applied sciences Review Planar Microwave Resonant Sensors: A Review and Recent Developments Jonathan Muñoz-Enano 1, * , Paris Vélez 1 , Marta Gil 2 and Ferran Martín 1 1 CIMITEC, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain; paris.velez@uab.cat (P.V.); ferran.martin@uab.es (F.M.) 2 Departamento de Ingeniería Audiovisual y Comunicaciones, Universidad Politécnica de Madrid, 28031 Madrid, Spain; Marta.Gil.Barba@upm.es * Correspondence: Jonatan.Munoz@uab.cat  Received: 2 March 2020; Accepted: 7 April 2020; Published: 10 April 2020  Abstract: Microwave sensors based on electrically small planar resonant elements are reviewed in this paper. By virtue of the high sensitivity of such resonators to the properties of their surrounding medium, particularly the dielectric constant and the loss factor, these sensors are of special interest (although not exclusive) for dielectric characterization of solids and liquids, and for the measurement of material composition. Several sensing strategies are presented, with special emphasis on differential-mode sensors. The main advantages and limitations of such techniques are discussed, and several prototype examples are reported, mainly including sensors for measuring the dielectric properties of solids, and sensors based on microfluidics (useful for liquid characterization and liquid composition). The proposed sensors have high potential for application in real scenarios (including industrial processes and characterization of biosamples). Keywords: microwave sensor; differential sensor; dielectric characterization; microfluidics; electrically small resonators; biosensors 1. Introduction Within the paradigm of the internet of things (IoT), or more generally the internet of everything (IoE), and the advent of the fourth industrial revolution (also known as Industry 4.0), the use of sensors has experienced an exponential growth. Moreover, this trend will continue with the progressive implantation of the 5th generation of mobile networks, designated as 5G, which is expected to satisfy the large-scale connectivity requirements that today’s modern society demands (an interesting example is the autonomous and connected vehicle, necessarily equipped with hundreds of sensors). There are many available technologies for the implementation of sensors. Aspects such as diverse as sensor cost, size, and complexity, as well as the type of measurand, among others, dictate the preferred option. Although the most extended technology in modern sensors is probably optics/photonics (examples include optical fiber sensors, laser-based sensors, wearable chemical and biological sensors, nanophotonic biosensors, image sensors, etc.), significant efforts have been dedicated in recent years to the research and development of microwave sensors, especially for applications related to material characterization and composition. Microwaves are very sensitive to the properties of the materials to which they interact. Therefore, microwave technology is very useful for material sensing. Moreover, microwaves exhibit further interesting properties for sensing, such as low-cost generation and detection systems, interaction to the materials at different scales (i.e., through the near-field or the far-field), compatibility with planar technology, wireless connectivity, and robustness against harsh environments, among others. Thus, highly sensitive, robust, low cost, small size, and low-profile microwave sensors and wireless sensors based on the above-cited properties can be implemented. Appl. Sci. 2020, 10, 2615; doi:10.3390/app10072615 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 2615 2 of 30 This review paper focuses on microwave sensors, and particularly on planar sensors based on resonant elements for material characterization, including solids or liquids. Planar sensors are of special interest as their low-profile is compatible with many applications, where bulk sensors (e.g., cavity sensors or waveguide-based sensors [1,2], among others) may find a severe limitation, e.g., conformal sensors [3], wearable sensors [4], submersible sensors [5], integrated sensors [6], lab-on-a-chip sensors [7], microfluidic sensors [8–11], etc. On the other hand, despite the fact that non-resonant planar sensors operating at microwave frequencies have been reported [12–14], the combination of sensor size and performance (sensitivity) of resonant-type sensor is difficult to achieve with non-resonant methods. Finally, to end this introductory section, let us mention that although probably most planar microwave resonant sensors have been devoted to material characterization (the main interest in this review paper, to be discussed in detail later), there are many reported realizations focused on motion control applications (linear and angular displacement and velocity measurements) [15–30]. 2. Classification of Planar Microwave Resonant Sensors The classification subject of this section obeys the operating principle of the considered sensors (alternatively, sensors can be categorized by their applications, or frequency range, etc.). Thus, according to their working principle, planar resonant sensors can be divided in four main types: (i) frequency variation sensors, (ii) coupling modulation sensors, (iii) frequency splitting sensors, and (iv) differential-mode sensors. Let us briefly describe their working principle in the next paragraphs. Frequency variation sensors are based on the variation of the resonance frequency (and eventually quality factor or peak/notch magnitude) of a resonant element, caused by the measurand. The typical, although not exclusive, configuration of such sensors is a transmission line loaded with the resonant element (either in contact or coupled to it), see Figure 1a. Although examples of frequency variation sensors devoted to the measurement of spatial variables have been reported [15], typically these sensors have been applied to dielectric characterization of solids and liquids [31–46], as far as the resonance frequency and quality factor depend on the complex dielectric constant of the surrounding material (the so-called material under test (MUT)). These sensors are very simple, but they are potentially subjected to cross-sensitivities caused by variations in ambient factors, such as temperature and humidity, and therefore they need calibration before their use. To alleviate or minimize the impact of cross-sensitivities, symmetry-based sensors are the solution [47]. As symmetry is invariant under potential changes in environmental factors, at least at the typical scales of the sensors, it is expected that sensors based on symmetry properties exhibit certain robustness against environment-related cross-sensitivities. Coupling modulation sensors belong to this category [16–27,48]. Such sensors are implemented by symmetrically loading a transmission line by means of a symmetric resonator (Figure 1b). However, the combination of line and resonant element should not be arbitrary. Namely, it is necessary that the symmetry plane of the resonator and the one of the line are of different electromagnetic sort, i.e., one must be an electric wall and the other one must be a magnetic wall. By this means, if symmetry is preserved, line-to-resonator coupling is prevented [47], the resonator is not excited, and the line is transparent, i.e., the frequency response does not exhibit any notch (lack of resonance). However, by truncating symmetry (e.g., by means of an asymmetric dielectric loading or through a relative linear or angular displacement between the line and the resonant element), line-to-resonator coupling arises and, consequently, the resonance appears. The magnitude of the notch (the typical output variable) is determined by the coupling degree, intimately related to the level of the asymmetry. Thus, coupling modulation by symmetry disruption is useful for sensing purposes. Nevertheless, as the most natural procedure for symmetry truncation is by a relative displacement between the resonator and the line, most sensors based on this principle have been devoted to angular and linear measurements [16–27,48]. For such application, the most limitative aspect of these sensors is the input dynamic range, related to the small dimensions of the sensing resonators. A variant of this approach, providing the solution to such limitation, was presented in [28–30], where circular chains of resonant elements were applied to the implementation Appl. Sci. 2020, 10, 2615 3 of 30 of microwave rotary encoders based on pulse counting (linear encoders, potentially exhibiting an unlimited dynamic range, were also presented in [49,50]). Another drawback of these sensors is related to the fact that measuring the notch magnitude is more sensitive to the effects of noise, as compared to frequency measurements. However, a small frequency scan, or even a single-frequency measurement, suffices to collect the sensor information. Frequency splitting sensors combine the advantages of frequency measurements (noise tolerant) and symmetry properties (robustness against cross-sensitivities) [24,51–59]. In these sensors, a symmetric transmission line-based structure is symmetrically loaded with a pair of (not necessarily symmetric) resonators (Figure 1c). If symmetry is preserved, a single notch in the transmission coefficient arises. However, if symmetry is truncated, e.g., by an asymmetric dielectric loading, the original notch splits in two notches separated a distance that depends on the level of asymmetry. Thus, in frequency splitting sensors, the output variable is such frequency separation, and, eventually, the difference in the notch magnitude (two variables are needed, for instance, for the measurement of the dielectric constant and loss tangent of materials [56,58]). A potential weakness of these sensors is the limited sensitivity and resolution if the resonant elements are coupled [51,52,55]. Nevertheless, solutions to this problem have been reported, as discussed in [56,57], at the expense of significantly separating the sensing resonators (either by using a splitter/combiner scheme [57,58] or a cascaded topology [56]). Although these sensors are not true differential sensors (in the sense that two independent sensors are not used), the input and the output variable are typically differential variables. The differential dielectric constant or loss tangent (between a reference (REF) sample, or material, and the material under test (MUT)) is the usual input variable, whereas the differential notch frequency and/or magnitude is the natural output variable/s. Moreover, frequency splitting sensors can be easily used as comparators, as they are able to detect differences between the REF and MUT samples. For this application, sensor resolution is the key aspect. However, in terms of resolution, such sensors cannot compete, in general, against true differential sensors, to be discussed next. Differential-mode sensors also belong to the group of symmetry-based sensors. Such devices are composed of two independent sensors, one sensitive to the REF sample (or measurand in general), and the other one sensitive to the MUT sample (Figure 1d). These sensors can operate as single-ended sensors as well, e.g., based on frequency variation, where only one of the individual sensing elements is used. However, exploiting the differential input and output variable/s provides robustness against cross-sensitivities. As far as independent sensing elements are used, the abovementioned coupling effects, which typically limit the resolution, can be prevented in differential sensors. The output variable in these sensors is merely the difference between the output variable of each sensing element. It has been demonstrated that highly sensitive differential sensors for dielectric constant measurements can be implemented by means of a pair of meander lines. These sensors are based on the measurement of the phase difference between the pair of lines, and the penalty to achieve high sensitivity is sensor size [14]. Nevertheless, it has been demonstrated that by replacing the meander lines with artificial lines, sensitivity optimization can be made compatible with moderate or even small sizes [12,60]. Many differential sensors based on resonator-loaded lines (the interest in this work) have been reported, including microfluidic sensors for liquid characterization [61–67]. In some realizations, the output variable is the cross-mode transmission coefficient [62–67], proportional to the difference between the transmission coefficients of both sensing lines, provided such lines are uncoupled. Huge sensitivities and resolutions, useful to detect, e.g., small volume fractions or electrolyte concentrations in liquid solutions, have been achieved by means of these sensors. Although, typically, differential-mode sensors involve four-port measurements (these sensors are four-port devices), it has been demonstrated that by adding extra (microwave) circuitry, differential sensing by means of two-port devices (and measurements) can be achieved [68,69]. In [69], the differential sensor works in reflection (other reflective-mode sensors have been reported [70], also including single-ended sensors [71]). The sensor reported in [72] is also remarkable, where symmetry truncation in a pair of slotted resonators generates quasi-microstrip to slot-mode conversion, useful for sensing. Appl. Sci. 2020, 10, 2615 4 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 30 Although examples of the different sensor types highlighted in this section will be provided, the mainAlthough emphasis examples of the different in this paper sensor types highlighted is on differential-mode in this sensors. section will before Nevertheless, be provided, the the reviewing main emphasis in this paper is on differential-mode sensors. Nevertheless, before reviewing different implementations, let us first present the potential candidates for resonant sensing elements, the different implementations, let us first present the potential candidates for resonant sensing elements, and discuss their advantages and disadvantages. and discuss their advantages and disadvantages. (a) (b) (c) (d) Figure Figure 1. Typical 1. Typical topology topology andand working working principle principle of the of the considered considered planar planar microwave microwave resonant resonant sensors. sensors. (a) Frequency variation; (b) coupling modulation; (c) frequency splitting; (d) differential- (a) Frequency variation; (b) coupling modulation; (c) frequency splitting; (d) differential-mode. mode. 3. Planar Resonant Elements for Sensing 3. Planar Resonant Elements for Sensing There are dozens of planar resonant elements that can be useful for sensing purposes. In this There are dozens of planar resonant elements that can be useful for sensing purposes. In this paper, the interest is in electrically small (quasi-lumped) resonators that can be described by means of paper, the interest is in electrically small (quasi-lumped) resonators that can be described by means a lumped-element of a lumped-element equivalent equivalentcircuit model circuit modelupup to frequenciesbeyond to frequencies beyond theirtheir fundamental fundamental resonance resonance (the (the authors recommend the books [73,74], and the paper [75], where a authors recommend the books [73,74], and the paper [75], where a review of many of these review of many of these resonators is carried out). Probably the simplest classification of such resonators resonators is carried out). Probably the simplest classification of such resonators can be made by can be made by differentiating differentiatingonon whether whetherthey theyare aremetallic orslot metallic or slotresonators. resonators. In In thethe firstfirst group, group, resonant resonant elements elements of interest of interest forfor sensinginclude sensing include the thestep stepimpedance impedance resonator (SIR) [76], resonator (SIR)the stepthe [76], impedance shunt stub shunt step impedance stub(SISS) (SISS)[77], [77],the thesplit-ring resonator split-ring resonator (SRR) [78],[78], (SRR) the the open split-ring open resonator split-ring (OSRR) resonator [79], and (OSRR) [79],the and the electric-LC (ELC) resonator [80], among others (see Figure 2). Slot resonators electric-LC (ELC) resonator [80], among others (see Figure 2). Slot resonators are typically etchedare typically etched in in the ground plane and are sometimes designated as defect ground structure (DGS) resonators. Examples of such resonators include the complementary counterparts of the SRR and the OSRR, that is, the Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 30 Appl. Sci. 2020, 10, 2615 5 of 30 the ground plane and are sometimes designated as defect ground structure (DGS) resonators. Examples of such resonators include the complementary counterparts of the SRR and the OSRR, that complementary split-ring resonator is, the complementary (CSRR) [81] split-ring resonator and[81] (CSRR) the and openthecomplementary split-ring open complementary resonator split-ring (OCSRR) [82], respectively, the dumbbell-shaped DGS (DB-DGS) resonator [83], and resonator (OCSRR) [82], respectively, the dumbbell-shaped DGS (DB-DGS) resonator [83], and the the magnetic-LC (MLC) resonator [84], magnetic-LC (MLC)among others resonator (see [84], Figure among 3). There others are many (see Figure other 3). There areelectrically many othersmall resonators, electrically small the including resonators, including S-shaped-SRR the the [85], S-shaped-SRR [85], the spiral resonator spiral [86], theresonator [86], the non-bi-anisotropic- non-bi-anisotropic-SRR [87] (as well as their SRR [87] (as well counterparts), complementary as their complementary counterparts), the broadside-coupled-SRR the broadside-coupled-SRR [88], etc., but their use[88], foretc., but has sensing their use for been more limited. sensing has been more limited. (a) (b) (c) (d) (e) FigureFigure 2. Typical 2. Typical topology topology of of someelectrically some electrically small small metallic metallicresonators resonatorsuseful for for useful sensing. (a) Step sensing. (a) Step impedance resonator (SIR), (b) step impedance shunt stub (SISS), (c) split-ring resonator (SRR), (d) impedance resonator (SIR), (b) step impedance shunt stub (SISS), (c) split-ring resonator (SRR), (d) open open split-ring resonator (OSRR), (e) electric-LC (ELC). split-ring resonator (OSRR), (e) electric-LC (ELC). (a) (b) (c) (d) FigureFigure 3. Typical 3. Typical topology topology of someofelectrically some electrically small slotsmall slot resonators resonators useful for useful for sensing. (a)sensing. (a) Complementary Complementary split-ring split-ring resonator (CSRR), (b)resonator (CSRR), (b) open open complementary complementary split-ring split-ring resonator (OCSRR), resonator (OCSRR), (c) dumbbell-shaped (c) dumbbell-shaped DGS (DB-DGS), (d) magnetic-LC (MLC). DGS (DB-DGS), (d) magnetic-LC (MLC). A comparative A comparative analysis analysis ofofelectrically electrically small small resonators, resonators,with withthethefocus focuson onmetamaterial metamaterialand and metamaterial-inspired circuit design, was carried out in [75]. For sensing, the most important aspect metamaterial-inspired circuit design, was carried out in [75]. For sensing, the most important aspect is is the effect of resonator topology on sensor performance, mainly sensitivity, resolution, and dynamic the effect of resonator topology on sensor performance, mainly sensitivity, resolution, and dynamic range. Nevertheless, compatibility of the sensing element (resonator), including the dielectric load, range. Nevertheless, compatibility of the sensing element (resonator), including the dielectric load, with the required hardware and mechanical parts of the sensor is also important. For instance, for with microfluidic the requiredapplications, hardware and mechanical the fluidic channels parts plusofthethe sensormechanical required is also important. accessoriesFor instance, should not for microfluidic affect theapplications, transmission linesthe fluidic used forchannels resonator’s plus the required excitation. mechanical In this regard, accessories slot resonators should not constitute, affectinthe transmission general, lines used a good solution, forground as the resonator’s excitation. plane provides In thisisolation, backside regard, thereby slot resonators preventingconstitute, for any potential effect of the dielectric load on sensor functionality. The size of in general, a good solution, as the ground plane provides backside isolation, thereby preventing for the resonant element may be also any potential important effect of theindielectric certain applications devotedfunctionality. load on sensor to the characterization The size of small of thedielectric resonant loads. element may be also important in certain applications devoted to the characterization of smallofdielectric Obviously, increasing the frequency is a possibility, but this has the effect of raising the cost the associated electronics. Therefore, considering resonant elements with small electrical size is expected loads. Obviously, increasing the frequency is a possibility, but this has the effect of raising the cost to provide a good tradeoff, allowing for the implementation of compact sensors (sensitive element) of the associated electronics. Therefore, considering resonant elements with small electrical size is operating at moderate (or even low) frequencies. In this regard, the OSRR and the OCSRR are expected to provide a good tradeoff, allowing for the implementation of compact sensors (sensitive electrically smaller than the SRR and the CSRR, respectively, by a factor of two [74,89], and are element) operating therefore at moderate good candidates from(ortheeven pointlow) frequencies. of view In this regard, the OSRR and the OCSRR of sensor size. are electrically Concerning sensitivity and resolution (intimately related), it isby smaller than the SRR and the CSRR, respectively, a factor difficult of twoestablish to firmly [74,89], the and are therefore goodresonator preferred candidates from the topology, as point it mayofbeview of sensor determined bysize. several aspects, including the sensing working principle, Concerning the considered sensitivity and resolutioninput and output variables, (intimately related), etc. it isFor instance, difficult to for complex firmly establish the preferred resonator topology, as it may be determined by several aspects, including the sensing working principle, the considered input and output variables, etc. For instance, for complex permittivity measurements, both the real and the imaginary part of the complex permittivity (input variables) must be determined, and two output variables (e.g., the frequency position and notch magnitude) are needed to unequivocally infer both measurands. For this kind of application, with more than one input Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 30 permittivity measurements, both the real and the imaginary part of the complex permittivity (input variables) must be determined, and two output variables (e.g., the frequency position and notch Appl. Sci. 2020, 10, 2615 6 of 30 magnitude) are needed to unequivocally infer both measurands. For this kind of application, with more than one input variable (or measurand), several sensitivities, including cross-sensitivities, can be defined, variable (or and this further measurand), prevents several from obtaining sensitivities, concluding including remarks with cross-sensitivities, regard can to the effects be defined, and this of resonator further topology prevents fromonobtaining sensitivityconcluding and resolution. However, remarks the real with regard parteffects to the of theofcomplex resonator permittivity topology (or the dielectric constant) of the MUT mainly affects the resonance frequency on sensitivity and resolution. However, the real part of the complex permittivity (or the dielectricof the sensing element (through the constant) effects of the MUTonmainlythe capacitance), whereas the affects the resonance imaginary frequency partsensing of the (relatedelement to the loss tangent) (through the primarily effects affects on the the quality capacitance), factorthe whereas or imaginary the notch magnitude. part (related For a given to the resonator, loss tangent) the strategy primarily for affects the optimizing such “natural sensitivities” (in terms of geometry) typically coincides quality factor or the notch magnitude. For a given resonator, the strategy for optimizing such “natural(e.g., for the OCSRR and dumbbell-DGS, sensitivities” (in terms asofit geometry) was demonstrated typicallyincoincides [62,64], respectively). (e.g., for the OCSRR and dumbbell-DGS, as it It is difficult, however, to was demonstrated in [62,64], respectively).determine absolutely the optimum resonator (among those depicted in Figure 2) in terms of sensitivity (and resolution) optimization. It is difficult, however, to determine absolutely the optimum resonator Nonetheless, to thedepicted (among those light ofina comparative Figure analysis 2) in terms of the circuit of sensitivity model of the (and resolution) consideredNonetheless, optimization. resonators, toit is thepossible light of atocomparative infer some helpful hints. As an example, let us compare three slot resonators: the CSRR, analysis of the circuit model of the considered resonators, it is possible to infer some helpful the OCSRR, and thehints. DB- DGS. The circuit models of such resonant elements loading a transmission line are As an example, let us compare three slot resonators: the CSRR, the OCSRR, and the DB-DGS. The circuit depicted in Figure 4. models of such resonant elements loading a transmission line are depicted in Figure 4. P1 P2 P1 P2 (a) (b) P1 P2 (c) Figure 4. Circuit models of the CSRR- (a), OCSRR- (b), and DB-DGS-loaded line line (c). (c). Let Let us us assume assumethatthatthe theresonant resonant element element (the sensing (the part) sensing is loaded part) withwith is loaded a dielectric material a dielectric slab material (MUT) of sufficient thickness to ensure that the field lines generated in the slot do not slab (MUT) of sufficient thickness to ensure that the field lines generated in the slot do not reach the reach the opposite interface, and let us and opposite interface, consider let usthat the substrate consider that thethickness substratesatisfies also satisfies thickness this requirement. If these sensors also this requirement. If are intended these sensorstoarework basedtoonwork intended frequency based variation, on frequency the variation, key figuretheof merit is theof key figure relative merit issensitivity of the relative the resonance sensitivity frequency, of the resonance f 0 , frequency, with the dielectric f0, with constant of the the dielectric MUT, εof constant the MUT , given MUT,by εMUT, given by 11 𝑑𝑓d f00 S 𝑆== 𝑓 𝑑  (1) (1) f00 dεMUT 𝑀𝑈𝑇 where the resonance frequency is given by where the resonance frequency is given by 1 𝑟 + 𝑀𝑈𝑇 −1/2 𝑓𝑜 = 1 {𝐿 (𝐶 + 𝐶𝑐 ε + ε )} −1/2 (2) fo = 2 L C + Cc 𝑟 + 1 r MUT (2) 2π εr + 1 Expression (2) is valid for the CSRR-loaded line, whereas for the OCSRR- and the DB-DGS- loadedExpression line, the(2) is valid expression previous for the CSRR-loaded is valid byline, whereasC,for skipping thethe OCSRR-capacitance coupling and the DB-DGS-loaded between the line, line, theandprevious expression the CSRR. The unloaded skipping C,are is valid byresonators thedescribed coupling capacitance between the by the capacitance Cc line, and and by the CSRR. inductanceThe unloaded resonators L. Notice that are described if the dielectric by the constant capacitance of the Cc and by MUT is different the the than one of airL.(i.e., inductance Noticeεair that = 1), ifthe the dielectric result constantofofthe is a variation thecapacitance MUT is different than the one of the resonator (andofhence air (i.e., εair in a shift = f1), theexpected. 0), as result is Appl. Sci. 2020, 10, 2615 7 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 30 aInvariation (1), εr is of thethe capacitance dielectric of theofresonator constant (and hence the substrate. Introducing in fin a shift(2) 0 ),(1), as expected. (1), εr is the Insensitivity the relative is dielectric found to beconstant of the substrate. Introducing (2) in (1), the relative sensitivity is found to be 11 𝐶c𝑐 C S 𝑆== −− 2 𝐶 ( +  (3) (3) 𝑀𝑈𝑇 )) + 2 Cc𝑐(εr𝑟+ εMUT C(ε𝑟r + + 𝐶( + 1) 1) In view In view ofof (3), (3), we we can canconclude concludethat thatititisisconvenient convenienttotoreduce reduce CC andandεr εas as muchmuchas possible as possible for r sensitivity optimization. Consequently, the DB-DGS and the OCSRR for sensitivity optimization. Consequently, the DB-DGS and the OCSRR are good candidates for are good candidates for the implementation the implementation of high sensitive of high frequency sensitive variation frequency sensors, variation at leastatasleast sensors, compared to CSRRs. as compared In [90], to CSRRs. it was demonstrated that the relative sensitivity of DB-DGS-loaded lines In [90], it was demonstrated that the relative sensitivity of DB-DGS-loaded lines is better than is better than the onetheof CSRR-loaded lines. To gain further insight on this, we have designed an OCSRR-loaded one of CSRR-loaded lines. To gain further insight on this, we have designed an OCSRR-loaded line line (Figure 5a), and5a), (Figure weandhave we inferred the relative have inferred sensitivity the relative as defined sensitivity as definedin in (1), (1),from fromthethesimulated simulated responses responses obtained by considering MUTs of different dielectric constant. The results, obtained by considering MUTs of different dielectric constant. The results, depicted in depicted in Figure Figure 6,6, and and compared to those reported in [90], confirm that the relative sensitivity of the compared to those reported in [90], confirm that the relative sensitivity of the OCSRR-loaded line is OCSRR-loaded line is comparableto comparable tothe theone oneofofthe theDB-DGS, DB-DGS,asas predicted predicted bybythethe theory. theory. Note Note thatthat oneone difference difference between between the OCSRR- and the CSRR- or the DB-DGS-loaded line is the type of response, with a maximum at f 0at the OCSRR- and the CSRR- or the DB-DGS-loaded line is the type of response, with a maximum forf0 for OCSRR-based the the OCSRR-based line,line, andand notched notched at resonance at resonance for other for the the other lines. lines. 0 0 -1 -2 -10 |S21| (dB) |S11| (dB) -3 -20 -4 -5 -30 -6 EM Simulation -40 -7 Eq. Model -8 -50 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Frequency (GHz) (a) (b) 0 0 -10 -1 |S21| (dB) |S11| (dB) -20 -2 -30 -3 -40 =1 -50 -4 =7 -60 =3 -5 -70 0.5 1.0 1.5 2.0 2.5 Frequency (GHz) (c) Figure 5. Figure 5. Topology of the the designed designed OCSRR-loaded OCSRR-loaded microstrip line (a), frequency frequency response response of of the the structure inferred from circuit and electromagnetic simulation (b), and simulated frequency structure inferred from circuit and electromagnetic simulation (b), and simulated frequency response response for various for various MUTs MUTs withwith the the indicated indicated dielectric dielectric constants (c). Dimensions (in mm) mm) are ext==4,4,c c= = are rext 0.1, 0.1,d d= = 1.81.8 and and = 1.4. s =s 1.4. The considered The considered substrate is the substrate Rogers is the RO4003C Rogers with RO4003C dielectric with constant dielectric constantεr =ε3.55 r = 3.55 and thickness and thickness h = 1.524 h = 1.524 mm. Circuit parameters mm. Circuit are Cc =are parameters 1.23 = 1.23 Cc pF and pF L = and L =nH. 5.1484 The nH. 5.1484 portsThein panel ports (a) in panel can be(a) can be separated separated (if needed(iffor needed for connector connector soldering) soldering) byadding by merely merely50adding 50 Ω Ω access access lines. lines. Appl. Sci. 2020, 10, 2615 8 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 30 Appl. Sci. 2020, 10, x FOR PEER-0.02 REVIEW 8 of 30 CSRR -0.02 -0.04 CSRR -0.04 -0.06 OCSRR S -0.06 OCSRR -0.08 S -0.08 -0.10 DB-DGS EM Simulation Using Eq. (3) -0.10 -0.12 DB-DGS EM Simulation 2 3 4 5 6 7 8Using9Eq. (3)10 MUT -0.12 2 3 4 5 6 7 8 9 10 Figure 6. Relative Figure sensitivity 6. Relative of of sensitivity the OCSRR-loaded the  line, OCSRR-loaded ascompared line, as comparedtoto MUT those those reported reported in [90]. in [90]. 4. Prototype Examples 4. Prototype Examples Figure 6. Relative sensitivity of the OCSRR-loaded line, as compared to those reported in [90]. In thisInsection, several this section, examples several examples of planar microwave of planar microwaveresonant resonant sensors, categorizedaccording sensors, categorized according to 4. Prototype Examples the classification of Section 2, are2, reported. These to the classification of Section are reported. Thesesensors sensors are devotedtotodielectric are devoted dielectric characterization, characterization, with the withexception the In this of the exception section, of coupling the coupling several modulation examples of planarsensor modulation sensor of of Section microwaveSection 4.2,asensors, 4.2, resonant arotary rotaryencoder. encoder. according categorized to the classification of Section 2, are reported. These sensors are devoted to dielectric characterization, 4.1. Frequency with Variation 4.1. Frequency ofSensors Variation the exception theSensors coupling modulation sensor of Section 4.2, a rotary encoder. The example The first first example is aisfrequency a frequency variationsensor variation sensor equipped equipped with witha amicrofluidic microfluidic channel channelfor liquid for liquid 4.1. Frequency Variation Sensors characterization [46]. In this sensor, the sensitive element is a SISS characterization [46]. In this sensor, the sensitive element is a SISS resonator, loading a microstrip resonator, loading a microstrip line.The Thefirst most relevantisaspect line. The most example relevant aspect of of a frequency thisvariation this sensor issensor sensor the high is the high achieved equipped achieved withrelative relativesensitivity, a microfluidic sensitivity, by virtue channel byfor of the liquid virtue of the specific arrangement, characterization [46]. Inwhere the ground this sensor, plane beneath the sensitive element theis SISS a SISS is removed, resonator,and a metallization loading a microstrip is specific arrangement, where the ground plane beneath the SISS is removed, and a metallization is added line. Theonmost the top surface, relevant surrounding aspect of this sensorthe rectangular SISS patch is the high achieved with asensitivity, relative gap of width s (see Figure by virtue of the added7).onSuch the metallization top surface, is surrounding connected the rectangular to the plane backside SISS plane ground patchby with a gapmetallic means of and of width s (see Figure 7). vias. By these specific arrangement, where the ground beneath the SISS is removed, a metallization is Such added metallization means, onthethesingle topissurface, connected capacitance tothe of surrounding theresonant backside ground element the rectangular plane isSISS the edgeby patch means a gapofofmetallic capacitance with the SISS, width vias. which s (see By Figurecanthese means, bethe 7). Suchsingle easily capacitance perturbed metallization byismeans of the connected resonant of theto MUT element (either the backside is the aground solid or aedge plane bycapacitance liquid), placed means on of topthe of metallic of SISS,Bywhich it. Note vias. that can these be easily withperturbed means, this singleby theconfiguration, means anyof capacitance ofthe extra MUT (either thecapacitance resonant thata degrades element solid is the oredge atheliquid), placed sensitivity capacitance on top isofremoved the SISS,of it.Section (see which Note can that 3). easily with this be This sensor configuration, perturbedhas been any by equipped with extraofcapacitance means the MUTa microfluidic that degrades (either a solidchannel, or athe insensitivity orderplaced liquid), to perform topmeasurements isonremoved of it.(see NoteSectionof 3). that the with complex this permittivity configuration, anyof liquids extra (Figure capacitance 8). that degrades the This sensor has been equipped with a microfluidic channel, in order to perform measurements of the sensitivity is removed (see Section 3). This complex sensor hasof permittivity been equipped liquids (Figurewith8). a microfluidic channel, in order to perform measurements of the complex permittivity of liquids (Figure 8). Figure 7. Topology of the SISS-based frequency variation sensor reported in [46], including the top (a) and bottom (b) views, and lumped element equivalent circuit model (c). From [46], reprinted with permission. Figure 7. Topology of the SISS-based frequency variation sensor reported in [46], including the top Figure 7. Topology of the SISS-based frequency variation sensor reported in [46], including the top (a) and bottom (b) views, and lumped element equivalent circuit model (c). From [46], reprinted with (a) and bottom (b) views, and lumped element equivalent circuit model (c). From [46], reprinted permission. with permission. Appl. Sci. 2020, 10, 2615 9 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 30 (a) (b) Figure Figure 8. Schematic views views (a) (a)and andphotographs photographs(b)(b)ofof the the fabricated fabricated sensor, sensor, including including the the top top (left)(left) and and bottom bottom (right) (right) views. views. FromFrom [46],[46], reprinted reprinted withwith permission. permission. The measured frequency The frequencyresponses responsesofofthe thesensor sensorfor fordifferent different mixtures mixtures of of DI DI water waterandand ethanol ethanolare depicted in Figure 9a, whereas Figure 9b shows the resonance frequency are depicted in Figure 9a, whereas Figure 9b shows the resonance frequency position and the position and the magnitude of the notch asof magnitude a function the notchofas thea volume functionfraction of water.fraction of the volume The water–ethanol of water. The solutions offer a wide water–ethanol range solutions offer a wide range of complex permittivity values, which are appropriate for sensor calibration.set of complex permittivity values, which are appropriate for sensor calibration. That is, with this Thatof measurements, a mathematical model for the sensor can be developed. is, with this set of measurements, a mathematical model for the sensor can be developed. Specifically,Specifically, a mathematical arelation linking the mathematical frequency relation linking shift theand the notch frequency magnitude shift and the notch to the magnitude complex relative to thepermittivity of the complex relative permittivity of the test water–ethanol solutions was derived in [46]. As the complex permittivitiesasofa test water–ethanol solutions was derived in [46]. As the complex permittivities of water–ethanol function of the as water–ethanol volume fraction a function can volume of the be independently fraction can inferred, a nonlinear least be independently square inferred, curve fitting a nonlinear in least MATLAB square canfitting curve be used inin order to derive MATLAB can be anused equation in order describing to derivethe anrelation equation between variations describing of the the relation resonancevariations between frequencyofand thenotch magnitude resonance frequencyas a function and notch of the complexas magnitude permittivity a function variations. of the complex In [46], variations. permittivity the authors used the complex permittivity values of water-ethanol mixtures provided in [91]. With In [46], thesuch model, authors used given in [46], the the complex complex values permittivity permittivity of other liquid of water-ethanol solutions mixtures can be provided in inferred from the measured values of the resonance frequency and notch [91]. With such model, given in [46], the complex permittivity of other liquid solutions can be inferred magnitude. For instance, in [46], from thethe authors characterized measured values of the solutions resonanceoffrequency water–methanol. and notch The measured resonance magnitude. For instance,frequency in [46], and the notch magnitude for the different concentrations is shown in Figure authors characterized solutions of water–methanol. The measured resonance frequency and notch 10, whereas Figure 11 depicts the real and thefor magnitude imaginary part concentrations the different of the permittivity inferred is shown from the in Figure 10,mathematical whereas Figure model. In thisthe 11 depicts figure, real the values and inferred part the imaginary fromof thetheliterature are also permittivity depicted, inferred fromand thethe good agreement mathematical model. between In thisboth setsthe figure, of data can be appreciated. It is remarkable that the relative sensitivity values inferred from the literature are also depicted, and the good agreement between both sets of of this sensor is very good, as compared data can betoappreciated. the one of similar sensors reported It is remarkable that the in relative the literature (see [46] sensitivity for further of this sensor isdetails). very good, as compared to the one of similar sensors reported in the literature (see [46] for further details). Appl. Sci. 2020, 10, 2615 10 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 30 Figure 9. Measured frequency response of the sensor for various water–ethanol solutions (a) and Figure 9. Figure 9. Measured Measured representation of thefrequency frequency resonance response response of theand of the frequency sensor sensor notchformagnitude for various water–ethanol various water–ethanol as a function solutions solutions (a) of the(a) and and water representation representation concentration of of the theFrom (b). resonance resonance frequency frequency and [46], reprinted and withnotch notch magnitude permission. magnitude as as a function In panel a function (a), theofstep the water of the water concentration variation of water concentration (b). From [46], content is 10%. (b). From reprinted [46], with reprinted permission. with In permission. panel (a), the In steppanel (a), variation the of step water variation content is of water 10%. content is 10%. Figure 10. Figure 10. Measured Measured frequency frequency response response of of the the sensor sensor for for various various water-methanol water-methanol solutions solutions (a) (a) and and Figure 10. Measured representation frequency response of theand sensor for magnitude various water-methanol solutions the (a) and representation ofofthethe resonance resonance frequency frequency and notch notch magnitude as aof function as a function the water of water concentration representation concentration of the resonance frequency and notch magnitude as a function of the water (b). From [46], (b). From with reprinted [46], permission. reprinted with permission. In panel In panel (a), the step (a), the variation step content of water variation of water is 10%. concentration content is 10%.(b). From [46], reprinted with permission. In panel (a), the step variation of water content is 10%. Appl. Sci. 2020, 10, 2615 11 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 30 11. Real Figure 11. Real (a) (a) and imaginary imaginary (b) part of the complex complex dielectric dielectric constant constant of of water–methanol water–methanol solutions as a function of the water content, inferred from the data of Figure 10 and the mathematical model developed in [46]. From [46], reprinted with permission. 4.2. Coupling Modulation 4.2. Coupling Modulation Sensors Sensors As As discussed discussed in in Section Section 2, 2, coupling coupling modulation modulation sensorssensors are are implemented implemented by by symmetrically symmetrically loading a transmission line with a symmetric resonator. The loading a transmission line with a symmetric resonator. The symmetry planes of the linesymmetry planes of the line and and resonant resonant element element should should be be of of different different electromagnetic electromagnetic sort, sort, i.e., i.e., one one should should be be aa magnetic magnetic wallwall and and the the other other one an electric wall. Figure 12 illustrates the working principle of one an electric wall. Figure 12 illustrates the working principle of coupling modulation sensors, by coupling modulation sensors, by considering considering a CPWa CPW loaded loaded withwith a SRR[47]. a SRR [47].The Theline lineexhibits exhibitsa amagnetic magneticwallwallat atthe the axial axial symmetry symmetry plane for the fundamental CPW mode, whereas the symmetry plane plane for the fundamental CPW mode, whereas the symmetry plane of the SRR is an electric wall of the SRR is an electric wall at the at fundamental resonance. For perfect symmetry, the electromagnetic the fundamental resonance. For perfect symmetry, the electromagnetic field generated by the line field generated by the line is notis able to excite not able the SRR, to excite the andSRR,the structure and is all-pass the structure in the vicinity is all-pass in theofvicinity the SRRoffundamental resonance. the SRR fundamental This situation resonance. This is situation preservedis ifpreserved the SRR is if symmetrically loaded with the SRR is symmetrically a dielectric loaded with amaterial. dielectricHowever, material. if symmetry is truncated, e.g., by means of an asymmetric However, if symmetry is truncated, e.g., by means of an asymmetric dielectric load,dielectric load, as depicted in Figure 12, then as depicted in the resonator Figure 12, then is driven by the line the resonator (i.e., line-to-resonator is driven coupling is activated), by the line (i.e., line-to-resonator and aisnotched coupling response activated), and a (bandstop-type) notched responseappears. Althoughappears. (bandstop-type) this typeAlthough of sensor thiscan type be used for dielectric of sensor can be characterization used for dielectric or for comparison purposes characterization by exploitingpurposes or for comparison their electromagnetic by exploiting symmetry properties, mostsymmetry their electromagnetic coupling modulation sensors have been applied to the implementation of properties, most coupling modulation sensors have been applied to the implementation of linearlinear or angular displacement and or velocity sensors [16–30,48]. The reason is that a relative linear or angular angular displacement and velocity sensors [16–30,48]. The reason is that a relative linear or angular displacement between the line and the resonant displacement elementthe between also linetruncates and the symmetry resonant(except element if the alsoresonant truncateselement displaces symmetry linearly (except in if the the direction of the line axis). Thus, in this subsection, this sensing approach resonant element displaces linearly in the direction of the line axis). Thus, in this subsection, this is illustrated by means of two examples, sensing approach to be is discussed illustratednext.by means of two examples, to be discussed next. Appl. Sci. 2020, 10, 2615 12 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 30 Figure 12. Illustration Figure 12. Illustration of symmetry symmetry disruption disruption by by means means of of square-shaped square-shapedinclusions inclusionsininaa CPW CPW loaded loaded with with aaSRR. Figure 12.From SRR. From [47], [47],reprinted Illustration reprintedwith with of symmetry permission. permission. disruption by means of square-shaped inclusions in a CPW loaded with a SRR. From [47], reprinted with permission. In In the the first first example example [22], [22], an an angular angular displacement displacement and and velocity velocity sensor sensor based based on on aa circular-shaped circular-shaped CPW loaded In the with first a movable example [22], an circular angular ELC resonator displacement and is reported. velocity CPW loaded with a movable circular ELC resonator is reported. The ELC resonator sensor The based ELC on isresonator a circular-shaped a bisymmetric is a CPW loaded bisymmetric particle, with aorthogonal particle, exhibiting movable circular exhibiting ELC orthogonal electric and resonator electric magneticis reported. and magnetic walls. Thewalls. Thus, ELC resonator is a bisymmetric Thus, significant significant variation variation of line-to- of particle, exhibiting line-to-resonator orthogonal coupling by electric ELC and rotation magnetic can be walls. achieved, Thus, and significant this is variation interesting resonator coupling by ELC rotation can be achieved, and this is interesting in terms of the output in of termsline-to- of the resonator output dynamic dynamiccoupling range. range. by ELC Figure Figure rotation 13 shows13 showscan be achieved, the picture the picture and of the of the CPWthis CPW is andinteresting andELC in terms ELCresonator, of the resonator,asaswell output well asas the the dynamic range. experimental experimental set-upFigure set-up used usedfor 13 measuring for shows thethe measuring picture the of displacement angular angular the CPW andand displacement and ELCvelocity. resonator, as well as the velocity. experimental set-up used for measuring the angular displacement and velocity. Figure Figure 13.13. Set-upfor Set-up forthe theangular angular displacement displacementandandvelocity velocitymeasurement. (a) Cross measurement. section (a) Cross view, view, section (b) Figure 13. Set-up photographs of for the the angular rotor displacement (circular ELC andand resonator) velocity stator measurement. (CPW), and (c)(a) Cross section photograph of view, the step-(b) (b) photographs of the rotor (circular ELC resonator) and stator (CPW), and (c) photograph of photographs motor of the rotor providing rotor (circular motion ELC and resonator) zoom view and of stator the (CPW), andFrom stator-rotor. (c) photograph [22], of the reprinted step- with the step-motor providing rotor motion and zoom view of the stator-rotor. From [22], reprinted motor providing rotor motion and zoom view of the stator-rotor. From [22], reprinted with permission. with permission. permission. Appl. Sci. 2020, 10, 2615 13 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 30 By rotor By rotormotion rotor motion motion with with with regard regard regard tostator, to to the the stator, the stator, the transmission the the transmission transmission coefficient coefficient coefficient at ff00,, the at f 0 , the at resonance the resonance resonance frequency frequency frequency of the of the ELC,ofexperiences ELC, experiences the ELC, experiences a roughly linear a roughly a roughlyvariationlinear linearwith variation variation the rotation with withangle,the rotation the rotation as can be angle, angle, as can as appreciatedcan be be in appreciated appreciated Figure 14. Thus, in Figure in Figure the output14. Thus, 14. Thus,variable the output the for output variable variableangular measuring for measuring for measuring displacement angular angular is thedisplacement displacement magnitude of is the is the magnitude of magnitude transmission ofcoefficient. the transmission the transmission coefficient. coefficient. The sensitivity The sensitivity The is reasonable,sensitivity but the isdynamic is reasonable, reasonable, rangebutisthe but the dynamic dynamic restricted range range to 90 is ◦ , as is it restricted restricted to 90°, to 90°, from can be explained as it can as it obvious be explained can be explained symmetry from from obvious obvious symmetry considerations. symmetry To measure considerations. considerations. the (average) angular To measure To measure the the velocity, (average) (average) the strategy angular angular proposed velocity, velocity, in [22] the the strategy is strategy proposed based onproposed an amplitude in [22] in [22] is based is based on(AM) modulation on an amplitude an amplitude scheme. By modulation modulation feeding the (AM) (AM) line scheme. scheme. with By feeding By a harmonic feedingsignal thetuned the line with line with to the aa harmonic harmonic signal resonance signal frequency tuned tuned of to to the the the ELC, resonance resonance the amplitude frequency frequency at theofofoutput the ELC, the ELC, the portthe is amplitude amplitude at expected toatbethe the output output port modulated port is expected dueistoexpected to be modulated to be modulated the time-varying couplingdue due to the to thethe between time-varying time-varying coupling line and thecoupling between resonant between element, the line the and line and two and pulses theofresonant the resonant the envelope element, element, and two and function twocycle per pulses pulses ofexpected. areof the envelope the envelope function Thus,function from theper per timecycle cycle distanceare expected. are expected. between Thus, from Thus, adjacent from pulses,the the the time time distance distance angular between between velocity can be adjacent adjacent inferred. pulses, pulses, the angular the The envelope angular velocity velocity function can be can can be inferred. be simply inferred. obtainedThe The by envelope envelope means of an function function envelope can be candetector,simply be simply obtained obtained preceded byby by means anmeans of an envelope isolatorof(implemented an envelope detector, detector, by meanspreceded preceded of a circulator) by an by an inisolator isolator order (implemented by (implemented to protect the CPW by means means of aa circulator) of line against circulator) mismatching in order in order to reflections to protect protect from the thediode the CPW(aline CPW line highly against against nonlinear mismatching mismatching device). reflections reflections The schematic from from the diode the diagram diode of the (aapproach (a highly nonlinear highly nonlinear is presented device). device). The schematic The in Figure schematic 16 15. Figure diagram diagram of pair depictsofa the the approach approach of recorded is is presented in presented in Figure Figure 15. 15. Figure Figure 16 16 depicts aa pair pair of recorded recorded envelopeenvelope functions (visualized (visualized in in anan envelope functions (visualized in andepicts oscilloscope inof[22]), corresponding tofunctions different angular velocities oscilloscope oscilloscope in [22]), corresponding in [22]), corresponding to different angular velocities of the rotor (particularly, 1 rpm of the rotor (particularly, 1 rpm and 50torpm). different angular velocities The measured envelopeof the rotor functions (particularly, reveal 1 rpm that the method and and 50 rpm). 50 rpm). The measured The measured envelope functions reveal that the method is useful to provide the is useful to provide the angularenvelopevelocity. functions However, reveal it is notthat the method possible to obtainisinstantaneous useful to provide the velocities angular velocity. angular velocity. However, However, itit is is not possible possible to to obtain obtain instantaneous instantaneous velocitiesvelocities with with this approach, approach, as as with this approach, as only twonot pulses per cycle are generated. Namely, only the this average angular only only two pulses per cycle are generated. Namely, only the average angular speed corresponding to speedtwo pulses per cycle corresponding to time arelapses generated. between Namely, adjacent only the can pulses average angular speed be measured. In order corresponding to improve this to time time lapses between lapsesaspect, between adjacent adjacent pulses pulses can can be measured. be measured. In order In order to improve this limitative aspect, aa limitative a very large number of pulses is necessary (liketoinimprove this limitative optical encoders [92–94]).aspect, Thus, very large very large number number of pulses pulses is is necessary necessary (like (like in in optical optical encoders encoders [92–94]). Thus, Thus, a different different approach approach a different approachoffor the measurement of angular displacements[92–94]). and velocities awas reported in [28], for the measurement for thea completely measurement of angular of angular displacements displacements and velocities and velocitiesproviding was reported was reported in [28], in [28], where aa where where different configuration (edge configuration), hundreds of pulses per completely different completely different configuration configuration (edge (edge configuration), configuration), providing providing hundreds hundreds of of pulses pulses per per revolution, was implemented. revolution, was implemented. revolution, was implemented. Figure 14. 14. Transmission coefficient Transmissioncoefficient atatf0fas coefficientat a function 0 as of the a function rotation of the angle. rotation From [22], [22], angle. reprinted with Figure Figure 14. Transmission f0 as a function of the rotation angle. FromFrom reprinted [22], reprinted with permission. with permission. permission. Figure 15. Sketch of the Sketch system of system for the measurement the system of angular velocitiesvelocities based on an AM modulation 15.Sketch Figure 15. of the for thefor the measurement measurement of velocities of angular angular based on anbased on an AM AM modulation scheme. modulation scheme. scheme. Appl. Sci. 2020, 10, 2615 14 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 30 (a) (b) Figure Figure 16. Measured 16. Measured envelope envelope functions.(a) functions. (a)11rpm; rpm; (b) (b) 50 50rpm. rpm.From From[22], reprinted [22], with reprinted permission. with permission. (a) (b) In the Inrotation the rotation sensor sensor of of Figure13, Figure 13,the theaxis axis ofof the the resonator resonatorcoincides coincides withwiththethe axisaxis of the ofrotor the rotor (axial configuration). Figure 16. Measured In [28], envelopea rotor consisting functions. (a) 1 of rpm; a circular (b) 50 rpm.chain From of (axial configuration). In [28], a rotor consisting of a circular chain of resonant elements etched along its resonant [22], reprintedelements with etched permission. along its edge was proposed as a means to boost the number of pulses (see Figure 17). The working edge was proposed as a means to boost the number of pulses (see Figure 17). The working principle is In the principle is rotation indeed very sensor of Figure similar to the13, onethe usedaxistoofinfer the the resonator angular coincides velocity withwith the axis sensor of based the rotoron indeed very (axial similar to the configuration). In one [28], used a rotor toconsisting infer theof angular a circular velocity chain ofwith the sensor resonant elements based etched onalong the axial the axial configuration. Namely, by rotor motion, the amplitude of the feeding harmonic signal is configuration. its edge was modulated, Namely, proposed but by rotor at least motion, asasa many means to the pulses boostamplitude as the number resonators ofinthe ofthefeeding pulses chain(see harmonic canFigure signal 17). be generated Theis modulated, working per each but atrevolution. least as ismany principle indeed Indeed, pulses very it was as resonators similar to the one demonstrated in the chain inused [29,30] that can to infer be generated theconveniently by angular velocity perwith choosing each the revolution. the sensor based frequency Indeed, on of the it wasfeeding demonstrated the axialsignal, upinto[29,30] configuration. two that by Namely, pulses byconveniently per rotor resonantmotion, choosing elementthe amplitude can be the frequency of the and achieved, ofthe feeding theharmonic feeding sensor signal,in signal reported isup to modulated, two pulses [30] exhibits but 1200atpulses per resonant least element as permanycan be pulses revolution as resonators achieved, (i.e., 600and in thewhich the sensor resonators), chain reportediscan be[30] in generated a relevant figure per exhibits of1200 each merit. pulses revolution. this Moreover, per revolution Indeed, (i.e., 600it was sensor demonstrated is equipped resonators), with which in [29,30] a resonator’sthat by is a relevant chainconveniently devoted figure tochoosing of merit. themotion detectMoreover, the frequency ofsensor direction this the is feeding (see signal, details in up [30]). to two Note pulses that in per this resonant sensor element based on thecan be achieved, so-called equipped with a resonator’s chain devoted to detect the motion direction (see details in [30]). Note that edge and the sensor configuration, reported the working in [30] exhibits 1200 pulses per revolution (i.e., 600 resonators), which is coefficient a relevant of figure of merit. in thisprinciple is coupling sensor based on the modulation so-calledas well.configuration, edge By this means, the working the transmission principle is coupling the line at the modulation Moreover, of frequency thisthesensor feeding is equipped with a resonator’s signal periodically varies with chain time,devoted generating to detect a pulsedthe AMmotion signaldirection at the as well. By this means, the transmission coefficient of the line at the frequency of the feeding signal (see details output port inof [30]). Note the line. that in this However, sensor modulation coupling based on theisso-called achievededge by the configuration, consecutive the working crossings of periodically principle the varies resonant with time, is coupling elementsmodulation generating of the chainasover well.athepulsed By this of axis AM means, signal the line at thewhen the(stator), transmission output port of themotion. coefficient the rotor isofinthe line. line atHowever, the The coupling modulation frequency working principle is of the feeding achieved is very signal similar by tothe theconsecutive periodicallyone of varies optical crossings with of theapertures time, generating encoders, with resonant a pulsedinelements aAM signal metallic of the at disc. Inchain the over the such axis output of the port encoders, of theline (stator), line. However, apertures when are the rotor coupling detected is inofmotion. bymodulation means anisoptical The achieved beam working by (when principle the consecutive an aperture islies very crossingsin thesimilar of to thepath one the of optical resonant between theencoders, elements source the with of and chain apertures over theaaxis the detector, in of pulse a metallic the is disc.By line (stator), generated). Inwhen suchthe contrast, encoders, rotor in inthe theissensor apertures motion. basedThe on are working detected the edge principle by means configuration,is very of an thesimilar optical beam resonatorsto the (whenone are of anoptical detected aperture encoders, by means with liesofinanthe apertures path between electromagnetic in asignal. metallic the source disc.and Therefore, In the such encoders, sensors canthebe apertures designated are asdetected by electromagnetic means (or of an optical microwave) beam detector, a pulse is generated). By contrast, in the sensor based on the edge configuration, the resonators rotary (when an encoders. aperture lies in the path between are detected by meansthe sourceof anand the detector, a pulse electromagnetic signal. is generated). Therefore,Bysuch contrast, in the sensors cansensor based on as be designated the edge configuration, the resonators are detected by means of an electromagnetic signal. Therefore, electromagnetic (or microwave) rotary encoders. such sensors can be designated as electromagnetic (or microwave) rotary encoders. Figure 17. Sketch of the rotation sensor based on the edge configuration. From [29], reprinted with permission. Figure Figure 17. 17. Sketch Sketch ofofthe therotation rotation sensor sensorbased basedonon thethe edge configuration. edge From [29], configuration. Fromreprinted with [29], reprinted permission. with permission. Appl. Sci. 2020, 10, 2615 15 of 30 Appl. Sci. 18 Figure 2020, 10, x FOR depicts thePEER REVIEW sketch of the sensor with a double chain of resonators to measure 15 the ofangular 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 30 speed, and an additional non-periodic chain to discriminate the motion direction. As it can be seen, Figure 18 depicts the sketch of the sensor with a double chain of resonators to measure the two harmonicFigure signals are needed 18 depicts in this the sketch case of the (injected sensor with through a double achain combiner), one ofto of resonators them tunedthe measure to the angular speed, and an additional non-periodic chain to discriminate the motion direction. As it can angular resonance speed, and frequency of an additional the resonators non-periodic of the chain velocity to discriminate chain, and the the motion other one direction. tuned to the As it can of resonance be seen, two harmonic signals are needed in this case (injected through a combiner), one of them be seen, two harmonic the resonant signals are needed in this motion case (injected through a combiner), one of them and tuned to elements the resonance of the direction frequency of chain. Rotor the resonators AM modulates of the velocity chain, andeach harmonic the other signal, one tuned to tuned to the corresponding the resonance envelope frequency functionsof the resonators canofbethe inferred of the velocity by chain. meansRotor chain, and of envelope the other detectors,one tuned aftereach to filtering the resonance of the resonant elements direction motion AM modulates the resonance of the resonant elements of the direction chain. Rotor motion AM modulates each each harmonic signal bysignal, meansand of the a diplexer. Figureenvelope corresponding 19 shows the photograph functions of rotor can be inferred (zoomofview) by means envelope and the harmonic signal, and the corresponding envelope functions can be inferred by means of envelope detectors, after filtering each signal by means of a diplexer. Figure 19 shows stator, as well as a picture of the overall experimental set-up. The envelope functions inferred with the photograph of rotor detectors, after filtering each signal by means of a diplexer. Figure 19 shows the photograph of rotor such (zoom sensing view) (zoom view) and the system,and the stator, as wellto corresponding as a picture stator, as well asthe angular a picture of the overalland of velocity the overall experimental direction set-up. experimental The envelope detection, set-up. Theare shown in envelope functions Figurefunctions inferred 20 (noteinferred with that thewith such direction sensing is system, detected by corresponding the increasing to or the angular decreasing velocity sequence andof direction pulses in the such sensing system, corresponding to the angular velocity and direction detection, are shown in Figure 20 (note that the direction is detected by the increasing or decreasing corresponding detection, are envelope shown function). in Figure 20 (note that the direction is detected by the increasing or decreasing sequence of pulses in the corresponding envelope function). sequence of pulses in the corresponding envelope function). Figure 18. Sketch and working principle of the rotation sensor based on the edge configuration with 18. Sketch FigureFigure andand 18. Sketch working workingprinciple principleofofthe therotation sensorbased rotation sensor basedononthe the edge edge configuration configuration withwith two velocity chains and one direction detection chain. From [30], reprinted with permission. two velocity chains two velocity andand chains oneone direction detection direction detectionchain. chain. From [30],reprinted From [30], reprinted with with permission. permission. (a) (b) (a) (b) (c) (c) Figure 19. Photograph of the rotor (a), experimental set-up (b), and stator (c). From [30], reprinted Figure Figure 19. Photograph Photograph 19.permission. of the of the rotor rotor (a), (a), experimental set-up experimental set-up (b), (b),and andstator stator(c).(c). From [30],[30], From reprinted reprinted with with permission. with permission. Appl. Sci. 2020, 10, 2615 16 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 30 (a) (b) Figure 20. Figure 20. Envelope Envelopefunctions functions providing providing the the angular angular velocity velocity (a)motion (a) and and motion direction direction (b). The (b). The nominal nominal rotary rotary speed speed is 60 rpm.isFrom 60 rpm. From [30], [30], reprinted reprinted with permission. with permission. In these angular displacement and velocity sensors based on the edge configuration, the number of cumulative pulses from a reference reference (REF)(REF) position position provides provides thethe angle angle of of rotation. rotation. Thus, the angular resolution resolution (in (in degrees) degrees) is is simply simply 360 360 /PPR, ◦ o /PPR, where where PPR PPR is the number number of pulses pulses per revolution. revolution. For the specific specific sensor sensor system system of of Figure Figure 19,19, with with PPRPPR == 1200, the angular resolution resolution is is thus 0.3◦o, a competitive thus 0.3 value. Further Further details details of this sensor (dimensions, considered substrates, specific components, and instrumentation) instrumentation)are aregiven giveninin[30]. [30].A A detailed analysis detailed of angular analysis of angularvelocity resolution velocity and error resolution for these and error for these sensors, sensors, out of out the of the scope scope of thisof this paper, paper, can becan be found found in [29].inAs [29]. As highlighted highlighted in [29,30], in [29,30], microwavemicrowave rotary rotary encoders encoders represent represent a low-costa low-cost alternative alternative to opticaltoencoders. optical encoders. Moreover, Moreover, microwave microwave encoders encoders can be of can be for interest of operation interest for operation in harsh in harsh and hostile and hostile(i.e., environments environments (i.e., subjected subjected to radiation, to radiation, pollution, dirtiness, pollution, grease, dirtiness, etc.), where thegrease, etc.),counterparts optical where the optical counterparts may offer a limitedmay offer a limited robustness. robustness. Note that Note the dynamic that the range ofdynamic rangesensors these rotation of thesefor rotation sensors for angle angle measurement measurement is theoretically is theoretically unlimited, as these unlimited, as sensors are these sensors based on pulseare based on counting. pulse This is a counting. This isas clear advantage a compared clear advantage as sensors to other compared to other based sensors on symmetry based on symmetry disruption disruptionby and implemented and implemented means by means of a single resonant of aelement single resonant element [21–23,26,27]. [21–23,26,27]. This unlimited This unlimited dynamic range plusdynamic range plus the achievable angularthe resolution achievablesituates angular resolution these sensors as situates these excellent sensors for candidates as excellentdisplacement angular candidates for andangular velocity displacement sensing. and velocity sensing. 4.3. Frequency Splitting 4.3. Frequency Splitting Sensors Sensors The The operation operationprinciple of frequency principle of frequencysplitting sensorssensors splitting is illustrated in Figure 21 is illustrated in [47]. A transmission Figure 21 [47]. A line is symmetrically loaded with a pair of (not necessarily symmetric) resonators. transmission line is symmetrically loaded with a pair of (not necessarily symmetric) resonators. If symmetry is If preserved, symmetry is a single notcha in preserved, the transmission single coefficient arises notch in the transmission (provided coefficient the arises resonators (provided theare coupled resonators to arethe line). Conversely, coupled to the line). ifConversely, symmetry is if disrupted, symmetry is two notches appear disrupted, (splitting), two notches appear and their relative (splitting), and distance depends their relative on symmetry distance depends imbalance. on symmetry Thus, this principle imbalance. Thus,can thisbeprinciple used for can sensing. Although be used most for sensing. frequency Although most splitting sensors frequency are implemented splitting by symmetrically sensors are implemented loading a line by symmetrically with aaline loading resonator with a pair resonator pair (as indicated in Figure 21), in some implementations a cascade configuration,the (as indicated in Figure 21), in some implementations a cascade configuration, where two where resonant elements the two resonant are placed elements at different are placed locations at different in a transmission locations line, has in a transmission line,been considered has been [56]. considered In this subsection, we report a frequency splitting sensor for dielectric characterization [56]. In this subsection, we report a frequency splitting sensor for dielectric characterization of liquids of liquids as an illustrative example, where a splitter/combiner configuration is used [58]. as an illustrative example, where a splitter/combiner configuration is used [58]. With such With such configuration, the effects of inter-resonator configuration, the effects coupling (with negative of inter-resonator coupling impact (withon sensor impact negative sensitivity) can besensitivity) on sensor avoided, as it can was discussed in [57]. be avoided, as it was discussed in [57]. Appl. Sci. 2020, 10, 2615 17 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 30 FigureFigure 21. Illustration 21. Illustration of frequency of frequency splitting splitting through through symmetry symmetry imbalance imbalance (considering (considering square- square-shaped shaped inclusions) in a CPW symmetrically loaded with a pair SRRs. From [47], reprinted inclusions) in a CPW symmetrically loaded with a pair SRRs. From [47], reprinted with permission. with Figure 21. Illustration of frequency splitting through symmetry imbalance (considering square- permission. shaped inclusions) in a CPW symmetrically loaded with a pair SRRs. From [47], reprinted with The topology of the designed sensor is shown in Figure 22a, whereas Figure 22b depicts permission. a The topology of the designed sensor is shown in Figure 22a, whereas Figure 22b depicts a photograph (in perspective view) of the device, equipped with fluidic channels (device dimensions, photograph (in perspective view) of the device, equipped with fluidic channels (device dimensions, substrate, as well The substrate, topology as other as well as thedetails of other designed related sensor details related totois the fluidic shown the fluidic in channels Figure 22a, channels andmechanical mechanical andwhereas Figure accessories 22b depicts accessories can be can a be foundphotograph in [58]). (in Figure perspective 23 depicts view) the of the frequency device, equipped response for with fluidic different found in [58]). Figure 23 depicts the frequency response for different configurations of channel channels configurations (device of dimensions, channel loading, wheresubstrate, loading, as well the splitting where theassplitting effectotherfordetails effect related those cases for those tocases of the fluidic device channels imbalance of device imbalance and can mechanical be be can observed. accessories observed. With With the candata the be data of found Figureof23Figurein [58]). (resonance Figure frequency 23 (resonance 23 depicts the frequency splittingsplitting frequency and difference response and difference for in the notch different in themagnitude, configurations notch magnitude, the outputof channel variables), the output loading, where the splittingmodel effect for those cases of device imbalance can be observed. With4.1 variables), a mathematical amodel mathematical following following a scheme a scheme similar to similar the one toreported the one reported in Sectionin Section 4.1 canthebe data can be inferred, of Figure inferred, 23 (resonance provided the frequency complex splitting permittivity and of difference mixtures of in DI the notch water, the magnitude, reference the sample,outputand provided the complex permittivity of mixtures of DI water, the reference sample, and ethanol can be variables), ethanol cana mathematical be obtained sources.modelindependent from following a scheme sources. similar Suchthe to the onelinks a model reportedthe in Section 4.1complex differential can be obtained from inferred, independent provided the complex Such a model permittivity of links mixtures of differential DI water, the complex reference permittivity sample, and (real permittivity (real and imaginary parts), i.e., the input variables, to the differential output variables. and imaginary ethanol parts), i.e., the input variables, to the differential output variables. Once the model Once thecan be obtained model is known,from it canindependent be used to determinesources. Such a model the complex links the differential permittivity of liquid samples,complex by is known, it can (real permittivity be used and to determine imaginary thei.e., parts), complex the input permittivity variables, ofthe to liquid samples, differential by considering output variables. DI considering DI water as reference (REF) sample. In Figure 24, the measured responses of the device waterOnceas reference the model (REF) is known, sample. it can In be Figure used to 24, the determine measured the complex for different solutions of water–ethanol injected in the MUT channel, considering water as the REF responses permittivity of the of device liquid for samples, different by considering solutions liquid, of are DI water as water–ethanol depicted. The reference inferred(REF) injected in thesample. output MUT variablesIn Figure channel, are also 24, the measured considering represented inresponses water theas theofREF figure. the device With liquid, these are for depicted. different results The and solutions inferred of water–ethanol output variables the mathematical model, the injected arecomplex in the also represented MUT permittivity channel, inof the considering figure. such water With these water–ethanol as the REF results mixtures and the was liquid, mathematical are depicted. model, the The inferred complex output permittivity variables of such are also represented water–ethanol obtained, and the results are depicted in Figure 25. It can be appreciated in that figure that the results in mixtures the figure. was With obtained, these and the results and the mathematical model, the complex permittivity of such water–ethanol mixtures was resultslieare within the limits depicted of the 25. in Figure WeinerIt canmodel, and consequently be appreciated in thatthesefigure results validate that the resultstheliefunctionality within theoflimits obtained, andAlthough the resultsthese are depicted in Figureto25. It can be appreciated in that figuresensors, that theandresults of thethe sensor. Weiner model, and consequently sensors thesebelong results the category validate theof functionality symmetry-based of the sensor. are Although lie within therefore the limits robust against of the Weiner the effectsof model, and ofsymmetry-basedconsequently ambient factors, the these resolution results and validate the sensitivity functionality ofrobust these sensors of thesethe sensors sensor. belong Although to the category these sensors belong to the categorysensors, of and are symmetry-based therefore sensors, against and are the is, in general, not as good as the one of true differential sensors, as is discussed in the next section. effects of ambient therefore robust factors, againstthe theresolution effects of ambientand sensitivity factors, the ofresolution these sensors is, in general, and sensitivity of these notsensors as good as the one of true differential sensors, as is discussed in the next section. is, in general, not as good as the one of true differential sensors, as is discussed in the next section. ls W w ls Ws W l1 w 2 w1 P1 l1 2 d W s P2 l2 w1 P1 c d P2 g l2 L c g L (a) (b) Figure 22. Layout (a) and (a) perspective view (b) of the designed frequency-splitting (b) sensor. From [58], reprinted with permission. Figure Figure 22. Layout 22. Layout (a) (a) and and perspectiveview perspective view (b) (b) of of the thedesigned designedfrequency-splitting sensor. frequency-splitting FromFrom sensor. [58], [58], reprinted with permission. reprinted with permission. Appl. Sci. 2020, 10, 2615 18 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 30 Figure Figure 23. Measured Figure 23. 23. Measured Measured responses responses of ofofthe responses thesensor the sensor for sensor different for different for combinations different combinations combinations of of of dielectric dielectric loads loads dielectric in the in the loads in the Figure 23. Measured responses of the sensor for different combinations of dielectric loads in the channels. channels. channels. FromFrom reprinted [58],[58], with reprinted reprinted permission. with with permission. permission. channels. From [58], reprinted with permission. (a) (b) (a) (b) Figure 24. (a) Measured 24. Measured frequency frequency response ofthe response the sensor for various (b) water–ethanol solutions (a) and Figure Figure 24. Measured frequency responseof of the sensor forvarious sensor for variouswater–ethanol water–ethanol solutions solutions (a) and (a) and representation of the resonance frequency splitting and notch magnitude difference, as a function of representation of representation Figure the of resonance the frequency resonance frequencysplitting and splitting andnotch notchmagnitude magnitude difference, difference, as as a a function function ofofand the the24. Measured ethanol frequency concentration response (b). From of the sensor [58], reprinted for various water–ethanol solutions (a) with permission. ethanol the concentration ethanol (b). concentration From (b). [58], From reprinted [58], with reprinted permission. with permission. representation of the resonance frequency splitting and notch magnitude difference, as a function of the ethanol concentration (b). From [58], reprinted with permission. (a) (b) (a) (b) Figure 25. Real (a) and imaginary (b) part of the complex dielectric constant of water–ethanol FigureFigure 25. (a) 25. Real Realand (a)imaginary and imaginary (b) of (b) part part the of the complex complex dielectric dielectric constant constant ofand of water–ethanol water–ethanol solutions solutions as a function of the ethanol content, inferred from the data of Figure 24 the mathematical solutions as a function as a function of the(a)ethanolof the ethanol content, inferred from the data of Figure 24 and the mathematical model developed in [58].content, From [58],inferred reprintedfrom withthe data of Figure 24 and permission. (b)the mathematical model model developed in [58]. From [58], reprinted with permission. developed in [58]. From [58], reprinted with permission. Figure 25. Real (a) and 4.4. Differential-Mode imaginary (b) part of the complex dielectric constant of water–ethanol Sensors 4.4. Differential-Mode 4.4. Differential-Mode solutions Sensors Sensors as a function of the ethanol content, inferred from the data of Figure 24 and the mathematical Differential sensors based on a pair of uncoupled lines each one loaded with a resonant sensing model developedsensors Differential Differential in [58]. From on based [58], on reprinted aapair with of uncoupled permission. lines each one loaded onewith a resonant sensing element havesensors based been reported. pair The considered of resonant uncoupled linesare elements each OCSRRs loaded [62], SRRswith [63], a resonant OSRRs element have been reported. The considered resonant elements are OCSRRs [62], SRRs [63], OSRRs sensing element [67,69], CSRRshave been [66], andreported. DB-DGS The considered resonators resonant [64,65]. We reportelements in thisare OCSRRs paper three[62], SRRs [63], prototype [67,69], CSRRs [66], 4.4. Differential-Mode and DB-DGS resonators [64,65]. We report in this paper three prototype Sensors OSRRs [67,69], CSRRs [66], and DB-DGS resonators [64,65]. We report in this paper three prototype Differential examples, sensors including based a sensor for on a pair permittivity complex of uncoupled lines each one measurement loaded(based of liquids with aon resonant sensing DB-DGSs) [64], element have been reported. The considered resonant elements are OCSRRs [62], SRRs [63], OSRRs [67,69], CSRRs [66], and DB-DGS resonators [64,65]. We report in this paper three prototype Appl. Sci. 2020, 10, 2615 19 of 30 a sensor for the determination of volume fraction of solute in liquid solutions (based on OSRRs) [69], and a sensor devoted to the measurement of extremely small concentrations of electrolytes in DI water [66]. 4.4.1. Measuring Electrolyte Concentration Electrolytes are ions, such as sodium (Na+ ), potassium (K+ ), calcium (Ca2+ ), chloride (Cl− ), and bicarbonate (HCO3 − ), among others, present in the blood and urine. Electrolytes play a key role in several vital functions, such as blood pH and pressure control, body hydration, nerve and muscle functions, etc. [95]. There are electrochemical methods to determine selectively the concentration of electrolytes in blood and urine, mainly based on the so-called ion-selective electrodes (ISE), but such methods are expensive. Measuring the total concentration of ions does not provide complete information, but it may be indicative of certain pathologies, or it can be useful as a prescreening diagnosis tool. Moreover, monitoring the real-time variations of the total electrolyte content in urine or blood samples, as compared to a reference (REF), is also of interest from a medical viewpoint. These functionalities can be achieved by means of the differential sensors reported in this section, where the main advantageous aspect is sensor cost (e.g., as compared to electrochemical sensors), and real-time functionality. Within this context, the development of low-cost microwave methods able to provide the electrolyte concentration in samples of blood and urine is of high interest. Nevertheless, to avoid using biosamples, and for the sake of easy comparisons, it is usual to estimate sensor performance by considering electrolyte solutions of standard liquid, typically DI water. The reported differential sensor aimed to the measurement of electrolyte concentration in DI water is the one reported in [66], as it provides (to the best of our knowledge) the finest achieved resolution (0.125 g/L). Such a sensor is based on a pair of CSRR-loaded microstrip lines. The topology and a perspective view, including the fluidic channels, are depicted in Figure 26, whereas Figure 27 shows a photograph of the fabricated device. The output variable in these sensors is the cross-mode transmission coefficient, proportional to the difference between the transmission coefficient of both lines (the REF and the MUT line), namely, 1 SDC 21 = (S21 − S43 ) (4) 2 This proportionality is valid provided the lines are uncoupled (otherwise, the cross-mode transmission coefficient is given by S21 DC = (1/2) · (S21 + S23 − S41 − S43 ). The input variable is the electrolyte concentration of the MUT sample (provided pure DI water is the REF sample). The cross-mode transmission coefficient obtained after subsequently injecting solutions with different electrolyte content (with DI water in the REF channel) is depicted in Figure 28a. The considered electrolyte precursor is NaCl (which dissociates into anions and cations when dissolved in water). As the electrolyte concentration increases, the magnitude of the cross mode transmission coefficient shifts up. As it can be seen, a concentration as small as 0.125 g/L can be discriminated, as far as the corresponding curve is perfectly differentiated form the one of the REF sample (with 0 g/L of electrolyte concentration, i.e., pure DI water). Figure 28b depicts the dependence of the maximum cross-mode transmission coefficient with the electrolyte concentration. The maximum sensitivity (achieved for small electrolyte concentrations) is 0.034 (g/L)−1 , whereas the input dynamic range is at least 60 g/L. From the data points of Figure 28, the following calibration curve, with correlation coefficient of R2 = 0.9996, results  g ∆SDC ∆SDC 21 21 NaCl = 0.41e( 4.2 ) + 4.91·10−8 e( 0.65 ) − 0.59 (5) L This calibration curve can be used to determine unknown concentrations of NaCl in DI water, from the measured cross mode transmission coefficient. Note that other similar sensors for the measurement of electrolyte concentration have been reported [62–65]. However, the sensor of Figure 27 is the one exhibiting better resolution. Appl. Sci. 2020, 10, 2615 20 of 30 Appl.Sci. Appl. Sci.2020, 2020,10, 10,xxFOR FORPEER PEERREVIEW REVIEW 20 of 20 of 30 30 wwTL TL TL PP111 l2l22 PP222 Wccc W dd gg cc ss lclcc PP333 hhTL TL TL PP444 Stainlesssteel Stainless steelscrew screw l1l11 (a) (a) (b) (b) PEEK PEEK PP222 PDMS PDMS Dry Dry PP111 PP444 Film Film (c) (c) LUT LUT PP333 Figure26. Figure Figure 26.Topology 26. Topology(top Topology (topview (top view(a) view (a)and (a) andbottom and bottomview bottom view(b)) view (b))and (b)) and3D and 3Dview 3D view(c) view (c)of (c) ofthe of theproposed the proposedCSRR-based proposed CSRR-based CSRR-based sensor. sensor. From From [66], [66], reprinted reprinted with with permission. permission. sensor. From [66], reprinted with permission. (a) (a) (b) (b) Figure27. Figure Figure 27. Perspective 27.Perspective Perspectivephotographs photographs ofthe of photographs thethe of CSRR-based CSRR-based differential differential CSRR-based sensor. sensor. differential (a)Top; (a) sensor. Top; (b) (a)(b) bottom. bottom. Top; From From (b) bottom. [66],reprinted [66], From reprinted withpermission. with [66], reprinted permission. with permission. -15 -15 14 14 000g/L g/L g/L 6060g/L 60 g/L g/L 4040g/L 40 g/L g/L 12 12 2020g/L 20 g/L g/L -20 -20 1010g/L g/L 10 Equation Equation Equation 10 g/L 10 |(dB) 555g/L g/L |(dB) |(dB) g/L |(dB) 2.5g/L 2.5 2.5 g/L g/L 88 111g/L g/L g/L -25 -25 Adj.R-Square Adj. R-Square DC DC 0.5g/L 0.5 g/L Adj. R-Square DC 0.5 g/L 21 DC 21 DC |S21 DC 66 21 21 SS21 0.25g/L 0.25 0.25 g/L g/L |S 0.125g/L 0.125 0.125 g/L g/L BB B  44 BB B -30 -30 BB B 22 BB B BB B -35 -35 00 BB B 0.9 0.9 1.0 1.0 1.1 1.1 1.2 1.2 1.3 1.3 00 55 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 55 55 60 60 BB B Frequency(GHz) Frequency (GHz) [NaCl] g/L [NaCl] g/L (a) (a) (b) (b) Figure 28. Figure Figure 28. Measured 28. Measured cross-mode cross-mode transmission transmission coefficient coefficient for for different different NaCl NaCl concentrations NaCl concentrations (a) concentrations (a) and (a) and and dependence dependence of the dependence ofofthethe maximum maximum maximum incremental incremental incremental cross-mode cross-mode cross-mode transmission transmission transmission coefficient coefficientcoefficient on the NaClonon the NaCl the NaCl concentration concentration concentration (b). (b).The (b). The calibration The calibration calibration curve curvein in (b) iscurve in(b) included. (b)isisincluded. From included. From[66], From [66], reprinted [66], reprinted withreprinted withpermission. with permission. permission. 4.4.2.Complex 4.4.2. ComplexPermittivity PermittivityMeasurement Measurementof ofLiquids Liquids Determinationof Determination ofthe thecomplex complexpermittivity permittivityof ofliquids liquidsfrom fromthe themeasurement measurementof ofthe thecross-mode cross-mode transmission coefficient transmission coefficient in in differential-mode differential-mode sensors sensors was was first first reported reported in in [62], [62], where where the the sensing sensing Appl. Sci. 2020, 10, 2615 21 of 30 4.4.2. Complex Permittivity Measurement of Liquids Determination of the complex permittivity of liquids from the measurement of the cross-mode Appl. Sci. 2020, 10, x FOR PEER REVIEW 21 of 30 transmission coefficient in differential-mode sensors was first reported in [62], where the sensing elements elements were were OCSRRs. OCSRRs. In In this this subsection, subsection, we we report report aa similar similar sensor, sensor, but but thethe sensing sensing elements elements are are DB-DGSs [64]. The device layout and photographs of the top and bottom DB-DGSs [64]. The device layout and photographs of the top and bottom view (including the fluidic view (including the fluidic channels) channels) are are depicted depicted in in Figure Figure 29. The considered 29. The considered reference reference (REF) (REF) liquid liquid isis pure pure DIDI water, water, whereas whereas different different solutions solutions of of isopropanol isopropanol in in DI DI water water constitute constitute the the MUT MUT liquids. The measured liquids. The measured cross cross mode mode transmission transmission coefficients for the different solutions (where the volume fraction of isopropanol is coefficients for the different solutions (where the volume fraction of isopropanol is the the varying parameter) are depicted in Figure 30a. From this figure, the varying parameter) are depicted in Figure 30a. From this figure, the variation of the maximum of the variation of the maximum of the crosscross mode mode transmission transmission coefficient coefficient (magnitude) (magnitude) and and thethevariation variationininthe thefrequency frequency where where the the maximum appears, as compared to the REF sample, are obtained. The maximum appears, as compared to the REF sample, are obtained. The results are depicted in Figure results are depicted in Figure 30b. These are theare 30b. These two thevariables requiredrequired two variables to determine the complex to determine the permittivity of MUT liquids complex permittivity of MUT (consisting liquids of the real and the imaginary parts). From the results of pure DI water, pure (consisting of the real and the imaginary parts). From the results of pure DI water, pure isopropanol, isopropanol, and a mixture of and50% isopropanol a mixture in DIisopropanol of 50% water, a mathematical in DI water, model linking the complex a mathematical model permittivity linking the with complex the above-cited permittivityoutput with the variables was inferred. above-cited Then thiswas output variables model was used inferred. Thentothisobtain model thewas complex used dielectric to obtain constant of the different mixtures of isopropanol in DI water from the complex dielectric constant of the different mixtures of isopropanol in DI water from the measured values of the outputthe variable. The results are depicted in Figure 31, where it can be appreciated measured values of the output variable. The results are depicted in Figure 31, where it can the good agreement withbe the results given appreciated the goodby the Weiner model. agreement with the results given by the Weiner model. It It is is remarkable remarkable that that the the device device isis able able toto resolve resolve volume volume fractions fractions of of at at least least 5%, 5%, i.e., i.e., better better thanthan the the volume fraction resolved volume fraction resolved withwith the frequency splitting the frequency splitting sensor sensor reported reported in in Section Section 4.3, 4.3, and identical and identical to the resolution to the resolution of of the thedifferential differentialsensor sensorreported reportedinin[62]. [62].ItItshould should bebe highlighted highlighted that that thethe sensor sensor of of Figure 29 can be also used as single-ended sensor, and, in this case, Figure 29 can be also used as single-ended sensor, and, in this case, the sensitivity is excellent, as the sensitivity is excellent, as discussed discussed in in [64].[64]. Finally, Finally, letlet ususemphasize emphasizethat, that,asascompared comparedtotothe thesensor sensorreported reportedin in [62], [62], in in the the sensor reported in this subsection, the fluidic channels are placed at the sensor reported in this subsection, the fluidic channels are placed at the opposite side of the stripopposite side of the strip lines, thereby being being lines, thereby simpler from the simpler fromfabrication viewpoint. the fabrication viewpoint. w1 w2 gd P1 P2 sd wTL ld P3 P4 lTL (a) (b) Fluidic Capillary Connectors PEEK PEEK Ref. Liquid (Ch1) LUT (Ch2) PDMS (c) Figure 29. Layout Layout (a) (a) and and photograph photograph (top (top view view (b) (b) and and 3D 3D view view (c)) (c)) of of the the DB-DGS-based DB-DGS-based sensor. sensor. with permission. From [64], reprinted with permission. Appl. Sci. 2020, 10, 2615 22 of 30 Appl. Appl.Sci. Sci.2020, 2020,10, 10,xxFOR FORPEER PEERREVIEW REVIEW 22 22 of of 30 30 26 26 70 70 100% 100%Isopropanol Isopropanol -5 -5 95% 24 24 95%Isopropanol Isopropanol 90% 90%Isopropanol Isopropanol 22 22 60 60 85% 85%Isopropanol Isopropanol -10 -10 80% Isopropanol 80% Isopropanol 20 20 50 (dB) 75% 75%Isopropanol 18 50 |max(dB) Isopropanol 18 (MHz) max(MHz) 70% 70%Isopropanol |(dB) Isopropanol 21 |(dB) -15 -15 65% 65%Isopropanol Isopropanol 16 16 60% 60%Isopropanol Isopropanol 14 40 40 14 21 |max 55% 55%Isopropanol Isopropanol DC -20 12 |SDC -20 50% Isopropanol 50% Isopropanol 12 21 30 DC ffmax 30 |SDC 45% 45%Isopropanol 21 Isopropanol 10 |S 40% Isopropanol 40% Isopropanol 10 |S -25 -25 35% 35%Isopropanol Isopropanol 88 20 30% 30%Isopropanol Isopropanol 20 25% 66 25%Isopropanol Isopropanol -30 -30 20% 20%Isopropanol Isopropanol 44 10 10 15% 15%Isopropanol Isopropanol 10% Isopropanol 22 10% Isopropanol 0.9 1.0 1.1 1.2 1.3 5% 5%Isopropanol Isopropanol 00 00 0.9 1.0 1.1 1.2 1.3 0% 0%Isopropanol Isopropanol Frequency 00 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 Frequency (GHz) (GHz) 100 Isopropanol Isopropanol Content Content (%) (%) (a) (a) (b) (b) Figure Figure 30. Figure 30. Measured 30. Measured cross-mode Measured cross-mode transmission cross-modetransmission coefficients transmissioncoefficients for coefficientsfor the forthe different thedifferent different solutionsofof solutions solutions of isopropanol isopropanol isopropanol in in DI water in water DI DI water (a) and representation (a) representation (a) and and representation of the output of thevariables of the output variables output variables as a functionas a as of function a the function of the isopropanol of theconcentration isopropanol isopropanol concentration From [64],(b). concentration (b). (b). From From [64], reprinted withreprinted [64], reprinted with withpermission. permission. permission. 90 90 6.0 6.0 Weiner Weinerupper upperlimit limit Weiner Weinerupper upperlimit limit 80 Weiner Weiner Weinerlower lowerlimit 80 Weinerlower lowerlimit limit limit part) 5.8 Weiner model (imaginary part) Weiner Weinermodel model 5.8 Weiner model 70 Extracting Extracting Extractingusing usingeq.(18 eq.(18-b-) 70 Extractingusing usingeq. eq.(18 (18-a-) -a-) -b-) part) (real part) 60 5.6 5.6 60  (imaginary 50 50 5.4  (real 5.4 40 40 5.2 5.2 ' ' 30 30 '''' 20 20 5.0 5.0 10 10 4.8 4.8 00 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 100 00 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 100 Isopropanol Isopropanol Content Content (%) (%) Isopropanol Isopropanol Content Content (%) (%) (a) (a) (b) (b) Figure Figure31. Figure 31. Real(a) 31.Real Real (a)and (a) andimaginary and imaginary(b) imaginary (b)parts (b) partsof parts ofthe of thecomplex the complexdielectric complex dielectricconstant dielectric constantfor constant forthe for thedifferent the differentsolutions different solutions solutions of of isopropanol of isopropanol isopropanol inin DI in DI water. DI water. From water. From [64], From [64], reprinted [64], reprinted with reprinted with permission. withpermission. permission. 4.4.3. Volume 4.4.3. Volume Fraction Determination Determination in LiquidLiquid Solutions 4.4.3. Volume Fraction Fraction Determination in in Liquid Solutions Solutions Obviously, Obviously, with the sensors reported in Sections 4.4.1 and and 4.4.2, determination determination of the the volume Obviously, with with thethe sensors sensors reported reported in in Sections Sections 4.4.1 4.4.1 and 4.4.2, 4.4.2, determination of of the volume volume fraction fraction in liquid solutions is possible. As this measurement involves only one input variable (the fraction in liquid solutions is possible. As this measurement involves only one input variable (the in liquid solutions is possible. As this measurement involves only one input variable (the volume fraction), volume fraction), a single output output variable suffices. suffices. Inthe the sensor of of Section 4.4.1, 4.4.1, devoted to to the volume fraction), aa single single output variable variable suffices. In In the sensor sensor of Section Section 4.4.1, devoted devoted to the the measurement of measurement of electrolyte electrolyte concentration concentration in in water, water, the the output output variable variable was was the the maximum maximum of of the thecross cross measurement of electrolyte concentration in water, the output variable was the maximum of the cross mode transmission mode transmission coefficient. The The frequencyposition position ofsuch such maximumslightlyslightly varies, butbut it is mode transmission coefficient. coefficient. The frequency frequency position of of such maximum maximum slightly varies, varies, but itit isis possible to possible to obtain the the valueat at a fixedfrequency, frequency, particularly the the resonance frequency frequency of the the resonant possible toobtain obtain thevaluevalue ataafixed fixed frequency,particularly particularly theresonance resonance frequencyof of theresonant resonant element. InInthis element. this case,aa single-frequency single-frequency measurementsuffices, suffices, and, inin this case, case, the cross-mode cross-mode element. In this case, case, a single-frequency measurement measurement suffices, and, and, in this this case, the the cross-mode transmission coefficient transmission coefficient can be be inferred by by means of of a reflective-mode differential differential measurement, transmission coefficient can can be inferred inferred by means means of aa reflective-mode reflective-mode differential measurement, measurement, involving involving a simple two-port measurement, as reported in [69]. The sensor device consists of two two pairs involvingaasimplesimpletwo-port two-portmeasurement, measurement,as asreported reportedin in[69]. [69].The Thesensor sensordevice deviceconsists consistsofof twopairs pairs of of grounded grounded OSRR-loaded OSRR-loaded lines lines connected connected to to the the coupled coupled ports ports of of a a rat rat race race coupler coupler by by means means of two of two of grounded OSRR-loaded lines connected to the coupled ports of a rat race coupler by means of two identical transmission identical transmission line sections. sections. The input input signal is is injected to ∆-port, whereas the to theΔ-port, the outputportport identical transmissionline line sections.The The inputsignal signal isinjected injected tothethe Δ-port,whereas whereas theoutput output port is is the Σ-port (see the schematic in Figure 32). is the the Σ-port Σ-port (see(see the the schematic schematic in in Figure Figure 32). 32). Appl. Sci. 2020, 10, 2615 23 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 23 of 30 Figure 32. Schematic Schematic of of the the reflective-mode reflective-mode differential sensor based in OSRRs. From From [69], [69], reprinted with permission. The transmission coefficient at f00,,the theoperating operatingfrequency frequency of ofthe therat-race rat-racecoupler, coupler, in in the the structure structure of Figure 32 can be expressed as 𝑗j −𝑗2 S𝑆12 12 = =− − 2 e𝑒− j2φ ((ρREF − 𝑀𝑈𝑇 )) 𝑅𝐸𝐹 − ρMUT (6) (6) 2 namely, S12 is proportional to the differential reflection coefficient. Therefore, by asymmetrically namely, S12 is proportional to the differential reflection coefficient. Therefore, by asymmetrically loading the sensing loads (OSRRs), it follows that differential sensing can be achieved. In Figure 33, loading the sensing loads (OSRRs), it follows that differential sensing can be achieved. In Figure 33, the the fabricated device, where microfluidic channels have been introduced in order to perform fabricated device, where microfluidic channels have been introduced in order to perform measurements measurements of liquids, is shown. The objective of this sensor was the measurement of volume of liquids, is shown. The objective of this sensor was the measurement of volume fraction of isopropanol fraction of isopropanol in DI water. The measured transmission coefficients after subsequently in DI water. The measured transmission coefficients after subsequently injecting different solutions of injecting different solutions of isopropanol–water in the MUT channel, with DI water in the REF isopropanol–water in the MUT channel, with DI water in the REF channel, are depicted in Figure 34. channel, are depicted in Figure 34. It can be seen that the transmission coefficient at f0 experiences a It can be seen that the transmission coefficient at f 0 experiences a strong variation as the concentration of strong variation as the concentration of isopropanol increases. Moreover, the sensor is able to resolve isopropanol increases. Moreover, the sensor is able to resolve amounts of isopropanol content as small amounts of isopropanol content as small as 2.5%. Figure 35 depicts the dependence of the as 2.5%. Figure 35 depicts the dependence of the transmission coefficient at f 0 with the isopropanol transmission coefficient at f0 with the isopropanol concentration, including the calibration curve (with concentration, including the2calibration curve (with a correlation coefficient of R2 = 0.9987), i.e., a correlation coefficient of R = 0.9987), i.e., 𝑆 S21 (dB) (𝑑𝐵) S21 ((𝑑𝐵) 𝑆 dB) Fv(%)==184.942𝑒 ( (21 184.942e 5.687 21 5.687 )) + 81.618e(( 45.449 45.449 ) )− 34.793 (7) (7) 𝐹𝑣(%) + 81.618𝑒 − 34.793 From thiscurve, From this curve, thethe concentration concentration of volume of volume fractionfraction of isopropanol of isopropanol can differentially, can be inferred be inferred differentially, by means of a single two-port by means of a single two-port measurement. measurement. The main differential aspect of the sensor of Figure 33 is the fact that a simple two-port measurement suffices to infer the differential output variable. Other differential sensor involving two-port measurements have been reported [12,68], but, in such sensors, neither resonant element is used, nor is operation in reflection mode considered. Nevertheless, note that in the recently presented sensor of [68], based on the phase difference generated in a pair of meandered lines, high sensitivity (11.52 dB/%) and resolution (1% of volume fraction) is obtained for the measurement of isopropanol content in DI water. This high sensitivity and resolution is in part due to the specific arrangement considered in [68], where a pair of rat race couplers is used (see further details in [68]). It is also important to highlight that in the sensor of Figure 33, a single rat-race coupler is used, because the Appl. Sci. 2020, 10, 2615 24 of 30 sensor operates in reflection. By contrast in [68], the sensing device utilizes a pair of rat race couplers, with Appl. the2020, Appl. Sci. Sci. consequently 2020, 10, 10, xx FOR penalty FOR PEER PEER in terms of size and cost. REVIEW REVIEW 24 24 of of 30 30 (a) (b) 33. Top Figure 33. Figure Topview viewofofthe thesensor sensortopology topology(a)(a) and and perspective perspective view view of the of the whole whole fabricated fabricated sensor sensor (b). (b). From [69], reprinted with permission. From [69], reprinted with permission. Ref Ref 10% 10% 40% 40% 70% 70% 100% 100% 0 2.5% 2.5% 20% 20% 50% 50% 80% 80% 5% 5% 30% 30% 60% 60% 90% 90% -10 |S 12| (dB) -20 -30 -40 1.65 1.70 1.75 1.80 1.85 1.90 Frequency (GHz) Figure 34. Frequency Figure 34. Frequency response responseof ofthe thesensing sensingstructure structurefor different for concentrations different of isopropanol concentrations of isopropanolin DI in water injected in the MUT channel, and pure DI water injected in the REF channel. From [69], DI water injected in the MUT channel, and pure DI water injected in the REF channel. From [69], reprinted with permission. reprinted with permission. Appl. Sci. 2020, 10, 2615 25 of 30 Appl. Sci. 2020, 10, x FOR PEER REVIEW 25 of 30 -5 -10 -15 |S21| (dB) -20 -25 -30 Measured mixtures -35 Using Eq. (13) -40 0 10 20 30 40 50 60 70 80 90 100 Isopropanol Content (%) Figure 35. Variation Figure 35. Variation of of the thetransmission transmissioncoefficient measuredatatf 0f0 (1.77GHz) coefficientmeasured (1.77GHz) with with the the isopropanol isopropanol content, and calibration curve. From [69], reprinted with permission. content, and calibration curve. From [69], reprinted with permission. 5. Conclusions The main differential aspect of the sensor of Figure 33 is the fact that a simple two-port measurement suffices In conclusion, to infer a review andthe differential recent developments outputofvariable. techniques Other differential for the sensor involving implementation of planar two-port measurements microwave resonant sensors have been have reported been reported [12,68], in thisbut, in such paper. Thesesensors, sensorsneither have beenresonant element classified in fouris used, nor groups, is operation according in reflection to their workingmode considered. principle, Nevertheless, i.e., frequency notesensors, variation that in the recently coupling presented modulation sensor offrequency sensors, [68], based on the sensors, splitting phase difference generated in asensors. and differential-mode pair of Their meandered lines, high advantages sensitivity and limitations (11.52been have dB/%) and resolution pointed (1% of volume out and discussed. We have fraction) is obtained also presented for the the most measurement usual electrically of isopropanol small resonant content inutilized elements DI water. for This high sensitivity of the implementation and resolution sensors, and is in part have due tosome provided the specific arrangement hints regarding the consideredresonator convenient in [68], where a pair topologies forof rat race and sensitivity couplers is used resolution (see furtherFinally, optimization. detailswe inhave [68]).illustrated It is also important the to highlight paper with that in the some prototype sensormainly sensors, of Figure 33, a single including sensorsrat-race couplercharacterization, for dielectric is used, becausebut the sensor operates in reflection. By contrast also sensors for measuring spatial variables. in [68], the sensing device utilizes a pair of rat race couplers, with the consequently penalty in terms of size and cost. Funding: This research activity was funded by MINECO-Spain (project TEC2016-75650-R), by Generalitat de Catalunya (project 2017SGR-1159), and by FEDER (European Union) funds. 5. Conclusions Acknowledgments: F.M. is in debt to Institució Catalana de Recerca i Estudis Avançats (ICREA) for supporting his work.In conclusion, J.M.E. a review acknowledges and recent Secreteraria developments d’Universitats of (Gen. i Recerca techniques for European Cat.) and the implementation Social Fund of forplanar the FI grant. P.V. acknowledges microwave the Juanhave resonant sensors de la been Ciervareported Program forin supporting this paper.him through These Project sensors haveIJCI-2017-31339. M.G. been classified in acknowledges the Universidad Politécnica de Madrid Young Researchers Support Program (VJIDOCUPM18MGB) for four groups, according to their working principle, i.e., frequency variation sensors, coupling its support. modulation sensors, frequency splitting sensors, and differential-mode sensors. Their advantages Conflicts of Interest: The authors declare no conflicts of interest. and limitations have been pointed out and discussed. We have also presented the most usual electrically small resonant elements utilized for the implementation of sensors, and have provided References some hints regarding the convenient resonator topologies for sensitivity and resolution optimization. 1. Gennarelli, Finally, we have G.;illustrated Romeo, S.; the Scarfì, paper M.R.; Soldovieri, with F. A microwave some prototype sensors,resonant mainlysensor for concentration including sensors for measurements of liquid solutions. IEEE Sens. 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