Piezoelectric membrane sensor for pressure measurement: Theory and experiment

This study presents a piezoelectric membrane pressure sensor by monitoring the resonant frequency shift (Δf) that changes with the pressure difference (ΔP) across the membrane. Theoretical and experimental investigations reveal two critical pressure thresholds (ΔP_α and ΔP_β) determined by the competition between flexural rigidity (D) and tensile stress (T). Accordingly, three distinct operational ranges are defined: (1) a D-dominated range below ΔP_α, (2) a T-dominated range above ΔP_β, and (3) a transitional range with resonant peak perturbation between ΔP_α and ΔP_β. The sensor demonstrates effective pressure measurement capability in both D- and T-dominated ranges, with an operational upper limit determined by the maximum tolerable pressure difference (ΔPₘₐₓ). The sensitivity (S_ΔP) exhibits unique mode- and operational range-dependent characteristics: higher resonant modes exhibit higher sensitivity; S_ΔP remains size-independent and exhibits relatively higher values below ΔP_α, but becomes size-dependent with reduced sensitivity above ΔP_β. These performance characteristics are analytically described using fundamental membrane parameters, including geometry (size a, thickness t) and material properties (Young's modulus E, density ρ). The dual-threshold behaviors and sensitivity characterizations provide comprehensive guidelines for design and optimization of piezoelectric membrane sensors in pressure measurement applications.