Received April 21, 2022, accepted June 1, 2022, date of publication June 8, 2022, date of current version June 17, 2022. Digital Object Identifier 10.1109/ACCESS.2022.3181195 Circuit Analysis of a Coplanar Waveguide (CPW) Terminated With a Step-Impedance Resonator (SIR) for Highly Sensitive One-Port Permittivity Sensing PAU CASACUBERTA 1 , PARIS VÉLEZ 1 , (Senior Member, IEEE), JONATHAN MUÑOZ-ENANO 1 , (Graduate Student Member, IEEE), LIJUAN SU 1, (Member, IEEE), MARTA GIL BARBA 2 , (Member, IEEE), AMIR EBRAHIMI 3 , (Member, IEEE), AND FERRAN MARTÍN 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 3 School of Engineering, Royal Melbourne Institute of Technology (RMIT University), Melbourne, VIC 3001, Australia Corresponding author: Pau Casacuberta (pau.casacuberta@uab.cat) This work was supported in part by Ministerio de Ciencia e Innovación (MCIN)/Agencia Estatal de Investigación (AEI), Spain, through European Regional Development Fund (ERDF) European Union under Grant 10.13039/501100011033 and Grant PID2019-103904RB-I00; in part by the European Union Next Generation EU/PRTR under Grant PDC2021-121085-I00; and in part by the Agència de Gestió d’Ajuts Universitaris i de Recerca (AGAUR) Research Agency, Catalonia Government, under Project 2017SGR-1159. The work of Pau Casacuberta was supported by the Ministerio de Universidades, Spain, through the FPU (Ayudas para la Formación de Profesorado Universitario) under Grant FPU20/05700. The work of Jonathan Muñoz-enano was supported 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 Lijuan Su was supported by the Juan de la Cierva Program under Project IJC2019-040786-I. The work of Marta Gil Barba was supported in part by the Polytechnic University of Madrid, and in part by the Administration of the Community of Madrid through the V PRICIT Excellence Program for University Professoriate under Grant M190020074B. The work of Ferran Martín was supported by the Institució Catalana de Recerca i Estudis Avançats. ABSTRACT This paper presents a single-frequency reflective-mode phase-variation microwave sensor devoted to the dielectric characterization of materials. The device is implemented in coplanar waveg- uide (CPW) technology and consists of two parts: (i) the sensing region, a step-impedance resonator (SIR) as termination of a CPW transmission line, and (ii) the design region, a cascade of high/low impedance quarter- wavelength inverters, used to boost up the sensitivity. By placing the so-called material under test (MUT) on top of the sensing region, the capacitance of the SIR is altered due to the effects of the dielectric constant of the MUT. This modifies the phase of the reflection coefficient seen from the input port, the output variable. From a circuit analysis, it is demonstrated that the sensitivity for small perturbations in the vicinity of the dielectric constant of a reference (REF) material can be optimized by setting the operation frequency of the sensor to the resonance frequency of the SIR loaded with such REF material. The maximum sensitivity in one of the reported sensors is as high as 66.5◦ , and the main figure of merit, defined as the ratio between the maximum sensitivity and the area of the sensing region expressed in terms of the squared guided wavelength, is FoM = 3643◦ /λ2 . Such figure of merit represents a significant improvement as compared to the one of the equivalent sensor implemented by means of an open-ended quarter-wavelength sensing line. Such equivalence between the semi-lumped element (i.e., SIR-based) sensor and the fully distributed counterpart is also analyzed in the paper. INDEX TERMS Coplanar waveguide (CPW), dielectric characterization, microwave sensor, phase-variation sensor, permittivity sensor, reflective-mode sensor, step-impedance resonator (SIR). I. INTRODUCTION Material sensing using electrically small planar microwave The associate editor coordinating the review of this manuscript and resonators has experienced a significant growth in recent approving it for publication was Wen-Sheng Zhao . years. The reason is twofold: (i) microwaves are very This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 10, 2022 62597 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR sensitive to the materials to which they interact, and (ii) elec- However, such coupling is activated when symmetry is trun- trically small planar resonators are ideal sensing elements cated, e.g., by the effects of an asymmetric dielectric loading, to implement devices with small sensing regions. Moreover, or as consequence of a relative displacement (either linear planar microwave resonators exhibit the inherent advantages or angular) between the sensing resonator and the host line of planar technology, including low cost and profile, potential (indeed, most coupling-modulation sensors are devoted to the implementation on flexible substrates (of interest, e.g., for measurement of space variables). In these sensors, the typical the development of conformal sensors [1], [2] and wearable output variable is the magnitude of either a transmission sensors [3]), compatibility with other technologies, such as coefficient or a voltage, and therefore coupling modulation microfluidics [4]–[11], or lab-on-a-chip [12], among others, sensors are less tolerant to effects of EMI and noise, at least and the possibility to integrate the associated electronics for as compared to frequency-variation and frequency splitting post-processing and, eventually, for communication purposes sensors. in the same substrate. Recently, a significant effort has been dedicated to the Most planar microwave sensors based on resonant ele- implementation of phase-variation sensors [27], [29], [33], ments (either devoted to the dielectric characterization of [35], [36], [48]–[57], since these sensors combine the materials or to the measurement of other parameters, e.g., advantages of coupling-modulation sensors, i.e., operation space variables) exploit frequency variation [6], [13]–[20]. at a single frequency, and frequency- variation/splitting In particular, for material characterization, the resonance fre- sensors, as far as phase measurements are noise- and quency of the sensing element is determined by the dielec- EMI-tolerant (nevertheless, in some realizations, the phase tric constant of the so-called material under test (MUT), information was transformed to magnitude information [27], provided it is located in the area of influence of the elec- [35], [36]). Although examples of phase-variation sensors tromagnetic field generated by the sensing resonator. Addi- devoted to the measurement of space variables have been tionally, the peak or notch magnitude of the resonance is reported [54]–[56], the canonical application of these sensors influenced by the loss factor of the MUT. Therefore, it is is the measurement of the permittivity of the MUT, and other possible to infer the complex dielectric constant of the variables related to it, e.g., material composition, solute con- MUT on the basis of the resonance frequency and mag- centration in liquid mixtures, etc. Phase-variation sensors are nitude variation measured, e.g., in a resonator-loaded line also of interest for the identification of tiny defects in samples (the typical topology of frequency-variation sensors in planar (based on the changes that such imperfections produce in the configuration) [16], [19]. effective dielectric constant of the MUT), by virtue of the Frequency-variation sensors are robust against the effects highly achievable sensitivity in such sensors [33], [36], [50]. of electromagnetic interference (EMI) and noise, but such Phase-variation permittivity sensors can be implemented sensors need wideband interrogation signals for measuring by means of a transmission line, as far as the electrical length, purposes, and this increases the cost of the associated elec- or phase, of the line is subjected to the effects of the dielectric tronics required for the generation of such signals, based on constant of the MUT, which should be placed on top of it wideband voltage controlled oscillators (VCOs). This limita- [29], [33], [36]. Such electrical length, in turn, determines tion applies also to the so-called frequency-splitting sensors the phase of the transmission or reflection coefficient, the [7], [21], [26], a variant of frequency-variation sensors where usual output variable. The sensitivity in these sensors, a key a host transmission line is loaded with a pair of identical parameter, is proportional to the physical length of the line, resonant elements. In frequency-splitting sensors, similar to provided the sensing region extends over the entire length differential-mode sensors [8], [9], [27]–[36], one of the res- of the line. For this reason, phase-variation sensors are typ- onators acts as reference (REF) resonator, thereby accom- ically implemented by means of meandered lines [33], [36]. modating the so-called reference (REF) material, whereas An alternative strategy to optimize the sensitivity is to replace the MUT should be placed on top of the other resonant the ordinary (meandered) sensing line with highly-dispersive element. The working principle is based on the frequency lines, e.g., composite right/left handed (CRLH) [27], electro- splitting caused when the REF and MUT samples exhibit inductive-wave (EIW) [35], or slow-wave [52], [53] trans- different properties. An advantage over frequency-variation mission lines. The sensitivity in the previous meander-line sensors concerns the fact that, operating quasi-differentially, and artificial-line based sensors is good. It is especially frequency-splitting sensors ‘‘perceive’’ the ambient factors, remarkable that the CRLH- [27] and EIW-based [35] sensors such as temperature and humidity, as common-mode stimuli, exhibit very high sensitivity with a small sensing region. and therefore are robust against cross-sensitivities due to Nevertheless, the design of such sensors is not simple, and changes in environmental conditions. sensor performance is subjected to potential detuning effects Single-frequency sensors constitute a good solution to of the involved resonators (eventually caused by fabrication reduce the costs of the associated electronics. Among them, related tolerances). coupling-modulation sensors have been proposed [37]–[47]. Recently, a different strategy for permittivity sensing, In such sensors, a transmission line is symmetrically loaded based on the measurement of the phase of the reflection coef- with a single symmetric resonator, and the combination ficient in one-port structures, has been reported [48]–[51]. of both elements should prevent their mutual coupling. These reflective-mode sensors exhibit an unprecedentedly 62598 VOLUME 10, 2022 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR high sensitivity with a small sensing area. The devices consist sensing line, is also included in Section III. In Section IV, of an open-ended sensing line (either a half- or a quarter- several prototype sensors are designed, fabricated, and val- wavelength line) cascaded to a set quarter-wavelength idated by means of electromagnetic simulation and exper- line sections with alternating high and low characteristic iment. Moreover, sensor performance is compared to the impedance (impedance inverters), and sensitivity optimiza- one of the distributed counterparts. A discussion relative tion is based on the impedance contrast of the inverters and to cross-sensitivities and effect of losses is carried out in sensing line. Section V. Section VI is devoted to a comparison with other The figure of merit (FoM) of phase-variation sensors is phase-variation sensors. Finally, Section VII concludes the the maximum sensitivity divided by the area of the sensing work. region expressed in terms of the guided wavelength at the operating frequency. Such FoM is high in these reflective- II. SENSOR TOPOLOGY, WORKING PRINCIPLE, AND mode phase-variation sensors, since the sensing region is CIRCUIT MODEL restricted only to the half- or quarter-wavelength open-ended It was demonstrated in [48] that highly sensitive phase- sensing line. However, the FoM can be further optimized variation permittivity sensors can be implemented by means by replacing the open-ended sensing lines with semi-lumped of either a quarter- or a half-wavelength open-ended sensing planar resonators, providing a similar behavior, but with a line cascaded to a set of quarter-wavelength transmission substantially smaller size. This approach was first reported line sections with alternating high and low characteristic in [51], where an open complementary split ring resonator impedance (impedance inverters), as compared to the ref- (OCSRR) [58], [59] is the sensing element that substitutes erence impedance of the ports (typically 50 ). Fig. 1(a) the half-wavelength open-ended sensing line of the fully depicts a typical topology by considering sensor implemen- distributed sensor. A significant improvement of the FoM was tation in CPW technology, and a quarter-wavelength sensing achieved by using the OCSRR sensing element [51]. line. By placing a certain MUT on top of the sensitive region Despite the very good sensor performance indicators (indicated with a dashed rectangle in Fig. 1), the phase of such reported in [51], the OCSRR is not exempt of certain design line is modified, due to the change in the effective dielectric complexity. It behaves essentially as a parallel resonant tank constant of the line, determined by the dielectric constant of (equivalent to an open-ended half-wavelength line at reso- the MUT, εMUT . This variation in the phase of the sensing nance), but it exhibits a series inductance and a parasitic shunt line in turn modifies the phase of the reflection coefficient, capacitance which are not easily controllable parameters, and the output variable. Thus, the sensitivity, a key parameter, should be taken into account for design purposes (specifically is defined as the derivative of the phase of the reflection the parasitic capacitance, as discussed in [51]). Moreover, coefficient with the dielectric constant of the MUT, the input the sensors in [51] were implemented in coplanar waveg- variable. uide (CPW) technology, thereby making necessary the use of For sensitivity optimization, the sensing line should exhibit vias and backside strips (with an equivalent functionality to a high characteristic impedance provided its length is a air bridges) for the suppression of the parasitic slot mode (the quarter-wavelength (or an odd multiple) at the operating fre- OCSRR-terminated CPW does not exhibit axial symmetry). quency [48]. Contrarily, for half-wavelength (or multiples of In this paper, the main aim is to design and imple- this length) open-ended sensing lines, the impedance should ment a reflective-mode phase-variation permittivity sensor be set to a low value in order to enhance the sensitivity. More- in CPW technology, where the sensing element is a series over, the impedance inverters must exhibit an alternating step-impedance resonator (SIR), a symmetric semi-lumped high and low impedance, but it is necessary that the inverter resonator that can be described to a very good approximation adjacent to the sensing line exhibits a high impedance for by means of a series LC tank [60]–[62]. It is also an objective low-impedance half-wavelength open-ended sensing lines, of the paper to demonstrate the equivalence between the and a low impedance when the sensing line is a quarter- proposed SIR-based sensor and the fully distributed counter- wavelength high-impedance line (the situation corresponding part, in this case based on a quarter-wavelength open-ended to the topology of Fig. 1). This set of inverters generates sensing line (also described by a series LC tank in the vicinity a multiplicative effect on the sensitivity, intimately related of resonance [63]). Design simplicity and the absence of to the square of the impedance contrast of the different line vias are clear advantages over the sensor version based on sections, as reported in [48]. The resulting sensors, thereby, OCSRRs, whilst the FoM is also very good, as it will be later exhibit an unprecedentedly high sensitivity. demonstrated. Fig. 1(b) depicts the circuit schematic, where the electrical The paper is organized as follows. Section II presents the parameters (i.e., the characteristic impedance and the phase, proposed SIR-based sensor, the working principle, and the or electrical length) of the different line sections are indi- circuit model. Moreover, this circuit model is validated in cated. The sub-index s is used to designate the parameters such section. A detailed circuit analysis of the equivalent in reference to the sensing line, Zs being the impedance circuit, focused on obtaining design guidelines for sensitivity and φs the phase of this line. The impedance and phase of optimization, is reported in Section III. The equivalence with the high/low impedance line sections are differentiated by the fully distributed sensor, based on a quarter-wavelength the numerical sub-index i, with i = 1, . . . N , where N is the VOLUME 10, 2022 62599 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR FIGURE 1. Typical topology (a), in CPW technology, and circuit schematic FIGURE 2. Typical topology (a) and circuit schematic (b) of the one-port (b) of the one-port reflective-mode phase-variation sensor based on a set reflective-mode phase-variation permittivity sensor identical to the one of high/low impedance quarter-wavelength impedance inverters and a of Fig. 1, with the quarter-wavelength sensing line replaced with a SIR quarter-wavelength open-ended sensing line. The sensing region is resonator (the sensing element). The sensing region is indicated with a indicated with a dashed rectangle. For the topology, a pair (N = 2) of dashed rectangle. The relevant dimension variables of the SIR are high/low impedance 90◦ line sections are considered. The electrical and indicated (the dimensions of the high/low impedance 90◦ lines are geometrical variables are indicated. designated by the same variables as in Fig. 1). For the simulations referred to in the text, the dimensions of the SIR (in mm) are: wL = 0.20, GL = 0.90, lL = 7.33, wC = 1.60, GC = 0.20, lC = 3.04. number of inverters. Finally, the access line, with impedance Z0 , identical to the reference impedance of the port, has a response of this one-port structure is depicted in Fig. 3. It has phase designated as φ0 . been inferred by means of the Keysight ADS electromag- The sensors subject of the present work are based on the netic simulator, and the considered substrate is the Rogers same principle. The difference with regard to the sensor RO3010 with dielectric constant εr = 10.2 and thickness depicted in Fig. 1 concerns the sensitive region, consisting h = 1.27 mm (losses are excluded in the simulation). For low in a step-impedance resonator (SIR), rather than a quarter- frequencies the structure exhibits a capacitive behavior, and wavelength open-ended line section. With such SIR termi- the input impedance is an open-circuit in the DC limit (the nation of the line, a substantially smaller sensing region is phase of the reflection coefficient is φρ = 0◦ in that limit). envisaged, by virtue of the small electrical size of the SIR, At the SIR resonance frequency, given by a semi-lumped resonator. Moreover, this reduction in the 1 sensing region can be achieved by maintaining the same f0 = √ (1) maximum sensitivity, as it will be later demonstrated. Thus, 2π LC a substantially improved figure of merit (FoM), or ratio the impedance seen from the input port is null. This frequency between the maximum sensitivity and the area of the sensing can be inferred from the discontinuity in the phase response, region, is expected in these new SIR-based phase-variation where the phase satisfies φρ = ±180◦ , corresponding to permittivity sensors, as compared to the FoM of the fully a short-circuit. Above resonance, the SIR exhibits a posi- distributed counterparts. This improved FoM is important in tive (inductive) reactance, and, as frequency increases, the applications requiring high sensitivity combined with small phase of the reflection coefficient progressively approaches MUT samples, for example, to monitor tiny variations in the φρ = 0◦ . To univocally determine the two reactive parameters composition of liquid samples (for that purpose, adding a of the SIR, an additional condition is needed. Such condition fluidic channel on top of the sensing region is an option, but is the phase slope at resonance, given by submersible sensors [64] are also possible). dφρ 4L The topology and circuit schematic of these SIR-terminated =− (2) dω ω0 Z0 CPW sensors are depicted in Fig. 2, where the same geometri- cal and electrical variables describing the quarter-wavelength where ω0 = 2πf0 is the angular resonance frequency. With inverters of the sensor of Fig. 1 are used. The SIR is modelled (1) and (2), L and C can be easily inferred from the frequency by means of a grounded series resonator, with inductance L dependence of the phase of the reflection coefficient. The and capacitance C [62]. values for the structure of Fig. 2 are found to be L = 4.375 nH For validation of the SIR-terminated CPW, we will con- and C = 1.164 pF. The phase of the reflection coefficient sider the structure of Fig. 2, but excluding the high/low that corresponds to an LC series resonator with such element impedance quarter-wavelength line sections and access lines values is also depicted in Fig. 3. The agreement with the (the dimensions are indicated in the caption). The phase phase inferred form electromagnetic simulation is very good, 62600 VOLUME 10, 2022 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR thereby, these results point out the validity of the model and the parameter extraction method. Let us now consider that the sensitive region is covered by a semi-infinite (in the vertical direction) MUT, so that the electromagnetic field generated in the SIR does not reach the MUT/air interface. If we also assume that the substrate can be considered to be semi-infinite, the capacitance of the MUT-loaded SIR, C 0 , can be expressed in terms of the capacitance of the bare SIR as follows [51] εr + εMUT C0 = C (3a) εr + 1 where εr is the substrate dielectric constant. This assump- tion was adopted in [51]. However, it was demonstrated in FIGURE 3. Phase of the reflection coefficient of the SIR-terminated CPW [65] that by introducing the concept of equivalent dielectric structure of Fig. 2, excluding the cascaded high/low impedance quarter-wavelength impedance inverters and access lines. The different constant of the substrate, εr,eq , defined as the dielectric con- curves correspond to the uncovered SIR (with capacitance C = 1.164 pF), stant of a hypothetical semi-infinite substrate providing the and to the SIR covered with various semi-infinite MUTs with the indicated dielectric constant and capacitance C’. The SIR inductance in all the cases same contribution to the capacitance of the resonant element, is L = 4.375 nH. The capacitances for the different considered MUTs the total capacitance of the MUT-loaded SIR, C 0 , can be obtained from the resonance frequency of the SIR, where the phase expressed as experiences a 180◦ jump, are C 0 = 1.195 pF (for εMUT = 1.25), C 0 = 1.223 pF (for εMUT = 1.50), and C 0 = 1.250 pF (for εMUT = 1.75). εr,eq + εMUT C0 = C (3b) impedances of the quarter-wavelength impedance inverters. εr,eq + 1 However, by increasing the sensitivity, the linearity is neces- providing a more accurate prediction. The equivalent dielec- sarily degraded [48]. Thus, the sensitivity of the sensor should tric constant of the considered substrate (Rogers RO3010 be optimized in the vicinity of a certain value of the dielectric with dielectric constant εr = 10.2 and thickness h = constant of the MUT. Such dielectric constant is designated as 1.27 mm) was determined by the method described in [65], εREF , and it is set to εREF = 3.55 in this work, corresponding based on electromagnetic simulations (using ANSYS HFSS to the dielectric constant of one of the substrates available in software). The value was found to be εr,eq = 9.48, i.e., some- our laboratory. This means that the intended sensors will be how smaller than εr , the nominal dielectric constant of the able to detect tiny variations of the dielectric constant of the substrate. MUT in the vicinity of εREF , where the sensitivity is going to To validate expression (3b), the phase responses of be optimized. the SIR-terminated CPW covered with several hypothet- In order to obtain design guidelines for sensitivity opti- ical semi-infinite MUT samples, with different value of mization, and to predict the value of the maximum sensitivity, εMUT , have been obtained by electromagnetic simulation. let us consider the circuit model of Fig. 2(b). However, let us As expected (the responses are also included in Fig. 3), first analyze only the SIR-terminated CPW structure. Then, as εMUT increases, the capacitance C 0 increases, and the the generalization to the whole device, with an arbitrary resonance of the SIR decreases. Fig. 3 also depicts the phase number of quarter-wavelength impedance inverters, will be responses inferred from circuit simulation of the series res- carried out. Finally, the analysis of the equivalent sensor, onators described by an identical inductance, namely, L (the based on a quarter-wavelength open-ended sensing line, will one extracted from the response of the bare SIR), and capac- be reported, and the conditions to obtain the same sensitivity itances given by (3b) for the different values of εMUT (such will be provided. capacitances are indicated in Fig. 3). As it can be seen, the agreement with the electromagnetically simulated phases is A. SIR-TERMINATED CPW excellent. Moreover, the capacitances C 0 deduced from the Let us designate by Zin the impedance seen from the input port resonance frequencies corresponding to the different elec- of the SIR-terminated CPW transmission line. The reflection tromagnetic simulations, indicated in the caption of Fig. 3, coefficient seen from this port, with reference impedance Z0 , are roughly identical to those given by (3b). These results is given by [63] validate the circuit model of the MUT-loaded SIR-terminated CPW with capacitance given by expression (3b), under the Zin − Z0 jχ − Z0 ρ= = in (4) mentioned semi-infinite MUT approximation. Zin + Z0 jχ in + Z0 where χin is the input reactance. From (4), the phase of the III. CIRCUIT ANALYSIS FOR SENSITIVITY OPTIMIZATION reflection coefficient, the output variable, is simply The proposed sensors (Fig. 2) can potentially exhibit an χin   unprecedentedly high sensitivity by adequately choosing the φρ = 2 arctan − +π (5) operating frequency, the SIR quality factor, as well as the Z0 VOLUME 10, 2022 62601 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR Such phase is influenced by the input variable, εMUT , through dielectric constant of the REF material εREF , it is necessary the effects of it on the SIR capacitance (see expression to identify the operation frequency that maximizes expression 3b), which, in turn, determines the input reactance of the (12). For that purpose, the derivative of (12) with frequency SIR-terminated CPW, χin . The sensitivity can therefore be is obtained, and the corresponding result is forced to be null. expressed as The resulting equation is found to be dC 0 ! S= dφρ = dφρ · (6) ω4 ω0 20 ω2 dεMUT dC 0 dεMUT 3 4 − 2− 2 −1=0 (14) ω0,REF ω0,REF ω0,REF 2 Let us call C 0 REF the capacitance of the SIR when it is where the following frequency variable has been defined in loaded with the REF material, given by (3b) with εMUT = order to simplify the notation εREF . Using (3b), the capacitance of the SIR loaded with an arbitrary MUT can be expressed in terms of C 0 REF as 2 Z02 ω0 0 = (15) εr,eq + εMUT L2 C 0 = C 0 REF (7) The solution of (14) is εr,eq + εREF v The capacitance C 0 REF is a constant, and the capacitance of ! ω2 ω0 20 1 ω0 40 ω0 20 u 1 1 2ut1+ 1 the MUT-loaded SIR can be expressed as C 0 = C 0 REF + 1C, = − + − ω0,REF 2 3 6 ω0,REF 2 3 4 4 ω0,REF 4 ω0,REF 2 with 1C = 0 for εMUT = εREF . Thus, expression (6) can be rewritten as (16) S= dφρ · d1C (8) From this solution, it follows that if ω0 20 /ω0,REF << 1, the 2 d1C dεMUT optimum frequency for sensitivity enhancement in the limit Let us now express the reactance of the SIR-terminated of small perturbations is roughly ω ≈ ω0,REF , the resonance CPW in terms of the resonance frequency of√the SIR loaded frequency of the SIR loaded with the REF sample. This with the reference material (ω0,REF = 1/ LC 0 REF ). The condition is equivalent to following result is obtained ω0 20 C 0 REF 16 Z 2 = Z02 = 2 02  1 (17) π Zs   ω0,REF 2 ω0,REF 2 L χin = ωL 1 −   (9) ω2 1 + C1C 0 REF and can be fulfilled if the SIR exhibits a high inductance and a low capacitance. In (17), the equivalent impedance of the and, from it, the phase of the reflection coefficient is simply SIR resonator, defined as (see Appendix)    s  ωL ω0,REF 2  4 L φρ = 2 arctan  − 1 + π (10) Zs = (18) π C 0 REF    Z0 ω2 1 + 1C  C 0 REF has been used. The first term of the sensitivity, dφρ /d1C, can be calculated Let us suppose that the SIR loaded with the REF material from (10) and is found to be exhibits reactive elements satisfying the above condition (17). 2 Introducing (12) and (13) in (8), the sensitivity in the limit dφρ −2 Lω0,REF 1/C 0 REF d1C = χ 2 · Z0 ω ·h i2 (11) of small perturbations (i.e., evaluated at εMUT = εREF , 1 + in2 Z 1 + C1C0 REF or 1C = 0) for the operating frequency set to ω ≈ ω0,REF 0 is found to be and such term in the limit of small perturbations of the dielectric constant of the MUT in the vicinity of εMUT = εREF dφρ S|1C=0,ω0,REF ≡ (or 1C = 0) is dεMUT 1C=0,ω0,REF 2ω0,REF L dφρ 2 −2Z0 Lω0,REF /C 0 REF ω =− (19) ≡ S 1C |1C=0 = 2 Z0 (ε r,eq + εREF ) d1C  2 1C=0 ω0,REF Z0 + L ω 2 2 2 ω2 −1 According to (19), sensitivity optimization requires a high value of L, and, consequently, a low value of C 0 REF , so that (12) the product of these reactive elements is coherent√with the The second term contributing to the sensitivity is simply frequency of operation ω0,REF = 2πf0,REF = 1/ LC 0 REF , in agreement with the condition (17). Therefore, in order to d1C C 0 REF = (13) enhance the sensitivity at small perturbations, the equivalent dεMUT εr,eq + εREF impedance of the SIR, Zs , must be high, and the frequency of This term, neither depends on the operating frequency, nor operation must be set to ω0,REF . on the dielectric constant of the MUT, contrary to the first To gain more insight on the validity of condition (17), term. Thus, for sensitivity optimization in the vicinity of the we have considered a SIR-terminated CPW identical to the 62602 VOLUME 10, 2022 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR where Zi is the characteristic impedance of line section i (with i = 1, 2, . . . N ), and 5 denotes the product operator. The reflection coefficient can thus be expressed as 2·(−1)i+N n o j (−1)N · χin (−1) · N N Q i=1 Zi − Z0 ρ= (21) 2·(−1)i+N n o j (−1)N · χin (−1) · N N Q i=1 Zi + Z0 and the phase of the reflection coefficient is    χin  φρ = 2 arctan −  +π (22a)   FIGURE 4. Dependence of the sensitivity in the limit of small   Z0  perturbations with frequency, as given by (12). The value of maximum QN 2·(−1)i+N i=1 Zi sensitivity alongside the one evaluated at the resonance frequency of the SIR is indicated. for N even, and one of Fig. 2, and a REF material with the dielectric constant   indicated before (εREF = 3.55). The reactive elements of the SIR loaded with such REF material are L = 4.375 nH and  χin  φρ = 2 arctan − Q (22b)     C 0 REF = 1.447 pF, and evaluation of (17) with Z0 = 50   N 2·(−1)i+N i=1 Zi   gives ω0 20 /ω0,REF 2 = 0.827 < 1. The exact solution of (14) Z0 gives ω /ω0,REF = 0.805, which means that the optimum 2 2 for N odd. The phases given by (22) and (5) are formally frequency is very close to ω0,REF (i.e., ωopt = 0.897ω0,REF ). identical. The single difference concerns the denominator Fig. 4 depicts the sensitivity at small perturbations as a of the argument of the arctan, which is simply Z0 in (5), function of frequency, as given by (12), for the above-cited and it exhibits a quadratic dependence with the impedances, reactive values of the SIR resonator. As expected, the maxi- Zi , of the different 90◦ line sections in (22). Thus, the mum (absolute value) is located at ωopt , where the sensitivity sensitivity for the SIR-terminated structure with cascaded is found to be S|1C=0 = −127.5◦ /pF, slightly above the high/low impedance 90◦ line sections is given by expression sensitivity at ω0,REF , given by (19), i.e., S|1C=0, ω0,REF = (19) by replacing Z0 with the denominators of expressions −120.9◦ /pF. Nevertheless, in practice, tuning the operating (22). The following results are obtained for N even and odd, frequency exactly to ωopt is difficult due to fabrication related respectively tolerances. If ω0,REF is similar to ωopt , targeting the operating frequency at ω0,REF is reasonable, since this is an easily iden- QN n 2·(−1)i+N o 2ω0,REF L i=1 Zi tifiable frequency. Moreover, any potential loss of sensitivity S|1C=0,ω0 = − · (N even) due to deviations regarding this value, or to the optimum (ε r,eq + 1) Z0 frequency, can be compensated with the quarter-wavelength (23a) high/low impedance line sections, to be discussed next. 2ω0,REF L Z0 S|1C=0,ω0 = − · o (N odd) (ε r,eq + 1) QN Z 2·(−1)i+N n i=1 i B. GENERALIZATION TO A SIR-TERMINATED STEP-IMPEDANCE CPW (23b) In this subsection, the objective is to demonstrate that by It is clear from (23) that if the impedances of the 90◦ cascading 90◦ line sections with alternating high and low line sections with odd index are set to low values, as com- characteristic impedance to the SIR-terminated CPW, the pared to Z0 , and those corresponding to line sections with sensitivity can be further, and substantially, enhanced. Indeed, even index are high, the resulting sensitivity is substantially a similar behavior to the one of reflective-mode phase- higher than the one given by (19). The reason is that there variation dielectric constant sensors based on an open-ended is a multiplicative effect that depends on the square of the 90◦ sensing line cascaded to a set of high/low impedance 90◦ normalized impedances of the different line sections, with line sections is expected [48]. The reason is that an open- the odd-index (low) impedances and the even-index (high) ended 90◦ (sensing) line, like the SIR, can be described to impedances appearing in the denominator and numerator of a good approximation by a series resonator in the vicinity of (23), respectively. The limit in the achievable multiplication resonance (see Appendix). factor (second term in the product of expressions 23) is Let us consider the structure of Fig. 2 generalized to an dictated by the maximum and minimum achievable values of arbitrary number, N, of 90◦ high/low impedance line sections. the CPW line impedance. Nevertheless, the sensitivity in the The impedance seen from the input port can be expressed as limit of small perturbations can be unprecedentedly increased (−1)N YN n 2·(−1)i+N o to the desired value by simply adding the necessary 90◦ Zin,N = Zin · Zi (20) high/low impedance line sections. Obviously, this penalizes i=1 VOLUME 10, 2022 62603 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR the overall sensor size, but not the sensitive region, circum- sensor in the limit of small perturbations, and given by (19). scribed to the area occupied by the SIR resonator (the sensing By including a certain set of high/low impedance 90◦ line element). As it will be shown, sensitivity enhancement in the sections (for sensitivity enhancement), the sensitivities of limit of small perturbations also degrades the linearity of the both the SIR-based sensor and the fully distributed coun- sensor. However, such sensitivity enhancement is of special terpart (based on a 90◦ sensing line) are also identical and interest for the implementation of highly sensitive devices, given by expressions (23), provided the mapping of (18) is able to resolve small variations in the dielectric constant fulfilled. It should be emphasized that these identical sensi- of the MUT in the vicinity of that of the REF material (if tivities between both sensing structures take place in the limit measurements over a wide input dynamic range are pursuit, of small perturbations and for sensor operation at ω0,REF (the in that case, a moderate sensor sensitivity in favor of better resonance frequency of the SIR loaded with the REF material, linearity might be preferred). which should be identical to the angular frequency providing It is worth mentioning that, recently, several strategies to a 90◦ electrical length to the sensing line covered by the same enhance the sensitivity in frequency variation sensors, with material). very competitive results, have been reported, including meta- The equivalence between both sensors will be demon- material coupling [66], intermodulation products using active strated in the next section, devoted to sensor validation resonators [67], and coupled resonators [68]. through simulation and experiment. Nevertheless, despite the similar behavior, the SIR resonator is significantly smaller C. COMPARISON TO THE EQUIVALENT SENSOR BASED than the equivalent 90◦ open-ended line. This has direct ON A QUARTER-WAVELENGTH OPEN-ENDED SENSING impact in the size of the sensing region, and, consequently, LINE in the main figure of merit (FoM) of planar phase-variation By virtue of the analogy between a 90◦ open-ended line and a sensors, as defined in the introduction section. series resonator in the vicinity of resonance (see Appendix), a similar behavior between the proposed SIR-based sensors and those reported in [48], where the sensing structure is a IV. SENSOR VALIDATION quarter-wavelength open-ended line, is expected. Let us next For sensor validation, two SIR-terminated CPW based sen- demonstrate the equivalence between the sensitivity in both sors have been designed and fabricated. The considered sub- sensor types. strate is the Rogers RO3010 with dielectric constant εr = By excluding the high/low impedance 90◦ line sections, 10.2, thickness h = 1.27 mm, and loss tangent tan δ = the sensitivity of the quarter-wavelength based sensor in the 0.0022. In the so-called sensor A, the SIR-terminated CPW vicinity of the dielectric constant of the REF sample is [48] is directly connected to the 50- access line, whereas for dφρ Zs ω0,REF ls 1 sensor B, a pair (N = 2) of high/low impedance quarter = −2 · √ ·p (24) wavelength transmission line sections is added between the dεMUT Z0 2 2c εr,eq + εREF SIR termination and the access line. The dimensions of the where ls and Zs are the length and characteristic impedance, SIR terminated CPW are those indicated in the caption of respectively, of the 90◦ open-ended sensing line, ω0,REF is Fig. 2. The impedances of the quarter-wavelength line sec- the operating frequency (providing the required 90◦ electrical tions are Z1 = 91  and Z2 = 34.4 , resulting in the dimen- length to the sensing line covered with the REF sample), and sions provided in the caption of Fig. 5, where the fabricated c is the speed of light in vacuum. Since the phase of the line sensors are depicted. Sensor fabrication has been carried out at ω0 is by means of the LPKF H100 milling machine. Contrary to π ω0,REF ls similar sensors based on other resonant elements, in particular φs = = , (25) those reported in [51], where OCSRRs are used for sensing, 2 vp sensors A and B do not require vias since the SIR resonators vp being the phase velocity exhibit axial symmetry (contrary to the OCSRRs). Due to c such axial symmetry, the appearance of the parasitic slot vp = √ , (26) mode of the CPW is prevented, and vias and backside strips εeff (with a functionality equivalent to the one of air-bridges, i.e., with the effective dielectric constant of a CPW given by the electrical connection of the ground plane regions) are εr,eq + εREF avoided. εeff = , (27) 2 We have also fabricated the fully distributed counterparts it follows that (24) can be rewritten as of sensors A and B, designated as A0 and B0 , where the SIR resonators are replaced with 90◦ open-ended lines with dφρ Zs π =− · (28) impedance Zs = 70 , equivalent to the one of the SIRs dεMUT 2Z 0 εr,eq + εREF (and given by equation 18). The photographs of the fabricated Let us now use the equivalent impedance of the SIR sensors A0 and B0 are also depicted in Fig. 5 (the dimensions resonator as defined in (18). By introducing it in (28), the of the quarter-wavelength open-ended sensing line are given sensitivity is found to be identical to the one of the SIR-based in the caption). 62604 VOLUME 10, 2022 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR results validate the sensitivity analysis of the previous section, as well as the equivalence between the SIR-based sensors and the fully distributed counterparts. Thanks to the multiplicative effect generated by the normalized impedances of the high/low impedance 90◦ line sections (see expressions 23), the sensitivity for small pertur- bations is as high as −66.5◦ and −64.9◦ for sensors B and B0 , respectively (simulated values). The FoM, or ratio between the sensitivity and the area of the sensing region expressed in terms of the squared guided wavelength, is found to be FoM = 3643◦ /λ2 and FoM = 2526◦ /λ2 for sensors B and B0 , respectively. Note that for the calculation of the FoM, we have considered the area of the sensing region as the one given by the length of the sensing element (either the SIR, sensor B, or the quarter-wavelength sensing line, sensor B0 ), and a width that extends 2 mm beyond the ground planes (i.e., 6 mm). With a distance between ground planes of 2 mm in all the cases, it is considered that the electric field lines do not extend beyond that limit. This means that the improvement in the FoM is mainly due to the reduction in the length of the SIR, as compared to the quarter-wavelength resonator. These results clearly prove that by replacing the 90◦ open- ended sensing line of the distributed sensor with a SIR, the FoM can be substantially improved. It should be mentioned that, in order to further increase the FoM (by decreasing the length of the sensor), we have FIGURE 5. Typical Photographs of the fabricated sensors A (a), A’ (b), B (c), and B’ (d). The dimensions of the SIR-terminated CPW are given in Fig. 2. surrounded the open end of the SIR-based sensor with a The dimensions of the high/low impedance CPW line sections (in mm) ground plane in order to obtain the same value of the SIR are: w1 = 1.6, G1 = 0.2, l1 = 16.67, w2 = 0.2, G2 = 0.9, l2 = 16.5. The capacitance while reducing the length of the wide line section dimensions of the high-impedance 90◦ open-ended sensing line (in mm) are: ws = 0.38, Gs = 0.81, ls = 14.57. In all the cases, the dimensions of of the SIR. Particularly, we have considered a gap of 0.2 mm the 50- access lines (in mm) are: w0 = 1.1, G0 = 0.45, l0 = 8. at the open end of the line. The effects of this modification have been analyzed through electromagnetic simulations, but Before experimental validation, the phase variation of the it has been concluded that it is not possible to obtain a different sensors with the dielectric constant of the MUT, competitive advantage by this procedure, since the reduction as well as the sensitivity, have been inferred by means of of the sensing area is approximately 1%. full-wave simulation using the ANSYS HFSS commercial Experimental validation has been carried out by cover- software. For that purpose, the sensing regions are considered ing the sensing regions of the four designed and fabricated to be covered by semi-infinite MUTs with varying dielectric sensors with several commercially available (uncladded) constant. The simulated phases obtained at the operating microwave substrates, with a MUT sample (PLA) fabricated frequency, f0,REF = ω0,REF /2π = 2 GHz, are depicted with a 3D printer (the Ultimaker 3 Extended), and by leaving in Fig. 6. Such frequency is the resonance frequency of the the sensing region unloaded (i.e., surrounded by air). The SIR loaded with the REF material, identical to the frequency thickness of the MUT samples is roughly 3 mm. With such that provides an electrical length of 90◦ to the sensing lines thickness, the samples can be considered to be semi-infinite in of sensors A0 and B0 . It should be mentioned that, actually, the vertical direction (stacking of two 1.5-mm thick samples, Fig. 6 depicts the differential phase, defined as the phase available in our laboratory, has been carried out for that of the reflection coefficient for a given value of εMUT in purpose). The specific samples exhibit dielectric constants reference to the one that results when the sensing region of 2.2 (estimated for PLA), 3.55 (for Rogers RO4003C), 4.4 is covered by the REF material. The sensitivity has been (for FR4), and 10.2 (for Rogers RO3010). The measured inferred from the numerical derivative of the phase data (the differential phases at the operating frequency for such MUTs results are also included in Fig. 6). and air, inferred by means of the Keysight 85072A vector In view of Fig. 6, it can be seen that the sensitivities in the network analyzer, are also included in Fig. 6. The measure- limit of small perturbations (i.e., for 1C = 0 pF, or εMUT = ments have been performed three times, in order to ensure εREF ) are very similar for the SIR-based and the open-ended repetitiveness (the corresponding error bars are included in 90◦ line-based sensors. The values, indicated in Fig. 6, agree Fig. 6). The agreement between the measured data points with the theoretical predictions, given by expressions (19) and the simulated values is very good in all the cases. This or (23), to a very good approximation. These simulation means that the curves corresponding to the simulated values VOLUME 10, 2022 62605 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR FIGURE 7. Measured differential phases for the different samples using sensors A and B. The set of defected samples, inferred from the REF samples by drilling arrays of holes of different densities, is shown with the corresponding phase measurements. appreciated. This is due to the higher sensitivity of sensor B at εMUT = εREF . With the results of Fig. 7, it is clear that the proposed sensor B is useful to detect small variations in the dielectric constant in the vicinity of that of the REF sample. It should be mentioned that in the analysis of the previous section, as well as in the validation of the designed and fabricated sensors of the present section, it has been assumed that the thickness of the MUT fulfills the semi-infinite MUT FIGURE 6. Typical phase (1φρ = φρ − φρ,εREF ) at f0,REF and sensitivity for approximation. Compact expressions providing the sensitiv- the designed and fabricated sensors. (a) Sensors A and A’; (b) sensors B ity for small perturbations have been obtained and validated and B’. (19 or 23) by virtue of such approximation. Nevertheless, can be used to infer the dielectric constant of any hypothetical the sensors are also useful for determining the dielectric material from the measurement of the differential phase. constant of thinner samples, not subjected to the semi-infinite As expected, sensitivity enhancement degrades the sensor approximation. For that purpose, curves equivalent to those of linearity, as revealed by the curves of Fig. 6. This means Fig. 6 for thinner MUT samples (with predefined thickness) that for dielectric measurements with a relatively large input can be generated. Thus, the considered approximation does dynamic range, it may be convenient to design the sensor not represent a loss of generality of the proposed sensors. with moderate value of the sensitivity, at the expense of a However, for thin MUT characterization, it is important to limited resolution. By contrast, for the use of the sensor as know the thickness of the sample in order to use the corre- comparator, e.g., to determine potential defects, irregularities, sponding calibration curve. or changes between a certain sample and a well-known refer- ence (REF) sample, the sensitivity should be high in order V. DISCUSSION to resolve (and hence detect) tiny variations in the sample An important aspect of the proposed SIR-based sensors con- under test (or MUT). Such variations are typically manifested cerns the lack of cross-sensitivity of the output variable, the through changes in the dielectric constant, and are therefore phase of the reflection coefficient, with the loss factor of the detectable with the proposed sensor, as far as the sensitivity MUT (or loss tangent, tan δMUT ). This has been corroborated in the vicinity of the REF sample is sufficiently high. from electromagnetic simulation using ANSYS HFSS. Thus, To illustrate the potential of the proposed sensors to detect Fig. 8(a) depicts the phase of the reflection coefficient at small defects in samples, we have deliberately drilled arrays the operating frequency for the sensor based only on the of holes of different densities in the REF sample (equivalent SIR and access line (sensor A), as a function of both the to reduce the dielectric constant). Photographs of the different dielectric constant and loss tangent of the MUT. It can be defected samples and the measured differential phases, using clearly appreciated that the phase of the reflection coefficient sensors A and B, at the operating frequency are shown in depends only on the dielectric constant of the MUT, being Fig. 7. The measurements have been performed 3 times in independent of the loss tangent. The fact that the device does order to analyze the repetitiveness, as well as the effects of not exhibit cross-sensitivity with the loss tangent of the MUT potential inaccuracies related to sample positioning (the cor- is relevant, since this means that the dielectric constant of the responding error bars are included in Fig. 7). The enhanced MUT, the input variable, can be retrieved regardless of the capacity to detect the defects by using sensor B can be clearly loss factor of the MUT. 62606 VOLUME 10, 2022 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR Let us suppose that a second output variable is considered for the (possible) determination of the loss tangent of the MUT. Obviously, the magnitude of the reflection coefficient at resonance should be influenced by the overall losses of the device, including tan δMUT . Therefore, it follows that such magnitude is the canonical second output variable, poten- tially useful for retrieving tan δMUT . Fig. 8(b) depicts the dependence of the magnitude of the reflection coefficient at resonance with both tan δMUT and εMUT . Contrary to the phase, the magnitude of the reflection coefficient at resonance depends on both the loss factor and the dielectric constant of the MUT. In other words, this second output variable exhibits cross sensitivity with the dielectric constant of the MUT. Thus, the determination of the loss tangent of the MUT with these sensors is not simple, since the surface of Fig. 8(b) cannot be considered as a calibration surface. The main reason is that, in experiment, there are several sources of losses, difficult to account in simulation, and generating such calibration surface from experiment is not possible due to the lack of a set of representative data points. On the other hand, a semi-analytical method for retrieving the loss tangent of the MUT, similar to that reported in [51] in reference to OCSRR- based reflective-mode phase-variation sensors, and based on the circuit model of the SIR-based sensor by including losses, is not possible, at least for MUTs with moderate and low loss levels. The reason is that the losses of the access lines and substrate obscure the losses associated to the MUT, as it has been demonstrated from electromagnetic simulations, not shown. Thus, with the SIR-based CPW sensors reported in this work, the dielectric constant of the MUT can be accurately predicted, but not the loss tangent. Nevertheless, there are many variables related to the dielectric constant of the MUT that can potentially be measured with these sensors, e.g., liquid composition in mixtures, or physical variables, such FIGURE 8. Phase of the reflection coefficient at the operating frequency as temperature or humidity, among others (in this case, func- (a), and magnitude of the reflection coefficient at resonance (b) for the SIR-based sensor A, inferred from electromagnetic simulation. tional materials with a dielectric constant dependent on the physical variable to be sensed might be necessary). Moreover, by virtue of the highly achievable sensitivity, these sensors is identical, i.e., 6 mm, in both sensors). The sensitivity in the can be used for the detection of tiny defects in samples, as it reflective-mode sensor reported in [48] is huge, and for this has been demonstrated in the previous section. main reason, the FoM in that sensor is so high, despite the fact that the size of the sensing region is not as small as the VI. COMPARISON WITH OTHER PHASE VARIATION one of the SIR-based sensors presented in this paper. SENSORS Nevertheless, further increasing the sensitivity in the Table 1 includes a list of various phase-variation sensors proposed sensors, as well as in other reflective-mode recently reported, and their main relevant parameters, as well phase variation sensors based on high/low impedance as other characteristics of interest. The table is restricted to quarter-wavelength line sections, is possible by merely cas- phase-variation sensors, since comparing sensors with dif- cading additional high/low impedance line sections to the ferent sensing principle is difficult (and even meaningless). sensing structure. It should be mentioned that sensors B and In view of the table, the proposed sensor B exhibits a good B0 in this paper, as well as the optimum sensor presented FoM, by virtue of the small area of the sensing region. Note in [48], include two (N = 2) high/low impedance 90◦ line that the FoM is superior to the one of the equivalent sensor sections (plus the sensing line, or SIR in the present paper). implemented by means of a 90◦ open-ended sensing line However, the sensors presented in this paper are implemented (sensor B0 ). As explained, the reason is the shorter length of in CPW technology, whereas the sensors in [48] were fabri- the sensing region in the SIR-based sensor B, as compared to cated in microstrip technology in a different substrate (with the distributed sensor counterpart B0 (by contrast, the width the possibility of implementing 90◦ line sections with a VOLUME 10, 2022 62607 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR TABLE 1. Comparison of various phase variation-sensors. for an accurate modeling. Moreover, since the OCSRR does not exhibit any symmetry plane, vias are required in order to avoid the generation of the parasitic slot mode. Thus, in sum- mary, the SIR-based sensors of the present paper exhibit more simple design and fabrication, and are considered to be the preferred option for the implementation of reflective-mode phase-variation sensors in CPW technology. The equivalence with the distributed quarter-wavelength-based sensor, but the smaller size of the SIR sensor, and comparable design and fabrication burden, justify the previous statement. Note also that it is possible to further improve the figure of merit of sensor B by merely cascading additional high/low impedance quarter-wavelength transmission line sections. VII. CONCLUSION In conclusion, highly-sensitive one-port reflective-mode phase-variation sensors useful for the measurement of the dielectric constant of solid samples have been presented in this paper. The sensing element in such sensors is an electrically small planar semi-lumped resonator, the larger impedance contrast). Indeed, the main objective of this step-impedance resonator (SIR), which is connected as paper has not been to design and fabricate a reflective-mode a termination load of a cascade of high/low impedance phase-variation sensor with the highest reported sensitivity quarter-wavelength transmission line sections. With the use (this would be possible by simply adding further high/low of such step-impedance transmission line configuration, the impedance line sections as indicated), but to demonstrate that sensitivity can be substantially enhanced, by keeping unal- there is an equivalence between the reported SIR-based sen- tered the size of the sensing region, determined by the size of sors and the distributed reflective-mode phase-variation sen- the SIR resonator. The (maximum) sensitivity achieved in one sors based on open-ended quarter-wavelength sensing lines, of the proposed sensors (designated as sensor B), based on and that the FoM is better in the sensors implemented by the the sensing SIR plus two additional quarter-wavelength line SIR sensing resonators, by virtue of their small electrical size. sections with alternating low and high impedance, is as high Table 1 includes transmission-mode sensors based on line as −66.5◦ , the output variable being the phase of the reflec- meandering [33], a technique to boost up the sensitivity tion coefficient, and the input variable the dielectric constant by considering long sensing lines with mode shape factors. of the MUT sample. The achieved figure of merit (FoM) in However, the resulting FoM is very limited as compared to such sensor, defined as the ratio of the maximum sensitivity those of the sensors reported in [48], [49], [51], and sensors and the area of the sensing region expressed in terms of B and B0 of the present work. An alternative strategy to the guided wavelength, is FoM = 3642◦ /λ2 , a competitive enhance the sensitivity in phase-variation sensors is to replace value that can be further increased by merely adding fur- the ordinary sensing lines with artificial lines. For example, ther quarter-wavelength high/low transmission line sections. in [52], [53], the reported sensors are implemented by means It has also been demonstrated in this paper that the effects of slow-wave transmission lines. The FoM in such sensors of both MUT and sensor losses do not affect the depen- is reasonably good, at least it is better than the one of the dence of the phase of the reflection coefficient (the output meander-line based sensor of [33], but not as good as those variable) with the dielectric constant of the MUT, provided of the sensors of [48], [49], [51], and sensors B and B0 of losses are small. In other words, the phase of the reflection this work. Finally, let us mention that in the phase-variation coefficient does not exhibit cross sensitivity with the loss sensors reported in [27], [35], [36], the phase is converted to factor of the MUT. Finally, it has been demonstrated in the magnitude, and for this reason, the FoM in such sensors is not paper that the proposed SIR-based sensors are equivalent to reported (nevertheless, the sensitivity of the sensors of [27] is their distributed counterparts, based on the replacement of very good). the SIR resonator with an open-ended quarter-wavelength The achieved FoM in sensor B is of the same order transmission line resonator. Indeed, an expression that pro- of magnitude as the one of the reflective-mode phase- vides the characteristic impedance of the quarter-wavelength variation sensor based on an open-complementary split ring sensing line (from the inductance and capacitance of the SIR resonator (OCSRR) reported in [51]. Thus, such sensors, both resonator), that is necessary to obtain the same sensitivity based on semi-lumped sensing resonators are comparable. has been inferred. However, the SIR-based sensors exhibit a However, the SIR resonator is simply described by a series LC superior FoM by virtue of their smaller electrical size, as com- resonator, contrary to the OCSRR, that needs the inclusion pared to the quarter-wavelength sensing lines. In this paper, of parasitic elements, besides a parallel LC resonant tank, sensor validation has been carried out by considering solid 62608 VOLUME 10, 2022 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR samples. However, this type of sensors is also useful for the length π/2), and 1Cl is the variation of the line capacitance characterization of liquids (dielectric characterization, com- caused by the MUT. For small perturbations, 1Cl is small as position, determination of solute content in diluted solutions, compared to Cl , and (A.3) can be approximated by etc.). For sensitivity optimization, the operating frequency s ! in this case should be tuned to the resonance frequency p 1Cl 1φs = ω0,REF Ll Cl 1+ −1 of the SIR loaded with the reference liquid. Nevertheless, Cl for significant variations in the permittivity of the liquids 1Cl p   under study, it might be convenient to limit the sensitiv- ≈ ω0,REF Ll Cl (A.4) 2C l ity in favor of the sensor linearity. For liquid characteriza- or tion, either fluidic channels or liquid containers should be π 1Cl added on top of the sensing area. Alternatively, submersible 1φs = · (A.5) sensors can be envisaged, a reasonable approach for liquid 2 2C l measurements. The reason is that this one-port reflective- Forcing (A.1) and (A.2) to be identical, using (A.5), and mode phase-variation sensors can be considered to be sensing identifying 1Cl /Cl with 1C/C 0 REF , the following equiva- probes, where, for measurement, it suffices to introduce the lence is obtained s sensing element (either the SIR or the quarter-wavelength 4Lω0,REF 4 L sensing line) within the liquid. Nevertheless, protection of Zs = = (A.6) π π C REF0 the high/low impedance quarter-wavelength line sections is required. Work is in progress in this direction, but this is the Therefore, for small perturbations, the response of the sensor subject of a future work. based on the SIR-terminated CPW and the one of the sensor based on a quarter-wavelength open-ended sensing line are APPENDIX expected to be identical provided the inductance and capac- EQUIVALENCE BETWEEN A 90◦ OPEN-ENDED SENSING itance of the SIR loaded with the REF material are selected LINE AND A SERIES LC SENSING RESONATOR according to Let us consider an open-ended terminated line with πZ s 4 impedance Zs and phase φs = π/2 when it is loaded L= , C 0 REF = (A.7) 4ω0,REF πZ s ω0,REF with an MUT, which is considered to be the REF material, and the equivalence between 1C and 1φs is given by: at the frequency designated as ω0,REF . Under these loading conditions and frequency, the input reactance is null, due 1C 1φs = π 0 (A.8) to the impedance inversion of the quarter-wavelength open- 4C REF ended line. However, if the dielectric constant of the MUT is Note that the relative variation of the line capacitance of a slightly perturbed, and losses are neglected, the input reac- CPW, 1Cl /Cl , as consequence of a change in the dielectric tance changes to [63] constant of the MUT, is identical to the relative variation χin,line = Zs 1φ s (A.1) experienced by the capacitance of the SIR, 1C/C 0 REF . Con- sequently, if the equivalence given by (A.6), or by (A.7), where 1φs is the variation experienced by the phase of the is satisfied, identical sensitivities in the limit of small pertur- line due to the changes in the dielectric constant of the MUT. bations are expected for both sensors, as it has been demon- Let us now consider a series LC resonator describing strated in Section IV. a planar resonant particle such as a SIR-terminated CPW, and let us assume that the particle resonates at the angular REFERENCES frequency ω0,REF , when it is loaded with the REF mate- [1] P. Wei, B. Morey, T. 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New York, NY, USA: Springer, structures in microstrip technology: Analysis, optimization, and applica- Nov. 2014. tions,’’ Sensors, vol. 19, p. 3189, Jul. 2019. [13] M. Puentes, C. Weiss, M. Schussler, and R. Jakoby, ‘‘Sensor array based [33] J. Muñoz-Enano, P. Vélez, M. Gil, and F. Martín, ‘‘An analytical method to on split ring resonators for analysis of organic tissues,’’ in IEEE MTT-S Int. implement high sensitivity transmission line differential sensors for dielec- Microw. Symp. Dig., Baltimore, MD, USA, Jun. 2011, pp. 1–4. tric constant measurements,’’ IEEE Sensors J., vol. 20, no. 1, pp. 178–184, [14] M. Schueler, C. Mandel, M. Puentes, and R. Jakoby, ‘‘Metamate- Jan. 2020. rial inspired microwave sensors,’’ IEEE Microw. Mag., vol. 13, no. 2, [34] P. Vélez, J. Muñoz-Enano, and F. Martín, ‘‘Differential sensing based on pp. 57–68, Mar. 2012. quasi-microstrip-mode to slot-mode conversion,’’ IEEE Microw. Wireless [15] M. S. Boybay and O. M. Ramahi, ‘‘Material characterization using com- Compon. Lett., vol. 29, pp. 690–692, 2019. plementary split-ring resonators,’’ IEEE Trans. Instrum. Meas., vol. 61, [35] M. Gil, P. Vélez, F. Aznar, J. Muñoz-Enano, and F. Martín, ‘‘Differ- no. 11, pp. 3039–3046, Nov. 2012. ential sensor based on electro-inductive wave (EIW) transmission lines [16] C.-S. Lee and C.-L. Yang, ‘‘Complementary split-ring resonators for mea- for dielectric constant measurements and defect detection,’’ IEEE Trans. suring dielectric constants and loss tangents,’’ IEEE Microw. Wireless Antennas Propag., vol. 68, pp. 1876–1886, 2020. Compon. Lett., vol. 24, no. 8, pp. 563–565, Aug. 2014. [36] J. Muñoz-Enano, P. Vélez, M. Gil, J. Mata-Contreras, and F. Martín, [17] C.-L. Yang, C.-S. Lee, K.-W. Chen, and K.-Z. Chen, ‘‘Noncontact mea- ‘‘Differential-mode to common-mode conversion detector based on rat- surement of complex permittivity and thickness by using planar res- race couplers: Analysis and application to microwave sensors and onators,’’ IEEE Trans. Microw. Theory Techn., vol. 64, no. 1, pp. 247–257, comparators,’’ IEEE Trans. Microw. Theory Techn., vol. 68, no. 4, Jan. 2016. pp. 1312–1325, Apr. 2020. [18] L. Su, J. Mata-Contreras, P. Vèlez, and F. Martín, ‘‘Estimation of the [37] J. Naqui, M. Durán-Sindreu, and F. Martín, ‘‘Novel sensors based on the complex permittivity of liquids by means of complementary split ring symmetry properties of split ring resonators (SRRs),’’ Sensors, vol. 11, resonator (CSRR) loaded transmission lines,’’ in IEEE MTT-S Int. Microw. no. 8, pp. 7545–7553, 2011. Symp. Dig., Pavia, Italy, Sep. 2017, pp. 20–22. [38] J. Naqui, M. Durán-Sindreu, and F. Martín, ‘‘Alignment and posi- [19] L. Su, J. Mata-Contreras, P. Vélez, A. Fernández-Prieto, and F. Martín, tion sensors based on split ring resonators,’’ Sensors, vol. 12, no. 9, ‘‘Analytical method to estimate the complex permittivity of oil samples,’’ pp. 11790–11797, Aug. 2012. Sensors, vol. 18, p. 984, Mar. 2018. [39] A. K. Horestani, C. Fumeaux, S. F. Al-Sarawi, and D. Abbott, ‘‘Displace- [20] A. K. Jha, N. Delmonte, A. Lamecki, M. Mrozowski, and M. Bozzi, ment sensor based on diamond-shaped tapered split ring resonator,’’ IEEE ‘‘Design of microwave-based angular displacement sensor,’’ IEEE Microw. Sensors J., vol. 13, no. 4, pp. 1153–1160, Apr. 2013. Wireless Compon. Lett., vol. 29, no. 4, pp. 306–308, Apr. 2019. [40] A. K. Horestani, D. Abbott, and C. Fumeaux, ‘‘Rotation sensor based [21] A. K. Horestani, J. Naqui, Z. Shaterian, D. Abbott, C. Fumeaux, and on horn-shaped split ring resonator,’’ IEEE Sensors J., vol. 13, no. 8, F. Martín, ‘‘Two-dimensional alignment and displacement sensor based pp. 3014–3015, Aug. 2013. on movable broadside-coupled split ring resonators,’’ Sens. Actuators A, [41] J. Naqui and F. Martín, ‘‘Transmission lines loaded with bisymmetric Phys., vol. 210, pp. 18–24, Apr. 2014. resonators and their application to angular displacement and velocity sen- [22] J. Naqui, C. Damm, A. Wiens, R. Jakoby, L. Su, and F. Martin, ‘‘Transmis- sors,’’ IEEE Trans. Microw. Theory Techn., vol. 61, no. 12, pp. 4700–4713, sion lines loaded with pairs of magnetically coupled stepped impedance Dec. 2013. resonators (SIRs): Modeling and application to microwave sensors,’’ in [42] J. Naqui and F. Martín, ‘‘Angular displacement and velocity sensors based IEEE MTT-S Int. Microw. Symp. Dig., Tampa, FL, USA, Jun. 2014, pp. 1–4. on electric-LC (ELC) loaded microstrip lines,’’ IEEE Sensors J., vol. 14, [23] L. Su, J. Naqui, J. Mata-Contreras, and F. Martín, ‘‘Modeling metamaterial no. 4, pp. 939–940, Apr. 2014. transmission lines loaded with pairs of coupled split ring resonators,’’ IEEE [43] A. K. Horestani, J. Naqui, D. Abbott, C. Fumeaux, and F. Martín, ‘‘Two- Antennas Wireless Propag. Lett., vol. 14, pp. 68–71, 2015. dimensional displacement and alignment sensor based on reflection coeffi- [24] L. Su, J. Naqui, J. Mata-Contreras, and F. Martín, ‘‘Modeling and appli- cients of open microstrip lines loaded with split ring resonators,’’ Electron. cations of metamaterial transmission lines loaded with pairs of coupled Lett., vol. 50, no. 8, pp. 620–622, Apr. 2014. complementary split ring resonators (CSRRs),’’ IEEE Antennas Wireless [44] A. Ebrahimi, W. Withayachumnankul, S. F. Al-Sarawi, and D. Abbott, Propag. Lett., vol. 15, pp. 154–157, 2016. ‘‘Metamaterial-inspired rotation sensor with wide dynamic range,’’ IEEE [25] J. Naqui, C. Damm, A. Wiens, R. Jakoby, L. Su, J. Mata-Contreras, and Sensors J., vol. 14, no. 8, pp. 2609–2614, Aug. 2014. F. Martín, ‘‘Transmission lines loaded with pairs of stepped impedance [45] J. Naqui, J. Coromina, B. Karami-Horestani, C. Fumeaux, and F. Martín, resonators: Modeling and application to differential permittivity mea- ‘‘Angular displacement and velocity sensors based on coplanar waveguides surements,’’ IEEE Trans. Microw. Theory Techn., vol. 64, no. 11, (CPWs) loaded with S-shaped split ring resonator (S-SRR),’’ Sensors, pp. 3864–3877, Nov. 2016. vol. 15, no. 5, pp. 9628–9650, 2015. [26] L. Su, J. Mata-Contreras, P. Vélez, and F. Martín, ‘‘Splitter/combiner [46] J. Mata-Contreras, C. Herrojo, and F. Martín, ‘‘Application of split microstrip sections loaded with pairs of complementary split ring res- ring resonator (SRR) loaded transmission lines to the design of onators (CSRRs): Modeling and optimization for differential sensing angular displacement and velocity sensors for space applications,’’ applications,’’ IEEE Trans. Microw. Theory Techn., vol. 64, no. 12, IEEE Trans. Microw. Theory Techn., vol. 65, no. 11, pp. 4450–4460, pp. 4362–4370, Dec. 2016. Nov. 2017. 62610 VOLUME 10, 2022 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR [47] J. Mata-Contreras, C. Herrojo, and F. Martín, ‘‘Detecting the rotation [66] M. Abdolrazzaghi, M. Daneshmand, and A. K. Iyer, ‘‘Strongly enhanced direction in contactless angular velocity sensors implemented with rotors sensitivity in planar microwave sensors based on metamaterial coupling,’’ loaded with multiple chains of split ring resonators (SRRs),’’ IEEE Sensors IEEE Trans. Microw. Theory Techn., vol. 66, no. 4, pp. 1843–1855, J., vol. 18, no. 17, pp. 7055–7065, Sep. 2018. Apr. 2018. [48] J. Munoz-Enano, P. Velez, L. Su, M. Gil, P. Casacuberta, and F. Martin, [67] M. Abdolrazzaghi and M. Daneshmand, ‘‘Exploiting sensitivity enhance- ‘‘On the sensitivity of reflective-mode phase-variation sensors based on ment in micro-wave planar sensors using intermodulation products with open-ended stepped-impedance transmission lines: Theoretical analysis phase noise analysis,’’ IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 67, and experimental validation,’’ IEEE Trans. Microw. Theory Techn., vol. 69, no. 12, pp. 4382–4395, Dec. 2020. no. 1, pp. 308–324, Jan. 2021. [68] A. M. Albishi, M. K. E. Badawe, V. Nayyeri, and O. M. Ramahi, ‘‘Enhanc- [49] L. Su, J. Munoz-Enano, P. Velez, P. C. Orta, M. Gil, and F. Martin, ing the sensitivity of dielectric sensors with multiple coupled complemen- ‘‘Highly sensitive phase variation sensors based on step-impedance copla- tary split-ring resonators,’’ IEEE Trans. Microw. Theory Techn., vol. 68, nar waveguide (CPW) transmission lines,’’ IEEE Sensors J., vol. 21, no. 3, no. 10, pp. 4340–4347, Oct. 2020. pp. 2864–2872, Feb. 2021. [50] P. Casacuberta, J. Muñoz-Enano, P. Vélez, L. Su, M. Gil, and F. Martín, ‘‘Highly sensitive reflective-mode defect detectors and dielectric constant sensors based on open-ended stepped-impedance transmission lines,’’ Sen- sors, vol. 20, no. 21, p. 6236, Oct. 2020. PAU CASACUBERTA was born in Sabadell [51] L. Su, J. Muñoz-Enano, P. Vélez, M. Gil-Barba, P. Casacuberta, and (Barcelona), Spain, in 1997. He received the F. Martín, ‘‘Highly sensitive reflective-mode phase-variation permittiv- bachelor’s degree in electronic telecommunica- ity sensor based on a coplanar waveguide (CPW) terminated with an tions engineering and computer engineering from open complementary split ring resonator (OCSRR),’’ IEEE Access, vol. 9, the Universitat Autònoma de Barcelona (UAB), pp. 27928–27944, 2021. in 2020, where he is currently pursuing the mas- [52] J. Coromina, J. Munoz-Enano, P. Velez, A. Ebrahimi, J. Scott, K. Ghorbani, ter’s degree in telecommunications engineering. and F. Martin, ‘‘Capacitively-loaded slow-wave transmission lines for In 2019, he received the Collaboration Fellowship sensitivity improvement in phase-variation permittivity sensors,’’ in Proc. by the Spanish Government for developing his 50th Eur. Microw. Conf. (EuMC), Utrecht, The Netherlands, Jan. 2021, bachelor’s thesis in highly sensitive microwave pp. 491–494. sensors-based in stepped impedance structures. He is currently working in [53] A. Ebrahimi, J. Coromina, J. Munoz-Enano, P. Velez, J. Scott, K. Ghorbani, the elaboration of his Ph.D. degree, which is focused on the development and F. Martin, ‘‘Highly sensitive phase-variation dielectric constant sensor of microwave sensors for the characterization of the composition of multi- based on a capacitively-loaded slow-wave transmission line,’’ IEEE Trans. component liquid substances with a research grant from FPU Program of the Circuits Syst. I, Reg. Papers, vol. 68, no. 7, pp. 2787–2799, Jul. 2021. Universities Spanish Ministry. [54] J. Munoz-Enano, P. Velez, L. Su, M. Gil-Barba, and F. Martin, ‘‘A reflective-mode phase-variation displacement sensor,’’ IEEE Access, vol. 8, pp. 189565–189575, 2020. [55] A. K. Jha, A. Lamecki, M. Mrozowski, and M. Bozzi, ‘‘A highly sensi- tive planar microwave sensor for detecting direction and angle of rota- PARIS VÉLEZ (Senior Member, IEEE) was born tion,’’ IEEE Trans. Microw. Theory Techn., vol. 68, no. 4, pp. 1598–1609, in Barcelona, Spain, in 1982. He received the Apr. 2020. bachelor’s degree in telecommunications engi- [56] A. K. Horestani, Z. Shaterian, and F. Martin, ‘‘Rotation sensor based on the neering, specializing in electronics, the master’s cross-polarized excitation of split ring resonators (SRRs),’’ IEEE Sensors degree in electronics engineering, and the Ph.D. J., vol. 20, no. 17, pp. 9706–9714, Sep. 2020. degree in electrical engineering from the Universi- [57] N. Kazemi, K. Schofield, and P. Musilek, ‘‘A high-resolution reflective tat Autònoma de Barcelona, Spain, in 2008, 2010, microwave planar sensor for sensing of vanadium electrolyte,’’ Sensors, and 2014, respectively. His Ph.D. thesis concerned vol. 21, no. 11, p. 3759, May 2021. common mode suppression differential microwave [58] A. Velez, F. Aznar, J. Bonache, M. C. Velazquez-Ahumada, J. Martel, and circuits based on metamaterial concepts and semi- F. Martin, ‘‘Open complementary split ring resonators (OCSRRs) and their lumped resonators. During the Ph.D. degree, he was awarded with a application to wideband CPW band pass filters,’’ IEEE Microw. Wireless pre-doctoral teaching and research fellowship by the Spanish Government, Compon. Lett., vol. 19, no. 4, pp. 197–199, Apr. 2009. from 2011 to 2014. From 2015 to 2017, he was involved in the subjects [59] M. Durán-Sindreu, F. Aznar, A. Vélez, J. Bonache, and F. Martín, ‘‘Anal- related to metamaterials sensors for fluidics detection and characterization ysis and applications of OSRR- and OCSRR-loaded transmission lines: at LAAS-CNRS through a TECNIOSpring Fellowship co-founded by the A new path for the design of compact transmission line metamaterials,’’ Marie Curie Program. From 2018 to 2020, he was worked in miniaturization Metamaterials, vol. 4, nos. 2–3, pp. 139–148, Aug. 2010. of passive circuits RF/microwave and sensors-based metamaterials through [60] M. Makimoto and S. Yamashita, ‘‘Compact bandpass filters using Juan de la Cierva Fellowship. His current research interests include the stepped impedance resonators,’’ Proc. IEEE, vol. 67, no. 1, pp. 16–19, Jan. 1979. miniaturization of passive circuits RF/microwave and sensors-based meta- [61] M. Makimoto and S. Yamashita, ‘‘Bandpass filters using parallel coupled materials. He is a Reviewer of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and for other journals. stripline stepped impedance resonators,’’ IEEE Trans. Microw. Theory Techn., vol. MTT-28, pp. 1413–1417, 1980. [62] J. Naqui, M. Durán-Sindreu, J. Bonache, and F. Martín, ‘‘Implementation of shunt connected series resonators through stepped-impedance shunt stubs: Analysis and limitations,’’ IET Microw., Antennas Propag., vol. 5, JONATHAN MUÑOZ-ENANO (Graduate Stu- pp. 1336–1342, Aug. 2011. dent Member, IEEE) was born in Mollet del Vallès [63] D. M. Pozar, Microwave Engineering, 4th ed. Hoboken, NJ, USA: Wiley, (Barcelona), Spain, in 1994. He received the bach- 2011. elor’s degree in electronic telecommunications [64] G. Galindo-Romera, F. J. Herraiz-Martínez, M. Gil, engineering and the master’s degree in telecommu- J. J. Martínez-Martínez, and D. Segovia-Vargas, ‘‘Submersible printed nications engineering from the Autonomous Uni- split-ring resonator-based sensor for thin-film detection and permittivity characterization,’’ IEEE Sensors J., vol. 16, no. 10, pp. 3587–3596, versity of Barcelona (UAB), in 2016 and 2018, May 2016. respectively. Actually, he is currently working with [65] J. Muñoz-Enano, J. Martel, P. Vélez, F. Medina, L. Su, and F. Martín, UAB in the elaboration of his Ph.D. degree, which ‘‘Parametric analysis of the edge capacitance of uniform slots and applica- is focused on the development of microwave sen- tion to frequency-variation permittivity sensors,’’ Appl. Sci., vol. 11, no. 15, sors based on metamaterials concepts for the dielectric characterization of p. 7000, Jul. 2021. materials and biosensors. VOLUME 10, 2022 62611 P. Casacuberta et al.: Circuit Analysis of a CPW Terminated With a SIR LIJUAN SU (Member, IEEE) was born in FERRAN MARTÍN (Fellow, IEEE) was born in Qianjiang (Hubei), China, in 1983. She received Barakaldo (Vizcaya), Spain, in 1965. He received the B.S. degree in communication engineering and the B.S. degree in physics from the Universitat the M.S. degree in circuits and systems from the Autònoma de Barcelona (UAB), in 1988, and the Wuhan University of Technology, Wuhan, China, Ph.D. degree, in 1992. in 2005 and 2013, respectively, and the Ph.D. From 1994 to 2006, he was an Associate degree in electronic engineering from the Univer- Professor in electronics with the Departament sitat Autònoma de Barcelona, Barcelona, Spain, d’Enginyeria Electrònica (Universitat Autònoma in 2017. From November 2017 to December 2019, de Barcelona), and since 2007, he has been a Full she worked as a Postdoctoral Researcher with Professor in electronics. In recent years, he has the Flexible Electronics Research Center, Huazhong University of Science been involved in different research activities, including modeling and simula- and Technology, Wuhan. She is currently a Postdoctoral Researcher with tion of electron devices for high frequency applications, millimeter wave and CIMITEC, Universitat Autònoma de Barcelona. Her current research inter- THz generation systems, and the application of electromagnetic bandgaps ests include the development of novel microwave sensors with improved to microwave and millimeter wave circuits. He is currently very active performance for biosensors, dielectric characterization of solids and liquids, in the field of metamaterials and their application to the miniaturization defect detection, and industrial processes. and optimization of microwave circuits and antennas. He is currently the Head of the Microwave Engineering, Metamaterials and Antennas Group (GEMMA Group), UAB, and the Director of CIMITEC, a Research Center MARTA GIL BARBA (Member, IEEE) was born on Metamaterials supported by TECNIO (Generalitat de Catalunya). He has in Valdepeñas, Ciudad Real, Spain, in 1981. She organized several international events related to metamaterials and related received the degree in physics from the Univer- topics, including Workshops at the IEEE International Microwave Sympo- sidad de Granada, Spain, in 2005, and the Ph.D. sium, in 2005 and 2007, and European Microwave Conference, in 2009, degree in electronic engineering from the Univer- 2015, and 2017, and the Fifth International Congress on Advanced Electro- sitat Autònoma de Barcelona, Barcelona, Spain, magnetic Materials in Microwaves and Optics (Metamaterials 2011), where in 2009. She studied one year with Friedrich he acted as the Chair of the Local Organizing Committee. He has acted as Schiller Universität Jena, Jena, Germany. During the Guest Editor for six Special Issues on metamaterials and sensors in five her Ph.D. thesis, she was a Holder of a META- international journals. He has authored and coauthored over 650 technical MORPHOSE NoE Grant and National Research conference, letter, journal articles, and book chapters. He is the coauthor of Fellowship from the FPU Program of the Education and Science Spanish the book on Metamaterials entitled Metamaterials with Negative Parameters: Ministry. As a Postdoctoral Researcher, she was awarded with a Juan de la Theory, Design and Microwave Applications (John Wiley & Sons Inc.), the Cierva Fellowship working with the Universidad de Castilla-La Mancha. She author of the book Artificial Transmission Lines for RF and Microwave was a Postdoctoral Researcher with the Institut für Mikrowellentechnik und Applications (John Wiley & Sons Inc.), a Co-Editor of the book Balanced Photonik, Technische Universität Darmstadt, and the Carlos III University of Microwave Filters (Wiley/IEEE Press), and the coauthor of the book Time- Madrid. She is currently an Associate Professor with the Universidad Politéc- Domain Signature Barcodes for Chipless-RFID and Sensing Applications nica de Madrid within the Excellence Program for University Professoriate of (Springer). He has generated 21 Ph.D.’s, has filed several patents on metama- the V Regional Plan for Scientific Research and Technological Innovation (V terials and has headed several development contracts. His research interests PRICIT) of the Administration of the Community of Madrid. She has worked include microwave sensors and RFID systems, with special emphasis on in metamaterials, piezoelectric MEMS, and microwave passive devices. Her the development of high data capacity chipless-RFID tags. He is a member current interest includes metamaterials sensors for fluidic detection. of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S). He is a Reviewer of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND AMIR EBRAHIMI (Member, IEEE) received TECHNIQUES and IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, and the B.Sc. degree in electrical engineering, in 2008, among many other journals. He serves as a member for the Editorial Board the M.Sc. degree in microelectronics, in 2011, of IET Microwaves, Antennas and Propagation, International Journal of and the Ph.D. degree from The University of RF and Microwave Computer-Aided Engineering, and Sensors. He was a Adelaide, Adelaide, SA, Australia, in 2016. recipient of three ICREA ACADEMIA Awards (calls 2008, 2013, and 2018). From 2014 to 2015, he was a Visiting Research He is a fellow of the IET. He is also a member of the Technical Committees of Fellow with Nanyang Technological University the European Microwave Conference (EuMC) and International Congress on (NTU), Singapore. He is currently a Postdoc- Advanced Electromagnetic Materials in Microwaves and Optics (Metamate- toral Researcher with the School of Engineer- rials). Among his distinctions, he has received the 2006 Duran Farell Prize ing, RMIT University, Melbourne, VIC, Australia. for Technological Research, he holds the Parc de Recerca UAB—Santander His research interests include metamaterial inspired microwave devices, Technology Transfer Chair. microwave circuit design, microwave filters, frequency-selective sur- faces (FSSs) and nonlinear RF, and microwave circuits design and analysis. He was a recipient of the Australian National Fabrication Facility (ANFF) Award, in 2013, the University of Adelaide D. R. Stranks Traveling Fellow- ship, in 2014, the Yarman–Carlin Best Student Paper Award at the Mediter- ranean Microwave Symposium, in 2015, the Simon Rockliff Scholarship, in 2016, the Best Paper Award at the Australian Microwave Symposium, in 2016, Gertrude Rohan Memorial Prize, in 2017, and the CASS Foundation Travel Award, in 2019. He is a Reviewer for several recognized interna- tional journals, such as the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATIONS, and the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS. 62612 VOLUME 10, 2022