Theoretical response of condenser microphones

An experimental procedure is described for obtaining the effective acoustic distance between pairs of microphones coupled by a free field, leading to the determination of the position of the acoustic center of the microphones. The procedure, which is based on measuring the modulus of the electrical transfer impedance, has been applied to a large number of microphones. In all cases effects due to reflections from the walls of the anechoic chamber and the interference between the microphones have been removed using a time-selective technique. The procedure of determining the position of the acoustic center from the inverse distance law is analyzed. Experimental values of the acoustic center of laboratory standard microphones are presented, and numerical results obtained using the boundary element method supplement the experimental data. Estimated uncertainties are also presented. The results reported confirm values previously defined in an international standard and extend the frequency range.

Section: Numerical Modelingmentioning

confidence: 99%

The acoustic center of laboratory standard microphones

Barrera‐Figueroa¹,

Rasmussen²,

Jacobsen³

2006

“…The very same solution enters also as the first term in the solution given by Zuckerwar 8 The motion of the air in the domain underneath the membrane D air composed of gap, holes and slits set in the backplate, peripheral slit surrounding it and backchamber is described by the Stokes approximation of the N-S compressible system written in the case of time harmonic dependence as…”

Section: B the Zero Order Solution For The Membrane Displacementmentioning

confidence: 99%

“…Thus, the fluid motion enters in the membrane equation by the reaction pressure p(r, h, 0) while the diaphragm displacement influences the fluid flow by means of the boundary condition, Eq. (8). To solve the problem we consider some iterations.…”

Section: B the Zero Order Solution For The Membrane Displacementmentioning

confidence: 99%

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

Homentcovschi

Miles

2011

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.

“…Furthermore, numerical calculations are sometimes used to complement experimental results at frequencies where the experimental methods might yield unreliable results. [1][2][3][4][5] However, the numerical calculations are usually carried out under a number of assumptions that are not necessarily completely realistic. Several attempts to develop a complete coupled model of a condenser microphone numerically are described in the literature.…”

Section: Introductionmentioning

confidence: 99%

Hybrid method for determining the parameters of condenser microphones from measured membrane velocities and numerical calculations

Barrera‐Figueroa¹,

Rasmussen²,

Jacobsen

2009

Typically, numerical calculations of the pressure, free-field, and random-incidence response of a condenser microphone are carried out on the basis of an assumed displacement distribution of the diaphragm of the microphone; the conventional assumption is that the displacement follows a Bessel function. This assumption is probably valid at frequencies below the resonance frequency. However, at higher frequencies the movement of the membrane is heavily coupled with the damping of the air film between membrane and backplate and with resonances in the back chamber of the microphone. A solution to this problem is to measure the velocity distribution of the membrane by means of a non-contact method, such as laser vibrometry. The measured velocity distribution can be used together with a numerical formulation such as the boundary element method for estimating the microphone response and other parameters, e.g., the acoustic center. In this work, such a hybrid method is presented and examined. The velocity distributions of a number of condenser microphones have been determined using a laser vibrometer, and these measured velocity distributions have been used for estimating microphone responses and other parameters. The agreement with experimental data is generally good. The method can be used as an alternative for validating the parameters of the microphones determined by classical calibration techniques.