Development, Characterization, and Circuit Modeling of Inkjet-Printed Coupled Ring Resonators for Application in Biological Samples

In the present study, the inkjet-printing (IJP) technique is used for the development of a planar microwave sensor aimed at the dielectric characterization of biological samples. The proposed sensor consists of two capacitively coupled split-ring resonators (SRRs) fabricated using the microstrip technology. A silver-based conductive ink is deposited by IJP on a conventional 1.6-mm-thick FR4 substrate, thus creating the resonant structure. The experimental analysis is carried out by considering a water–ethanol mixture as a test solution in which the ethanol volume fraction is varied, thereby changing the effective permittivity of the mixture. In this contribution, the authors focused their analysis on the dielectric constant of the solution under test (i.e., the real part of the complex relative permittivity). The water–ethanol mixture is placed into a low-density polyethylene (LDPE) sample vial that is arranged on the surface of the planar sensor. No direct contact is needed between the microwave device and the solution under test. The effect of the ethanol volume fraction change is related to the behavior of the two resonances occurring in the forward transmission coefficient ( ${S}_{21}$ ) of the sensor in the frequency range from 2 to 3 GHz. The permittivity change of the sample under test affects the capacitive coupling between the two SRRs altering the separation between two resonant frequencies. This enables the sensor to differential measurements, thereby improving its robustness. The frequency separation is used to track variations in the ethanol concentration and, thus, the dielectric constant of the solution under test. In addition, a lumped-element equivalent-circuit model is presented, and the changes in the values of the lumped elements with ethanol concentration are estimated and discussed.

onto a rigid or flexible substrate [1]. This technology has been successfully used with a variety of substrates (e.g., paper, polyimide, polyethylene terephthalate, plastic, fiberglass, and ceramic) and different types of inks, including polymer, metal, and carbon [2], [3], [4]. Because of its many interesting qualities and high applicability for adoption in a wide range of applications, IJP stands out among the other competing technologies. Among others, IJP has the advantages of being a contactless (i.e., no physical contact between the printing equipment and the substrate) and mask-free process that allows for quick production times, cost-effectiveness, material savings, good reproducibility, and high spatial resolution [5]. Recently, IJP technology based on flexible substrates has attracted increasing attention due to its use in the production of flexible and wearable electronic devices [6], [7], widely used for healthcare applications [8]. Moreover, this technology represents a highly attractive solution for sensor development since it is applicable to large-scale production of cost-effective devices with an acceptable level of reproducibility [5], [9].
The prototype proposed in this study consists of two capacitive coupled split-ring resonators (SRRs). To the best of our knowledge, so far this type of geometry has not been used for differential measurements, which can significantly improve the sensing robustness [26]. As a matter of fact, possible variations in the surrounding environment are seen as a common mode effect that can be minimized by the differential detection mechanism of the device [27].
The prototype is fabricated by printing on an FR4 substrate a silver-based conductive ink. The employed ink is a commercial conductive ink characterized by a high oxidation resistance and a low electrical resistivity. The sensor is designed by means This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ of a professional computer-aided design (CAD) simulation tool, whereas the experimental validation is performed by measuring the scattering (S-) parameters with a vector network analyzer (VNA).
This study is an extension of our previous work [7] in which a microwave-coupled resonator was proposed for the dielectric characterization of cell cultures. The present study extends the previous findings by means of an extraction procedure based on a lumped-element equivalent-circuit model. This model allows us to describe the proposed device locally, specifically near its two resonances. The lumped-element equivalentcircuit model is an important tool for understanding the behavior of the sensor and its response to changes in the dielectric properties of the liquid under test. Furthermore, the extraction of the relative variation of the lumped-element values provides a thorough characterization of the sensor and its performance. This is crucial for the design and optimization of the sensor and for the development of new sensing applications. The microwave sensor is validated by considering a variable mixture of water and ethanol as a case study. The mixture is placed into a low-density polyethylene (LDPE) sample vial and arranged on the surface of the planar sensor for its characterization. This is carried out by relating the effect of the ethanol volume fraction change in the testing solution to the behavior of the two resonances occurring in the forward transmission coefficient (S 21 ) of the sensor in the frequency range from 2 to 3 GHz. It is worth noting that planar resonators have been widely employed for sensing purposes and have exhibited good performance when used in the frequency range between 1 and 3 GHz [23], [25], [28], [29]. The obtained results demonstrate the validity of the designed sensor and its possible application to the dielectric characterization of other types of materials. In a future perspective, the sensor performance will be evaluated considering different types of biological samples. Moreover, since the proposed device operates in the RF range, it may be possible to integrate it into an antenna for remote sensing applications [30].
The article is organized as follows: Section II is devoted to the description of the topology and working principle of the planar microwave resonator; Section III includes a description of the design and fabrication of the prototype sensor; Section IV deals with the extraction of the main resonant parameters from the acquired forward transmission coefficient; Section V is aimed at presenting the experimental characterization; and Section VI is focused on the analysis and discussion of the achieved results. Conclusive remarks are given in Section VII.

II. COUPLED SRRS
This section is divided into two subsections. The first one is devoted to the introduction of the equivalent-circuit model topology of the studied sensor, whereas the second one is dedicated to the description of its operating principle.

A. Equivalent-Circuit Model
The microwave sensor employed in this work consists of two capacitively coupled SRRs designed in microstrip technology. The selected geometry is depicted in Fig. 1. Two 50- microstrip lines are used as feedlines for the coupled resonator. By using the TXLINE tool of the AWR Design Environment 16 software, the nominal line impedance is estimated to vary only slightly over the whole explored frequency range (i.e., from 50.0 at 2 GHz to 50.1 at 3 GHz). This resonator structure has been already used in previous studies for sensing applications, and the achieved results showed good performance in terms of NaCl detection in water and ice [31], [32].
Each ring is characterized by a resonant frequency f r that can be expressed as [31] where c is the speed of light in the vacuum, l is the physical length of the ring, and ε eff is the effective permittivity of the ambient nearby the microwave resonator. Since the two rings have the same geometry, they are supposed to resonate at the same frequency. However, the two rings are capacitively coupled, and this coupling leads to a frequency-splitting phenomenon. The splitting is tunable by changing the geometrical parameters of the resonators that affect the coupling factor between the two rings [31]. A lumped-element equivalentcircuit model for the selected microwave resonator is shown in Fig. 2. It is the same equivalent-circuit topology described in [33], which is here exploited for the lumped-element extraction procedure and the subsequent analysis. The elements L and C r represent the self-inductance and self-capacitance, i.e., the equivalent inductance and capacitance exhibited by the uncoupled resonator. Without coupling, the resonator is characterized by a resonant frequency f r = 1/(2π √ LC r ). The mutual capacitance C m represents the capacitive coupling effect [33]. The equivalent-circuit model depicted in Fig. 2 is characterized by two resonant frequencies [33] f L = 1 2π Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. The resonant frequency f L is lower in comparison with that of the uncoupled SRR. A physical interpretation of such behavior is that the coupling effect increases the ability of the resonator in charge storing. On the other hand, at f H , the coupling effect limits this ability since f H is higher in comparison with that of the uncoupled SRR [33].

B. Sensor Operating Principle
The two resonant frequencies of the coupled resonator depend on geometrical parameters as well as the dielectric properties of both the resonator materials and the ambient surrounding the resonator itself. Once the final design is selected and the resonator is fabricated on its substrate, the device is still affected by an alteration in the permittivity in the near ambient. This can be exploited for sensor development. In a planar microwave resonant sensor, a change in the dielectric properties of a surrounding material is transduced into an alteration in the electric field that results in a change in the resonant frequency [34], [35], [36], [37].
The working principle of the presented microwave sensor relies on the change in the dielectric properties of the ambient near the sensor itself. For instance, a variation of the dielectric constant ε r of a medium surrounding the microwave device leads to an alteration in the features of the two resonances. This can be observed as a deviation of the main resonant parameters, i.e., the resonant frequency f r and the quality (Q-) factor. Such deviations can be related to the ε r of the medium under test so that, after a calibration procedure, it is possible to exploit f r and Q to track the change in ε r of the medium. Regions A, B, and C, which are shown in Fig. 1, are the most sensible regions of the sensor surface [31], [32]. In light of the information published in the literature [31], if a testing material is placed over the sensor surface in region A or B and its ε r is varied, one resonance results to be more affected than the other one. In other words, a frequency shift is observed mainly in one resonance. On the other hand, if the testing material is placed above the sensor covering also the region C, both resonances are affected [32]. In the present study, the sample under test is placed in region B, as far as possible from central region C, thus making only one resonance sensible to the ε r variation of the sample. This allows one to select one resonant frequency as reference (e.g., the less sensitive one) and consider the difference f r 2 − f r 1 as a tracker for the sample ε r changes. If a bias error affects both resonant frequencies, it will be minimized by considering their difference. Frequency-dependent behavior of the magnitude of the forward transmission coefficient for the developed sensor: measurements (blue line) and simulations (orange line). The selected frequency range is from 2 to 3 GHz with a step of 625 kHz. The inset shows a photograph of the top view of the developed two-port resonator. It is fabricated on a 1.6-mm-thick FR4 substrate. The overall board dimensions are 60 × 20 × 1.6 mm.

III. SENSOR DESIGN AND FABRICATION
The microwave device is intended to operate at frequencies ranging from 2 to 3 GHz. The sensor geometry has been selected in order to optimize both the peak amplitude and the Q-factor. In addition, the resonance frequency spacing (i.e., f r 2 − f r 1 ) has been carefully selected: a large frequency separation will result in an increase in the device bandwidth, which is not an advantage in most cases; on the other hand, if the separation is too small, it will be difficult to distinguish between the two resonances, thus making the accurate evaluation of the resonant frequencies and the quality factors challenging. For the selected prototype, a frequency spacing of about 250 MHz is chosen as a good compromise. The sensor design has been performed using professional CAD software (AWR Design Environment 16). Once the design process is finalized, the sensor is fabricated using the IJP technique by means of the Voltera V-One printed circuit board (PCB) printing machine. As the device under test is an inkjet-printed sensor, the uniformity of the geometry is a major concern. The printing process may lead to imperfections if the inkjet printer is not set up properly, and the setup might depend on various factors, such as the resonator geometry, nozzle dimension, conductive ink used, and substrate. To ensure that the printing results are of the highest possible quality and that there is minimal nonuniformity in the resonator geometry, a calibration procedure is carried out before the printing process on a commercial FR4 substrate, by considering also its nonperfect planarity. This calibration procedure is used to set all the printer parameters properly. As shown in Fig. 3, a comparison between the simulated forward transmission coefficient and the measured one shows a good agreement, which serves as evidence of the effectiveness of the calibration procedure.
A silver-based conductive ink (Voltera Conductor 2, nominal resistivity = 1.265 × 10 −7 · m) is deposited by IJP on a 1.6-mm-thick FR4 substrate according to the sensor final geometry (see Fig. 1). On the opposite side of the substrate, a uniform layer of the silver-based conductive ink is deposited in order to create the ground plane of the microstrip structure. The prototype is then cured in an oven at 200 • C for approximately 30 min. This step is essential for triggering the chemical processes in the conductive ink that will allow the metallic particles to combine and form the conductive layer. Next, the sensor is cleaned with isopropyl alcohol and burnished to remove any possible solvent residues or oxides. Finally, two SMA connectors are soldered at the end of the two 50-feedlines for the VNA connection. A photograph of the top view of the fabricated sensor is shown in the inset of Fig. 3.
The sensor is connected to the VNA for the acquisition of the (S-) parameters in the frequency range from 2 to 3 GHz. As illustrated in Fig. 4, the microwave resonator behaves, in the first approximation, as a symmetrical device (i.e., S 11 = S 22 and S 21 = S 12 ). In the present study, the forward transmission coefficient (i.e., S 21 ) is considered for data analysis. Fig. 3 reports a comparison of the simulated and measured |S 21 |. It is worth noting that, as expected, the two resonant peaks, which appear in the magnitude of the transmission coefficient, occur in both simulations and measurements. The frequency spacing appears wider in the measured data (320 MHz) than in the simulations (250 MHz). Furthermore, it is observed that the Q-factors of two resonances in the measurements are lower than those in the simulations, owing to a higher resistivity of the conductive ink compared with its nominal value used for the simulations. The experimental analysis of the device under test verified the presence of two resonant peaks at 2.30 and 2.62 GHz. These resonance frequencies are here denoted by the symbols f L and f H and are characterized by a Q-factor of 40 and 44, respectively.

IV. EXTRACTION OF THE RESONANT PARAMETERS
The evaluation of the Q-factor and the resonant frequency from the two peaks is fulfilled by means of a double-Lorentzian curve fitting algorithm. The developed software is similar to that used in [38], [39], and [40]. The fitting software is written in Python using the scikitrf package and the lmfit library. This software is able to read the touchstone files and extract the two Lorentzian curves from the acquired forward transmission coefficient by means of a curve-fitting method. In particular, among the various fitting methods allowed by the lmfit library, in this work, the Levenberg-Marquardt algorithm is selected since its performance fits well with the project requirements (i.e., R 2 > 0.9 with an execution time of about 60 ms for each fitting). The complex forward transmission coefficient, as a function of the frequency f , is modeled as the sum of two Lorentzian functions and a background signal The Lorentzian functions L i ( f ) are two identical complex functions in the form where a i and f i are two complex coefficients. In particular, f i can be expressed as The real part f r i is the resonant frequency, whereas the imaginary part is used for the Q-factor estimation The function B( f ) represents the background signal, and it is a complex polynomial function of order N . In this case, N = 2 was enough for a good fitting where b n are complex coefficients.
The developed software draws out the two Lorentzian complex functions from the acquired S 21 parameter and, for each Lorentzian function, the software returns the best estimation of the resonant frequency, the Q-factor, and the resonant-peak amplitude. The fitting process is essential in this case since the two resonant peaks in the magnitude of the transmission coefficient are coupled with each other, and their overlap may result in an inaccurate evaluation of the main resonant parameters (i.e., f r and Q) [41]. The double-Lorentzian fitting is illustrated in Fig. 5. The red line is the acquired S 21 , whereas the blue line is the fitting function. It is the result of a combined contribution of the two Lorentzian functions, depicted in Fig. 5 by dashed lines.

V. MEASUREMENTS
For the sensor validation, a liquid testing mixture of water and ethanol is considered. The mixture is placed into an LDPE sample vial that is put above the sensor surface, as shown in Fig. 6. It is worth noting that the liquid mixture is not directly in contact with the microwave resonator.
The proposed sensor is tested toward the water/ethanol solution, and a parameter extraction procedure is applied for a better understanding of the device's performance. A schematic of the experimental workflow can be found in   Fig. 7. The extraction procedure will be described in detail in Section VI.
The vial is filled with a variable mixture of ethanol (ε r = 25.16 [42]) and pure water (ε r = 80.2 [42]) at different volume ratios in five different steps. The vial diameter, height, and wall thickness are 22.8, 32.9, and 1.35 mm, respectively. Its total capacity is 7 mL. For each volume fraction, the mixture  Measurements of the magnitude of the forward transmission coefficient at five different ethanol concentrations in water. The selected frequency range is from 2 to 3 GHz with a step of 625 kHz. exhibits a different ε r , from 25.16 (pure ethanol) to 80.2 (pure water). This enabled the sensor to be tested on a relatively wide range of ε r , compatible with the typical ε r changes in biological samples [43]. The relationship between the ethanol concentration in water and the corresponding ε r of the solution is reported in [44] and [45].
During the whole experimental activity, the solution volume is maintained constant at 2 cm 3 . Whenever the ethanol volume fraction is varied, a good alignment between the resonator and the vial is ensured by means of some references drawn on the substrate to improve the measurement repeatability. The S-parameters are acquired for each test with the Agilent 8753ES VNA. It is set to acquire 1601 points in the frequency range from 2 to 3 GHz, with an intermediate frequency (IF) bandwidth of 1 kHz. A full two-port coaxial short-open-loadthru (SOLT) calibration is performed on the VNA before the measurement session.
The magnitude of the measured S 21 parameter at different ethanol volume fractions is reported in Fig. 8. The two resonant peaks clearly show a shift in frequency as well as a change in amplitude. It is worth noting that one resonant peak has a larger sensitivity to the ethanol concentration than the other, as described previously in Section II.

VI. RESULTS AND DISCUSSION
The two resonant frequencies and the Q-factors are derived from the measured S-parameters by means of the extraction procedure described in Section IV. The estimated values of f L and f H are plotted in Fig. 9 as a function of the ethanol volume fraction. The frequency f L is characterized by a sensitivity of 105 kHz/%ethanol, estimated from a linear regression model (R 2 = 0.71), whereas f H exhibits a sensitivity of 290 kHz/%ethanol (R 2 = 0.91), which is almost three times higher. The frequency separation f r = f H − f L is plotted in Fig. 10. In this case, the linearity is improved with an R 2 = 0.97 and a sensitivity of 188 kHz/%ethanol. The limit of detection (LOD) has been estimated using the following equation [46]: where RSD is the residual standard deviation of the linear regression and S represents the device sensitivity. This calculation resulted in an LOD of 21% of ethanol. This value may be further reduced by improving the experimental reproducibility of the test, for example, by ensuring consistent vial positioning and accurate preparation of the water/ethanol mixture. It is worth noting that using only f H as a tracker for the ethanol volume fraction instead of f results in a higher LOD (i.e., 34% of ethanol), further demonstrating the improved performance of the sensor using the differential approach. The main benefit of using f r rather than f H or f L as the tracker for ε r measurement is that common mode disturbance and other effects that could affect the measurement of both f L and f H (such as calibration problems and environmental temperature drift) can be reduced by considering the difference between the two resonant frequencies.
The Q-factors of the two resonant peaks are shown in Fig. 11. They exhibit a monotonic trend with the increase Fig. 10. Behavior of the frequency separation ( fr) between the two resonant peaks as a function of the ethanol concentration: measurements (orange circles) and linear fitting (dashed black lines). The best fitting assumed linear is characterized by R 2 = 0.97. in the ethanol volume fraction in water; in particular, Q L decreases, whereas Q H increases. In general, comparing the performance of sensors with different topologies, materials, and operating frequencies is not a straightforward task. However, for the purpose of providing a general overview of the state-of-the-art, Table I presents a comparative overview of the performance of the proposed sensor with other similar sensors that have been reported in the literature for investigating water/ethanol mixtures. The relationship between the resonant frequency and the ethanol volume fraction can be reasonably considered linear with a good approximation for all the sensors reported in the table. The proposed sensor exhibits a sensitivity value that is consistent with those reported in the table; however, this value is slightly lower than those of the other sensors. This can be attributed to the fact that the sensor has been fabricated using a low-cost technique (i.e., IJP) and a low-cost substrate (i.e., FR4 with ε r = 4.8 and tan δ = 0.02). In addition, the proposed sensor is designed to be used for contactless measurements, specifically for the dielectric characterization of liquids inside a container (e.g., a Petri dish), and, then, the distance (or the container thickness) may be the inherent reason for the reduced Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. sensor sensitivity. By using low-loss microwave dielectric substrates or by minimizing the distance between the sensor and the material under test, it might be possible to further improve the sensitivity of the developed sensor. However, despite this, the proposed sensor still exhibits a good level of performance and its low-cost fabrication technique and contactless measurement approach make it a cost-effective and attractive solution for the dielectric characterization.
The study has been extended considering the relative change of the capacitive contribution associated with the two resonances. Each resonance is characterized by an inductive and capacitive contribution. Considering that, in the first approximation, the inductance depends mainly on the geometrical parameters of the microwave resonator, it can be considered constant with respect to the ethanol concentration. Let C L 0 be the capacitive contribution of the first resonance at 0% ethanol (i.e., the reference), and let C L E be the capacitive contribution at a generic ethanol concentration. Then, the resonant frequency f L has two different expressions at 0% ethanol and at any other ethanol volume fraction. Similarly, f H can be expressed as From (10) and (11), the relative change in the capacitive contribution of the first resonance ( f L ) is derived Similarly, from (12) and (13), it is possible to derive the capacitive contribution of the second resonance ( f H ) The variation of these two relative capacitive contributions as a function of the ethanol concentration is shown in Fig. 12. As can be expected, since the inductive contribution has been considered constant and the two resonant frequencies are Relative change with the ethanol variation of the capacitive contributions associated with the two resonances and the two capacitances C r and C m of the equivalent-circuit model. shifted toward higher frequencies as the ethanol concentration increases, the two capacitive contributions decrease with the ethanol concentration. Intuitively, this reduction of the capacitive effects associated with the two resonances might be ascribed to the decrease of ε r when the ethanol concentration is increased. As a matter of fact, by increasing the ethanol concentration from 0% to 100%, ε r decreases from 80.2 to 25.16.
As an alternative perspective, the achieved results can be analyzed by considering the two capacitances of the equivalent-circuit model shown in Fig. 2. Once again, the inductive contribution is here considered independent of the ethanol concentration. As done previously, f L and f H can be expressed in two different ways according to the ethanol content [33] From these equations, it is possible to derive straightforwardly the relative variation of C r and C m with the ethanol content in the testing mixture The two quantities C r E /C r 0 and C m E /C m 0 are plotted in Fig. 12 as a function of the ethanol volume fraction. C r decreases with increasing ethanol concentration. This decrease in C r results in an increase in the two resonant frequencies, as can be clearly observed from (16)- (19) or their more general form in (2) and (3). On the other hand, the capacitance C m , which represents the capacitive coupling between the two rings, increases as a result of the variation of the electrical coupling between the two resonant rings. It is worth noting that the relative variation of C m is higher in comparison with the relative variations in the C r capacitances. This is due to the position of the sample vial, which mainly affects the capacitive coupling between the two rings. Consequently, C m can be considered the most representative sensing element of the equivalent-circuit model. This increase in C m results in the increase in the frequency splitting f r , as can be clearly observed from (16)- (19) or their more general form in (2) and (3). The variation of the electric coupling is the cause of the variation of the frequency splitting f r . The electric coupling coefficient k E between the two resonant rings can be calculated as [33] k As shown in Fig. 13, k E increases with the ethanol content in the mixture as the mutual capacitance C m increases. As a result, the frequency separation f r becomes wider.

VII. CONCLUSION
In this article, the development and validation of a differential two-port microwave sensor based on two capacitive coupled ring resonators have been presented and discussed. The sensor has been fabricated using IJP technology by depositing a silver-based conductive ink on an FR4 substrate.
The validation procedure has been carried out by the extraction of the resonant parameters (i.e., resonant frequencies and Q-factors) from the behavior of the magnitude of S 21 measured over the frequency range from 2 to 3 GHz and at different ε r of the testing sample. This is the first time that the structure based on two capacitive coupled SRRs has been successfully used for differential measurements. To accomplish this task, the separation between the two resonant frequencies occurring in the band from 2 to 3 GHz was used as the sensing parameter.
The study has been extended by considering the lumpedelement equivalent-circuit model of the selected microwave resonator. This model provides a deeper understanding of the sensor behavior and its response to changes in the dielectric properties of the liquid under test. In particular, the relative change in the capacitances that contribute to the two resonances has been evaluated. It emerged that the electrical coupling between the two rings is affected by the ε r of the mixture. By increasing the ethanol volume fraction in the solution, which implies a decrease in the effective ε r , the mutual capacitance C m increases, thus increasing the coupling coefficient. As a result, the frequency separation becomes higher. The described extraction procedure enabled a more accurate description of the sensor response, which is crucial for the design and optimization of the sensor and for the development of new sensing applications. Furthermore, the extraction of the relative change of the lumped-element values provides valuable information for future work on circuit design and optimization of the sensor.
In future work, the experimental validation will be extended by considering additional liquid mixtures and/or cell cultures for accomplishing their dielectric characterization, since the operation of the developed prototype is not limited to the considered samples, consisting of a variable mixture of ethanol and pure water at different volume ratios. Moreover, the effect of the parasitic capacitances on the sensing performance will be evaluated and minimized by investigating tailored design upgrades [52], [53].