I. Introduction
There are several approaches for the implementation of displacement and velocity sensors based on microwave technologies. In particular, a significant research effort has been dedicated in the last decade to the development of sensing systems where a transmission line is loaded with resonant elements in relative motion respect to it [1]–[10] (other sensors based on resonator-loaded lines, useful for dielectric characterization and related applications, have been also reported [11]–[25]). In several of the previous spatial sensors, the relative displacement is determined from the variation in the resonance frequency that results when the transmission line and the resonant element are in relative motion (either linear or angular) [2], [6]. In other displacement and velocity sensors, the working principle is coupling modulation [3]–[5], [7]. Although frequency variation and coupling modulation sensors are simple from a technological viewpoint, their resolution and dynamic range are typically limited. Moreover, frequency variation sensors may be subjected to cross sensitivities caused by environmental factors (e.g., frequency drifts caused by temperature variations or changes in ambient moisture), and coupling modulation sensors are very sensitive to noise.