# Microwave Planar Resonant Solutions for Glucose Concentration Sensing: A Systematic Review
## 6 Phase-Based Sensors
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Ref.** & **Sensor Type** & \begin{tabular}{c} **Sample** \\ **(Volume)** \\ \end{tabular} & \begin{tabular}{c} \(\rho_{\text{g}}\) \\ **Range** \\ **(wt\%)** \\ \end{tabular} & \begin{tabular}{c} **Op. \(f\)** \\ **(GHz)** \\ \end{tabular} & \begin{tabular}{c} **Bare \(Q_{\text{u}}\)** \\ **(GHz)** \\ \end{tabular} & \
\begin{tabular}{c} **Operating** \\ **Q\({}_{\text{u}}\)** \\ **(Pr** \\ **mg/dL)** \\ \end{tabular} &
\begin{tabular}{c} **SQu** \\ **(Pr** \\ **mg/dL)** \\ \end{tabular} & **Remarks** \\ \hline
[81] &
\begin{tabular}{c} Open-loop \\ line resonator \\ \end{tabular} & AG (5 \(\mu\)L) & 0–4 & 1.11 & — & 187.14 & — & 0.186 & — \\
[143] &
\begin{tabular}{c} Single SRR \\ Asymmetric \\ single SRR \\ \end{tabular} & AG (200 \(\mu\)L) & 0–20 & 2.45 & — & 60.00 & — & 0.948 & Coplanar WG \\
[149] &
\begin{tabular}{c} Coplanar \(\lambda/4\) \\ resonator \\ \end{tabular} & AG (5 \(\mu\)L) & 0–5 & 4.50 & 118.78 & 116.18 & — & 1.511 & — \\
[150] & \
\begin{tabular}{c} Coplanar \(\lambda/4\) \\ resonator \\ \end{tabular} & AG (5 \(\mu\)L) & 0–10 & 4.79 & 96.80 & 85.46 & — & 0.901 &
\begin{tabular}{c} Temperature \\ effect analysis \\ \end{tabular} \\
[94] &
\begin{tabular}{c} Single SRR \\ \end{tabular} & AG (25 \(\mu\)L) & 0–10 & 5.16 & 112.31 & 60.65 & — & 0.978 & — \\
[94] &
\begin{tabular}{c} Single SRR \\ \end{tabular} & AG (5 \(\mu\)L) & 0–10 & 7.16 & 109.27 & 72.68 & — & 0.584 & — \\
[31] & \begin{tabular}{c} Single SRR \\ \end{tabular} & \
\begin{tabular}{c} Blood plasma \\ (25 \(\mu\)L) \\ \end{tabular} & 0–10 & 5.17 & 112.31 & 58.16 & — & 0.829 &
\begin{tabular}{c} Multicomponent \\ solutions study \\ \end{tabular} \\
[31] & \begin{tabular}{c} Single SRR \\ \end{tabular} & \
\begin{tabular}{c} Blood plasma \\ (5 \(\mu\)L) \\ \end{tabular} & 0–10 & 7.17 & 109.27 & 64.99 & — & 0.571 &
\begin{tabular}{c} Multicomponent \\ solutions study \\ \end{tabular} \\
[105] & \
\begin{tabular}{c} Two coupled \\ SRR \\ \end{tabular} & AG (5 \(\mu\)L) & 0–10 & 4.23 & 89.85 & 47.63 & — & 4.115 &
\begin{tabular}{c} Inter- \\ resonators \\ coupling \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quality factor-based sensors. AG = aqueous glucose solutions; WG = waveguide. A similar analysis can be applied to a transmission line, in which the electrical length of a section of microstrip line of physical length \(l\) is defined as \(\theta=kl,k=2\pi f_{\mathrm{r}}/v_{\mathrm{p0}}\) being the phase constant, and \(v_{\mathrm{p0}}\) the phase velocity at the resonant frequency. This phase velocity is given by  
\[v_{\mathrm{p0}}=\frac{c}{\sqrt{\varepsilon_{\mathrm{r,eff}}}}. \tag{15}\]  
Since the phase velocity depends on the effective permittivity, a change in \(\varepsilon_{\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{f}}\) results in a change in the phase of the reflection coefficient. This, thus, leads to a similar working principle to that for the \(f_{\mathrm{r}}\)-based sensors presented in Section 3, but with the measured phase as a sensing parameter. The use of phase-based sensors with SRR-based approaches has been reported in the literature for dielectric properties measurement [103], although this has not been widely applied for glucose sensing. A microfluidic attempt considering a triple SRR design was proposed in [123] for aqueous glucose samples, combined with \(f_{\mathrm{r}}\)-based measurements. In [86] a microstrip resonator was used for glucose sensing in aqueous solutions at physiological concentrations, combining phase and insertion loss measurements. An interesting design aimed at measurements in human fingers was presented in that work. A similar microstrip line-based approach was studied in [153] by means of full-wave simulations, hitherto lacking experimental validation. A microstrip line-based sensor was proposed in [154] for measuring aqueous glucose solutions at several frequencies using a pseudo-random noise driving system.