Ing. Petr Honzík, Ph.D.

An experimental investigation on the nonlinear behaviour of the MEMS microphones is of rising interest as their use is growing rapidly not only in the domain of consumer audio devices but also in the measurement applications where higher precision is needed. The present work uses a recently published method allowing a distortionless harmonic excitation at high-pressure levels to measure and examine the distortion of single backplate MEMS microphones. The measured distortion is compared with the values predicted by a simple model of the nonlinearities originating in the electrostatic transduction principle. A good agreement between the predicted and the measured values of the second harmonic is shown. The level of the third harmonic is influenced by nonlinear effects not taken into account in the simple model and therefore deviates from the predicted values.

The objective of the paper is to provide a suitable analytical approach to describe the behaviour of a square miniaturised (MEMS) receiving transducer made up of a square membrane having the same dimensions as the external dimensions of the transducer itself, loaded by both a thin square small sized fluid-gap and a peripheral cavity connected together and set rear the membrane. This device departs from the other previous square devices in that the peripheral cavity is rear the membrane at the periphery of the backing plate (backing electrode). This architecture (derived from the circular one suggested previously) enables to optimize the sensitivity of the transducer while retaining both a cartesian geometry and the smallest dimensions possible (surface area and thickness). The analytical approach accounting for the effects of the interior geometrical discontinuity on the displacement field of the membrane used here to describe such square transducers (electrostatic or piezoelectric) departs from previous ones in that it avoids multi-modal analysis which exhibits procedural difficulties due to the coupling of Dirichlet-like (membrane) and Neumann-like (fluid) eigenfunctions (emphasized here by presence of the geometrical discontinuity in the fluid-filled part of the device). Additionally, an approximate analytical solution appropriate to express the displacement field of the membrane and to estimate the sensitivity with a good accuracy in the lower frequency range is presented. FEM solutions are provided, against which the analytical results have been tested.

The paper is mainly concerned with the analytical approach of the behaviour of a two-dimensional miniaturized MEMS transducer, namely a rectangular or square clamped plate loaded by a fluid-gap (squeeze film), surrounded by a small cavity (reservoir), and excited by an incident acoustic field (assume to be uniform on the plate). Until now, the problem has not been analytically solved owing to the geometry of the device in conjunction with the nature of the diaphragm (elastic plate) and its boundary conditions (zero deflection and zero normal slope along all edges); namely analytical eigenfunctions do not exist for the clamped plate. On the other hand, the analytical approach classically used to express the acoustic field in the fluid-gap relies on a modal expansion which does not match correctly with both the displacement field of the diaphragm and the boundary conditions at the entrance of the reservoir. Then, two particular questions arise: how to derive analytically the modal behaviour of the loaded clamped plate, and what analytical approach for the acoustic field in the fluid gap is convenient to describe its coupling with the displacement field of the plate? The aim of the paper is both to provide basically an exact analytical approach and to handle a numerical implementation (FEM) against which the analytical results are tested.

More and more applications, such as noise control in hostile environments, acoustic thermometry, gas metrology or optimization of thermoacoustic engines, require performing acoustic measurements with microphones in "extreme"€ atmospheric conditions or even non atmospheric ones.Being able to predict and characterize the sensitivity and frequency response of microphones in these conditions of use is then of fundamental purpose. However, regarding the variety of potential applications, it is not realistic to perform microphones calibrations for all environmental conditions of possible interest. The main global properties of microphones should then be predicted by a reliable modelling procedure that enables to take into account the effects of environmental conditions on its mechanical-acoustic properties. Basically, the sensitivity and frequency response of a microphone are determined almost by its geometrical structure and dimensions, and by the mechanical properties of its membrane, which are both related to the temperature of the cartridge. On the other hand, the acoustic behaviour of a microphone strongly depends on the physical properties of the gas in the cartridge, which are function of the nature, static pressure and temperature of the gas and can easily be calculated.For the sake of the present work, an analytical model available in the literature is used to describe the behaviour of a 1/4" microphone. This global modelling is associated to a mechanical study for predicting the temperature effects on the properties of the constituting materials. A comparison is presented with experimental results obtained for the resonance properties of the membrane in vacuum and for the frequency response under helium atmosphere of a 1/4" microphone in order to check the validity of the theoretical approach suggested here.

To model linear acoustics in a thermoviscous fluid in open domain and time-harmonic regime, a Finite Element formulation in a bounded meshed domain is combined with the integral representation of the field for the propagative solution. The integrals are non-singular and involve the only Finite Element node values for temperature variation and particle velocity variables. To overcome the non-uniqueness of solutions at fictitious resonant frequencies, a Burton-Miller combination of integral representation is used. This formulation is suitable to compute acoustic radiation, scattering and diffraction by objects or mutual interaction between transducers. Two-dimensional computational experiments are presented in an infinite, open domain (exterior), showing that the model can be achieved in meshing only a thin domain surrounding the physical boundaries of a device.

Condenser microphones are generally designed for airborne acoustic measurements. Their accurate behaviour is then well understood almost in atmospheric conditions. However, more and more applications, such as acoustic thermometry, gas metrology or thermoacoustics for example, require the use of electrostatic transducers (as sound source or sensors) in gas conditions far from atmospheric ones. A previous experiment using the electrostatic actuator technique already evidenced the influence of static pressure and nature of the gas on a condenser microphones’s frequency response. The same technique is carried out here to characterize the mechanical properties of a 1/4’’ microphone’s membrane in vacuum at temperatures from about 80 K to 300 K. From the results then obtained, the resonance properties of the membrane are expressed as function of the temperature. Then they can be used in global mecano-acoustic modellings of condenser microphones which validity at several temperatures is experimentally checked too. Furthermore, a new global modelling of a condenser microphone coupled to an electrostatic actuator is developed here. Finally, the expected impacts of this work are to provide improved theoretical bases and advanced experimental tools for the deep understanding, the calibration and the design of new electrostatic transducers dedicated to new specific applications.

Maximum-length sequences (MLS) are widely used for measurement of impulse responses of linear time-invariant systems in acoustic and audio systems. It is usually believed that one of the drawbacks of the MLS technique is a requirement on a synchronization of the devices used for the generation and acquisition of the MLS signals. The study presented in this paper shows that the MLS technique can easily be improved and applied to devices that are not synchronous, or even operating at different sampling frequencies. To show the efficiency of the proposed modification to MLS technique we provide several experiments such as a measurement with devices working at 44.1 kHz on the generation side and 96 kHz on the acquisition side, or a measurement of the frequency response function of a cheap mobile phone in which the synchronous clocking would be impossible to realize.

In recent years the acoustic receivers are becoming specialized, their fabrication is more complicated and more expensive. As a result the importance of the modelling of these systems is rising. This contribution deals with miniature silicon condenser microphones with different shapes of moving and back electrodes and microphone with direct analog-to-digital conversion. The model is based on electro-acoustic analogy and the study leads to the equivalent lumped element circuit.

This paper deals with the problem of radiation impedance of transducer array for digital loudspeaker (DL), which has special characteristics in comparison with single transducers. In case of digital loudspeakers this impedance fluctuates according to the input signal. Some alternative solutions and examples are shown and discussed.

V příspěvku je popsán model elektrostatického měniče s čtvercovou membránou a nerovinnou pevnou elektrodou. Model zahrnuje základní rovnice, které popisují funkci měniče, a odvození impedancí mechanických a akustických částí měniče. Pomocí těchto vztahů lze stanovit modulovou frekvenční charakteristiku a sestavit náhradní obvod soustavy se soustředěnými prvky.

This paper presents the theory of an electrostatic transducer with thin rectangular diaphragm and circular non-planar and non-perforated back electrode, which can be realized by micromechanical technologies. The study leads to the equivalent lumped element circuit.