A laser probe based on a Sagnac interferometer with fast mechanical scan for RF surface and bulk acoustic wave devices

This paper describes the development of a phasesensitive laser probe with fast mechanical scan for RF surface and bulk acoustic wave (SAW/BAW) devices. The Sagnac interferometer composed of micro-optic elements was introduced for the selective detection of RF vertical motion associated with RF SAW/BAW propagation and vibration. A high-pass characteristic of the interferometer makes the measurement very insensitive to low-frequency vibration. This feature allows us to apply the fast mechanical scan to the interferometric measurement without badly sacrificing its SNR and spatial resolution. The system was applied to the visualization of a field pattern on the vibrating surface of an RF BAW resonator operating in the 2 GHz range. The field pattern was obtained in 17 min as a 2-D image (500 × 750 pixel with 0.4 μm resolution and SNR of 40 dB). The system was also applied to the characterization of an RF SAW resonator operating in the 1 GHz range, and the applicability of the system was demonstrated.     

Acoustic, piezoelectric, and dielectric nonlinearities of AlN in coupled resonator filters for high RF power levels

Coupled resonator filters (CRFs) are the new generation of BAW filters recently designed for the front-end modules of mobile transmission systems. Looking for designers' requirements, CRF devices have been characterized and modeled. The model based on equivalent circuits relies on material constants such as stiffness and electro-coupling coefficients, and works only for linear-mode propagation. Because of their positions between antennas and power amplifiers, they often work under high RF power, inducing nonlinear response in the AlN piezoelectric layer. In this work, we analyze for the first time the nonlinear behavior of AlN material particularly for coupled BAW resonators. To characterize the nonlinear effects in CRFs, we measure the 1-dB gain compression point (P1dB) and the intercept point (IP(3)). Then, we develop a nonlinear model of CRFs using harmonic balance (HB) simulation in commercially available software. The HB environment allows fitting simulations to measurements in terms of P(1dB) and IP(3). We find that a high RF power induces nonlinear changes in the material constants' real parts: elastic stiffness c(33) (4.9%), piezoelectric e(33) (17.4%), and permittivity ?(33) (5.2%). These nonlinear variations of material constants describe the nonlinear behavior of CRF devices using the same deposit process for AlN material.     

Theory and design of piezoelectric resonators immune to acceleration: present state of the art

A typical low noise oscillator uses a crystal resonator as the frequency-determining element. An understanding of the fundamental nature of acceleration sensitivity in crystal oscillators resides primarily in understanding the behavior of the crystal resonator. The driving factor behind the acceleration-induced frequency shift is shown to be deformation of the resonator. The deformation drives two effects: an essentially linear change in the frequency-determining dimensions of the resonator and an essentially nonlinear effect of changing the velocity of the propagating wave. In this paper, the fundamental nature of acceleration sensitivity is reviewed and clarified, and attendant design guidance is developed for piezoelectric resonators. The basic properties of acceleration sensitivity and general design guidance are developed through the simple examples of “bulk acoustic wave (BAW) in a box” and “surface transverse wave (STW) in a box.” These examples serve to clarify a number of concepts, including the role of mode shape and the basic difference between the BAW and STW cases. The design equations clarify the functional dependencies of the acceleration sensitivities on the full range of crystal resonator design and fabrication parameters     

Effects of H2O partial pressure on the crystallinity of ZnO thin film and electrical characteristics of film bulk acoustic wave resonators

We have improved electrical characteristics of a film bulk acoustic wave (BAW) resonator that features the injection of H₂O gas into a process chamber. The preferred crystallinity of piezoelectric ZnO film was obtained by RF sputtering at a high H₂O partial pressure 1.5×10⁻⁴ Pa. The effective electromechanical coupling coefficient () of the BAW resonator remarkably goes up from 1.8% to 4.7% for which the corresponding H₂O partial pressures are 2.7×10⁻⁵ and 1.5×10⁻⁴ Pa. Injection of H₂O during the deposition process contributes to the improvement of crystallinity of ZnO thin film and the electrical characteristics of the BAW resonator.     

Determination of ZnO temperature coefficients using thin film bulk acoustic wave resonators

Thin film bulk acoustic wave (BAW) resonators have been the subject of research in RF microelectronics for some time. Much of the interest lay in utilizing the resonators to design filters for wireless applications. Some of the major advantages BAW devices present over other filter technologies in use today include size reduction and the possibility of on-chip integration. As the technology matures, the necessity to more fully characterize the performance of the devices and to develop more accurate models describing their behavior is apparent. In this investigation, the effects that temperature variations have on 1.8-2.0 GHz zinc oxide (ZnO)-based solidly mounted BAW resonators (SMRs) are studied. The average temperature coefficients of the series and parallel resonant frequencies of the fabricated devices are found to be -31.5 ppm//spl deg/C and -35.3 ppm//spl deg/C, respectively. The slight decrease in separation between the two resonant frequencies with temperature implies there is slightly less effective coupling with increased temperature. No definite trend is found describing the behavior of the quality factor (Q) of the resonator with temperature variations. With little temperature coefficient data for thin film ZnO available in the literature, the importance of an accurate model is evident. The resonator device performance is simulated using Ballato's electronic circuit model for acoustic devices on a SPICE-based platform. By virtue of the comparison between the predicted and measured device response, various material parameters are extracted.     

Theoretical considerations on influence of circuit impedance on IMD2 measurement of radio-frequency bulk acoustic wave duplexers

This paper discusses theoretically how the impedance of peripheral circuits influences the measurement of second-order inter-modulation distortion (IMD2) generated in RF BAW duplexers. First, IMD2 properties of RF BAW duplexers are expressed by a rank three tensor. Then, the tensor expression is used to evaluate how the port termination affects the IMD2 output. It is shown that variation of IMD2 output is caused mainly by five mechanisms: 1) variation of the transmit (Tx) signal intensity caused by impedance mismatching at the Tx port; 2) variation of the jammer signal intensity caused by impedance mismatching at the antenna (ANT) port; 3) variation of detector read caused by impedance mismatching at the receive (Rx) port; 4) reentry of the IMD2 signal to the ANT port caused by impedance mismatching at the ANT port; and 5) reentry of the Tx signal to the ANT port caused by impedance mismatching at the ANT port. Because input impedance of the ANT port is usually not defined for jammer signals, a large attenuator must be added to the ANT port to suppress the impedance mismatching. This result is consistent with experiments reported previously.     

Synthesis and bulk acoustic wave properties on the dual mode frequency shift of solidly mounted resonators

This study focused on the fabrication and the theoretical analysis of solidly mounted resonators (SMR) concerning dual-mode frequency responses and their frequency shift of bulk acoustic wave (BAW) resonance. For this device fabrication, RF/DC magnetron sputtering and photolithography were employed to constitute the required multilayer structure. For the theoretical analysis, the dualmode frequency shift was characterized by the Sauerbrey's formula, and a modified formula was carried out following the trend for the large frequency shift. In the fabrication of the SMR device, Mo/SiO2 was chosen to construct the Bragg reflector as the high/low acoustic impedance materials, respectively, and aluminum nitride (AlN) was used as a piezoelectric layer. To investigate the characteristics of BAW on the dual-mode frequency shift, the c-axis tilted angle of AlN was altered as well as the various mass loading on the SMR. Based on the experimental results, the dual-resonance frequencies showed a nonlinear decreasing trend with a linear increase of the mass loading. Therefore, a modified formula was carried out. Furthermore, the ratio of the longitudinal-resonant frequency to the shear-resonant frequency remained at a range around 1.76 despite the various c-axis tilted angles of AlN and gradual mass loading on the SMR. The electromechanical coupling coefficient, k2(eff), of the shear resonance rose with the increase of the c-axis tilted angle of AlN.     

Design and Construction of a Helical Resonator for Delivering Radio Frequency to an Ion Trap

Supplying high voltage radio frequency (RF) is a critical part of ion trapping system due to impedance mismatching between RF source and the ion trap. A helical resonator has been constructed in order to deliver narrow bandwidth and high voltage RF to the ion trap for stable confinement of ions. The performances of the helical resonator have been studied for different capacitive load of the ion trap. Both the resonant frequency and quality factor of the resonator show strong dependence on external capacitive loads.     

Modeling of quartz crystal oscillators by using nonlinear dipolar method

A quartz crystal oscillator can be thought of as a resonator connected across an amplifier considered as a nonlinear dipole the impedance of which depends on the amplitude of the current that flows through it. The nonlinear amplifier resistance and reactance are obtained by using a time domain electrical simulator like SPICE (Simulation Program with Integrated Circuit Emphasis): the resonator is replaced with a sinusoidal current source of the same frequency and a set of transient analyses is performed by giving the current source a larger amplitude. A Fourier analysis of the steady-state voltage across the dipolar amplifier is performed to calculate both real and imaginary parts of the dipolar impedance as a function of the current amplitude. From these curves, it is then possible to accurately calculate the oscillation amplitude and frequency without having to perform unacceptably long transient analyses needed by a direct oscillator closed loop simulation. This method implemented in the Analyse Dipolaire des Oscillateurs a Quartz or Quartz Crystal Oscillators Dipolar Analysis (ADOQ) program calculates the oscillation start-up condition, the oscillation steady-state features (oscillation amplitude and frequency), and the oscillator sensitivity to various parameters. The oscillation nonlinear differential equation is solved by using the slowly varying function method so that the program quickly and accurately calculates the current amplitude and frequency transients. Measurements performed on an actual amplifier show a very good agreement with the results obtained by the simulation program.     

Precision close-to-carrier phase noise simulation of BAW oscillators

Based on a commercial simulation tool, the influence of BAW resonator noise on the resulting oscillator phase noise is revisited. The parametric model of the resonator uses experimental data, and includes an f(-2) noise not often considered in measurements, in addition to its flicker noise.     

Estimating materials parameters in thin-film BAW resonators using measured dispersion curves

The dispersion curves of Lamb-wave modes propagating along a multilayer structure are important for the operation of thin-film bulk acoustic wave (BAW) devices. For instance, the behavior of the side resonances that may contaminate the electrical response of a thin-film BAW resonator depends on the dispersion relation of the layer stack. Because the dispersion behavior depends on the materials parameters (and thicknesses) of the layers in the structure, measurement of the dispersion curves provides a tool for determining the materials parameters of thin films. We have determined the dispersion curves for a multilayer structure through measuring the mechanical displacement profiles over the top electrode of a thin-film BAW resonator at several frequencies using a homodyne Michelson laser interferometer. The layer thicknesses are obtained using scanning electron microscope (SEM) measurements. In the numerical computation of the dispersion curves, the piezoelectricity and full anisotropy of the materials are taken into account. The materials parameters of the piezoelectric layer are determined through fitting the measured and computed dispersion curves.     

Nonlinear modal analysis via non‐parametric machine learning tools

Modal analysis is an important tool in the structural dynamics community; it is widely utilised to understand and investigate the dynamical characteristics of linear structures. Many methods have been proposed in recent years regarding the extension to nonlinear analysis, such as nonlinear normal modes or the method of normal forms, with the main objective being to formulate a mathematical model of a nonlinear dynamical structure based on observations of input/output data from the dynamical system. In fact, for the majority of structures where the effect of nonlinearity becomes significant, nonlinear modal analysis is a necessity. The objective of the current paper is to demonstrate a machine learning approach to output‐only nonlinear modal decomposition using kernel independent component analysis and locally linear‐embedding analysis. The key element is to demonstrate a pattern recognition approach which exploits the idea of independence of principal components from the linear theory by learning the nonlinear manifold between the variables. In this work, the importance of output‐only modal analysis via “blind source” separation tools is highlighted as the excitation input/force is not needed and the method can be implemented directly via experimental data signals without worrying about the presence or not of specific nonlinearities in the structure.     

Comparison between BAW and SAW sensor principles

A comparison is given between piezoelectrically excited bulk acoustic wave (BAW) and surface acoustic wave (SAW) elements with respect to their primary sensitivity functions and principal capabilities for sensor applications. The importance of mode purity for high dynamic range sensors is emphasized. Characteristic sensor examples are reviewed, and the special demands on the electronics for BAW and SAW elements in the sensor field are described (e.g., cable problem, wireless SAW sensors). For a fair evaluation, a performance figure, SQ, defined as the product of reduced sensitivity S and resonator Q-value, is introduced. The potential of alternative piezoelectric materials for future sensor developments is discussed briefly.     

An X-band, high power dielectric resonator oscillator for future military systems

A 9.0-GHz dielectric resonator oscillator (DRO), generating a CW output power of 2.5 W at room temperature, has been designed and fabricated using a high-power GaAs MESFET and a dielectric resonator (DR) in a parallel feedback configuration. The oscillator exhibited a frequency stability of better than 130 ppm, without any temperature compensation, over the range -50 degrees C to +50 degrees C. The output power varied from +35 dBm (3.2 W) at -50 degrees C to +33 dBm (2 W) at +50 degrees C. The single-sideband phase noise levels were measured and found to be -105 and -135 dBc/Hz, at 10- and 100-kHz carrier offset frequencies, respectively. The oscillator output was then fed into a single-stage high-power MESFET amplifier, resulting in a total RF power output of 6.5 W. The overall DC to RF conversion efficiency of the 6.5-W unit was approximately 15.3%     

Unstable Cr:LiSAF laser resonator with a variable reflectivity output coupler

The performance of a flash-lamp-pumped Cr:LiSAF unstable laser resonator utilizing a fourth-order super-Gaussian variable reflectivity mirror as an output coupler is described. The super-Gaussian mirror results in a smooth, flattop transverse beam profile in the near field that is advantageous for nonlinear frequency-conversion applications. Long-pulse and Q-switched operation of the Cr:LiSAF unstable laser resonator are described and compared with stable resonator operation. We obtained tunable ultraviolet radiation extending from 267 to 290 nm by frequency mixing theQ-switched Cr:LiSAF laser output with lithium triborate and beta-barium borate nonlinear crystals.     

Electroelastic effect of thickness mode langasite resonators

Langasite is a very promising material for resonators due to its good temperature behavior and high piezoelectric coupling, low acoustic loss, and high Q factor. The biasing effect for langasite resonators is crucial for resonator design. In this article, the resonant frequency shift of a thickness-mode langasite resonator is analyzed with respect to a direct current (DC) electric field applied in the thickness direction. The vibration modes of a thin langasite plate fully coated with an electrode are analyzed. The analysis is based on the theory for small fields superposed on a bias in electroelastic bodies and the first-order perturbation integral theory. The electroelastic effect of the resonator is analyzed by both analytical and finite-element methods. The complete set of nonlinear elastic, piezoelectric, dielectric permeability, and electrostrictive constants of langasite is used in the theoretical and numerical analysis. The sensitivity of electroelastic effect to nonlinear material constants is analyzed.     

AlN薄膜体声波谐振器研究

采用一维Mason模型,研究了体声波谐振器的频率特性,探讨了压电薄膜AlN和上电极膜厚对谐振频率的影响,压电参数d33及压电薄膜与电极的厚度比率对机电耦合系数的影响,同时研究了谐振区域的面积和声能在衬底中的损耗对品质因数的影响.测量的体声波谐振器频率特性曲线与模拟结果吻合的较好.     

Sputtered SiO2 as low acoustic impedance material for Bragg mirror fabrication in BAW resonators

In this paper we describe the procedure to sputter low acoustic impedance SiO₂ films to be used as a low acoustic impedance layer in Bragg mirrors for BAW resonators. The composition and structure of the material are assessed through infrared absorption spectroscopy. The acoustic properties of the films (mass density and sound velocity) are assessed through X-ray reflectometry and picosecond acoustic spectroscopy. A second measurement of the sound velocity is achieved through the analysis of the longitudinal ?/2 resonance that appears in these silicon oxide films when used as uppermost layer of an acoustic reflector placed under an AlN-based resonator.     

Absolute linearity measurement of photodetectors using sinusoidal modulated radiation

A method is presented for characterizing the linearity of photodetectors based on time-domain analysis of response to sinusoidal excitation. Nonlinearity is quantified solely from the output distortion. Relative response is converted to absolute response by including two calibration points. For low signal level, one calibration point is required, while using dark current as the second point. The response is mapped over a wider range using a series of overlapping sinusoids for calibration transfer. The method is demonstrated with a relatively linear photodiode and a nonlinear phototransistor. A Michelson interferometer is used to generate sinusoidal modulation of a laser source. Results demonstrate the potential of the proposed technique.     

An Iterative Method for Computing the Surface Resistance of YBCO Thin Films in the Nonlinear Regime of RF Power

A numerical method to find, in the nonlinear regime, the quality factor, the surface resistance, and the resonance frequency of YBCO microstrip line resonator, deposited on both sides of an MgO substrate, is presented. The numerical method is based on an iterative self-consistent technique used to find the RF magnetic field in the nonlinear regime of the dissipation mechanisms. The determination of the RF magnetic field yields to the corresponding surface resistance and resonance frequency. The dependence of the geometrical factor of the film on the RF magnetic field is discussed. This latter is usually used as constant in the literature. However, in our calculation this factor has a maximum at a certain RF input power.