This is the accepted version of the article: Muñoz Enano, Jonathan; Vélez Rasero, Paris; Gil Barba, Marta; [et al.]. «Differential-mode to common-mode conversion detector based on rat-race hy- brid couplers : analysis and application to differential sensors and comparators». IEEE Transactions on Microwave Theory and Techniques, Vol. 68, issue 4 (April 2020), p. 1312-1325. DOI 10.1109/TMTT.2019.2955676 This version is avaible at https://ddd.uab.cat/record/221398 under the terms of the license Differential-Mode to Common-Mode Conversion Detector Based on Rat-Race Hybrid Couplers: Analysis and Application to Differential Sensors and Comparators Jonathan Muñoz-Enano, Student Member IEEE, Paris Vélez, Member IEEE, Marta Gil, Javier Mata- Contreras, and Ferran Martín, Fellow IEEE  Abstract—A microwave device able to detect differential- mode noise, which in turn may affect device performance. mode to common-mode conversion (or vice versa) in a four- For that reason, many efforts have been dedicated to the port balanced circuits is proposed. For mode conversion design of common-mode filters [2],[3]-[22], as well as to detection, the balanced circuit should be fed by a differential- the design of balanced circuits with inherent common-mode mode signal, generated by means of a rat-race balun from a single-ended signal. By connecting the pair of output ports of rejection [23]-[57]. Nevertheless, mode conversion in the balanced circuit under test to one of the two pairs of balanced circuits should be avoided, or minimized as much isolated ports of a second rat-race coupler, conversion to the as possible, by ensuring accurate fabrication processes that common-mode (if it exists) can be detected, and recorded in prevent from symmetry disruption (imbalances). the -port. Since the signal level at the output (single-ended) Balanced structures have been also applied to the design port depends on mode conversion efficiency, the complete two- of differential sensors [58]-[62]. Such sensors offer a high port structure, including the pair of rat-race couplers plus the level of robustness against cross sensitivities related to balanced circuit in between, can be used as a comparator or differential microwave sensor based on mode conversion. In environmental conditions (e.g., temperature, moisture, etc.), such sensor, the working principle is symmetry disruption as far as ambient factors are seen as common-mode (caused, e.g., by an asymmetric dielectric load), and the output stimulus. Typically, these sensors consist of a pair of mirror variable is the transmission coefficient, related to the level of structures (independent sensors), sensitive to the variable to asymmetry. A detailed analysis, considering an arbitrary be sensed (measurand). Sensing principle is symmetry unbalanced four-port test structure (to account for symmetry truncation caused by a difference in the measurand in both disruption), is carried out. Then, such analysis is particularized to the case of a pair of unbalanced and sensing parts, one for the reference (REF) measurand (well uncoupled matched lines, and the conditions for sensitivity known), and the other one for the measurand under test optimization are obtained. Finally, a differential sensor and (MUT). The output variable is usually inferred from the comparator based on a pair of balanced (and meandered) difference between a certain magnitude (sensitive to the matched lines, designed according to the guidelines for measurand) recorded in the REF and MUT sensing parts. It sensitivity optimization, is fabricated and validated. should be mentioned that other similar sensors which are Index Terms–Common-mode, differential-mode, differential also based on symmetry disruption but cannot be sensor, microstrip, microwave sensor, rat-race coupler. considered true differential sensors, have been recently reported [63]-[77]. I. INTRODUCTION A useful parameter to detect symmetry imbalances caused by differences between the REF and MUT T HE INTEREST for differential-mode (or balanced) microwave circuits has increased in recent years due to their high immunity to electromagnetic interference (EMI), measurand in differential sensors is the cross-mode transmission coefficient. This parameter, sensitive to mode noise and crosstalk (at least as compared to single-ended conversion, has been used as output variable in differential circuits) [1],[2]. A critical aspect in balanced circuits is sensors based on pairs of balanced transmission lines mode conversion, typically caused by an imperfect balance loaded with resonant elements (the sensing element) [78]- and responsible for the generation of (undesired) common [80]. In [79],[80], such sensors were applied to the determination of solute concentration in very diluted Manuscript received Month DD, YYYY; revised Month DD, YYYY; solutions, by adding fluidic channels on top of the resonant accepted Month DD, YYYY. elements. Very competitive resolution and sensitivity, as This work was supported by MINECO-Spain (project TEC2016-75650- compared to the reported literature to date [81]-[85], was R), by Generalitat de Catalunya (project 2017SGR-1159), by Institució Catalana de Recerca i Estudis Avançats (who awarded Ferran Martín), and achieved. However, in the sensors reported in [79],[80], by FEDER funds. J. Muñoz-Enano acknowledges Secreteraria four-port devices, the output variable (cross-mode d’Universitats i Recerca (Gen. Cat.) and European Social Fund for the FI transmission coefficient) was obtained from the grant. Paris Vélez acknowledges the Juan de la Cierva Program for supporting him through Project IJCI-2017-31339. M. Gil acknowledges measurement of the mixed-mode S-parameters the Universidad Politécnica de Madrid Young Researchers Support [1],[2],[86],[87], which involves either a four-port vector Program (VJIDOCUPM18MGB) for its support. network analyzer, or multiple two-port measurements of J. Muñoz-Enano, P. Vélez, and F. Martín are with GEMMA/CIMITEC, Departament d’Enginyeria Electrònica, Universitat Autònoma de single-ended S-parameters with the corresponding Barcelona, 08193 Bellaterra, Spain. E-mail: Ferran.Martin@uab.es. conversion to mixed-mode S-parameters. M. Gil is with Departamento Ingeniería Audiovisual y Comunicaciones, In this work, we propose a simple strategy to detect mode Universidad Politécnica de Madrid, 28031 Madrid, Spain. conversion in balanced structures (potentially subjected to J. Mata-Contreras is with Departamento de Ingeniería de Comunicaciones, Universidad de Málaga, 29016 Málaga, Spain. symmetry imbalances), which is then applied to the implementation of differential sensors. This strategy where the mixed mode S-parameters are related to the consists of adding a pair of rat-race couplers conveniently single-mode S-parameters according to well-known connected to the pair of input and output ports of the transformations (see, e.g., [2]), i.e., balanced sensing structure, resulting in a simple two-port 1 𝑆 − 𝑆𝐴𝐵 − 𝑆𝐵𝐴 + 𝑆𝐵𝐵 𝑆𝐴𝐴′ − 𝑆𝐴𝐵′ − 𝑆𝐵𝐴′ + 𝑆𝐵𝐵′ 𝐒𝐝𝐝 = ( 𝐴𝐴 ) (3a) device. The main advantage is the simplicity in the 2 𝑆𝐴′𝐴 − 𝑆𝐴′𝐵 − 𝑆𝐵′𝐴 + 𝑆𝐵′𝐵 𝑆𝐴′𝐴′ − 𝑆𝐴′𝐵′ − 𝑆𝐵′𝐴′ + 𝑆𝐵′𝐵′ measurement of the output variable, the single-ended 1 𝑆 + 𝑆𝐴𝐵 + 𝑆𝐵𝐴 + 𝑆𝐵𝐵 𝑆𝐴𝐴′ + 𝑆𝐴𝐵′ + 𝑆𝐵𝐴′ + 𝑆𝐵𝐵′ 𝐒𝐜𝐜 = ( 𝐴𝐴 ) (3b) transmission coefficient of the whole two-port structure, 2 𝑆𝐴′𝐴 + 𝑆𝐴′𝐵 + 𝑆𝐵′𝐴 + 𝑆𝐵′𝐵 𝑆𝐴′𝐴′ + 𝑆𝐴′𝐵′ + 𝑆𝐵′𝐴′ + 𝑆𝐵′𝐵′ intimately related to the cross-mode transmission 1 𝑆 + 𝑆𝐴𝐵 − 𝑆𝐵𝐴 − 𝑆𝐵𝐵 𝑆𝐴𝐴′ + 𝑆𝐴𝐵′ − 𝑆𝐵𝐴′ − 𝑆𝐵𝐵′ 𝐒𝐝𝐜 = ( 𝐴𝐴 ) (3c) coefficient of the balanced sensing part. A detailed analysis 2 𝑆𝐴′𝐴 + 𝑆𝐴′𝐵 − 𝑆𝐵′𝐴 − 𝑆𝐵′𝐵 𝑆𝐴′𝐴′ + 𝑆𝐴′𝐵′ − 𝑆𝐵′𝐴′ − 𝑆𝐵′𝐵′ of the proposed system, which will provide important hints 1 𝑆 − 𝑆𝐴𝐵 + 𝑆𝐵𝐴 − 𝑆𝐵𝐵 𝑆𝐴𝐴′ − 𝑆𝐴𝐵′ + 𝑆𝐵𝐴′ − 𝑆𝐵𝐵′ 𝐒𝐜𝐝 = ( 𝐴𝐴 ) (3d) for sensitivity optimization, is also carried out. This is a 2 𝑆𝐴′𝐴 − 𝑆𝐴′𝐵 + 𝑆𝐵′𝐴 − 𝑆𝐵′𝐵 𝑆𝐴′𝐴′ − 𝑆𝐴′𝐵′ + 𝑆𝐵′𝐴′ − 𝑆𝐵′𝐵′ relevant contribution of the present work. Moreover, such Note that the pair of composite differential- and common- analysis is validated from full-wave electromagnetic mode ports, necessary to derive the above transformations, simulations, and then used for the design of a simple are considered to be the ports A-B and A’-B’ (driven as a differential sensor and comparator, based on a pair of pair). Thus, for perfect symmetry conditions, with regard to meandered lines (intended to demonstrate/validate the the indicated bisection plane O-O’, the cross-mode (or proposed sensing strategy, including sensitivity mode conversion) matrices, Scd and Sdc, are null. By optimization). contrast, in the use of the mode conversion detector as The work is organized as follows. The proposed mode differential sensor or comparator (Section V), a symmetry conversion detector and working principle are presented in imbalance will be deliberately generated. Particularly, in Section II. The analysis focused on the determination of the such application, the sensitive parts of the structure transmission coefficient (the key parameter) for the general (symmetrically located with regard to the O-O’ plane) are case of an arbitrary four-port test structure (to account for loaded with different samples (the reference sample, REF, possible symmetry imbalances, the case of actual interest) is and the sample sunder test, SUT). The result of such carried out in Section III. Then, Section IV considers the imbalance is mode conversion, and, consequently, Scd  0 particular case of a pair of uncoupled matched lines, and the and Sdc  0. conditions for sensitivity optimization (i.e., enhancement of the transmission coefficient with the phase difference of the two lines), are discussed. In Section V, the conclusions of the previous analysis are applied to the design of a differential sensor/comparator, which is experimentally validated in Section VI. Such validation includes a defect detector, a sensor to determine the dielectric constant of low-loss samples, and a sensor to determine the volume fraction of liquid solutions. Finally, the main conclusions of the work are highlighted in Section VII. Fig. 1. Structure of the proposed mode conversion detector. II. THE PROPOSED MODE CONVERSION DETECTOR AND The input port of the two-port mode conversion detector WORKING PRINCIPLE is the -port of the first coupler (port 2), whereas the output port is the -port of the second coupler (port 1’). The ports The proposed mode conversion detector consists of a pair in both couplers are differentiated by means of a super- of rat-race hybrid couplers connected to the four-port index prime (‘) in the second coupler. For a matched (arbitrary) circuit under study as shown in Fig. 1. Such isolated port (-port) in coupler 1 (port 1), such coupler acts four-port circuit, not necessarily reciprocal, can be either as a balun, providing out of phase signals at ports 3 and 4 described by the single-ended S-parameters, or by the (i.e., a pure differential signal in the differential port 3-4, or mixed-mode S-parameters. According to the port A-B). Similarly, by terminating the -port in the second designation (Fig. 1), the single-ended S-parameter matrix is coupler (port 2’) with a matched load, the -port (port 1’) 𝑆𝐴𝐴 𝑆𝐴𝐴′ 𝑆𝐴𝐵 𝑆𝐴𝐵′ only detects common-mode signals, if they are present, at 𝑆𝐴′𝐴 𝑆𝐴′𝐴′ 𝑆𝐴′𝐵 𝑆𝐴′𝐵′ the composite port 3’-4’ (or A’-B’). Therefore, the structure 𝐒𝐬𝐞 =( ) (1) 𝑆𝐵𝐴 𝑆𝐵𝐴′ 𝑆𝐵𝐵 𝑆𝐵𝐵′ is sensitive to differential-mode to common-mode 𝑆𝐵′𝐴 𝑆𝐵′𝐴′ 𝑆𝐵′𝐵 𝑆𝐵′𝐵′ conversion, potentially caused by symmetry imbalances, either undesired or deliberated. In the former case, the whereas the mixed-mode S-parameter matrix can be structure can be used to detect fabrication inaccuracies in expressed as a combination of four order-2 matrices as follows balanced circuits. In the second case (deliberate symmetry truncation), the device is useful as differential sensor (as it 𝑑𝑑 𝑑𝑑 𝑑𝑐 𝑑𝑐 𝑆11 𝑆12 𝑆11 𝑆12 has been pointed out), the case of interest in this work. 𝐝𝐝 𝑑𝑑 𝐒 𝐝𝐜 ) = 𝑆21 𝑑𝑑 𝑆22 𝑑𝑐 𝑆21 𝑑𝑐 𝑆22 According to the previous words, it is expected that the 𝐒𝐦𝐦 = (𝐒 𝐜𝐝 𝐜𝐜 𝑐𝑑 𝑐𝑑 𝑐𝑐 𝑐𝑐 (2) transmission coefficient of the complete two-port structure 𝐒 𝐒 𝑆11 𝑆12 𝑆11 𝑆12 𝑐𝑑 𝑐𝑑 𝑐𝑐 𝑐𝑐 (including the pair of couplers and the four-fort network in ( 𝑆21 𝑆22 𝑆21 𝑆22 ) between) is related to the cross-mode S-parameters of the four-port network, in turn correlated with the level of asymmetry of such network. The calculation of such transmission coefficient is carried out in the next section, 𝑎𝐵′ = 𝑏4′ (8g) where the general case of ports 1 and 2’ terminated with 𝑏𝐵′ = 𝑎4′ (8h) arbitrary loads is considered. The normalized amplitudes of the reflected voltage waves III. GENERAL ANALYSIS (referred to the couplers) that appear in the right-hand side The working principle of the proposed mode conversion members in (7) are given by: detector has been explained by considering the isolated 𝑗 𝑗 𝑏3 = − (𝑎1 + 𝑎2 ) = − (𝑏1 + 𝑎2 ) (9a) ports of the couplers (ports 1 and 2’) terminated with √2 √2 matched loads. However, it does not mean that this 𝑗 𝑗 𝑏3′ = − (𝑎1′ + 𝑎2′ ) = − ′𝑏2′ (9b) termination is the optimum one in order to obtain a √2 √2 maximum variation of the modulus of the transmission 𝑗 𝑗 𝑏4 = − (𝑎1 − 𝑎2 ) = − (𝑏1 − 𝑎2 ) (9c) coefficient of the structure as symmetry imbalances √2 √2 increase (sensitivity optimization). Therefore, the following 𝑗 𝑗 𝑏4′ = − (𝑎1′ − 𝑎2′ ) = − (−′𝑏2′ ) (9d) analysis, devoted to obtain the transmission coefficient of √2 √2 the mode conversion detector, is carried out by considering with a1 = b1 and a’2 = ’b’2. Note also that a’1 = 0 in (9), arbitrary loads in ports 1 and 2’, described by reflection since port 1’ should be matched for the calculation of the coefficients  and ’, respectively (see Fig. 1). Let us call f0 transmission coefficient (see expression 5). By introducing the operating frequency of the device, at which the length of the right-hand side terms of (9) in (7), and the resulting the ring couplers is exactly 1.5 ( being the guided expressions in (6), the normalized amplitude of the output wavelength), and let Z0 be the reference impedance of the voltage wave at port 1’ is found to be: ports. With the port designation of Fig. 1, the S-parameter matrix of the couplers (at f0) is [88] 𝑐𝑐 𝑏1′ = −{𝑆21 𝑏1 + 𝑆21 𝑐𝑑 𝑐𝑑 𝑎2 + 𝑆22 ′𝑏2′ } (10) 0 0 1 1 where the correspondence between mixed-mode and single- 𝑗 0 0 1 −1 ended S-parameters of the four-port network (expressions ′ 𝐒=𝐒 =− ( ) (4) 3) has been used. √2 1 1 0 0 1 −1 0 0 In order to obtain the transmission coefficient of the whole structure according to (5), the first and third terms of In the present analysis, we will deal with the normalized the second member in (10) must be written as a function of amplitudes of the voltage waves incident to (ai) or reflected a2. For that purpose, the first step is to express b1 and b’2, from (bi) the ports, where the sub-index i identifies the port. given by The variable of interest in this study, the transmission 𝑗 coefficient of the whole structure, is given by 𝑏1 = − (𝑎3 + 𝑎4 ) (11a) √2 𝑏1′ 𝑗 𝑆1′2 = | (5) 𝑏2′ = − (𝑎3′ − 𝑎4′ ) (11b) 𝑎2 𝑎′ =0 √2 1 where, again, the super index prime is used to distinguish in terms of the same variables that appear in the second between the normalized amplitudes of the incident and member of (10). The procedure is very similar to the one reflected waves in both couplers. According to (4), b1’ is detailed before to obtain equation (10), and for that reason it 𝑗 is not repeated. The obtained results are found to be: 𝑏1′ = − (𝑎3′ + 𝑎4′ ) (6) √2 𝑐𝑐 𝑏1 = −{𝑆11 𝑏1 + 𝑆11 𝑐𝑑 𝑐𝑑 𝑎2 + 𝑆12 ′𝑏2′ } (12) where the normalized amplitude of the incident voltages at 𝑏2′ = 𝑑𝑐 −{𝑆21 𝑏1 + 𝑑𝑑 𝑆21 𝑎2 + 𝑑𝑑 𝑆22 ′𝑏2′ } (13) ports 3’ and 4’ can be expressed as a function of the elements of the single-ended S-parameter matrix of the where, again, (3) has been used. From (12), b1 can be four-port network, i.e., expressed in terms of a2 and b’2, i.e., 𝑐𝑑 𝑎 +𝑆 𝑐𝑑 ′𝑏 ′ 𝑎3′ = 𝑆𝐴′𝐴 𝑏3 + 𝑆𝐴′𝐴′ 𝑏3′ + 𝑆𝐴′𝐵 𝑏4 + 𝑆𝐴′𝐵′ 𝑏4′ (7a) 𝑏1 = − 𝑆11 2 12 2 (14) 𝑐𝑐  1+𝑆11 𝑎4′ = 𝑆𝐵′𝐴 𝑏3 + 𝑆𝐵′𝐴′ 𝑏3′ + 𝑆𝐵′𝐵 𝑏4 + 𝑆𝐵′𝐵′ 𝑏4′ (7b) By introducing (14) in (13), b’2 can be isolated and Note that (7) results from the following (trivial) expressed in terms of a2 as follows correspondence between normalized amplitudes of incident and reflected voltages waves of the couplers (right side 𝑏2′ = 𝑀′𝑎2 (15) members) and the four-port network (left side members): where M’, introduced to simplify the notation, depends only 𝑎𝐴 = 𝑏3 (8a) on the mixed-mode S parameters of the four-port network, as well as on the reflection coefficients of the loads present 𝑏𝐴 = 𝑎3 (8b) at ports 1 and 2’, i.e., 𝑎𝐴′ = 𝑏3′ (8c) 𝑑𝑑 − 𝑆𝑑𝑐 𝑐𝑑 21 𝑆11 𝑆21 1+𝑆𝑐𝑐 11 𝑏𝐴′ = 𝑎3′ (8d) 𝑀′ = − ′𝑆𝑑𝑐 𝑐𝑑 (16) 𝑑𝑑 − 1+′𝑆22 21 𝑆12 1+𝑆𝑐𝑐 11 𝑎𝐵 = 𝑏4 (8e) 𝑏𝐵 = 𝑎4 (8f) From (14), b1 can be expressed in terms of a2 as 𝑏1 = 𝑀𝑎2 (17) respectively. The other term needed for the determination of where S1’2 is M, given by 𝑐𝑑 +′𝑀′𝑆 𝑐𝑑 𝑆11 12 ′ 𝑒 −𝑗𝐴 +𝑒 −𝑗𝐵 𝑀=− 𝑐𝑐 1+𝑆11 (18) 𝑀= (𝑒 −𝑗𝐴 − 𝑒 −𝑗 𝐵 ) { ′ 2 } (22) 4 1− (𝑒 −𝑗𝐴 −𝑒 −𝑗𝐵 ) 4 Finally, by introducing (15) and (17) in (10), b’1 can be expressed as proportional to a2, and the transmission and the transmission coefficient (19) is found to be 2 coefficient, given by (5), is found to be 1 ′ (𝑒 −𝑗𝐴 +𝑒 −𝑗𝐵 ) 𝑆1′2 = − (𝑒 −𝑗𝐴 − 𝑒 −𝑗𝐵 ) {1 + } (23) 4 1−′ (𝑒 −𝑗𝐴 −𝑒 −𝑗𝐵 )2 𝑆1′2 = − {𝑆21 𝑀 + 𝑆21 + 𝑆22 ′𝑀′} 𝑐𝑐 𝑐𝑑 𝑐𝑑 2 (19) 4 Inspection of (19) reveals that for perfectly balanced four- Note that expression (23) has been obtained by neglecting port networks (i.e., with Scd = Sdc = 0), S1’2 = 0, as expected losses. This approximation is justified as far as the (note that M = 0 for balanced structures). A detailed considered substrate (for device implementation) is a low- analysis of (19) indicates that for unbalanced four-port loss microwave substrate, and provided the imbalances (if networks, S1’2 can be also null. However, this occurs for they are present) are caused by dielectric loading of the very specific combinations of port loading (i.e.,  and ’) lines (the REF and SUT samples in lines A and B, and mixed-mode S-parameters of the four-port network respectively) with low-loss materials. Nevertheless, the [89]. Thus, when symmetry is truncated, in general S1’2 is generalization of (23) by considering the lines loaded with not zero. Hence, the structure can be used as a detector able lossy materials (e.g., liquids) is carried out in Appendix A. to determine the level of asymmetry in a four-port network (mode conversion detector). Interestingly, for matched terminations at ports 1 and 2’ ( = ’ = 0), the transmission coefficient of the mode conversion detector is found to be 𝑐𝑑 𝑆1′2 = −𝑆21 (20) which coincides with the cross-mode transmission coefficient of the four-port network (except the sign). Thus, the proposed structure provides a straightforward way to Fig. 2. Mode conversion detector applied to a pair of matched and obtain the cross-mode transmission coefficient in four-port uncoupled lines. networks. Note, however, that M and M’ depend on various Let us now designate the first and second term of the elements of the cross-mode matrices. Therefore, it is not a right-hand side member of (23) as P and Q, respectively. priori clear that the preferred option for sensitivity The modulus of (23), the variable of interest for the use of optimization is to terminate ports 1 and 2’ with matched the considered structure for sensing purposes, is given by loads. To determine the convenient terminations at those the modulus of P, i.e.,  − ports (for sensitivity enhancement), the mixed-mode (or |𝑃| = |sin ( 𝐴 𝐵 )| (24) 2 single-ended) S-parameters of the four-port network must be known. Nevertheless, from the point of view of times the modulus of Q. This later quantity cannot be fabrication simplicity and cost, terminating the ports with expressed in a straightforward form. However, for small open-circuits ( = ’ = 1) is equivalent to eliminate one port asymmetries (imbalances), corresponding to similar (but not of each coupler, thereby avoiding the connection of surface identical) values of the electrical lengths of both lines mount devices (SMD), as required for matched terminations (A  B), the modulus of the transmission coefficient can be or for arbitrary loads, or vias (corresponding to short-circuit approximated by terminations, i.e.,  = ’ = 1). 𝐴 −𝐵 |𝑆1′2 |  | |  |1 + ′𝑒 −𝑗(𝐴 +𝐵 ) | (25) A case of special interest is the one corresponding to a 2 pair of matched and uncoupled lines, to be discussed in the The case of small imbalances is justified since the detection next section, and then applied to the implementation of a of tiny differences between the phases of both lines (e.g., differential sensor and comparator. caused by slightly different sample loading in the lines) is of interest for high sensitive detectors and sensors, as it will IV. ANALYSIS RESULTS FOR MATCHED AND UNCOUPLED be discussed in the next section. LINES AND SENSITIVITY OPTIMIZATION In view of (25), it follows that for small asymmetries, For a four-port network consisting of a pair of matched termination of any of the isolated ports (1 or 2’) with a and uncoupled lines (Fig. 2), the mixed-mode S-parameters matched load (i.e., ’ = 0) is a sufficient condition to that explicitly appear in (19) are obtain a proportional dependence of the modulus of the transmission coefficient with the phase difference. Thus, by 𝑐𝑑 𝑆22 =0 (21a) considering the phase difference,  = A  B, as the input 1 variable, the sensitivity for small perturbations is constant 𝑐𝑑 𝑆21 = (𝑒 −𝑗 𝐴 − 𝑒 −𝑗𝐵 ) (21b) 2 and given by 𝑐𝑐 1 −𝑗 𝐴 −𝑗 𝐵 𝑆21 = (𝑒 +𝑒 ) (21c)  |𝑆1′2 | 1 2 𝑆= = (26) where A and B are the electrical lengths of the lines  () 2 between ports A-A’ (line A) and B-B’ (line B), For ’  0, the sensitivity (as defined above) for small perturbations is not constant, but it can be either enhanced or degraded, depending on the phase of the lines ( A  B). Let us now consider two canonical cases: (i) ’ = 1 (corresponding, e.g., to  = ’ = 1, and (ii) ’ = 1 (corresponding, e.g., to  = 1 and ’ = 1, or to  = 1 and ’ = 1). In the former case, Q  0 if A  B  (2n+1)/2 (with n = 0, 1, 2, 3,…), and Q  2 if A  B  n. Thus, if ports 1 and 2’ are left open ( = ’ = 1) or grounded ( = ’ = 1), sensitivity is optimized when the length of the pair of matched and uncoupled lines is roughly a half wavelength (or a multiple of this length). In this case, the sensitivity in the limit of small asymmetries is S = 1. Conversely, for ’ = 1, Q  2 if A  B  (2n+1)/2, and Q  0 if A  B  n. Thus, if one port is left open and (a) the other one is short-circuited to ground, the optimum line length for sensitivity optimization (with S = 1, as well) is an odd multiple of a quarter wavelength. It should be mentioned that such canonical cases can be also obtained by means of purely reactive loads. For instance, case (i) results by considering, e.g.,  = j (pure inductance) and ’ = j (pure capacitance). Nevertheless, the most interesting case from a practical viewpoint is case (i) with  = ’ = 1, since neither a specific load nor a via is required in the isolated ports (1 and 2’) of the couplers. For the validation of the previous sensitivity analysis, we have represented the exact value of the term Q [in brackets in expression (23)] (Fig. 3). Such term can be rewritten as 1 𝑄= ′[cos(𝐴 −𝐵 )+1] (27) 1− 2[′ +𝑗 sin(𝐴 +𝐵 )+cos(𝐴 +𝐵 )] (b) It can be seen in Fig. 3 that when A  B, Q approaches 0 or Fig. 3. Variation of the term Q as a function of the electrical lengths of line 2 for the phase conditions indicated above, depending on A (A) and line B (B). (a) Q for ’ = 1; (b) Q for ’ = 1. the specific case (’ = 1 or ’ = 1). Figure 4 depicts the exact value of the transmission 1.0 1.0 coefficient (expression 23), as well as the sensitivity, as a 0.8 0.8 0.6 function of the phase difference between the lines 0.4 ( = A  B) by considering the phase of line A set to a S (rad-1) |S21| 0.6 0.2 fixed value of A = /2 [Fig. 4(a)] and A =  [Fig. 4(b)]. 0.0 0.4 -0.2 For small values of , the sensitivity is optimized for ’ -0.4 = 1 and A =  (or n), or for ’ = 1 and A = /2 [or 0.2 ·' = 0 ·' = 1 Using eq. (23) Using eq. (25) -0.6 -0.8 (2n+1)/2], in agreement to the previous analysis based on 0.0 ·' = -1 -1.0 the approximate expression (25). Indeed, we have also 0 0.25 0.5 0.75  inferred the transmission coefficient and the sensitivity that  results from (25), valid for small perturbations, and we have (a) depicted it in Fig. 4. The agreement is progressively better as  tends to zero, as expected. Figure 4 also depicts the 1.0 1.0 transmission coefficient and sensitivity corresponding to 0.8 0.8 0.6 ’ = 0. In this case, the sensitivity varies with , being 0.4 roughly constant for small perturbations (  0), but it S (rad-1) 0.6 0.2 |S21| does not depend on the phase of line A. 0.0 0.4 -0.2 According to these results, a differential sensor and -0.4 comparator based on a pair of matched and uncoupled lines 0.2 ·' = 0 Using eq. (23) -0.6 ·' = 1 Using eq. (25) -0.8 with the phases set to 2, and with open-ended loads at 0.0 ·' = -1 -1.0 ports 1 and 2’ ( = ’ = 1) has been designed and fabricated 0 0.25 0.5 0.75  for validation purposes (to be discussed in the next section).  (b) Fig. 4. Variation of the transmission coefficient and the sensitivity as a function of the phase difference ( = A  B) by considering the electrical length of line A (A) set to a fixed value. (a) A = /2; (b) A = . For comparison purposes, the transmission coefficient and the sensitivity that results when ’ = 0 is also included in the figures. V. SENSOR/COMPARATOR DESIGN AND FABRICATION The analysis of the previous section has been used to design the proposed sensor/comparator. The operating frequency has been set to f0 = 2 GHz, and the considered substrate for sensor fabrication is the Rogers RO4003C with dielectric constant r = 3.55, thickness h = 0.8128 mm and dissipation factor tan = 0.0021. With these substrate parameters and frequency, the dimensions of the rat-race hybrid couplers are those indicated in Fig. 5, where the whole sensor is depicted (the width of the ring lines is the one corresponding to a characteristic impedance of 70.71 Ω). Identical meandered lines with 50- impedance and length of 84.93 mm complete the sensing structure. This Fig. 5. Photograph of the fabricated sensor/comparator. Dimensions are line length corresponds to an electrical length of 2π at f0, given in mm (millimeters). provided the sensing regions (indicated in Fig. 5 with dashed rectangles) are covered by a piece of non-metalized 0 Rogers RO3010 substrate with dielectric constant r = 10.2, -10 thickness h = 1.27 mm and dissipation factor tan = 0.0022, -20 |S21| (dB) the reference (REF) sample in our study. With this electrical -30 length of the lines, the sensitivity is optimized (see section -40 IV), provided ’ = 1 (note that the isolated ports of both -50 couplers are opened, and thereby  = ’ = 1). It should be -60 Air-Air (Simulation) -70 mentioned that the characteristic impedance of the line Air-Air (Measurement) RO3010-RO3010 (Measurement) -80 varies slightly in the sensing region, due to the presence of the REF sample. Nevertheless, the conclusions relative to 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 Frequency (GHz) the previous analysis prevail, as it will be shown later. The device has been fabricated by means of a Fig. 6. Frequency response (measured and simulated) of the fabricated LPKF H100 drilling machine. The simulated and measured sensor/comparator without line loading, and measured frequency response with the sensing region loaded with the REF sample in both lines. responses of the device without any material in the sensing regions, inferred by means of the Keysight Momentum From independent simulations, corresponding to line B commercial software and through the Agilent N5221A PNA with the different SUTs, we have inferred the phase of such vector network analyzer, respectively, are depicted in line for each case, and we have evaluated expression (23), Fig. 6. The measured transmission coefficient at f0 is as well as the output variable that results from the low- smaller than 60 dB, indicating that the fabricated structure perturbation approximation (expression 25). Note that the exhibits good balance between the meandered lines. This is phase of line A does not vary and corresponds to the an essential aspect with direct impact on sensor/comparator optimum case for sensitivity optimization (with ’ = 1, as resolution. The measured response that results by loading indicated before). The agreement between the simulated both lines with the REF sample indicated before is also value of the transmission coefficient and the value inferred included in Fig. 6. The response exhibits an insertion loss of from (23) is good The curve corresponding to the 60 dB at f0, pointing out that line balance is maintained by approximate expression (25) is undistinguishable from the loading the lines with identical samples (to minimize the one of (23) because the phase difference between the lines effects of the air gap, the samples have been attached to the is small, even for the larger variation of the dielectric lines by means of screws). constant (20%). This points out the validity of the In order to validate the sensitivity analysis of Section IV, considered approximation (25), at least up to moderate we have obtained the simulated transmission coefficient at variations in the differential dielectric constant. f0 by considering the REF line loaded with the REF sample, We have repeated the previous simulations by and the other line loaded with a hypothetical material of considering an identical structure but elongating the lines, identical dimensions and different dielectric constants (the so that the electrical length that results by loading them loss tangent being identical). Figure 7(a) depicts the with the REF sample is 2.5π, corresponding to the worst modulus of the transmission coefficient at f0, as a function case in terms of sensitivity (with Q = 0). The variation of of the variation of the dielectric constant of the sample the transmission coefficient with the differential dielectric under test (SUT), where such variation is expressed as constant for this second case is also included in Fig. 7(a). percentage with regard to the nominal value of the REF As it can be seen, the variation of the transmission sample (with dielectric constant r = 10.2). As it can be seen coefficient for small values of the differential dielectric in the figure, the output variable exhibits a roughly linear constant is roughly negligible, in agreement with a variation with the differential dielectric constant, and the negligible value of the sensitivity for small perturbations. average sensitivity with this variable has been found to be In Fig. 7(b), we have depicted the dependence of the S = S21 / %r = 0.0052. transmission coefficient with the simulated differential phase for the two considered cases in Fig. 7(a). For the optimum case (electrical length of the lines of 2π), the average slope has been found to be 0.9762, corresponding to an average sensitivity with the differential phase very close to the theoretical value (S = 1). 0.12 corresponding to the different SUT samples are depicted in A = 2 Simulation 0.10 A =  Using eq. (23) Fig. 8, where it can be appreciated the significant variation Using eq. (25) of the transmission coefficient at the operating frequency, 0.08 f0, as the density of holes varies. The comparator is able to |S21| 0.06 detect tiny differences between the REF and SUT samples, 0.04 as derived from the different transmission coefficient that 0.02 results when line B is loaded with the REF sample and with the SUT with the smaller density of holes (the photograph 0.00 of the eight fabricated SUTs is shown in Fig. 9). 0 2 4 6 8 10 12 14 16 18 20  -10 (a) -20 0.12 -30 |S21| (dB) A = 2 0.10 A = 2.5 -40 -50 0.08 Ref (5) |S21| = 0.97620.0012 -60 |S21| (1) (6) 0.06 (2) (7) -70 (3) (8) 0.04 -80 (4) 0.02 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 |S21| = 0.00650.0023 Frequency (GHz) 0.00 0.00 0.02 0.04 0.06 0.08 0.10 Fig. 8. Measured transmission coefficient that results by loading line A  (rad) with the REF sample and line B with the SUT samples depicted in Fig. 9. (b) Fig. 7. (a) Simulated transmission coefficient at f0, inferred by loading the REF line (A) with the REF sample and line B with SUT samples of different dielectric constant, expressed as percentage variation with regard to the dielectric constant of the REF sample. (b) Representation of the transmission coefficient at f0 as a function of the differential phase inferred from the simulations. The transmission coefficient that results by evaluating (23) and (25) with the phases of line B inferred from electromagnetic simulation is also included in (a). The previous simulations validate the analysis of Section IV relative to the dependence of the sensitivity with the Fig. 9. Photograph of the SUT samples obtained by drilling hole arrays of length of the lines and with the termination of the isolated different densities in samples identical to the REF sample. ports of the couplers. The slight discrepancies between the simulations and the exact expression providing the output B. Dielectric Constant Measurements variable, S21, are due to the fact that the lines are not We have also loaded line B with different samples with perfectly matched, as discussed before. well-known dielectric constant, particularly different types It should be pointed out that the sensitivity of the output of un-cladded dielectric substrates (i.e., FR4 with r = 4.6 variable with the differential dielectric constant increases as and RO4003C with r = 3.55). The measured responses of the length of the line increases. The reason is that the the sensor that result by loading line B with such SUT differential phase is proportional to the length l of the lines, samples and line A with the REF sample, are depicted in according to Fig. 10. The transmission coefficients at f0 are depicted in 2𝑓 𝑙 𝐴 − 𝐵 = (𝛽𝐴  𝛽𝐵 )𝑙 = (√𝑒𝑓𝑓,𝐴 √𝑒𝑓𝑓,𝐵 ) 0 (28) 𝑐 Fig. 11, from which we have obtained the calibration curve, also depicted in the figure. From this curve, the dielectric and, obviously, the effects of the differential dielectric constant of the SUT can be inferred by measuring the constant on the differential phase are more pronounced as l corresponding transmission coefficient. Note that such increases. For this reason, we have designed the sensor with curve is useful for the dielectric characterization of relatively long lines (nevertheless, a tradeoff is necessary in materials with dielectric constant smaller than the one of the order to avoid an excessively large sensor). In (28), c is the REF sample, with r = 10.2. Moreover, it is necessary that speed of light in vacuum, and eff,A and eff,B are the effective the thickness of the SUT is comparable to the one of the dielectric constants of line A and B, related to the dielectric REF samples and SUTs used for calibration. Nevertheless, constants of the REF and SUT samples, respectively. if the REF sample and the SUTs are thick enough, such that VI. EXPERIMENTAL VALIDATION the electric field lines generated by the lines do not reach the interface between the sample and air, the response of the A. Comparator Functionality sensor does not depend on sample thickness. The functionality of the structure as comparator has been carried out by loading line A, the REF line, with the REF sample, and line B subsequently with eight identical samples, but with arrays of drilled holes of different densities. The measured transmission coefficient 0 According to (30), the phase of the transmission coefficient -10 is +90º for A < B (corresponding to a smaller dielectric -20 constant for the REF sample), and 90º for A > B (with a |S21| (dB) -30 larger dielectric constant for the REF sample). Hence, the -40 phase of the transmission coefficient at f0 allows us to -50 distinguish whether the dielectric constant of the SUT is -60 larger or smaller than the one of the REF sample, if it is -70 RO3010-RO3010 RO3010-FR4 RO3010-3D(7.6) needed. RO3010-4003C RO3010-Air RO3010-3D(3) -80 It should be mentioned that the proposed sensor is useful 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 to measure the dielectric constant of the SUT (subjected to Frequency (GHz) the required thickness, i.e, identical to the one of the REF Fig. 10. Measured transmission coefficient that results by loading line A sample, as indicated before). In the considered samples, the with the REF sample and line B with SUT samples corresponding to the loss tangent is small or moderately small, so that the low- indicated materials. loss approximation holds (and therefore the analysis of Section IV can be adopted). The proposed system is not as 0.6 |S21|=0.53567+0.00114SUT-0.00524SUT2 sensitive to the effects of losses (in the SUT sample) as 0.5 resonant methods are [90]-[94]. This means that the system is not appropriate for the measurement of the loss tangent of 0.4 the SUT sample, and for this reason the measurement of |S21| 0.3 this material parameter is not considered in the present 0.2 work. Nevertheless, it does not mean that differential 0.1 Measured substrates sensing involving lossy materials, e.g.. liquids, is not Calibration curve 0.0 3D Samples possible. On the contrary, the proposed sensor is very appropriate to measure the volume fraction of solute in 1 2 3 4 5 6 7 8 9 10 SUT diluted liquid solutions, to be discussed next. Since liquids, Fig. 11. Transmission coefficient at f0 corresponding to the SUT samples are lossy materials, line imbalance may be caused not only of Fig. 10. by variations in the dielectric constant between the REF and SUT sample, but also by changes in the loss tangent. For We have fabricated a pair of SUT samples by means of a this reason, the generalization of the formulation of Section 3D printer (Ultimaker 3 Extended). The measured dielectric IV for the lossy case is considered in Appendix A. From constants, inferred by means of a commercial resonant this appendix, it is concluded that the same phase cavity (Agilent 85072A), have been found to be 3 for PLA conditions for the lines resulting for the lossless case should and 7.6 for RS Pro MT-COPPER material, respectively. be applied for sensitivity optimization. Such samples have the same thickness to the one of the REF sample and to those of the samples used for sensor C. Solute Concentration Measurements in Liquid Solutions calibration. The measured transmission coefficients corresponding to such samples are also included in Fig. 10 In the last campaign of experiments, we have and Fig. 11, and are in close proximity to the calibration demonstrated the potential of the sensor for the curve, which means that the proposed sensor provides a determination of volume fraction in liquid solutions. In good estimation of the dielectric constant of the SUT particular, we have considered mixtures of isopropanol in samples. The calibration curve taken from the measured deionized (DI) water. In order to determine small volume substrates (excluding the 3D-printed SUT samples) for the fractions of isopropanol, the natural REF liquid should be determination of the dielectric constant is included in DI water. Moreover, for sensitivity optimization, the sensor, Fig.11. The resulting correlation factor has been found to be particularly the length of the meandered sensing lines, R2 = 0.9998. The maximum sensitivity, inferred from the should be re-dimensioned, so that the electrical length of the calibration curve, has been found to be S = 0.097, and the REF line (line A) is A  n, when such line is loaded with maximum sensitivity, in dB, as derived from the results of the REF liquid. This has provided a total line length of Fig. 10 at f0 is 17.62 dB. 131.77 mm, corresponding to n = 3, i.e., 46.84 mm longer In order to discern if the dielectric constant of the SUT is than the one of the previous device. larger or smaller than the one of the REF sample, let us For the determination of the volume fraction of different consider again that the phase variation of line B does not solutions, we have equipped the sensing regions of lines A experience a strong change when it is loaded with the SUT and B with microfluidic channels. Such channels and the sample. Under these conditions, expression (23) can be necessary accessories for liquid injection (through syringes) approximated by are described in [80]. It should be mentioned that in order to  avoid liquid absorption by the substrate, it has been 𝑆1′2  𝑒𝑗(2−𝐴 ) (𝐴 − 𝐵 )(1 + ′𝑒 −𝑗(𝐴 +𝐵 ) ) 1 2 (29) protected by a dry film with thickness 50 μm and dielectric constant 3.56 (see Fig. 12). The presence of such film does For A =  and A  B, the last term in (29) is roughly not substantially modify the electrical characteristics of the Q  2, as discussed before, and the transmission coefficient lines. The photograph of the sensor, with the channel and can be expressed as other mechanical parts, including the capillaries for liquid 𝑆1′2  − 𝑗(𝐴 − 𝐵 ) (30) injection, is depicted in Fig. 12. -20 Measured mixtures Using eq. (31) -30 |S21| (dB) -40 -50 -60 -70 0 10 20 30 40 50 60 70 80 90 100 Isopropanol Content (%) Fig. 14. Value of the transmission coefficient (dB) at f0 GHz as a function of the isopropanol content. TABLE I COMPARISON OF VARIOUS MICROWAVE FLUIDIC SENSORS FOR VOLUME FRACTION MEASUREMENT IN LIQUID SOLUTIONS Ref. f0 (GHz) FV (%) [95] 20 5 Fig. 12. Photograph of the sensor equipped with fluidic channels. [96] 2 10 [97] 1.9 10 After adapting the sensor for liquid characterization, we [98] 3.5 10 have injected the REF liquid in the REF channel of line A, [77] 0.87 10 and subsequently different mixtures of isopropanol in DI [99] 1.83 0.005 water in the SUT channel (line B), starting with a null [79] 0.9 5 volume fraction (corresponding to the REF liquid), and [100] 5.3 3.3 progressively increasing the volume fraction of isopropanol. [101] 2.3 10 The responses for the different mixtures are depicted in Fig. [102] 5.2 20 13, where it can be seen that the sensor is able to detect [103] 1.1 5 small concentrations of isopropanol in DI water. This work 1.97 1 Particularly, a volume fraction as small as 1% of isopropanol can be resolved. In Table I, a comparison of various fluidic sensors The dependence of the transmission coefficient at f0 as a devoted to measure the volume fraction of isopropanol, function of the isopropanol content is depicted in Fig. 14. methanol or ethanol is reported. As it can be seen, the The calibration curve, useful for the determination of the proposed sensor is able to resolve 1% of volume fraction. volume fraction (Fv) of solute in unknown mixtures of This is a relevant result, only improved by the sensor isopropanol and DI water, is also depicted in the figure. reported in [99], where a solute concentration as small as 0.005% of volume fraction is detected, although with Such curve, with a correlation factor of R2 = 0.9992, is frequency variations smaller than 1MHz centered around 𝑆21(𝑑𝐵)+0.0803 𝑆21(𝑑𝐵)+0.0803 𝐹𝑣 (%) = 154.105 − 18.012𝑒 −( 1.94967 ) − 204.76𝑒 −( 580.9732 ) (31) 1.83 GHz. An advantage of the proposed sensor is that it does not By properly modifying sensor dimensions, the sensitivity require a wide frequency span for measuring purposes, for different REF liquids could be also optimized contrary to most sensors reported in Table I, based on (particularly by adjusting the electrical length of the REF frequency variation or frequency splitting. The sensors line loaded with the REF liquid, so that it satisfies A  n). reported in [79],[103] (resonant differential sensors) are The proposed differential sensor can be of interest, for based on the measurement of the cross mode transmission instance, for monitoring variations of alcohol content in coefficient. The output variable is indeed the maximum fermentation processes. magnitude of the cross mode transmission coefficient, but it occurs at different frequencies (dictated by the SUT). 0 Ref 1% 10% 20% 40% 50% 70% 80% 100% Therefore, a wideband frequency measurement is also -10 5% 30% 60% 90% required in this case. Despite the fact that the results of -20 Fig. 13 depict the transmission coefficient of the reported |S21| (dB) -30 sensor in a relatively wide frequency range, the output -40 variable is actually the magnitude of the transmission -50 coefficient at f0, the operating frequency. Namely, the -60 sensor operates at a single frequency. This single-frequency -70 operation also applies to the dielectric constant sensor of the previous subsection. 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 Sensitivity comparison of the reported sensor with other Frequency (GHz) sensors available in the literature is not easy, as far as most Fig. 13. Measured transmission coefficient that results by loading line A sensors are based on frequency variation or frequency with the REF liquid (DI water) and line B with SUT samples splitting. Nevertheless, it is worth mentioning that, as corresponding to the indicated volume fractions if isopropanol in DI water. compared to [79],[103] (sensors that use similar working principle) the maximum sensitivity of the reported sensor for the measurement of volume fraction is superior (i.e., 11.52 dB/%, as compared to 0.70 dB/% in [79] and APPENDIX A 0.62 dB/% in [103]). For dielectric constant measurements, GENERALIZATION OF THE TRANSMISSION COEFFICIENT BY the sensitivity of the sensor of the previous subsection CONSIDERING LOSSES (17.62 dB) is by far superior to those of the sensors reported in [79] (0.71 dB) and [103] (0.63 dB). By considering lines A and B loaded with lossy materials, To end this section, we would like to mention that in the e.g., liquids, the low-loss approximation used to obtain (23) proposed sensor, the considered sensing mechanism is is no longer valid. However, expression (23) can be easily phase variation in the meandered transmission lines. generalized by simply replacing jA = jAl and jB = jBl Alternatively, it is possible to consider a sensing region with Al and Bl, respectively, where A = A + jA and based on a pair of resonator-loaded lines, as in many other B = B + jB are the complex propagation constant of lines differential sensors [79],[80],[103]-[105] not based on a A and B, respectively. In the limit of small asymmetries two-port measurement by means of hybrid couplers. In this (imbalances), i.e., A  B, P and Q can be expressed as case, resonator loading modifies the resonance frequency, 1 1 as well as the peak or notch magnitude (depending on the 𝑃 = − 𝑒 −𝐴 𝑙 (1 − 𝑒 −(𝐵−𝐴)𝑙 ) − 𝑒 −𝐴 𝑙 (𝐵 − 𝐴 )𝑙 (A.1) 2 2 specific configuration). However, in such potential −(𝐴 +𝐵 )𝑙 configuration based on a pair of resonator-loaded lines and 𝑄 1 + ′𝑒 (A.2) a pair of rat-race couplers, mode conversion at the operating The modulus of the transmission coefficient is thus given frequency of the rat-race couplers is expected to occur, by provided the sensing resonators are asymmetrically loaded. |𝑆1′2 | = |𝑃| |𝑄| (A.3) Therefore, the proposed mode conversion detector can be also applied in this case. Concerning sensor size, it is with mainly dictated by the pair of couplers. Size reduction is 1 possible, obviously, by increasing the operational |𝑃| = 𝑒 −𝐴 𝑙 √(𝐵 − 𝐴 )2 𝑙 2 + (𝐵 − 𝐴 )2 (A.4) 2 frequency. Alternatively, the ordinary couplers can be replaced by couplers based on slow-wave artificial lines, |𝑄| = |1 + ′𝑒 −(𝐴 +𝐵 )𝑙 𝑒 −𝑗(𝐴 +𝐴 ) | (A.5) with substantially smaller size (see, e.g., [106] and Inspection of (A.3)-(A.5) reveals that in order to enhance references therein). All these aspects are left for future the sensitivity with either the differential phase (mainly works. related to the differential dielectric constant) or the VII. CONCLUSIONS differential attenuation constant (mainly dictated by the differential loss tangent), the same phase conditions for the In conclusion, a differential sensor and comparator, based lines resulting for the lossless case (see Section IV), should on a differential-mode to common-mode conversion be applied. Namely, if ’ = 1, it is convenient to choose detector implemented by means of a pair of rat-race hybrid A  B  n. By contrast, for ’ = 1, the phases should couplers, has been presented in this paper. The measuring satisfy A  B  (2n+1)/2. In both cases, the modulus of Q principle of the device is phase variation in a pair of is optimized and given by meandered lines. The output variable in such sensor/comparator is the transmission coefficient at the |𝑄| = |1 + 𝑒 −(𝐴 +𝐵 )𝑙 | (A.6) operating frequency, whereas the input variable can be, e.g., Note that the resulting Q is smaller than 2 (the lossless the differential dielectric constant (i.e., the one of the value), due to the effect of losses. Note also that the sample under test relative to the one of the reference optimum sensitivity for small imbalances is no longer S = 1 sample), or the volume fraction of solute in a liquid (lossless case), but given by solution. The designed device is also useful to detect tiny 1 (𝐵 −𝐴 ) differences between the sample under test and the reference 𝑆 = 𝑒 −𝐴 𝑙 |1 + 𝑒 −(𝐴 +𝐵 )𝑙 | (A.7) 2 √(𝐵 −𝐴 )2 𝑙2 +(𝐵 −𝐴 )2 sample (comparator functionality). The conditions for sensitivity optimization have been obtained analytically, by considering the differential phase as input variable. If the and from such analysis it has been concluded that the length input variable is considered to be the differential attenuation of the pair of meandered lines (the sensing regions of the constant, the resulting sensitivity is found to be device) must be a multiple of a half wavelength, provided 1 (𝐵 −𝐴 )𝑙2 the isolated ports of the rat race are left opened (this is a 𝑆 = 𝑒 −𝐴 𝑙 |1 + 𝑒 −(𝐴 +𝐵 )𝑙 | (A.8) 2 relevant contribution of the paper). The results of the √(𝐵 −𝐴 )2 𝑙2 +(𝐵 −𝐴 )2 analysis have been corroborated through electromagnetic Inspection of (A.7) indicates that if losses can be neglected simulation, by considering sensing structures with different (A = B = 0), then the optimum sensitivity satisfies line length. Then, a prototype device has been fabricated S = S = 1, as expected. and used in different scenarios, including the detection of defects (emulated by drilling hole arrays of different REFERENCES densities in dielectric samples), the measurement of the [1] W.R. Eisenstadt, B. Stengel, and B.M. Thompson, Microwave dielectric constant of slabs, and the measurement of the differential circuit design using mixed-mode S-parameters, Artech volume fraction of solute (isopropanol) in liquid solutions House, Norwood, MA, 2006. (with DI water as solvent). The proposed approach is useful [2] F. Martín, L. Zhu, J. Hong, and F. Medina, Balanced Microwave for the implementation of single frequency differential Filters, Wiley-IEEE Press, Hoboken, NJ, 2018. [3] B. C. Tseng and L. K. Wu, “Design of miniaturized common-mode sensors with very competitive sensitivity and resolution. filter by multilayer low-temperature co-fired ceramic”, IEEE Trans. Electromagn. Compat., vol. 46, no. 4, pp. 571–579, Nov. 2004. [4] W. T. Liu, C.-H. Tsai, T.-W. Han, and T.-L. Wu, "An embedded suppression and stopband extension”, IEEE Trans. Microw. Theory common-mode suppression filter for GHz differential signals using Techn., vol. 55, pp. 1756-1763, Aug. 2007. periodic defected ground plane," IEEE Microw. Wireless Compon. [25] C.-H. Wu, C-H. Wang, C. H. Chen, “Stopband-extended balanced Lett., vol. 18, no. 4, pp. 248-250, Apr. 2008. bandpass filter using coupled stepped-impedance resonators”, IEEE [5] S. J. Wu, C. H. Tsai, T. L. Wu, and T. Itoh, “A novel wideband Microw. Wireless Compon. Lett., vol. 17, pp. 507-509, Jul. 2007. common-mode suppression filter for gigahertz differential signals [26] Y. Zhou, H.-W Deng, Y. Zhao, “Compact balanced-to-balanced using coupled patterned ground structure”, IEEE Trans. Microw. microstrip diplexer with high isolation and common-mode Theory Techn., vol. 57, no. 4, pp. 848–855, Apr. 2009. suppression,” IEEE Microw. Wireless Compon. Lett., vol. 24, pp. [6] C.H. Tsai and T.L. Wu, "A broadband and miniaturized common- 143-144, Mar. 2014. mode filter for gigahertz differential signals based on negative [27] A. Fernández-Prieto, A. Lujambio, J. Martel, F. Medina, F. Mesa, and permittivity metamaterials", IEEE Trans. Microw. Theory. Techn., R. R. Boix, “Simple and compact balanced bandpass filters based on vol. 58, pp. 195-202, Jan. 2010. magnetically coupled resonators”, IEEE Trans. Microw. Theory [7] F. de Paulis, L. Raimondo, Sam Connor, B. Archambeault, and A, Techn., vol. 63, pp. 1843-1853, Jun. 2015. Orlandi, “Design of a common mode filter by using planar [28] A. Fernández-Prieto, J. Martel, F. Medina, F. Mesa, R.R. Boix, electromagnetic bandgap structures”, IEEE Trans. Adv. Packag., vol. “Compact balanced FSIR bandpass filter modified for enhancing 33, no. 4, pp. 994-1002, Nov. 2010. common-mode suppression”, IEEE Microw. Wireless Compon. Lett., [8] J. Naqui, et al., “Split rings-based differential transmission lines with vol. 25, pp. 154-156, Mar. 2015. common-mode suppression”, IEEE MTT-S Int. Microwave [29] A. Fernández-Prieto, J. Bhatker, A. Lujambio, J. Martel, F. Medina, Symposium, Baltimore (USA), June 2011. R.R. Boix, “Balanced bandpass filter based on magnetically coupled [9] J. Naqui, et al., “Common mode suppression in microstrip differential coplanar waveguide folded-stepped impedance resonators”, Elect. lines by means of complementary split ring resonators: theory and Lett., vol. 52, pp. 1229-1231, Jul. 2016. applications”, IEEE Trans. Microw. Theory Techn., vol. 60, pp. 3023- [30] T. B. Lim and L. Zhu, “A differential-mode wideband bandpass filter 3034, Oct. 2012. on microstrip line for UWB applications,” IEEE Microw. Wireless [10] A. Fernandez-Prieto, et al., “Dual-band differential filter using Compon. Lett., vol. 19, pp. 632-634, Oct. 2009. broadband common-mode rejection artificial transmission line”, [31] T. B. Lim and L. Zhu, “Highly selective differential-mode wideband Prog. Electromagn. Research (PIER), vol. 139, pp. 779-797, 2013. bandpass filter for UWB application,” IEEE Microw. Wireless [11] F.X. Yang, M. Tang, L.S. Wu, and J.F. Mao, “A novel wideband Compon. Lett., vol. 21, pp. 133-135, Mar. 2011. common-mode suppression filter for differential signal transmission”, [32] P. Vélez, et al., “Differential bandpass filter with common mode 2014 IEEE Electrical Design of Advanced Packaging & Systems suppression based on open split ring resonators and open Symposium (EDAPS), Bangalore, Dec. 2014, pp. 129-132. complementary split ring resonators”, IEEE Microw. Wireless [12] T.W. Weng, C.H. Tsai, C.H. Chen, D.H. Han, and T.L. Wu, Compon. Lett., vol. 23, pp. 22-24, Jan. 2013. "Synthesis model and design of a common-mode bandstop filter [33] W. Feng, W. Che, Y. Ma, and Q. Xue, “Compact wideband (CM-BSF) with an all-pass characteristic for high-speed differential differential bandpass filters using half-wavelength ring resonator”, signals", IEEE Trans. Microw. Theory Techn., vol. 62, no. 8, pp. IEEE Microw. Wireless Compon. Lett., vol. 23, pp. 81-83, Feb. 2013. 1647-1656, Aug. 2014. [34] P. Vélez, et al., “Differential bandpass filters with common-mode [13] G.H. Shiue, C.M. Hsu, C.L. Yeh, and C.F. Hsu, “A comprehensive suppression based on stepped impedance resonators (SIRs)”, IEEE investigation of a common-mode filter for gigahertz differential MTT-S Int. Microwave Symp., June 2013, Seatle (USA). signals using quarter-wavelength resonators”, IEEE Trans. Compon. [35] A. K. Horestani, M. Durán-Sindreu, J. Naqui, C. Fumeaux, and F. Packag., Manuf. Technol., vol. 4, no. 1, pp. 134-144, Jan. 2014. Martín, “S-shaped complementary split ring resonators and [14] J. H. Choi, P. W. C. Hon, and T. Itoh, “Dispersion analysis and application to compact differential bandpass filters with common- design of planar electromagnetic bandgap ground plane for mode suppression”, IEEE Microw. Wireless Compon. Lett., vol. 24, broadband common-mode suppression”, IEEE Microw. Wireless pp. 150-152, March 2014. Comp. Lett., vol. 24, no. 11, pp. 772-774, Nov. 2014. [36] X-H. Wangand and H. Zhang, “Novel balanced wideband filters [15] C.Y. Hsiao, Y.C. Huang, and T.L. Wu, “An ultra-compact common- using microstrip coupled lines”, Microw. Opt. Technol. Lett., vol. 56, mode bandstop filter with modified-t circuits in integrated passive pp. 1139-1141, May 2014. device (IPD) process”, IEEE Trans. Microw. Theory Techn., vol. 63, [37] L. Li, J. Bao, J-J. Du, and Y-M. Wang, “Compact differential no 11, pp. 3624-3631, Nov. 2015. wideband bandpass filters with wide common-mode suppression”, [16] A. Fernández-Prieto, et al., “Common-mode suppression for balanced IEEE Microw. Wireless Compon. Lett., vol. 24, no. 3, pp. 164-166, bandpass filters in multilayer liquid crystal polimer technology”, IET Mar. 2014. Microw. Ant. Propag., vol. 9, pp. 1249-1253, Sep. 2015. [38] H. Wang, L-M. Gao, K-W. Tam, W. Kang, and W. Wu, “A wideband [17] B.-F. Su and T.-G. Ma, "Miniaturized common-mode filter using differential BPF with multiple differential- and common-mode coupled synthetsized lines and mushroom resonators for high-speed transmission zeros using cross-shaped resonator”, IEEE Microw. differential signals", IEEE Microw. Wireless Compon. Lett., vol. 25, Wireless Compon. Lett., vol. 24, pp. 854-856, Oct. 2014. pp.112-114, Feb. 2015. [39] W. Feng, W. Che, and Q. Xue, “High selectivity wideband [18] Z. Zeng, Y. Yao, and Y. Zhuang, “A wideband common-mode differential bandpass filter with wideband common mode suppression suppression filter with compact-defected ground structure pattern”, using marchand balun”, IEEE Int. Wireless Symp., Mar. 2014, Xian IEEE Trans. Electromagn. Compt., vol. 57, pp. 1277-1280, Oct. (China). 2015. [40] L. Li, J. Bao, J-J. Du, and Y-M. Wang, “Differential wideband [19] P. Vélez, J. Bonache, and F. Martín, “Differential Microstrip Lines bandpass filters with enhanced common-mode suppression using with Common-Mode Suppression based on Electromagnetic internal coupling technique”, IEEE Microw. Wireless Compon. Lett., Bandgaps (EBGs)”, IEEE Ant. Wireless Propag. Lett., vol. 14, pp. vol. 24, pp. 300-302, Feb. 2014. 40-43, 2015. [41] J. G. Zhou, Y-C. Chiang, and W. Che, “Compact wideband balanced [20] P. Vélez, et al., “Enhancing common-mode suppression in microstrip bandpass filter with high common-mode suppression based on differential lines by means of chirped electromagnetic bandgaps cascade parallel coupled lines” IET Microw. Ant. Propag., vol. 8, pp. (EBGs)”, Microw. Opt. Technol. Lett., vol. 58, pp. 328–332, Feb. 564-570, Jun. 2014. 2016. [42] P. Velez, J. Selga, M. Sans, J. Bonache, and F. Martin, “Design of [21] F. Martin, et al., "The Beauty of Symmetry: Common-Mode differential-mode wideband bandpass filters with wide stop band and Rejection Filters for High-Speed Interconnects and Band Microwave common-mode suppression by means of multisection mirrored Circuits", IEEE Microw. Mag., vol. 18, no. 1, pp. 42-55, Jan. 2017. stepped impedance resonators (SIRs)”, IEEE MTT-S Int. Microwave [22] A. Ebrahimi, T. C. Baum, K. Wang, J. Scott, and K. Ghorbani, Symp., May 2015, Phoenix, Arizona (USA). "Differential Transmission Lines Loaded With Magnetic LC [43] M. Sans, et al., “Automated design of common-mode suppressed Resonators and Application in Common Mode Suppression," IEEE balanced wideband bandpass filters by means of agressive space Trans. Circuits Syst. I: Reg. Papers, vol. 66, pp. 3811 – 3821, Oct. mapping (ASM)”, IEEE Trans. Microw. Theory Techn., vol. 63, no. 2019. 12, pp. 3896-3908, Dec. 2015. [23] W. Feng, W. Che, and Q. Xue “The proper balance: overview of [44] M. Sans, et al., “Automated design of balanced wideband bandpass microstrip wideband balance circuits with wideband common mode filters based on mirrored stepped impedance resonators (SIRs) and suppression”, IEEE Microw. Mag., vol. 16, pp. 55-68, Jun. 2015. interdigital capacitors”, Int. J. Microw. Wireless Technol., vol. 8, [24] C-H. Wu, C.-H. Wang, and C. H. Chen, “Balanced coupled-resonator Issue 4-5, pp. 731-740, Jun. 2016. bandpass filters using multisection resonators for common-mode [45] M. Sans, et al., “Optimized wideband differential-mode bandpass filters with broad stopband and common-mode suppression based on multi-section stepped impedance resonators and interdigital resonators,” IET Electron Lett., vol. 50, no. 8, pp. 620-622, Apr. capacitors”, IEEE MTT-S Int. Conference on Numerical 2014. Electromagnetic and Multiphysics Modeling and Optimization for [70] J. Naqui and F. Martín, “Transmission lines loaded with bisymmetric RF, Microwave and Terahertz Applications (NEMO,17), Seville, resonators and their application to angular displacement and velocity Spain, May 2017. sensors,” IEEE Trans. Microw. Theory Tech., vol. 61, no. 12, pp. [46] W. Feng and W. Che, “Novel wideband differential bandpass filters 4700-4713, Dec. 2013. based on T-shaped structure”, IEEE Trans. Microw. Theory. Tech., [71] J. Naqui and F. Martín, “Angular displacement and velocity sensors vol. 60, pp. 1560–1568, Jun. 2012. based on electric-LC (ELC) loaded microstrip lines,” IEEE Sensors [47] X.-H. Wu, Q.-X. Chu, and L.-L Qiu, “Differential wideband J., vol. 14, no. 4, pp. 939-940, Apr. 2014. bandpass filter with high-selectivity and common-mode suppression”, [72] J. Naqui, J. Coromina, A. Karami-Horestani, C. Fumeaux, and F. IEEE Microw. Wireless Compon. Lett., vol. 2, pp. 644–646, Dec. Martín, “Angular displacement and velocity sensors based on 2013. coplanar waveguides (CPWs) loaded with S-shaped split ring [48] T. B. Lim and L. Zhu, “Differential-mode ultra-wideband bandpass resonator (S-SRR)”, Sensors, vol. 15, pp. 9628-9650, 2015. filter on microstrip line,” Electron. Lett., vol.45, pp. 1124–1125, Oct. [73] A. K. Horestani, J. Naqui, Z. Shaterian, D. Abbott, C. Fumeaux, and 2009. F. Martín, “Two-dimensional alignment and displacement sensor [49] X-H. Wu and Q-X. Chu, “Compact differential ultra-wideband based on movable broadside-coupled split ring resonators”, Sensors bandpass filter with common-mode suppression”, IEEE Microw. and Actuators A, vol. 210, pp. 18-24, Apr. 2014. Wireless Compon. Lett., vol. 22, pp. 456-458, Sep. 2012. [74] J. Naqui, et al., “Transmission lines loaded with pairs of stepped [50] A. M. Abbosh, “Ultrawideband balanced bandpass filter”, IEEE impedance resonators: modeling and application to differential Microw. Wireless Compon. Lett., vol. 21, pp. 480-482, Sep. 2011. permittivity measurements”, IEEE Trans. Microw. Theory Techn., [51] H. T. Zhu, W. J. Feng, W. Q. Che, and Q. Xue, “Ultra-wideband vol. 64, no. 11, pp. 3864-3877, Nov. 2016. differential bandpass filter based on transversal signal-interference [75] L. Su, J. Mata-Contreras, J. Naqui, and F. Martín, “Splitter/combiner concept”, Electron. Lett., vol.47, pp. 1033-1035, Sep. 2011. microstrip sections loaded with pairs of complementary split ring [52] X.-H. Wang, H. Zhang, and B.-Z. Wang, “A novel ultra-wideband resonators (CSRRs): modeling and optimization for differential differential filter based on microstrip line structures”, IEEE Microw. sensing applications”, IEEE Trans. Microw. Theory Techn., vol. Wireless Compon. Lett., vol. 23, pp. 128-130, Mar. 2013. 64(12), pp. 4362-4370, Dec. 2016. [53] S. Shi, W.-W. Choi, W. Che, K.-W- Tam, and Q. Xue, “Ultra-wide- [76] L. Su, J. Mata-Contreras, P. Vélez, and F. Martín, "Configurations of band differential bandpass filter with narrow notched band and Splitter/Combiner Microstrip Sections Loaded with Stepped improved common-mode suppression by DGS,” IEEE Microw. Impedance Resonators (SIRs) for Sensing Applications", Sensors, Wireless Compon. Lett., vol. 22, pp. 185-187, Apr. 2012. vol. 16, no. 12, Dec. 2016. [54] C-H Lee, C-I.G. Hsu, and C-J. Chen, “Band-notched balanced UWB [77] P. Vélez, L. Su, K. Grenier, J. Mata-Contreras, D. Dubuc, and F. BPF with stepped-impedance slotline multi-mode resonator,” IEEE Martín, "Microwave Microfluidic Sensor Based on a Microstrip Microw. Wireless Compon. Lett., vol. 22, pp. 182-184, Apr. 2012. Splitter/Combiner Configuration and Split Ring Resonators (SRRs) [55] J. Shi, C. Shao, J-X. Chen, Q-Y. Lu, Y. Peng, and Z-H. Bao, for Dielectric Characterization of Liquids", IEEE Sensors J., vol. 17, “Compact low-loss wideband differential bandpass filter with high no. 20, pp. 6589-6598, Oct. 2017. common-mode suppression”, IEEE Microw. Wireless Compon. Lett., [78] P. Vélez, J. Mata-Contreras, L. Su, D. Dubuc, K. Grenier, and F. vol. 23, pp. 480-482, Sep. 2013. Martín, "Modeling and Analysis of Pairs of Open Complementary [56] P. Vélez, et al., “Ultra-compact (80mm2) differential-mode ultra- Split Ring Resonators (OCSRRs) for Differential Permittivity wideband (UWB) bandpass filters with common-mode noise Sensing", 2017 IEEE MTT-S International Microwave Workshop suppression”, IEEE Trans. Microw. Theory Techn., vol. 63, pp. 1272- Series on Advanced Materials and Processes (IMWS-AMP 2017), 1280, Apr. 2015. Pavia, Italy, 20-22 September 2017. [57] M. Sans, et al., "Compact Wideband Balanced Bandpass Filters With [79] P. Vélez, K. Grenier, J. Mata-Contreras, D. Dubuc, and F. Martín, Very Broad Common-Mode and Differential-Mode Stopbands", "Highly-Sensitive Microwave Sensors Based on Open IEEE Trans. Microw. Theory Techn., vol. 66, no. 2, pp. 737 - 750, Complementary Split Ring Resonators (OCSRRs) for Dielectric Feb. 2018. Characterization and Solute Concentration Measurement in Liquids", [58] C. Damm, M. Schussler, M. Puentes, H. Maune, M. Maasch, and R. IEEE Access, vol. 6, pp. 48324-48338, Aug. 2018. Jakoby, “Artificial transmission lines for high sensitive microwave [80] P. Vélez, J. Muñoz-Enano, K. Grenier, J. Mata-Contreras, D. Dubuc, sensors,” IEEE Sensors Conf., Christchurch, New Zealand, and F. Martín, "Split ring resonator (SRR) based microwave fluidic pp.755−758, Oct. 2009. sensor for electrolyte concentration measurements", IEEE Sensors J., [59] C. Damm, Artificial Transmission Line Structures for Tunable vol. 19, no. 7, pp. 2562-2569, Apr. 2019. Microwave Components and Microwave Sensors, Shaker, 2011. [81] A. Babajanyan, J. Kim, S. Kim, K. Lee, and B. Friedman, “Sodium [60] M. Schueler, C. Mandel, M. Puentes, and R. Jakoby, “Metamaterial chloride sensing by using a near-field microwave microprobe,” Appl. inspired microwave sensors,” IEEE Microw. Mag., vol. 13, no. 2, pp. Phys. Lett., vol. 89, no. 18, p. 183504, 2006. 57–68, Mar. 2012. [82] A. Bababjanyan, H. Melikyan, S. Kim, J. Kim, K. Lee, and B. [61] J. G. Webster, The Measurement Instrumentation and Sensors Friedman, “Real-time noninvasive measurement of glucose Handbook. Boca Raton, FL, USA: CRC, 1999. concentration using a microwave biosensor,” J. Sensors, vol. 2010, [62] J. Fraden, Handbook of Modern Sensors: Physics, Design, and 2010. Applications, 3rd ed. New York, NY, USA, Springer, 2004. [83] S. Kim, et al., “Noninvasive in vitro measurement of pig-blood D- [63] J. Naqui, M. Durán-Sindreu, and F. Martín, “Novel Sensors Based on glucose by using a microwave cavity sensor,” Diabetes Res. Clin. the Symmetry Properties of Split Ring Resonators (SRRs)”, Sensors, Pract., vol. 96, no. 3, pp. 379–384, 2012. vol 11, pp. 7545-7553, 2011. [84] N. Sharafadinzadeh, M. Abdolrazzaghi1, and M. Daneshmand, [64] J. Naqui, M. Durán-Sindreu, and F. Martín, “Alignment and position “Highly sensitive microwave split ring resonator sensor using gap sensors based on split ring resonators,” Sensors, vol. 12, no. 9, pp. extension for glucose sensing”, 2017 IEEE MTT-S International 11790-11797, Aug. 2012. Microwave Workshop Series on Advanced Materials and Processes [65] J. Naqui, M. Durán-Sindreu, and F. Martín, “Transmission lines (IMWS-AMP 2017), Pavia, Italy, 20-22 Sep. 2017. loaded with bisymmetric resonators and applications,” IEEE MTT-S [85] J. Kim, A. Babajanyan, A. Hovsepyan, K. Lee, and B. Friedman, Int. Microw. Symp., Seattle, WA, USA, Jun. 2013. “Microwave dielectric resonator biosensor for aqueous glucose [66] J. Naqui and F. Martín, “Mechanically reconfigurable microstrip lines solution”, Rev. Sci. Instrum., vol. 79, paper 086107, 2008. loaded with stepped impedance resonators and potential [86] D.E. Bockelman and W. R. Eisenstadt, “Combined differential and applications,” Int. J. Antennas Propag., vol. 2014, ID 346838, 8 common-mode scattering parameters: theory and simulation”, IEEE pages, Feb. 2014. Trans. Microw. Theory, Techn., vol. 43, pp. 1530-1539, Jul. 1995. [67] A. Karami-Horestani, C. Fumeaux, S.F. Al-Sarawi, and D. Abbott, [87] A. Ferrero and M. Pirola, "Generalized mixed-mode S parameters", “Displacement sensor based on diamond-shaped tapered split ring IEEE Trans. Microw. Theory. Techn., vol. 54, pp. 458-463, Jan. resonator,” IEEE Sensors J., vol. 13, no. 4, pp. 1153-1160, Apr. 2013. 2006. [68] A. Horestani, D. Abbott, and C. Fumeaux, “Rotation sensor based on [88] D.M. Pozar, Microwave Engineering, 4th Ed., John Wiley, Hoboken, horn-shaped split ring resonator,” IEEE Sens. J., vol. 13, no. 8, pp. NJ, 2011. 3014–3015, May 2013. [89] J. Muñoz-Enano, P. Vélez, and F. Martín, “Signal balancing in [69] A. K. Horestani, J. Naqui, D. Abbott, C. Fumeaux, and F. Martín, unbalanced transmission lines”, IEEE Trans. Microw. Theory Techn., “Two-dimensional displacement and alignment sensor based on vol. 67, pp. 3339 – 3349, Aug. 2019. reflection coefficients of open microstrip lines loaded with split ring [90] M. S. Boybay and O. M. Ramahi, “Material characterization using Paris Vélez (S’10–M’14) was born in Barcelona, complementary split-ring resonators,” IEEE Trans. Instrum. Meas., Spain, in 1982. He received the degree in vol. 61, no. 11, pp. 3039−3046, Nov. 2012. Telecommunications Engineering, specializing in [91] C.-S. Lee and C.-L. Yang, “Complementary split-ring resonators for electronics, the Electronics Engineering degree, and measuring dielectric constants and loss tangents,” IEEE Microw. the Ph.D. degree in Electrical Engineering from the Wireless Compon. Lett., vol. 24, no. 8, pp. 563−565, Aug. 2014. Universitat Autònoma de Barcelona, Barcelona, in [92] C.-L. Yang, C.-S. Lee, K.-W. Chen, and K.-Z. Chen, “Noncontact 2008, 2010, and 2014, respectively. His Ph.D. thesis measurement of complex permittivity and thickness by using planar concerned common mode suppression differential resonators,” IEEE Trans. Microw. Theory Techn., vol. 64, no.1, pp. microwave circuits based on metamaterial concepts 247−257, Jan. 2016. and semi-lumped resonators. During the Ph.D., he [93] L. Su, J. Mata-Contreras, P. Vélez, and F. Martín, "Estimation of the was awarded with a pre-doctoral teaching and research fellowship by the complex permittivity of liquids by means of complementary split ring Spanish Government from 2011 to 2014. From 2015-2017, he was resonator (CSRR) loaded transmission lines", 2017 IEEE MTT-S involved in the subjects related to metamaterials sensors for fluidics International Microwave Workshop Series on Advanced Materials detection and characterization at LAAS-CNRS through a TECNIOSpring and Processes (IMWS-AMP 2017), Pavia, Italy, 20-22 Sep. 2017. fellowship cofounded by the Marie Curie program. His current research [94] L. Su, J. Mata-Contreras, P. Vélez, A. Fernández-Prieto, and F. interests include the miniaturization of passive circuits RF/microwave and Martín, “Analytical method to estimate the complex permittivity of sensors-based metamaterials through Juan de la Cierva fellowship. Dr. oil Samples”, Sensors, 18(4), paper 984, 2018. Vélez is a Reviewer for the IEEE Transactions on Microwave Theory and [95] T. Chretiennot, D. Dubuc, and K. Grenier, "A Microwave and Techniques and for other journals. Microfluidic Planar Resonator for Efficient and Accurate Complex Permittivity Characterization of Aqueous Solutions," IEEE Trans. Marta Gil Barba (S’05-M’09) was born in Microw. Theory Techn., vol. 61, no. 2, pp. 972-978, Feb. 2013. Valdepeñas, Ciudad Real, Spain, in 1981. She [96] A. Ebrahimi, W. Withayachumnankul, S. Al-Sarawi, and D. Abbott, received the Physics degree from Universidad de "High-Sensitivity Metamaterial-Inspired Sensor for Microfluidic Granada, Spain, in 2005, and the Ph.D. degree in Dielectric Characterization," IEEE Sensors J., vol. 14, no. 5, pp. electronic engineering from the Universitat 1345-1351, May 2014. Autònoma de Barcelona, Barcelona, Spain, in 2009. [97] W. Withayachumnankul, K. Jaruwongrungsee, A. Tuantranont, C. She studied one year with the Friedrich Schiller Fumeaux, and D. Abbott, “Metamaterial-based microfluidic sensor Universität Jena, Jena, Germany. During her PhD for dielectric characterization”, Sensors and Actuators A, Physical, Thesis she was holder of a METAMORPHOSE vol. 189, pp. 233-237, 2013. NoE grant and National Research Fellowship from [98] A. Salim and S. Lim, “Complementary split-ring resonator-loaded the FPU Program of the Education and Science Spanish Ministry. As a microfluidic ethanol chemical sensor”, Sensors, vol. 16, Oct. 2016. postdoctoral researcher, she was awarded with a Juan de la Cierva [99] M. Abdolrazzaghi, M. Daneshmand, and A. K. Iyer, "Strongly fellowship working in the Universidad de Castilla-La Mancha. She was Enhanced Sensitivity in Planar Microwave Sensors Based on postdoctoral researcher in the Institut für Mikrowellentechnik und Metamaterial Coupling," IEEE Trans. Microw. Theory Techn., vol. Photonik in Technische Universität Darmstadt and in the Carlos III 66, no. 4, pp. 1843-1855, Apr. 2018. University of Madrid. She is currently assistant professor in the [100] B. D. Wiltshire and M. H. Zarifi, "3-D Printing Microfluidic Universidad Politécnica de Madrid. She has worked in metamaterials, Channels With Embedded Planar Microwave Resonators for RFID piezoelectric MEMS and microwave passive devices. Her current interests and Liquid Detection," IEEE Microw. Wireless Compon. Lett., vol. include metamaterials sensors for fluidic detection. 29, no. 1, pp. 65-67, Jan. 2019. [101] X. Zhang, C. Ruan, T. ul Haq, and K. Chen, “High-Sensitivity Javier Mata-Contreras was born in 1976 in Microwave Sensor for Liquid Characterization Using a Málaga (Spain). He received the Ingeniería de Complementary Circular Spiral Resonator”, Sensors, vol. 19. Feb. Telecomunicación Degree from the Universidad de 2019. Málaga (UMA) in 2000 and the PhD degree from [102] J. Kilpijärvi, N. Halonen, J. A. Juuti, and J. Hannu, “Microfluidic the same university in 2010, with the Thesis Microwave Sensor for Detecting Saline in Biological Range”, “Distributed Amplifiers and Mixers with Sensors, vol.19, Feb. 2019. Transmission Lines based on Metamaterials”. In [103] P. Vélez, J. Muñoz-Enano, M. Gil, J. Mata-Contreras, and F. Martín, 2000, he joined the UMA Department of Ingeniería "Differential Microfluidic Sensors Based on Dumbbell-Shaped de Comunicaciones UMA as Assistant Professor. Defect Ground Structures in Microstrip Technology: Analysis, He is currently working at CIMITEC and the Optimization, and Applications", Sensors, vol. 19, no 14, pp. 3189, Universitat Autònoma de Barcelona as Visitant Professor. His research Jul. 2019. interests include active and passive microwave devices and active [104] A. Ebrahimi, J. Scott, and K. Ghorbani, "Transmission Lines distributed circuits based on metamaterials, among others. Terminated With LC Resonators for Differential Permittivity Sensing," IEEE Microw. Wireless Compon. Lett., vol. 28, no. 12, pp. Ferran Martín (M’04-SM’08-F’12) was born in 1149-1151, Dec. 2018. Barakaldo (Vizcaya), Spain in 1965. He received [105] A. Ebrahimi, J. Scott, and K. Ghorbani, "Differential Sensors Using the B.S. Degree in Physics from the Universitat Microstrip Lines Loaded With Two Split-Ring Resonators," IEEE Autònoma de Barcelona (UAB) in 1988 and the Sensors J., vol. 18, no. 14, pp. 5786-5793, 15 Jul. 2018. PhD degree in 1992. From 1994 up to 2006 he was [106] J. Selga, J. Coromina, P. Vélez, A. Fernández-Prieto, J. Bonache, and Associate Professor in Electronics at the F. Martín, "Miniaturised and harmonic-suppressed rat-race couplers Departament d’Enginyeria Electrònica (Universitat based on slow-wave transmission lines", IET Microw. Ant. Propag., Autònoma de Barcelona), and since 2007 he is Full vol. 13, no. 9, pp. 1293-1299. Jul. 2019. Professor of Electronics. In recent years, he has been involved in different research activities including modelling and simulation of electron devices for high frequency applications, millimeter wave and THz generation systems, and the application of electromagnetic bandgaps to microwave and millimeter wave circuits. He is now very active in the field of metamaterials and their application to the miniaturization and optimization of microwave circuits Jonathan Muñoz-Enano was born in Mollet del and antennas. Other topics of interest include microwave sensors and RFID Vallès (Barcelona), Spain, in 1994. He received the systems, with special emphasis on the development of high data capacity Bachelor's Degree in Electronic Telecommunications chipless-RFID tags. He is the head of the Microwave Engineering, Engineering in 2016 and the Master's Degree in Metamaterials and Antennas Group (GEMMA Group) at UAB, and Telecommunications Engineering in 2018, both at the director of CIMITEC, a research Center on Metamaterials supported by Autonomous University of Barcelona (UAB). TECNIO (Generalitat de Catalunya). He has organized several Actually, he is working in the same university in the international events related to metamaterials and related topics, including elaboration of his PhD, which is focused on the Workshops at the IEEE International Microwave Symposium (years 2005 development of microwave sensors based on and 2007) and European Microwave Conference (2009, 2015 and 2017), metamaterials concepts for the dielectric characterization of materials and and the Fifth International Congress on Advanced Electromagnetic biosensors. Materials in Microwaves and Optics (Metamaterials 2011), where he has acted as chair of the Local Organizing Committee. He has acted as Guest Editor for five Special Issues on Metamaterials and Sensors in five International Journals. He has authored and co-authored over 550 technical conference, letter, journal papers and book chapters, he is co-author of the book on Metamaterials entitled Metamaterials with Negative Parameters: Theory, Design and Microwave Applications (John Wiley & Sons Inc.), author of the book Artificial Transmission Lines for RF and Microwave Applications (John Wiley & Sons Inc.), and co-editor of the book Balanced Microwave Filters (John Wiley & Sons Inc.). Ferran Martín has generated 19 PhDs, has filed several patents on metamaterials and has headed several Development Contracts. Prof. Martín is a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S). He is reviewer of the IEEE Transactions on Microwave Theory and Techniques and IEEE Microwave and Wireless Components Letters, among many other journals, and he serves as member of the Editorial Board of IET Microwaves, Antennas and Propagation, International Journal of RF and Microwave Computer-Aided Engineering, and Sensors. He is also a member of the Technical Committees of the European Microwave Conference (EuMC) and International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamaterials). Among his distinctions, Ferran Martín has received the 2006 Duran Farell Prize for Technological Research, he holds the Parc de Recerca UAB – Santander Technology Transfer Chair, and he has been the recipient of three ICREA ACADEMIA Awards (calls 2008, 2013 and 2018). He is Fellow of the IEEE and IET.