sensors Article Differential Microfluidic Sensors Based on Dumbbell-Shaped Defect Ground Structures in Microstrip Technology: Analysis, Optimization, and Applications Paris Vélez 1, * , Jonathan Muñoz-Enano 1 , Marta Gil 2 , Javier Mata-Contreras 3 and Ferran Martín 1 1 CIMITEC, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain 2 Departamento de Ingenieria Audiovisual y Comunicaciones, Universidad Politécnica de Madrid, 28031 Madrid, Spain 3 Departamento de Ingeniería de Comunicaciones, Universidad de Málaga, 29016 Málaga, Spain * Correspondence: paris.velez@uab.cat; Tel.: +34-93-581-3513  Received: 17 June 2019; Accepted: 17 July 2019; Published: 19 July 2019  Abstract: A microstrip defect ground structure (DGS) based on a pair of dumbbell-shaped slots is used for sensing. The device is a differential sensor consisting of a pair of mirrored lines loaded with a dumbbell-shaped DGS, and the output variable is the cross-mode transmission coefficient. Such a variable is very sensitive to asymmetries in the line pair, e.g., caused by an asymmetric dielectric load in the dumbbell-shaped DGSs. Therefore, the sensor is of special interest for the dielectric characterization of solids and liquids, or for the measurement of variables related to complex permittivity changes. It is shown in this work that by adding fluidic channels on top of the dumbbell-shaped DGSs, the device is useful for liquid characterization, particularly for the measurement of solute concentration in very diluted solutions. A sensitivity analysis useful for sensor design is carried out in this paper. Keywords: microwave sensors; differential sensors; fluidic sensors; dielectric characterization; microstrip technology; defect ground structure (DGS) 1. Introduction Defect ground structures (DGSs) are slot patterns of different shapes that have been exhaustively used in microwave engineering in applications as diverse as filters, antennas, and sensors [1–6]. In this work, the focus is on dumbbell-shaped DGSs [1] and their application to the design of novel differential sensors sensitive to changes in the complex dielectric constant of the so-called sample under test (typically a solid slab or a liquid). The proposed sensor consists of a pair of mirrored microstrip lines, each one loaded with a dumbbell-shaped DGS transversally oriented to the axis of the lines. The dumbbell-shaped DGS behaves as a series-connected parallel resonant tank, providing a notch in the transmission coefficient of each line, with the position and depth being dependent on the complex permittivity of the region surrounding the resonator. However, in the proposed sensor, the working principle is symmetry disruption [7–26], rather than frequency variation (the most usual working principle in resonator-based sensors [27–35]). The advantage of using symmetry disruption for sensing is the major robustness against cross sensitivities caused by environmental changes (e.g., temperature or moisture) [8]. Most sensors based on symmetry properties utilize coupling modulation [7–16] or frequency splitting [15–22]. Recently, Sensors 2019, 19, 3189; doi:10.3390/s19143189 www.mdpi.com/journal/sensors Sensors 2019, 19, 3189 2 of 18 it has been demonstrated that the cross-mode transmission coefficient is very useful for detecting tiny alterations of symmetry in a pair of lines [24,25], and differential sensors based on several types of resonant elements have been reported [24–26]. In [24–26,36,37], the resonant elements are metamaterial-inspired resonators coupled to the pair of lines, and fluidic channels are located on top of the most sensitive region of such resonant elements, in order to detect changes in the dielectric properties of liquids (liquid under test, LUT), as compared to a reference (REF) liquid. The method has been demonstrated to be useful for the measurement of the complex dielectric constant of liquids [25], as well as for the determination of solute content in extremely diluted solutions. For instance, in [37], the measurement of NaCl concentrations in deionized (DI) water with a resolution as small as 0.125 g/L and sensitivity of 0.034 (g/L)−1 was reported in a complementary split ring resonator (CSRR)-based sensor. It is also worth mentioning the application of the split ring resonator (SRR)-based differential sensor of [26], used for the measurement of the total electrolyte concentration in urine samples. Despite the fact that a good sensor performance was achieved in [26,37], a sensitivity analysis, providing design guidelines for the resonant elements, is not straightforward when considering either SRRs or CSRRs. By contrast, in [25,36], where the open complementary split ring resonators (OCSRRs) and open split ring resonators (OSRRs) were the considered resonant elements, such analysis was achieved, and important hints for sensor design were obtained. For example, it was concluded in [36] that for sensitivity optimization, high inductance and small capacitance of the resonant element (OSRR) were required. In the present paper, we focus on a differential sensor where the output variable is also the cross-mode transmission coefficient, but based on a pair of lines loaded with dumbbell-shaped DGSs. Such DGS can be modeled by a series-connected parallel resonator, and a simple sensitivity analysis can be carried out, as it will be shown. On the basis of this analysis, the dumbbell-shaped DGS has been designed for sensitivity optimization. Then, by adding fluidic channels, the structure has been applied to the measurement of the electrolyte concentration in very diluted solutions, and to the determination of the complex dielectric constant in mixtures of deionized (DI) water and isopropanol. 2. The Proposed Sensor, Functionality, Circuit Model, and Analysis The sensor consists of two parts: the microwave structure and the fluidic/mechanical part (Figure 1). The former is a pair of microstrip lines, each one loaded with a dumbbell DGS (etched in the ground plane). The fluidic/mechanical part is composed of the fluidic channels (fabricated by means of Polydimethylsiloxane-PDMS-polymer), plus the accessories required to provide mechanical stability (Polyether Ether Ketone-PEEK-material) and to inject the liquids into the channels. The fluidic channels are placed in contact with the ground plane, specifically on top of the capacitive regions of the dumbbell DGSs, with the most sensitive parts to the effects of liquids being in contact with them. Similar to the sensors reported in [25,26,36,37], the proposed sensor is based on symmetry disruption, and the output variable is the cross-mode transmission coefficient. Due to substrate absorption, a dry film of a clear polyester, with an estimated thickness of 50 µm and dielectric constant of 3.5, has been deposited on top of the dumbbell DGS, which is the sensing region of the sensor (this somehow degrades the sensitivity, but the presence of such a film is necessary to avoid absorption by the substrate). The sensor is able to detect differences between a reference liquid, injected into one of the channels (REF channel), and the liquid under test (LUT), injected into the other channel (LUT channel), manifested as a non-negligible cross-mode transmission coefficient. Note that if symmetry is preserved (identical liquids in both channels), mode conversion is not possible, and thereby the cross-mode transmission coefficient is ideally null. Sensors 2019, 19 FOR PEER REVIEW 3 Sensors 2019, 19, 3189 3 of 18 (a) (b) (c) Figure 1. 1. The Theproposed proposeddumbbell dumbbelldefect defectground ground structure structure (DGS)-based (DGS)-based sensor. sensor.(a) Topology (a) Topology of theof microwave the microwave part;part; (b) (b) lateral andand lateral toptopviews views of ofthethemechanical mechanicaland andfluidic fluidic parts; parts; (c)(c) complete three-dimensional three-dimensional view. view. Relevant Relevantdimensions dimensionsare are(in mm):ww1 1==ww (inmm): 2 = = 2, 2 2, wTLwTL = 1.14, = 1.14, lLT =lLT50,= l50, ld =g28, d = 28, d = gd =and 0.2, d = 44. 0.2,Sand = 44. Channel Sd Channel dimensions are (inare dimensions mm):(inhmm): hchlch== 1.5, ch = 1.5, 26, wlchch = = 4.6, 26, wlf ch = 4.6, = 46, = 46,hw wf =lf 12.6, 1=f=3, 12.6, and h21 == 9. 3, The 2 = 9. The substrate and hconsidered considered is substrate Rogers RO3010 is Rogers with a dielectric RO3010 dielectricεrconstant with aconstant εr = 10.2, = 10.2, thickness hthickness = 1.27 mm,h = and 1.27 loss mm,tangent and losstan δ = 0.0035. tangent = 0.0035. tanδ In (a), the In ground (a), theplane ground is depicted in light grey. plane is depicted in light grey. The equivalent equivalentcircuit circuitmodel model of the sensor of the is depicted sensor in Figure is depicted 2. The dumbbell in Figure DGSs areDGSs 2. The dumbbell modeledare series-connected parallel resonant tanks. The reactive elements L modeled as series-connected parallel resonant tanks. The reactive elements L and C are and as and C are the inductance the capacitance,and inductance respectively, of therespectively, capacitance, dumbbell DGSs without of the liquidDGSs dumbbell in the without channels,liquid whereas in G theaccounts channels,for the conductance, mainly related to substrate losses (provided that such conductance whereas G accounts for the conductance, mainly related to substrate losses (provided that such does not take into account the effects conductance of the does not takeliquid in the channel). into account the effects Byof introducing the liquid in liquid into the channels, the channel). the elements By introducing liquid that are into the expected channels,totheexperience elementsvariation that are are the capacitance expected and conductance to experience variation areofthethe capacitance dumbbell DGSs.and Therefore, we have included conductance of the dumbbell DGSs. C ref and G to Therefore, ref account for the effects of the liquid in the REF we have included Cref and Gref to account for the channel (if it is of effects present), the liquid in theCREF whereas and GLUT LUT channel (if are it isthe corresponding present), whereas element CLUT andvalues GLUT areforthe thecorresponding LUT channel. element values for the LUT channel. Finally, the transmission lines are0 described bylength Finally, the transmission lines are described by their characteristic impedance, Z , and electrical their kl, with l beingimpedance, characteristic the physical Z0length and k thelength , and electrical phasekl,constant. with l being the physical length and k the phase constant. Sensors 2019, 19, 3189 4 of 18 Sensors 2019, 19 FOR PEER REVIEW 4 Figure 2. Equivalent circuit model of the proposed sensor. sensor. Model Model validation validation has has been been carried carried out out byby comparing comparing electromagnetic electromagnetic simulations simulations (inferred (inferred by by means means of ANSYS HFSS) with circuit simulations (obtained by means of the schematic simulator of ANSYS HFSS) with circuit simulations (obtained by means of the schematic simulator included included in in Keysight Keysight ADS).ADS). SinceSince the the REF REF andand LUT LUT lines lines are are uncoupled, uncoupled, it it suffices suffices to to consider consider the the simulation (circuit and electromagnetic) of any of the lines. The absence simulation (circuit and electromagnetic) of any of the lines. The absence of coupling between of coupling between both lines both has linesbeen has verified from the been verified from electromagnetic the electromagnetic simulation of the single-ended simulation S-parameters, of the single-ended which are S-parameters, not which shown (where it has been found that the S-parameters involving are not shown (where it has been found that the S-parameters involving ports of both lines are ports of both lines are negligible). Particularly, we have considered negligible). Particularly, we have the REF linethe considered with REF anline emptywithchannel an empty (i.e., with air). channel (i.e.,The with frequency air). The response frequency(transmission coefficient)coefficient) response (transmission inferred from HFSSfrom inferred simulation is depicted is HFSS simulation indepicted Figure 3,in where Figure it is 3, compared with the circuit simulation. The extracted parameters are where it is compared with the circuit simulation. The extracted parameters are indicated in theindicated in the caption of Figure 3 (note that the presence of the channel and dry film has been taken into account caption of Figure 3 (note that the presence of the channel and dry film has been taken into account in in the electromagnetic simulations from which the electromagnetic parameters simulations from have beenparameters which extracted). Excellent have beenagreement extracted).inExcellent both the magnitude agreement and in both the magnitude and phase responses can be appreciated, indicative of have phase responses can be appreciated, indicative of the validity of the model. We also simulated the validity of the the REFWe model. linehave by considering also simulated the channel the REF full line ofbyDI water. Forthe considering thatchannel purpose, fulltheof complex DI water.dielectric For that constant purpose,ofthe water has been complex introduced dielectric in the constant ofHFSS watersimulator. has been The responseinisthe introduced alsoHFSS depicted in Figure simulator. The 3. The extracted parameters with an unloaded channel, i.e., C, L, and G, have response is also depicted in Figure 3. The extracted parameters with an unloaded channel, i.e., C, L, been maintained, whereas, to andinclude G, have thebeen effects of DI water maintained, in the channel, whereas, to include Creftheand Gref have effects of DIbeen water adjusted (the values in the channel, Cref are andalso Gref indicated in the caption of Figure 3). The circuit response corresponding have been adjusted (the values are also indicated in the caption of Figure 3). The circuit response to these circuit parameters is also included in Figure 3, and again, the agreement with the full wave corresponding to these circuit parameters is also included in Figure 3, and again, the agreement withelectromagnetic simulation is very good. the full wave Theelectromagnetic presence of DI water in the channel simulation has the is very good. effect The of decreasing presence the resonance of DI water frequency in the channel has of the dumbbell DGS and the notch magnitude. This is an expected the effect of decreasing the resonance frequency of the dumbbell DGS and the notch magnitude. result as far as the high dielectric This constant of DI water is an expected resultsignificantly as far as the increases the overall high dielectric capacitance constant of DIofwater the dumbbell significantlyDGS, increases and the high the dissipation factor of DI water (corresponding to a high value of the overall capacitance of the dumbbell DGS, and the high dissipation factor of DI water (correspondingimaginary part of the complex dielectric constant, to a high value of theor imaginary loss tangent) partenhances the losses of the complex of the resonant dielectric constant,element. or loss tangent) enhances the lossesThe of cross-mode the resonanttransmission element. coefficient of the structure depends on the length and characteristic impedance of the access lines (with impedance Z0 and electrical length kl). However, if the line impedance 0 is set to the reference impedance of 180 the ports, the 0 magnitude of the cross-mode transmission 180 coefficient only depends on the impedance of the dumbbell DGSs, according to [38]: phase S21(degree ) phase S21(degree ) -10 90 -5 90 1 |S21| (dB) |S21| (dB) Sdc 21 = 2 (S21 − S43 ) (1) -20 0 -10 0 where S21 and S43 are the transmission coefficients of the individual DGS-loaded lines, by excluding -30 lines. -90 -15 -90 the access HFSS EM Sim. 1 HFSS EM Sim. S21 = Eq. circuit Sim. Eq. circuit Sim. (2a) -40 -1801 + 1 -20 -180 0.5 1.0 1.5 2.0 2.5 2Z0 ZREF 3.0 0.5 1.0 1.5 2.0 Frequency (GHz) Frequency (GHz) (a) (b) Figure 2. Equivalent circuit model of the proposed sensor. Sensors 2019, 19, 3189 5 of 18 Model validation has been carried out by comparing electromagnetic simulations (inferred by means of ANSYS HFSS) with circuit simulations (obtained 1 by means of the schematic simulator included in Keysight ADS). Since the REF S43and = LUT1 lines are uncoupled, it suffices to consider(2b) the 1 + 2Z ZLUT simulation (circuit and electromagnetic) of any of the0 lines. The absence of coupling between both lines Additionally, the impedance has been verified from the electromagnetic DGSs, ZREFof of the dumbbell simulation theZsingle-ended and LUT , for the REF and LUT channels, S-parameters, which respectively, are given by are not shown (where it has been found that the S-parameters involving ports of both lines are jωL negligible). Particularly, we have considered ZREF = the REF line 2with an empty channel (i.e., with air). The (3a) 0 ω frequency response (transmission coefficient)jωLG inferredref −from ωref 2 + 1 simulation is depicted in Figure 3, HFSS where it is compared with the circuit simulation. The extracted parameters are indicated in the jωL caption of Figure 3 (note that the presence ZLUT =of the channel and dry film has been taken into account in (3b) 0 ω2 the electromagnetic simulations from whichjωLG LUT − ω2have parameters + been 1 extracted). Excellent agreement LUT in both the magnitude and phase responses can be appreciated, indicative of the validity of the In Equation (3a) and (3b), we have defined the following variables in order to simplify the notation: model. We have also simulated the REF line by considering the channel full of DI water. For that purpose, the complex dielectric constant of0 water has been introduced in the HFSS simulator. The C ref = C + Cref (4a) response is also depicted in Figure 3. The extracted parameters with an unloaded channel, i.e., C, L, and G, have been maintained, whereas, to G include 0 the effects of DI water in the channel, Cref and(4b) Gref ref = G + Gref have been adjusted (the values are also indicated in the caption of Figure 3). The circuit response 0 corresponding to these circuit parametersCisLUT also=included C + CLUTin Figure 3, and again, the agreement with (4c) the full wave electromagnetic simulationGis 0 very good. The presence of DI water in the channel has LUT = G + GLUT (4d) the effect of decreasing the resonance frequency of the dumbbell DGS and the notch magnitude. This is an expected result as far as the high dielectricω−2ref = LC 0 constant ref of DI water significantly increases (4e) the overall capacitance of the dumbbell DGS, and −2 the high ωLUT = LC LUT 0 dissipation factor of DI water (corresponding (4f) to a high value of the imaginary part of the complex dielectric constant, or loss tangent) enhances the lossesAlso note of the that Equation resonant (1) is correct as far as the REF and LUT lines are uncoupled. element. 0 180 0 180 phase S21(degree ) phase S21(degree ) -10 90 -5 90 |S21| (dB) |S21| (dB) -20 0 -10 0 -30 -90 -15 -90 HFSS EM Sim. HFSS EM Sim. Eq. circuit Sim. Eq. circuit Sim. -40 -180 -20 -180 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 Frequency (GHz) Frequency (GHz) (a) (b) Figure 3. Transmission coefficient (magnitude and phase) of the reference (REF) channel without liquid (a), and with deionized (DI) water (b), inferred from electromagnetic and circuit simulation. The element values of the equivalent circuit model are (in reference to Figure 2): Z0 = 50 Ω, kl = 78.51◦ , L = 2.40 nH, C = 2.51 pF, Cref = 5.74 pF, G = 0.18 mS, and Gref = 1.31 mS. Note that in the circuit simulations of (a), Cref = 0 pF and Gref = 0 mS, as corresponds to the absence of any liquid in the channel. Let us consider that the output variable is the cross-mode transmission coefficient evaluated at the resonance frequency of the reference channel, ωref . For small perturbations and low losses, ωref and ωLUT are not very different, and both G0 ref and G0 LUT are small compared to Y0 ≡ 1/Z0 . Under these circumstances, we can express S21 and S43 as 1 S21 |ωref = 1  2Z0 G0 ref (5a) 1+ 2Z0 G0 ref Sensors 2019, 19 FOR PEER REVIEW 6 Sensors 2019, 19, 3189 1 6 of 18 𝑆43 | = 1 1+ 1 2𝑍 𝐺′ 𝑟𝑒𝑓 1 ω1ref  1   1  S43 |ωref = 0 𝐿𝑈𝑇 − 𝑗 2Z 0 𝐿 0 GLUT − 2 − j2  − 2  (5b) (5b) 1+ 1 ! 𝑟𝑒𝑓 L  ω2 𝐿𝑈𝑇 ωLUT ω ref 2Z0 G0 LUT −j ref L 1 − 1 ω2 ω2 𝑟𝑒𝑓 1 1 ref LUT ≅ 2𝑍0 𝐺′𝐿𝑈𝑇 − 𝑗 − 𝐿 2𝑟𝑒𝑓 2𝐿𝑈𝑇 and the modulus of the cross-mode transmission coefficient is found to be and the modulus of the cross-mode transmission coefficient is found to be Sdc 21 ω  Z0 Gref − GLUT + jωref (Cref − CLUT ) (6) 𝑆𝑑𝑐 ≅ 𝑍0 𝐺𝑟𝑒𝑓 − 𝐺𝐿𝑈𝑇 + 𝑗𝑟𝑒𝑓 (𝐶𝑟𝑒𝑓 − 𝐶𝐿𝑈𝑇 ) ref 21 (6)  Since Z0 is not a design parameter, the sensitivity of the output variable, |S21 DC |ωref , with the Since Z differential 0 is not a design conductance, Gref −Gparameter, the sensitivity of the output variable, |S21DC|ωref, with the LUT , cannot be controlled. On the other hand, it follows from (6) that differential the sensitivity conductance, of the outputGrefvariable −GLUT, cannot with thebe differential controlled. On the other Chand, capacitance, it follows from (6) that ref −CLUT , increases with the the sensitivity resonance of theofoutput frequency the REF variable channel,with ωref .the differential It also capacitance, follows from (6) that ifCGref−C= ref LUTG,LUT increases with the , the magnitude resonance frequency of the REF channel, ω . It also follows from (6) that of the cross-mode transmission coefficient should not depend on L and C, provided these elements ref if G ref = G LUT, the magnitude of the and Crefcross-mode transmission give a constant value ofcoefficient ωref . This should not depend is corroborated on L and in Figure C, provided 4, where these elements the magnitude of the and Cref givetransmission cross-mode a constant value of ωreffor coefficient . This is corroborated different in FigureIn4,all cases is depicted. where the magnitude the cases, ωref = 1.13 of the GHz, cross-mode transmission coefficient for different cases is depicted. In all but different combinations of L and C have been considered in order to obtain the above cited valuethe cases, ω ref = 1.13 GHz, butωdifferent of combinations of L and C have been considered in order to obtain the above cited value ref with the same value of Cref = 5.74 pF. Nevertheless, rather than the differential capacitance of ω or conductance,same ref with the value variables the input of Cref = 5.74 in apF. realNevertheless, scenario are, rather than the typically, differential material (liquid capacitance in our case)or conductance, the input variables in a real scenario are, typically, material parameters, such as the dielectric constant and the loss tangent, or other variables related to them (liquid in our case) parameters, (e.g., such asconcentration). the electrolyte the dielectric constant Therefore, anda the loss step further tangent, or other in is necessary variables order torelated determine to them the dependence of the cross-mode transmission coefficient with these material parameters, which willthe (e.g., the electrolyte concentration). Therefore, a further step is necessary in order to determine be dependence discussed next.of the cross-mode transmission coefficient with these material parameters, which will be discussed next. 0 0 0 CLUT=6.2 pF CLUT = 6.2 pF CLUT = 6.2 pF -10 -10 -10 CLUT=5.9 pF CLUT = 5.9 pF CLUT = 5.9 pF -20 CLUT=5.8 pF -20 CLUT = 5.8 pF -20 CLUT = 5.8 pF CLUT = 5.745 pF -30 CLUT=5.745 pF -30 -30 CLUT = 5.745 pF |S21 | dB |S21 | dB |S21 | dB -40 -40 -40 DC DC DC -50 -50 -50 -60 -60 -60 -70 -70 -70 -80 -80 -80 1.0 1.1 1.2 1.3 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 Frequency(GHz) Frequency(GHz) Frequency(GHz) (a) (b) (c) Figure 4. Figure 4. Cross-mode Cross-mode transmission transmission coefficient inferred by by circuit circuit simulation simulation for different different cases, cases, and and the indicated the indicated values valuesof (a) L == 0.1 LUT. (a) ofCCLUT nH, C == 192.63 0.1 nH, pF; (b) L = 192.63 pF; = 1.7 nH, C = = 5.93 pF; (c) L = = 2.9 nH, CC == 1.10 pF. In all the cases, Cref ref ==5.74 5.74pF pFand andG’ 0 Gref == ref G’G 0 = 1.489 = 1.489 LUTLUT mS.mS. Let Let us us assume assume that that the the capacitive capacitive slot slot of of the the dumbbell dumbbell DGSDGS isis narrow narrow compared compared to to the the thickness thickness of of the thesubstrate, substrate,and andthatthat the the substrate is thick substrate enough is thick to consider enough that the that to consider electric thefield lines field electric generated lines in the slot region do not reach the air region present at the opposite side of the substrate. generated in the slot region do not reach the air region present at the opposite side of the substrate. Let us also consider that the height of the channels is great enough to guarantee that the electric Let us also consider that the height of the channels is great enough to guarantee that the electric field field lines generated in the dumbbell lines generated DGS slot in the dumbbell do not DGS slotextend do notbeyond extend the regionthe beyond occupied region by the liquid occupied by present in the liquid the channel. Under these conditions, it can be considered that two uniform half-spaces, present in the channel. Under these conditions, it can be considered that two uniform half-spaces, the substrate and the liquid,and the substrate surround the slot the liquid, capacitance. surround According the slot to [35], capacitance. C’ref andtoC’ According [35], can LUT C’ ref be andexpressed C’LUT canasbe expressed as εr + ε   C0 ref = C  + ref (7a) ε + 1 𝐶′ =𝐶 r (7a)   +1  εr + ε C0 LUT = C  + LUT εr +1 (7b) 𝐶′ =𝐶 (7b)  +1 Therefore, the differential capacitance that appears in the imaginary part of Equation (6) is Sensors 2019, 19, 3189 7 of 18 Therefore, the differential capacitance that appears in the imaginary part of Equation (6) is C Cref − CLUT = C0 ref − C0 LUT = (ε − εLUT ) (8) εr + 1 ref If we now express C as the contribution of the substrate and air capacitance, i.e., C = Csubs + Cair (9) and we take into account that Csubs = εr ·Cair , it follows that εr + 1 C = Csubs (10) εr Therefore, Equation (8) can be expressed as Csubs Cref − CLUT = (εref − εLUT ) (11) εr Since Csubs is proportional to the dielectric constant of the substrate, εr , it follows that the sensitivity of the output variable with the differential dielectric constant, εref −εLUT , is proportional to ωref , and determined by the geometry of the slot, particularly by its length and width. Note that Csubs is roughly proportional to the slot length and it increases by decreasing the slot width. Hence, for sensitivity optimization with regard to the differential permittivity, narrow and long slots for the dumbbell DGS are required. The relation between the conductance of the REF or LUT liquid and the corresponding loss tangents is given by [35] Gref Gref (εr + 1) tan δref = = (12a) (Cair + Cref )ωref Cεref ωref GLUT GLUT (εr + 1) tan δLUT = = (12b) (Cair + CLUT )ωLUT CεLUT ωLUT Therefore, Csubs ωref Gref − GLUT = (εref tan δref − εLUT tan δLUT ) (13) εr where the approximation ωref ≈ ωLUT has been used. In this case, it is not possible to express the differential conductance, Gref − GLUT , as proportional to the differential loss tangent. Nevertheless, the inspection of Equation (13) reveals that the differential conductance is proportional to ωref and it is also determined by the slot dimensions (through Csubs ), with identical dependence to the differential capacitance. Introducing Equations (11) and (13) into Equation (6), the cross-mode transmission coefficient is found to be Csubs ωref Sdc 21 ωref  Z0 εref tan δref − εLUT tan δLUT + j(εref − εLUT ) (14) εr Let us analyze Equation (14) more carefully, or, more precisely, the relevant term providing the sensitivity of the output variable with the differential dielectric constant and loss tangent. Such a term can be expressed as Csubs ωref C εr + εref −1/2   = subs L(Csubs + Cair ) (15) εr εr εr + 1 and after some straightforward calculation, one obtains r Csubs ωref 1 Cair = √ (16) εr εr + εref L Sensors 2019, 19 FOR PEER REVIEW 8 Sensors 2019, 19, 3189 8 of 18 That is, for sensitivity optimization, it is convenient to choose a substrate with a small value of the dielectric That is, for constant. sensitivity Nevertheless, optimization, if it the dielectric constant is convenient to choose ofathe REF liquid, substrate with asmall , isvalue high,of(astheis usual in constant. dielectric liquids), Nevertheless, it follows that thedielectric if the dependence constantof the of the sensitivity REF liquid, onεref , isis high, small(as(since is usual inis obscureditby liquids),  ). On follows thatthetheother hand, sensitivity dependence optimization of the sensitivity on εr depends on theεratio is small (since by εref ). Cair/L. Increasing r is obscured the the On slotother length, hand,ld, has the effectoptimization sensitivity of increasingdepends both Cairon and the L.ratio Cair /L.whereas However, Increasing Cairthe increases roughly slot length, ld , proportionally has the effect of with the length increasing both Cof air the and slot, L. L However, does not whereas (it has C air been increases corroborated roughly by extracting proportionally parameters with the length in several structures of the slot, L doeswherenot (it the has geometry of the slots been corroborated by has been modified). extracting parameters The in result several is that the sensitivity structures where the increases geometry with of thetheslotsslot haslength, and for this been modified). Thereason, result isa that dumbbell DGS with the sensitivity a long increases slot has with thebeen considered slot length, and in forthe designed this reason,sensor.a dumbbell On the DGS other withhand, the width a long slot has of been the slot, gd, does not considered in have the any influence designed sensor.on OnL,the whereas, other hand, by reducing the width it, of Cairthe increases, slot, gd , thereby does notenhancing have any influencethe sensitivity. on L, For this reason, whereas, by reducing we have it, Cairsetincreases, gd to thethereby minimum value of enhancing thethe availableFor sensitivity. fabrication this reason, technology we have (0.2 set gmm). d to the minimum value of the available fabrication technology (0.2 mm). Equation (14) Equation (14) gives gives thethe magnitude magnitude of of the the cross-mode cross-mode transmission transmission coefficient coefficient as as aa function function of of the dielectric the dielectricproperties propertiesofofthe theREFREF and and LUT LUT liquids liquids (εref(ε, ref, εLUT εLUT , tanδ , tanδ , refref , andand tanδ tanδ LUTLUT ). Considering DI DI water as water asthe thereference referenceliquid liquid(with(withaacomplex complexdielectric dielectricconstantconstantof of80.66–j4.92 80.66–j4.92at atωωref ), and ref), and thethe LUT LUT channelfull channel fullwithwith a hypothetical a hypothetical liquid liquid exhibiting exhibiting complex complex dielectric dielectric constantconstant variationvariation of 3% of 3% (smaller) (smaller) compared compared to the one to of the the oneREFof the REF liquid (i.e.,liquid (i.e., 78.24–j4.77), 78.24–j4.77), we have obtained we havethe obtained responses theof responses both lines, of bothfrom and lines, andthe them, from them, thetransmission cross-mode cross-modecoefficienttransmission (Figure coefficient 5). The (Figure circuit and 5). electromagnetic The circuit and electromagnetic simulation responsessimulation responses are depicted in thearefigure. depicted in the figure. Moreover, Figure Moreover, 5b includes Figure 5b includes the results derivedthe results from thederived analytical from the analytical Equations (6) and (14). Equations Equations (6) (6) and and (14). (14) Equations provide an(6) and (14) provide undistinguishable an result, undistinguishable which in turn coincides result, which in well reasonably turnwith coincides reasonably the results inferred well fromwith thethe results inferred electromagnetic and from the circuit electromagnetic simulations at ωrefand. In circuit simulations other words, at ωref. (and the analytical In other words, the approximate) analytical formulas predict,(andinapproximate) a reasonable formulas way, predict, the value of the in cross-mode a reasonabletransmission way, the value coefficient at ωref . Suchtransmission of the cross-mode good agreement coefficient validates at ω ref. the Such good proposed agreement equivalent validates circuit modelthe proposed (Figure equivalent 2), including liquid circuit model (Figure properties (Cref , Gref 2), , Cincluding LUT , and Gliquid LUT ), properties (C , G , C , and G ), as well as the low-loss and as well as the low-loss and small perturbation assumptions for the considered case. Once the proposed ref ref LUT LUT small perturbation assumptions for the considered sensor case. Once analyzed, has been presented, the proposed sensor has the and optimized, been presented, results experimental analyzed, willand optimized, the be summarized in experimental the next section. results will be summarized in the next section. 0 -15 HFSS EM Sim. HFSS EM Sim. Equivalent Circuit Sim. -20 Equivalent Circuit Sim. Equation (1) using Equation (2) |S21| , |S43| (dB) -5 -25 Equation (6) |S21 |(dB) Equation (14) -30 -10 DC -35 -40 -15 -45 ref. Liquid (DI Water) LUT (DI Water -Δε∗(3%)-) -20 -50 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 Frequency (GHz) Frequency (GHz) (a) (b) Figure 5.5. (a) Simulated frequency response for the magnitude Figure magnitude ofof the the transmission transmission coefficients coefficients considering deionized (DI) water in the reference (REF) channel and 3% perturbed considering deionized (DI) water in the reference (REF) channel and 3% perturbed DI water in DI water in the the liquidunder liquid undertesttest (LUT) (LUT) channel; channel; (b) magnitude (b) magnitude of the cross-mode of the cross-mode transmission transmission coefficient coefficient considering considering the presentedthe presented equivalent equivalent circuit model,circuit model, the HFSS the HFSS electromagnetic electromagnetic (EM) simulations,(EM)and simulations, Equationsand (6) Equations and (14). (6) and (14). 3. 3. Results Results The The experimental experimental results results obtained obtained by by using using the the proposed proposed sensor sensor for for the the characterization characterization of of electrolyte concentration (particularly NaCl) in DI water and for the measurement of the electrolyte concentration (particularly NaCl) in DI water and for the measurement of the complex complex dielectric dielectric constant constantof ofliquids liquids(mixtures (mixturesofofisopropanol isopropanoland andDIDIwater), water),are arepresented presentedininthis thissection. section. Sensors Sensors 2019, 19, Sensors 2019, 2019, 19 3189 PEER 19 FOR FOR PEER REVIEW REVIEW 9 of 1899 3.1. Electrolyte (NaCl) Concentration Measurements in DI Water 3.1. Electrolyte (NaCl) Concentration Measurements in DI Water The measurement of electrolyte concentration in urine and/or blood can be used as an indicator The measurement of electrolyte concentration in urine++and/or blood 2+ can be used as an indicator of of certain pathologies. Electrolytes are cations (e.g., Na , K++, and Ca2+ ) and anions (e.g., Cl−− and certain−− pathologies. Electrolytes are cations (e.g., Na+ , K+ , and Ca2+ ) and anions (e.g., Cl− and HCO3 − ) HCO33 ) that result from the dissociation of polar solvents, e.g., NaCl. In this work, the experimental that result from the dissociation of polar solvents, e.g., NaCl. In this work, the experimental study is study is focused on the determination of NaCl concentration (the solute) in DI water (the solvent), focused on the determination of NaCl concentration (the solute) in DI water (the solvent), through the through the measurement of the maximum value of the cross-mode transmission coefficient. The measurement of the maximum value of the cross-mode transmission coefficient. The pure DI water pure DI water acts as the REF liquid, whereas the LUT is the solution of NaCl in DI water (different acts as the REF liquid, whereas the LUT is the solution of NaCl in DI water (different levels of NaCl levels of NaCl concentration are considered). The proposed sensor is able to detect very small concentration are considered). The proposed sensor is able to detect very small concentrations of NaCl, concentrations of NaCl, as it will be shown, thereby providing a very good resolution. as it will be shown, thereby providing a very good resolution. The fabricated microwave sensor, including the screws used to assemble the mechanical and The fabricated microwave sensor, including the screws used to assemble the mechanical and fluidic fluidic parts, is shown in Figure 6. The considered substrate for the microwave circuitry is the Rogers parts, is shown in Figure 6. The considered substrate for the microwave circuitry is the Rogers RO3010 RO3010 with a dielectric constant εrr = 10.2, thickness h = 1.27 mm, and loss tangent tan δ = 0.0035. The with a dielectric constant εr = 10.2, thickness h = 1.27 mm, and loss tangent tan δ = 0.0035. The different different mixtures of DI water and NaCl have been prepared carefully in the laboratory. The mixtures of DI water and NaCl have been prepared carefully in the laboratory. The measurements measurements have been carried out by the well-known stop-flow technique. This means that the have been carried out by the well-known stop-flow technique. This means that the two channels are two channels are filled (by syringe) with the REF liquid (DI water) and LUT (DI water with NaCl filled (by syringe) with the REF liquid (DI water) and LUT (DI water with NaCl content), see Figure 7. content), see Figure 7. Then, the flow is stopped for measurement, and the relevant information Then, the flow is stopped for measurement, and the relevant information (maximum cross-mode (maximum cross-mode transmission coefficient, or other potential information of interest, such as transmission coefficient, or other potential information of interest, such as the resonance frequency, the resonance frequency, quality factor, etc.) is recorded and processed (if it is needed). quality factor, etc.) is recorded and processed (if it is needed). (a) (b) Figure 6. Figure 6. Photographs Photographs of the fabricated microwave sensor. The The considered considered materials materials are are indicated. indicated. (a) Top (a) Top view view (b) (b) Lateral Lateral view. view. Figure Figure 7. 7. Setup Setup for for experimental experimental sensor sensor verification verification in in the the laboratory. laboratory. Following the aforementioned technique, the measured cross-mode transmission coefficient for the different mixtures of DI water and NaCl is plotted in Figure 8a. To evaluate the symmetry of the Following structure, the aforementioned both channels technique, are filled with the same theliquid measured cross-mode (the REF liquid). transmission The maximum coefficient for cross-mode the different mixtures of DI water and NaCl is plotted in Figure 8a. To evaluate the symmetry insertion loss (the cross-mode transmission coefficient expressed in dB) for this case is −31.94 dB, of the structure, which both channels is considered to beare filled with the a reasonable same result, liquid (the indicating REF that theliquid). Theismaximum structure cross-mode quite balanced when insertion loss (the cross-mode transmission coefficient expressed in dB) for this case is −31.94 identical liquids are present in both channels. It should be mentioned that for proper balance, we first dB, which is considered to be a reasonable result, indicating that the structure is quite balanced when Sensors 2019, 19 FOR PEER REVIEW 10 Sensors 2019, 19, 3189 10 of 18 identical liquids are present in both channels. It should be mentioned that for proper balance, we first measured the cross-mode transmission coefficient of the structure without fluidic channels, in measured the cross-mode transmission coefficient of the structure without fluidic channels, in order to order to verify that the cross-mode transmission coefficient is very small (ideally null in a perfectly verify that the cross-mode transmission coefficient is very small (ideally null in a perfectly balanced balanced structure). Then, we repeated this procedure after adding the fluidic channels, in order to structure). Then, we repeated this procedure after adding the fluidic channels, in order to verify that verify that the structure is also balanced with the presence of the fluidic channels. If necessary, the the structure is also balanced with the presence of the fluidic channels. If necessary, the pressure of the pressure of the channels on the microwave substrate can be tailored by means of the screws. Once channels on the microwave substrate can be tailored by means of the screws. Once the structure exhibits the structure exhibits good balance (typically with a cross-mode insertion loss better than 30 dB), good balance (typically with a cross-mode insertion loss better than 30 dB), then it is quite robust from then it is quite robust from a mechanical viewpoint. As the concentration of NaCl in DI water a mechanical viewpoint. As the concentration of NaCl in DI water increases, the maximum cross-mode increases, the maximum cross-mode insertion loss also increases, as expected, due to an increasing insertion loss also increases, as expected, due to an increasing symmetry imbalance between both symmetry imbalance between both channels. The main effect of the presence of electrolytes in DI channels. The main effect of the presence of electrolytes in DI water is the variation of the dissipation water is the variation of the dissipation factor (loss tangent or imaginary part of the complex factor (loss tangent or imaginary part of the complex permittivity), due to the fact that electrolytes permittivity), due to the fact that electrolytes are ions, significantly contributing to the increase in the are ions, significantly contributing to the increase in the conductivity of the solution. The results of conductivity of the solution. The results of Figure 8a, indicating that the frequency of maximum Figure 8a, indicating that the frequency of maximum cross-mode insertion loss (for each concentration cross-mode insertion loss (for each concentration level) does not experience a significant change, level) does not experience a significant change, corroborate the previous assertion. It should also be corroborate the previous assertion. It should also be pointed out that concerning environmental pointed out that concerning environmental parameters, changes in temperature and pressure may alter parameters, changes in temperature and pressure may alter the response of the lines, but these the response of the lines, but these environmental parameters are seen as a common mode stimulus in environmental parameters are seen as a common mode stimulus in a differential sensor like this, a differential sensor like this, and, therefore, their influence is not expected to be important. and, therefore, their influence is not expected to be important. -10 0.25 60 g/L Calibration measurement 40 g/L Calibration curve. Equation (15) Measurement 2 -15 20 g/L 0.20 10 g/L 0.100 |S21 |max(linear) 5 g/L |S21 |(dB) 2.5 g/L -20 0.15 0.075 |S21 |max(linear) 1 g/L 0.5 g/L DC 0.050 0.25 g/L -25 0.10 DC 0 g/L DC 0.025 -30 0.05 0.000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 [NaCl] (g/L) -35 0.00 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0 10 20 30 40 50 60 Frequency (GHz) [NaCl] (g/L) (a) (b) Figure 8. Figure 8. (a) Cross-mode insertion insertion loss loss for for different differentconcentrations concentrationsof ofNaCl NaCl(b) Variationofof|S|S (b)Variation 2121 || DCDC max max with NaCl with NaCl content. content. 2121DC|| The DC The variation variation of of the the maximum maximum value value ofof the the cross-mode cross-modetransmission transmissioncoefficient coefficient(|S (|S max) with max with the the concentration concentration of of NaCl NaCl (in (in g/L) g/L) isis depicted depicted in in Figure Figure 8b. 8b. The The calibration calibration curve curve (Equation (Equation 17) 17) with with the the correlation coefficient R correlation coefficient R22 = = 0.99992 is also plotted in the the figure. figure. The sensitivity increases as the the NaCl concentration decreases (see the zoom inset in Figure 8b). The highest value NaCl concentration decreases (see the zoom inset in Figure 8b). The highest value of the sensitivity of the sensitivity has been found to beto0.035 −1 , with (g/L)(g/L) a sensor resolution of 0.25 g/L.g/L. To To evaluate thethe repetitiveness of has been found be 0.035 -1, with a sensor resolution of 0.25 evaluate repetitiveness the sensor of the response, sensor a seta of response, setmixtures of mixtures of DIofwater and NaCl DI water (corresponding and NaCl (correspondingto the to concentrations the concentrationsof the first of thecampaign) has been first campaign) hasinjected in aleatory been injected order in the in aleatory LUT order in channel. the LUT The results channel. areresults The also plotted are alsoin Figure plotted8b,inand designated Figure 8b, and as Measurement designated as2. Measurement The small differences 2. Thebetween the calibration small differences curve and between the the Measurement calibration 2 curve curve and the verify the correct Measurement functionality 2 curve verify theand repetitiveness correct of the functionality andsensor. repetitiveness of the sensor.  g SDC SDC 21 21 [NaCl] = 3.425e( 0.085 ) + 3.295e−4 e( 0.019 ) − 4.98 (17) 𝑔L . [NaCl] = 3.425𝑒 + 3.295𝑒 𝑒 . − 4.98 (17) 𝐿 3.2. Dielectric Characteritzation of Isopropanol in DI Water The functionality of the proposed microwave sensor also extends to the dielectric characterization of liquids, i.e., the determination of the complex dielectric constant. In this case, the output variable will be the difference between the maximum cross-mode insertion loss (∆ SDC 21 max = SDC21 max,REF − SDC 21 max,LUT ) and the difference between the frequencies of the maximum cross-mode insertion loss (∆ fmax = Sensors 2019, 19 FOR PEER REVIEW 11 3.2. Dielectric Characteritzation of Isopropanol in DI Water Sensors 2019, 19, 3189 11 of 18 The functionality of the proposed microwave sensor also extends to the dielectric characterization of liquids, i.e., the determination of the complex dielectric constant. In this case, the fmax,LUT output− fvariable max,REF ) for each will bemeasurement. the difference Thebetween reason for thismaximum the is that the complex cross-mode dielectric constant insertion loss is composed ( ∆|𝑆 | of real = |𝑆 | and imaginary− |𝑆 | parts, thereby ) and the difference between the frequencies of for requiring two independent output variables theits , , univocal maximum determination. cross-mode insertion loss (∆𝑓 =𝑓 , − 𝑓 , ) for each measurement. The reason The dielectric characterization of liquids for this is that the complex dielectric constant is composed proceeds as follows. of First of all,imaginary real and the maximum parts,cross-mode thereby insertion loss and its frequency position when both channels requiring two independent output variables for its univocal determination. are loaded with pure DI water (the REF liquid) The are recorded. dielectric These values correspond characterization of liquidsto the reference proceeds level, namely as follows. SDC First of 21all, and fmax,REF , the maximum max,REF respectively. cross-modeThen, pureloss insertion isopropanol is injected and its frequency into the position whenLUT channel both channels andaretheloaded corresponding with purevalues DI water (the REF liquid) are recorded. These values correspond of the maximum cross-mode insertion loss and frequency position are obtained. This is repeated to the reference level, namely for|𝑆a mixture | , ofand𝑓 , respectively. 50% of, isopropanol. The Then, pure isopropanol cross-mode insertionislossinjected into the LUTtochannel corresponding these LUTsand is the corresponding depicted in Figure 9a.values Knowing of the themaximum cross-mode complex dielectric constant (at ω insertion loss ref ) and of frequency pure DI water position are (80.66–j4.92), obtained. This is repeated for a mixture of 50% of isopropanol. The of pure isopropanol (13–j5.9), and of a mixture of 50% of isopropanol (32.38−5.38 j), and assuming cross-mode insertion loss corresponding a linear dependence to these of the LUTs is depicted complex in Figure dielectric 9a. Knowing constant with ∆ S the DCcomplex and dielectric ∆ fmax , itconstant is possible (at to 21 max ωref) of express thepure DI water variation of the(80.66–j4.92), of pure isopropanol real and imaginary (13–j5.9), permittivity parts of the complex and of a mixture with theof 50% of following isopropanol (32.38−5.38 j), and assuming linear regression in order to calibrate the sensor: a linear dependence of the complex dielectric constant with ∆|𝑆 | and ∆𝑓 , it is possible to express the variation of the real and imaginary parts of the complex permittivity with the ∆ε following 0 = k ∆linear SDC regression + k ∆ in f order to calibrate the sensor: (18a) 11 21 max 12 max ∆𝜀 = 𝑘 ∆|𝑆 | + 𝑘 ∆𝑓 (18a) ∆ε00 = k21 ∆ SDC 21 max + k22 ∆ fmax (18b) ∆𝜀 = 𝑘 ∆|𝑆 | + 𝑘 ∆𝑓 (18b) -5 100% Isopropanol 26 70 95% Isopropanol 90% Isopropanol 24 85% Isopropanol 22 60 -10 80% Isopropanol 75% Isopropanol 20 18 50 Δ|S21 |max(dB) 70% Isopropanol Δfmax(MHz) |S21 |(dB) -15 65% Isopropanol 16 60% Isopropanol 14 40 55% Isopropanol 12 DC -20 50% Isopropanol 30 DC 45% Isopropanol 10 40% Isopropanol -25 35% Isopropanol 8 20 30% Isopropanol 6 25% Isopropanol 4 10 -30 20% Isopropanol 2 15% Isopropanol 10% Isopropanol 0 0 5% Isopropanol 0.9 1.0 1.1 1.2 1.3 0% Isopropanol 0 10 20 30 40 50 60 70 80 90 100 Frequency (GHz) Isopropanol Content (%) (a) (b) Figure Figure 9. (a) 9. (a) Cross-mode Cross-mode insertion insertion lossloss for for different different mixtures mixtures of isopropanol of isopropanol andand deionized deionized (DI)(DI) water water (b) dependence of Δ|S21 DC|max and Δfmax with isopropanol content. (b) dependence of ∆|S21 |max and ∆f max with isopropanol content. DC TheThe unknown unknown variables variables k11k,11k,12k12 , k, 21 k21, ,and andkk2222 were were found found toto be 11 = be kk11 = 3.789 3.789 dB k12= = dB−1−1, ,k12 0.441 0.441MHz MHz−1,−1 , k21k= 21 = 0.009dB 0.009 −1 dB ,, and −1 22 ==0.010 and kk22 0.010MHz MHz. Then, −1 −1 we we . Then, sequentially injected sequentially the different injected the different mixtures of DI of mixtures DI water waterand andisopropanol isopropanolinto intothe theLUT LUTchannel channelwithwitha avolume volumefraction fraction ranging rangingfrom from 0%0%to to 100% in in 100% steps of 5%. All of these measurements are plotted in Figure 9a. The ∆|𝑆 steps of 5%. All of these measurements are plotted in Figure 9a. The ∆ S21 max and ∆ fmax for each |DC and ∆𝑓 for each measurement measurement are are shownininFigure shown Figure9b. 9b.FromFrom Equation Equation (18) (18) and andthethedata dataofofFigure Figure9b, 9b,the real the and real thethe and imaginary part of the complex dielectric constant, as a function of isopropanol imaginary part of the complex dielectric constant, as a function of isopropanol content in DI water, content in DI water, have been obtained (Figure 10). In the same figure, the Weiner model [44] has been used to establish have been obtained (Figure 10). In the same figure, the Weiner model [39] has been used to establish the the upper and lower limits of the real and imaginary part of the complex dielectric constant for upper and lower limits of the real and imaginary part of the complex dielectric constant for mixtures mixtures of both liquids. The calculated values for the complex dielectric constant of mixtures of DI of both liquids. The calculated values for the complex dielectric constant of mixtures of DI water and water and isopropanol are between the limits predicted by the Weiner model. These results validate isopropanol are between the limits predicted by the Weiner model. These results validate the correct the correct functionality of the proposed sensor for the dielectric characterization of liquids. functionality of the proposed sensor for the dielectric characterization of liquids. Sensors 2019, 19 FOR PEER REVIEW 12 Sensors 2019, 19, 3189 12 of 18 90 6.0 Weiner upper limit Weiner upper limit 80 Weiner lower limit Weiner lower limit 5.8 ε (imaginary part) Weiner model Weiner model 70 Extracting using Equation (18a) Extracting using Equation (18b) ε (real part) 60 5.6 50 5.4 40 5.2 ' 30 '' 20 5.0 10 4.8 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Isopropanol Content (%) Isopropanol Content (%) (a) (b) Figure10.10. Extracted Figure Extracted value value for for the the complex complex dielectric dielectric constant constant inin mixtures mixturesofofdeionized deionized(DI) (DI) water/isopropanol. water/isopropanol. (a)(a) Real part. Real (b) Imaginary part. part.part. (b) Imaginary The static Weiner The static model model Weiner (upper (upper and lower andlimits) lower islimits) also included for comparison is also included purposes.purposes. for comparison ItItshould shouldalso alsobebepointed pointedout outthat thatthe thesensor sensorisisuseful usefulfor formonitoring monitoringthetheconcentration concentrationofof isopropanol isopropanolininDIDIwater, water,with witha aresolution resolutionofofatatleast least5% 5%ofofthe thevolume volumefraction, fraction,asasderived derivedfrom fromthe the results of Figure 9a. results of Figure 9a. 4.4.Comparison Comparisonwith withOtherOtherMicrowave MicrowaveSensor SensorApproaches Approachesand andDiscussion Discussion Let us now compare the proposed sensor with other sensors devoted to measuring the solute Let us now compare the proposed sensor with other sensors devoted to measuring the solute content contentinindiluted dilutedsolutions solutionsofofDIDIwater. water.Due Duetotothe thedifficulty difficultyininfinding findingother othermicrowave microwavesensors sensors reported in the literature, measuring the same solute (in this case NaCl) reported in the literature, measuring the same solute (in this case NaCl) and the same, or similar, and the same, or similar, output outputvariable, variable,we wehave haveincluded includedcomparative comparativeworks workswhere wheresolutions solutionsofofglucose glucose(and (andevenevenheavy heavy metals metals like Zn) have been considered. As it can be seen in Table 1, the reported solutionbased like Zn) have been considered. As it can be seen in Table 1, the reported solution basedon on dumbbell DGS resonators offers a good sensor performance (i.e., combination dumbbell DGS resonators offers a good sensor performance (i.e., combination of sensitivity, of sensitivity, resolution, and input dynamic resolution, and input range). In references dynamic range). In [25,26,40,41], the authors use references [25,26,39,47], theNaCl as the authors usesolute, NaCl whereas the as the solute, other sensors are used for glucose concentration measurement, except whereas the other sensors are used for glucose concentration measurement, except [48,49], devoted[42,43], devoted to measurement oftothe Zn concentration measurement of theinZn DIconcentration water. According in DItowater.TableAccording 1, for the NaCl or glucose to Table concentration, 1, for the NaCl or glucose the proposed sensor and the one presented in [26] offer the best sensitivity concentration, the proposed sensor and the one presented in [26] offer the best sensitivity and and resolution, the key sensor parameters. resolution, the Indeed, the sensitivity key sensor parameters. of both sensors Indeed, theissensitivity comparable, but itsensors of both shouldisbecomparable, mentioned but thatit inshould [26], thebeconsidered mentionedsubstrate that in is FR4, [26], thewith a significantly considered smaller substrate dielectric is FR4, with constant, compared a significantly to smaller the one of the sensor reported in this work. As it has been previously dielectric constant, compared to the one of the sensor reported in this work. As it has been discussed, a small dielectric constant previouslysubstrate favorsasensitivity. discussed, Moreover, small dielectric the measurement constant substrate favorsof the maximum sensitivity.sensitivity Moreover,may the bemeasurement somehow inaccurate because it is influenced by the cross-mode of the maximum sensitivity may be somehow inaccurate because it is influenced insertion loss under balancedby conditions (i.e., with the cross-mode the REF insertion lossliquid underinbalanced both channels). conditionsThe(i.e., achieved with thevalue REFin liquid this work is −31.94 in both dB, channels). asThe indicated achieved before, valuewhereas in [26],is−38.95 in this work −31.94 dB dB,was obtained. before, as indicated Although the sensor whereas reported in [26], −38.95 in dB[26], was based obtained. Although the sensor reported in [26], based on split ring resonators (SRRs), is the on split ring resonators (SRRs), is very competitive, the analysis of SRR-loaded lines for very determination competitive, of thethe sensitivity analysis and the dependence of SRR-loaded lines foron thethedetermination main parameters is not of the straightforward. sensitivity and the Bydependence on the main parameters is not straightforward. By contrast, in thisdesign, contrast, in this paper, we have provided expressions which are useful for sensor paper, as wefarhave as they predict the output variable as a function of material parameters reasonably provided expressions which are useful for sensor design, as far as they predict the output variable as well, and provide useful hints for a function of sensitivity material optimization (this is indeed parameters reasonably theand well, mainprovide relevant useful contribution hints of forthesensitivity present paper). On the other hand, the sensors reported in [42,43], for Zn concentration optimization (this is indeed the main relevant contribution of the present paper). On the other measurements, exhibit hand, antheextremely good resolution (but a limited dynamic range), at the sensors reported in [48,49], for Zn concentration measurements, exhibit an extremely good expense of using functionalized bismuth resolutionoxide coatings. (but a limited dynamic range), at the expense of using functionalized bismuth oxide coatings. Sensors 2019, 19, 3189 13 of 18 Table 1. Comparison of various microwave fluidic sensors for solute concentration measurement in liquid solutions. Max. Sensitivity Dynamic Range Reference Resolution (g/L) (dB·L/g) (g/L) [25] 4.3 0.25 80 [26] 12.27 0.25 60 [23] 1.609 0.5 100 [40] 0.005 2 10 [44] 0.003 1 300 [45] 1.75 1.5 5.5 [46] 0.017 10 150 [47] 0.003 5 300 [37] 6.54 0.125 60 [41] 0.822 0.5 40 [42] 7 0.0001 0.01 [43] 65 0.001 0.1 [This work] 10.08 0.25 60 For the measurement of dielectric properties of liquids in the microwave range using resonant elements, the comparison is often based on the relative sensitivity of the resonance frequency with the real part of the complex dielectric constant, defined as 1 d f0 Sav, f = (19) f0 dεr Note that in the reported differential sensor, the frequency considered as the output variable is f max , i.e., the frequency where the cross-mode insertion loss is maximized. This frequency does not correspond to the resonance frequency of the dumbbell DGS loaded with the LUT under consideration. Therefore, for a useful comparison, we should consider the relative sensitivity as derived by the variation experienced by the resonance frequency of the LUT channel, f 0 , with the relative dielectric constant of the LUT. This relative sensitivity, identified in Table 2 as “single ended (SE)”, is excellent, indicating that the dumbbell DGS resonator is very sensitive to changes in the dielectric constant of its surroundings. Nevertheless, we have also included in the table the relative sensitivity derived by considering the variation of f max with εr,LUT , and identified in the table as “Diff.” (which is worse than the previous one). According to these words, if differential sensing is not due, “single-ended measurements” provide a better sensitivity of the resonance frequency with the real part of the dielectric constant of the material under test. The reported sensor provides a good resolution in regard to the volume fraction (Fv ) of solute content, regardless of its functionality as a differential or single-ended sensor, and it exhibits the best SE sensitivity among all the sensors of Table 2. Moreover, operation in differential mode is convenient due to the major robustness against cross sensitivities, as mentioned before, and it is used in applications of the sensor as a comparator, where real-time monitoring of the differences between a sample under test and a reference sample is typically required. Sensors 2019, 19, 3189 14 of 18 Table 2. Comparison of various microwave fluidic sensors for dielectric characterization. Reference f 0 (GHz) Diff. Sav,fmax /“SE” Sav,f0 Fv (%) [48] 20 -/2.98 5 [28] 2 -/2.38 10 [33] 1.9 -/0.81 10 [34] 3.5 -/2.61 10 [22] 0.87 -/0.91 10 [49] 2.5 -/3.2 0.005 [25] 0.9 1.86/2.28 5 [50] 5.5 -/0.53 0.1 [51] 5.28 -/0.193 - [52] 2.3 -/4.08 10 [53] 2.29 -/3.26 [54] 0.077 -/1.08 0.5 [55] 5.2 -/1.12 20 This work 1.05 1.02/5.98 5 Note that the analysis of Section 2, providing Equation (14), has been mainly devoted to inferring the design strategy of the dumbbell DGS, in order to enhance sensor sensitivity (i.e., to achieve the maximum variation of the modulus of the cross-mode transmission coefficient at ωref with either the differential dielectric constant or loss tangent). The validity of Equation (14), by considering small perturbations, has been demonstrated in Section 2. However, such an expression has not been used for the determination of NaCl concentration in Section 3a, or for the measurement of the complex dielectric constant in mixtures of isopropanol and DI water in Section 3b. In the former case, the relationship between the loss tangent and the NaCl content in solutions of NaCl in DI water is not easy to infer, so we have opted to obtain the calibration curve depicted in Figure 8b. Moreover, the validity of Equation (14) is constrained to small perturbations. Concerning the determination of the complex dielectric constant in solutions of isopropanol and DI water, not only is the small perturbation approximation not always satisfied, but also, it is not possible to obtain the material parameters (dielectric constant and loss tangent), using Equation (14), from the measurement of the cross-mode transmission coefficient. This is because the determination of two parameters requires two independent measurements. For these main reasons, the interest of Equation (14) is not the analytical determination of the variables of interest, but the deduction of the shape of the dumbbell DGS for sensitivity optimization. Additionally, in the fabricated sensor, a dry film is necessary in order to avoid substrate absorption, and this is an additional limitation concerning the validity of Equation (14). Nevertheless, to gain insight into the limitations relative to the validity of Equation (14) in a real scenario (sensor with a dry film and/or subjected to significant imbalances), we have considered the sensor with DI water in the REF channel and with a mixture of isopropanol and DI water in the LUT channel. In such mixtures, we have first considered a volume fraction of 5% isopropanol, corresponding to a relatively small imbalance in the sensor. The material parameters for DI water are εref = 80.66 and tanδref = 0.0609; for the considered 5% isopropanol solution, they are εLUT = 77.277 and tanδLUT = 0.0643, as derived from the Weiner model. From the simulation of the transmission coefficient of the individual lines, we have obtained the resonance (notch) frequency for both the REF line, f 0,ref , and LUT line, f 0,LUT . Such frequencies are related to the dielectric constants of the REF and LUT liquids according to 2 f0,ref εr + εLUT = (20) f2 εr + εref 0,LUT From the previous expressions, it is possible to derive the dielectric constant of the LUT, provided that εref is known. The result is εLUT = 77.38, i.e., very close to the nominal value introduced in the simulation (77.277). Then, we have introduced this value, as well as the material parameters of DI water given above, into expression (14). From the simulated value of the cross-mode transmission Sensors 2019, 19, 3189 15 of 18 coefficient at ωref , we have isolated the loss tangent of the considered LUT liquid, and the resulting value has been found to be tanδLUT = 0.0630, i.e., in good agreement with the nominal value (0.0643). By repeating the simulation with a dry film with the thickness and dielectric constant indicated in Section 2, the material parameters are found to be εLUT = 78.11 and tanδLUT = 0.0682. That is, the discrepancies are higher, and such discrepancies are even higher when the material parameters are obtained from the measured data (εLUT = 79.63 and tanδLUT = 0.0687). These results indicate that with a 5% volume fraction of isopropanol, the small perturbation approximation is valid, and the substrate, the REF liquid, and the LUT liquid can be considered to be semi-infinite. In other words, for this level of isopropanol content (5%), Equation (14) is valid, provided the sensor is not equipped with a dry film. However, the presence of the dry film limits the validity of Equation (14), providing only approximate values. By considering values of the isopropanol content above 10%, Equation (20) provides good results concerning the dielectric constant of the LUT liquid, provided a dry film is not used. The reason for this is that this expression is valid, regardless of the sensor imbalance. However, the determination of the loss tangent of the LUT is not as accurate, compared to the 5% case, since the imbalance cannot be considered small. In addition, the discrepancies further increase by considering the presence of the dry film. Therefore, the determination of material (liquid) parameters through Equation (14) is limited to small perturbations and REF and LUT liquids in direct contact with the sensitive element (the dumbbell DGS). Although we have added a dry film in order to avoid absorption (as justified before), there are substrates that prevent absorption. In those cases, Equation (14) can be used to predict liquid parameters, provided that the REF and LUT liquids are not very different. Nevertheless, the determination of εLUT through Equation (20) is first required. Then, this parameter is introduced in Equation (14), and from this expression, and the measured cross-mode transmission coefficient, the loss tangent of the LUT can be obtained. 5. Conclusions In conclusion, a real-time differential microwave sensor based on a pair of transmission lines loaded with dumbbell-shaped DGS resonators has been presented, analyzed, and validated. The sensing method is based on symmetry disruption, produced by the presence of two different materials in the sensing regions, the capacitive slots of the dumbbell DGSs. This work has focused on the characterization of liquid solutions, where the reference (REF) material has been deionized (DI) water, and the liquid under test (LUT) has included different solutions of either NaCl or isopropanol (the solutes) in DI water (the solvent). For that purpose, the sensor has been equipped with a pair of fluidic channels: one for the REF liquid and the other one for the LUT. The sensor has been optimized in order to detect tiny differences between the REF liquid and the LUT, measured through the cross-mode transmission coefficient, the output variable. For sensitivity optimization, the circuit model and an accurate analysis, from which we have derived the dependence of the output variable with the material parameters, have been the key aspects, and the main relevant contribution of this paper. It has been found that the sensitivity is optimized by designing a dumbbell DGS with narrow and long slots. The sensor has been used for the measurement of NaCl concentrations in DI water, where a resolution as good as 0.25 g/L, with a maximum sensitivity of 10.08 (dB·L/g), has been achieved. Then, the functionality of the sensor for the measurement of the complex dielectric constant of liquids (particularly solutions of isopropanol in DI water), has been demonstrated. The sensor can be used for the characterization of many other types of liquids and solutions, and it is especially useful for monitoring real-time changes in an LUT compared to an REF liquid. Author Contributions: P.V. developed and designed the methodology and the creation of the models, as well as the validation of the experimental results. He also participated in the writing of the article. J.M.-E. analyzed the data and was involved in the writing of the paper. M.G. simulated the different models in the 3D Electromagnetic solver software (HFSS). J.M.-C. contributed with his knowledge on the sensors field and checked the paper. F.M. conceived the work and wrote the article. Sensors 2019, 19, 3189 16 of 18 Funding: This work was supported by MINECO-Spain (project TEC2016-75650-R), by Generalitat de Catalunya (project 2017SGR-1159), by Institució Catalana de Recerca i Estudis Avançats (who awarded Ferran Martín), and by FEDER funds. Acknowledgments: J. Muñoz-Enano thanks Secretaria d’Universitats i Recerca (Gen. Cat.) and European Social Fund for the FI grant. Paris Vélez thanks the Juan de la Cierva Program for supporting him through Project IJCI-2017-31339. M. Gil thanks the Universidad Politécnica de Madrid Young Researchers Support Program (VJIDOCUPM18MGB) for its support. Conflicts of Interest: The authors declare no conflicts of interest. References 1. Ahn, D.; Park, J.S.; Kim, C.S.; Qian, Y.; Itoh, T. A Design of the Lowpass Filter Using the Novel Microstrip Defected Ground Structure. IEEE Trans. Microw. Theory Tech. 2001, 49, 86–93. [CrossRef] 2. Kumar, A.; Kartikeyan, A. 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