Simscape Models for Nonlinear Ported MEMS Microphones

Ported and unported Simscape models for MEMS microphones with nonlinearities included for the electrostatic gap and diaphragm damping

This download includes 2 Simscape files for modelling the behavior of bottom ported MEMS microphones with nonlinear effects and different porting schemes. These models utilize Dr. Stephen Thompson's Acoustical Domain library for Simscape, which can be found here.

The first model is a non-ported MEMS microphone with nonlinear effects. A linear lumped-element model and necessary parameters was acquired from Structure-based equivalent circuit modeling of a capacitive-type MEMS microphone by Lee et. al. This model was then adapted to include nonlinear effects by Max Lacoma. The first nonlinear effect modelled is the acoustic resistance due to the viscous forces in the gap between the membrane and back plate. This resistance is dependent on the diaphragm displacement, which is dynamically computed in this model. Secondly, the force and capacitance of the electrostatic gap are dependent on both the diaphragm displacement and the voltage across the gap. Both of these are used to compute the variable capacitance and electrostatic force for the models. Various scopes have been added to the model to explore the nonlinearities. For example, if the bias voltage is set too high, the collapse of the microphone diaphragm is correctly predicted. Running the included companion script will plot the linearized frequency response at varying bias voltages.

The second model is the same nonlinear microphone model with the addition of an acoustic porting scheme consisting of the PCB, sealing gasket, outer casing, and resistive acoustic mesh. The baseline parameters in the model are for a porting scheme of increasing diameters, as explained in Finite Element Modeling of MEMS Microphone Ports by Jerad Lewis. Running the companion script will plot the linearized frequency response of this ported mic against the non-ported version in the first model. Note that thermoviscous effects of the port are not modelled, but are important due to the small size of the porting. These may be implemented at another time using frequency dependent components.

Files Included:

• nonlinear_mems_mic.slx - Non-ported MEMS microphone Simscape model
• nonlinear_ported_mems_mic.slx - Ported MEMS microphone Simscape model
• mems_mic_script.m - Companion script with all parameters and some frequency responses

Sources:

[1] S. Thompson, Acoustical Domain for Simscape. Mathworks, Jan. 11, 2024

[2] J. M. Lewis, “Finite element modeling of MEMS microphone ports,” thesis, 2018

[3] J. Lee, C. H. Je, W. S. Yang, and J. Kim, “Structure-based equivalent circuit modeling of a capacitive-type MEMS microphone,” 2012 International Symposium on Communications and Information Technologies (ISCIT), Oct. 2012. doi:10.1109/iscit.2012.6380896