A novel microwave dielectric resonator-based differential frequency sensor for angular displacement detection

Abstract

A differential frequency microwave sensor for angular displacement detection is reported. A metal strip-loaded cylindrical dielectric resonator (SL-CDR) is excited with a 50 Ω-microstrip transmission line through a rectangular slot made on the transmission line’s ground plane. Analysis of the transmission coefficient spectrum (|S₂₁| vs frequency) of the resulting circuit shows that for the parallel alignment of SL-CDR relative to the slot (θ = 0⁰), dual-transmission zeros are excited at frequencies f_L and f_H. In contrast, for the perpendicular alignment (θ = 90⁰), a single transmission zero is excited at f₀ where f_L < f₀ < f_H. When θ increases from 0⁰ to 90⁰, f_L increases towards f₀ while f_H decreases towards f₀. This opposing trend observed at f_L and f_H is attributed to the difference in the perturbation experienced by the respective electromagnetic modes of the SL-CDR after loading the metal strip. The resulting differential frequency parameter Δf = f_H−f_L is adopted to indicate θ, the angular displacement, following a simulation study with ANSYS HFSS. Subsequent prototype fabrication and Vector Network Analyzer (VNA) measurement confirm the simulations with 15.5 MHz/⁰ sensitivity and excellent linearity over the dynamic range of 90⁰. As the final step, the measured differential frequencies are mapped to the angular displacement (θ←Δf) using linear inverse regression, and the extracted regression parameters confirm accurate mapping.