# Microwave Planar Resonant Solutions for Glucose Concentration Sensing: A Systematic Review
## 2 Microwave Planar Resonant Glucose Sensors: Fundamentals and Classification
### Proposal of Classification  
Among the different possibilities for classification, in a wide application context, the working principle was proposed as the most convenient criterion [48], especially to ease the comparison. This classification yields five kinds of sensors: frequency-variation sensors (e.g., [94, 101, 102]), phase-variation sensors (e.g., [103, 88]), frequency-splitting sensors (e.g., [104, 105]), coupling-modulation sensors (e.g., [106, 107, 108]) and differential-mode sensors (e.g., [109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 1  
The proposed classification allows us to make direct comparison between the sensors found in each category, since they all rely on the same sensing parameter, i.e., all the measurements are made in the same units, relying on the same physical processes. For example, in a broad application context aimed at dielectric permittivity measurements, for \(f_{r}\)-based sensors a normalized sensitivity relative to a percentage change in the permittivity of MUT was proposed in [102; 112] as  
\[S_{f_{\mathrm{r}}}=\frac{\Delta f_{\mathrm{r}}}{f_{r0}\cdot\Delta\varepsilon_{ \mathrm{r}}}\times 100\ [\%], \tag{3}\]  
where \(f_{r0}\) is the operating resonant frequency, \(\Delta f_{\mathrm{r}}=f_{r1}\ -f_{r0}\) is the measured resonant frequency shift (\(f_{r1}\) is the absolute measured resonant frequency for a certain MUT) and \(\Delta\varepsilon_{\mathrm{r}}\)' is the dielectric permittivity change in the MUT with respect to the minimum measurable considered permittivity (for general permittivity sensors it is usually considered \(\Delta\varepsilon_{\mathrm{r}}\)' = \(\varepsilon_{\mathrm{r}\mathrm{MUT}}\)' - 1). Nevertheless, the main disadvantage of this classification criterion is the difficulty in making comparisons between different categories, where a change in the units is involved. Since the sensitivities found in the literature are heterogeneous and they depend on the sensing parameter, a common generalized metric seems desirable, which has not been hitherto proposed. As it may be of interest to analyze, compare and select sensing approaches with different sensing parameters, we propose an extension of the sensitivity concept introduced in (3) aimed to provide a generalized relative sensitivity which can be applied to different sensing parameters and to different application scenarios. For the sake of analysis, comparison and decision making, we suggest computing the sensitivity as the percentage change of the sensing parameter relative to a percentage change in the parameter under tracking. Consequently, we propose a Relative Sensitivity (\(RS\)) as  
\[RS=\frac{\Delta SP}{SP_{0}\cdot\Delta a}\times 100\ [\%/\%], \tag{4}\]  
where \(a\) is the parameter to be measured. \(\Delta a\) is the relative change in \(a\) with respect to the lowest \(a\) involved in the operating range of the sensor, expressed as a percentage (\(\%\)). \(SP_{0}\) is the operating value of the Sensing Parameter (\(SP\))--i.e., the \(SP\) value obtained for the lowest \(a\)--and \(\Delta SP=SP_{1}-SP_{0}\) is the measured shift of the \(SP\) (\(SP_{1}\) is the absolute measured value of the \(SP\) for a certain \(a\)). Introducing \(RS\) is relevant as it may enable the fair comparison of various sensors monitoring the same parameter using neither the same sensing parameter nor the same operating range for the tracked parameter. All other parameters being equivalent, higher \(RS\) means more sensitivity. Figure 2: Proposed sensing parameter-based classification scheme. In our case, we compute the Relative Sensitivity to Glucose \(RS(G)\), where \(a=\rho_{\text{g}}\) is the glucose concentration expressed in wt% and \(SP\) is the sensing parameter to be related to the glucose concentration, which will be discussed throughout the paper.