Modified Butterworth-Van Dyke Model Research Articles

Analysis of near field mutual coupling in wideband magnetoelectric antennas array

The operating bandwidth of miniaturized magnetoelectric (ME) antenna is generally narrow due to the acoustic wave driven magneto-electromechanical resonance effect, parallel connection of multiple ME antennas with different resonant frequencies is an effective way to broaden the operating bandwidth of the antenna. This paper presents an ME antenna array consisting of three units, which are constructed of a sandwich stack of Metglas/Pb(Mg1/3Nb2/3)O3–PbTiO3/Metglas. The −3 dB operating bandwidth of 152.4–172.8 kHz is achieved, and the relative bandwidth is 12.5%. Experimental results indicated that the bias magnetic field and coupling effect between the ME antenna units significantly influence the performance of ME antenna array. A modified Butterworth–Van Dyke (MBVD) equivalent circuit model is used and improved to analyze the influence of sound waves, electric fields, magnetic fields, parasitic capacitance, and bias magnetic field on the ME antenna array. The simulation results of the MBVD equivalent circuit model are agreed well with the experimental results. The improved MBVD model is beneficial for the design of acoustic wave driven antenna array.

Laterally-excited bulk acoustic wave resonator with an adjustable piezoelectric coupling coefficient

This paper reports on a design journey for a laterally-excited bulk acoustic wave resonator (XBAR) with an adjustable piezoelectric coupling coefficient (K 2). The vibration principle and resonant characteristics of XBAR are investigated by theoretical and simulation analysis, and the way to adjust K 2 by introducing two grooves in the area between interdigital electrodes (IDEs) is proved to be effective by using the finite-element method (FEM) simulation and the Modified Butterworth–Van Dyke model with series capacitor C r (MBVD-C r ) first, and then the impact of groove depth (H g) and groove width (W g) on K 2 of XBAR is theoretically analyzed. Specifically, K 2 can be effectively adjusted by setting different values of H g and W g. After optimization, the maximum regulation range of K 2 is from 2.02% to 45.05%. The fluted XBAR has remarkable potential in building an XBAR bandpass filter for specific frequency bands, which greatly optimizes the XBAR filter design.

Al0.7Sc0.3N butterfly-shaped laterally vibrating resonator with a figure-of-merit (kt2·Qm) over 146

This work presents the laterally vibrating Lamb wave resonators (LVRs) based on a 30% aluminum scandium nitride (Al0.7Sc0.3N) thin film with three interdigited transducer pairs operating in the S0 mode. In order to reduce the anchor loss, perfect matched layer-based finite element analysis simulations are utilized to design and optimize the device. Thanks to the high quality AlScN using magnetron sputtering with a single alloy target, vertical etching profile, and designed device structure, 1-μm-thick Al0.7Sc0.3N-based LVRs with high performance are fabricated. The resonator equivalent electric parameters are extracted utilizing the modified Butterworth–Van Dyke model. The best Al0.7Sc0.3N LVR achieves an electromechanical coupling coefficient (kt2) of 9.7% and a loaded quality factor (Qr) of 1141.5 operating at approximately 305 MHz. The same resonator shows a motional quality factor (Qm) of 1507.2, resulting in a high figure-of-merit (FoM = kt2 · Qm) of 146.2. A 1.8 MHz tuning range is measured for an Al0.7Sc0.3N LVR by applying DC voltage in the range of −40 to 40 V due to the ferroelectric property of high Sc doping in Al0.7Sc0.3N. With the high FoM, Qr, Qm, and low motional resistance (Rm), the Al0.7Sc0.3N-based LVRs show strong potential in applications of radio frequency communications and piezoelectric transducers.

Simulation of Wide Band BAW Filter for N78 Application

Based on the requirements of large bandwidth filters for 5G communications, finite element models for material analysis and filter design are established. Characteristics of lithium niobate under different cut angle are simulated, and 36° Y cut lithium niobate is used in resonator with SiO2/Mo acoustic reflector. The influence of top electrode is evaluated and the area of the electrode is designed. A method of co-simulation using finite element model and modified Butterworth van Dyke model is introduced. A wide band filter with relative bandwidth of 10.1% is designed while the insertion loss is less than 2 dB, which can satisfy the requirement of N78 band.

Dependence of Modified Butterworth Van-Dyke Model Parameters and Magnetoimpedance on DC Magnetic Field for Magnetoelectric Composites.

This study investigates the impedance curve of magnetoelectric (ME) composites (i.e., Fe80Si9B11/Pb(Zr0.3Ti0.7)O3 laminate) and extracts the modified Butterworth–Van Dyke (MBVD) model’s parameters at various direct current (DC) bias magnetic fields Hdc. It is interesting to find that both the magnetoimpedance and MBVD model’s parameters of ME composite depend on Hdc, which is primarily attributed to the dependence of FeSiB’s and neighboring PZT’s material properties on Hdc. On one hand, the delta E effect and magnetostriction of FeSiB result in the change in PZT’s dielectric permittivity, leading to the variation in impedance with Hdc. On the other hand, the magnetostriction and mechanical energy dissipation of FeSiB as a function of Hdc result in the field dependences of the MBVD model’s parameters and mechanical quality factor. Furthermore, the influences of piezoelectric and electrode materials properties on the MBVD model’s parameters are analyzed. This study plays a guiding role for ME sensor design and its application.

Dual-mode thin film bulk acoustic wave resonator and filter

Bulk acoustic wave (BAW) filters have been extensively used in consumer products for mobile communication systems due to their high performance and a standard CMOS compatible integration process. However, a traditional BAW filter generally presents only one frequency transmission band; hence, it cannot meet the demands of multi-mode wireless communication systems. In this work, we propose a radio frequency dual-band filter based on a dual-mode film bulk acoustic resonator (FBAR). The dual-mode FBAR consists of molybdenum electrodes and an aluminum nitride film with a c axis tilt angle, which leads to the coexistence of the longitudinal mode and the shear mode in the resonator. The influence of the tilt angle on the resonant frequency and electromechanical coupling coefficient of the dual-mode FBAR is investigated. Subsequently, the behaviors of the dual-mode FBAR have been emulated by a modified Butterworth–Van Dyke model with two motional branches, which is further used to design and optimize the dual-band filter. The dual-mode FBAR-based filters connected in a ladder configuration present two dual passbands of 43 MHz and 105 MHz, respectively. The developed filters with dual passbands can give an inspiration to the design of BAW devices in modern wireless communications.

Synthesis of Chebyshev/Elliptic Filters Using Minimum Acoustic Wave Resonators

Acoustic wave (AW) filters for next-generation wireless communication systems are designed to prevent signal interference and to be as small as possible. Using a pole-zero extraction method with a ladder-type AW filter, this paper proposes an algorithm to optimize the parameters for each AW resonator. The pole-zero positions of the equivalent circuit model are aligned with those of a Chebyshev or elliptic filter in the s-domain in order to give a frequency response that satisfies the system requirements in terms of insertion loss, out-band attenuation, and selectivity. The optimized parameters produce a system that has the minimum number of resonators to fulfill the filter performance specifications, with reduced manufacturing cost, which occupies a smaller area. Finally, the system is validated using a simulation with a LTE Band3 Rx elliptic filter and the parameters for an equivalent modified Butterworth-Van Dyke model (mBVD) for each resonator.

An artificial neural network‐based approach for the impedance modeling of piezoelectric energy harvesting devices

AbstractIn this paper, the equivalent series resistance (ESR) and capacitance (ESC) of piezoelectric energy harvesting devices have been modeled accurately over a wide frequency range for the first time. It is shown that the impedance modeling of the ESR and ESC is demonstrated as an important factor for the design of the Bias Flip (or the parallel synchronized switching harvesting on an inductor) interface circuit, which affects the performance of energy harvesting seriously. The conventional Butterworth‐Van Dyke (BVD) model and the modified BVD model are analyzed to state their imprecise modeling performance. To address this problem, an artificial neural network (ANN) technique with prior knowledge input method is employed to improve the model accuracy of the ESR and ESC. Also, a least‐squares curve fitting method is presented to compare with the ANN model. A good matching has been obtained between the measured and ANN‐predicted ESR and ESC in the frequency range of 2600 to 3600 Hz. The excellent performance on the accuracy of the proposed method is further illustrated through the comparison on the average relative error and maximum relative error with the conventional BVD, modified BVD model, and the curve fitting method.

A Wideband Bandpass Filter With Frequency Selectivity Controlled by SAW Resonators

A wideband bandpass filter (BPF) with two cascaded sections, each consisting of a surface acoustic wave (SAW) resonator and one or two transmission lines in parallel, is proposed. The lower and upper rolloffs of the passband are separately controlled by the narrowband characteristics of the SAW resonators to realize high frequency selectivity. The filter principle is analyzed for the two sections using the modified Butterworth-Van Dyke model for SAW resonators. The effects of cascading the two sections using a transmission line are also discussed. To demonstrate the proposed filter topology, two types of resonators are chosen from a limited set of available SAW resonator chips. The filter is designed and simulated based on the data of on-wafer measurements of the chip resonators. It is shown that the wideband behavior of the SAW resonators has impact on the filter. A prototype BPF centered at 2.02 GHz is implemented on PCB combining the discrete chip SAW resonators and microstrip lines. The chips are assembled using 1-mil wire bond technique. The measured filter has a 3-dB fractional bandwidth of 28.8% with high frequency selectivity.

Grey Box Non-Linearities Modeling and Characterization of a BandPass BAW Filter

In this work, the non-linearities of a 3G/UMTS geared BandPass Bulk Acoustic Wave ladder filter com- posed of five resonators were modeled using non-linear modified Butterworth-Van Dyke model. The non-linear characteristics were measured and simulated, and they were compared and found to be fairly identical. The filter's central frequency is 2.12 GHz, the corresponding band- width is 61.55 MHz, and the quality factor is 34.55.

Parasitic analysis and π-type Butterworth-Van Dyke model for complementary-metal-oxide-semiconductor Lamb wave resonator with accurate two-port Y-parameter characterizations.

The parasitic effects from electromechanical resonance, coupling, and substrate losses were collected to derive a new two-port equivalent-circuit model for Lamb wave resonators, especially for those fabricated on silicon technology. The proposed model is a hybrid π-type Butterworth-Van Dyke (PiBVD) model that accounts for the above mentioned parasitic effects which are commonly observed in Lamb-wave resonators. It is a combination of interdigital capacitor of both plate capacitance and fringe capacitance, interdigital resistance, Ohmic losses in substrate, and the acoustic motional behavior of typical Modified Butterworth-Van Dyke (MBVD) model. In the case studies presented in this paper using two-port Y-parameters, the PiBVD model fitted significantly better than the typical MBVD model, strengthening the capability on characterizing both magnitude and phase of either Y11 or Y21. The accurate modelling on two-port Y-parameters makes the PiBVD model beneficial in the characterization of Lamb-wave resonators, providing accurate simulation to Lamb-wave resonators and oscillators.

Response of an electrodeless quartz crystal microbalance in gaseous phase and monitoring adsorption of iodine vapor on zeolitic-imidazolate framework-8 film

In this work, the response of an electrodeless quartz crystal microbalance (EL-QCM) in gaseous phase was investigated by an impedance analysis method. The influence of the gap size, area, position and shape of the electrodes on the resonant and equivalent circuit parameters of the EL-QCM was analyzed and discussed in a modified Butterworth–Van Dyke model. Compared with a conventional QCM, the intensity of resonant peak in EL-QCM is reduced remarkably. An EL-QCM has a quality factor in the order of 105 even at an air gap of 1cm, ensuring an excellent frequency stability of this type of sensor. The excitation electrode can be mounted beside of the center of the quartz disc or outside the detection cell if needed, which offers the convenience in combination with mass and optical measurements. As an example of applications, two EL-QCM sensors in a parallel combination were used to monitor the adsorption processes of iodine vapor on quartz surface and zeolitic-imidazolate framework-8 (ZIF-8) film. The transfer process of iodine between two ZIF-8 films was investigated by the series combination of two EL-QCM sensors.

Numerical and experimental analysis of the parameters of an electroacoustic thin-film microwave resonator

The results of numerical and experimental analysis of the parameters of a single-frequency microwave thin-film electroacoustic resonator based on an (0001)AlN piezofilm with an acoustic reflector operating at a frequency of 10 GHz are presented. The effect of the reflector design on the resonator characteristics is considered. Using the modified Butterworth-Van Dyke model, it was shown that the ohmic resistance of electrodes and entrance paths substantially decreases the Q-factor at the resonance frequency of series and the acoustic losses in the resonator deteriorate the Q-factor at the parallel resonance frequency.

CMOS-compatible ruggedized high-temperature Lamb wave pressure sensor

This paper describes the development of a novel ruggedized high-temperature pressure sensor operating in lateral field exited (LFE) Lamb wave mode. The comb-like structure electrodes on top of aluminum nitride (AlN) were used to generate the wave. A membrane was fabricated on SOI wafer with a 10 µm thick device layer. The sensor chip was mounted on a pressure test package and pressure was applied to the backside of the membrane, with a range of 20–100 psi. The temperature coefficient of frequency (TCF) was experimentally measured in the temperature range of −50 °C to 300 °C. By using the modified Butterworth–van Dyke model, coupling coefficients and quality factor were extracted. Temperature-dependent Young's modulus of composite structure was determined using resonance frequency and sensor interdigital transducer (IDT) wavelength which is mainly dominated by an AlN layer. Absolute sensor phase noise was measured at resonance to estimate the sensor pressure and temperature sensitivity. This paper demonstrates an AlN-based pressure sensor which can operate in harsh environment such as oil and gas exploration, automobile and aeronautic applications.

Design and Analysis of Film Bulk Acoustic Resonator (FBAR) Filter for RF Applications

The RF band pass filters are important for wireless communication applications. They can be realized using Thin Film Bulk Acoustic Resonator (TFBAR).TFBAR is designed using Aluminium Nitride (AlN) and electrodes of piezoelectric material are made with Platinum (Pt). Various modelling techniques has been used for realizing three layered TFBAR structure. Modified Butter worth-van Dyke model (MBVD) is one used for numerical simulation of AlN film and thin electrodes. The result shows that Lm, Cm, Rm and Co model is perfectly applicable for predicting the response of TFBAR. The proposed design is realized by connecting three series and two shunt FBARs in ladder configuration. In the present work, the filter has been designed for a bandwidth of 270 MHz at −3 dB. The minimum insertion loss of −0.9 dB and return loss of –25 dB are obtained for VSWR ≤ 2 at resonance frequency.

A general procedure for the design of bulk acoustic wave filters

This article presents a procedure for the design of bulk acoustic wave (BAW) filters. The procedure consists of optimizing the modified Butterworth-Van Dyke model of each resonator, considering appropriate technological parameters. The approach is demonstrated first to design a classical aluminum nitride-based BAW filter but remains valid for other piezoelectric layers, considering either longitudinal or transverse acoustic wave coupling. The approach is finally applied to the design of a lithium niobate (LiNbO3) BAW filter for wide-band filtering applications. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011. © 2011 Wiley Periodicals, Inc.

Bulk acoustic wave filters synthesis and optimization for multi-standard communication terminals

This article presents a design methodology for bulk acoustic wave (BAW) filters. First, an overview of BAW physical principles, BAW filter synthesis, and the modified Butterworth-van Dyke model are addressed. Next, design and optimization methodology is presented and applied to a mixed ladder-lattice BAW bandpass filter for the Universal Mobile Telecommunications System (UMTS) TX-band at 1.95 GHz and to ladder and lattice BAW bandpass filters for the DCS1800 TX-band at 1.75 GHz. In each case, BAW filters are based on AlN resonators. UMTS filter is designed with conventional molybdenum electrodes whereas DCS filters electrodes are made with innovative iridium.

Modeling of RF filter component based on film bulk acoustic resonator

Film bulk acoustic resonator (FBAR) is widely used as an individual component RF filter in RF circuit because of its very high Q factor and low temperature coefficient. However, the RF pads and bonding wires of FBAR component will lower its Q factor. This effect is modeled by a new model named as PMBVD based on the traditional modified Butterworth-Van Dyke (MBVD) model in this paper. PMBVD model can describe FBAR individual component more exactly than MBVD model, especially near FBAR operating frequency, as proved by test results. The influences by different kinds of RF pads are also analyzed based on PMBVD. The simulations based on PMBVD show that optimized RF pads can enhance whole device Q factor to meet demands.

Equivalent-circuit model for the thickness-shear mode resonator with a viscoelastic film near film resonance.

We derive a lumped-element, equivalent-circuit model for the thickness-shear mode (TSM) resonator with a viscoelastic film. This modified Butterworth-Van Dyke model includes in the motional branch a series LCR resonator, representing the quartz resonance, and a parallel LCR resonator, representing the film resonance. This model is valid in the vicinity of film resonance, which occurs when the acoustic phase shift across the film is an odd multiple of pi/2 rad. For low-loss films, this model accurately predicts the frequency changes and damping that arise at resonance and is a reasonable approximation away from resonance. Elements of the parallel LCR resonator are explicitly related to film properties and can be interpreted in terms of elastic energy storage and viscous power dissipation. The model leads to a simple graphical interpretation of the coupling between the quartz and film resonances and facilitates understanding of the resulting responses. These responses are compared with predictions from the transmission-line and Sauerbrey models.

Mechanical resonance effects in electroactive polycarbazole films

Abstract We describe crystal impedance data acquired dynamically during the electropolymerization of carbazole, to produce polycarbazole films on the electrode surface. Data were obtained at the fundamental and third harmonic modes of a 10 MHz thickness shear mode resonator. At a critical thickness, the system exhibits mechanical resonance, a special condition in which the mechanical shear deformation across the polymer film corresponds to one quarter of the acoustic wavelength. This situation has not been reported previously for electroactive polymer films exposed to a liquid phase. At this point, the resonant frequency and admittance data show dramatic changes with polymer coverage. Prior to mechanical resonance, the impedance spectra can be fitted readily to a modified Butterworth–Van Dyke model, recognizing the presence of an ideal mass layer, a finite viscoelastic layer and a semi-infinite Newtonian fluid (the electrolyte). The data indicate spatial variation of shear modulus.