Development of a micromachined piezoelectric microphone for aeroacoustics applications

This paper describes the design, fabrication, and characterization of a bulk-micromachined piezoelectric microphone for aeroacoustic applications. Microphone design was accomplished through a combination of piezoelectric composite plate theory and lumped element modeling. The device consists of a 1.80-mm-diam, 3-microm-thick, silicon diaphragm with a 267-nm-thick ring of piezoelectric material placed near the boundary of the diaphragm to maximize sensitivity. The microphone was fabricated by combining a sol-gel lead zirconate-titanate deposition process on a silicon-on-insulator wafer with deep-reactive ion etching for the diaphragm release. Experimental characterization indicates a sensitivity of 1.66 microVPa, dynamic range greater than six orders of magnitude (35.7-169 dB, re 20 microPa), a capacitance of 10.8 nF, and a resonant frequency of 59.0 kHz.     

A two-dimensional model of a directional microphone: calculation of the normal force and moment on the diaphragm

It has been shown that the parasitoid fly Ormia Ochracea exhibits exceptional sound localization ability achieved through the mechanical coupling of its eardrums [R. N. Miles et al., J. Acoust. Soc. Am. 98, 3059-3070 (1995)]. Based on this biological system a new directional microphone has been designed, having as a basic element a special diaphragm undergoing a rocking motion. This paper considers a 2D model of the microphone in which the diaphragm is considered as a 2D plate having slits on the sides. The slits lead to a backing volume limited by an infinite rigid wall parallel to the diaphragm in its neutral position. The reflection and diffraction of an incoming plane wave by this system are studied to determine the resultant force and resultant moment of pressure upon the diaphragm. The results show that such a microphone will be driven better in the case of narrow slits and deep cavities.     

Large signal performance of micromachined silicon condenser microphones

A mathematical model for the open-circuit output voltage of a micromachined silicon condenser microphone with a single deeply corrugated diaphragm as a function of the applied acoustic pressure is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the amplitudes of the output components resulting from a multisinusoidal input acoustic pressure. The special case of an equal-amplitude two-tone acoustic pressure input is considered in detail. The results show that the microphone generates only odd-order harmonic and intermodulation products. The results also show that the amplitudes of these components are strongly dependent on the microphone parameters, the corrugation depth and the ratio between the half-length of the diaphragm and its thickness. Moreover, the results show that the acoustic pressure required to produce a pre-specified output open-circuit voltage is strongly dependent on these parameters.     

Measurement of resonance frequency and loss factor of a microphone diaphragm using a laser vibrometer

The pressure sensitivity of a laboratory standard microphone is determined using a reciprocity technique that measures the electrical transfer impedance of two microphones connected acoustically by a coupler. The electrical transfer impedance is a function of the coupler volume and the equivalent volumes of the microphones. The equivalent volume given as a function of the frequency can be determined in experiments or can be calculated if the equivalent volume at a low frequency as well as the resonance frequency and loss factor of the microphone diaphragm are known. Therefore, it is necessary to determine the resonance frequency and the loss factor accurately to obtain an accurate reading of the pressure sensitivity.In this paper, a new method to determine the resonance frequency and loss factor of a microphone diaphragm is proposed. The frequency response of the diaphragm displacement is measured by a laser vibrometer and the part of the response near the resonance frequency is used to determine the microphone parameters via least square fitting with the equation of a vibration model with one degree-of-freedom. Since the values measured by this method are close to the nominal values and the repeatability is highly feasible, the proposed method will be useful to determine the resonance frequency and loss factor of a microphone diaphragm.     

Micromachined optical microphone structures with low thermal-mechanical noise levels

Micromachined microphones with diffraction-based optical displacement detection have been introduced previously [Hall et al., J. Acoust. Soc. Am. 118, 3000-3009 (2005)]. The approach has the advantage of providing high displacement detection resolution of the microphone diaphragm independent of device size and capacitance-creating an unconstrained design space for the mechanical structure itself. Micromachined microphone structures with 1.5-mm-diam polysilicon diaphragms and monolithically integrated diffraction grating electrodes are presented in this work with backplate architectures that deviate substantially from traditional perforated plate designs. These structures have been designed for broadband frequency response and low thermal mechanical noise levels. Rigorous experimental characterization indicates a diaphragm displacement detection resolution of 20 fm radicalHz and a thermal mechanical induced diaphragm displacement noise density of 60 fm radicalHz, corresponding to an A-weighted sound pressure level detection limit of 24 dB(A) for these structures. Measured thermal mechanical displacement noise spectra are in excellent agreement with simulations based on system parameters derived from dynamic frequency response characterization measurements, which show a diaphragm resonance limited bandwidth of approximately 20 kHz. These designs are substantial improvements over initial prototypes presented previously. The high performance-to-size ratio achievable with this technology is expected to have an impact on a variety of instrumentation and hearing applications.     

Improved eigenvalues for combined dynamical systems using a modified finite element discretization scheme

New approaches are presented to discretize an arbitrarily supported linear structure carrying various lumped attachments. Specifically, the exact eigendata, i.e., the exact natural frequencies and mode shapes, of the linear structure without the lumped attachments are first used to modify its finite element mass and stiffness matrix so that the eigensolutions of the discretized system coincide with the exact modes of vibration. This is achieved by identifying a set of minimum changes in the finite element system matrices and enforcing certain constraint conditions. Once the updated matrices for the linear structure are found, the finite element assembling technique is then used to include the lumped attachments by adding their parameters to the appropriate elements in the modified mass and stiffness matrices. Numerical experiments show that for the same number of elements, the proposed scheme returns higher natural frequencies that are substantially more accurate than those given by the finite element model. Alternatively, the proposed discretization scheme allows one to efficiently and accurately determine the higher natural frequencies of a combined system without increasing the number of elements in the finite element model.     

平衡衔铁受话器的非线性特性与失真仿真模型

平衡衔铁受话器(BAR)具有尺寸小、电声转换效率高和灵敏度高等特点。在大振幅振动时, BAR存在显著的非线性,并导致较严重的失真。利用磁路的集总参数模型(LPM)深入研究BAR的非线性,确立可表征其非线性特性的4个非线性参数,采用迭代计算方法研究平衡衔铁磁阻对非线性特性的重要影响。基于所提出的网格移动和旋转等效的有限元模型(FEM),考虑平衡衔铁磁阻的非线性,准确仿真计算得到非线性参数,再将它们代入到非线性LPM模型中,最终建立FEM与LPM相结合的失真仿真模型。实验结果表明,该失真仿真模型可比较准确地预测BAR在不同加载电压时的总谐波失真以及二次和三次谐波失真。     

Noise in miniature microphones

The internal noise spectrum in miniature electret microphones of the type used in the manufacture of hearing aids is measured. An analogous circuit model of the microphone is empirically fit to the measured data and used to determine the important sources of noise within the microphone. The dominant noise source is found to depend on the frequency. Below 40 Hz and above 9 kHz, the dominant source is electrical noise from the amplifier circuit needed to buffer the electrical signal from the microphone diaphragm. Between approximately 40 Hz and 1 kHz, the dominant source is thermal noise originating in the acoustic flow resistance of the small hole pierced in the diaphragm to equalize barometric pressure. Between approximately 1 kHz and 9 kHz, the noise originates in the acoustic flow resistances of sound entering the microphone and propagating to the diaphragm. To further reduce the microphone internal noise in the audio band requires attacking these sources. A prototype microphone having reduced acoustical noise is measured and discussed.     

弯曲振动薄圆盘的共振频率和等效电路参数研究

机电等效电路是分析复合换能器常用的一种解析方法, 但对薄圆盘而言, 由于弯曲振动的复杂性, 其等效集中参数很难获得, 该方法很少被应用. 本文从分布参数系统与集中参数系统等效角度, 根据动能相等原则和势能相等原则, 给出了弯曲振动薄圆盘的集中参数: 等效质量和等效弹性系数, 得到了共振频率方程, 并用ATILA软件模拟了其振动分布情况, 可以看出解析结果与数值结果趋于一致. 最后给出了分析复合振动系统时薄圆盘集中参数模型的等效电路. 本文的结果对弯曲振动复合换能器的设计提供了理论参考.     

Foil electret transducer for blood pressure monitoring

A foil electret microphone for use under the cuff of an automatic blood pressure monitoring system is described. The transducer is designed to operate with relatively flat sensitivity over a static pressure range of 40 to 250 mm Hg (5.33 X 10(4) to 3.33 X 10(5) dyn/cm2). The new electret microphone differs from conventional microphones used for airborne sound reception in two ways: (1) the diaphragm thickness is 50 micron rather than the typical 12.5 or 25 micron, and (2) the backplate contains a set of annular ridges spaced at 4 mm rather than the typical 7-10 mm. This microphone offers three advantages over the piezoelectric microphone now in use: (1) greater tolerance in positioning the microphone over the brachial artery, (2) nearly 20-dB higher sensitivity and signal-to-noise ratio, and (3) the ability to obtain measurements with the microphone placed midway between the elbow and shoulder. Tests of the new foil electret microphone in conjunction with the automatic blood pressure monitoring system indicate that the automatic and conventional measurements of systolic and diastolic blood pressure agree to within 5 mm Hg at least 90% of the time. In addition, the electret microphone is able to obtain automatic measurements on subjects with a wider range of ages and sizes.     

An analytical-numerical method for determining the mechanical response of a condenser microphone

The paper is based on determining the reaction pressure on the diaphragm of a condenser microphone by integrating numerically the frequency domain Stokes system describing the velocity and the pressure in the air domain beneath the diaphragm. Afterwards, the membrane displacement can be obtained analytically or numerically. The method is general and can be applied to any geometry of the backplate holes, slits, and backchamber. As examples, the method is applied to the Bruel & Kjaer (B&K) 4134 1/2-inch microphone determining the mechanical sensitivity and the mechano-thermal noise for a domain of frequencies and also the displacement field of the membrane for two specified frequencies. These elements compare well with the measured values published in the literature. Also a new design, completely micromachined (including the backvolume) of the B&K micro-electro-mechanical systems (MEM) 1/4-inch measurement microphone is proposed. It is shown that its mechanical performances are very similar to those of the B&K MEMS measurement microphone.     

Electromechanical coupling factor of capacitive micromachined ultrasonic transducers

Recently, a linear, analytical distributed model for capacitive micromachined ultrasonic transducers (CMUTs) was presented, and an electromechanical equivalent circuit based on the theory reported was used to describe the behavior of the transducer [IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 159-168 (2002)]. The distributed model is applied here to calculate the dynamic coupling factor k(w) of a lossless CMUT, based on a definition that involves the energies stored in a dynamic vibration cycle, and the results are compared with those obtained with a lumped model. A strong discrepancy is found between the two models as the bias voltage increases. The lumped model predicts an increasing dynamic k factor up to unity, whereas the distributed model predicts a more realistic saturation of this parameter to values substantially lower. It is demonstrated that the maximum value of k(w), corresponding to an operating point close to the diaphragm collapse, is 0.4 for a CMUT single cell with a circular membrane diaphragm and no parasitic capacitance (0.36 for a cell with a circular plate diaphragm). This means that the dynamic coupling factor of a CMUT is comparable to that of a piezoceramic plate oscillating in the thickness mode. Parasitic capacitance decreases the value of k(w), because it does not contribute to the energy conversion. The effective coupling factor k(eff) is also investigated, showing that this parameter coincides with k(w) within the lumped model approximation, but a quite different result is obtained if a computation is made with the more accurate distributed model. As a consequence, k(eff), which can be measured from the transducer electrical impedance, does not give a reliable value of the actual dynamic coupling factor.     

Modeling of a rotor speed transient response with radial rubbing

A rotor-stator model of a turbogenerator is introduced in order to investigate speed transients with rotor-to-stator rubbing caused by an accidental blade-off imbalance. In order to assess the angular deceleration of the rotor due to rubbing, the angular position of its cross-section is considered as an unknown of the problem. Displacement fields are discretized through a finite element formulation. The highly nonlinear equations due to contact conditions are solved through an explicit prediction-correction time-marching procedure combined with the Lagrange multiplier approach dealing with a node-to-line contact strategy. The developed numerical tool is suitable for analyzing rotor-stator interactions in turbomachines as the system passes through critical speeds during an accidental shutdown. The sensitivity of the system response to modeling, physical and numerical parameters is investigated. The results highlight the significant role of the friction coefficient together with the diaphragm modeling, from rigid to fully flexible, in the interaction phenomenon. Rigid models have the advantage of simplicity and provide reasonable estimations of the overall response of the turbine. A flexible model, however, may be more computationally intensive but is more appropriate in order to accurately capture quantities of interest such as shaft eccentricity and bearing loads.     

Time domain responses of hydraulic bushing with two flow passages

Hydraulic bushings are commonly employed in vehicle suspension and body sub-frame systems to control motion, vibration, and structure-borne noise. Since literature on this topic is sparse, a controlled bushing prototype which accommodates a combination of long and short flow passages and flow restriction elements is first designed, constructed and instrumented. Step-up and step-down responses of several typical fluid-filled bushing configurations are measured along with steady harmonic time histories of transmitted force and internal pressures. To analyze the experimental results and gain physical insights into the hydraulic bushing system, lumped system models of bushings with different design features are developed, and analytical expressions of transmitted force and internal pressure responses are derived by using the convolution method. Parametric studies are also conducted to examine the effect of hydraulic element parameters. System parameters are successfully estimated for both harmonic and step responses using theory and measurements, and the dynamic force measurements are analyzed using analytical predictions. Finally, some nonlinearities of the system are also observed, and the fluid resistance of flow passage is found to be the most nonlinear element.     

Parametric oscillator based on a single-layer resonant metamaterial

We perform numerical simulations demonstrating parametric generation and oscillation processes in a single-layer of metamaterial composed of split ring resonators (SRRs). In general, a parametric resonance is achieved by introducing a time-modulation of one of the energy-storing parameters of a resonant system. An individual SRR is a resonant system that can be modeled as an RLC-circuit inductively coupled to an applied time-varying magnetic field. The relatively simple circuit model can be employed to establish the range of parameters providing the growth of parametric oscillations within the SRR medium. We relate the numerically predicted circuit parameters that ensure the buildup of parametric oscillations to those parameters expected to be available in a modified SRR medium, in which lumped element varactors integrated into the SRRs are used as modulable capacitance elements.     

Experimental determination of cascade parameters of a hearing-aid microphone via the two-load method

Presented in this article is a computer-aided experimental method for obtaining the cascade parameters of the two-port model of a miniature hearing-aid microphone. The method is an adaptation of the "two-load" method [D.P. Egolf and R.G. Leonard, J. Acoust. Soc. Am. 62, 1013-1023 (1977)] to acoustoelectric, rather than electroacoustic, transducers. The cascade parameters of a particular microphone, determined by this method, were within 2.5 dB of the manufacturer's published open-circuit sensitivity data. In an attempt to further verify the numerical cascade-parameter data, a two-port model of the microphone was used to simulate experimental voltages developed across two different complex electrical load impedances attached to the microphone. The results showed experimental/simulation differences of no greater than 3.0 dB at any frequency. The two-port microphone model and associated cascade parameters are currently being incorporated into a computer-based plan for mathematical simulation of an entire in situ hearing aid.     

A method for analyzing vibration power absorption density in human fingertip

In the current study, we hypothesize that the vibration power absorption density (VPAD) is a good measure for the vibration exposure intensity of the soft tissues of the fingers. In order to calculate the VPAD at a fingertip, we proposed a hybrid modeling approach, which combines a 2D finite element (FE) model with a lumped parameter model. Whereas the lumped components are used to represent the global biodynamic characteristics of the hand-arm system, the FE component is used to predict the detailed stresses, strains, and VPAD in the fingertip. The lumped parameters are determined by using the vibration transmissibilities measured at the fingertip, while the material parameters of the soft and hard tissues of the FE model are adopted from the published experimental data. The proposed model was applied to predict the distributions of dynamic displacement, velocity, and VPAD in the soft tissues of the fingertip. Furthermore, we have derived the frequency weighting based on the VPAD of the soft tissue. The preliminary analysis indicated that the VPAD-based frequency weighting is substantially different from the ISO weighting in that the ISO frequency weighting emphasizes the effect of the vibration at frequencies lower than 25 Hz whereas the VPAD-based weighting generally emphasizes the resonant responses of the finger. Our analysis indicated that the VPAD-based weighting was fairly consistent with the finger surface vibration transmissibility at frequencies greater than the first resonance, suggesting that the finger surface transmissibility may be used as an alternative frequency weighting for assessing the finger vibration exposure. The proposed method provides a practical and efficient tool to simulate the detailed biodynamic responses of a complex biological system to vibration.     

Camera calibration based on paraxial raytracing

Traditional camera calibration is based on the pinhole model, which is an approximation algorithm using untrue geometrical assumptions and giving a single lumped result for the multiple optical elements in a camera. To provide an alternative method of camera calibration, we extend the traditional 2×2 matrix-based paraxial raytracing method to 6×6 in order to trace paraxial rays by using the first-order Taylor series expansion of Snell’s laws. Then we establish the geometric relationship between images and objects. Compared with the Snell’s Law camera calibration model of our previous work, the paraxial model offers explicit analytical sensitivity analysis for the mathematical manipulation of problematical conditions. Compared with the existing pinhole model, the proposed method, in addition to five intrinsic and six extrinsic parameters, gives the position parameters of each optical element of the camera system.     

Nonlinear dynamics of planetary gears using analytical and finite element models

Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.     

Effects of Line Parameters on Soliton-Like Propagation in Nonlinear Transmission Lines: Application to the Optimization of Frequency Triplers

In this paper, soliton propagation in nonlinear transmission lines (NLTLs) periodically loaded with heterostructure barrier varactors is studied. From the lumped element equivalent circuit of the line we have analyzed the influence of transmission line parameters (i.e, per-section inductance and capacitance) on soliton propagation characteristics. It is shown that by increasing these parameters, a faster separation of input signals into solitons is achieved. From the point of view of NLTL harmonic generation, this gives additional flexibility to optimize multiplier performance by appropriate circuit design. These conclusions are supported from the analysis of a frequency tripler, where device losses are included.