Large signal performance of micromachined silicon inductive microphones

A mathematical model for the open-circuit output voltage of a micromachined silicon inductive microphone 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 both even and odd-order harmonic and intermodulation products.     

Large Signal Analysis of the Michelson Interferometer with Gires-Tournois Interferometers in its Arms

A mathematical model for the transfer function of the Michelson interferometer with Gires-Tournois interferometers in its arms is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the amplitudes of the harmonic and intermodulation components of the output when the input is formed of large-amplitude multisinusoidal voltage. The special case of two-tone equal-amplitude input voltage is considered in detail. The results show that the third-order intermodulation component is always higher than the third-harmonic component. The results also show that the linearity of the Michelson interferometer with Gires-Tournois interferometers in its arms improves with the increase of the front mirror reflectivity. Moreover, the results show that the third-order intermodulation exhibits a minimum for relatively large values of the front mirror reflectivity. Furthermore, compared with the traditional Mach-Zehnder interferometer, the results show that a reduction of 15 dB in the third-order intermodulation can be achieved even for relatively small values of the front mirror reflectivity.     

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.     

Dynamic response of an insonified sonar window interacting with a Tonpilz transducer array

This paper derives and evaluates an analytical model of an insonified sonar window in contact with an array of Tonpilz transducers operating in receive mode. The window is fully elastic so that all wave components are present in the analysis. The output of the model is a transfer function of a transducer element output voltage divided by input pressure versus arrival angle and frequency. This model is intended for analysis of sonar systems that are to be built or modified for broadband processing. The model is validated at low frequency with a comparison to a previously derived thin plate model. Once this is done, an example problem is studied so that the effects of higher order wave interaction with acoustic reception can be understood. It was found that these higher order waves cause multiple nulls in the region where the array detects acoustic energy and that their locations in the arrival angle-frequency plane can be determined. The effects of these nulls in the beam patterns of the array are demonstrated.     

Modelling the pressure field in the vicinity of a microphone membrane using PIV

A new approach for estimating the acoustic pressure in the near field of a microphone based on non-intrusive direct measurement of acoustic particle velocity is proposed.This method enables the estimation of the acoustic pressure inside a domain located in front of the microphone membrane. The acoustic pressure is calculated using the acoustic particle velocity on the frontiers of this domain and a physical model based on the Green function of the system.Results are obtained using the acoustic velocity measured with Particle Image Velocimetry (PIV) in front of a microphone excited with a plane wave inside a rectangular waveguide. They show that the diffraction of the plane wave by the microphone leads to an increase of the acoustic pressure on the microphone edge in the order of magnitude of 0.1 dB.     

Nonlinear model and system identification of a capacitive dual-backplate MEMS microphone

This paper presents the nonlinear identification of a capacitive dual-backplate microelectromechanical systems (MEMS) microphone. First, a nonlinear lumped element model of the coupled electromechanical microphone dynamics is developed. Nonlinear finite element analyses are performed to verify the accuracy of the lumped linear and cubic stiffnesses of the diaphragm. In order to experimentally extract the system parameters, an approximate solution using the second-order multiple scales method is synthesized for a nonlinear microphone model, subject to an electrical step input. A nonlinear least-squares technique is then implemented to extract system parameters from laser vibrometry data of the diaphragm motion. The results indicate that the theoretical fundamental resonant frequency, damping ratio and nonlinear stiffness parameter agree with the corresponding extracted experimental parameters with 95% confidence interval estimates.     

Harmonic and intermodulation performance of hearing aids under large sound pressure levels

A mathematical model for the input-output functions of the hearing aids is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the amplitudes of the harmonic and intermodulation components of the output when the input is formed of multitone large sound pressure levels. The special case of two-tone equal-amplitude incident pressure level is considered in detail. The results show that the third-order intermodulation component is always higher than the third-harmonic component. The results also show that the input-output functions exhibiting peak clipping exhibit the worst harmonic and intermodulation performance for large sound pressure levels. The simple wide-dynamic range compression (WDRC) input-output function exhibits the best harmonic and intermodulation distortion performance under large sound pressure levels. These results are consistent with the previously reported observations and reveal that there is a correlation between intelligibility of high-level speech and the harmonic and intermodulation performance of the hearing aid under large sound pressure levels.     

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.     

电动扬声器悬置系统蠕变效应建模

对电动扬声器悬置系统的蠕变效应进行了分数阶建模。通过将标准线性固体模型中的牛顿黏壶替换为分数阶Abel黏壶,提出了悬置系统分数阶标准线性固体力顺模型。使用Klippel扬声器单元电阻抗激光测量系统,测量了2只具有不同橡胶折环的中频扬声器单元的电阻抗和传递函数(振膜输出位移/输入声压),并采用最小二乘法拟合实测曲线,得到了模型参数。通过与已有的考虑蠕变效应的4参数对数模型和标准线性固体模型拟合结果的对比,结果表明:分数阶标准线性固体模型能够准确描述力顺损耗因数随频率的变化规律,对蠕变效应具有更好的模拟精度。      

Preliminarily modeling of creep effect in electro-dynamic loudspeaker suspensions

The creep effect of suspensions in electro-dynamic loudspeakers was modeled based on fractional order derivatives.The fractional standard linear solid(FSLS) model was presented by substituting the Abel dashpot for Newton dashpot in Standard Linear Solid(SLS) model.The electrical impedance as well as the transfer function between diaphragm displacement and input voltage of the two tested midrange loudspeakers was measured by Klippel laser analyzer system,and the model parameters were identified by the least-mean-square method.By comparing the fitting results of FSLS model with the other two classical models- 4 Parameter Logarithmic model and SLS model,the results show that the FSLS model can rightly predict the frequency dependent compliance loss factor and yield higher accuracy for modeling the creep effect in loudspeaker suspensions.     

Development of a multi-microphone calibrator

This paper presents the theory, design, and validation of a microphone calibrator used to simultaneously calibrate the amplitudes of multiple microphones on a single probe. The probe uses four 6 mm diameter electret microphones to acquire the data needed to compute acoustic energy density. This probe has prompted the need for simultaneous, multi-microphone amplitude calibration. The calibration process simultaneously subject each microphone on the probe to the same known acoustic pressure using four equal-length, small-diameter tubes connected to a single excitation source. A reference microphone connected to a fifth tube is used to calibrate the microphones. Test results show that the calibrator can calibrate each probe microphone within ±0.5 dB up to 2 kHz, and within ±1 dB up to 4.9 Hz with a confidence level of 95%.     

Constrained adaptation for feedback cancellation in hearing aids.

In feedback cancellation in hearing aids, an adaptive filter is used to model the feedback path. The output of the adaptive filter is subtracted from the microphone signal to cancel the acoustic and mechanical feedback picked up by the microphone, thus allowing more gain in the hearing aid. In general, the feedback-cancellation filter adapts on the hearing-aid input signal, and signal cancellation and coloration artifacts can occur for a narrow-band input. In this paper, two procedures for LMS adaptation with a constraint on the magnitude of the adaptive weight vector are derived. The constraints greatly reduce the probability that the adaptive filter will cancel a narrow-band input. Simulation results are used to demonstrate the efficacy of the constrained adaptation.     

Effects of Microphone Type on Acoustic Measures of Voice

Acoustic measures provide an objective means to describe pathological voices and are a routine component of the clinical voice examination. Because the voice sample is obtained using a microphone, microphone characteristics have the potential to influence the values of parameters obtained from a voice sample. This project examined how the choice of microphone affects key voice parameters and investigated how one might compensate for such microphone effects through filtering or by including additional parameters in the decision process. A database of 53 normal voice samples and 100 pathological voice samples was used in four experiments conducted in an anechoic chamber using four different microphones. One omnidirectional microphone and three cardioid microphones were used in these experiments. The original voice samples were presented to each microphone through a speaker located in an anechoic chamber, and the output of each microphone sampled to computer disk. Each microphone modified the frequency spectrum of the voice signal; this, in turn, affected the values of the voice parameters obtained. These microphone effects reduced the accuracy with which acoustic measures of voice could be used to discriminate pathological from normal voices. Discrimination performance improved when the microphone output was filtered to compensate for microphone frequency response. Performance also improved when spectral moment coefficient parameters were added to the vocal function parameters already in use.     

Theoretical modeling and experimental realization of dynamically magnified thermoacoustic-piezoelectric energy harvesters

Conventional thermoacoustic-piezoelectric (TAP) harvesters convert thermal energy, such as solar or waste heat energy, directly into electrical energy without the need for any moving components. The input thermal energy generates a steep temperature gradient along a porous medium. At a critical threshold of the temperature gradient, self-sustained acoustic waves are developed inside an acoustic resonator. The associated pressure fluctuations impinge on a piezoelectric diaphragm, placed at the end of the resonator. In this study, the TAP harvester is coupled with an auxiliary elastic structure in the form of a simple spring–mass system to amplify the strain experienced by the piezoelectric element. The auxiliary structure is referred to as a dynamic magnifier and has been shown in different areas to significantly amplify the deflection of vibrating structures. A comprehensive model of the dynamically magnified thermoacoustic-piezoelectric (DMTAP) harvester has been developed that includes equations of motions of the system?s mechanical components, the harvested voltage, the mechanical impedance of the coupled structure at the resonator end and the equations necessary to compute the self-excited frequencies of oscillations inside the acoustic resonator. Theoretical results confirmed that significant amplification of the harvested power is feasible if the magnifier?s parameters are properly chosen. The performance characteristics of experimental prototypes of a thermoacoustic-piezoelectric resonator with and without the magnifier are examined. The obtained experimental findings are validated against the theoretical results. Dynamic magnifiers serve as a novel approach to enhance the effectiveness of thermoacoustic energy harvested from waste heat by increasing the efficiency of their harvesting components.     

Field emission pressure sensors with non-silicon membranes

We report on the fabrication of cold cathode emitter and the design parameter simulation of a functional field emission-based pressure sensor. This device comprises a membrane made of metallic compound acting as the anode in front of a flat cold cathode emitter. First, the mechanical deflection of a diaphragm under selected input pressures is modeled. The current density distribution in the deflected diaphragm is then calculated using realistic field emission characteristics from fabricated sulfur doped boron nitride (S-BN) cold cathode device. The total current output was found by integrating the measured current density of the fabricated electron emitter device over the entire diaphragm area of the membrane as function of external pressure. The results show that conventional silicon membranes would pose problems when implemented in a real field emission device, and show how the use of unconventional materials (i.e., TiN) can help overcome these problems.     

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.     

A selective two microphone acoustic intensity method

A multiple input, two output model is proposed which enables the two microphone acoustic intensity method to decompose the intensity vector into contributions from individual sources, even when they are coupled and in close proximity within the measurement surface. By treating characteristic signals from each source as the inputs, and the sound pressure signals from the two closely spaced microphones as the outputs, the model's frequency response functions are developed from a least squares approximation. The cross spectrum between the two microphones can then be expressed as a function of the input signal spectra and the model's frequency response functions. By manipulating the model terms the selective cross spectrum associated with the radiation from each individual source can then be estimated. The selective cross spectrum is then processed via standard methods to obtain the acoustic intensity vector from each source. A series of laboratory experiments is summarized which demonstrates that the technique can accurately decompose the acoustic intensity vector from highly coherent sources (γ₁₂² > 0·9) buried in background noise in a semireverberant environment, to within 1 dB of the directly measured intensities.     

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.     

Acoustic temperature measurement in a rocket noise field

A 1 μm diameter platinum wire resistance thermometer has been used to measure temperature fluctuations generated during a static GEM-60 rocket motor test. Exact and small-signal relationships between acoustic pressure and acoustic temperature are derived in order to compare the temperature probe output with that of a 3.18 mm diameter condenser microphone. After preliminary plane wave tests yielded good agreement between the transducers within the temperature probe's ～2 kHz bandwidth, comparison between the temperature probe and microphone data during the motor firing show that the ±～3 K acoustic temperature fluctuations are a significant contributor to the total temperature variations.     

A hybrid SEA/modal technique for modeling structural-acoustic interior noise in rotorcraft

This paper describes a hybrid technique that combines Statistical Energy Analysis (SEA) predictions for structural vibration with acoustic modal summation techniques to predict interior noise levels in rotorcraft. The method was applied for predicting the sound field inside a mock-up of the interior panel system of the Sikorsky S-92 helicopter. The vibration amplitudes of the frame and panel systems were predicted using a detailed SEA model and these were used as inputs to the model of the interior acoustic space. The spatial distribution of the vibration field on individual panels, and their coupling to the acoustic space were modeled using stochastic techniques. Leakage and nonresonant transmission components were accounted for using space-averaged values obtained from a SEA model of the complete structural-acoustic system. Since the cabin geometry was quite simple, the modeling of the interior acoustic space was performed using a standard modal summation technique. Sound pressure levels predicted by this approach at specific microphone locations were compared with measured data. Agreement within 3 dB in one-third octave bands above 40 Hz was observed. A large discrepancy in the one-third octave band in which the first acoustic mode is resonant (31.5 Hz) was observed. Reasons for such a discrepancy are discussed in the paper. The developed technique provides a method for modeling helicopter cabin interior noise in the frequency mid-range where neither FEA nor SEA is individually effective or accurate.