# Microwave Planar Resonant Solutions for Glucose Concentration Sensing: A Systematic Review
## 5 Quality Factor-Based Sensors  
The use of the quality factor in resonant sensors for measurements of variations in the dielectric properties of the MUT was proposed and studied some years ago, especially for lossy solutions [81; 107; 142]. However, it was not until recent years that this approach started to be exploited for glucose concentration measurement with planar sensors [31; 94; 105; 143]. Indeed, the measured loaded quality factor (\(Q_{\text{L}}\)) is defined as  
\[Q_{\text{L}}=\frac{f_{\text{r}}}{\Delta f_{\text{3 dB}}}, \tag{8}\]  
where \(f_{\text{r}}\) is the resonant frequency and \(\Delta f_{\text{3 dB}}\) is the measured bandwidth at 3 dB fall from the amplitude maximum at the resonant frequency. The influence of the loading of the ports due to the feed and measurement equipment (usually a Vector Network Analyzer) is involved in the computation of \(Q_{\text{L}}\). To avoid it, for a two-port planar resonator with a low enough I/O coupling, the unloaded quality factor (\(Q_{\text{u}}\)) can be computed as:  
\[Q_{\text{u}}=\frac{Q_{\text{L}}}{1-10^{\frac{S_{21 max}}{2\pi}}}, \tag{9}\]  
where \(S_{21 max}\) is the maximum amplitude (in dB) of the transmission parameter, given at the resonant frequency. Therefore, Equations (8) and (9) show how this approach seeks to benefit from the information included both in \(f_{\text{r}}\) and \(S_{21 max}\) (two prior sections) and it also introduces a new source of information, \(\Delta f_{\text{3 dB}}\), which can also be useful for tracking effects specifically associated with changes in the glucose concentration [90]. Going back to the illustrative lumped-element example in Figure 1, for a homogeneous dielectric sample at a sufficiently high frequency to neglect DC conductivity, its loss tangent (tan \(\delta_{\text{s}}=\varepsilon_{\text{fs}}\)\({}^{\prime\prime}\)/\(\varepsilon_{\text{fs}}\)) at the resonant frequency can be expressed in terms of its lumped elements:  
\[\tan\delta_{\text{s}}=\frac{G_{\text{s}}}{2\pi f_{\text{r}}G_{\text{s}}}. \tag{10}\]  
Hence, the definition of \(Q_{\text{u}}\) for the model in Figure 1, given in (2), can be rearranged and expressed as a function of tan \(\delta_{\text{s}}\):  
\[Q_{\text{u}}=\frac{\frac{G_{\text{r}}}{G_{\text{s}}}+1}{\tan\delta_{\text{s}} \Big{(}\frac{G_{\text{r}}}{G_{\text{s}}}+1\Big{)}}, \tag{11}\]  
thus showing the relationship of this parameter with the sample loss tangent. This analysis shows coherence with the conclusions reached in [144] for a microstrip patch resonator. Equation (11) therefore shows how \(Q_{\text{u}}\)-based sensors are related to variations both in real and imaginary parts of the permittivity of the sample without ranking or giving  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Ref. **} & **Sensor** & **Sample** & \multirow{2}{*}{ \begin{tabular}{c} \(\rho_{\text{g}}\) \\ **(Volume)** \\ \end{tabular}  } & **Op. \(f\)** & **Bare** & **Operating** & \(S_{S1I}\)/\(S_{2I}\) & \multirow{2}{*}{\ \begin{tabular}{c} \(RS(G)\) \\ **(dB Per** \\ **(dB)** \\ \end{tabular}  } & \multirow{2}{*}{**Remarks**} \\  & **Type** & **(Volume)** & **Range** & **(tWt\%)** & **(GHz)** & **(dB)** & **(dB)** & **mg/dL** & **(\%/\%)** & **Remarks** \\ \hline \multirow{3}{*}{[139]} & Coplanar & \multirow{3}{*}{
\begin{tabular}{c} \(\rho_{\text{g}}\) \\ **Type**  
relative qualification between them. Indeed, their dependence on the loss tangent of the MUT seems interesting for tracking glucose concentration changes [77]. Actually, recent studies of the dielectric signature of glucose solutions showed the convenience of tracking parameters influenced by the dielectric losses of the MUT at microwave frequencies up to roughly 10 GHz [71]. In fact, the loss factor has also been proposed for measuring other biomedical water-based processes at these frequencies [145]. As a matter of fact, the importance of properly tracking loss tangent variations in microwave sensors aimed to glucose concentration retrieval was pointed out in [146].