Microwave Displacement Sensor with Good Linearity and Dynamic Range Based on a Microstrip Line Pair Loaded with Movable Electric-LC Resonators

This paper presents a linear displacement sensor exhibiting good linearity and dynamic range. The sensor consists of a pair of parallel microstrip lines both terminated with a matched load (the static part) and a pair of electric-LC (ELC) resonators tuned to different (but closely spaced) frequencies, etched in a movable substrate. By feeding the lines with harmonic signals tuned to the resonance frequencies of the ELC resonators, such signals are completely reflected back to the source provided the ELCs are on top of the lines, coupled to them (i.e., at short distance and with the adequate orientation). The phase of the reflection coefficient of each line depends on the frequency of the feeding signal as well as on the distance between the input port and the corresponding ELC resonator, and repats every half wavelength. Thus, by displacing the ELC pair longitudinally (axially) along the line pair, the position of the ELC pair with regard to the input ports can be retrieved. The main relevant advantage of the proposed structure is that the pair of phases of the reflection coefficients (the output variable) exhibits a periodic pattern with ELC position that repeats each time the ELC pair is displaced a distance corresponding to the minimum common multiple (MCM) of the half-wavelengths of each signal. Thus, by considering closely spaced ELC frequencies (and hence half-wavelengths), the input dynamic range can be dramatically enhanced. This idea is validated by means of two designed and fabricated prototype displacement sensors fed with harmonic signals tuned to 2.0 GHz and 2.5 GHz in one case and tuned to 2.1 GHz and 2.3 GHz in the other case.