# Planar Microwave Resonant Sensors: A Review and Recent Developments
## 2 Classification of Planar Microwave Resonant Sensors
Another drawback of these sensors is related to the fact that measuring the notch magnitude is more sensitive to the effects of noise, as compared to frequency measurements. However, a small frequency scan, or even a single-frequency measurement, suffices to collect the sensor information. Frequency splitting sensors combine the advantages of frequency measurements (noise tolerant) and symmetry properties (robustness against cross-sensitivities) [24; 51; 52; 53; 54; 55; 56; 57; 58; 59]. In these sensors, a symmetric transmission line-based structure is symmetrically loaded with a pair of (not necessarily symmetric) resonators (Figure 1c). If symmetry is preserved, a single notch in the transmission coefficient arises. However, if symmetry is truncated, e.g., by an asymmetric dielectric loading, the original notch splits in two notches separated a distance that depends on the level of asymmetry. Thus, in frequency splitting sensors, the output variable is such frequency separation, and, eventually, the difference in the notch magnitude (two variables are needed, for instance, for the measurement of the dielectric constant and loss tangent of materials [56; 58]). A potential weakness of these sensors is the limited sensitivity and resolution if the resonant elements are coupled [51; 52; 55]. Nevertheless, solutions to this problem have been reported, as discussed in [56; 57], at the expense of significantly separating the sensing resonators (either by using a splitter/combiner scheme [57; 58] or a cascaded topology [56]). Although these sensors are not true differential sensors (in the sense that two independent sensors are not used), the input and the output variable are typically differential variables. The differential dielectric constant or loss tangent (between a reference (REF) sample, or material, and the material under test (MUT)) is the usual input variable, whereas the differential notch frequency and/or magnitude is the natural output variable/s. Moreover, frequency splitting sensors can be easily used as comparators, as they are able to detect differences between the REF and MUT samples. For this application, sensor resolution is the key aspect. However, in terms of resolution, such sensors cannot compete, in general, against true differential sensors, to be discussed next. Differential-mode sensors also belong to the group of symmetry-based sensors. Such devices are composed of two independent sensors, one sensitive to the REF sample (or measurand in general), and the other one sensitive to the MUT sample (Figure 1d). These sensors can operate as single-ended sensors as well, e.g., based on frequency variation, where only one of the individual sensing elements is used. However, exploiting the differential input and output variable/s provides robustness against cross-sensitivities. As far as independent sensing elements are used, the abovementioned coupling effects, which typically limit the resolution, can be prevented in differential sensors. The output variable in these sensors is merely the difference between the output variable of each sensing element. It has been demonstrated that highly sensitive differential sensors for dielectric constant measurements can be implemented by means of a pair of meander lines. These sensors are based on the measurement of the phase difference between the pair of lines, and the penalty to achieve high sensitivity is sensor size [14]. Nevertheless, it has been demonstrated that by replacing the meander lines with artificial lines, sensitivity optimization can be made compatible with moderate or even small sizes [12; 60]. Many differential sensors based on resonator-loaded lines (the interest in this work) have been reported, including microfluidic sensors for liquid characterization [61; 62; 63; 64; 65; 66; 67]. In some realizations, the output variable is the cross-mode transmission coefficient [62; 63; 64; 65; 66; 67], proportional to the difference between the transmission coefficients of both sensing lines, provided such lines are uncoupled.