# Planar Microwave Resonant Sensors: A Review and Recent Developments
## 2 Classification of Planar Microwave Resonant Sensors  
The classification subject of this section obeys the operating principle of the considered sensors (alternatively, sensors can be categorized by their applications, or frequency range, etc.). Thus, according to their working principle, planar resonant sensors can be divided in four main types: (i) frequency variation sensors, (ii) coupling modulation sensors, (iii) frequency splitting sensors, and (iv) differential-mode sensors. Let us briefly describe their working principle in the next paragraphs. Frequency variation sensors are based on the variation of the resonance frequency (and eventually quality factor or peak/notch magnitude) of a resonant element, caused by the measurand. The typical, although not exclusive, configuration of such sensors is a transmission line loaded with the resonant element (either in contact or coupled to it), see Figure 1a. Although examples of frequency variation sensors devoted to the measurement of spatial variables have been reported [15], typically these sensors have been applied to dielectric characterization of solids and liquids [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46], as far as the resonance frequency and quality factor depend on the complex dielectric constant of the surrounding material (the so-called material under test (MUT)). These sensors are very simple, but they are potentially subjected to cross-sensitivities caused by variations in ambient factors, such as temperature and humidity, and therefore they need calibration before their use. To alleviate or minimize the impact of cross-sensitivities, symmetry-based sensors are the solution [47]. As symmetry is invariant under potential changes in environmental factors, at least at the typical scales of the sensors, it is expected that sensors based on symmetry properties exhibit certain robustness against environment-related cross-sensitivities. Coupling modulation sensors belong to this category [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 48]. Such sensors are implemented by symmetrically loading a transmission line by means of a symmetric resonator (Figure 1b). However, the combination of line and resonant element should not be arbitrary. Namely, it is necessary that the symmetry plane of the resonator and the one of the line are of different electromagnetic sort, i.e., one must be an electric wall and the other one must be a magnetic wall. By this means, if symmetry is preserved, line-to-resonator coupling is prevented [47], the resonator is not excited, and the line is transparent, i.e., the frequency response does not exhibit any notch (lack of resonance). However, by truncating symmetry (e.g., by means of an asymmetric dielectric loading or through a relative linear or angular displacement between the line and the resonant element), line-to-resonator coupling arises and, consequently, the resonance appears. The magnitude of the notch (the typical output variable) is determined by the coupling degree, intimately related to the level of the asymmetry. Thus, coupling modulation by symmetry disruption is useful for sensing purposes. Nevertheless, as the most natural procedure for symmetry truncation is by a relative displacement between the resonator and the line, most sensors based on this principle have been devoted to angular and linear measurements [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 48]. For such application, the most limitative aspect of these sensors is the input dynamic range, related to the small dimensions of the sensing resonators. A variant of this approach, providing the solution to such limitation, was presented in [28, 29, 30], where circular chains of resonant elements were applied to the implementation of microwave rotary encoders based on pulse counting (linear encoders, potentially exhibiting an unlimited dynamic range, were also presented in [49; 50]).