Two-Dimensional Wide Dynamic Range Displacement Sensor Using Dielectric Resonator Coupled Microwave Circuit
Premsai Regalla, A. V. Praveen Kumar
Abstract
In this article, the authors propose a two-dimensional (2-D), wide dynamic range, linear displacement sensor based on the microwave resonator principle. The sensor employs a cylindrical dielectric resonator (DR) proximity coupled to a pair of 50- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> microstrip lines that are laid orthogonally over a microwave substrate. The DR is free to move on the substrate in the 2-D space between the microstrips so that the coupling strength of the excited DR mode varies with the DR’s proximity to the microstrips. This variation in coupling strength can be measured in terms of the two-port scattering (S) parameters of the circuit, from which the DR’s displacement can be estimated. The above circuit operates at a fixed frequency determined by the resonant frequency of the particular mode of the DR. Initially, one-dimensional (1-D) analysis using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert {S}_{{21}}\vert $ </tex-math></inline-formula> sensitivity of the DR displacement reveals a dynamic range of more than 23 mm for the horizontal, vertical, and diagonal displacements. To enable full 2-D scanning by differentiating the horizontal and vertical displacements, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert {S}_{{11}} \vert $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert {S} _{{22}}\vert $ </tex-math></inline-formula> parameters are also taken into account in addition to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert {S}_{{21}} \vert $ </tex-math></inline-formula> . Note that in all the above measurements, the sensor’s operating frequency remains constant at 3.67 GHz which is the resonant frequency of the DR. Such single-frequency sensors are highly robust to frequency offsets and are also cost-effective in practical realization compared with variable frequency sensors. This aspect as well as other performance parameters of the proposed sensor are compared with that of the existing 2-D sensors.