cylinders vibrating at higher frequencies.…”

Section: Materials and Methodsmentioning

confidence: 99%

“…For the reduced order models [22][23][24][25][26], the approximation of the fluid force in Equation 7is added to the equation of motion of the resonator (see Section 2.3), yielding models for the resonance parameters of the fluid loaded resonator shown in Equation (12). A consequence of the agreement between Equation (7) and Equation (2) being best for large β is that the model approximation is more accurate for thicker cylinders vibrating at higher frequencies.…”

Section: Vibrating Cylinder Immersed In Viscous Fluidmentioning

confidence: 99%

“…The task of the sensor designer is to guarantee that the resonance parameters can be correctly measured and that a fluid model is available which can be transformed to yield unique and accurate fluid parameters from the resonance parameters. As the exact hydrodynamic function is only known for some special cases, the conventionally used fluid models derived, e.g., by [22][23][24][25][26] are all based on an approximation of the hydrodynamic function of a vibrating prismatic beam featuring a cylindrical cross-section by means of a truncated power series. A remarkable fact, shown by a many researchers in experimental work [22][23][24][25][26][27][28][29][30][31], is that the resulting reduced order models with adjustable parameters are suitable for representing various different types of fluid loaded vibrating structures, including cantilevers of different cross-sections, large steel and miniaturized quartz tuning forks, spiral springs, platelets, U-shaped wires, piezo buzzers in fluids, etc.…”

Section: Introductionmentioning

confidence: 99%

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Higher-Order Models for Resonant Viscosity and Mass-Density Sensors

Voglhuber-Brunnmaier

Jakoby

2020

Sensors

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Advanced fluid models relating viscosity and density to resonance frequency and quality factor of vibrating structures immersed in fluids are presented. The numerous established models which are ultimately all based on the same approximation are refined, such that the measurement range for viscosity can be extended. Based on the simple case of a vibrating cylinder and dimensional analysis, general models for arbitrary order of approximation are derived. Furthermore, methods for model parameter calibration and the inversion of the models to determine viscosity and/or density from measured resonance parameters are shown. One of the two presented fluid models is a viscosity-only model, where the parameters of it can be calibrated without knowledge of the fluid density. The models are demonstrated for a tuning fork-based commercial instrument, where maximum deviations between measured and reference viscosities of approximately ±0.5% in the viscosity range from 1.3 to 243 mPas could be achieved. It is demonstrated that these results show a clear improvement over the existing models.

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“…The determination of the fluid parameters from the fluid loaded resonator is difficult, as

and

appear also in the arguments of two Bessel functions. The fluid models presented in this work, are based on an expansion the hydrodynamic function in Equation ( 2 ) into a power series around

, yielding

is that the model approximation is more accurate for thicker cylinders vibrating at higher frequencies.…”

Section: Materials and Methodsmentioning

confidence: 99%

Section: Vibrating Cylinder Immersed In Viscous Fluidmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Higher-Order Models for Resonant Viscosity and Mass-Density Sensors

Voglhuber-Brunnmaier

Jakoby

2020

Sensors

View full text Add to dashboard Cite

show abstract

“…Firstly, the behaviour of the resonator was tested by making open-loop measurements. These were performed using a lock-in amplifier to excite and collect the signal from the actuator within an interface circuit (see Figure 4) [35]. The main objective of the interface circuit is to reduce the parasitic effects of the resonator and to obtain an appropriate resonance curve for the later closed-loop measurements.…”

Section: Interface Circuitmentioning

confidence: 99%

Piezoelectric Actuators for Tactile and Elasticity Sensing

et al. 2020

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Piezoelectric actuators have achieved remarkable progress in many fields, being able to generate forces or displacements to perform scanning, tuning, manipulating, tactile sensing or delivering functions. In this work, two piezoelectric PZT (lead zirconate titanate) bimorph actuators, with different tip contact materials, were applied as tactile sensors to estimate the modulus of elasticity, or Young’s modulus, of low-stiffness materials. The actuators were chosen to work in resonance, taking advantage of a relatively low resonant frequency of the out-of-plane vibrational modes, associated with a convenient compliance, proven by optical and electrical characterization. Optical measurements performed with a scanning laser vibrometer confirmed that the displacement per applied voltage was around 437 nm/V for the resonator with the lower mass tip. In order to determine the modulus of elasticity of the sensed materials, the stiffness coefficient of the resonator was first calibrated against a force sensor, obtaining a value of 1565 ± 138 N/m. The actuators were mounted in a positioning stage to allow approximation and contact of the sensor tip with a set of target materials. Electrical measurements were performed using the resonator as part of an oscillator circuit, and the modulus of elasticity of the sample was derived from the contact resonant frequency curve of the cantilever–sample system. The resulting sensor is an effective, low-cost and non-destructive solution compared to atomic force microscopy (AFM) techniques. Materials with different modulus of elasticity were tested and the results compared to values reported in the literature.

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“…The resonator driving circuit that reads out the motional resistance or inductance change can be applied to resonator-based biochemical sensors. In this paper, we focus on the motional resistance readout method for the detection of biochemical properties, such as the density and viscosity of fluid, (7)(8)(9)(10)(11) or blood glucose.…”

Section: Introductionmentioning

confidence: 99%

Open-loop Spectrum Analyzer Integrated Circuit for Nanoresonator Sensing

Heo¹,

Han²,

Kim³

et al. 2020

Sensors and Materials

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A nanoresonator can be applied as a biochemical sensor based on the change in the mass of the nanoresonator, and the mass change can be interpreted in the frequency domain. In this paper, we present an open-loop spectrum analyzer integrated circuit (IC) for a nanoresonator. The circuit determines the frequency characteristics of a nanoresonator, such as quality factor (Q-factor) and resonant frequency, and detects minute resistance changes of the nanoresonator that result in changes in Q-factor or resonant frequency. The proposed nanoresonator driver circuit is implemented using an open-loop system, and to characterize the open-loop frequency response of the nanoresonator, the IC includes a voltage-controlled oscillator, a transimpedance amplifier, and a 16-bit delta-sigma analog-to-digital converter. To compensate for the parasitic components that cause the distortions of the phase and magnitude response, a shunt-capacitance cancelling amplifier is used to cancel the effect of the shunt-parasitic capacitance of the nanoresonator. The simulated target nanoresonator is modeled using the Butterworth-Van Dyke equivalent circuit model with a resonant frequency of 10 MHz. The proposed nanoresonator driver circuit is fabricated using a standard 0.18 μm complementary metal oxide semiconductor process with an active area of 2.346 mm 2. The simulated resistive sensitivity of the IC is 5.1 mV/kΩ.

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Piezoelectric resonators and oscillator circuit based on higher-order out-of-plane modes for density-viscosity measurements of liquids

Cited by 20 publications

References 34 publications

Higher-Order Models for Resonant Viscosity and Mass-Density Sensors

Higher-Order Models for Resonant Viscosity and Mass-Density Sensors

Piezoelectric Actuators for Tactile and Elasticity Sensing

Open-loop Spectrum Analyzer Integrated Circuit for Nanoresonator Sensing

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