# Microwave Planar Resonant Solutions for Glucose Concentration Sensing: A Systematic Review
## 2 Microwave Planar Resonant Glucose Sensors: Fundamentals and Classification  
### Approach to Microwave Planar Resonant Glucose Sensors  
The utility of microwave techniques for the measurement of glucose concentration is due to the influence of this magnitude in the complex permittivity of water, blood and other aqueous solutions [59]. The presence of glucose affects the orientational polarization process of water, shifting the relaxation spectrum towards lower frequencies [60; 61; 62]. The influence of glucose concentration in the permittivity of water-glucose solutions has been reported for a wide variety of frequency ranges using different techniques (e.g., [63; 64; 65; 66; 67]). This dielectric signature of glucose can find applications in the industrial production of sugar-containing drinks. In the diabetes community, the effect of glucose on the permittivity of blood [68; 69] and plasma [70] opens the way for the design of non-invasive glucose sensors [71], although there remain serious technological problems to be solved in this field. Within the common microwave techniques, planar devices have received the greatest attention for this concern. They are usually considered for many applications due to their cost-effectiveness and ease of integration. However, other approaches have also been studied, such as waveguide techniques [72; 73], although their bulky nature hinders their evolution towards feasible commercial devices. Among the possibilities of planar technology for glucose sensing, resonant sensors are the most frequently found in the scientific literature, although other approaches have been studied, such as microstrip lines in transmission/reflection modes [74] or planar antennas in transmission [75; 76] or reflection modes [77]. Resonant planar sensors present the advantage of concentrating the electric field in a small volume at frequencies around the resonant frequency, thus intensifying the sensor-MUT (Material Under Test) interaction. Additionally, they require a narrow bandwidth due to their sharp electrical response, which facilitates the design of the associated electronics. Since the first proposals 30 years ago [78], planar resonators have been widely used for dielectric permittivity measurements in a plethora of contexts. As a simple example of resonant glucose sensor, let us consider a planar resonator loaded with a dielectric sample (an aqueous glucose solution). This can be represented by the parallel \(RLC\) lumped-element model shown in Figure 1, where the subscripts \"r\" and \"s\" make reference to the contribution of the resonator itself and the sample to each element, \(J\) elements are admittance inverters modeling the I/O couplings and \(P_{1}\) and \(P_{2}\) are the input and output ports, respectively. The response of a microwave resonator is generally defined by means of the resonant frequency \(\left(f_{\mathrm{r}}\right)\) and unloaded quality factor (\(Q_{\mathrm{u}}\)). Applying classical circuit analysis techniques, from the model in Figure 1 it can be easily shown [79]:  
\[f_{\mathrm{r}}=\frac{1}{2\pi\sqrt{L_{\mathrm{r}}(C_{\mathrm{r}}+C_{\mathrm{s} })}}, \tag{1}\]  
\[Q_{\mathrm{u}}=2\pi f_{\mathrm{r}}\frac{C_{\mathrm{r}}+C_{\mathrm{s}}}{G_{ \mathrm{r}}+C_{\mathrm{s}}}, \tag{2}\]  
thus, showing how the response of the resonator will be affected by the properties of the sample. Considering that \(G_{\mathrm{s}}\) and \(C_{\mathrm{s}}\) will depend on the complex dielectric permittivity of the sample (defined as \(\varepsilon^{\mathrm{s}}\kappa_{\mathrm{s}}=\varepsilon_{\mathrm{r}\mathrm{s} }{}^{-j}\varepsilon_{\mathrm{r}\mathrm{s}}\)\"), which is linked to its glucose content, these devices therefore seem useful for glucose sensing. It is worthy to note that the dielectric properties of the unloaded planar resonators exhibit very low losses compared to the high dielectric losses of aqueous or biological glucose samples, and that this is a factor in favor of the sensitivity.