Large-Signal Equivalent-Circuit Model of Asymmetric Electrostatic Transducers

Monsalve, Jorge M.; Melnikov, Anton; Kaiser, Bert; Schuffenhauer, David; Stolz, Michael; Ehrig, Lutz; Schenk, Hermann A. G.; Conrad, Holger; Schenk, Harald

doi:10.1109/tmech.2021.3112267

Cited by 17 publications

(8 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Certainly, time dependent FEM simulations will always allow to handle substantially more complex MEMS actuator geometries. However the process of basic actuator design, as well as the circuit simulation of complex systems embracing MEMS actuators, see Monsalve et al 33 , greatly benefit from the availability of powerful LPM models.…”

Section: Discussionmentioning

confidence: 99%

Coulomb actuated microbeams: A Chebyshev-Edgeworth approach to highly efficient lumped parameter models

Schenk¹,

Melnikov²,

Wall³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

In a previous publication we demonstrated that the stable and unstable equilibrium states of prismatic Coulomb actuated Euler-Bernoulli micro-beams, clamped at both ends, can successfully be simulated combining finite element analysis (FEM) with continuation methods. Simulation results were experimentally scrutinised by combining direct optical observations with a modal analysis regarding Euler-Bernoulli eigenmodes. Experiment and simulation revealed convincing evidence for the possibility of modelling the physics of such a micro-beam by means of lumped parameter models involving only a single degree of freedom, the Euler-Bernoulli zero mode. In this paper we present the corresponding analytical single degree of freedom lumped parameter model (LPM). This comprehensive model demonstrates the impact of the beam bending on the nature of the Coulomb singularity, allows for an easy and accurate computation of the pull-in voltage in the presence of stress stiffening and is apt for efficient frequency response computations. Our method to derive the zero-mode LPM is based on a Chebyshev-Edgeworth type method as is common in analytical probability theory. While used here for a very particular purpose, this novel approach to non-linear dynamic systems has a much broader scope. It is apt to analyse different boundary conditions, electrostatic fringe field corrections and squeeze film damping, to name a few applications.

show abstract

Section: Discussionmentioning

confidence: 99%

Coulomb actuated microbeams: A Chebyshev-Edgeworth approach to highly efficient lumped parameter models

Schenk¹,

Melnikov²,

Wall³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…While the definition of the stroke is entirely obvious in the case of a rigid-plate-like shuttle, its meaning is less clear in the case of an elastic electrode that changes its shape under the influence of the Coulomb force. However, this dynamic variable can be identified, in a very welldefined sense, with the maximum deflection of a Coulombactuated Euler-Bernoulli beam, as used here [31][32][33] .…”

Section: Theoretical Descriptionmentioning

confidence: 99%

“…In order to simulate this lumped-parameter model as an equivalent circuit, the procedure proposed by Monsalve et al 33 was implemented for the case of the push-pull actuator. This work describes how the large-signal behavior of a spring-capacitor system can be fully represented by an equivalent circuit, which allows its harmonic distortion and the interaction with the acoustical load (IEC 60318-4 ear simulator) to be simulated.…”

Section: Lumped-parameter Modelmentioning

confidence: 99%

See 1 more Smart Citation

The push-pull principle: an electrostatic actuator concept for low distortion acoustic transducers

et al. 2022

Self Cite

View full text Add to dashboard Cite

Electrostatic actuators are of particular interest for microsystems (MEMS), and in particular for MEMS audio transducers for use in advanced true wireless applications. They are attractive because of their typically low electrical capacitance and because they can be fabricated from materials that are compatible with standard complementary metal-oxide semiconductor (CMOS) technology. For high audio performance and in particular low harmonic distortion (THD) the implementation of the push-pull principle provides strong benefits. With an arrangement of three electrodes in a conjunct moving configuration on a beam, we demonstrate here for the first time a balanced bending actuator incarnating the push-pull principle operating at low voltages. Our first design already exhibits a harmonic distortion as low as 1.2% at 79 dB using a signal voltage of only 6 Vp and a constant voltage of only ±10 Vdc in a standard acoustic measurement setup. Thus, exceeding our previously reported approach in all three key performance indications at the same time. We expect that our novel electrode configurations will stimulate innovative electrostatic actuator developments for a broad range of applications. In this paper we report the basic theory, the fabrication and the performance of our novel actuator design acting as an audio transducer.

show abstract

“…However, for piezoelectric transduction, such a model has not been reported yet. Recently, a model for the simulation of nonlinear effects in coupler for electrostatic transduction was reported [26]. Accurately, modeling the nonlinear behavior of loudspeakers from static nonlinear measurements of the transduction transfer function could be an efficient way for estimating the total harmonic distortion, without using expensive prototypes.…”

Section: Introductionmentioning

confidence: 99%

Total Harmonic Distortion of a Piezoelectric MEMS Loudspeaker in an IEC 60318-4 Coupler Estimation Using Static Measurements and a Nonlinear State Space Model

et al. 2021

View full text Add to dashboard Cite

We propose a method to evaluate the Total Harmonic Distortion generated by a cantilever-based PZT loudspeaker inside an IEC 60318-4 coupler. The model is validated using experimental data of a commercial loudspeaker. Using the time domain equations of the equivalent electrical circuit of the loudspeaker inside the coupler and a state space formulation, the acoustic pressure response is calculated and compared to the measurement of the manufacturer. Next, the stiffness, transduction and capacitance nonlinear functions are evaluated with a Double-Beam Laser Interferometer (DBLI) and a nanoindenter on test devices and on the commercial loudspeaker. By introducing the nonlinear functions into the model as amplitude-dependent parameters, the THD generated by the loudspeaker is calculated and compared to the value provided by the manufacturer. The good agreement between the measurement and the simulation could allow for a rather quick simulation of the performance of similarly designed loudspeakers at the early stage of the design, by only estimating the static linearity of the main nonlinearity sources.

show abstract

Large-Signal Equivalent-Circuit Model of Asymmetric Electrostatic Transducers

Cited by 17 publications

References 22 publications

Coulomb actuated microbeams: A Chebyshev-Edgeworth approach to highly efficient lumped parameter models

Coulomb actuated microbeams: A Chebyshev-Edgeworth approach to highly efficient lumped parameter models

The push-pull principle: an electrostatic actuator concept for low distortion acoustic transducers

Total Harmonic Distortion of a Piezoelectric MEMS Loudspeaker in an IEC 60318-4 Coupler Estimation Using Static Measurements and a Nonlinear State Space Model

Contact Info

Product

Resources

About