Thesis Defence: Toward a Mechanical Fast Fourier Transform

Haley Goguen, supervised by Dr. Ian Foulds, will defend their thesis titled “Toward a Mechanical Fast Fourier Transform (FFT): Fabrication and Resonance Testing of Silicon Dioxide (SiO₂) Microelectromechanical Systems (MEMS) Cantilevers” in partial fulfillment of the requirements for the degree of Master of Applied Science in Electrical Engineering.

An abstract for Haley Goguen’s thesis is included below.

Defences are open to all members of the campus community as well as the general public. Please email ian.foulds@ubc.ca to receive the Zoom link for this defence.

Abstract

Low frequency infrasonic vibrations in the 1–20 Hz range are useful for condition monitoring as mechanical systems can generate frequency components that change when faults develop. Conventional frequency analysis often relies on electronic sensing, signal conditioning, data acquisition, and computational Fast Fourier Transform (FFT) processing, however,
low frequency measurements are susceptible to 1/f noise, which increases as frequency decreases and can obscure signal components. This thesis investigates an alternative approach in which microelectromechanical systems (MEMS) resonators perform part of the frequency separation mechanically. The long term goal is a passive resonator array in where individual
structures respond to assigned infrasonic frequencies, forming a mechanical FFT for vibration condition monitoring.

The work combines literature review, analytical design, mask development, microfabrication, and preliminary resonance testing of silicon dioxide (SiO₂) cantilevers. Current MEMS devices for infrasonic detection in industrial, environmental, and biomedical applications were reviewed to distinguish broadband pressure sensors from resonant mechanical structures.
SiO₂ was selected as the structural material, and rectangular cantilevers were used as the primary geometry because their clamped-free resonance behavior is well established and tunable through length, thickness, and added mass. Additional circular, zigzag, and M-shaped geometries were included for exploratory release studies. Devices were fabricated using photolithography, chromium hard masking, buffered oxide etching, and anisotropic tetramethylammonium
hydroxide (TMAH) silicon release. Released structures were characterized visually and through speaker driven resonance testing under atmospheric and reduced pressure conditions.

The results show that rectangular SiO₂ cantilevers were the most reliable geometry for release, while more complex geometries were limited by stiction, fracture, or incomplete undercutting. Released cantilevers exhibited curvature, requiring effective length correction for improved agreement between predicted and measured resonances. Selected cantilevers
showed repeatable resonant response, and reduced pressure increased response sharpness relative to atmospheric testing. Although a complete 1–20 Hz mechanical FFT was not achieved, this work demonstrates fabrication and resonance feasibility and identifies the key design, release, curvature, and testing challenges for future passive infrasonic MEMS resonator arrays.