A Behavioral Non-Linear Modeling Implementation for MEMS Capacitive Microphones

Abstract

<p>We highlight the behavioral non-linear system-level modeling approach for MEMS capacitive microphones. The combination of the finite element modeling and the large signal non-linear circuit modeling provide a strong capability to predict electro-acoustic performance for capacitive transductions. The circuit simulator tool such as Cadence Virtuoso has emerged as a powerful tool in designing behavioral models both in linear as well as in non-linear regimes. Typical small signal lumped element models fail to capture the MEMS behavior which changes over pressure and bias conditions. The models described herein capture diaphragm displacement and capacitance change over large pressure ranges for a simply supported circular plate. This can be coupled with the electrostatic force, due to the applied bias voltage, and is converted back to pressure thereby realizing a feedback loop in the circuit model. The non-linear model capability is extended to predict capacitance-bias behavior and estimate pull-in of the MEMS device. The microphone sensitivity, signal-to-noise ratio and harmonic distortions are accurately predicted using the non-linear large signal model when compared with measured microphone data.</p>

A Non-Dimensional Time-Domain Lumped Model for Externally Dc Biased Capacitive Microphones with Two Electrodes

“…A phenomenon that is being neglected in the circuit models is that of the pull-in instability [13], namely a physical phenomenon by which when a certain voltage is applied at a certain distance of the electrodes the electrostatic forces become so large that the elastic forces in the system are no longer capable of keeping the two electrodes apart as they rapidly collapse into one another. We expand upon such a model by also including parasitic capacitances usually present in such devices that are a combination of regions in the sensor element that do not respond to acoustic pressure and can also include the input capacitance of the following amplification stage [17,16]. We also take into account the thin film of air between the electrodes to the device's operation, the fringing fields due to the nonhomogeneous electric field between the electrodes, and the amount and number of perforations.…”

“…Taking into account all the forces acting on the moving electrode, namely the acoustic force, the electrostatic force, the viscous force, the elastic force, and the charging of the electrodes, as well as capacitances that do not respond to acoustic pressure [17] (which from now on we will be referring to as parasitic), we built a nonlinear nondimensional…”

Nonlinear Factors in Single and Double Backplate Capacitive Transducers

“…Figure 3 shows that the electrodes are charged using a resistor (R bias ) in series with the electrodes and the DC bias voltage (V bias ). A parasitic capacitance (C p ) is included in the model, which represents the capacitance of the conductive elements in the transducer that do not respond to an impinging acoustic signal and the input capacitance of the following amplification stage [6]. This capacitance is connected in parallel to the electrodes.…”