## 2 Design and Simulation  
Most transmission line-based structures are based on changes in electric and magnetic fields. The electric field plays an important role in the characterization of edible oil samples. Oil samples are placed directly on the sensor so the electric field can easily contact the CSRR. Ideally, the introduction of pure dielectric oil should not affect the inductance of the sensor. Only the sensor's overall capacitance is altered by the placement of oil samples on the sensing zone, with the outcome that the sensor's resonating frequency is shifted. This change in resonant frequency is attributed to the real part of permittivity of the oil under test (OUT). The top and bottom views of the proposed sensor with all the dimensions are shown in Figure 1. A four square CSRR structure was etched in the ground plane, whereas the top surface consisted of a feeding transmission line only. When the electromagnetic wave was fed, the rings induced a magnetic field and acted as an inductor, whereas the split gap acted as a capacitor. The combined effect of capacitance and inductance determined the resonance frequency, at which the sensor behaved as a narrow band stop filter. Using a time domain solver, the sensor was designed on a low-cost FR-4 substrate in CST MicrowaveStudio. The sensor's dimensions were optimized in CST Microwave Studio to obtain a confined electric field and a resonance frequency of 5.20 GHz, as shown in Figure 1.  
In the design, a two port network was used to feed the sensor, such that the input was provided at port 1 and output was measured at port 2, using National Instruments Vector Network Analyzer (NI--VNA). When the electromagnetic wave was transmitted from port-1, most energy was stored in the CSRR at resonance. This energy then interacted with OUT and shifted the resonance frequency. The transmission coefficient (S\({}_{21}\)) was used to estimate the resonance frequency. The ports were connected with CSRR in the ground plane and had an impedance of 50 \(\Omega\). The ground plane was designed in such a way so that 50 \(\Omega\) impedance was matched. The simulated result for the forward transmission coefficient (S\({}_{21}\)) is shown in Figure 1.  
The equivalent circuit model for our CSRR was extracted using the techniques presented in [35]. The equivalent circuit model is shown in Figure 2b and was used to calculate the dimensions required to operate the sensor on the desired resonating frequency. The resonance frequency of the circuit presented in Figure 2b was calculated by Equation (1), and it matched well with the resonance frequency of our CSRR. In Equation (1), \(L\) and \(C\) are equivalent inductance and capacitance of CSRR, respectively.  
\[f_{r}=\frac{1}{2\pi\sqrt{LC}} \tag{1}\]  
Figure 2c presents the electric field profile of the resonator at the resonance frequency, and a concentrated electric field can be seen in the ground plane in the region of CSRR.  
Figure 1: (**a**) Four-ring resonator in the ground plane of the sensor. (**b**) Feed line of sensor. (**c**) Transmission coefficient (S\({}_{21}\)) at different frequencies.  
Figure 2: (**a**) Simulated and experimental values of transmission coefficient (S\({}_{21}\)) at different frequencies. (**b**) Equivalent LC model of the CSRR sensor. (**c**) Electric field profile at the resonance frequency.  
This region of the high electric field was utilized for detection because this region had the highest sensitivity to changes in the dielectric permittivity.