# Planar Microwave Resonant Sensors: A Review and Recent Developments
## 3 Planar Resonant Elements for Sensing  
There are dozens of planar resonant elements that can be useful for sensing purposes. In this paper, the interest is in electrically small (quasi-lumped) resonators that can be described by means of a lumped-element equivalent circuit model up to frequencies beyond their fundamental resonance (the authors recommend the books [73; 74], and the paper [75], where a review of many of these resonators is carried out). Probably the simplest classification of such resonators can be made by differentiating on whether they are metallic or slot resonators. In the first group, resonant elements of interest for sensing include the step impedance resonator (SIR) [76], the step impedance shunt stub (SISS) [77], the split-ring resonator (SRR) [78], the open split-ring resonator (OSRR) [79], and the electric-LC (ELC) resonator [80], among others (see Figure 2). Slot resonators are typically etched in the ground plane and are sometimes designated as defect ground structure (DGS) resonators. Examples of such resonators include the complementary counterparts of the SRR and the OSRR, that is, the  
Figure 1: Typical topology and working principle of the considered planar microwave resonant sensors. (**a**) Frequency variation; (**b**) coupling modulation; (**c**) frequency splitting; (**d**) differential-mode. complementary split-ring resonator (CSRR) [81] and the open complementary split-ring resonator (OCSRR) [82], respectively, the dumbbell-shaped DGS (DB-DGS) resonator [83], and the magnetic-LC (MLC) resonator [84], among others (see Figure 3). There are many other electrically small resonators, including the S-shaped-SRR [85], the spiral resonator [86], the non-bi-anisotropic-SRR [87] (as well as their complementary counterparts), the broadside-coupled-SRR [88], etc., but their use for sensing has been more limited. A comparative analysis of electrically small resonators, with the focus on metamaterial and metamaterial-inspired circuit design, was carried out in [75]. For sensing, the most important aspect is the effect of resonator topology on sensor performance, mainly sensitivity, resolution, and dynamic range. Nevertheless, compatibility of the sensing element (resonator), including the dielectric load, with the required hardware and mechanical parts of the sensor is also important. For instance, for microfluidic applications, the fluidic channels plus the required mechanical accessories should not affect the transmission lines used for resonator's excitation. In this regard, slot resonators constitute, in general, a good solution, as the ground plane provides backside isolation, thereby preventing for any potential effect of the dielectric load on sensor functionality. The size of the resonant element may be also important in certain applications devoted to the characterization of small dielectric loads. Obviously, increasing the frequency is a possibility, but this has the effect of raising the cost of the associated electronics. Therefore, considering resonant elements with small electrical size is expected to provide a good tradeoff, allowing for the implementation of compact sensors (sensitive element) operating at moderate (or even low) frequencies. In this regard, the OSRR and the OCSRR are electrically smaller than the SRR and the CSRR, respectively, by a factor of two [74,89], and are therefore good candidates from the point of view of sensor size. Concerning sensitivity and resolution (intimately related), it is difficult to firmly establish the preferred resonator topology, as it may be determined by several aspects, including the sensing working principle, the considered input and output variables, etc. For instance, for complex permittivity measurements, both the real and the imaginary part of the complex permittivity (input variables) must be determined, and two output variables (e.g., the frequency position and notch magnitude) are needed to unequivocally infer both measurands.