Measurement Data of Two Coupled MEMS Resonators Used as Acoustic Sensors

This dataset contains experimental measurement data from two coupled MEMS resonators used as an acoustic sensor.
The data are organized into six zipped folders, each corresponding to a specific measurement analysis.

Unless stated otherwise:

• MEMS time-series files are stored in .mat format.

• Sampling frequency of MEMS measurements: 125 kHz.

• In every .mat file:

  • Row 1 = resonator with higher listed frequency

  • Row 2 = resonator with lower listed frequency

1. Sensitivity_analysis_measurements.zip

Subfolder (I): 3630_3790_Hz_sweep_high_resolution_recheck_2/

Time-series measurements of two coupled resonators with natural frequencies 3790 Hz and 3630 Hz.

• Sampling frequency: 125 kHz

• Response to a 1–10 kHz acoustic sweep

• Filename example:
  Cantilever_3790_Hz_3630_Hz_DC_0xfffff667_cf_0.5_excitation_0.01.mat

Parameter meaning:

• 3790_Hz → Resonator 1 (row 1)

• 3630_Hz → Resonator 2 (row 2)

• DC_0xfffff667 → DC = −150 mV (2’s complement, hexadecimal)

• cf → coupling strength

• excitation → signal-generator driving voltage

Subfolder (II): Input_sound_sweep_1k_10kHz_2/

Microphone recordings of the loudspeaker sweeps.

• Sampling frequency: 44 kHz

• Files stored as .wav

• Example:
  Old_speaker_amplitude_frequency_1000-10000Hz0.01.wav

Notes:

• Sweep range: 1–10 kHz

• Driving amplitude: e.g., 0.01 V

• Convert voltage to sound pressure (Pa) by:

  Sound pressure (Pa) = voltage_from_wav / 0.0149

Included MATLAB code

File: Sensitivity_determining_plot_code.m

• Computes peak-to-peak amplitudes of MEMS responses

• Converts microphone recordings into pressure

• Computes sensitivity (V/Pa)

• Plots sensitivity vs. coupling strength and input amplitude

• Uses the relation:

  gamma_12 * gamma_21 = (cf / 2)^2
  

  due to FPGA buffer-board scaling and symmetric coupling.

➡️ Run the script directly to reproduce sensitivity plots.

2. Frequency_tunability_analysis_measurements.zip

Subfolder: Sweep_near_bifurcation_Negative_to_positive_af/

Time-series responses to a 3–4.5 kHz acoustic sweep with varying feedback and coupling parameters.

Example filename:
Cantilever_3790_Hz_3630_Hz_DC_0xfffff667_af1_-0.5_af2_-0.5_cf_1.375.mat

Parameter meaning:

• af1 → feedback strength of resonator 1

• af2 → feedback strength of resonator 2

• cf → coupling strength

Included MATLAB code

File: Frequency_analysis_3D_plot_code.m

• Computes FFT for all (af1, af2, cf) combinations

• Extracts resonance frequencies from FFT maxima

• Generates 3D colormap plots of resonance vs. feedback

• Also plots effective coupling vs feedback

• Values in plots are halved due to the FPGA buffer board.

➡️ Run the script to reproduce resonance-frequency maps.

3. Frequency_tunable_Regime_1_DC_vs_C_crit.zip

Measurements in Regime 1 (frequency-tunable), no sound excitation.

Example filename:
Cantilever_3630_Hz_3790_Hz_DC_100mV_Cf_0.5.mat

Includes measurements for varying:

• DC offset

• Coupling strength (Cf)

Included MATLAB code

File: Amplitude_vs_Cf_different_DC_3630Hz_3790Hz.m

• Plots amplitude vs. coupling strength for several DC values

• The critical coupling CcritC_{\text{crit}}Ccrit is defined as the value of Cf where the amplitude exceeds 100 mV

➡️ Run the script to extract amplitude vs Cf for different DC values.

4. Frequency_tunable_Regime_2_DC_vs_C_crit.zip

Same structure as Regime 1, but corresponding to Regime 2 (another frequency-tunable region).

Included MATLAB scripts

Run the script corresponding to each resonance pair:

• Amplitude_vs_Cf_different_DC_3630Hz_3730Hz.m

• Amplitude_vs_Cf_different_DC_3630Hz_3790Hz.m

• Amplitude_vs_Cf_different_DC_3790Hz_3730Hz.m

➡️ Run the script to extract amplitude vs Cf for different DC values.

5. Frequency_untunable_Regime_DC_vs_C_crit.zip

Measurements from the frequency-untunable regime, with varying DC and coupling strength.

Included MATLAB scripts

• Amplitude_vs_Cf_different_DC_3630Hz_4380Hz.m

• Amplitude_vs_Cf_different_DC_5190Hz_3630Hz.m

• Amplitude_vs_Cf_different_DC_5190Hz_4380Hz.m

➡️ Run the script to extract amplitude vs Cf for different DC values.

6. Frequency_response_different_regimes_before_bifurcation.zip

Contains .fig files showing frequency responses of the coupled resonators just before Hopf bifurcation in:

• Frequency-untunable regime

• Frequency-tunable regime 1

• Frequency-tunable regime 2

These figures illustrate how the system behaves in the non-linear regime near the bifurcation point.

7. code_availibility.zip      

• mems_parameters.m: The parameters of the 6 MEMS resonators are saved in this file. The parameters follow Table B1. 
• gamma_crit.m: Script to compute the critical point of two injectively coupled MEMS. 
• critical_point_vs_dc_voltage.m: Figure 3B and 3C can be generated with this file. For this, a u_DC array and the struct containing the parameters of two MEMS resonators is initialized. Then gamma.m is called iteratively to compute the critical coupling strength in terms of u_DC. The result is then plotted.
• critical_point_and_frequency_vs_feedback_strength.m: Figure 2 can be generated with this file. For this, two feedback strength array and the struct containing the parameters of two MEMS resonators is initialized. Then gamma.m is called iteratively to compute the critical coupling strength and characteristic frequency in terms of the feedback strengths. The result is then plotted.

8. Sound_demonstration_files.zip   

• Consists of .flac sound files demostrating frequency tunability of coupled MEMS resonator -1 and MEMS resonator -2 with resonance frequency of 3790Hz and 3630Hz respectively. The frequency tunability is demonstrated in two regimes:

  • Frequency tunable Regime 1 : frequency tuning for MEMS-1 and MEMS-2  in frequency range 3630-3790Hz.

  • Frequency tunable Regime 2 : frequency tuning for MEMS-1 and MEMS-2  in frequency range 100-3630Hz.

• Additionally an audio file of frequency untunable regime is also demonstrated for MEMS-1 and MEMS-2.