# Planar Microwave Resonant Sensors: A Review and Recent Developments
## 4 Prototype Examples
### Frequency Splitting Sensors  
The operation principle of frequency splitting sensors is illustrated in Figure 21[47]. A transmission line is symmetrically loaded with a pair of (not necessarily symmetric) resonators. If symmetry is preserved, a single notch in the transmission coefficient arises (provided the resonators are coupled to the line). Conversely, if symmetry is disrupted, two notches appear (splitting), and their relative distance depends on symmetry imbalance. Thus, this principle can be used for sensing. Although most frequency splitting sensors are implemented by symmetrically loading a line with a resonator pair (as indicated in Figure 21), in some implementations a cascade configuration, where the two resonant elements are placed at different locations in a transmission line, has been considered [56]. In this subsection, we report a frequency splitting sensor for dielectric characterization of liquids as an illustrative example, where a splitter/combiner configuration is used [58]. With such configuration, the effects of inter-resonator coupling (with negative impact on sensor sensitivity) can be avoided, as it was discussed in [57].  
Figure 20: Envelope functions providing the angular velocity (**a**) and motion direction (**b**). The nominal rotary speed is 60 rpm. From [30], reprinted with permission.  
The topology of the designed sensor is shown in Figure 22a, whereas Figure 22b depicts a photograph (in perspective view) of the device, equipped with fluidic channels (device dimensions, substrate, as well as other details related to the fluidic channels and mechanical accessories can be found in [58]). Figure 23 depicts the frequency response for different configurations of channel loading, where the splitting effect for those cases of device imbalance can be observed. With the data of Figure 23 (resonance frequency splitting and difference in the notch magnitude, the output variables), a mathematical model following a scheme similar to the one reported in Section 4.1 can be inferred, provided the complex permittivity of mixtures of DI water, the reference sample, and ethanol can be obtained from independent sources. Such a model links the differential complex permittivity (real and imaginary parts), i.e., the input variables, to the differential output variables. Once the model is known, it can be used to determine the complex permittivity of liquid samples, by considering DI water as reference (REF) sample. In Figure 24, the measured responses of the device for different solutions of water-ethanol injected in the MUT channel, considering water as the REF liquid, are depicted. The inferred output variables are also represented in the figure. With these results and the mathematical model, the complex permittivity of such water-ethanol mixtures was obtained, and the results are depicted in Figure 25. It can be appreciated in that figure that the results lie within the limits of the Weiner model, and consequently these results validate the functionality of the sensor. Although these sensors belong to the category of symmetry-based sensors, and are therefore robust against the effects of ambient factors, the resolution and sensitivity of these sensors is, in general, not as good as the one of true differential sensors, as is discussed in the next section.  
Figure 21: Illustration of frequency splitting through symmetry imbalance (considering square-shaped inclusions) in a CPW symmetrically loaded with a pair SRRs. From [47], reprinted with permission.  
Figure 22: Layout (**a**) and perspective view (**b**) of the designed frequency-splitting sensor. From [58], reprinted with permission.