## 2 Design of Meteresonator Sensor  
The design of the proposed sensor is straightforward with five different layers, as shown in Figure 1. The first layer consists of 0.035 mm thick copper in a 3 mm microstrip transmission line (MTL) configuration. The second layer comprises a 1.6 mm FR-4 substrate with the dimensions 30 mm \(\times\) 25 mm. The relative permittivity (\(\epsilon_{r}\)) and dielectric loss tangent (\(tan\delta\)) of FR-4 substrate are 4.4 and 0.02, respectively. The effective dielectric constant (\(\epsilon_{re}\)) of MTL is 3.326, and characteristic impedance (\(Z_{c}\)) is 50 \(\Omega\). These parameters (\(\epsilon_{re}\) and \(Z_{c}\)) are calculated using the following equations [44]:  
\[e_{re}=\frac{\epsilon_{r}+1}{2}+\frac{\epsilon_{r}-1}{2}\bigg{(}1+\frac{10}{u} \bigg{)}^{-ab}, \tag{1}\]  
where \(u=w/h\), \(a=1+\frac{1}{48}ln\bigg{(}\frac{u^{4}+\big{(}\frac{u}{8}\big{)}^{2}}{u^{4}+0.43 2}\bigg{)}+\frac{1}{18.7}ln\bigg{[}1+\big{(}\frac{u}{18.1}\big{)}^{3}\bigg{]}\), and \(b=0.564\bigg{(}\frac{\epsilon_{r}-0.9}{\epsilon_{r}+3}\bigg{)}^{0.053}\).  
\[Z_{c}=\frac{\eta}{2\pi\sqrt{\epsilon_{re}}}ln\Bigg{[}\frac{F}{u}+\sqrt{1+ \bigg{(}\frac{2}{u}\bigg{)}^{2}}\Bigg{]}, \tag{2}\]  
where \(u=w/h\), \(\eta=120\pi\)\(\Omega\), and \(F=6+(2\pi-6)exp\Big{[}-\big{(}\frac{30.666}{u}\big{)}^{0.7528}\Big{]}\).  
Complementary mirror-symmetric S resonator (CMSSR) is etched in the third layer known as the ground plane. The fourth layer consists of 0.01 mm thick polyimide double-sided adhesive film, which is used to connect the third and fifth layers. The fifth layer consists of a 1 mm thick Teflon container that will act as a pool for OUT.  
The size of the CMSSR resonator is 6 mm \(\times\) 6 mm, and the width of resonator lines is 0.5 mm. The effect of geometrical dimensions on the bandwidth and unloaded \(Q\) factor is already discussed in Reference [45]. According to [45], the maximum value of the \(Q\) factor is achieved using a 0.5 mm wide resonator. The substrate and pool material are selected due to low cost, and the thickness is chosen due to easy availability. The proposed meteasonator sensor is simulated in ANSYS Electronics Suite 2021 with the conditions given in Table 1. The magnitude and phase of transmission (\(S_{21}\)) and reflection (\(S_{11}\)) coefficients for the meteasonator sensor are shown in Figure 2 and Figure 3, respectively. The simulated transmission spectrum shows that the meteasonator sensor provides dual notch resonance with wide bandwidth. The first and second notch has a resonance at 7.21 GHz with a notch depth of \(-\)23.85 dB, and 8.97 GHz with a notch depth of \(-\)21.57 dB, respectively. The unloaded quality (\(Q\)) factor of first notch is 55.38, and that of the second notch is 21.26. The unloaded (\(Q\)) factor of the meteasonator sensor is measured by the \(S_{21}\) using the following equation [46]:  
\[Q=\frac{f_{r}}{\Delta f_{3 dB}}. \tag{3}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline Analysis Area & Size & 25 \(\times\) 30 \(\times\) 1.6 mm\({}^{3}\) \\  & Boundary Condition & Radiation \\ \hline Cells & Number & 14,201 \\  & Shape & Tetrahedron \\ \hline Feed & & Wave port (50 \(\Omega\)) \\ \hline Solution Type & Driven Model \\ \hline Frequency Sweep & & 0.1 GHz to 30 GHz \\ \hline Convergence condition determination & & Maximum number of passes; 20 \\  & & Maximum delta S; 0.02 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation conditions for ANSYS Electromagnetics Suite 2020R1.  
Figure 1: Three dimensional view of complementary meteasonator sensor. (**a**) Top view of the sensor where \(w\) = 3 mm, (**b**) Bottom view of the sensor, (**c**) Dimetric view of the sensor where \(h\) = 1.6 mm.