Abstract
This article presents a circuit model that is able to capture the full nonlinear behavior of an asymmetric electrostatic transducer whose dynamics are governed by a single degree of freedom. Effects such as stress-stiffening and pull-in are accounted for. The simulation of a displacement-dependent capacitor and a nonlinear spring is accomplished with arbitrary behavioral sources, which are a standard component of circuit simulators. As an application example, the parameters of the model were fitted to emulate the behavior of an electrostatic MEMS loudspeaker whose finite-element (FEM) simulations and acoustic characterisation where already reported in the literature. The obtained waveforms show good agreement with the amplitude and distortion that was reported both in the transient FEM simulations and in the experimental measurements. This model is also used to predict the performance of this device as a microphone, coupling it to a two-stage charge amplifier. Additional complex behaviors can be introduced to this network model if it is required.
Highlights
INTRODUCTIONE LECTROSTATIC transduction has been recently proven to be an effective means of generating and measuring sound waves with micro electro mechanical systems (MEMS)
E LECTROSTATIC transduction has been recently proven to be an effective means of generating and measuring sound waves with micro electro mechanical systems (MEMS)Manuscript received March 23, 2021; accepted September 8, 2021
It was mentioned that Pham and Nathan [10] had already proposed a methodology to simulate a nonlinear capacitor whose expression is of the form C (x) = C0 /(1 + g(x)); we extended this principle to simulate a spring (“inductor”) with Duffing coefficients and simulate the Duffing–Coulomb oscillator—the result is the circuit of Fig. 4
Summary
E LECTROSTATIC transduction has been recently proven to be an effective means of generating and measuring sound waves with micro electro mechanical systems (MEMS). Grixti et al [12] show the design of a diaphragmbased electrostatic MEMS microphone whose sensitivity has negligible temperature dependency (unlike traditional electret condenser microphones) Applications of this principle extend to the ultrasound range, where capacitive micromachined transducers (CMUTs) have emerged as an interesting alternative to piezoelectric transducers [13], [14]. We present a method to expand the classical small-signal representation of an electromechano-acoustical network towards a large-signal, nonlinear network capable of reproducing effects like signal distortion and instabilities ( the catastrophic collapse of electrostatic transducers, commonly known as pull-in [21]) This circuit representation is done in such a way that no code-specific “derivative” or “integral” elements are used, enabling its implementation in a standard circuit simulator—it only requires using controlled sources that compute algebraic equations.
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