# Planar Microwave Resonant Sensors: A Review and Recent Developments
## 4 Prototype Examples
### Frequency Variation Sensors  
The first example is a frequency variation sensor equipped with a microfluidic channel for liquid characterization [46]. In this sensor, the sensitive element is a SISS resonator, loading a microstrip line. The most relevant aspect of this sensor is the high achieved relative sensitivity, by virtue of the specific arrangement, where the ground plane beneath the SISS is removed, and a metallization is added on the top surface, surrounding the rectangular SISS patch with a gap of width \(s\) (see Figure 7). Such metallization is connected to the backside ground plane by means of metallic vias. By these means, the single capacitance of the resonant element is the edge capacitance of the SISS, which can be easily perturbed by means of the MUT (either a solid or a liquid), placed on top of it. Note that with this configuration, any extra capacitance that degrades the sensitivity is removed (see Section 3). This sensor has been equipped with a microfluidic channel, in order to perform measurements of the complex permittivity of liquids (Figure 8). Figure 6: Relative sensitivity of the OCSRR-loaded line, as compared to those reported in [90]. Figure 7: Topology of the SISS-based frequency variation sensor reported in [46], including the top (**a**) and bottom (**b**) views, and lumped element equivalent circuit model (**c**). From [46], reprinted with permission. The measured frequency responses of the sensor for different mixtures of DI water and ethanol are depicted in Figure 9a, whereas Figure 9b shows the resonance frequency position and the magnitude of the notch as a function of the volume fraction of water. The water-ethanol solutions offer a wide range of complex permittivity values, which are appropriate for sensor calibration. That is, with this set of measurements, a mathematical model for the sensor can be developed. Specifically, a mathematical relation linking the frequency shift and the notch magnitude to the complex relative permittivity of the test water-ethanol solutions was derived in [46]. As the complex permittivities of water-ethanol as a function of the volume fraction can be independently inferred, a nonlinear least square curve fitting in MATLAB can be used in order to derive an equation describing the relation between variations of the resonance frequency and notch magnitude as a function of the complex permittivity variations. In [46], the authors used the complex permittivity values of water-ethanol mixtures provided in [91]. With such model, given in [46], the complex permittivity of other liquid solutions can be inferred from the measured values of the resonance frequency and notch magnitude. For instance, in [46], the authors characterized solutions of water-methanol. The measured resonance frequency and notch magnitude for the different concentrations is shown in Figure 10, whereas Figure 11 depicts the real and the imaginary part of the permittivity inferred from the mathematical model. In this figure, the values inferred from the literature are also depicted, and the good agreement between both sets of data can be appreciated. It is remarkable that the relative sensitivity of this sensor is very good, as compared to the one of similar sensors reported in the literature (see [46] for further details). Figure 8: Schematic views (**a**) and photographs (**b**) of the fabricated sensor, including the top (**left**) and bottom (**right**) views. From [46], reprinted with permission. Figure 10: Measured frequency response of the sensor for various water-methanol solutions (**a**) and representation of the resonance frequency and notch magnitude as a function of the water concentration (**b**). From [46], reprinted with permission. In panel (a), the step variation of water content is 10%. Figure 9: Measured frequency response of the sensor for various water–ethanol solutions (**a**) and representation of the resonance frequency and notch magnitude as a function of the water concentration (**b**). From [46], reprinted with permission.