## 5 Conclusions  
In this work, a dual notch complementary metaresonator sensor is designed, simulated, fabricated, and measured to evaluate vegetable oils. Furthermore, a mathematical model for the proposed sensor is obtained using the least square curve-fitting technique, and a good agreement is achieved between measured and formulated results. The complementary metaresonator sensor is based on five layers: one FR-4, one polyimide, one Teflon, and two copper layers. A complementary mirror-symmetric S resonator (CMSSR) unit is used as a metaresonator with some unique features like dual notch resonance, strong electromagnetic field concentration, and high sensitivity. The sensitivity of the first notch is 31.4%, and that of the second notch is 46.5%, of the complementary metaresonator sensor due to interaction with the corn oil. The normalized average sensitivity of the proposed metaresonator sensor is high compared to that of the other microwave sensors. Due to its unique design, broad sensing range, and high sensitivity, evaluating the vegetable oils with a very close dielectric constant is possible. The simple and inexpensive fabrication makes the proposed sensor very attractive for the oil industry.  
A.A. designed, simulated, fabricated, and measured the proposed complementary metaresonator sensor with technical help from INZA Research Laboratory for Electromagnetic Field and Microwave Engineering. All authors have read and agreed to the published version of the manuscript.  
The author extends his appreciation to the Deanship of Scientific Research at Jouf University for funding this work through research grant No 466/39.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**References**} & **Sensor** & **Method** & **Operating** & & \\  & **Design** & **of Sensing** & **Frequency (GHz)** & **Sensitivity (GHz)** & **Applications** \\ \hline
[41] & CSRR & Transmission Coefficient S21 & 2.52 & 0.08 & Oil Characterization \\
[50] & SIW & Reflection Coefficient S11 & 16 & 0.14 & Chemical \\
[51] & CSRR & Transmission Coefficient S & 2.3 & 0.1 & Water-Ethanol Mixtures \\
[52] & ECRs & Electric Coupling Coefficient k & - & - & Dielectric Materials \\
[53] & OISIR & Electric Coupling & 4.40 & - & Glucose Concentration \\
[54] & OLMR & Unloaded Q factor & 1.92 & 0.46 & Glucose Concentration \\
[55] & PSRR & Transmission Coefficient S21 & 1.9 & 0.2 & Bacterial Growth \\
[56] & Omega & Transmission Coefficient S21 & 2 & 0.05 & Methanol \\
[57] & M-CRR & Transmission Coefficient S21 & 2.4 & 0.06 & Liquids \\
[58] & PMWR & Transmission Coefficient S21 & 1.5 & 0.01 & Liquids \\
[59] & SRRs & Transmission Coefficient S21 & 0.87 & 0.07 & Liquids \\
[60] & SIRs & Transmission Coefficient S21 & 3 & 0.05 & Dielectric Materials \\
[61] & CSRRs & Transmission Coefficient S21 & 1.7 & 0.03 & Substrates \\ Proposed & CMSSR & Transmission Coefficient S21 & 7.20 & 0.48 & Vegetable Oils \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of the proposed complementary metaresonator sensor with various state of art sensors.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Oil Under** \\ **Test (OUT)** \\ \end{tabular} & \begin{tabular}{c} **Dielectric** \\ **Constant** \\ \end{tabular} & \begin{tabular}{c} **Measured** \\ \(f_{1}\) **(GHz)** \\ \end{tabular} & \begin{tabular}{c} **Formulated** \\ **\(f_{2}\) **(GHz)** \\ \end{tabular} & \
\begin{tabular}{c} **Measured** \\ **\(f_{2}\) **(GHz)** \\ \end{tabular} &
\begin{tabular}{c} **Formulated** \\ **\(f_{2}\) **(GHz)** \\ \end{tabular} \\ \hline Air & 1.0006 & 7.20 & 7.13 & 8.93 & 8.85 \\ Corn Oil & 2.526 & 6.72 & 6.75 & 8.22 & 8.26 \\ Coconut Oil & 2.83 & 6.64 & 6.67 & 8.12 & 8.15 \\ Olive Oil & 3.352 & 6.50 & 6.53 & 7.91 & 7.94 \\ Castor Oil & 4.47 & 6.26 & 6.22 & 7.56 & 7.51 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of measured and formulated resonance frequencies of the proposed complementary metaresonator sensor.