Compact and Highly Sensitive Bended Microwave Liquid Sensor Based on a Metamaterial Complementary Split-Ring Resonator

: In this paper, we present the design of a compact and highly sensitive microwave sensor based on a metamaterial complementary split-ring resonator (CSRR), for liquid characterization at microwave frequencies. The design consists of a two-port microstrip-fed rectangular patch resonating structure printed on a 20 × 28 mm 2 Roger RO3035 substrate with a thickness of 0.75 mm, a relative permittivity of 3.5, and a loss tangent of 0.0015. A CSRR is etched on the ground plane for the purpose of sensor miniaturization. The investigated liquid sample is put in a capillary glass tube lying parallel to the surface of the sensor. The parallel placement of the liquid test tube makes the design twice as efﬁcient as a normal one in terms of sensitivity and Q factor. By bending the proposed structure, further enhancements of the sensor design can be obtained. These changes result in a shift in the resonant frequency and Q factor of the sensor. Hence, we could improve the sensitivity 10-fold compared to the ﬂat structure. Subsequently, two conﬁgurations of sensors were designed and tested using CST simulation software, validated using HFSS simulation software, and compared to structures available in the literature, obtaining good agreement. A prototype of the ﬂat conﬁguration was fabricated and experimentally tested. Simulation results were found to be in good agreement with the experiments. The proposed devices exhibit the advantage of exploring multiple rapid and easy measurements using different test tubes, making the measurement faster, easier, and more cost-effective; therefore, the proposed high-sensitivity sensors are ideal candidates for various sensing applications.


Introduction
Wireless sensor networks are essential in our society, and are becoming an integral part of our environment [1][2][3][4][5][6]. These sensors are the object of very active research because of the growing interest in them in many areas, such as environmental monitoring [1,2], industrial control [3], information security [4], the Internet of vehicles [5] and network lifetime [6]. The goal of these studies is to develop sensitive, fast, and easy-to-use sensors. Microwave sensor technology may provide wireless passive sensors in addition to wireless sensor networks. Microwave sensors are the current technological framework that has most attracted the attention of researchers in recent years. These sensors offer many advantages, including low manufacturing costs, high sensitivity, and high durability; these advantages make them very attractive and preferred choices in a variety of research fields, including biomedicine [7][8][9][10], chemistry [11][12][13], electronics, and industry [7,14,15]; they have even recently been used in food safety applications and mechanical systems [16][17][18].
In the field of microwave sensor technology, a new perspective has been developed using the concept of metamaterials [19,20]. These are engineered materials first invented by Veselago [21], composed of subwavelength resonators, and have been experimentally validated in recent years. Metamaterials are of great interest, as they effectively contribute to the design of many new devices, ensuring unusual electromagnetic properties that may not be readily available in nature [22,23], such as the realization of passive double-negative metamaterials (DNMs) for simultaneously negative permittivity (ε) and permeability (µ), and single-negative metamaterials (SNMs), where either (ε) or (µ) is negative, referred to as ENGs and MNGs, respectively [24][25][26][27].
In the earlier literature, a variety of split-ring resonator (SRR) [28][29][30][31] and complementary split-ring resonator (CSRR) [32][33][34][35] sensors have been proposed and studied. SRRs and CSRRs are popular in the design of microwave components, meeting the highest standards of accuracy and sensitivity [36], and show great miniaturization capabilities as they allow a shift of the resonant frequency to lower values [28,37,38]. The disadvantage of SRR-based sensors is that they do not support high electric fields and are not suitable for the detection of large microwave signals. Efforts are constantly deployed to improve microwave sensor systems and overcome this problem. The CSRR-based microwave sensors are based on the electric coupling of CSRRs, which are generally etched in the ground plane and have large electric fields [39], and are the most widely used topology of metamaterials in the design of highly sensitive liquid concentration sensors, due to their low profile and adaptability for various practical applications [40].
In this simulation work, a symmetrical CSRR-based compact and highly sensitive bended microstrip sensor for liquid characterization is presented. This study is based on the flat sensor model studied by Chuma in [41], where the capillary tube placement was arranged to be normal to the surface of the sensor, crossing the patch, the substrate, and the ground plane. Modifications were made to the latter in order to improve its performance. First, the liquid test tube placement was readjusted to lie down on the sensor surface, helping to increase the interaction between the electric field and the examined liquid; this improved both the sensor sensitivity and the Q factor. Second, the flat thin structure was folded around a cylinder of radius R in order to further increase the contact area between the test tube and the sensor surface.
The resulting bended shape strengthens the slow wave propagation within the structure. Thus, the slow wave effect leads to increased interaction time between the electric field and the liquid under test [27]. This phenomenon allows for higher sensitivity. A simulation study was carried out to characterize diverse mixtures of ethanol and water dielectric liquids with different ethanol concentrations. In practice-for example, in engine fuels, pharmaceuticals, and medicinal formulations [41]-ethanol liquids are generally characterized by their high concentration and versatility. The ethanol samples are placed in a glass tube on the surface of the sensor for sensor safety, the possibility of reuse, and ease of operability. This allows rapid analysis of the liquid's dielectric properties at microwave frequencies.

Sensor Structure and Design Steps
The basic flat sensor structure [41], consisting of a two-port microstrip-fed rectangular patch, was printed on a 0.75 mm thick Roger RO3035 substrate with a dielectric constant ε r = 3.5 and a loss tangent of tanδ = 0.0015. The structure had overall dimensions of L × W = 20 × 28 mm 2 ( Figure 1). The ground copper layer held a complementary split-ring resonator (CSRR). The conductors used in this design (patch and ground plane) consisted Appl. Sci. 2022, 12, 2144 3 of 16 of 35 µm thick copper layers. The final bended sensor configuration is presented in Figure 2. The novelty of this work lies in the investigation of a new bended-shape structure aiming at enhancing the performance of the microwave sensor. The geometric properties of our proposed sensor are given in Table 1. L × W = 20 × 28 mm 2 ( Figure 1). The ground copper layer held a complementary split-ring resonator (CSRR). The conductors used in this design (patch and ground plane) consisted of 35 μm thick copper layers. The final bended sensor configuration is presented in Figure  2. The novelty of this work lies in the investigation of a new bended-shape structure aiming at enhancing the performance of the microwave sensor. The geometric properties of our proposed sensor are given in Table 1.  The sensitivity of the sensor was analyzed according to the S21 presented results. The shift in the resonant frequency (∆fr = fr_0% − fr_100%) of S21 was deduced. The percentage of relative frequency shift or Q factor (∆fr (3 dB)/fr_ref (%)) was also considered. Next, the sensitivity of the sensors was defined as the ratio of the resonant frequency change to the permittivity change (S = ∆fr/∆εr = |(fr_0% − fr_100%)|/|(εr_0% − εr_100%)|) [42,43].
The S21 parameter and Q factor of the proposed bended sensor, along with CST simulation results of mixing with different water-ethanol concentrations, are presented in Figure 3a,b, respectively. The final designed sensor exhibited a very high sensitivity and an acceptable quality factor compared to those reported in [41]. The frequency range was 400 MHz for a permittivity range of 65 [44] (see Appendix A). This enabled us to achieve  L × W = 20 × 28 mm 2 ( Figure 1). The ground copper layer held a complementary split-ring resonator (CSRR). The conductors used in this design (patch and ground plane) consisted of 35 μm thick copper layers. The final bended sensor configuration is presented in Figure  2. The novelty of this work lies in the investigation of a new bended-shape structure aiming at enhancing the performance of the microwave sensor. The geometric properties of our proposed sensor are given in Table 1.  The sensitivity of the sensor was analyzed according to the S21 presented results. The shift in the resonant frequency (∆fr = fr_0% − fr_100%) of S21 was deduced. The percentage of relative frequency shift or Q factor (∆fr (3 dB)/fr_ref (%)) was also considered. Next, the sensitivity of the sensors was defined as the ratio of the resonant frequency change to the permittivity change (S = ∆fr/∆εr = |(fr_0% − fr_100%)|/|(εr_0% − εr_100%)|) [42,43].
The S21 parameter and Q factor of the proposed bended sensor, along with CST simulation results of mixing with different water-ethanol concentrations, are presented in Figure 3a,b, respectively. The final designed sensor exhibited a very high sensitivity and an acceptable quality factor compared to those reported in [41]. The frequency range was 400 MHz for a permittivity range of 65 [44] (see Appendix A). This enabled us to achieve  The sensitivity of the sensor was analyzed according to the S 21 presented results. The shift in the resonant frequency (∆fr = fr_0% − fr_100%) of S 21 was deduced. The percentage of relative frequency shift or Q factor (∆fr (3 dB)/fr_ref (%)) was also considered. Next, the sensitivity of the sensors was defined as the ratio of the resonant frequency change to the permittivity change (S = ∆fr/∆εr = |(fr_0% − fr_100%)|/|(εr_0% − εr_100%)|) [42,43].
The S 21 parameter and Q factor of the proposed bended sensor, along with CST simulation results of mixing with different water-ethanol concentrations, are presented in Figure 3a,b, respectively. The final designed sensor exhibited a very high sensitivity and an acceptable quality factor compared to those reported in [41]. The frequency range was 400 MHz for a permittivity range of 65 [44] (see Appendix A). This enabled us to achieve a very high sensitivity of 6.15. Moreover, the sensor operates at a central frequency of 1.8 GHz.

Simulation, Results, and Discussion
In the following subsections, we present the stepwise evolution of the proposed design, starting from the validation of Chuma's basic prototype [41], and ending with the final design with the applied modifications-the parallel test tube placement and the bent shape of the sensing structure folded around a cylinder of radius R. Figure 4a illustrates the symmetrical two-port rectangular microstrip-fed patch metamaterial-based flat microwave sensor presented in [41]. A CSRR cell is etched on the ground plane, with a centered hole crossing the patch and substrate, so as to place the test tube of liquid samples normally relative to the surface of the sensor. First, we validated the first basic sensor structure ( Figure 4a) by comparing CST simulation results with experiments published in [41], where only experimental results were reported, without simulation validation. The second structure, where the test tube placement was changed to be parallel to the lower side of the sensor from the CSRR side (Figure 4b), was fabricated as illustrated in Figure 5. The simulations showed good agreement with the experiments (Figure 6).

Simulation, Results, and Discussion
In the following subsections, we present the stepwise evolution of the proposed design, starting from the validation of Chuma's basic prototype [41], and ending with the final design with the applied modifications-the parallel test tube placement and the bent shape of the sensing structure folded around a cylinder of radius R. Figure 4a illustrates the symmetrical two-port rectangular microstrip-fed patch metamaterial-based flat microwave sensor presented in [41]. A CSRR cell is etched on the ground plane, with a centered hole crossing the patch and substrate, so as to place the test tube of liquid samples normally relative to the surface of the sensor. First, we validated the first basic sensor structure ( Figure 4a) by comparing CST simulation results with experiments published in [41], where only experimental results were reported, without simulation validation. The second structure, where the test tube placement was changed to be parallel to the lower side of the sensor from the CSRR side (Figure 4b), was fabricated as illustrated in Figure 5. The simulations showed good agreement with the experiments (Figure 6).

Simulation, Results, and Discussion
In the following subsections, we present the stepwise evolution of the proposed design, starting from the validation of Chuma's basic prototype [41], and ending with the final design with the applied modifications-the parallel test tube placement and the bent shape of the sensing structure folded around a cylinder of radius R. Figure 4a illustrates the symmetrical two-port rectangular microstrip-fed patch metamaterial-based flat microwave sensor presented in [41]. A CSRR cell is etched on the ground plane, with a centered hole crossing the patch and substrate, so as to place the test tube of liquid samples normally relative to the surface of the sensor. First, we validated the first basic sensor structure ( Figure 4a) by comparing CST simulation results with experiments published in [41], where only experimental results were reported, without simulation validation. The second structure, where the test tube placement was changed to be parallel to the lower side of the sensor from the CSRR side (Figure 4b), was fabricated as illustrated in Figure 5. The simulations showed good agreement with the experiments ( Figure 6). The glass capillary tube was easily produced using a Creality Ender-3 Pro 3D printer using a 0.2 mm nozzle and PLA filament. This was used in the case of the flat structure measurements. This kind of capillary tube is commonly used in clinical and laboratory settings; it is 75 mm long, with an outer radius of 0.75 mm, an inner radius of 0.5 mm, and relative permittivity of 5.5. After the confirmation of the microwave sensing application's potential through the numerical computations, the microwave sensor model was fabricated on 0.75 mm thick Roger RO3035 substrate with Eleven Lab PCB prototyping system, as shown in Figure 5.  The glass capillary tube was easily produced using a Creality Ender-3 Pro 3D printer using a 0.2 mm nozzle and PLA filament. This was used in the case of the flat structure measurements. This kind of capillary tube is commonly used in clinical and laboratory settings; it is 75 mm long, with an outer radius of 0.75 mm, an inner radius of 0.5 mm, and relative permittivity of 5.5. After the confirmation of the microwave sensing application's potential through the numerical computations, the microwave sensor model was fabricated on 0.75 mm thick Roger RO3035 substrate with Eleven Lab PCB prototyping system, as shown in Figure 5. This new tube placement brought a significant benefit in terms of field interaction with the liquid being tested, significantly enhancing the sensor sensitivity. Figure 6a illustrates the simulated S21 parameter compared to the experimental data reported in [41]. Validation tests on the design show that the simulation results and measurement data are in good agreement for the three considered cases (water concentration 0%, 100%, and air (Figures 6a and 7b)). It should be noted that the higher the concentration of water in the mixture, the lower the frequency of the peak. On the other hand, the resonant frequency and quality factor patterns are nearly overlapping, with a shift of less than 5 MHz. Figures 6b and 7b illustrate the parallel glass tube design simulations of waterethanol mixture, with an outer radius of r = 0.75 mm. As a result, the sensitivity and quality factor values are doubled compared to the normal test tube case. Note that the normal test tube sensor sensitivity factor was 38 MHz [41], while it was 89 MHz for the parallel case, and the quality factors were 47% and 73%, respectively (Figures 6b and 7b). This new tube placement brought a significant benefit in terms of field interaction with the liquid being tested, significantly enhancing the sensor sensitivity. Figure 6a illustrates the simulated S 21 parameter compared to the experimental data reported in [41]. Validation tests on the design show that the simulation results and measurement data are in good agreement for the three considered cases (water concentration 0%, 100%, and air (Figures 6a and 7b)). It should be noted that the higher the concentration of water in the mixture, the lower the frequency of the peak. On the other hand, the resonant frequency and quality factor patterns are nearly overlapping, with a shift of less than 5 MHz. Figures 6b and 7b illustrate the parallel glass tube design simulations of water-ethanol mixture, with an outer radius of r = 0.75 mm. As a result, the sensitivity and quality factor values are doubled compared to the normal test tube case. Note that the normal test tube sensor sensitivity factor was 38 MHz [41], while it was 89 MHz for the parallel case, and the quality factors were 47% and 73%, respectively (Figures 6b and 7b).  . Q factor and resonant frequency versus water-ethanol concentration of (a) normal glass tube design compared to measurements [41], and (b) the designed parallel test tube compared to measurements.

Effect of the Cylinder's Radius
In an effort to obtain the highest possible sensitivity factor, various modifications were made to the original configuration. The flat structure was bent into a cylindrical form, and the original size remained unchanged (Figure 8a). Simulations were performed for different values of the cylinder radius R. The results for a test tube of radius R = 3.75 mm are presented in Figure 8b. The response S21 was affected by the bended form of the sensing structure. The frequency band increased proportionally with smaller bending radii. It can be seen that the frequency interval between the upper (100% water) and lower (0% water) water concentrations increases with the decrease in the bending radius for 10 mm, 7 mm, and the minimum possible value of 5 mm. Beyond that, the structure is no   . Q factor and resonant frequency versus water-ethanol concentration of (a) normal glass tube design compared to measurements [41], and (b) the designed parallel test tube compared to measurements.

Effect of the Cylinder's Radius
In an effort to obtain the highest possible sensitivity factor, various modifications were made to the original configuration. The flat structure was bent into a cylindrical form, and the original size remained unchanged (Figure 8a). Simulations were performed for different values of the cylinder radius R. The results for a test tube of radius R = 3.75 mm are presented in Figure 8b. The response S21 was affected by the bended form of the sensing structure. The frequency band increased proportionally with smaller bending radii. It can be seen that the frequency interval between the upper (100% water) and lower (0% water) water concentrations increases with the decrease in the bending radius for 10 mm, 7 mm, and the minimum possible value of 5 mm. Beyond that, the structure is no Figure 7. Q factor and resonant frequency versus water-ethanol concentration of (a) normal glass tube design compared to measurements [41], and (b) the designed parallel test tube compared to measurements.

Effect of the Cylinder's Radius
In an effort to obtain the highest possible sensitivity factor, various modifications were made to the original configuration. The flat structure was bent into a cylindrical form, and the original size remained unchanged (Figure 8a). Simulations were performed for different values of the cylinder radius R. The results for a test tube of radius R = 3.75 mm are presented in Figure 8b. The response S 21 was affected by the bended form of the sensing structure. The frequency band increased proportionally with smaller bending radii. It can be seen that the frequency interval between the upper (100% water) and lower (0% water) water concentrations increases with the decrease in the bending radius for 10 mm, 7 mm, and the minimum possible value of 5 mm. Beyond that, the structure is no longer practically feasible, due to structure deformation; consequently, the sensitivity increases, and reaches its maximum. longer practically feasible, due to structure deformation; consequently, the sensitivity increases, and reaches its maximum.  Bending the structure on a smaller cylinder radius improves and increases the sensor's sensitivity. Table 2 summarizes the main obtained results. In addition to its quick and easy handling, the test tube's parallel position configuration enabled us to investigate more possible structure cases according to the tube radius, for optimization purposes. However, the normal configuration [41] allowed only a single radius case (r = 0.75 mm), since the tube was inserted through a hole drilled in the substrate. Figure 9 presents a CST simulation validated by Ansys HFSS for a test tube of radius r = 0.75 mm. The two software S21 response results at resonance were similar for different concentrations, with a 50 MHz offset (Figure 9a,b). A sensor sensitivity of 1.7 kHz and a quality factor of 88.35% were achieved using CST. These results were close to those obtained at HFSS 1.5 kHz and 62.25%, respectively. For this case, the device operates at around 2.4 GHz. Bending the structure on a smaller cylinder radius improves and increases the sensor's sensitivity. Table 2 summarizes the main obtained results.

Effect of the Test Tube Radius
In addition to its quick and easy handling, the test tube's parallel position configuration enabled us to investigate more possible structure cases according to the tube radius, for optimization purposes. However, the normal configuration [41] allowed only a single radius case (r = 0.75 mm), since the tube was inserted through a hole drilled in the substrate. Figure 9 presents a CST simulation validated by Ansys HFSS for a test tube of radius r = 0.75 mm. The two software S 21 response results at resonance were similar for different concentrations, with a 50 MHz offset (Figure 9a,b). A sensor sensitivity of 1.7 kHz and a quality factor of 88.35% were achieved using CST. These results were close to those obtained at HFSS 1.5 kHz and 62.25%, respectively. For this case, the device operates at around 2.4 GHz.  Similarly, as shown in Figure 10, the sensitivity increased almost 2.5-fold compared to the case with r = 0.75 mm, while the quality factor (which has a direct link with the imaginary component of the permittivity) decreased by 15%. The CST and HFSS results curves almost overlap. The resonant frequency of this case decreased, averaging 2.2 GHz. For r = 2.5 mm, an improvement in the performance of the proposed sensor was noticed. The frequency band decreased and reached an average value of 2 GHz at resonance, with stable sensitivity and a slight decrease in the quality factor. In addition, the CST-and HFSS-simulated S21 results are quite close-almost superimposed ( Figure 11). Similarly, as shown in Figure 10, the sensitivity increased almost 2.5-fold compared to the case with r = 0.75 mm, while the quality factor (which has a direct link with the imaginary component of the permittivity) decreased by 15%. The CST and HFSS results curves almost overlap. The resonant frequency of this case decreased, averaging 2.2 GHz.  Similarly, as shown in Figure 10, the sensitivity increased almost 2.5-fold compared to the case with r = 0.75 mm, while the quality factor (which has a direct link with the imaginary component of the permittivity) decreased by 15%. The CST and HFSS results curves almost overlap. The resonant frequency of this case decreased, averaging 2.2 GHz. For r = 2.5 mm, an improvement in the performance of the proposed sensor was noticed. The frequency band decreased and reached an average value of 2 GHz at resonance, with stable sensitivity and a slight decrease in the quality factor. In addition, the CST-and HFSS-simulated S21 results are quite close-almost superimposed ( Figure 11). For r = 2.5 mm, an improvement in the performance of the proposed sensor was noticed. The frequency band decreased and reached an average value of 2 GHz at resonance, with stable sensitivity and a slight decrease in the quality factor. In addition, the CST-and HFSS-simulated S 21 results are quite close-almost superimposed (Figure 11).  For r = 3.75 mm (Figure 12), the simulation results were closer, and almost overlapped at lower concentrations. On the other hand, they moved slightly further apart at other concentrations, and a remarkable increase in sensitivity compared to the previous cases was observed. In the same way, a slight decrease in the quality factor was observed. The resonant frequency decreased until it reached 1.8 GHz. In the same way, for r = 5 mm (Figure 13), the sensitivity was improved by more than 3 times relative to that of r = 0.75 mm, with a decrease in the quality factor by 30%. The S21 HFSS validation results were close to those obtained by CST for different concentrations of water in the mixture. The resonant frequency reached values of around 1.4 GHz. For r = 3.75 mm (Figure 12), the simulation results were closer, and almost overlapped at lower concentrations. On the other hand, they moved slightly further apart at other concentrations, and a remarkable increase in sensitivity compared to the previous cases was observed. In the same way, a slight decrease in the quality factor was observed. The resonant frequency decreased until it reached 1.8 GHz.  For r = 3.75 mm (Figure 12), the simulation results were closer, and almost overlapped at lower concentrations. On the other hand, they moved slightly further apart at other concentrations, and a remarkable increase in sensitivity compared to the previous cases was observed. In the same way, a slight decrease in the quality factor was observed. The resonant frequency decreased until it reached 1.8 GHz. In the same way, for r = 5 mm (Figure 13), the sensitivity was improved by more than 3 times relative to that of r = 0.75 mm, with a decrease in the quality factor by 30%. The S21 HFSS validation results were close to those obtained by CST for different concentrations of water in the mixture. The resonant frequency reached values of around 1.4 GHz. In the same way, for r = 5 mm (Figure 13), the sensitivity was improved by more than 3 times relative to that of r = 0.75 mm, with a decrease in the quality factor by 30%. The According to Table 3, the accuracy and reliability of the proposed device was improved through five measurements for different tube radii. For instance, tubes with r = 0.75 and 1.5 mm had higher Q factors, and were mainly used to extract the imaginary part (ε″). Tubes with larger radii (r = 3.75 and 5 mm) had a sensitivity range frequency of 400 MHz; hence, they were advantageously used for permittivity and the real part (ε′) extraction, since ε' and ε″ are directly related to Δfr and to Q factor, respectively [45].

Complex Permittivity Extraction
The least squares method [32] was used to determine the complex permittivity for different concentrations of ethanol in water. The complex permittivity functions are related to the change in the resonant frequency and the Q factor. The change in the resonant frequency and the Q factor is described in terms of the complex permittivity of the liquid sample, using the linear equations [32,41] translated into matrix M (Equation (1)). For a mathematical analysis allowing the determination of the matrix coefficients, the reference values of the complex permittivity for different concentrations were extracted from [43]. These values are given in tables and illustrated by figures in Appendix A, so as to provide a better understanding of water-ethanol mixture concentrations for important frequency ranges. 11 12 where: According to Table 3, the accuracy and reliability of the proposed device was improved through five measurements for different tube radii. For instance, tubes with r = 0.75 and 1.5 mm had higher Q factors, and were mainly used to extract the imaginary part (ε ). Tubes with larger radii (r = 3.75 and 5 mm) had a sensitivity range frequency of 400 MHz; hence, they were advantageously used for permittivity and the real part (ε ) extraction, since ε and ε are directly related to ∆fr and to Q factor, respectively [45].

Complex Permittivity Extraction
The least squares method [32] was used to determine the complex permittivity (ε x + jε x ) for different concentrations of ethanol in water. The complex permittivity functions are related to the change in the resonant frequency and the Q factor. The change in the resonant frequency and the Q factor is described in terms of the complex permittivity of the liquid sample, using the linear equations [32,41] translated into matrix M (Equation (1)). For a mathematical analysis allowing the determination of the matrix coefficients, the reference values of the complex permittivity for different concentrations were extracted from [43]. These values are given in tables and illustrated by figures in Appendix A, so as to provide a better understanding of water-ethanol mixture concentrations for important frequency ranges. where: where m 11 , m 12 , m 21 , and m 22 are unknown coefficients, ∆ε is the complex permittivity, ∆ f is the resonant frequency, and ∆Q is the Q factor. The reference value for analysis purposes is taken at 50% water concentration. The shifts in the values related to the variation in the complex permittivity, the resonant frequency, and the Q factor for different samples of the water-ethanol mixture are defined by the matrices X, Y 1 , and Y 2 , respectively, as follows: After having obtained the complex permittivity, the resonant frequency, and the Q factor for the different samples of the water-ethanol mixtures, we had only to apply the initial matrix model given in (1). Thanks to a detailed algebraic analysis, Equations (5) and (6) were generated [32]. Thus, the unknown coefficients can be determined as given in (7): The final matrix providing data on the different water-ethanol samples is described by (8). These calculated coefficients are used to determine the complex permittivity of any given sample as a function of the change in the sample's resonant frequency and Q factor:  Table 4 shows a comparison of the proposed sensing structures with the literature in terms of sensitivity and Q factor.

Conclusions
This paper proposes two small, low-cost, and highly sensitive microwave CSRR-based sensors for liquid characterization. The capillary glass test tube is filled with a waterethanol mixture placed parallel to the sensor's ground surface in order to determine the dielectric parameters of different mixture concentrations. The CSRR-based bended sensor was designed by folding the flat sensor around an arbitrary cylinder. Very important results were obtained. The originality of the bended sensor offers the possibility of changing the test tube quickly and easily for multiple measurements. The diversity of the sensor's bended shape and the modification of the radius of the test tube significantly improve the sensitivity at different resonant frequencies (1.8 GHz, 1.9 GHz, 2 GHz, and 2.4 GHz). The proposed sensors have several advantages, such as small size, low cost, multi-performance ability, high sensitivity, and easy handling, making them ideal candidates for various applications.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
The properties of water-ethanol mixture concentration and complex permittiv given in [44], and are represented in the following figures. The difficulty encou when reading the data as described in [44] forced us to reproduce these data in Figu Two tables describing the properties of the water-ethanol (real and imaginary p permittivity) mixture are given in Tables A1 and A2 from [44]. In this appendix, the was based mainly on the work presented in [44], so as to provide the frequency de ence of the complex permittivity of any water concentration ( Figure A1), which wil as a basis for future research. In our case, the work is limited to the 1.5-3.5 GHz freq band for water-ethanol mixtures (Tables A1 and A2).