Received February 2, 2021, accepted February 7, 2021, date of publication February 10, 2021, date of current version February 19, 2021. Digital Object Identifier 10.1109/ACCESS.2021.3058575 INVITED PAPER Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide Terminated With an Open Complementary Split Ring Resonator (OCSRR) LIJUAN SU 1 , (Member, IEEE), JONATHAN MUÑOZ-ENANO 1 , (Graduate Student Member, IEEE), PARIS VÉLEZ 1 , (Member, IEEE), MARTA GIL-BARBA 2 , (Member, IEEE), PAU CASACUBERTA 1 , AND FERRAN MARTIN 1 , (Fellow, IEEE) 1 GEMMA/CIMITEC, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain 2 Departamento Ingeniería Audiovisual y Comunicaciones, Universidad Politécnica de Madrid, 28031 Madrid, Spain. Corresponding author: Lijuan Su (lijuan.su@uab.cat) This work was supported in part by the Ministerio de Ciencia e Innovación (MICINN)-Spain under Grant TEC2016-75650-R and Grant PID2019-103904RB-I00, in part by the Generalitat de Catalunya under Grant 2017SGR-1159, in part by the Institució Catalana de Recerca i Estudis Avançats (who awarded Ferran Martín), in part by the European Regional Development Fund (ERDF), in part by the Secreteraria d’Universitats i Recerca (Gen. Cat.), and in part by the European Social Fund for the FI grant. The work of Paris Vélez and Lijuan Su was supported by the Juan de la Cierva Program under Grant IJCI-2017-31339 and Grant IJC2019-040786-I. ABSTRACT This paper presents a one-port reflective-mode phase-variation microwave sensor consisting of a coplanar waveguide (CPW) transmission line terminated with a grounded open complementary split ring resonator (OCSRR). The sensor is useful for measuring the dielectric constant of the so-called material under test (MUT), which should be placed in contact with the OCSRR, the sensitive element. The output variable is the phase of the reflection coefficient. Design guidelines for the implementation of highly sensitive sensors are derived in the paper, and validated through simulation and experiment. As compared to other reflective- mode phase-variation sensors based on open-ended sensing lines, the designed and fabricated devices exhibit a very small sensitive region by virtue of the use of an electrically small resonant element, the OCSRR. The relevant figure of merit, defined as the ratio between the maximum sensitivity and the size of the sensing area (expressed in terms of the squared wavelength), is as high as FoM = 5643◦ /λ2 in one of the reported prototypes. Moreover, the paper analyzes the effects of losses. From this study, it is concluded that MUT losses do not significantly affect the output variable, provided losses are small. It is also demonstrated that the sensor is useful to estimate the loss tangent of the considered MUT samples. INDEX TERMS Coplanar waveguide (CPW), dielectric characterization, microwave sensor, open comple- mentary split ring resonator (OCSRR), phase-variation sensor, reflective-mode sensor. I. INTRODUCTION related to it, including material composition (e.g., solute One-port reflective-mode phase-variation sensors are very content in diluted solutions), or defect detection, among interesting devices for material characterization, including others. solid and liquids [1], [2]. Such sensors are especially use- The main advantage of phase-variation sensors over ful for determining the dielectric constant of the so-called microwave sensors based on frequency variation [3]–[11] material under test (MUT), as well as other variables and frequency splitting [12]–[18] concerns single frequency operation. Namely, phase-variation sensors can be designed The associate editor coordinating the review of this manuscript and in order to operate at a single frequency, thereby reduc- approving it for publication was Derek Abbott . ing the costs of the associated electronics, needed for the This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 27928 VOLUME 9, 2021 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide generation of the interrogation signal. By contrast, frequency- design guidelines for that purpose. Such design guidelines are variation and frequency-splitting sensors intrinsically require inferred from an exhaustive analysis of the sensor, based on wideband signals for sensing (in a real scenario, such sig- the circuit schematic. nals should be generated by means of expensive broadband Indeed, the reported OCSRR-terminated CPW sensor voltage-controlled oscillators –VCOs). Coupling-modulation is similar to previous reflective-mode phase-variation sen- sensors operating at a single frequency have also been sors where the sensing element is a low-impedance half- reported [19]–[29]. However, the phase is, in general, more wavelength open-ended line cascaded to a high-impedance robust against the effects of noise and electromagnetic inter- quarter-wavelength transmission line (or a cascade of ferences than the magnitude of the transmission coefficient high/low impedance quarter-wavelength transmission line (the typical output variable in coupling modulation sensors). sections) [1], [2]. Indeed, a grounded OCSRR behaves similar Moreover, the phase is less sensitive to the effects of sensor to an open-ended half-wavelength transmission line in the losses and the presence of connectors, which are typically vicinity of resonance [55], and therefore a similar behavior needed for sensing. is expected. However, by replacing the 180◦ line with an Additionally, one-port reflective-mode sensors are typi- OCSRR, significant size reduction in the sensing area is cally simpler than sensors operating in transmission, where achieved. This constitutes the main advantage of the proposed at least a pair of ports is required for sensor implementation sensor. Nevertheless, the equivalence between both sensors (two and four ports are needed in differential-mode reflection (the one based on the OCSRR, presented in this work for the and transmission sensors, respectively [30]–[41]). Reflective- first time, and the one based on a half-wavelength open-ended mode sensors are of special interest for liquid characterization sensing line), is exhaustively analyzed. based on submersing the sensitive part of the sensor in the The paper is organized as follows: the proposed sensor MUT liquid [42]. topology, working principle, as well as the equivalent circuit The reflective-mode phase-variation sensors reported model of the CPW terminated with a grounded OCSRR are in [1], [2] are implemented in planar technology, thereby reported in Section II. Based on this circuit model, a sensitiv- representing a good solution in terms of cost. Moreover, ity analysis of the proposed OCSRR-based sensors is carried fully planar structures can be implemented in flexible sub- out in Section III, where the link to the sensors based on strates (thus opening the path to the implementation of a half-wavelength open-ended sensing line is also included. conformal sensors [43], [44] and wearable sensors [45]), Sensor validation through simulation and experiment is the and are compatible with other technologies, e.g., microflu- subject of Section IV, which includes a comparison with idics [4], [18], [33], [36], [46]–[49], lab-on-a-chip [50], the equivalent sensors based on half-wavelength open-ended etc. Most planar reflective-mode phase-variation sensors are sensing lines. The effects of losses are discussed in Section V, based on open-ended transmission lines [1], [2], and are where a method to estimate the loss tangent of the MUT is devoted to the characterization of solid or liquid samples also included. Section VI is devoted to the comparison of the (excellent sensitivities are reported in [1]). An exception is the proposed sensors to other phase-variation microwave sensors phase-variation sensor presented in [51], which is applied to reported in the literature. Finally, the main conclusions are the measurement of small displacements between a movable highlighted in Section VII. slab and the static part of the sensor (the open-ended line). Phase-variation sensors based on electrically small single II. THE PROPOSED OCSRR-BASED REFLECTIVE-MODE resonant elements (the sensitive part) have also been reported, PHASE-VARIATION SENSOR, WORKING PRINCIPLE, AND but in such sensors the focus is the measurement of spatial CIRCUIT MODEL variables [52], [53] (other sensors based on chains of reso- In a recent paper [1], it was demonstrated that high- nant elements acting as electro-inductive-wave transmission impedance quarter-wavelength or low-impedance half- lines, which also exploit phase-variation, have been recently wavelength open-ended sensing lines are useful for the reported [40]). implementation of highly sensitive reflective-mode phase- In this paper, reflective-mode phase-variation microwave variation dielectric constant sensors. Moreover, it was shown sensors devoted to material characterization, where the sens- that the sensitivity, defined as the derivative of the phase ing element is an electrically small planar resonator, are of the reflection coefficient (the output variable) with the presented. Specifically, the considered resonant element is dielectric constant of the MUT, can be further enhanced an open complementary split ring resonator (OCSRR), first by cascading quarter-wavelength transmission line sections reported in [54]. The paper shows that by terminating a copla- with alternating high/low characteristic impedance to the nar waveguide (CPW) transmission line with a grounded sensing line. The specific topology/schematic of such sensors OCSRR, very high sensitivity in the phase of the reflection for half-wavelength sensing line is depicted in Fig. 1. It is coefficient (the output variable) with the dielectric constant important to mention that the sensing region in the sensor of of the MUT (the input variable) is achievable. To do so, Fig. 1 is restricted to the half-wavelength open-ended sensing the characteristic impedance and the electrical length of the line. That is, sensitivity enhancement by cascading high/low CPW transmission line, as well as the quality factor of the impedance 90◦ transmission line sections entails an overall OCSRR, must be adequately chosen. The paper provides increase of the sensor size, but such sensitivity improvement VOLUME 9, 2021 27929 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide FIGURE 2. Typical topology (a) and circuit model (b) of the one-port reflective-mode phase-variation sensor based on a step-impedance CPW configuration terminated with an OCSRR, the sensing element. The sensing region is indicated with a dashed rectangle. For the topology, FIGURE 1. Typical topology (a) and schematic (b) of the one-port a pair of high/low impedance 90◦ line sections are considered. The reflective-mode phase-variation sensor based on a step-impedance CPW relevant dimension variables of the OCSRR are indicated. The dimensions configuration and a 180◦ open-ended sensing line. The sensing region is of the 90◦ lines are designated by the same variables as in Fig. 1. For the indicated with a dashed rectangle. For the topology, a pair of high/low simulations referred to in the text, the dimensions of the OCSRR (in mm) impedance 90◦ line sections are considered. The electrical and are: ws = 10, ls = 10, c = 0.2, d = 3.3. geometrical variables are indicated, where the sub-index s refers to the sensing line, the numerical sub-indexes 1 and 2 denote the 90◦ line sections, and the numerical sub-index 0 corresponds to the access line. ring resonator (OCSRR) [54]. The main reason is that this resonator is electrically very small (by virtue of its topol- does not imply increasing the sensing region dimensions ogy, as discussed in [54], [58]). Moreover, the sensor to (unlike most phase-variation sensors [30], [32], [38], [40], be designed will be implemented in CPW technology, and [41], [56], [57]). Nevertheless, the size of the sensitive region, therefore vias are not required for OCSRR grounding (nev- dictated by the length of the open-ended sensing line, cannot ertheless, as it will be shown, vias are needed to suppress be considered to be small, especially in the case of the 180◦ the parasitic slot mode, since the OCSRR is not a sym- sensing line sensor. metric resonator). The typical topology and circuit model Based on the similar behavior between an open-ended of these OCSRR-terminated CPW transmission line sensors half-wavelength transmission line and a grounded paral- are depicted in Fig. 2 (note that the step-impedance discon- lel resonator, the objective of this work is to replace the tinuities are considered to be ideal, i.e., not modelled by low-impedance 180◦ open-ended sensing line of the sensors any equivalent circuit model). Other CPW sensors based on reported in [1], [2] with a semi-lumped (i.e., electrically terminated CPWs are reported in [59], [60], whereas [61] small) planar resonator that can be described (to a good reports a CSRR-loaded CPW transmission mode sensor, but approximation) by a parallel resonant tank. The expected devoted to the measurements of rotation and proximity. result is a reflective-mode phase-variation sensor with behav- The working principle of the sensor of Fig. 2 is very similar ior, in terms of performance, similar to the one of the sen- to the one of the purely distributed counterparts (Fig. 1). sors based on a purely distributed approach (Fig. 1), but In brief, the presence of a MUT on top of the OCSRR with substantially reduced sensing area. This is an impor- modifies the capacitance of such element, and consequently tant aspect, since, for certain applications, the size of the the phase of the reflection coefficient seen from the plane of MUT may be limited. For example, for liquid characteriza- the particle also varies. Then, by virtue of the multiplicative tion, small amounts of MUT are typically available. This effect of the step-impedance transmission line configuration applies to submersible sensors, a canonical application of (cascaded to the sensing element) on the variation of the reflective-mode sensors [42], and also to microfluidic-based phase of the reflection coefficient (seen from the input port) sensors [4], [18], [33], [36], [46]–[49] (in this latter case, with the capacitance of the OCSRR, the sensitivity can be the sensitive region must be covered by the fluidic channel, unprecedentedly enhanced [1]. containing the liquid under test). However, small sensitive Concerning the circuit model, it has been demonstrated that regions are also convenient for the characterization of solids, a microstrip line loaded with a shunt-connected OCSRR can in order to reduce the size of the MUTs (this may have direct be adequately, and accurately, described by means of a pure impact on cost reduction). parallel resonant tank [62]. However, the precise description Among the semi-lumped planar resonators, probably the of the OCSRR-terminated CPW requires the presence of an most interesting candidate for the implementation of the additional series inductance, Ls , as depicted in Fig. 2. The intended sensors is the so-called open complementary split inductance Ls is, indeed, a parasitic of the model, but it does 27930 VOLUME 9, 2021 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide Expressions (1) and (2) are two conditions which are nec- essary to determine the reactive parameters of the circuit model of the OCSRR-terminated CPW transmission line. Nevertheless, an additional condition is required in order to univocally infer the three unknowns, L, C and Ls . Such condition may be, for instance, the phase at a certain arbitrary frequency in the region of interest. Alternatively, the three elements can be inferred by means of expressions (1) and (2), providing a unique degree of freedom, and curve fitting. This has been the considered procedure. Application of this parameter extraction method to the phase response of Fig. 3, has provided the reactive parameters indicated in the cap- tion of such figure. The excellent agreement between the FIGURE 3. Phase of the reflection coefficient of the OCSRR-terminated CPW structure of Fig. 2, excluding the cascaded step-impedance CPW phases inferred from full-wave electromagnetic simulation transmission line sections and access lines. The different curves and circuit simulation with the extracted parameters validates correspond to the uncovered OCSRR (with capacitance C = 4.90 pF), and the proposed model, as well as the parameter extraction to the OCSRR covered with various semi-infinite MUTs with the indicated dielectric constant and capacitance, C 0 = C + 1C . The inductances in all method. the cases are L = 2.48 nH and Ls = 2.63 nH. The capacitances for the For further validation of the model, the reflection coef- different considered MUTs obtained from the resonance frequency of the OCSRR of the EM. simulation, where the phase is null, are C 0 = 5.04 pF ficient of the OCSRR-terminated CPW of Fig. 2 has been (for εMUT = 1.3), C 0 = 5.19 pF (for εMUT = 1.6), and C 0 = 5.35 pF (for simulated by considering that the OCSRR is covered by εMUT = 1.9). semi-infinite (in the vertical direction) MUTs of different dielectric constants. The effect is an increase in the capaci- not jeopardize the performance of the sensor, as it will be tance of the OCSRR, determined by the dielectric constant of demonstrated. Thus, the intrinsic reactive elements of the the MUT, εMUT , according to [10] OCSRR are the capacitance C and the inductance L, and the element subjected to changes caused by the MUT is the εr + εMUT C 0 = C + 1C = C (3) capacitance C. εr + 1 To validate the model of the OCSRR-terminated CPW, The validity of expression (3) is also restricted to substrate we have extracted the reactive parameters from the simulated thicknesses significantly larger than the width of the slots of phase of the reflection coefficient corresponding to the struc- the OCSRR (the case in the present study). The simulated ture shown in Fig. 2, but excluding the high/low impedance phase responses for the different MUTs are also included 90◦ CPW line sections and access lines (the dimensions of the in Fig. 3, where the dielectric constants and the capacitances OCSRR are indicated in the caption). Moreover, the OCSRR inferred from (3) are indicated. Note that the capacitances of is considered to be surrounded by air. The considered sub- the OCSRR covered with the different considered MUTs, C 0 , strate is the Rogers RO3010 with dielectric constant εr = can also be obtained from the resonance frequency (where the 10.2 and thickness h = 1.27 mm (losses are excluded in the phase is null), provided neither L nor Ls are perturbed by the simulation). The simulated phase of the reflection coefficient, MUT. The capacitance values inferred from this procedure, inferred from Keysight Momentum, is depicted in Fig. 3. It can included in the caption of Fig. 3, are in good agreement be observed that the phase of the reflection coefficient reaches with those inferred from (3). From the capacitance values the value −π at a finite frequency, designated as fz . At such inferred by means of (3), the resulting phases obtained from frequency, the impedance seen from the input port of the circuit simulation are also depicted in Fig. 3. The good agree- OCSRR-terminated CPW nulls. Consequently, the structure ment between the circuit and electromagnetic simulations cannot be described merely by means of a grounded parallel for the different values of εMUT validates the model of the LC resonant tank. A series inductance, Ls , is required to OCSRR-terminated CPW, the dependence of the OCSRR compensate the negative reactance of the OCSRR at fz (note capacitance on εMUT , given by (3), as well as the parameter that at the OCSRR resonance, f0 , the impedance seen from extraction procedure. the input port is an open-circuit, and above f0 the reactance of the OCSRR is negative). Obviously, the reflection coefficient III. SENSITIVITY ANALYSIS at f0 exhibits a 0◦ phase, corresponding to an open-circuit. The main objective in the present paper is to implement According to the circuit model, these relevant (and easily highly sensitive dielectric constant sensors based on the identifiable) frequencies are given by: OCSRR-CPW configuration shown in Fig. 2. Therefore, 1 a sensitivity analysis based on the validated circuit model f0 = √ (1) is pertinent, in order to infer design guidelines that link 2π LC s the required (maximum) sensitivity to the parameters of 1 1 1 the model. Nevertheless, let us first consider only the fz = + (2) 2π LC Ls C OCSRR-terminated CPW. The generalization to the complete VOLUME 9, 2021 27931 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide sensor structure, also including the step-impedance CPW (εMUT = 1), i.e., at 1C = 0. Evaluation of (9) when 1C = 0 line sections, is very simple, as will be shown below (such gives step-impedance configuration has a multiplicative effect on dφρ the sensitivity, dictated by the impedance contrast of the d1C 1C=0 different transmission line sections). ≡ S1C |1C=0 A. OCSRR-TERMINATED CPW −2Z0 Lω3 /Cω02 =  2   Let us call the impedance seen from the input port of the ω2 ω2 Z0 + LS ω 2 2 + 2LLS ω 1 − + L 2 ω2  2 1− 2 OCSRR-terminated CPW transmission line Zin . The reflec- ω0 2 ω02 tion coefficient seen from that port, with reference impedance (10) Z0 , is simply [55] Note that sensitivity optimization in the vicinity of εMUT = 1 Zin − Z0 jχin − Z0 does not represent a loss of generality. Namely, if the inter- ρ= = (4) Zin + Z0 jχin + Z0 est is to maximize the sensitivity for a different (arbitrary) value of εMUT , it suffices to obtain the capacitance of the χin being the input reactance. Thus, the phase of the reflection OCSRR when it is covered with an MUT with such dielectric coefficient, the output variable, is given by constant value, and the corresponding resonance frequency. χin   In particular, it is possible to optimize the sensitivity in the φρ = 2arctan − +π (5) vicinity of the dielectric constants of liquids, or other high Z0 dielectric constant materials (examples of highly sensitive The input variable, εMUT , modifies the capacitance of the sensors devoted to liquid characterization, based on different OCSRR, see expression (3), which, in turn, perturbs the principles, have been reported [63], [64]). reactance of the structure, χin . Thus, the sensitivity can be Given a set of reactive parameters of the OCSRR- expressed as terminated CPW (L, C and Ls ), the sensitivity in the limit dφρ dφρ dC 0 dφρ d1C of small perturbations (1C = 0) depends on the operating S= = 0 · = · (6) frequency. In order to find the frequency that maximizes dεMUT dC dεMUT d1C dεMUT the sensitivity, it is necessary to derive S1C |1C=0 with fre- where 1C = C 0 − C is the variation of the capacitance of the quency, and force the result to be zero. After a straightforward OCSRR when it is covered by a certain MUT (i.e., 1C = 0 (but cumbersome) calculation, the following equation results: for εMUT = εMUT,air = 1). ! 2ω Z02 ω4 6 For the OCSRR-terminated CPW described by the circuit 2 −3Ls 4 + 2LLs + 2Ls − 2 model of Fig. 2, excluding the different CPW line sections, ω0 ω0 ω02 " # the reactance and the phase of the reflection coefficient can z 2 be expressed as + (L + Ls )2 − 2 02 ω2 + 3Z02 = 0 (11)   ω0 " #−1  ω2 1C Finding the value of  in the previous equation is not easy   χin = ω Ls + L 1 − 2 1 + (7) (nevertheless, it is apparent that  = ω0 is not a solution).  ω0 C  Since the inductance Ls is a parasitic of the model, let us and neglect it in (11). The resulting equation is found to be    biquadratic in the variable , and it can be expressed as  ω  " #−1  ω2 1C  ! φρ = 2 arctan − L +L 1 − 2 1 + ω4 ω02 ω2  Z0  s ω0 C + 2− 2 −3=0 (12) ω04 ω0 ω02  (8) where the following frequency variable has been defined in respectively, where  = 2πf is the angular frequency, order to simplify the notation and 0 = 2πf0 is the resonance (angular) frequency 2 Z02 of the uncovered OCSRR, see expression (1). From (8), ω0 0 = (13) L2 the first term of the sensitivity, dφρ /d1C, can be calculated, The solution of (12) is i.e., v  4 ω2 ω02 ω04 ω02 u dφρ −2 Lω3 1 1 u 1 1 = · · (9) = −1 + + 2t1 + −  (14) ω02 ω002 ω0 0 ω02 1 + in2 CZ0 ω0 d1C χ2 2   2  2 4 4 ω2 1C Z0 1− 1+ ω02 C Inspection of (14) reveals that if ω02 /ω020  1, the solution Let us now assume that the interest is the optimization of is ω ≈ ω0 . In other words, for ω02 /ω020  1 and Ls the sensitivity in the vicinity of the dielectric constant of air negligible, the sensitivity in the limit of small perturbations 27932 VOLUME 9, 2021 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide is optimized by setting the operating frequency of the sensor to roughly 0 , the resonance frequency of the bare OCSRR. From (10), the sensitivity of φρ with 1C, at 1C = 0 and  = ω0 , is found to be: dφρ ≡ S1C = −2Z0 ω0 (15) d1C 1C=0,ω0 1C=0,ω0 It can be seen that (15) does not depend on Ls , namely, we can neglect the effects of the parasitic inductance, Ls , provided the sensors is tuned to 0 . The whole sensitivity at this frequency, in the limit of small perturbations, can be calculated according to (6), where the first term is given by (15), and the second term can be easily obtained from (3), FIGURE 4. Dependence of the normalized optimum frequency, ω/ω0 , with i.e., Ls , as derived from the numerical solution of (11). d1C C = (16) for low values of Ls , as compared to L, the optimum fre- dεMUT εr + 1 quency approaches 0 , as expected. As Ls increases, the opti- Therefore, mum frequency progressively diverges from 0 . For the dφρ −2Z0 ω0 C specific value of Ls corresponding to the OCSRR-terminated S|1C=0,ω0 ≡ = (17) dεMUT 1C=0,ω0 εr + 1 structure under study (Ls = 2.63 nH), the optimum fre- quency is close to 0 (i.e., 1.123 0 , according to Fig. 4). From (17), it follows that, in order to optimize the sensi- From this study, it can be concluded that it is convenient tivity, C should be high and, consequently, L must be low, to tune the operating frequency of the sensor to 0 . Such so that the product LC is√coherent with the frequency of frequency is very close to the optimum one, and the sensi- operation ω0 = 2πf0 = 1/ LC. According to the definition tivity for small perturbations can be easily predicted, i.e., it of 0 and 00 , the squared ratio of these angular frequencies is given by (17). Moreover, at ω0 , the parasitic induc- is tance Ls , a parameter difficult to control, does not affect the ω02 L 4 ZS2 sensitivity. = = (18) ω02 CZ02 π 2 Z02 B. STEP-IMPEDANCE CPW CASCADED TO THE where the equivalent impedance of the OCSRR resonator, OCSRR-TERMINATED CPW defined as (see Appendix A) Let us now analyze the effects of a cascaded step-impedance π L r CPW transmission line to the OCSRR-terminated structure. Zs = (19) 2 C As it was demonstrated in [1], in reference to dielectric has been used. Note that the requirement of a high value constant reflective-mode phase-variation sensors based on of C and a low value of L for sensitivity optimization (or, open-ended low-impedance 180◦ and high-impedance 90◦ equivalently, a low equivalent impedance, Zs ), is consistent sensing lines, the phase of the high/low transmission line with ω02 /ω020 < 1. Therefore, tuning the intrinsic resonance sections must be 90◦ (or an odd multiple) for sensitivity frequency of the OCSRR to 0 with a high value of its optimization. Due to the similar behavior between an open- capacitance C (and a low value of L) is a good strategy ended 180◦ line and a parallel LC resonator (see Appendix A, for sensitivity optimization. Moreover, at such frequency, where it is demonstrated that both structures are equivalent in the effects of Ls on the sensitivity for small perturbations are the vicinity of resonance), it follows that such phase condition null, as demonstrated before. (90◦ ) should also be preserved for the high/low impedance Nevertheless, Ls is a parameter difficult to control in prac- sections of the step-impedance CPW structure in the consid- tice, and it is not necessarily very small as compared to L (see, ered sensor. e.g., the reactive parameters of the sensor structure of Fig. 2, The impedance seen from the input port of the struc- indicated in the caption of Fig. 3). Under these conditions ture, consisting of N high/low impedance 90◦ line sections, (i.e., if Ls cannot be neglected), it is not obvious that the opti- plus the OCSRR-terminated CPW sensing structure, can be mum frequency for sensitivity enhancement is roughly 0 . expressed as To gain insight on this aspect, and due to the complexity of N n (−1)N 2·(−1)i+N o expression (11), where the dependence on Ls is not omitted, Y Zin,N = Zin · Zi (20) we have numerically solved such expression for different i=1 values of Ls and the values of L and C given in the caption of Fig. 3, with Z0 = 50  (the usual reference impedance where Zi is the characteristic impedance of line section i (with of the ports). The results, depicted in Fig. 4, indicate that i = 1, 2, . . . N ), and 5 denotes the product operator. Thus, VOLUME 9, 2021 27933 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide the reflection coefficient can be expressed as where ls and Zs are the length and characteristic impedance, respectively, of the 180◦ open-ended sensing line, ω0 is the (−1)N QN 2·(−1)i+N n o j (−1)N · χin · i=1 Zi − Z0 operating frequency (providing the required 180◦ electrical ρ= (21) length to the uncovered sensing line), and c is the speed of (−1)N QN 2·(−1)i+N n o j (−1)N · χin · i=1 Zi + Z0 light in vacuum. Taking into account that the phase of the line and the phase of the reflection coefficient is at 0 can be expressed as ω0 ls φs = π = ,   (25) vp  χin  φρ = 2arctan − (22a)     Z0   where vp is the phase velocity, given by QN 2·(−1)i+N i=1 Zi c vp = √ , (26) εeff For N even, and   and the effective dielectric constant of a CPW line is εr + εMUT  χin  εeff = , (27) φρ = 2arctan − Q      (22b) 2 N 2·(−1)i+N  i=1 Zi  expression (24) can be written as Z0 dφρ Z0 π =− (28) for N odd. By comparing expressions (22) and (5), it follows dεMUT Zs εr + 1 that the phases are identical, except the denominator of the Using the equivalence between a 180◦ open-ended line and a argument of the arctan. However, the single difference is a parallel resonant tank with inductance L and capacitance C constant factor that depends on the impedances, Zi , of the (see Appendix A), the impedance of the sensing line in (28), different line sections. Thus, the sensitivity for the OCSRR- Zs , can be replaced with the elements of the equivalent LC res- based structure with cascaded high/low impedance 90◦ line onator according to expression (A.8) in the Appendix A. With sections is given by expression (17) by replacing Z0 with the this mapping, the sensitivity given by (28) is identical to the denominators of expressions (22) for each case, N even or one given by (17). Naturally, if the step-impedance structure odd, i.e., is present, the sensitivity of both the OCSRR-based sensor −2ω0 C Z0 and the sensor implemented by means of a 180◦ sensing line, S|1C=0,ω0 = · εr + 1 Q N o (N even) (23a) are also identical and given by expressions (23). 2·(−1)i+N n Zi The identical behavior of both sensor types, predicted by i=1 the sensitivity analysis, will be validated in the next section. N n 2·(−1)i+N o Q Zi Nevertheless, it should be mentioned, and highlighted, that −2ω0 C i=1 such identical sensitivities are obtained for sensor operation S|1C=0,ω0 = · (N odd) (23b) εr + 1 Z0 at 0 (the intrinsic resonance of the bare OCSRR, which should be identical to the angular frequency providing a From (23), it follows that the step-impedance CPW structure 180◦ sensing line), and in the limit of small perturbations. introduces a multiplicative effect on the overall sensitivity, Moreover, the mapping indicated in (A.8) must be satisfied. magnified by the impedance contrast of the different 90◦ Despite the similar achievable performance, the key advan- transmission line sections. That is, for sensitivity optimiza- tage of the novel OCSRR-based sensors, as compared to the tion, it is convenient to set the high/low impedances of the dif- fully distributed counterparts, concerns the size of the sensing ferent line sections to as high/low values as possible, as com- region. It is substantially smaller in the OCSRR-based sensor, pared to Z0 . Moreover, the 90◦ line sections must exhibit high by virtue of the small electrical size of the OCSRR. This characteristic impedance for i odd and low impedance of i size reduction of the sensing region, and the derivation of even. design guidelines, given by expressions (17) and (23) for the OCSRR-terminated CPW and for the same structure includ- C. COMPARISON TO THE EQUIVALENT SENSOR BASED ing the step-impedance configuration, respectively, constitute ON A HALF-WAVELENGTH OPEN-ENDED SENSING LINE the main relevant contributions of the present paper (addi- As mentioned before, a similar behavior between the pro- tionally, a method to estimate the loss tangent of the MUT posed OCSRR-based sensor and the fully distributed coun- in these reflective-mode phase-variation sensors is reported terpart (i.e., implemented by means of a 180◦ open-ended for the first time, as demonstrated in Section V). sensing line) is expected. Indeed, according to [2], the sensitivity of such fully distributed sensor (excluding the IV. SENSOR VALIDATION step-impedance structure) for εMUT = 1 is given by For sensor validation, three different OCSRR-terminated dφρ dφρ dφs z0 ω0 ls 1 CPW based sensors have been designed and fabricated. In all = = −2 · √ √ (24) dεMUT dφs dεMUT Zs 2 2c εr + 1 cases, the considered substrate is the Rogers RO3010 with 27934 VOLUME 9, 2021 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide dielectric constant εr = 10.2, thickness h = 1.27 mm, and loss tangent tanδ = 0.0022. There is not a specific reason for choosing such substrate, with relatively high dielectric constant. Indeed, reducing the dielectric constant of the sub- strate helps in increasing the sensitivity, but the actual impact on the sensitivity in the proposed sensors is achieved by the step-impedance discontinuities. The difference between the three sensors concerns the step impedance configuration, being the OCSRR-terminated CPW sensing region identical in all the cases (dimensions indicated in Fig. 2). Thus, in sen- sor A, the structure merely consists of the sensing part (i.e., the OCSRR-terminated CPW), whereas in sensors designated as B and C, the devices include a step-impedance config- uration for sensitivity enhancement. For sensor B, a sin- gle high-impedance 90◦ line section (N = 1) cascaded to the OCSRR-terminated CPW is considered, whereas sensor C is implemented by including two high/low impedance 90◦ line sections (N = 2). In sensor B, the characteristic impedance of the high-impedance 90◦ line section has been set to Z1 = 70 . In sensor C, an identical impedance for the high-impedance 90◦ line adjacent to the sensing region has been considered, whereas the impedance of the cascaded low-impedance 90◦ line section has been set to Z2 = 35.35 . Additionally, we have designed the fully distributed coun- terparts of sensors A, B and C, designated as A0 , B0 and C0 , respectively, where the OCSRR-terminated CPW sensing FIGURE 5. Photographs of sensors A (a), B (b), C (c), A0 (d), B0 (e) and C0 structure has been replaced with a low-impedance 180◦ open- (f). The dimensions of the OCSRR-terminated CPW are given in Fig. 2. The ended sensing line. The impedance of such line is calculated dimensions of the high/low step-impedance CPW line sections (in mm) according to expression (A.8) of the Appendix A, which gives are: w1 = 0.72, G1 = 1.04, l1 = 22.40 (for sensors B0 and C0 only), w2 = 2.25, G2 = 0.28, l2 = 22.53. The dimensions of the low-impedance Zs = 35.35  (the extracted values of L and C are given in 180◦ open-ended sensing line are (in mm): ws = 2.25, Gs = 0.28, the caption of Fig. 3). ls = 44.78. In all the cases, the dimensions of the access line (50 ohm) are (in mm): w0 = 1.39, G0 = 0.71, l0 = 10. The photographs of all these sensors, fabricated by means of the LPKF H100 drilling machine, are depicted in Fig. 5, where the dimensions are indicated. It should be mentioned in the back-substrate side, in order to avoid the appearance of that for sensors B and C, the length of the high-impedance the parasitic slot mode (this is necessary since the OCSRRs 90◦ line adjacent to the OCSRR has been adjusted (reduced do not exhibit axial symmetry). as compared to the nominal value) in order to compensate Prior to sensor validation through experiment, we have for the phase shift generated by the parasitic capacitance carried out full-wave simulations by means of the CST that appears in the contact plane between such line and the Microwave Studio commercial software. Specifically, OCSRR. For that purpose, we have forced the simulated we have considered the sensing regions (OCSRR-terminated phase of the reflection coefficient of sensor B (without access CPW in sensors A, B and C, and 180◦ open-ended line in lines) to be 180◦ , corresponding to a short circuit, since this sensors A0 , B0 , and C0 ) covered by a semi-infinite MUT with is the impedance that should be seen from the input port varying dielectric constant. The simulated phases for all the when a 90◦ line is cascaded to the OCSRR operating at sensors, as a function of the dielectric constant of the MUT, its intrinsic resonance frequency. Obviously, for sensor C, εMUT , are depicted in Fig. 6. It should be mentioned that inferred from sensor B by cascading a low-impedance 90◦ the frequency of operation has been set to f0 = ω0 /2π = line, the input impedance should correspond to an open- 1.442 GHz, the intrinsic resonance frequency of the bare circuit. Nevertheless, this does not need any modification in OCSRR (and the frequency providing an electrical length the length of this added line, since the parasitic capacitance of 180◦ to the bare sensing line). By numerically obtaining of the step-impedance discontinuity has been found to be the derivative of such phases with εMUT , the sensitivities are negligible. Thus, the length l1 that appears in the caption of inferred (the results are also included in Fig. 6). Fig. 5 (in reference to the line section designated with the It can be appreciated that the sensitivities in the limit index i = 1) is only valid for sensors B0 and C0 . For sensors of small perturbations (i.e., for 1C = 0 pF, or B and C, such reduced length is l1 = 16.15 mm. Note also εMUT = 1) are nearly identical for the OCSRR-based that in sensors A, B and C, the ground plane regions of the and the open-ended 180◦ line-based sensors. The values CPW are short-circuited by means of vias and strips etched are indicated in Fig. 6. Moreover, these values coincide VOLUME 9, 2021 27935 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide with the theoretical predictions, given by expressions (17) or (23), to a good approximation. Thus, with these simu- lation results, the sensitivity analysis and the equivalence between the OCSRR-based sensors and the fully distributed counterparts is demonstrated. The multiplicative effect of the step-impedance configuration, first reported in [1], provides a maximum sensitivity for sensors C and C0 of −83.35◦ and −80.14◦ , respectively (simulated values). These sensitivities are very high, especially for sensor C, taking into account the small size of the sensing region. A figure of merit (FoM) in phase-variation sensors is the ratio between the sensitivity and the size of the sensing region expressed in terms of the squared guided wavelength, λ2 . The values for sensors C and C0 (for the maximum sensitivity) are FoM = 5643◦ /λ2 and FoM = 801◦ /λ2 , respectively. The value for sensor C is very competitive thanks to the use of an OCSRR as sensing element (and obviously, by virtue of the multiplicative effect of the step-impedance configuration). Finally, we have experimentally validated the sensors of Fig. 5 by covering the sensing regions with several commer- cially available (uncladded) microwave substrates, and with a MUT sample (PLA) fabricated with a 3D printer (the Ulti- maker 3 Extended). In all the cases, the thickness of the MUT samples is roughly 3 mm, so that such samples can be con- sidered to be semi-infinite in the vertical direction (stacking of two 1.5-mm thick samples, available in our laboratory, has been carried out for that purpose). The measured phases at the operating frequency for such MUTs, inferred by means of the Keysight 85072A vector network analyzer, are also included in Fig. 6. Actually, we have performed the measurements three times, in order to ensure that the measurements are repetitive (the error bars are included in Fig. 6). Nevertheless, the measurements have not been carried out by varying the environmental conditions (temperature and humidity) in a controllable way. The agreement with the simulated data points is good in all the cases, and, consequently, the reported sensors are experimentally validated. FIGURE 6. Differential phase (1φρ = φρ − φρ,εMUT=1 ), measured at f0 , and sensitivity for the designed and fabricated sensors. (a) Sensors A We would like to mention that the analytical study carried and A0 ; (b) sensors B and B0 ; (c) sensors C and C0 . out in the previous section and sensor validation by means of electromagnetic simulation and phase measurements con- sider that the MUT is thick enough to ensure that the elec- thickness of the MUT [i.e., an equivalent expression to (3) tromagnetic field lines do not reach the MUT/air interface. for samples with limited thickness] is also possible, but this With such semi-infinite MUT approximation, the maximum aspect is out of the scope of this paper. sensitivity, i.e., the one corresponding to εMUT = 1, can be predicted by means of simple expressions (17 or 23, V. EFFECTS OF LOSSES depending on the sensor configuration). The simplicity of In this paper, the main aim is the implementation of highly such expressions is consequence of the compact dependence sensitive sensors devoted to the determination of the dielectric of the capacitance of the OCSRR on the dielectric constant constant of the MUT, or other magnitudes related to it, e.g., of the MUT, given by (3) and valid for semi-infinite MUTs, material composition, defect detection, etc. Nevertheless, as mentioned before. Nevertheless, it does not mean that the the effects of losses on the sensitivity should be analyzed. For dielectric constant of thin MUT samples cannot be inferred that purpose, we have considered as representative sensor for by means of the proposed sensors. Similar curves to those this study sensor A, based solely on the OCSRR-terminated depicted in Fig. 6 can be generated for thinner MUT sam- CPW. The circuit model by including losses is depicted ples, and from the measured phase, the dielectric constant in Fig. 7. Substrate and conductor losses are modelled by the of the MUT sample can be obtained. Obtaining the OCSRR conductance G, whereas GMUT accounts for MUT losses. The capacitance as a function of both the dielectric constant and input impedance of the structure, evaluated at the operating 27936 VOLUME 9, 2021 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide frequency, 0 , is ( ) GT 1C Zin = 2 + jω0 Ls − 2 (29) GT + ω02 1C 2 GT + ω02 1C 2 where GT = G + GMUT . Using (4), with Zin given by (29), the reflection coefficient is obtained, and from it, the phase is found to be     FIGURE 7. Circuit model of the lossy OCSRR-terminated CPW. 1C  ω0 Ls − G2 +ω2 1C 2      T 0 φρ = arctan −     Z0 1 −  GT    Z0 G2T +ω02 1C 2      1C  ω0 L S −  G2T +ω02 1C 2     + tarctan −   (30)   Z0 1 +  GT   Z0 GT +ω0 1C 2 2 2   Under the assumption that losses are small, we can assume that GT 1 (31) Z0 (GT + ω02 1C 2 ) 2 and from the first-order Taylor expansion arctan[A/(1 + x)] = arctan[A] − Ax/(1 + A2 ), considering small x values, expression (30) can be approximated by ( !) ω0 1C φρ = 2 arctan − Ls − 2 (32) Z0 GT + ω02 1C 2 If we now assume that 1G2T  ω02 C 2 , it follows that (30) is identical to (8), the lossless case, evaluated at  = ω0 . Note that this last condition is necessary in order to satisfy (31) if GT is small. This is the usual situation with low-loss samples. However, for MUTs with extremely small dielectric constants (i.e., εMUT → 1, or 1C → 0), the condition G2T  ω02 1C 2 is not necessarily true despite the fact that GT is small. Let us consider now that G2T  ω02 1C 2 , with GT small. In this case, the intrinsic impedance (i.e., excluding the effects of Ls ) of the lossy OCSRR is dominated by the resistive part FIGURE 8. Phase (a) and magnitude (b) of the reflection coefficient for (see 29), which is necessarily high by virtue of the small sensor A as a function of the dielectric constant and loss tangent of the MUT, inferred from electromagnetic simulation. value of GT and because G2T  ω02 1C 2 (indeed, the real part of the impedance can be approximated by 1/GT ). Under these conditions, the impedance seen from the input port is the dielectric constant of the MUT is the one of Fig. 6, essentially an open-circuit, and the phase of the reflection whereas for the loss tangent, it is limited to the interval coefficient is null. Such phase is also the resulting one for [0.001-0.01] (note that the variation in tanδMUT modifies the lossless case and 1C → 0, since the OCSRR opens at GT through GMUT , i.e., G is kept unaltered). The results the operating frequency. are depicted in Fig. 8(a), which shows that the effects of From the previous analysis, it can be concluded that the losses on the phase are not relevant, as predicted by the effects of losses on the phase of the reflection coefficient and, theory. Consequently, from the measurement of the phase of consequently on the sensitivity, are not significant, provided the reflection coefficient, the dielectric constant of the MUT losses are small (this is the case in the considered sensors can be directly inferred, provided the MUT is a low-loss and the MUT samples used for experimental validation). material. Although the effects of losses on the phase of the Nevertheless, we have inferred the phase of the reflection reflection coefficient have been analyzed on the basis of coefficient of the structure as a function of both the dielec- sensor A, the same conclusions apply to sensors B and C. tric constant, εMUT , and the loss tangent, tanδMUT , of the Thus, the curves for the different considered sensors shown MUT, by full-wave electromagnetic simulation using CST in Fig. 6 are useful for determining the dielectric constant of Microwave Studio. The considered input dynamic range for the MUT. VOLUME 9, 2021 27937 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide Another important aspect to consider is to what extent surrounded by air is |ρ|air = 0.923, and the corresponding the proposed sensors are useful for determining the loss conductance is found to be G = 8.01 × 10−4 S. tangent of the MUT. In general, resonant methods, based The next step is to load the OCSRR with the MUT and on the measurement of the magnitude of the resonant notch measure the modulus of the reflection coefficient at 0 , or peak, are convenient for that purpose. For the proposed |ρ|. Using (33), GT can be numerically calculated, provided sensors, a semi-lumped resonator (the OCSRR) subjected to the reactive parameters of the OCSRR, as well as 1C, are the effects of losses in the MUT (and also in the sensing known (note that isolating GT in expression 33 represents structure) is the considered sensing element. Losses should an excessive analytical burden). Therefore, the conductance be manifested by a reduction in the magnitude of the reflec- associated to the MUT sample can be simply obtained as tion coefficient at resonance. We have obtained (through GMUT = GT − G, since G is calculated from the previous full-wave simulation) the magnitude of the reflection coef- step. ficient at the resonance frequency of the bare OCSRR, 0 , In the previous approach, the measured modulus of the i.e., |ρ| = |S11 |, as a function of εMUT and tanδMUT . The reflection coefficient at 0 is the variable considered for results, depicted in Fig. 8(b), show that |S11 | does not depend determining G and GT . At such frequency, the intrinsic solely on tanδMUT , but also on εMUT . Since εMUT can be impedance of the OCSRR (excluding the effect of Ls ) is determined from Fig. 8(a), or from calibrated curves inferred not purely resistive except for εMUT = 1 (or 1C = 0). from the experimental data in Fig. 6, the loss tangent of the Thus, the modulus of the reflection coefficient experiences MUT, tanδMUT , can potentially be inferred from the measured a significant variation with frequency at that frequency, and value of |S11 | and the value of εMUT . However, this approach the accuracy of the method is very limited, especially tak- needs experimental calibration curves for the dependence of ing into account that the samples under consideration may |ρ|=|S11 | on εMUT and tanδMUT , and this is not easy due to exhibit loss tangents comparable to the one of the considered the lack of available materials (MUTs) with a wide range of sensor substrates. Thus, we have proceeded by recording loss tangents. the measured modulus of the reflection coefficient at the To solve the previous issue, an analytical approach, based resonance frequency of the OCSRR covered by each MUT on the lossy circuit model and the link between the loss tan- sample. This frequency can be easily identified from the mea- gent of the MUT and the model parameters, is proposed next. sured data, since at resonance, the magnitude of the reflec- The key aspect is to determine GMUT from the experimental tion coefficient is a minimum. Using an expression identical data relative to the modulus of the reflection coefficient. The to (35), the total conductance for each sample, GT , can be modulus of the reflection coefficient at 0 is given by obtained. For that purpose, |ρair | and 0 must be replaced v with |ρMUT | and 0,MUT , respectively, in (35), where 0,MUT u  2  2 is the intrinsic resonance frequency of the OCSRR loaded u ω Ls − 2 1C2 2 + Z 2 1 − GT u 2 u 0 GT +ω0 1C 0 Z0 (G2T +ω02 1C 2 ) with the MUT, and |ρMUT | is the measured modulus of the |ρ| =u u  2  2 reflection coefficient at that frequency. From the different 1C ω0 Ls − 2 2 2 + Z0 1+ GT t 2 2 values of GT , corresponding to the MUT samples used in GT +ω0 1C Z0 (GT +ω0 1C ) 2 2 2 the previous experimental validation, the conductance of (33) each sample, GMUT , has been inferred (it is shown in the third column of Table 1). As mentioned before, the exper- By considering absence of MUT (i.e., OCSRR surrounded by imental reflection coefficients are those corresponding to air), 1C = 0 and GMUT = 0, and the reflection coefficient Sensor A. at 0 simplifies to The loss tangent and the conductance of the MUT are related by [10] v u ω2 L 2 + Z 2 1 − 1 2 u   u 0 S 0 Z0 G |ρ|air = u (34) GMUT t  2 tan δMUT = (36) ω02 LS2 + Z02 1 + Z01G ω0 C MUT Using (34) and the measured value of |ρ|air , the circuit where CMUT is the portion of the total capacitance of the parameter modelling the effects of sensor losses, G, can be OCSRR (C 0 = C + 1C) corresponding to the MUT (see isolated. The result is as follows Fig. 9). Note that, according to this figure, the capacitance of the uncovered OCSRR can be expressed as C = Csubs + Cair ,  q whereas the capacitance of the loaded OCSRR is C 0 = C + 2 Z0 1 + |ρ|2air ± 4Z02 |ρ|2air − ω02 LS2 1 − |ρ|2air G= 1C = Csubs + CMUT , where Csubs and Cair are the capac- ω02 LS2 + Z02 1 − |ρ|2air   itances of the substrate region and air (uncovered OCSRR), (35) respectively, see Fig. 9. Thus, the capacitance of the MUT can be expressed as where the negative sign must be taken, as justified in Appendix B. The measured magnitude of the reflection coef- εMUT CMUT = C 0 − Csubs = C (37) ficient at resonance for the Sensor A when the OCSRR is 1 + εMUT 27938 VOLUME 9, 2021 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide TABLE 1. Loss tangent and relevant parameters for the different TABLE 2. Comparison of various phase variation-sensors. considered MUT samples. it is expected that the sensors provide also a reasonable FIGURE 9. Cross-sectional view of the slot region of the OCSRR, with estimation of the loss factor). electric field lines and contributions to the total OCSRR capacitance and dielectric conductance. (a) Uncovered OCSRR; (b) MUT-covered OCSRR. VI. COMPARISON WITH OTHER PHASE VARIATION where (3) and SENSORS εr Table 2 includes a list of various phase-variation sensors Csubs = C 0 (38) εMUT + εr recently reported, and their main relevant parameters, as well have been used. It should be mentioned that the validity of as other characteristics of interest. The table is restricted to (38) requires not only a semi-infinite MUT in the vertical phase-variation sensors, since comparing sensors with differ- direction, but also a semi-infinite substrate. This approxima- ent sensing principle is difficult (and even meaningless). tion is adopted in this work, provided the considered substrate In view of the table, the proposed sensor C exhibits an is relatively thick (and the slots of the OCSRR are very excellent FoM, by virtue of the small area of the sensing narrow). Introducing (37) in (36), the loss tangent of the region. Note that the FoM is by far superior to the one MUT, in terms of well-known parameters (εr and 0 ) or of the equivalent sensors implemented by means of a 180◦ previously calculated variables (C, GMUT , and εMUT ), can be open-ended sensing line (sensor C’). The sensitivity in the obtained, i.e., reflective-mode sensor reported in [1] is very huge, and for this reason the FoM is very high, despite the fact that the GMUT (εr + 1) tan δMUT = (39) size of the sensing region is not as small as the one of the Cω0 εMUT OCSRR-based sensors presented in this paper. Nevertheless, Using (39), the loss tangent of the different samples it should be noted that further increasing the sensitivity in has been estimated. The obtained values (tan δMUT,ex ) are the proposed sensors and sensor [1] (and [2]) is possible depicted in Table 1, where they are compared with the the- by merely cascading additional quarter-wavelength high/low oretical values reported in the datasheets, and designated as impedance transmission line sections. It should be mentioned tan δMUT,th (for the PLA MUT sample, fabricated by means that sensors C and C0 in this paper, as well as the optimum sen- of a 3D printer, δMUT,th has been alternatively obtained by sor presented in [1], include two (N = 2) high/low impedance means of a resonant cavity). 90◦ line sections (plus the sensing line or OCSRR). How- According to Table 1, the method reasonably predicts the ever, the sensors presented in this paper are implemented in value of the loss tangent of the considered materials, although CPW technology, whereas the sensors in [1] were fabricated the discrepancy is higher for the MUTs exhibiting a smaller in microstrip technology in a different substrate (with the loss factor. Nevertheless, it should be taken into account the possibility of implementing 90◦ line sections with a larger considered approximations, the effects of connectors, and the impedance contrast). difficulty to accurately measure the magnitude of the reflec- Line meandering, as reported in the device presented tion coefficient. The proposed sensors are especially suited in [38], is a technique to enhance the sensitivity, avoiding for the accurate and highly sensitive determination of the real the implementation of sensing regions with excessively elon- part of the permittivity, from the measurement of the phase gated shape factors. However, the resulting FoM in these sen- of the reflection coefficient at a single frequency. Neverthe- sors is not very good. Also, phase-variation sensors based on less, this section demonstrates that the sensors can be used slow-wave transmission lines have been reported [56], [57]. to estimate the loss factor of the considered MUT samples In such sensors, the sensitivity is improved, as compared to (in liquids, with higher loss tangents, or other lossy materials, that of ordinary meandered lines with similar sensing area. VOLUME 9, 2021 27939 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide However, the reported sensitivities and FoM are not as com- the phase of the reflection coefficient (the output variable) petitive as those of the sensors reported in the present paper. with the dielectric constant of the MUT, provided losses are We would like to mention that other phase-variation small. Moreover, an analytical method to estimate the loss sensors based on electro-inductive wave (EIW) [40] and tangent of the MUT from the measurement of the magni- composite right/left-handed (CRLH) [30] artificial lines have tude of the reflection coefficient at the resonance frequency been reported, but in such sensors the phase information of the MUT-loaded OCSRR, has been reported and exper- was converted to magnitude information. Nevertheless, these imentally validated. Besides the small size of the sensing sensors are also included in the comparative Table 2. Though region, the planar nature and one-port configuration of the these sensors are competitive in terms of sensitivity and whole sensing structure, as well as the operation at a single size, their main limitation is the lack of robustness due to frequency, are other important aspects of the proposed device. potential effects of detuning (this is particularly critical in Though in this paper the main focus has been the dielectric the narrowband structures based on EIW transmission lines). characterization of solid samples, these sensors may also be By contrast, the proposed sensors are based on a single reso- interesting for the study and characterization of liquid sam- nant element, and sensor design and fabrication are relatively ples (dielectric characterization, composition, determination simple. In the sensors reported in [41], based on meandered of solute content in mixtures, etc.). For such purpose, a fluidic sensing lines and operating in differential mode, the phase channel may be added on top of the sensing region. Alter- information is also transformed to magnitude information. natively, by virtue of the reflective-mode one-port operation, The sensitivity in these sensors is reasonably good, and submersible sensors based on the proposed OCSRR-based sensor design is simple, but the total sensor size is large structures can be also envisaged (these aspects are left for a since two rat-race couplers are used for phase-to-magnitude future work). transformation. In summary the combination of size (sensing region), sen- APPENDIX A sitivity, simplicity of design/fabrication, and device operation EQUIVALENCE BETWEEN A 180◦ OPEN-ENDED SENSING (single-frequency and reflective mode), makes the proposed LINE AND A PARALLEL LC SENSING RESONATOR sensors strong candidates for applications in several scenar- The reactance of an open-ended line with impedance Zs and ios, including dielectric characterization of solids and defect phase φs , at certain frequency 0 , perturbed by the presence detection. By adding a fluidic channel on top of the OCSRR, of a MUT on top of it, and neglecting losses, can be expressed or by submersing the sensitive part of the structure in a certain as [55] MUT liquid, these sensors can also be useful for the charac- χin,line = −(Z s + 1Zs ) cot (φs + 1φs ) (A.1) terization of liquid samples. Specifically, sensing in industrial processes (e.g., wine fermentation analysis), and bio-sensing where 1 Zs and 1φs are the variations experienced by the (e.g., electrolyte content in blood or urine), among others, are impedance and the phase of the line, respectively, due to envisaged as potential applications. the MUT. For φs = π, the case under study, and small perturbations, (A.1) can be approximated by VII. CONCLUSION Zs In conclusion, highly-sensitive one-port reflective-mode χin,line = − (A.2) 1φs phase-variation sensors useful for dielectric characterization On the other hand, the reactance of a parallel LC resonator of solid samples have been presented in this paper. The describing a certain planar resonant particle (e.g., an OCSRR) sensing element is an electrically small planar resonator, perturbed by a MUT is given by (7), excluding Ls , where the OCSRR, which is connected as a termination load of a 1C accounts for the variation in C caused by the MUT. step-impedance CPW transmission line. It is demonstrated in At the intrinsic resonance frequency of the bare OCSRR, 0 , this paper that the step-impedance transmission line is useful the reactance is to boost up the sensitivity. The sensitivity achieved in one of the proposed sensors (sensor C) is as high as −83.35◦ , C χin = −ω0 L (A.3) considering as output variable the phase of the reflection 1C coefficient, and the dielectric constant of the MUT sample For small perturbations, 1φs can be expressed as as input variable. However, the main relevant aspect of the p p  1φs = ω0 Ll (Cl + 1Cl ) − Ll Cl (A.4) proposed sensor is the small size of the sensing region. Con- sequently, the main figure of merit of these sensors, the ratio where Ll and Cl are the line inductance and capacitance, between the (maximum) sensitivity and the surface of the respectively, corresponding to the considered line section (of sensing region expressed in terms of the squared wavelength, electrical length π), and 1Cl is the variation of the line is very competitive (particularly, the figure of merit has been capacitance caused by the MUT. Since for small perturbations found to be FoM = 5643◦ /λ2 in the designed OCSRR-based 1Cl is necessarily small, (A.4) can be expressed as sensor exhibiting the highest sensitivity, i.e., sensor C). It has s ! also been demonstrated in the paper that the effects of both p 1Cl 1φs = ω0 Ll Cl 1+ −1 (A.5) MUT and sensor losses do not affect the dependence of Cl 27940 VOLUME 9, 2021 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide dN  2 − 12 1 4Z02 |ρ|2air − ω02 Ls2 1 − |ρ|2air 4Z02 + 2ω02 Ls2 1 − |ρ|2air  d|ρ|2air Z0 − 2 dD = (B.1) −(20 Ls2 + Z02 ) d|ρ|2air which in turn can be written as Note that, for the OCSRR-based sensor, the effect of Ls on the p  Cl  sensitivity for sensor operation at 0 and small perturbations 1φs = ω0 Ll 1Cl (A.6) is null. 2C l For 180◦ microstrip sensing lines, with different depen- or dence of the capacitance of the line with εMUT , the sensitivity 1Cl cannot be identical to the one of the OCSRR-based structure, 1φs = π (A.7) 2C l simply because 1Cl /Cl cannot be directly identified with By equating (A.2) and (A.3), using (A.7) and identifying 1C/C for a certain value of εMUT . However, the sensitiv- 1Cl /Cl with 1C/C, it follows that: ity of the phase of the reflection coefficient with the phase of the line, dφρ /dφs , in any considered line technology, πLω0 π L r Zs = = (A.8) is related to the sensitivity of the reflection coefficient with 2 2 C the capacitance of the resonator in the OCSRR-based sensor, Thus, in order to obtain identical responses for small pertur- dφρ /d1C, through (A.11), provided 1Cl /Cl is identified bations in the sensor based on a parallel LC resonator and the with 1C/C. one based on an open-ended 180◦ sensing line, L and C must satisfy APPENDIX B DEPENDENCE OF G ON |ρ|air 2Z s π L= , C= (A.9) Let us consider the circuit model in Fig. 7 with GMUT = 0, πω0 2Z s ω0 corresponding to the bare (uncovered) sensor. According to and the equivalence between 1C and 1φs is given by: this model, two extreme cases provide |ρ|air = 1, (i) G = 0, 1C and (ii) G = ∞. For G = 0, the impedance seen from 1φs = π (A.10) the input port is purely reactive and, therefore, |ρ|air = 1 2C regardless of the operating frequency. Moreover, ρair = 1 Indeed, the relative variation in the line capacitance of a CPW, at 0 , since the LC resonant tank opens at this frequency. 1Cl /Cl , caused by a certain semi-infinite MUT, is identical For G = ∞, the input impedance is merely the one of the to the relative variation in the capacitance of an OCSRR, inductance Ls , and |ρ|air = 1, as well. In view of (35), it is 1C/C, that results when it is covered with an identical MUT. obvious that considering the positive sign in the numerator This means that using (A.8), or (A.9), suffices to obtain and |ρ|air = 1 gives G = ∞. However, this case is mean- identical sensitivities in the limit of small perturbations in ingless from a physical viewpoint since the considered losses both considered sensors, as it is demonstrated in Section IV. are small, and thereby G should be very small. This suggests However, if the purely distributed sensor is implemented, e.g., that the negative sign in (35) is the one to be considered, in microstrip technology, in such case 1Cl /Cl = 1C/C However, with such sign and |ρ|air = 1, both the numerator for different dielectric constants of the MUT. Nevertheless, and the denominator in (35) vanish. Consequently, in order we can express the differential phase as dφs = π · dC 0 /2C, to obtain the value of G in this case, it is necessary to solve and thereby the indeterminacy by applying the L’Hô pital rule. For that dφρ dφρ π dφρ purpose, the derivative of both the numerator, N , and the = = · (A.11) d1C dC 0 2C dφs denominator, D, of G with |ρ|2air is obtained, and the ratio is found to be (B.1), as shown at the top of the page. where the derivative in the right-hand side member is (see 24) It is apparent from (B.1) that the numerator nulls for dφρ 2Z0 |ρ|2air = 1 (or |ρ|air = 1). Thus, G = 0 if |ρ|air = 1 and =− (A.12) dφs Zs the negative sign in the numerator of (35) is adopted. Thus, Introducing Zs as given by (A.8) in (A.12), and the result in in summary, the conductance G must be obtained from the (A.11), one obtains measured value of |ρ|air , by means of (35), using the negative sign in the numerator. dφρ = −2Z0 ω0 (A.13) d1C REFERENCES i.e., an expression identical to (15). This further validates [1] J. Munoz-Enano, P. Velez, L. Su, M. Gil, P. Casacuberta, and F. 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Grenier, ‘‘A microwave and microfluidic in 2005 and 2013 respectively, and the Ph.D. planar resonator for efficient and accurate complex permittivity characteri- degree in electronic engineering from the Univer- zation of aqueous solutions,’’ IEEE Trans. Microw. Theory Techn., vol. 61, sitat Autonoma de Barcelona, Barcelona, Spain, no. 2, pp. 972–978, Feb. 2013. in 2017. From November 2017 to December 2019, [48] A. Salim, S.-H. Kim, J. Y. Park, and S. Lim, ‘‘Microfluidic biosensor she worked as a Postdoc Researcher in Flexible based on microwave substrate-integrated waveguide cavity resonator,’’ Electronics Research Center, Huazhong University of Science and Technol- J. Sensors, vol. 2018, pp. 1–13, Feb. 2018. [49] M. H. Zarifi, H. Sadabadi, S. H. Hejazi, M. Daneshmand, and ogy, Wuhan, China. She is currently a Postdoc Researcher with CIMITEC, A. Sanati-Nezhad, ‘‘Noncontact and nonintrusive microwave-microfluidic Universitat Autonoma de Barcelona, Spain. Her current research interests flow sensor for energy and biomedical engineering,’’ Sci. Rep., vol. 8, no. 1, focus on the development of novel microwave sensors with improved perfor- pp. 1–10, Dec. 2018. mance for biosensors, dielectric characterization of solids and liquids, defect [50] J. Castillo-León, and W. E. Svendsen, Lab-on-a-Chip Devices and Micro- detection, and industrial processes. Total Analysis Systems: A Practical Guide. New York, NY, USA: Springer, 2014. [51] J. Munoz-Enano, P. Velez, L. Su, M. Gil-Barba, and F. Martin, JONATHAN MUÑOZ-ENANO (Graduate Stu- ‘‘A reflective-mode phase-variation displacement sensor,’’ IEEE Access, vol. 8, pp. 189565–189575, Oct. 2020. dent Member, IEEE) was born in Mollet del Vallès [52] A. K. Jha, A. Lamecki, M. Mrozowski, and M. Bozzi, ‘‘A highly sensi- (Barcelona), Spain, in 1994. He received the bach- tive planar microwave sensor for detecting direction and angle of rota- elor’s degree in electronic telecommunications tion,’’ IEEE Trans. Microw. Theory Techn., vol. 68, no. 4, pp. 1598–1609, engineering and the master’s degree in telecommu- Apr. 2020. nications engineering from the Autonomous Uni- [53] A. K. Horestani, Z. Shaterian, and F. Martin, ‘‘Rotation sensor based on the versity of Barcelona (UAB), in 2016 and 2018, cross-polarized excitation of split ring resonators (SRRs),’’ IEEE Sensors respectively. Actually, he is working in the same J., vol. 20, no. 17, pp. 9706–9714, Sep. 2020. university in the elaboration of his Ph.D., which [54] A. Velez, F. Aznar, J. Bonache, M. C. Velazquez-Ahumada, J. Martel, and is focused on the development of microwave sen- F. Martin, ‘‘Open complementary split ring resonators (OCSRRs) and their sors based on metamaterials concepts for the dielectric characterization of application to wideband CPW band pass filters,’’ IEEE Microw. Wireless materials and biosensors. Compon. Lett., vol. 19, no. 4, pp. 197–199, Apr. 2009. [55] D. M. Pozar, Microwave Engineering, 4th ed. Hoboken, NJ, USA: Wiley, 2011. [56] J. Coromina, J. Munoz-Enano, P. Velez, A. Ebrahimi, J. Scott, K. Ghorbani, PARIS VÉLEZ (Member, IEEE) was born in and F. Martin, ‘‘Capacitively-loaded slow-wave transmission lines for Barcelona, Spain, in 1982. He received the degree sensitivity improvement in phase-variation permittivity sensors,’’ in Proc. in telecommunications engineering, specializing 50th Eur. Microw. Conf. (EuMC), Utrecht, The Netherlands, Jan. 2021, in electronics, the electronics engineering degree, pp. 491–494. and the Ph.D. degree in electrical engineering [57] A. Ebrahimi, J. Coromina, J. Muñoz-Enano, P. Vélez, J. Scott, K. Ghorbani, from the Universitat Autònoma de Barcelona, and F. Martín, ‘‘Highly sensitive phase-variation dielectric constant sensor Barcelona, in 2008, 2010, and 2014, respec- based on a capacitively-loaded slow-wave transmission line,’’ IEEE Trans. tively. His Ph.D. thesis concerned common mode Circuit Syst., submitted for publication. suppression differential microwave circuits based [58] F. Martín, Artificial Transmission Lines for RF and Microwave Applica- on metamaterial concepts and semi-lumped res- tions. Hoboken, NJ, USA: Wiley, 2015. onators. During the Ph.D., he was awarded with a pre-doctoral teaching [59] S. Mohammadi, B. Wiltshire, M. C. Jain, A. V. Nadaraja, A. Clements, K. Golovin, D. J. Roberts, T. Johnson, I. Foulds, and M. H. Zarifi, and research fellowship by the Spanish Government from 2011 to 2014. ‘‘Gold coplanar waveguide resonator integrated with a microfluidic chan- From 2015 to 2017, he was involved in the subjects related to metamaterials nel for aqueous dielectric detection,’’ IEEE Sensors J., vol. 20, no. 17, sensors for fluidics detection and characterization at LAAS-CNRS through pp. 9825–9833, Sep. 2020. a TECNIOSpring fellowship cofounded by the Marie Curie program. His [60] S. Harnsoongnoen and A. Wanthong, ‘‘A non-contact planar microwave current research interests include the miniaturization of passive circuits sensor for detection of high-salinity water containing NaCl, KCl, CaCl2 , RF/microwave and sensors-based metamaterials through Juan de la Cierva MgCl2 and Na2 CO3 ,’’ Sens. Actuators B, Chem., vol. 331, Mar. 2021, fellowship. He is a Reviewer for the IEEE TRANSACTIONS ON MICROWAVE Art. no. 129355. THEORY AND TECHNIQUES and for other journals. VOLUME 9, 2021 27943 L. Su et al.: Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensor Based on a Coplanar Waveguide MARTA GIL-BARBA (Member, IEEE) was born FERRAN MARTIN (Fellow, IEEE) was born in in Valdepeñas, Ciudad Real, Spain, in 1981. Barakaldo (Vizcaya), Spain, in 1965. He received She received the physics degree from Universi- the B.S. degree in physics from the Universi- dad de Granada, Spain, in 2005, and the Ph.D. tat Autònoma de Barcelona (UAB), in 1988, and degree in electronic engineering from the Univer- the Ph.D. degree in 1992. From 1994 to 2006, sitat Autònoma de Barcelona, Barcelona, Spain, he was an Associate Professor in electronics with in 2009. She studied one year with the Friedrich the Departament d’Enginyeria Electrònica (Uni- Schiller Universität Jena, Jena, Germany. During versitat Autònoma de Barcelona), and since 2007, her Ph.D. Thesis, she was holder of a META- he is a Full Professor of electronics. In recent MORPHOSE NoE grant and National Research years, he has been involved in different research Fellowship from the FPU Program of the Education and Science Spanish activities including modeling and simulation of electron devices for high Ministry. As a postdoctoral researcher, she was awarded with a Juan de frequency applications, millimeter wave and THz generation systems, and la Cierva fellowship working in the Universidad de Castilla-La Mancha. the application of electromagnetic bandgaps to microwave and millimeter She was a Postdoctoral Researcher with the Institut für Mikrowellentechnik wave circuits. He is now very active in the field of metamaterials and their und Photonik in Technische Universität Darmstadt and in the Carlos III application to the miniaturization and optimization of microwave circuits University of Madrid. She is currently an Associate Professor with the and antennas. Other topics of interest include microwave sensors and RFID Universidad Politécnica de Madrid. She has worked in metamaterials, piezo- systems, with special emphasis on the development of high data capacity electric MEMS, and microwave passive devices. Her current interests include chipless-RFID tags. He is the Head of the Microwave Engineering, Meta- metamaterials sensors for fluidic detection. materials and Antennas Group (GEMMA Group) at UAB, and the Director of CIMITEC, a research Center on Metamaterials supported by TECNIO (Generalitat de Catalunya). He has organized several international events related to metamaterials and related topics, including Workshops at the IEEE International Microwave Symposium (years 2005 and 2007) and European Microwave Conference (2009, 2015 and 2017), and the Fifth International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamaterials 2011), where he acted as Chair of the Local Organizing Com- mittee. He has acted as Guest Editor for six Special Issues on metamaterials and sensors in five International Journals. He has authored or coauthored over 650 technical conference, letter, journal papers and book chapters, he is co-author of the book on Metamaterials entitled Metamaterials with Negative Parameters: Theory, Design and Microwave Applications (John Wiley & Sons Inc.), author of the book Artificial Transmission Lines for RF and Microwave Applications (John Wiley & Sons Inc.), co-editor of the book Balanced Microwave Filters (Wiley/IEEE Press), and co-author of the book Time-Domain Signature Barcodes for Chipless-RFID and Sensing Applications (Springer). He has generated 21 PhDs, has filed several patents on metamaterials and has headed several Development Contracts. Dr. Martín is a member of the IEEE Microwave Theory and Tech- niques Society (IEEE MTT-S). He is reviewer of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, among many other journals, and he serves as member PAU CASACUBERTA was born in Sabadell of the Editorial Board of IET Microwaves, Antennas and Propagation, (Barcelona), Spain, in 1997. He received the International Journal of RF and Microwave Computer-Aided Engineering, bachelor’s degree in electronic telecommunica- and Sensors. He is also a member of the Technical Committees of the tions engineering and the bachelor’s degree in European Microwave Conference (EuMC) and International Congress on computer engineering in 2020 from the Uni- Advanced Electromagnetic Materials in Microwaves and Optics (Metama- versitat Autònoma de Barcelona (UAB), where terials). Among his distinctions, he has received the 2006 Duran Farell Prize he is currently pursuing the master’s degree in for Technological Research, he holds the Parc de Recerca UAB—Santander telecommunications engineering. He received the Technology Transfer Chair, and he has been the recipient of three ICREA Collaboration fellowship by the Spanish Govern- ACADEMIA Awards (calls 2008, 2013 and 2018). He is a Fellow of the ment in 2019 for developing his Bachelor’s Thesis IET. in highly sensitive microwave sensors based in stepped impedance structures. 27944 VOLUME 9, 2021