Butterworth-Van Dyke Research Articles

Parametric Synthesis of Single-Stage Lattice-Type Acoustic Wave Filters and Extended Multi-Stage Design.

This study proposes a single-stage lattice-type acoustic filter using an analytical solution method for either a narrow passband filter or a wider passband filter using two kinds of parameter assignments in the Butterworth-Van Dyke (BVD) model. To achieve the goal of a large bandwidth or high return loss, two first-order all-pass conditions are used. For multi-stage lattice-type filters, the cost function is defined and design parameters are extracted by using pattern search, while the initial values are provided through single-stage design to shorten optimization time and allow convergence to a better solution. This method provides the S-parameter frequency response for the filter on the YX 42° cut angle of lithium tantalate (electromechanical coupling coefficient of about 6%) that can meet the system specifications as much as possible. Finally, the three-stage lattice-type was applied to various 5G bands with a fractional bandwidth of 2-5%, resulting in a passband return loss of 10 dB and an out-of-band rejection of 40 dB or more.

Optimizing hydrophone-preamplifier systems: Theoretical design, computational analysis, and experimental validation for towed array applications

Hydrophone response parameters greatly influence the design of pre-amplifier and analog to digital conversion (ADC) components. Here, we show a comprehensive methodology for the modeling of hydrophone response, focusing on the theoretical, computational, and experimental approach for low and high frequency SONAR applications. Theoretical calculation of hydrophone response based on electromechanical properties is compared with Finite Element Analysis (FEA) and experimental measurement. An electrical equivalent hydrophone simulator Butterworth-Van Dyke (BVD) circuit is constructed based on admittance and susceptance measurements to represent the transducer's electrical behavior for testing pre-amplifier and ADC response without the presence of environmental or hydrophone noise. This model facilitates a systematic approach to towed array front-end design with hardware in the loop to update models to improve performance prediction. Measurements of the constructed transducer system validate the theoretical and computational models, providing insights into real-world performance.

Parameters identification of an ultrasonic transducer based on right-semicircle fitting of admittance circle

We propose an accurate parameter identification method for Butterworth-Van Dyke (BVD) model via Fast Identification of BVD model based on Right-semicircle Fitting of Admittance (FIRFA), which is composed of the fast search algorithm for series resonant frequency (FSSRF) and the identification of BVD model based on Right-semicircle Fitting of Admittance (IRFA). In order to verify the algorithm, we establish an Ultrasonic Transducer Identification System (UTIS) to measure the BVD model of the 62 kHz and the 140 kHz ultrasonic transducer. The accuracy and the time consumption of the FSSRF algorithm are investigated. Besides, the nonlinear phenomenons of the BVD model parameters varying with the driving voltage are qualitatively analyzed. The results show that R1 and L1 will increase, C1 will decrease when the driving voltage increases.

Effect of Load on Quartz Crystal Microbalance Sensor Response Addressed Using Fractional Order Calculus.

To accurately model the effect of the load caused by a liquid medium as a function of its viscosity, the fractional order Butterworth-Van Dyke (BVD) model of the QCM sensor is proposed in this study. A comprehensive understanding of the fractional order BVD model followed by a simulation of situations commonly encountered in experimental investigations underpins the new QCM sensor approach. The Levenberg-Marquardt (LM) algorithm is used in two fitting steps to extract all parameters of the fractional order BVD model. The integer-order electrical parameters were determined in the first step and the fractional order parameters were extracted in the second step. A parametric investigation was performed in air, water, and glycerol-water solutions in ten-percent steps for the fractional order BVD model. This indicated a change in the behavior of the QCM sensor when it swapped from air to water, modeled by the fractional order BVD model, followed by a specific dependence with increasing viscosity of the glycerol-water solution. The effect of the liquid medium on the reactive motional circuit elements of the BVD model in terms of fractional order calculus (FOC) was experimentally demonstrated. The experimental results demonstrated the value of the fractional order BVD model for a better understanding of the interactions occurring at the QCM sensor surface.

Estimation Method of an Electrical Equivalent Circuit for Sonar Transducer Impedance Characteristic of Multiple Resonance.

Improving the operational efficiency and optimizing the design of sound navigation and ranging (sonar) systems require accurate electrical equivalent models within the operating frequency range. The power conversion system within the sonar system increases power efficiency through impedance-matching circuits. Impedance matching is used to enhance the power transmission efficiency of the sonar system. Therefore, to increase the efficiency of the sonar system, an electrical-matching circuit is employed, and this necessitates an accurate equivalent circuit for the sonar transducer within the operating frequency range. In conventional equivalent circuit derivation methods, errors occur because they utilize the same number of RLC branches as the resonant frequency of the sonar transducer, based on its physical properties. Hence, this paper proposes an algorithm for deriving an equivalent circuit independent of resonance by employing multiple electrical components and particle swarm optimization (PSO). A comparative verification was also performed between the proposed and existing approaches using the Butterworth-van Dyke (BVD) model, which is a method for deriving electrical equivalent circuits.

Assessing Impedance Analyzer Data Quality by Fractional Order Calculus: A QCM Sensor Case Study

The paper presents the theoretical, simulation, and experimental results on the QCM sensor based on the Butterworth van Dyke (BVD) model with lumped reactive motional circuit elements of fractional order. The equation of the fractional order BVD model of the QCM sensor has been derived based on Caputo definitions and its behavior around the resonant frequencies has been simulated. The simulations confirm the ability of fractional order calculus to cover a wide range of behaviors beyond those found in experimental practice. The fractional order BVD model of the QCM sensor is considered from the perspective of impedance spectroscopy to give an idea of the advantages that fractional order calculus brings to its modeling. For the true values of the electrical parameters of the QCM sensor based on the standard BVD model, the experimental investigations confirm the equivalence of the measurements after the standard compensation of the virtual impedance analyzer (VIA) and the measurements without compensation by fitting with the fractional order BVD model. From an experimental point of view, using fractional order calculus brings a new dimension to impedance analyzer compensation procedures, as well as a new method for validating the compensation.

Direct Synthesis of Acoustic Wave Multiplexers Built on Fully Canonical Multiport Functions

This work proposes the first analytical method for the direct synthesis of multiplexers based on acoustic wave (AW) ladder filters connected in a star junction topology. It describes the computation of the polynomial representation of a multiport ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K} +$ </tex-math></inline-formula> 1 ports) network with fully canonical (FC) channels and derives a set of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> distorted channel polynomials from which each of the AW ladder filters is synthesized. The channel polynomials are distorted in a way such that when connected together at the star junction, the desired multiplexer response is obtained avoiding degradation due to channel loading. The method allows to freely set the fractional bandwidth (FBW), return loss (RL), and transmission zeros (TZs) of each channel enabling the search for multiplexers that fulfill the technological requirements of AW technology in terms of electromechanical coupling coefficient and area occupancy among others. Moreover, since the multiport network polynomials incorporate the complete effects of the loading between channels as, for example, additional TZs, the synthesized multiplexers depict an improvement of isolation when compared with a design based on only controlling the reflection phase of each channel filter. The proposed method is rigorously demonstrated by means of a synthesized multiplexer example providing the Butterworth–Van Dyke (BVD) elements of each channel filter. This approach avoids intensive optimization procedures and represents a useful technique for the design of carrier aggregation (CA) filter modules in a direct and controlled manner.

Analysis of spurious peaks at series resonance in solidly mounted resonators by combined BVD-Mason modelling

Solidly Mounted Resonators (SMRs) for high frequency RF filters and sensing applications often display spurious resonances that distort their frequency response. In this work, we try to identify the origin of spurious resonances accompanying the main series resonances in AlN-based SMRs with the help of modified Butterworth Van Dyke (BVD) and Mason’s models. By manufacturing SMRs of different sizes and shapes and studying the influence of the position of the electrical probing spot, we have demonstrated both theoretically and experimentally that devices with larger areas are more likely to display these additional peaks. Our updated models accurately simulate the frequency response of the SMRs, revealing that spurious peaks are mostly related to the resistance of the electrodes. Our study clarifies the origin of the spurious resonances and offers solutions for both, the optimal design and measurement method of SMRs.

Modeling of Delta-E Effect Magnetic Field Sensors

In this article, we study magnetic field sensors based on the delta-E effect occurring in a magnetostrictive layer coupled to a piezoelectric resonator. The sensors consist in suspended beams that essentially vary in the bounded conditions at the edges. We examine a clamped-free and a double-clamped sensor. A finite-element model (FEM) is implemented and validated versus published experimental measurements. The latter are considered as reference results. A Butterworth–Van Dyke (BVD) model is also given in each case. The performances of these two types of resonators are pointed out and compared, especially in terms of sensitivity and equivalent magnetic noise level. The given approach gives the way of sensor optimization.

Advanced Impedance Spectroscopy for QCM Sensor in Liquid Medium.

Technological evolution has allowed impedance analysis to become a versatile and efficient method for the precise measurement of the equivalent electrical parameters of the quartz crystal microbalance (QCM). By measuring the dissipation factor, or another equivalent electrical parameter, the QCM sensor provides access to the sample mass per unit area and its physical parameters, thus ensuring a detailed analysis. This paper aims to demonstrate the benefits of advanced impedance spectroscopy concerning the Butterworth–van Dyke (BVD) model for QCM sensors immersed with an electrode in a liquid medium. The support instrument in this study is a fast and accurate software-defined virtual impedance analyzer (VIA) with real-time computing capabilities of the QCM sensor’s electric model. Advanced software methods of self-calibration, real-time compensation, innovative post-compensation, and simultaneous calculation by several methods are the experimental resources of the results presented in this paper. The experimental results validate the theoretical concepts and demonstrate both the capabilities of VIA as an instrument and the significant improvements brought by the advanced software methods of impedance spectroscopy analysis related to the BVD model.

Synthesis of wideband bulk acoustic wave coupled resonator filter combined with lumped components

SummaryA novel wideband bulk acoustic wave (BAW) coupled resonator filter (CRF) combined with external lumped inductors and capacitors is proposed. The filter synthesis method based on the Butterworth–van Dyke (BVD) model of CRF (CRF‐BVD) is also presented. To improve the synthesis accuracy, the CRF‐BVD model is modified and the CRF configuration with a single rather than the traditional multiple coupling layer is adopted in this paper. By establishing equivalence relationships between the modified CRF‐BVD model and the filter prototype synthesis network, exact CRF dimensions are solved through a set of equations without any further parameters tuning. The proposed method exhibits a maximum 37.4% (FBW) for a Chebyshev filter with 9.4‐dB return loss, which overcomes the narrowband limitation of regular BAW filters with FBW below 5%. To demonstrate the synthesis procedure, an n77 band filter with 3.723‐GHz center frequency and 24.2% FBW is designed and simulated. Good agreements are obtained among the simulation results of the prototype synthesis network, the modified CRF‐BVD model, and the co‐simulations of physical model based on the finite element method (FEM) and the CMOS 130‐nm technology.

Al0.68Sc0.32N Lamb wave resonators with electromechanical coupling coefficients near 10.28%

Aluminum scandium nitride (Al1−xScxN/AlScN) (x = 0.32) Lamb wave resonators (LWR) have been fabricated and tested to demonstrate electromechanical coupling coefficients (kt2) in excess of 10%. The resonators exhibited an average kt2 and unloaded quality factor (Qu) of 10.28% and 711, respectively, when calculated from the measured data. Applying the Butterworth Van-Dyke (BVD) model to the measured data enabled the extraction of the resonator's lumped element parameters to calculate the motional quality factor (Qm), which neglects the contributions of the electrical traces. For the best measured resonator response, results from the BVD model showed a Qm of 1184 and a resulting figure-of-merit (FOM = K2 · Qm) of 100. Comparing the response of similar AlScN and AlN resonators shows that the AlScN LWR has a significantly lower motional resistance (Rm), suggesting that AlScN has a strong potential for use in piezoelectric microelectromechanical oscillators.

Model-Based Analysis and Regulating Approach of Air-Coupled Transducers with Spurious Resonance.

As an essential characteristic of air-coupled transducers, electrical impedance can provide valuable information for quality control during manufacturing of transducers. It is also found feasible to directly read the optimal operating frequency from the impedance plots when the resonance is independent of the others. However, the spurious resonance emerges when two neighboring resonances are closely spaced, resulting in distorted impedance and ambiguous optimal operating frequency. In this paper, the electrical impedance of air-coupled transducers with spurious resonance is modeled using the Butterworth–Van Dyke (BVD) equivalent circuit. Then model-based sensitivity analysis is performed to evaluate the mutual interference between adjacent resonances. Based on the analysis results, the prestress method is proposed to regulate and suppress the spurious resonance by adjusting the equivalent parameters of the BVD model. Experimental study was carried out on the response of the electrical impedance and the vibration velocity of the transducer with spurious resonance to pre-tightening force. The results show that the spurious resonance disappeared when the pre-tightening force was initially loaded. Moreover, the vibration velocity of two main resonance peaks increases about 45.6% and 33.9% as the pre-tightening torque increases to 0.25 N∙m. Hence it is validated that the proposed prestress method is efficient to suppress the spurious resonance and improve the transducers performance.

Rapid and dynamic detection of antimicrobial treatment response using spectral amplitude modulation in MZO nanostructure-modified quartz crystal microbalance

We report a dynamic and rapid detection of the response of S. epidermidis to various antimicrobial treatments utilizing the real-time spectral amplitude modulations of the magnesium zinc oxide nanostructure-modified quartz crystal microbalance (MZOnano-QCM) biosensor. The sensor consists of a quartz crystal microbalance (QCM) with magnesium zinc oxide (MZO) nanostructures grown directly on the sensing electrode using metalorganic chemical vapor deposition (MOCVD). Combining the high sensitivity detection of bacteria provided by the MZO nanostructures with the QCM's dynamic acoustic spectrum makes a highly-sensitive dynamic biosensor well-suited for monitoring viscoelastic transitions during drug treatment compared to the QCM's conventional frequency shift signals. We demonstrated dynamically monitoring the response of S. epidermidis to various concentrations of the drug ciprofloxacin, and response to three different antimicrobials vancomycin, oxacillin, and ciprofloxacin, using spectral amplitude modulations of the MZOnano-QCM. Our results indicate that the amplitude modulations exhibit high sensitivity to S. epidermidis response to different drug treatments compared to the conventional frequency shift signals of the device, allowing for rapid determination (within 1.5 h) of the efficacy of the antimicrobial drug. The high sensitivity demonstrated by the spectral amplitude modulations is attributed to the direct relationship of these signals to the viscoelastic transitions of the bacterial cells on the device's sensing area while responding to drug treatment. This relationship is established by the Butterworth-Van-Dyke (BVD) model of the MZOnano-QCM. Standard microbiological protocols and assays were performed to determine the optimal drug dosages and the minimum inhibitory concentrations to serve as the benchmark for the sensor data.

BVD model for QCM loaded by viscoelastic film in gas phase application

As an ultra-sensitivity sensor, a quartz crystal microbalance (QCM) could be used to quantitatively characterize the relation between QCM parameters and the characteristics of viscoelastic films. When a QCM coated with a viscoelastic thin film is in the gas phase, based on the constructive equation of the quartz crystal and ignoring the capacitance effect, the equivalent Butterworth–Van Dyke (BVD) model of the QCM and the explicit expression for its frequency shift are derived. The “extra mass effect” deduced by the complex modulus is also obtained. It is found that the tendency of the BVD model in this work agrees well with that of Voinova’s model, although both are derived in different ways. Meanwhile, it can be seen that the two above-mentioned models exhibit different characteristics when compared with Sauerbrey’s model and Arnau’s model. The BVD model will help analyze the properties of viscoelastic films in the gas phase.

A Broadband Resonant Noise Matching Technique for Piezoelectric Ultrasound Transducers

A novel resonant noise matching technique is proposed to improve the sensitivity and output SNR of ultrasound receivers. Diverse from the power matching, the resonant noise matching technique proposed in this paper applies resonant LC networks to raise the transducers’ input impedance to a high impedance. As a consequence, in addition to the function of improving the output signal strength, the prominent advantage of the resonant noise matching technique is that the passive gain provided by the matching network can reduce equivalently the receiver’s input-referred noise and thus obtain the minimum noise figure. Furthermore, broadband matching which can cover the transducers’ working bandwidth is also developed to reduce the ringing in received signals, which can significantly improve axial resolution in applications of imaging. For this, an accurate electrical model extended from Butterworth Van-Dyke (BVD) model is obtained to co-simulate with the new matching network in the design. Measurement results show that, the output signal is improved by 5 times through the proposed technique, which is 66.7% larger than that of conventional methods. In addition, the sensitivity of the receiver is significantly improved by more than 10.4 dB which is beneficial for piezoelectric ultrasound transducers in a variety of applications.

Design, Analysis and Finite Element Modeling of Solidly Mounted Film Bulk Acoustic Resonator for Gas Sensing Applications

This paper reports the effect of the design parameters of a solidly mounted film bulk acoustic resonator (SMFBAR) for better gas sensing performance. The electrical equivalent circuit of the proposed device has been developed with the help of a Butterworth Van-Dyke (BVD) circuit. The electro-mechanical response of the SMFBAR has been obtained with the help of 3-D finite element method (FEM) analysis. The analytical modeling and FEM simulation results are compared. The physical parameters of the proposed design such as piezoelectric layer material, its thickness, active area of the device and sensing layer thickness affecting the characteristics of the SMFBAR have been investigated in detail. To achieve enhanced sensitivity, the variation of square active area has been analysed with one side dimension ranging from 700 μm to 300 μm. Gas sensing performance of the proposed sensor is tested by exposing toluene gas concentration ranging from 0 ppm to 500 ppm and enhanced sensitivity of 20 kHz/ppm has been achieved and reported. Also, it is reported that the variation in ratio of electrode layer thickness to piezoelectric layer thickness results in improvement of coupling coefficient (keff2) up to 7.46%.

Frequency-dependent equivalent modelling of broadband air-coupled transducers

Electrical impedance is an essential parameter for characterizing the performance of transducers during manufacturing and application phases. The conventional method to model the electrical impedance is based on Butterworth–Van Dyke (BVD) model with constant equivalent parameters, which is valid only in the neighborhood of resonance frequency. In this study, we present a method for modelling the electrical impedance over broadband featuring an improved BVD model with frequency-dependent equivalent parameters. In order to obtain frequency-dependent parameters from the measured impedance, estimation is performed in a constrained piecewise and stepwise manner. Firstly, a concise calculation method to obtain initial values of equivalent parameters is presented. Then, the original impedance is equally divided into multiple segments and the resonant segments containing the resonant frequencies are located. New impedance data is reconstructed with one of non-resonant segments and the resonant segments. Finally, with the initial values refined by genetic algorithm (GA), equivalent parameters are obtained from the reconstructed impedance based on GA. The estimation results are assigned to the central frequency point of the non-resonant segment. A new segment is generated by shifting the last non-resonant segment one frequency interval, and data reconstruction and estimation process are repeated till all parameters at each frequency are gained. Frequency-dependent parameters are obtained by the combination of a series of constant parameters at each frequency. The proposed method is verified with good accuracy in modelling of electrical impedance and transmitting response of broadband air-coupled transducer used for gas flow measurement which are difficult to be accurately modelled by the traditional method.

Digital ammonia gas sensor based on quartz resonator tuned by interdigital electrode coated with polyaniline film

Abstract This paper reported an ammonia gas sensor which was constructed by an interdigital electrode (IDE) coated with PANI thin film connected to quartz resonator in series. The sensor could convert concentration change of ammonia into frequency shift of the quartz resonator through the frequency tuning effect of IDE. Test result showed that the digital ammonia gas sensor exhibited a large frequency shift approximately 1500 Hz in ammonia concentration range of 20–1200 ppm, namely the proposed sensor showed higher frequency change compared with the majority of QCM ammonia sensors. The experiment suggested that the resistance of IDE coated with PANI film increased and meanwhile its capacitance decreased with increasing of ammonia gas concentration. Simulation on Butterworth-van Dyke (BVD) circuit of the sensor revealed that the capacitance of IDE coated with PANI played a major role in tuning of the quartz resonator although the capacitance changed little, while the resistance tuning effect was relatively weak. Compared with the traditional QCM gas sensors, the proposed sensor had a very fast response speed and a good anti-interference ability to pollutants and electromagnetic fields due to encapsulation of quartz crystal.

In-situ polymerization of metal organic frameworks-derived ZnCo2O4/polypyrrole nanofilm on QCM electrodes for ultra-highly sensitive humidity sensing application

A metal organic frameworks (MOFs)-derived ZnCo2O4/polypyrrole (ZnCo2O4/PPy) nanocomposite coated QCM humidity sensor with high performance was demonstrated in this paper. The element composition, morphology and nanostructure of the ZnCo2O4/PPy nanocomposite were characterized by energy dispersive spectroscopy (EDS), FT-IR spectrums, X-ray diffraction (XRD), scanning electron microscopy (SEM), and atomic force microscopy (AFM). All humidity sensing tests of ZnCo2O4/PPy QCM sensor were performed under room temperature environment. The experimental results revealed that the ZnCo2O4/PPy sensor exhibits excellent humidity sensing behavior. Comparing with pure PPy and pure ZnCo2O4 sensor, ZnCo2O4/PPy film coated QCM humidity sensor displays higher sensitivity (58.4 Hz/%RH) and better response/recovery properties (8 s/7 s). Besides, the equivalent circuit elements parameters of ZnCo2O4/PPy coated QCM sensor at various RH environments were determined by the modified Butterworth-Van-Dyke (BVD) equivalent circuit model. And the adsorption kinetics of water molecules was investigated by bimodal exponential kinetic adsorption model.