非线性端口 MEMS 麦克风的 Simscape 模型.zip

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Nonlinear Simulink Model for a MEMS Microphone - Companion Script % % Max Lacoma, 2024 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Details % % This is a companion script for two Simulink models (nonlinear_mems_mic % and nonlinear_ported_mems_mic). % % The first model explores the behavior of a MEMS microphone when certain % nonlinearities have been included in the model. The first nonlinearity 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 force for the model. % % Various scopes have been added to the model to explore the % nonlinearities. Additionally, running this script will show the % linearized approximation of the frequency response at varying bias % voltages. The linear part of the model and all parameters were found in % "Structure-based equivalent circuit modeling of a capacitive-type MEMS % microphone" by Lee et. al. The model was then expanded upon by Max Lacoma % to include the nonlinearities. % % The second model looks at the effect of a microphone port on the % frequency response. Specifically, it models the outer case, gasket, % acoustic mesh, and PCB hole for a porting scheme with increasing % diameter. Realistic geometry for this porting scheme was found in "Finite % Element Modeling of MEMS Microphone Ports" by Jerad Lewis. Running this % script will show the linearized frequency responses of the non-ported and % ported geometries. %% Set Parameters for Models clear; close all; clc %Frequency for computing the frequency dependent radiation resistance at f = 20000; w = 2*pi*f; %Geometric parameters r = 300e-6; %Diaphragm radius [m] N = 1668; %Number of backplate holes tb = 2.5e-6; %Backplate thickness [m] rb = 4e-6; %Radius of backplate holes [m] Ap = (pi*rb^2*N)/(pi*r^2); %Fraction of backplate covered in holes Vbc = 6e-9; %Back volume [m^3] Deff = 0.6e-3; %Effective diameter of diaphragm [m] Aeff = Deff^2*pi/4; %Effective area of diaphragm [m^2] t = 0.9e-6; %Diaphragm thickness [m] d0 = 2.45e-6; %Diaphragm displacement at zero bias [m] %Material parameters rho = 1.21; %Air density [kg/m^3] nu = 1.9841e-05; %Dynamic viscocity of air [kg/(m*s)] c = 343; %Speed of sound in air [m/s] rhod = 3809; %Equivalent density of diaphragm [kg/m^3] %Acoustic domain parameters %Note that Rg is nonlinear - needs d as an input - gap separation Mr = 8*rho/(3*pi^2*r); %Acoustic radiation inductance [kg/m^4] Rr = rho*w^2/(2*pi*c); %Acoustic radiation resistance [kg/(s*m^4)] Rh = 8*nu*tb/(N*pi*rb^4); %Acoustic resistance of backplate holes [kg/(s*m^4)] Rgtimesd3 = 12*nu/(N*pi)* (Ap/2-Ap^2/8-log(Ap)/4-3/8); %Acoustic resistance of backplate gap [kg/(s*m^4)] Cbc = Vbc/(rho*c^2); %Acoustic compliance of rear volume [m^3/Pa] %Mechanical domain parameters Md = 78.56e-11; %Effective mass of the diaphragm [kg] Cd = 3.43e-3; %Effective compliance of diaphragm [m/N] %Electrical domain parameters Cp = 0.2e-12; %Parasitic capacitance of microphone [F] e0 = 8.85e-12; %Vacuum permittivity [F/m] %% Plot Frequency Responses @ Varying Bias Voltages - Non-Ported %Set bias voltage Vbias_vec = [3.3 5 10.4]; %[V] %Define input and output points for linearization io(1) = linio('nonlinear_mems_mic/1 kHz 1 Pa Input',1,'input'); io(2) = linio('nonlinear_mems_mic/Vout',1,'output'); %Create a figure figure; hold on %Loop through each bias voltage for ii = 1:numel(Vbias_vec) %Set bias voltage in model Vbias = Vbias_vec(ii); %Linearize the model at 1 second sys = linearize('nonlinear_mems_mic',io,1); %Compute the frequency response [mag,phase,wout] = bode(sys); %Parse system mag2 = zeros(1,numel(mag)); phase2 = mag2; for ii = 1:numel(mag) mag2(ii) = mag(1,1,ii); phase2(ii) = phase(1,1,ii); end clear mag phase %Plot in dBV/Pa semilogx(wout/(2*pi),20*log10(mag2)) end %Set plot settings xlabel('Frequency [Hz]') ylabel('Magnitude [dBV/Pa, re: 1 V]') leg = legend('V_b_i_a_s = 3.3 V','V_b_i_a_s = 5.0 V','V_b_i_a_s = 10.4 V'); title('Linearized MEMS Mic Frequency Response') axis tight set(gca,'XScale','log') leg.Location = 'northwest'; %% Port Parameters %Geometry of ports a_pcb = 0.8e-3; %PCB hole radius [m] L_pcb = 0.5e-3; %PCB hole length [m] a_gasket = 1e-3; %Gasket hole radius [m] L_gasket = 1.6e-3; %Gasket hole length [m] a_case = 1e-3; %Case hole radius [m] L_case = 4e-3; %Case hole length [m] %Acoustic masses and compliances for the ports [m_pcb C_pcb ~] = acs_mass_comp(a_pcb,L_pcb,rho,c); [m_gasket C_gasket ~] = acs_mass_comp(a_gasket,L_gasket,rho,c); [m_case C_case A_case] = acs_mass_comp(a_case,L_case,rho,c); %Acoustic mesh Rmesh = 40; %[Rayl] Rmesh = Rmesh/a_gasket; %[Rayl/m^2] %% Compare Ported vs Non-Ported Frequency Responses %Define input and output points for linearization io(1) = linio('nonlinear_ported_mems_mic/1 kHz 1 Pa Input',1,'input'); io(2) = linio('nonlinear_ported_mems_mic/Vout',1,'output'); %Create a figure - plot 10.4V response of nonported mic figure; hold on semilogx(wout/(2*pi),20*log10(mag2)) %Linearize the model at 1 second sys = linearize('nonlinear_ported_mems_mic',io,1); %Compute the frequency response [mag,phase,wout] = bode(sys); %Parse system mag2 = zeros(1,numel(mag)); phase2 = mag2; for ii = 1:numel(mag) mag2(ii) = mag(1,1,ii); phase2(ii) = phase(1,1,ii); end clear mag phase %Plot in dBV/Pa semilogx(wout/(2*pi),20*log10(mag2)) %Set plot settings xlabel('Frequency [Hz]') ylabel('Magnitude [dBV/Pa, re: 1 V]') leg = legend('Non-Ported','Ported'); title('Linearized MEMS Mic Frequency Response') axis tight xlim([0 200000]) set(gca,'XScale','log') leg.Location = 'northwest'; %% Functions %Function to compute the acoustic mass and compliance of the ports function [m C A] = acs_mass_comp(a,L,rho,c) %Compute area and volume A = pi*a^2; V = A*L; %Compute mass and compliance m = rho*L/A; C = V/(rho*c^2); end