Modified Butterworth-Van Dyke Research Articles

Effect of Si substrate conductivity on surface acoustic wave resonator

A surface acoustic wave (SAW) filter’s bandwidth and quality are determined by its resonators’ electromechanical coupling coefficient (k2) and impedance ratio (IR). Research commonly focuses on the effects of piezoelectric material and cutting direction on these parameters. This paper investigates the effect of the conductivity of the Si substrate on k2 and IR through finite element method (FEM) simulations. A new model based on the modified Butterworth-van-Dyke (MBVD) model is presented. This new model takes into account the substrate parasitic capacitance and resistance to predict resonator performance on low resistivity (LR) Si piezoelectric on insulator (POI) substrates. Both high resistivity (HR) Si and LR-Si are utilized to fabricate POI SAW resonators, which are subsequently tested. The high conductivity of the Si support layer leads to a decrease in both k2 and IR. By employing Si substrates with different resistances during fabrication, it becomes possible to manufacture resonators with varying k2 values, thus meeting diverse bandwidth requirements for filters.

Analysis and measurement of high frequency piezoelectric ring resonator

This paper introduces a piezoelectric ring resonator, comprising a Mo-ScAlN-Mo sandwich structure and shaped into a ring with a hollow center. The vibrational modes of the resonator are elucidated through simulation and theoretical analysis, and the impact of diverse geometric parameters on the resonant frequency is explored. A HF resonator with a resonance frequency of 4.168 GHz has been fabricated. The electrical parameters of this resonator are extracted by fitting the Modified Butterworth-Van Dyke equivalent circuit model and the measured results. This work establishes a theoretical foundation for designing resonators with adjustable frequencies on a single wafer.

Magnetic field tunable piezoelectric resonator for MEMS applications

In this report, the Ni0.50Mn0.35In0.15/Pb0.96La0.04Zr0.52Ti0.48O3 (Ni-Mn-In/PLZT) bulk acoustic wave (BAW) resonator has been fabricated using the sputtering deposition technique. The magnetoelectric effect in the Ni-Mn-In/PLZT resonator has been investigated. The increase in magnetoelectric coupling coefficient (MECC) with the increment in the frequency of applied HAC is observed. The potential of the Ni-Mn-In/PLZT BAW resonator as a magnetic sensor is tested by measuring the shift in the resonant frequency of the reflective (S11 parameter) response in the presence of the externally applied magnetic field. The Ni-Mn-In/PLZT resonator exhibits a frequency shift of 730 MHz in the 1200 Oe magnetic field, among the largest magnetic field-induced frequency shifts in literature. The rarely reported complete dependence of acoustic velocity, coupling coefficients, magnetic sensitivity, and frequency peak shift on the strength of the external magnetic field is investigated. The acoustic velocity increases from 1237 m/s to 1394 m/s, and the electromechanical coupling coefficient increases from 0.0199 % to 0.0206 % after applying the 1200 Oe magnetic field. The reflective responses have been fitted using the Modified-Butterworth Van Dyke (MBVD) model in terms of hardly reported RLC equivalent circuits. The experimental results and extracted parameters from MBVD modeling exhibit high accuracy. This interaction between multiferroic orders and elastic resonance peaks opens a new window for highly sensitive future magnetic field sensors, wireless communication devices, and magnetic field tunable filters.

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.

Area Dependence of Effective Electromechanical Coupling Coefficient Induced by On-Chip Inductance in LiNbO3-Based BAW Resonators

To solve the problem of filter bandwidth in 5G communication, it is urgent to develop an acoustic resonator with a large effective electromechanical coupling coefficient (Keff2). In this paper, the dependence between the resonance area and the performance of the bulk acoustic wave (BAW) resonator is studied. The solidly mounted resonators (SMRs) based on 43° Y cut lithium niobate (LN) were fabricated by the wafer transfer technique. The on-chip inductor was integrated with the BAW resonator through a pad electrode. Resonators with different resonant areas were fabricated and tested. Finite element modeling (FEM) simulation of acoustic resonators and electromagnetic (EM) simulation of layout were carried out, respectively. The Modified Butterworth Van Dyke (MBVD) model was used to analyze the results, and simulation of the Mason model was adopted. The results show that the dependency relationship between the resonant area and the effective electromechanical coupling coefficient can be induced by on-chip inductance. In the resonant area range of 20 × 20 μm2~160 × 160 μm2, the Keff2 increases from 11.97% to 43.28%.

Investigation into the impedance characteristics of magnetoelectric antennas

Mechanical antenna is recently considered a novel scheme for realizing very low frequency (VLF) and portable transmitters. In this paper, the impedance characteristics of 1-1 typed and 2-1 typed magnetoelectric (ME) mechanical antennas are systematically studied and compared. Based on measured frequency-impedance curves and the corresponding MBVD (Modified Butterworth-Van Dyke) model, three characteristic frequency points, i.e., the minimum impedance frequency <i>f<sub>m</sub></i>, the series resonance frequency <i>f<sub>s</sub></i> and the resonance frequency <i>f<sub>r</sub></i> are obtained and discussed. On this basis, the influence of driving voltage, bias magnetic field, and the quality factor (Q value) on ME antenna impedance characteristics is experimentally explored. Finally, the reactance components of both 1-1 typed and 2-1 typed ME antenna are collected by referring to the actual working frequency <i>f<sub>d</sub></i>. Experimental results prove that resonant ME antennas are basically pure resistive vibrators, while a ME antenna with high Q value normally fails to support high driving field because of the low resistance (< 100Ω) and the strong nonlinearity. Thus, the field radiation capability in 2-1 typed ME antenna is higher than that of 1-1 typed one. This work provides perspectives for Q value selection and further optimization of a magnetoelectric antenna based on the understanding of its impedance characteristics.

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.

Development of PVDF-TrFE/SiO2 composite film bulk acoustic resonator

This paper reports a film bulk acoustic resonator (FBAR) using polyvinylidene fluoride- trifluoroethylene (PVDF-TrFE)/SiO2 composite. The PVDF-TrFE/SiO2 composite FBAR was designed, simulated and developed. A Micro Electro Mechanical Systems (MEMS) process including xenon difluoride (XeF2) release etching was adopted with some tuning for PVDF-TrFE. The influences of the process on the surface morphology and crystal orientation of PVDF-TrFE were evaluated for RIE, gold sputtering and XeF2 etching. After poling PVDF-TrFE, the thickness expansion mode was observed at 387–398 MHz. Impedance characteristics was evaluated using a modified Butterworth-Van Dyke (MBVD) model for a lossy piezoelectric transducer. Impedance ratio, coupling coefficient (k2), mechanical quality factor (Qm) and figure of merit increase with the radius of the device. The maximum Qm is 33 for 80 μm radius of the device. The residual film stress of PVDF-TrFE was estimated as 34.8 MPa in tensile mean stress and −79.7 kPa in gradient stress. Elastic stiffness constants c33D and c33E at electrical displacement D = 0 and electric field E = 0 were obtained as 4.45 GPa and 4.46 GPa, respectively.

Effect of quality factor on frequency stability of filmbulk acoustic resonator oscillator

The loaded quality factor (QL) of the film bulk acoustic resonator(FBAR) oscillator and the quality factor (Q value) of FBAR are related to the frequency stability of FBAR oscillator. In order to study the effect of the two kinds of quality factors on the frequency stability, the multi physical field model of FBAR was established in the COMSOL multiphysics software. The parameters of the modified Butterworth-Van Dyke (MBVD) model were got by frequency domain simulation and model parameter fitting. A model of MBVD circuit was established in the ADS software, and Q value for different loss was obtained by the simulation of S parameters and computing the corresponding Q value with the Bode method. The Pierce-based oscillator was established and simulated with the harmonic balance, thus the phase noise was obtained by changing QL and Q, and the effect of the two factors on frequency stability was got. The results show that the frequency stability increased with the increase of QL and Q, Q decreased with the increase of different losses. If the Q is lower than 338, the effect of increasing QL to improve the frequency stability is poor. Using this kind of FBAR to construct oscillator will not meet the requirements of FBAR wireless communication RF front-end as the reference signal source and the readout circuit of FBAR sensor. This paper provides a reference for FBAR frequency reference design and FBAR sensor readout circuit.

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.

A new model for film bulk acoustic wave resonators

Based on cavity resonance and sandwich composite plate theory, this paper presents a universal three-dimensional (3D) theoretical model for frequency dispersion characterization and displacement profile shapes of the film bulk acoustic resonator (FBARs). This model provides results of FBAR excited thickness-extensional and flexure modes, and the result of frequency dispersion is proposed in which the thicknesses and impedance of the electrodes and the piezoelectric material are taken into consideration; its further simplification shows good agreement with the modified Butterworth—Van-Dyke (MBVD) model. The displacement profile reflects the vibration stress distribution of electrode shapes and the lateral resonance effect, which depends on the axis ratio of the electrode shapes a/b. The results are consistent with the 3D finite element method modeling and laser interferometry measurement in general.

Simulation and Tuning of Film Bulk Acoustic Resonator Filters with Different Ladder Topologies

Different topologies and tuning of ladder filter made up of film bulk acoustic resonator (FBAR) using Modified Butterworth-Van Dyke (MBVD) model is studied. The influence to the filter by singly adding series or shunt FBAR is separately simulated. The three-stage ladder filter with different topologies is especially investigated. The five-stage ladder filter is studied by changing the inherent components of Lm and C0 in the FBAR.

Processing Chip for Thin Film Bulk Acoustic Resonator Mass Sensor

Aimed at portable application, a new integrated process chip for thin film bulk acoustic resonator (FBAR) mass sensor is proposed and verified with 0.18 um CMOS processing in this paper. The longitudinal mode FBAR with back-etched structure is fabricated, which has resonant frequency 1.878 GHz and Q factor 1200. The FBAR oscillator, based on the current-reuse structure, is designed with Modified Butterworth Van Dyke (MBVD) model. The result shows that the FBAR oscillator operates at 1.878 GHz with a phase noise of -107 dBc/Hz and -135 dBc/Hz at 10 KHz and 100 KHz frequency offset, respectively. The whole process chip size with pads is 1300 µm × 950 µm. The FBAR and process chip are bonded together to sense tiny mass. The measurement results show that this chip precision is 1 KHz with the FBAR frequency gap from 25 kHz to 25MHz.

Generalised Butterworth-Van Dyke equivalent circuit for thin-film bulk acoustic resonator

A generalised Butterworth-Van Dyke (GBVD) equivalent circuit model for a thin-film bulk acoustic resonator (FBAR), especially for a FBAR with a high electromechanical coupling constant (kt2), is presented. The derivation starts from the ideal impedance formula for the FBAR, then acoustic loss, dielectric loss, and electrode electrical loss are introduced step by step. Results show that the widely used modified Butterworth-Van Dyke (MBVD) model is a special case of a GBVD model using a low kt2 approximation.

Piezoelectric aluminum nitride resonator for oscillator

This work investigates properties of the thin film elongation acoustic resonator (TFEAR) operating at megahertz frequencies in air. This resonator is composed of a piezoelectric layer of AlN sandwiched between 2 Al electrodes. TFEAR works in the extensional mode excited via AlN d31 piezoelectric coefficient. A 3D finite element method (3D-FEM) analysis using ANSYS software has been performed to model static modal and harmonic behavior of the TFEAR. To consider insertion losses into the substrate, equivalent electrical models based on a modified Butterworth-Van Dyke (MBVD) circuit have been improved by adding extra dissipative elements. Thus, a whole model for the on-wafer characterization setup is given, allowing for automatic de-embedding of the present TFEAR equivalent circuit. Quality factors Q as high as 2500 in air have been recorded with motional resistance lower than 400 ohms. A first oscillator based on a TFEAR resonator was also designed and tested.

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.

MEMS BASED BULK ACOUSTIC WAVE RESONATORS FOR MOBILE APPLICATIONS

ABSTRACT A silicon based film bulk acoustic wave resonator (FBAR) composed with a filter and a duplexer is fabricated using the bulk micro-machining process. It has a simple MIM (metal-insulator-metal) membrane structure using molybdenum (Mo) for the top and bottom electrodes. The bulk acoustic wave resonances are generated by the piezoelectricity of aluminum nitride (AlN) with an air gap cavity fabricated below the membrane by silicon deep-etch process to reduce acoustic loss of FBAR. The fabricated FBAR is measured with HP 8510C vector network analyzer in wide (0.5∼10.5 GHz) and narrow (1.7∼2.1 GHz) frequency range. The measured series and parallel resonance frequencies are 1856 MHz and 1907 MHz, respectively. The minimum insertion losses are less than 0.07 dB at the series resonance frequency. With the increase of the membrane area, insertion loss decreases and effective electromechanical coefficient increases. The measured effective electromechanical coefficients are higher than 6.4%. The circuit modeling of FBAR is preformed based on the MBVD (modified Butterworth Van-Dyke) model. The above results demonstrate that the fabricated FBAR has sufficient performance to be the building block of RF filters for mobile applications.

Piezoelectric Properties of Aluminum Nitride for Thin Film Bulk Acoustic Wave Resonator

A film bulk acoustic wave resonator (FBAR) was fabricated by using RF-sputtered aluminum nitride (AlN) between 400 nm-thick molybdenum (Mo) bottom and top electrodes. To reduce the acoustic loss of FBARs, an air gap cavity is fabricated below the membrane by a silicon deep-etch process. The sputtered 950 nm-thick AlN film was oriented in the (002) direction. The FBARs were measured by using a HP 8510C vector network analyzer in a wide frequency range of 0.5 ∼ 10.5 GHz. A resonance frequency was observed near 2 GHz as well as another, a third mode about 7 GHz. The minimum insertion loss was 0.056 dB at 1858 MHz. An equivalent circuit modeling regarding this FBAR was performed with modified Butterworth Van-Dyke (MBVD) models, wellknown piezoelectric equivalent circuit models. The calculated effective electromechanical coupling coefficient (keff ) was greater than 6.59 %.

Air‐gap type TFBAR‐based filter topologies

AbstractExtremely small bandpass filters with TFBARs using aluminum nitride piezoelectric material have been realized in this study. Resonator modeling has been performed based on the modified Butterworth–Van Dyke (MBVD) model from the measured frequency responses of a single resonator. The predicted filter responses are compared with measured frequency data. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 386–387, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10470