An extended Butterworth Van Dyke model for quartz crystal microbalance applications in viscoelastic fluid media

Arnau, Antonio; Jiménez, Yolanda; Sogorb, T.

doi:10.1109/58.949746

Cited by 49 publications

(24 citation statements)

References 37 publications

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“…For the stated purpose, we employ the commonly accepted Butterworth-Van Dyke model [39] which represents each resonance of the BAW resonator as a series connection of inductance L x , capacitance C x and resistance R x . All these motional branches are connected in parallel with a shunt capacitance created by the system electrodes.…”

mentioning

confidence: 99%

Observation of the fundamental Nyquist noise limit in an ultra-high Q-factor cryogenic bulk acoustic wave cavity

Goryachev

Ivanov

Kann

et al. 2014

Applied Physics Letters

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Thermal Nyquist noise fluctuations of high-Q Bulk Acoustic Wave (BAW) cavities have been observed at cryogenic temperatures with a DC Superconducting Quantum Interference Device (SQUID) amplifier. High Q modes with bandwidths of few tens of milliHz produce thermal fluctuations with a Signal-To-Noise ratio of up to 23dB. The estimated effective temperature from the Nyquist noise is in good agreement with the physical temperature of the device, confirming the validity of the equivalent circuit model and the non-existence of any excess resonator self-noise. The measurements also confirm that the quality factor remains extremely high (Q > 10 8 at low order overtones) for very weak (thermal) system motion at low temperatures, when compared to values measured with relatively strong external excitation. This result represents an enabling step towards operating such a high-Q acoustic device at the standard quantum limit.Phonon-trapping Bulk Acoustic Wave (BAW) cavity resonator technology shows great potential for use in applications that require precision control, measurement and sensing at the quantum limit [1]. This is mainly due to the relatively high mechanical frequencies and extremely high Q-factors achievable in such devices at cryogenic temperatures (Q > 10 9 ), which potentially lead to extraordinarily large coherence times [2][3][4] beyond the capability of any other competing technology compared in [5]. This uniqueness has been perfected for decades for precision room temperature oscillators and related devices [6,7], culminating in Q × f -products as high as 2 · 10 13 Hz [8]. Interestingly, it is no longer the deficiency of the Q-factor, which halts further progress in the reduction of phase fluctuations, but rather the intrinsic fluctuations of the BAW resonator itself [9,10]. In particular, it has been concluded that further improvement of BAW based frequency sources could only be achieved by reducing the resonator flicker phase self-noise, since this is the dominant noise source of ultra-stable BAW oscillators both at cryogenic and room temperature [9,11].The origin of the flicker frequency noise is still poorly understood despite its significant influence on many systems [12,13] ranging from biological substances[14] to superconducting electronics [15,16]. The influence on the frequency stability of high-performance quartz oscillators on time scales of order 1-10 seconds is welldocumented [10,17,18] with several attempts to understand its origins [19][20][21]. It is also important for other mechanical resonators such as High Overtone [22] and Thin Film[23] BAW devices. On the other hand, coherence times of ultra-high Q quartz BAW cavities are predicted * maxim.goryachev@uwa.edu.au to exceed 10 seconds. Thus, the question of the influence of low Fourier frequency noise has never been raised with respect to these types of measurements due to the relatively low Q factors of the mechanical resonators utilised so far [24][25][26]. So, this type of noise can be another limiting factor on the coherence times of...

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mentioning

confidence: 99%

Observation of the fundamental Nyquist noise limit in an ultra-high Q-factor cryogenic bulk acoustic wave cavity

Goryachev

Ivanov

Kann

et al. 2014

Applied Physics Letters

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“…Usually the resonant frequencies are represented and modelled by a parallel combination of RLC legs. Several electrical models of an ultrasound transducer are introduced in literature [12,[15][16][17]. Fig.…”

Section: Introductionmentioning

confidence: 99%

“…2 illustrates the most well-known models. The Van Dyke model is the basic model of the transducer which is a parallel connection of a series RLC leg and a capacitor [17]. The Sherrit model proposes a parallel combination of a series LC leg and a capacitor.…”

Section: Introductionmentioning

confidence: 99%

Dissimilar trend of nonlinearity in ultrasound transducers and systems at resonance and non-resonance frequencies

et al. 2017

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Abstract-Several factors can affect performance of an ultrasound system such as quality of excitation signal and ultrasound transducer behaviour. Nonlinearity of piezoelectric ultrasound transducers is a key determinant in designing a proper driving power supply. Although, the nonlinearity of piezoelectric transducer impedance has been discussed in different literatures, the trend of the nonlinearity at different frequencies with respect to excitation voltage variations has not been clearly investigated in practice. . In this paper, to demonstrate how the nonlinearity behaves, a sandwich piezoceramic transducer was excited at different frequencies. Different excitation signals were generated using a linear power amplifier and a multilevel converter within a range of 30 V-200V. Empirical relation was developed to express the resistance of the piezoelectric transducer as a nonlinear function of both excitation voltage and resonance frequency. The impedance measurements revealed that at higher voltage ranges, the piezoelectric transducer can be easily saturated. Also, it was shown that for the developed ultrasound system composed of two transducers (one transmitter and one receiver), the output voltage measured across receiver is a function of a voltage across the resistor in the RLC branches and is related to the resonance frequencies of the ultrasound transducer. Index TermsHigh power ultrasound transducer, nonlinear behaviour, ultrasound system excitation, power electronic converters Dissimilar trend of nonlinearity in ultrasound transducers and systems at resonance and non-resonance frequencies 2

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“…The Van-Dyke model of a piezoelectric resonator [1] models the vibrator resonating at the frequency ω m with an equivalent electrical impedance. The motional capacitance C m and motional inductance L m represent the rigidity and the inertia of the vibrator, respectively.…”

Section: Resonance Matchingmentioning

confidence: 99%

Adaptive control of ultrasonic motors using the maximum power point tracking method

Flueckiger

Fernández

Perriard

2008

2008 IEEE Ultrasonics Symposium

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Abstract-The properties of ultrasonic piezoelectric motors depend on applied load and temperature. The output behaviour is characterized by the nonlinearity of the power transmission at the friction interface between stator and rotor. Because of these inherently nonlinear characteristics, a resonant frequency tracking control is imperative for some particular applications where direct speed or position sensing is not applicable and harsh environment conditions with large thermal gradients and important load variations subsist. We suggest a maximum power point tracking (MPPT) approach, which is well known from contactless energy transmission systems. The MPPT controller was compared to a phase-locked loop controller for ultrasonic motors known from literature. The resonant frequency can be tracked over a far wider working range compared to the phase locking range. Also, the MPPT control circuit is very easy to tune and no sophisticated loop gain design is needed. The analog version of the MPPT controller was built and tested with linear and rotary ultrasonic motors.

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An extended Butterworth Van Dyke model for quartz crystal microbalance applications in viscoelastic fluid media

Cited by 49 publications

References 37 publications

Observation of the fundamental Nyquist noise limit in an ultra-high Q-factor cryogenic bulk acoustic wave cavity

Observation of the fundamental Nyquist noise limit in an ultra-high Q-factor cryogenic bulk acoustic wave cavity

Dissimilar trend of nonlinearity in ultrasound transducers and systems at resonance and non-resonance frequencies

Adaptive control of ultrasonic motors using the maximum power point tracking method

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