Complementary Metaresonator Sensor with Dual Notch Resonance for Evaluation of Vegetable Oils in C and X Bands

Abstract

This paper investigates the effect of complementary metaresonator for evaluation of vegetable oils in C and X bands. Tremendously increasing technology demands the exploration of complementary metaresonators for high performance in the related bands. This research probes the complementary mirror-symmetric S resonator (CMSSR) that can operate in two bands with compact size and high sensitivity features. The prime motivation behind the proposed technique is to utilize the dual notch resonance to estimate the dielectric constant of the oil under test (OUT). The proposed sensor is designed on a compact 30 × 25 mm${}^2$ and 1.6 mm thick FR-4 substrate. A 50 $\mathsf{\Omega }$ microstrip transmission line is printed on one side, while a unit cell of CMSSR is etched on the other side of the substrate to achieve dual notch resonance. A Teflon container is attached to CMSSR in the ground plane to act as a pool for the OUT. According to the simulated transmission spectrum, the proposed design manifested dual notch resonance precisely at 7.21 GHz (C band) and 8.97 GHz (X band). A prototype of complementary metaresonator sensor is fabricated and tested using CEYEAR AV3672D vector network analyzer. The comparison of measured and simulated data shows that the difference between the first resonance frequency is 0.01 GHz and the second is 0.04 GHz. Furthermore, a mathematical model is developed for the complementary metaresonator sensor to evaluate dielectric constant of the OUT in terms of the relevant, resonant frequency.

1. Introduction

Complementary metaresonator-based microwave sensors have high sensitivity, fast response time, broad sensing range, inexpensive fabrication, and high accuracy and are appropriate for diverse climates; therefore, these sensors are very popular in research and industrial applications. These sensors can be employed for the identification of electromagnetic properties of gases [1,2], liquids [3,4], and solids [5,6] in various frequency bands. Metamaterials were theoretically predicted by V. G. Veselago in 1968 [7] and experimentally verified by D. R. Smith in 2000 [8]. The main components of metamaterials are split-ring resonators (SRRs) [9] and complementary split-ring resonators (CSRRs) [10]. Recently, the development of theoretical and experimental models within the scope of microwave sensing using SRR and CSRR has led to the potential applications for biomedical [11,12], chemical [13,14], and electronic sector [15,16].

SRR was a superconducting resonator [17] before its introduction as a microstructure with imaginary magnetic permeability components. Initially, it was used to demonstrate left-handed behavior [18], negative refraction [19], backward wave radiation [20], negative group velocity [21], stopband [22], and passband filters [23]. Later on it was used to design alignment sensor [24], biosensor [25], displacement sensor [26], microfluidic sensor [27], rotation sensor [28], strain sensor [29], thin-film sensor [30], and velocity sensor [31]. SRR based sensors have a very narrow region for the electric field concentration between the splits at the resonance, which interacts with the material under test (MUT). These sensors are not suitable for testing large samples due to the small sensing area; CSRR solves this problem. By applying the babinet principle on SSR [32], its dual counterpart was introduced as CSRR. Initially, CSRR was used to design metamaterial transmission lines [33], passband [34] and stopband filters [35]. Later on, it was used to measure dielectric loss tangent [36], liquid characterization [37], thickness measurement [38], and evaluation of permittivity [39].

In the recent past, several techniques have been proposed to calculate the dielectric properties of oil samples [40,41,42,43]. In [40], a single port sensor based on CSRR is presented to detect adulteration of edible oils with a minimum frequency shift of 14 MHz in the X band. An analytical method is proposed in [41] to calculate the dielectric constant and loss tangent of oils based on a CSRR sensor with a resonant frequency of 2.5 GHz and an average sensitivity of 3.58%. In [42], a metamaterial sensor operating at millimeter-wave is designed to evaluate the oils and their chemical characteristics with a frequency shift of 1.12 GHz. A submersible single-port microwave sensor is presented in [43] to evaluate the complex permittivity of oils based on multiple complementary SRR with a resonant frequency of 8.49 GHz and an average sensitivity 7.25%. However, the aforementioned sensors have sensitivity limitations due to noncompact structure design and minor interaction of electromagnetic fields with the OUT. Furthermore, most of the proposed sensors for oil testing are based on single resonance frequency, which causes low precision and less accuracy in measurement.

This paper proposes a dual notch metaresonator sensor with high sensitivity, compact size, low cost, and convenient operation. The proposed complementary mirror-symmetric S resonator (CMSSR) shows dual notch resonance in the C and X bands. The CMSSR is coupled electrically with the microstrip transmission line for excitation, and a Teflon container is attached to the CMSSR, which makes it suitable for oil characterization. The unique design of the proposed metaresonator sensor and simulation analysis is explained in Section 2. Measurement setup and characterization of oil samples are accomplished in Section 3. Mathematical modeling of the measured data is performed in Section 4. Finally, the main results and technical contributions are summarized in Section 5.

2. Design of Metaresonator 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 × 25 mm. The relative permittivity (${ϵ}_r$) and dielectric loss tangent ($tan\delta$) of FR-4 substrate are 4.4 and 0.02, respectively. The effective dielectric constant (${ϵ}_{re}$) of MTL is 3.326, and characteristic impedance ($Z_c$) is 50 $\mathsf{\Omega }$. These parameters (${ϵ}_{re}$ and $Z_c$) are calculated using the following equations [44]:

$${ϵ}_{re}=\frac{{ϵ}_r+1}{2}+\frac{{ϵ}_r-1}{2}{\left(1+\frac{10}{u}\right)}^{-ab},$$

(1)

where u = $w/h$, $a=1+\frac{1}{49}ln\left(\frac{u^4+{\left(\frac{u}{52}\right)}^2}{u^4+0.432}\right)+\frac{1}{18.7}ln\left[1+{\left(\frac{u}{18.1}\right)}^3\right],$ and $b=0.564{\left(\frac{{ϵ}_r-0.9}{{ϵ}_r+3}\right)}^{0.053}.$

$$Z_c=\frac{\eta }{2\pi \sqrt{{ϵ}_{re}}}ln\left[\frac{F}{u}+\sqrt{1+{\left(\frac{2}{u}\right)}^2}\right],$$

(2)

where u = $w/h$, $\eta =120\pi$$\mathsf{\Omega }$, and $F=6+\left(2\pi -6\right)exp\left[-{\left(\frac{30.666}{u}\right)}^{0.7528}\right].$

Figure 1. Three dimensional view of complementary metaresonator 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.

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 × 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 metaresonator 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 metaresonator sensor are shown in Figure 2 and Figure 3, respectively. The simulated transmission spectrum shows that the metaresonator 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 metaresonator sensor is measured by the $S_{21}$ using the following equation [46]:

$$Q=\frac{f_r}{\Delta f_{3dB}}.$$

(3)

Table 1. Simulation conditions for ANSYS Electromagnetics Suite 2020R1.

Analysis Area	Size	25 × 30 × 1.6 mm${}^3$
	Boundary Condition	Radiation
Cells	Number	14,201
	Shape	Tetrahedron
Feed		Wave port (50 Ω)
Solution Type		Driven Model
Frequency Sweep		0.1 GHz to 30 GHz
Convergence condition determination		Maximum number of passes; 20 Maximum delta S; 0.02

Figure 2. The magnitude of transmission ($S_{21}$) and reflection ($S_{11}$) coefficients for the metaresonator sensor. The first and second notches have a resonance at 7.21 GHz with notch depth −23.85 dB and 8.97 GHz with notch depth −21.57 dB.

Figure 3. The phase of transmission ($S_{21}$) and reflection ($S_{11}$) coefficients for the metaresonator sensor. Near resonance frequencies, there is sudden change in phase.

3. Measurement Setup

For experimental verification, the proposed complementary metaresonator sensor was fabricated using standard PCB fabrication technique and measured on CEYEAR AV3672D series vector network analyzer (VNA), as shown in Figure 4. The VNA is calibrated with a frequency sweep of 4 GHz to 12 GHz and a step size of 0.01 GHz. The fabricated prototype of the complementary metaresonator sensor is connected to VNA using SMA connectors, and $S_{21}$ is measured. The measured resonance frequency of the first notch is 7.20 GHz and the second notch is 8.93 GHz, as shown in Figure 5. The percentage errors between the measured and simulated results for the first and second notch are 0.13% and 0.44%, respectively. Figure 6 shows the measurement environment for oil characterization, and a single adjustable channel automatic pipette (Dragon Lab, 10–100 µL) is used to measure the quantity of oils. The quantity of each OUT is chosen 40 µL to fill the Teflon container, and measurements are performed at room temperature. Measurements are taken very carefully to characterize the oils with dielectric constant ranges from 2.52 to 4.47. The dielectric and chemical properties of common available vegetable oils are given in Table 2. Figure 7 shows the complementary metaresonator sensor loaded with the OUT. In order to reduce the contamination of the previous OUT, the sensor is cleaned with alcohol using a cotton ball. Before the subsequent measurement, it ensures that the alcohol is evaporated and the resonance frequency of the unloaded sensor is returned to its original state. Four samples of vegetable oils are used to measure the $S_{21}$ of the sensor as shown in Figure 8, and results are listed in Table 3. The effect of the dielectric constant of the OUT on the resonance frequencies of the complementary metaresonator sensor is shown in Figure 9.

Figure 4. (a) Photograph of CEYEAR AV3672D series vector network for measurement, (b) fabricated prototype of the complementary metaresonator sensor.

Figure 5. The magnitude of transmission ($S_{21}$) coefficient for simulated and measured metaresonator sensor. The unloaded Q factor of the first notch is 55.38 and that of the second notch is 21.26.

Figure 6. Measurement environment (a) dragon lab 10–100 µL adjustable single channel automatic pipette, (b) oil quantity measurement, (c) pouring the OUT into the Teflon container.

Table 2. Dielectric and chemical properties of OUT [42,47].

Name	Chemical Name	Molecular Formula	Iodine Contents (gI${}_2$/100 g)	Dielectric Constant	Dielectric Loss Tangent
Corn Oil	-	-	110	2.526	0.0566
Coconut Oil	Trilaurin	$C_3{H}_5{\left(C_{12}{H}_{23}{O}_2\right)}_3$	-	2.83	-
Olive Oil	Triolein	$C_3{H}_5{\left(C_{18}{H}_{33}{O}_2\right)}_3$	84	3.352	0.0331
Castor Oil	Triricinolein	$C_3{H}_5{\left(C_{18}{H}_{33}{O}_3\right)}_3$	85	4.47	0.0322

Figure 7. Complementary metaresonator sensor loaded with the OUT.

Figure 8. The magnitude of transmission ($S_{21}$) coefficients for the complementary metaresonator sensor due to interaction with different OUT.

Table 3. Measured $S_{21}$ for the complementary metaresonator sensor due to interaction with different OUT.

Oil Under Test (OUT)	Dielectric Constant	Measured First Resonance Frequency (GHz)	Notch Depth (dB)	Measured Second Resonance Frequency (GHz)	Notch Depth (dB)
Air	1.0006	7.20	−23.51	8.93	−21.57
Corn Oil	2.526	6.72	−18.71	8.22	−20.21
Coconut Oil	2.83	6.64	−18.39	8.12	−20.14
Olive Oil	3.352	6.50	−19.28	7.91	−21.06
Castor Oil	4.47	6.26	−18.43	7.56	−21.11

Figure 9. Dielectric constant of OUT versus the resonance frequency of the sensor due to interaction with the OUTs.

In Figure 9, the slopes of the first (red curve), and second (blue curve) curves provide the fabricated metaresonator sensor’s sensitivity, which can be measured mathematically using the following relation [48]:

$$S=\frac{\partial f_d}{\partial {ϵ}_{rd}}=\underset{(\Delta {ϵ}_{r2}-\Delta {ϵ}_{r1})\to 0}{lim}\frac{\Delta f_u-\Delta f_l}{\Delta {ϵ}_{r2}-\Delta {ϵ}_{r1}}.$$

(4)

Using (4), the sensitivity of the complementary metaresonator sensor is calculated and tabulated in Table 4. The sensitivity of second resonance is higher than the first resonance due to the higher resonance frequency for all the OUTs. The sensitivity of corn oil is maximum due to small dielectric constant. The sensitivity due to the first resonance frequency lies between 31.4% to 27% and that due to the second resonance is between 46.5% and 39.4%.

Table 4. Relative sensitivity of the complementary metaresonator sensor with respect to OUT.

Oil Under Test (OUT)	Dielectric Constant	Sensitivity of First Resonance (%)	Sensitivity of Second Resonance (%)
Corn Oil	2.526	31.4	46.5
Coconut Oil	2.83	30.6	44.2
Olive Oil	3.352	29.7	43.3
Castor Oil	4.47	27	39.4

4. Mathematical Modeling for Oil Characterization

The mathematical model for the measured data is obtained using the curve fitting technique. To achieve the best fitting curve, the technique of least squares is used. According to this technique, the sum of deviation must be minimum for a best fitting curve [49]:

$$\sum _1^n{e}_i^2=\sum _1^n{\left[y_i-f\left(x_i\right)\right]}^2,$$

(5)

where $e_i$ is the deviation, x is the independent variable and y is the dependent variable. The least error (E) for the best fitting polynomial $y=a_1+a_{2}x+a_3{x}^2$ is:

$$E=\sum _1^n{e}_i^2=\sum _1^n{\left[y_i-\left(a_1+a_2{x}_i+a_3{x}_i^2\right)\right]}^2,$$

(6)

For E to be minimum, the following conditions are compulsory: $\frac{\partial E}{\partial a}=0$, $\frac{\partial E}{\partial b}=0$, and $\frac{\partial E}{\partial c}=0$. By applying these conditions to Equation (6), the unknown coefficients ($a_1$, $a_2$, and $a_3$) for the best fitted polynomial are calculated in the form of the following matrix:

$$\left[\begin{array}{c}{a}_1\\ a_2\\ a_3\end{array}\right]={\left[\begin{array}{ccc}n& \sum x_i& \sum x_i^2\\ \sum x_i& \sum x_i^2& \sum x_i^3\\ \sum x_i^2& \sum x_i^3& \sum x_i^4\end{array}\right]}^{-1}\left[\begin{array}{c}\sum y_i\\ \sum x_i{y}_i\\ \sum x_i^2{y}_i\end{array}\right],$$

(7)

The best fitting polynomial for the complementary metaresonator sensor can be expressed as:

$$f_i=a_1+a_2{ϵ}_r+a_3{ϵ}_r^2,$$

(8)

where $f_i$ is the dependent variable and ${ϵ}_r$ is the independent variable. For the first and second resonance of the fabricated complementary metaresonator sensor, the unknown coefficients ($a_1$, $a_2$, and $a_3$) are calculated using matrix (7), and the results given in Table 3. The equations for $f_1$ and $f_2$ are given as:

$$f_1=7.362-0.221{ϵ}_r-0.007{ϵ}_r^2,$$

(9)

$$f_2=9.234-1.079{ϵ}_r-0.0005{ϵ}_r^2.$$

(10)

Equations (9) and (10) are used to calculated to the resonance frequencies of the complementary metaresonator sensor due to interaction with the OUT and tabulated in Table 5. The measured and formulated results are very close to each other. The complementary metaresonator sensor is compared for sensitivity and application with others available sensors in the literature. The sensitivity of proposed complementary metaresonator sensor is high as compared to other state-of-the-art sensors, as tabulated in Table 6.

Table 5. Comparison of measured and formulated resonance frequencies of the proposed complementary metaresonator sensor.

Oil Under Test (OUT)	Dielectric Constant	Measured ${\mathit{f}}_1$ (GHz)	Formulated ${\mathit{f}}_1$ (GHz)	Measured ${\mathit{f}}_2$ (GHz)	Formulated ${\mathit{f}}_2$ (GHz)
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

Table 6. Comparison of the proposed complementary metaresonator sensor with various state of art sensors.

References	Sensor Design	Method of Sensing	Operating Frequency (GHz)	Sensitivity (GHz)	Applications
[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 ke	-	-	Dielectric Materials
[53]	OLSIR	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

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.