# Microwave Planar Resonant Solutions for Glucose Concentration Sensing: A Systematic Review
## 3 Resonant Frequency-Based Sensors  
The sensors based upon resonant frequency as the sensing parameter to be related to the glucose content rely on the dependence of the resonant frequency on the relative effective permittivity (\(\epsilon_{\text{r,eff}}\)). For example, for an open-loop half-wavelength transmission line resonator [79]:  
\[f_{\text{r}}=\frac{c}{2l\sqrt{\epsilon_{\text{r,eff}}}}, \tag{5}\]  
where \(c\) is the speed of the light in free space and \(l\) is the length of the resonant line. This effective permittivity is indeed affected by the relative permittivity of the substrate and that of the media upon the sensor, where the glucose-containing sample is to be placed. Since the glucose concentration modifies the relative permittivity of the sample, the resonant frequency is expected to be affected by its changes. This can be more easily seen in (1) for the lumped-element model of a simple resonator loaded with a glucose-containing sample, where the influence on the sample is modeled by \(C_{\text{s}}\). However, the relationship between the different relative permittivities involved is not trivial and it depends on the configuration. This aspect, in addition to the different possibilities for maximizing the sensitivity of the resonant frequency to variations in \(\epsilon_{\text{r,eff}}\), calls for research on \(f_{\text{r}}\)-based sensors. This section will review the most relevant planar resonant \(f_{\text{r}}\)-based glucose-sensing approaches of the last years. As a general rule, some premises have been proposed to optimize the performances of these sensors. Firstly, as the quality factor is inversely related to the resonance bandwidth, a high \(Q_{\text{u}}\) is convenient to obtain a high resolution in the measured \(f_{\text{r}}\). It should be noted that this is a requirement related to the measurement process, and it does not imply a high sensitivity of \(f_{\text{r}}\) to glucose concentration, since there is not a theoretical relationship between \(Q_{\text{u}}\) and the \(f_{\text{r}}\) sensitivity. Other convenient design aspects consist of reducing as much as possible the coupling capacitance between the I/O lines and the resonant elements, and using low-loss substrates [48]. Finally, highly capacitive configurations have been proved desirable for glucose level measurements [30; 113]. Under these assumptions, the research community has made a number of attempts at and proposals for \(f_{\text{r}}\)-based glucose sensors. The most common one is the use of SRR with different configurations, which was recently studied in [114]. Single SRR configurations have been proposed with an extended capacitive gap [115], with an enzyme coating [91; 96], with a microfluidic configuration measuring physiological glucose concentrations in water [116], with a CSRR-loaded square patch configuration [22; 110; 117; 118; 119; 120], with a defected ground design for measuring physiological concentrations in blood plasma samples [98] or with an RF tag configuration able to measure physiological concentrations in phantom interstitial fluid [121] (Figure 3a). A double SRR on a gold-on-glass substrate was proposed in [122], able to measure physiological concentrations of glucose in water with a differential configuration. A structure based on open SRR was tested for microfluidic measurement [123]. More complex approaches combining a larger number of SRR have reported interesting sensitivity raises [41]. In order to increase the line capacitance of the sensor, interdigital capacitor gaps have been considered in different configurationsfor water-glucose measurements [30; 124; 125]. The use of complementary electric \(LC\) resonators has also been reported for microfluidic applications with aqueous and biological samples [108; 126] (see Figure 3b).