This is the accepted version of the article: Muñoz Enano, Jonathan; Vélez Rasero, Paris; Gil Barba, Marta; [et al.]. «An analytical method to implement high-sensitivity transmission line differential sensors for dielectric constant Measurements». IEEE sensors journal, Vol. 20, issue 1 (Jan. 2020), p. 178-184. DOI 10.1109/JSEN.2019.2941050 This version is avaible at https://ddd.uab.cat/record/221400 under the terms of the license > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 An Analytical Method to Implement High Sensitivity Transmission Line Differential Sensors for Dielectric Constant Measurements Jonathan Muñoz-Enano, Graduate Student Member, IEEE, Paris Vélez, Member, IEEE, Marta Gil, and Ferran Martín, Fellow, IEEE 1Abstract— A simple analytical method useful to optimize the to potential cross sensitivities related to changes in sensitivity in differential sensors based on a pair of meandered environmental factors (e.g., temperature or humidity). By microstrip lines is presented in this paper. Sensing is based on the contrast, sensors based on symmetry disruption are robust phase difference of the transmission coefficients of both lines, against such cross-sensitivities [9],[10]. The reason is that, in when such lines are asymmetrically loaded. The analysis provides these symmetry-based sensors, variations in ambient the combination of operating frequency and line length (the main conditions are seen as common mode stimulus, unable to design parameters) that are necessary to obtain the maximum possible differential phase (180º) for a given level of the generate an appreciable response in the sensor. differential dielectric constant (input dynamic range). The Coupling modulation [11]-[19], frequency splitting [20]-[26] proposed sensor is useful to detect tiny defects of a sample under and differential sensors [27]-[30] belong to the category of test (SUT) as compared to a reference (REF) sample. It can also microwave sensors based on symmetry properties. Differential be applied to the measurement of the complex dielectric constant sensors consist of two independent sensing elements, and the of the SUT, where the real part is inferred from the differential output variable is generated in response to a differential input phase, whereas the imaginary part, or the loss tangent, is derived variable, e.g., the difference in the dielectric constant of a from the modulus of the transmission coefficient of the line reference sample (REF) and the SUT. In frequency splitting loaded with the SUT. It is experimentally demonstrated that the sensors, a single transmission line based sensor is used, but it proposed device is able to detect the presence of few and small is equipped with two independent sensitive elements (purposely generated) defects in a commercial microwave substrate, as well as subtle variations in their density, pointing (resonators) symmetrically loading the line. In this case, the out the high achieved sensor sensitivity. Sensor validation is also measurand is also a differential magnitude. By contrast, carried out by determining the dielectric constant and loss coupling modulation sensors are based on a single sensor tangent of commercial microwave substrates. structure and a unique sensitive element (a symmetric Index Terms — Dielectric characterization, differential resonator symmetrically loading the line). Thus, this later type sensors, microstrip, microwave sensors. of sensors is not appropriate for differential sensing (most reported coupling modulation sensors have been applied to the I. INTRODUCTION measurement of linear and angular displacements and T HERE are many approaches for the dielectric characterization of solids and liquids using microwaves. Among the methods that use transmission line based velocities [11]-[19]). Many differential sensors devoted to dielectric characterization of solids and liquids are based on resonator structures, an extended sensing principle is based on the loaded lines (like frequency splitting sensors). Examples are variation of the resonance frequency and notch/peak the sensors reported in [29],[30], able to detect tiny magnitude of a resonator-loaded line, caused by loading the concentrations of electrolytes in deionized (DI) water, or sensitive part of the resonator with the sample under test variations in the composition of liquids, as compared to a (SUT) [1]-[8]. These sensors are simple but they are subjected reference, caused by the difference in the permittivity [29]. In such sensors, the output variable is the cross-mode This work was supported by MINECO-Spain (project TEC2016-75650-R), transmission coefficient, whose magnitude is dictated by the by Generalitat de Catalunya (project 2017SGR-1159), by Institució Catalana level of asymmetry (in turn given by the input differential de Recerca i Estudis Avançats (who awarded Ferran Martín), and by FEDER variable). funds. J. Muñoz-Enano acknowledges Secreteraria d’Universitats i Recerca (Gen.Cat.) and European Social Fund for his FI grant (2018FI_B_00111). The resolution and sensitivity of the resonator-based P. Vélez acknowledges the Juan de la Cierva Program for supporting him differential sensors reported in [29],[30] for the measurement (Project IJCI-2017-31339). M. Gil acknowledges the Universidad Politécnica of the electrolyte concentration in aqueous solutions are good. de Madrid Young Researchers Support Program (VJIDOCUPM18MGB) for This is attributed to the fact that the loss tangent of water is its support. J. Muñoz-Enano, P. Vélez and F. Martín are with GEMMA/CIMITEC, very sensitive to changes in the electrolyte content. Therefore Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, appreciable variations in the magnitude of the resonance, 08193 Bellaterra, Spain. E-mail: Jonatan.Munoz@uab.cat. related to changes in the electrolyte concentration, are caused M. Gil is with DIEMAG, Audiovisual Engineering and Communications Department, Universidad Politécnica de Madrid, 28031, Madrid, Spain. in the SUT sensing line (as compared to the REF line), thereby > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 providing significant variations in the cross mode transmission where SUB is the dielectric constant of the substrate, and F is a coefficient. Despite the fact that electrolyte concentrations as function of the line geometry given by small as 0.25 g/L have been resolved [29], and sensitivities as ℎ −1/2 high as 12.27 dB/(g/L) have been experimentally 𝐹 = (1 + 12 ) (3) 𝑊 demonstrated [30], the output dynamic range of the sensors is In (2) and (3), it has been assumed that the thickness of the limited. Moreover, the resonator-based differential sensors line strip is negligible (as compared to substrate thickness, h), exhibit a limited resolution and sensitivity in regard to liquid and that the width of the line, W, is larger than h. The effective composition, mainly related to the dielectric constant. dielectric constant for the SUT line is also given by (2), by In this paper, differential sensors, based on a pair of simply replacing REF with SUT. Expression (2) is obtained meandered lines, for the measurement of differential dielectric from the formula of the effective dielectric constant of a constants are proposed. Moreover, an analytical method, microstrip line (covered by air), as detailed in [31], but useful for sensor design on the basis of the required sensitivity replacing the dielectric constant of air (r = 1) with the and input dynamic range, is presented. Application of this dielectric constant of the REF sample (REF). method provides a sensor with extremely high (adjustable) Introducing the effective dielectric constants of both lines in sensitivity, able to detect tiny changes in material composition (1), one obtains and defects. The proposed sensing method is similar to the one 0 𝑙 reported in [28]. The novelty of the paper concerns the fact  = (√𝑆𝑈𝐵 (1 + 𝐹) + 𝑅𝐸𝐹 (1 − 𝐹) − √𝑆𝑈𝐵 (1 + 𝐹) + 𝑆𝑈𝑇 (1 − 𝐹)) (4) √2 that from the reported analysis, the length of the meander lines and assuming that  << REF, expression (4) can be (given the operational frequency) that is needed in order to approximated by obtain the required sensor sensitivity, is provided. Moreover, 0 𝑙 (1−𝐹) the paper demonstrates that not only the differential dielectric  = (5) 2√2 √𝑆𝑈𝐵 (1+𝐹)+𝑅𝐸𝐹 (1−𝐹) constant can be obtained (from which the dielectric constant of the SUT is inferred), but also the loss tangent of the SUT can Note that the interest in this paper is to obtain very good be obtained from the response of the SUT line. Additionally, sensor resolution and sensitivity, in order to discriminate and the sensor can be useful as comparator, able to detect tiny measure small differential dielectric constants. For this reason, differences between the REF and the SUT samples, thanks to the above-cited approximation is justified. However, the the high sensitivity of the structure as differential mode sensor can be also designed to measure larger input dynamic sensor. ranges (differential dielectric constants), at the expense of a degradation in the sensitivity (considering the same output dynamic range, between +180º and -180º). II. SENSING PRINCIPLE AND ANALYSIS The sensing principle of the proposed differential sensor is III. SENSOR DESIGN AND FABRICATION the variation of the electrical length of the sensing line, as In order to optimize sensor sensitivity, the output dynamic compared to the reference line, when such lines are loaded range must be (ideally) max = , for differential dielectric with the SUT and REF samples, respectively. The considered constants varying within a range delimited by a certain lines are meandered microstrip lines, with a phase velocity maximum value,  = max, max being a design that depends on the dielectric constant of the surrounding specification. Introducing these values in (5) and isolating 0l, material. Therefore, the differential dielectric constant, the following result is obtained  = REF  SUT (where REF and SUT are the dielectric constants of the REF and SUT samples, respectively), will √𝑆𝑈𝐵 (1+𝐹)+𝑅𝐸𝐹 (1−𝐹) 0𝑙 = 2√2 (6) determine the differential phase,  = REF  SUT (where REF 𝑚𝑎𝑥 (1−𝐹) and SUT are the electrical lengths of the REF and SUT line, From the geometry of the line (W), substrate parameters respectively). In order to express  in terms of , let us first (SUB, h), dielectric constant of the REF sample, REF, and write the differential phase as a function of the effective max, equation (6) provides the single design parameter of the dielectric constants of the REF line, eff,REF, and SUT line, sensor, i.e., 0l. For small values of max, the case of interest, eff,SUT, i.e., either a high operating frequency or long lines are necessary in  = 0𝑙(√𝑒𝑓𝑓,𝑅𝐸𝐹 − √𝑒𝑓𝑓,𝑆𝑈𝑇 ) (1) order to optimize the sensitivity. Since operation at high where l is the length of the meandered lines, and 0 = /c is frequencies may increase the cost of the sensor in a real the phase constant in vacuum,  and c being the angular scenario, it is convenient to assume the need of long lines, frequency and the speed of light in vacuum, respectively. which can be meandered in order to obtain a reasonable shape Let us now assume that the REF and SUT samples, in factor of the sensitive area of the sensor. Nevertheless, contact with the sensor lines, are thick enough, so as to inspection of (6) reveals that considering substrates with small consider them as semi-infinite in the transverse direction to the dielectric constant, SUB, helps in reducing the length of the plane of the lines. Under this approximation, the effective lines (this also applies to REF, but this parameter is not a dielectric constant of the REF line can be expressed as [31] design variable). 𝑆𝑈𝐵 +𝑅𝐸𝐹 𝑆𝑈𝐵 −𝑅𝐸𝐹 The considered sensor substrate is the Rogers RO4003C 𝑒𝑓𝑓,𝑅𝐸𝐹 = + 𝐹 (2) 2 2 with dielectric constant SUB = 3.5, thickness h = 0.8128 mm > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3 and loss tangent tanSUB = 0.0027. The REF sample is by means of the LPKF H100 drilling machine), whereas the considered to exhibit the characteristics of the Nelco sensor loaded with the REF and SUT samples is depicted in N4350-13RF substrate, with dielectric constant REF = 3.55, Fig. 2(b). The lines have been meandered in order to achieve a and dissipation factor tanREF = 0.0065 (a semi-infinite sample roughly square shape factor for the sensing area (indicated in in the vertical direction has been considered). With these the figure). We have then obtained from full-wave material properties, the width of the REF line necessary to electromagnetic simulation (using Keysight Momentum) the provide a 50-Ω characteristic impedance is found to be differential phase of the structure as a function of the dielectric W = 1.6 mm. Let us consider that the measurement range of constant of the SUT, by considering variations in the vicinity the dielectric constant of the SUT sample corresponds to a of REF = 3.55 with max = 0.45. The results, for different differential dielectric constant of max = 0.45, i.e., limited to values of the loss tangent of the SUT, are depicted in Fig. 3. 12.7 % variations of the dielectric constant of the REF sample. The curves are almost undistinguishable, which means that the Evaluation of (5) gives 0l = 84.23 rad. By considering an loss factor of the SUT does not play an important role on the operating frequency of f0 = /2 = 6 GHz, the length of the differential phase. Moreover, the simulated curves of Fig. 3 meandered lines is found to be l = 670.3 mm. Such long line are in very good agreement with the analytical expression (5), length line is the reason for line meandering, but similar also included in the figure. These results validate the analysis results are achievable by using straight lines (obviously, with of the previous section, and point out that it is not necessary to the penalty of an excessive sensor dimension in the direction know in advance the loss tangent of the SUT sample in order of the line axis). to determine its dielectric constant. Note that for the SUT sample with the highest or lowest dielectric constant (corresponding to max),  = REF  SUT = . The sensitivity, roughly constant, has been found to be S = d/d = 415.6º (very close to the theoretical value, i.e., −400º) and the sensor is able to detect extremely small differential dielectric constants. For the determination of the loss tangent of the SUT, the output variable can be the magnitude of the transmission coefficient of the SUT line (S43). Figure 4 depicts the simulated S43 at f0 as a function of the dielectric constant, by considering the loss tangent of the SUT as a parameter. It can be appreciated that the dependence of S43 on the dielectric Fig. 1. 3D plot showing the dependence of the sensitivity on the dielectric constant is roughly negligible. That is, S43 is dictated by the constant and thickness of the substrate, as derived from expression (5).The loss factor of the SUT, and thereby it can be considered as the necessary parameters for the calculation of S from (5) are given in the text. output variable for the determination of the loss tangent of the SUT. Interestingly, according to (5), a small value of the dielectric constant of the substrate, SUB, is convenient for sensitivity optimization (for a fixed value of 0l). Concerning substrate thickness, h, increasing h has the effect of decreasing F (expression 3), and this, in turn, has the effect of enhancing the sensitivity. Figure 1 depicts the dependence of the sensitivity (S = d/d) as inferred from the approximate expression (5), as a function of both the dielectric constant, SUB, and thickness, h, of the substrate. It should be clarified, however, that if 0l is determined from (6), the sensitivity is S = d/d = max/max regardless of h and SUB. But note that the resulting 0l value increases with SUB and decreases with h. For these reasons we have selected the considered sensor substrate, with relatively small dielectric constant and relatively thick dielectric layer. Thus, the proposed design procedure of the sensor allows us to set the sensitivity to a required value, and the resulting line length is determined by the substrate characteristics. The plot of Fig. 1, corresponding to a fixed value of 0l, i.e., the nominal value given by (6), must be understood as the tolerance of the sensitivity against changes in the dielectric constant and thickness of the (a) (b) substrate. Fig. 2. Photograph of the designed differential sensor without (a) and with (b) Figure 2(a) depicts the photograph of the bare sensor with REF and SUT samples on top of it (dimensions are given in mm). relevant dimensions indicated (the sensor has been fabricated > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 180 measurement have been carried out) is  = 24.23º (Fig. 5), i.e., in very good agreement, taking into account the relatively 120 large value of SUT. We have also carried out the experiment REF - SUT (º) 60 RO4003C by considering as SUT a piece of Rogers RO4003C substrate with SUT = 3.5 (satisfying  << REF) and thickness 3.05 mm 0 FR4 (also achieved by stacking two samples). The resulting mean -60 Using eq. (5) of the measured differential phases at 6 GHz (also with N = 3 Ideal lines -120 Meandered lines (tanSUT = 0.0022) independent measurements) is  = 28.97º (Fig. 5), in good Meandered lines (tanSUT = 0.02) agreement with the expected value ( = 20.34º). The -180 measured differential phases at 6GHz are depicted in Fig. 3 to 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 SUT ease the comparison with the theoretical value. Note that from the measured phases, the dielectric constant values inferred Fig. 3. Simulated differential phase at f0 = 6 GHz of the proposed sensor as a function of the dielectric constant of the SUT, parameterized by the loss from expression (5) for FR4 and RO4003C are found to be tangent of the SUT. The curve given by expression (5) is also included. The 4.51 and 3.48, respectively, i.e., very close to the nominal mean of the measured differential phases (with N = 3 independent values. It should be mentioned that the alignment of the REF measurements) for the indicated materials, as well as the error bars inferred and SUT samples is not critical as far as these samples cover from the standard deviation, are also included. the same extension in both lines, delimited by the sensing area 1.0 [indicated in Fig. 2(b)]. In order to minimize the effects of the tanSUT = 0 tanSUT = 0.025 tanSUT = 0.003 tanSUT = 0.05 air gap (between the substrate and the REF and SUT samples), 0.8 tanSUT = 0.01 tanSUT = 0.1 we have used Teflon screws and we have added pressure to 0.6 the SUT and REF samples against the substrate. |S43| Concerning material losses, Fig. 4 can potentially be used to 0.4 determine the loss tangent from the value of the transmission coefficient (magnitude) of the SUT line. However, 0.2 discrepancies between the simulated and measured transmission coefficient are inevitable due to the effects of the 0.0 access lines and connectors (not accounted for in the 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 SUT simulations). Indeed, determining the loss tangent from analytical expressions is not feasible because of the above Fig. 4. Simulated transmission coefficient of the SUT line at f0 = 6 GHz, as a cited effects, and also due to meandering of the lines and function of the dielectric constant of the SUT, for different values of the loss tangent of the SUT. metal losses. Consequently, we have measured the magnitude of the transmission coefficient for several samples with IV. EXPERIMENTAL VALIDATION different value of the loss tangent. The obtained S43 values at f0 are depicted in Fig.6. From these values, a calibration curve Experimental validation has been first carried out by loading can be generated (see Fig. 6, inset), and this curve is useful to the sensing region with a commercial microwave substrate determine the loss tangent of the SUT from the measured with well-known dielectric constant, i.e., the FR4 substrate value of S43. The considered samples for the generation of the with SUT = 4.5. The thickness of the REF sample is 3.3 mm, calibration curve are the FR4 and Rogers 4003C substrates whereas the one of the SUT is 3.2 mm (achieved by stacking indicated in the previous paragraph, as well as the Nelco two samples). With these thicknesses, the samples can be N4350-13RF substrate (the REF sample for the differential roughly considered to be semi-infinite. Namely, the phase measurements). Nevertheless, we have also measured electromagnetic field generated by the lines do not reach the the transmission coefficient of the unloaded SUT line REF/air (or SUT/air) interface (under these conditions, the (corresponding to tanSUT = 0), as it provides an additional analysis of Section II is valid). This aspect has been data point. corroborated by means of simulations, not included in the To validate the approach for the determination of the loss paper, which demonstrate that 3 mm is a sufficient sample tangent, we have fabricated two samples with a 3D-printer thickness (for thicker samples, the phase of the lines does not (model Ultimaker 3 Extended). The loss factor of such experience an appreciable variation). samples, measured by means of the Agilent Keysight 85072A Note that SUT (or ) is out of the considered input dynamic commercial resonant cavity, are tanSUT = 0.010 (for SUT1, range. However, the measured differential phase, , is a fabricated by considering PLA as filament) and periodic function with  (actually,  varies linearly with , tanSUT = 0.016 (for SUT2, fabricated by considering RS Pro but any measured value of  out of the range [,+] is MT-COPPER as filament). The measured values of the expressed by its equivalent value within that range). Thus, insertion loss at f0 that are obtained by loading the SUT line from the measured differential phase, it is possible to check with these 3D-printed samples are indicated in Fig. 6. It can be the validity of the approach (the limitation is dictated by the seen that the resulting points are in reasonable agreement with requirement  << REF). According to the results of Fig. 3, the the calibration curve. Therefore, it is demonstrated that such expected value of the differential phase for SUT = 4.5 is curve can be used to estimate the loss tangent of the SUT  = 19.18º (equivalent to SUT = 3.6), whereas the mean of sample. the measured values at 6 GHz (N = 3 independent > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 5 180 V. COMPARISON TO OTHER SENSORS 120 The comparison of the reported sensor in terms of sensor performance with other sensors available in the literature is REF - SUT (º) 60 not straightforward, since the working principle of most dielectric constant sensors is based on frequency variation or 0 frequency splitting. Due to the different output variables in -60 such sensors, a sensitivity comparison with the sensor reported REF-REF REF-SMP1 REF-FR4 REF-SMP2 in this work is not possible. The sensor reported in [28] is -120 REF-RO4003C REF-SMP3 based on similar principle. Nevertheless, sensitivity -180 comparison is not concluding even in this case, since the 5.80 5.85 5.90 5.95 6.00 6.05 6.10 6.15 6.20 sensitivity of the proposed sensor can be made as high as Frequency (GHz) required by simply increasing the length of the meander lines Fig. 5. Measured differential phase for different SUT samples, including FR4 (as discussed before). and Rogers RO4003C slabs, as well as samples identical to the REF sample An advantage of the proposed sensor is that it operates at a and different densities of holes across the substrate. Measurements have been single frequency. Moreover, due to the high sensitivity, the performed by means of the Keysight N5221A four-port vector network analyzer. For FR4 and RO-4003C, the mean measured differential phase with sensor exhibits high resolution in the determination of the N = 3 independent measurement is depicted. differential dielectric constant. Assuming that phase 0.65 differences of  = 5º can be detected (a conservative value), AIR it follows that the resolution is as small as 0.0120. Table I 0.60 summarizes some characteristics of various sensors devoted to 0.55 tan = -2.6775·10-4 + 35.003e-|S43 |/0.0503 dielectric constant measurements, where the operating principle, the frequency span required for measurement (i.e., a |S43| 0.50 RO4003C single frequency or a frequency scan), the sensitivity and the 0.45 N4350-13RF resolution, are indicated. Note that the sensitivity units are not the same due to the different working principles, as MT-COPPER 0.40 FR4 mentioned. Sensor resolution is not given in most works. PLA 0.35 Nevertheless, assuming that frequency variations as small as 0.000 0.005 0.010 0.015 0.020 1 MHz can be detected in frequency variation or frequency tan splitting sensors (an extremely small value for sensors Fig. 6. Measured transmission coefficient at f0 = 6 GHz for different operating at GHz frequencies), the corresponding variation of (indicated) SUT samples. The mean values, as well as the error bars, obtained the dielectric constant (equivalent to the resolution) can be from N = 3 independent measurements are depicted. calculated. The results are given in the Table I. It can be appreciated that the proposed sensor exhibits very competitive Let us now demonstrate the potential of the designed resolution in the measurement of the dielectric constant (note structure as highly sensitive comparator, able to detect small differences between the SUT and REF samples. Due to the that the considered phase discrimination,  = 5º, is a lack of available substrates, or materials, with small variations conservative value, as compared to the considered frequency discrimination, 1 MHz). of the dielectric constant in the vicinity of REF, we have TABLE I emulated the differences between the REF and SUT samples COMPARISON OF VARIOUS SENSORS DEVOTED TO DIELECTRIC by generating sparse defects (holes across the substrate) of CONSTANT MEASUREMENTS different densities in samples identical to the REF sample Working Freq. (Fig. 7). The measured differential phases for such SUT Ref. principle* span Sensitivity Resolution samples are also included in Fig. 5. As it can be appreciated, [26] f yes 1.13 MHz 0.8849 the sensor is able to detect the presence of extremely small [29] f yes 2.05 MHz 0.4878 densities of holes in the SUT sample, pointing out the [32] f yes 81.25 MHz 0.0123 potential to detect tiny defects in the SUT sample (as [25] f yes 47.81 MHz 0.0210 compared to the REF sample). [33] f yes 46.51 MHz 0.0215 [24] f yes 29.34 MHz 0.0341 [5] f yes 62.12 MHz 0.0161 [6] f yes 66.30 MHz 0.0151 [34] f yes 73.03 MHz 0.0137 [35] f yes 32 MHz 0.0312 [36] f yes 116.86 MHz 0.0086 [37] f yes 70.51 MHz 0.0142 [38] f yes 6.28 MHz 0.1592 Fig. 7. Photographs of the SUT samples generated by opening hole arrays of [28]  no 54.85º 0.0911 different densities across the Nelco N4350-13RF substrate (the REF sample). T.W.  no 415.6º 0.0120 The diameter of the holes is 1 mm, and the hole density is 0.84 holes/cm2, 1.81 holes/cm2, and 3.50 holes/cm2 in samples SMP1, SMP2 and SMP3, * f and  stands for frequency variation and phase variation, respectively. respectively. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 6 VI. CONCLUSIONS [12] J. Naqui, M. Durán-Sindreu, and F. Martín, “Alignment and position sensors based on split ring resonators,” Sensors, vol. 12, pp. In conclusion, an analytical method to implement highly 11790−11797, 2012. sensitive differential permittivity sensors based on meandered [13] A.K. Horestani, C. Fumeaux, S.F. Al-Sarawi, and D. Abbott, lines has been reported and experimentally validated. In such “Displacement sensor based on diamond-shaped tapered split ring resonator,” IEEE Sens. J., vol. 13, pp. 1153–1160, 2013. sensor, the differential output variable is the phase balance [14] A.K. Horestani, D. Abbott, and C. Fumeaux, “Rotation sensor based on between the pair of lines, whereas the differential dielectric horn-shaped split ring resonator,” IEEE Sens. J., vol. 13, pp. 3014–3015, constant (between the REF and SUT samples) is the 2013. considered input variable. It has been shown that for small [15] J. Naqui and F. Martín, “Transmission lines loaded with bisymmetric resonators and their application to angular displacement and velocity values of the input variable, the sensitivity is roughly constant sensors,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 12, pp. and proportional to the length of the meandered lines. 4700–4713, Dec. 2013. Particularly, the fabricated sensor has been designed in order [16] J. Naqui and F. Martín, “Angular displacement and velocity sensors based on electric-LC (ELC) loaded microstrip lines,” IEEE Sensors J., to exhibit a nominal sensitivity of |S| = 400º. It has been vol. 14, no. 4, pp. 939–940, Apr. 2014. found that the differential phase does not depend on the loss [17] A.K. Horestani, J. Naqui, D. Abbott, C. Fumeaux, and F. Martín, “Two- tangent of the SUT sample. Thus, the dielectric constant of the dimensional displacement and alignment sensor based on reflection SUT sample can be easily inferred from the measured coefficients of open microstrip lines loaded with split ring resonators,” Elec. Lett., vol. 50, pp. 620–622, Apr. 2014. differential phase. It has been also shown in the paper that the [18] A. Ebrahimi, W. Withayachumnankul, S. F. Al-Sarawi and D. Abbott, dielectric constant of the SUT has very small impact on the "Metamaterial-Inspired Rotation Sensor With Wide Dynamic Range," magnitude of the insertion loss of the SUT line, mainly IEEE Sensors J., vol. 14, no. 8, pp. 2609-2614, Aug. 2014. determined by the loss tangent of the SUT sample. Therefore, [19] J. Naqui, J. Coromina, A. Karami-Horestani, C. Fumeaux, and F. Martín, “Angular displacement and velocity sensors based on coplanar such insertion loss magnitude has been used as the output waveguides (CPWs) loaded with S-shaped split ring resonator (S-SRR),” variable for the determination of the loss factor of the SUT. Sensors, vol. 15, pp. 9628–9650, 2015. Finally, it has been demonstrated that the designed differential [20] A. K. Horestani, J. Naqui, Z. Shaterian, D. Abbott, C. Fumeaux, and F. sensor can be used as highly sensitive comparator, able to Martín, “Two-dimensional alignment and displacement sensor based on movable broadside-coupled split ring resonators,” Sensors and Actuators detect tiny defects (sparse hole arrays) in a sample, as A, vol. 210, pp. 18–24, April 2014. compared to a reference one. As compared to other planar [21] J. Naqui, et al., “Transmission lines loaded with pairs of magnetically dielectric constant sensors, the reported device exhibits a good coupled stepped impedance resonators (SIRs): modeling and application combination of sensitivity (with measured value of 415.6º) to microwave sensors,” IEEE MTT-S Int. Microwave Symp., Tampa, FL, USA, June 2014, pp. 1–4. and resolution (0.0120). Moreover, as it is not based on [22] L. Su, J. Naqui, J. Mata-Contreras, and F. Martín “Modeling frequency variation, wideband frequency measurements for metamaterial transmission lines loaded with pairs of coupled split ring the determination of the permittivity of the samples under test resonators,” IEEE Ant. Wireless Propag. Lett., vol. 14, pp. 68–71, 2015. are not required. [23] L. Su, J. Naqui, J. Mata-Contreras, and F. Martín, “Modeling and applications of metamaterial transmission lines loaded with pairs of REFERENCES coupled complementary split ring resonators (CSRRs),” IEEE Ant. [1] M. Puentes, C. Weiß, M. Schüßler, and R. Jakoby, “Sensor array based Wireless Propag. Lett., vol. 15, pp. 154–157, 2016. on split ring resonators for analysis of organic tissues,” in IEEE MTT-S [24] L. Su, J. Mata-Contreras, J. Naqui, and F. Martín, “Splitter/combiner Int. Microw. Symp., Baltimore, MD, USA, Jun. 2011, pp. 1−4. microstrip sections loaded with pairs of complementary split ring [2] M. Puentes, Planar Metamaterial Based Microwave Sensor Arrays for resonators (CSRRs): modeling and optimization for differential sensing Biomedical Analysis and Treatment, Springer, Heidelberg, Germany, applications,” IEEE Trans. Microw. Theory Techn., vol. 64, pp. 4362- 2014. 4370, Dec. 2016. [3] A. Ebrahimi, W. Withayachumnankul, S. Al-Sarawi, D. Abbott, “High- [25] A. Ebrahimi, J. Scott and K. Ghorbani, "Differential sensors using sensitivity metamaterial-inspired sensor for microfluidic dielectric microstrip lines loaded with two split ring resonators," IEEE Sensors J., characterization,” IEEE Sensors J., vol. 14, pp. 1345−1351, May 2014. vol. 18, pp. 5786-5793, Jul. 2018. [4] M. Schueler, C. Mandel, M. Puentes, and R. Jakoby, “Metamaterial [26] P. Vélez, L. Su, K. Grenier, J. Mata-Contreras, D. Dubuc, and F. Martín, inspired microwave sensors,” IEEE Microw. Mag., vol. 13, no. 2, pp. “Microwave microfluidic sensor based on a microstrip splitter/combiner 57–68, Mar. 2012. configuration and split ring resonators (SRR) for dielectric [5] M. S. Boybay and O. M. Ramahi, “Material characterization using characterization of liquids”, IEEE Sensors J., vol. 17, pp. 6589-6598, complementary split-ring resonators,” IEEE Trans. Instrum. Meas., vol. Oct. 2017. 61, no. 11, pp. 3039−3046, Nov. 2012. [27] C. Damm, et al., “Artificial transmission lines for high sensitive [6] C.-S. Lee and C.-L. Yang, “Complementary split-ring resonators for microwave sensors,” IEEE Sensors Conf., Christchurch, New Zealand, measuring dielectric constants and loss tangents,” IEEE Microw. 2009, pp. 755–758. Wireless Compon. Lett., vol. 24, no. 8, pp. 563−565, Aug. 2014. [28] F.J. Ferrández-Pastor, J.M. García-Chamizo and M. Nieto-Hidalgo, [7] C.-L. Yang, C.-S. Lee, K.-W. Chen, and K.-Z. Chen, “Noncontact “Electromagnetic differential measuring method: application in measurement of complex permittivity and thickness by using planar microstrip sensors developing”, Sensors, vol. 17, p. 1650, 2017. resonators,” IEEE Trans. Microw. Theory Techn., vol. 64, no.1, pp. [29] P. Vélez, K. Grenier, J. Mata-Contreras, D. Dubuc, and F. Martín, 247−257, Jan. 2016. “Highly-sensitive microwave sensors based on open complementary [8] L. Su, J. Mata-Contreras, P. Vélez, A. Fernández-Prieto, and F. Martín, split ring resonators (OCSRRs) for dielectric characterization and solute “Analytical method to estimate the complex permittivity of oil samples”, concentration measurements in liquids”, IEEE Access, vol. 6, pp. 48324- Sensors, vol. 18, p. 984, 2018. 48338, Dec. 2018. [9] F. Martín, Artificial Transmission Lines for RF and Microwave [30] P. Vélez, J. Muñoz-Enano, K. Grenier, J. Mata-Contreras, D. Dubuc, F. Applications, John Wiley, Hoboken, NJ, 2015. Martín, ”Split ring resonator (SRR) based microwave fluidic sensor for [10] J. Naqui, Symmetry Properties in Transmission Lines Loaded with electrolyte concentration measurements”, IEEE Sensors J., vol. 19, no. Electrically Small Resonators, Springer, Heidelberg, Germany, 2016. 7, pp. 2562-2569, Apr. 2019. [11] J. Naqui, M. Durán-Sindreu and F. Martín, “Novel sensors based on the [31] D.M. Pozar, Microwave Engineering, 4th Ed., Wiley, Hoboken, NJ, symmetry properties of split ring resonators (SRRs),” Sensors, vol 11, 2011. pp. 7545−7553, 2011. [32] A. Ebrahimi, J. Scott and K. Ghorbani, "Transmission Lines Terminated With LC Resonators for Differential Permittivity Sensing," in IEEE > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 7 Microwave and Wireless Components Letters, vol. 28, no. 12, pp. 1149- Ferran Martín (M’04-SM’08-F’12) was born in 1151, Dec. 2018. Barakaldo (Vizcaya), Spain in 1965. He received the [33] A. Ebrahimi, A. Ahmed, B. Mapleback, J. Scott and K. Ghorbani, B.S. Degree in Physics from the Universitat Autònoma "Microstrip lines loaded with bandstop resonators for high resolution de Barcelona (UAB) in 1988 and the PhD degree in permittivity sensing," 2018 Asia-Pacific Microw. Conf. (APMC), Kyoto, 1992. From 1994 up to 2006 he was Associate 2018, pp. 926-928. Professor in Electronics at the Departament [34] J. Naqui, C. Damm, A. Wiens, R. Jakoby, L. Su, J. Mata-Contreras, F. d’Enginyeria Electrònica (Universitat Autònoma de Martín, "Transmission lines loaded with pairs of stepped impedance Barcelona), and since 2007 he is Full Professor of resonators: modeling and application to differential permittivity Electronics. In recent years, he has been involved in measurements", IEEE Trans. Microw. Theory Techn., vol. 64, no. 11, different research activities including modelling and pp. 3864-3877, Nov. 2016. simulation of electron devices for high frequency applications, millimeter [35] D. Isakov, C. J. Stevens, F. Castles and P. S. Grant, “"A split ring wave and THz generation systems, and the application of electromagnetic resonator dielectric probe for near-field dielectric imaging", Sci. Rep., bandgaps to microwave and millimeter wave circuits. He is now very active in vol. 7, article number 2038, 2017. the field of metamaterials and their application to the miniaturization and [36] N. M. Shebani, B. M. Khamoudi, and A. S. Abul-kassem, “Measurement optimization of microwave circuits and antennas. Other topics of interest of Dielectric Constant of Some Materials Using Planar Technology”, include microwave sensors and RFID systems, with special emphasis on the Second Int. Conf. on Comp. and Electrical Engineering, Dubai, United development of high data capacity chipless-RFID tags. He is the head of the Arab Emirates, Dec. 2009, pp. 352-356. Microwave Engineering, Metamaterials and Antennas Group (GEMMA [37] D. Shimin, “A new method for measuring dielectric constant using the Group) at UAB, and director of CIMITEC, a research Center on resonant frequency of a patch antenna, ”IEEE Trans. Microw. Theory Metamaterials supported by TECNIO (Generalitat de Catalunya). He has Tech., vol. 34, no. 9, pp. 923–931, Sep. 1996. organized several international events related to metamaterials and related [38] P. Vélez, J. Muñoz-Enano, M. Gil, J. Mata-Contreras, and F. Martín, topics, including Workshops at the IEEE International Microwave “Differential Microfluidic Sensors Based on Dumbbell-Shaped Defect Symposium (years 2005 and 2007) and European Microwave Conference Ground Structures in Microstrip Technology: Analysis, Optimization, (2009, 2015 and 2017), and the Fifth International Congress on Advanced and Applications”, Sensors, vol. 2019, pp. 1-18, July 2019. Electromagnetic Materials in Microwaves and Optics (Metamaterials 2011), where he has acted as chair of the Local Organizing Committee. He has acted Jonathan Muñoz-Enano (GS’19) was born in Mollet as Guest Editor for five Special Issues on Metamaterials and Sensors in five del Vallès (Barcelona), Spain, in 1994. He received the International Journals. He has authored and co-authored over 550 technical Bachelor's Degree in Electronic Telecommunications conference, letter, journal papers and book chapters, he is co-author of the Engineering in 2016 and the Master's Degree in book on Metamaterials entitled Metamaterials with Negative Parameters: Telecommunications Engineering in 2018, both at the Theory, Design and Microwave Applications (John Wiley & Sons Inc.), Autonomous University of Barcelona (UAB). Actually, author of the book Artificial Transmission Lines for RF and Microwave he is working in the same university in the elaboration of Applications (John Wiley & Sons Inc.), and co-editor of the book Balanced his PhD, which is focused on the development of Microwave Filters (John Wiley & Sons Inc.). Ferran Martín has generated 19 microwave sensors based on metamaterials concepts for PhDs, has filed several patents on metamaterials and has headed several the dielectric characterization of materials and biosensors. Development Contracts. Prof. Martín is a member of the IEEE Microwave Theory and Techniques Paris Vélez (S’10–M’14) was born in Barcelona, Spain, Society (IEEE MTT-S). He is reviewer of the IEEE Transactions on in 1982. He received the degree in Telecommunications Microwave Theory and Techniques and IEEE Microwave and Wireless Engineering, specializing in electronics, the Electronics Components Letters, among many other journals, and he serves as member of Engineering degree, and the Ph.D. degree in Electrical the Editorial Board of IET Microwaves, Antennas and Propagation, Engineering from the Universitat Autònoma de International Journal of RF and Microwave Computer-Aided Engineering, and Barcelona, Barcelona, in 2008, 2010, and 2014, Sensors. He is also a member of the Technical Committees of the European respectively. His Ph.D. thesis concerned common mode Microwave Conference (EuMC) and International Congress on Advanced suppression differential microwave circuits based on Electromagnetic Materials in Microwaves and Optics (Metamaterials). Among metamaterial concepts and semi-lumped resonators. his distinctions, Ferran Martín has received the 2006 Duran Farell Prize for During the Ph.D., he was awarded with a pre-doctoral Technological Research, he holds the Parc de Recerca UAB – Santander teaching and research fellowship by the Spanish Government from 2011 to Technology Transfer Chair, and he has been the recipient of three ICREA 2014. From 2015-2017, he was involved in the subjects related to ACADEMIA Awards (calls 2008, 2013 and 2018). He is Fellow of the IEEE metamaterials sensors for fluidics detection and characterization at LAAS- and IET. CNRS through a TECNIOSpring fellowship cofounded by the Marie Curie program. His current research interests include the miniaturization of passive circuits RF/microwave and sensors-based metamaterials through Juan de la Cierva fellowship. Dr. Vélez is a Reviewer for the IEEE Transactions on Microwave Theory and Techniques and for other journals. Marta Gil Barba (S’05-M’09) was born in Valdepeñas, Ciudad Real, Spain, in 1981. She received the Physics degree from Universidad de Granada, Spain, in 2005, and the Ph.D. degree in electronic engineering from the Universitat Autònoma de Barcelona, Barcelona, Spain, in 2009. She studied one year with the Friedrich Schiller Universität Jena, Jena, Germany. During her PhD Thesis she was holder of a METAMORPHOSE NoE grant and National Research Fellowship from the FPU Program of the Education and Science Spanish Ministry. As a postdoctoral researcher, she was awarded with a Juan de la Cierva fellowship working in the Universidad de Castilla-La Mancha. She was postdoctoral researcher in the Institut für Mikrowellentechnik und Photonik in Technische Universität Darmstadt and in the Carlos III University of Madrid. She is currently assistant professor in the Universidad Politécnica de Madrid. She has worked in metamaterials, piezoelectric MEMS and microwave passive devices. Her current interests include metamaterials sensors for fluidic detection.