Received 30 September 2022; revised 26 October 2022; accepted 24 November 2022. Date of publication 19 December 2022; date of current version 6 January 2023. Digital Object Identifier 10.1109/JMW.2022.3226003 Balanced Microwave Transmission Lines, Circuits, and Sensors FERRAN MARTIN 1 (Fellow, IEEE) AND FRANCISCO MEDINA 2 (Fellow, IEEE) (Invited Paper) 1 CIMITEC, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain 2 Departamento de Electrónica y Electromagnetismo, Facultad de Física, Universidad de Sevilla, 41012 Sevilla, Spain CORRESPONDING AUTHOR: Ferran Martín (e-mail: Ferran.Martin@uab.cat). This work was supported by MCIN/AEI 10.13039/501100011033, Spain, through the projects PID2019-103904RB-I00 (ERDF European Union) and PID2020-116739GB-I00, by the AGAUR Research Agency, Catalonia Government, through the project 2017SGR-1159, and by Institució Catalana de Recerca i Estudis Avançats (ICREA). This work did not involve human subjects or animals in its research. ABSTRACT This paper provides an overview of balanced (or differential-mode) structures operating at microwaves, including common-mode suppression filters, balanced filters and circuits with intrinsic common-mode suppression, and differential-mode sensors. The increasing interest for balanced structures within the framework of communication circuits and sensors, related to their major robustness against electromagnetic interference (EMI), noise, and environmental factors, is duly justified. Then the paper reports various approaches for the implementation of common-mode suppression filters, balanced filters and circuits (including narrowband and wideband filters, multi-band filters, power dividers, couplers and phase shifters), and differential-mode sensors (mainly devoted to the measurement of permittivity and related variables). Rather than providing a detailed analysis of the different considered implementations/approaches, the main goal of this review paper is to discuss, and compare in some cases, the main proposed strategies (pointed out in the up-to-date state-of-the-art) for optimizing the performance of the various differential-mode devices under study. INDEX TERMS Absorptive common-mode filters, balanced circuits, balanced couplers, balanced microwave filters, balanced phase shifters, balanced power dividers, common-mode rejection ratio (CMRR), common- mode suppression, differential transmission lines, differential-mode sensors, even and odd mode, microstrip technology, MTT 70th Anniversary Special Issue, reflection-less filters. I. INTRODUCTION design and fabrication of balanced interconnects (transmis- Balanced, or differential-mode, transmission lines, microwave sion lines) and circuits, and this is not absent of a certain level circuits, and sensors have been the subject of an inten- of complexity. This explains that unbalanced circuits have sive research activity in recent years. Traditionally, balanced dominated the design of RF and microwave communication structures have been applied to the implementation of low- systems for decades. However, with the recent technological frequency analog systems and high-speed digital systems. advances, balanced structures and systems are progressively The reason is that, as compared to single-ended (unbalanced) penetrating the RF/microwave area [7], [8], [9], and this jus- signals, differential-mode signals are robust against electro- tifies the huge activity of research in the field of balanced magnetic interference (EMI), noise, and crosstalk [1], [2], [3], microwave circuits and systems in recent years (see [10] and [4], [5], [6]. Consequently, differential systems inherently pro- references therein). vide good signal integrity and signal-to-noise ratio (SNR), as Despite the inherent advantages of balanced circuits over compared to the single-ended counterparts. Nevertheless, the their single-ended counterparts, perfect balance cannot be implementation of differential-mode structures requires the achieved in real systems. Therefore, differential-mode to This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 398 VOLUME 3, NO. 1, JANUARY 2023 common-mode conversion (i.e., cross-mode coupling) is un- transmission line based structure loaded with at least one res- avoidable in practice, and constitutes a source of radiation onant element, when the resonator/s is/are under the influence and EMI problems in differential systems, that may degrade of the so-called material under test (MUT). Nevertheless, res- the integrity of the differential signals. Thus, the design onant sensors that exploit the phase (rather than the frequency) of differential transmission lines and circuits with intrinsic variation of a resonator loaded, or terminated, line have also common-mode suppression, yet keeping the integrity of the been reported [11], [15], [16]. The main limitation of these differential mode, are highly demanded. Within the frame- single-ended sensors (regardless on whether the output vari- work of balanced microwave circuits, the main research able is either a frequency or a phase) is their cross-sensitivity effort has been focused on the design of differential filters to environmental factors (mainly temperature and humidity). with intrinsic common-mode suppression, where topologies Although more complex, differential-mode sensors constitute that generate a differential-mode passband (or passbands, in a solution to such problem, since environmental factors are multiband structures) with simultaneous common-mode re- seen as common-mode stimuli at the typical scales of the sen- jection within that/those band/s have been reported [10]. This sors (few centimeters or even less). Thus, a significant effort topic constitutes a significant part of the present review pa- has been dedicated in recent years to investigate differential- per. Nevertheless, we also include a review of the so-called mode structures useful for sensing [11], [17], and some of the common-mode rejection filters, where typically, although not reported implementations are reviewed in this paper. exclusively, defected ground structures (DGS), conveniently The paper is organized as follows. Section II briefly disposed in the ground plane and transparent to differential- presents the fundamentals of balanced transmission lines, mode signals, are applied to suppress the common mode in and introduces the mixed-mode S-parameters. Section III is differential lines. With regard to balanced circuits, this pa- focused on the different approaches for the implementation per also discusses some other devices, in particular, power of common-mode suppression filters. Balanced filters with dividers, couplers and phase shifters. intrinsic common-mode noise suppression, including narrow- Concerning sensors, despite the fact that optical tech- band, wideband and multiband differential-mode responses, nologies dominate the market, microwaves exhibit a series are the subject of Section IV. In Section V, other balanced of benefits that make microwave sensors, and specifically circuits are reported. The topic of differential-mode sensors is wireless sensors and radiofrequency identification (RFID) treated in Section VI. Finally, Section VII highlights the main sensors, an enabling technology for the so-called Internet of conclusions of the work. Things (IoT) (see [11] and references therein). Among such advantages, microwaves are very sensitive to the dielectric properties of the medium to which they interact. Therefore, II. FUNDAMENTALS OF BALANCED TRANSMISSION microwave sensors are canonical permittivity sensors. How- LINES ever, as far as the permittivity of a material correlates with A. TOPOLOGIES AND FUNDAMENTAL PROPAGATING many other variables, such as humidity, temperature, mate- MODES rial composition, etc., microwave sensors can be applied to In unbalanced transmission lines, one of the two conductors many diverse scenarios. Of special interest are the so-called (or wires) is connected to the common ground, and the (single- planar microwave sensors [11], due to their low cost and ended) signal is referenced to that ground [see Fig. 1(a)]. In profile, as well as to their compatibility with both additive such lines, the conductors are fed by single-ended ports, in (e.g., screen- or inkjet-printing) and subtractive (e.g., pho- which there is an active terminal and a ground terminal (that toetching) fabrication processes. Moreover, planar sensors can is, one of the conductors is fed, whereas the other one is tied be fabricated not only on rigid materials (e.g., commercial to ground potential) [11], [18]. Thus, one conductor transports microwave substrates), but also by using flexible substrates, the signal current and the other conductor, considered as refer- including polymers and organic substrates, such as paper. This ence, is the return current path. A microstrip transmission line opens the possibility of implementing conformal sensors, as [Fig. 2(a)] is a good example of a single-ended (unbalanced) well as environmentally friendly (green) sensors. Addition- line. ally, planar sensors are compatible with other technologies Differential, or balanced, transmission lines can be im- of interest for sensing, such as microfluidics (for liquid sens- plemented by means of two or three conductors (wires), as ing) [12], textiles (for wearables) [13], micromachining, etc., depicted in Fig. 1(b) and (c), respectively. Coplanar strips and the associated electronics needed for signal generation, [Fig. 2(b)] or slotlines are examples of two-wire balanced post-processing, and, eventually, communication purposes, lines, whereas symmetric microstrip coupled lines [Fig. 2(c)] can be integrated within the sensor substrate (thereby repre- constitute a representative (and exhaustively used) type of senting a cost reduction). three-wire differential transmission lines. In two-wire bal- Most reported planar microwave sensors are single-ended anced lines, the signal in one line is referenced to the other. structures, operating either in reflective- or in transmission- The conductors exhibit equal potential and impedance with mode, and most of them are resonant [11], [14]. Their working respect to (the virtual) ground with 180◦ phase shift (bal- principle is the variation in the resonance frequency and qual- anced lines carry balanced currents). Nevertheless, it should ity factor, or magnitude, of the notch, or peak, generated in a be mentioned that the nature (balanced or unbalanced) of VOLUME 3, NO. 1, JANUARY 2023 399 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS a two-wire transmission line is determined by the type of feeding (balanced or unbalanced), rather than by the physical structure [18]. Most reported balanced transmission lines include a third conductor acting as a ground plane (three-wire transmission lines), and the canonical implementation is the one depicted in Fig. 2(c), a pair of identical lines on top of a ground plane. Such configuration is usually referred to as microstrip coupled lines, though for the implementation of differential-mode transmission lines, electromagnetic coupling between the lines is not a requisite. Under perfect balance, the active conductors carry identical and opposite currents, since the impedance of each line to ground is identical. However, if the lines are not identical (line unbalance), the presence of the ground plane may unbalance the currents in the conductors. Three-wire balanced lines (the most extensively used, due to the presence of the ground plane) support two fundamental propagating modes: the balanced (or differential) mode and the unbalanced (or common) mode (by contrast, two-wire balanced lines do not support the unbalanced mode). The differential mode is the fundamental mode in balanced lines, and it is an odd-type mode (according to the definition of such mode within the framework of electromagnetic sym- metry properties), where the symmetry plane is an electric FIGURE 1. Schematic of a two-wire unbalanced line (a), two-wire wall (and a virtual ground) [19], [20], [21]. By contrast, the balanced line (b) and three-wire balanced line (c). In (c) the coupling between the lines is not a requisite. symmetry plane for the common mode is a magnetic wall, and the nature of such mode is even (in the common mode, the active conductors carry identical currents in both magnitude and phase). B. EVEN/ODD MODES VERSUS COMMON/DIFFERENTIAL MODES In [11], subtle differences between the even/odd modes and the common/differential modes in differential lines, related to signal definitions, were pointed out (nevertheless, along this review paper, we will indistinctly refer to the balanced mode as odd or differential, and to the unbalanced mode as even or common). Fig. 3 depicts the currents and voltages for the odd and even modes in the individual lines of a three-wire transmission line, as well as their excitation by means of single-ended ports. The odd and even voltages are defined as [20], 1 Vo = (V1 − V2 ) (1a) 2 1 Ve = (V1 + V2 ) (1b) 2 whereas the odd and even currents are 1 Io = (I1 − I2 ) (2a) FIGURE 2. Examples of unbalanced and balanced lines. (a) Unbalanced 2 microstrip line. (b) two-wire balanced transmission line consisting of 1 coplanar strips (CPS). (c) three-wire balanced line based on microstrip Ie = (I1 + I2 ) (2b) coupled lines. 2 400 VOLUME 3, NO. 1, JANUARY 2023 FIGURE 4. Voltages and currents in a balanced line and generation of the differential (a) and common (b) modes. FIGURE 3. Voltages and currents in a balanced line and generation of the odd (a) and even (b) modes. The single ended ports are indicated. whereas the differential current is In expressions (1) and (2), V1 (V2 ) and I1 (I2 ) are the voltage 1 and current, respectively, in line 1 (line 2) of the differen- Id = (I1 − I2 ) (5) 2 tial pair. Note that these voltages and currents are not those of Fig. 1, which refer to the ports, rather than to the lines. Note that these are the natural definitions of the differential For a pure odd mode, it follows that Vo = V1 = −V2 , Ve = voltage and current, according to Fig. 4(a), since it is expected 0, Io = I1 = −I2 , and Ie = 0, whereas Ve = V1 = V2 , Vo = 0, that the differential driving voltage source, Vd , generates iden- Ie = I1 = I2 , and Io = 0 for the even mode. The characteristic tical currents of opposite signs in the single-ended ports. impedances for the odd and even modes are According to Fig. 4(b), the common-mode source will gen- erate in-phase (identical) currents at both single-ended ports. Vo Thus, in this case, the common-mode current is defined as Zco = (3a) Io Ic = I1 + I2 (6) and Ve corresponding to the total current flowing in the lines, whereas Zce = (3b) the common-mode voltage is the average between the voltages Ie in the lines, i.e., respectively. If the lines are uncoupled, both impedances are identical, and coincide with the characteristic impedance of 1 Vc = (V1 + V2 ) (7) the isolated line. 2 The differential and common modes are indeed equiva- According to the previous definitions of voltages and cur- lent to the odd and even modes, respectively, the unique rents for the even/odd modes and common/differential modes, difference being related to signal definitions. That is, in the the following relationships are found differential and common modes, it is considered that the two (input) single-ended ports are driven as a pair, called com- Vd = 2Vo (8a) posite port [8], which can be decomposed in its differential and common mode portions [7] (see, Fig. 4). The differential Id = Io (8b) voltage is defined as [7] Vc = Ve (8c) Vd = V1 − V2 (4) Ic = 2Ie (8d) VOLUME 3, NO. 1, JANUARY 2023 401 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS described by the so-called mixed-mode S-parameter ma- trix [7], [8], [11], [22], [23], i.e., ⎛ ⎞ ⎛ dd dd S dc S dc ⎞⎛ ⎞ bd1 S11 S12 11 12 ad1 ⎜b ⎟ ⎜S dd S dd S dc S dc ⎟ ⎜a ⎟ ⎜ d2 ⎟ ⎜ 21 22 ⎟ ⎜ d2 ⎟ ⎜ ⎟ = ⎜ cd 22 21 cc ⎟ ⎜ ⎟ (10) ⎝ bc1 ⎠ ⎝ S11 S12 cd cc S11 S12 ⎠ ⎝ ac1 ⎠ bc2 cd S21 cd S22 cc S21 cc S22 ac2 where it has been considered that the pairs of single-ended ports 1-3 and 2-4 are driven as pairs, i.e., as differential and common mode ports. This gives the conceptual diagram of mixed-mode S-parameters shown in Fig. 5(b). Note, however, that the four ports of Fig. 5(b) are conceptual tools only, rather than physically separated ports. The left- and right-hand side column vectors are the positive and negative, respectively, voltages waves at the composite ports 1 and 2 [see Fig. 5(b)], and the sub-index “d” or “c” is used to differentiate the differential and common modes. Such order-4 mixed mode S-parameter matrix, typically designated as Smm , can be ex- pressed as [7], [8], [11]  Sdd Sdc Smm = (11) Scd Scc FIGURE 5. (a) Single-ended four-port circuit described by the single-ended S-parameter matrix, and indication of the positive (ai ) and negative (bi ) where Sdd is the differential-mode order-2 S-parameter ma- normalized (single-ended) voltage waves. (b) conceptual diagram of the trix, Scc is the common-mode order-2 S-parameter matrix, mixed-mode S-parameters in a differential two-port network, with indication of the normalized common-mode positive (aci ), and Scd and Sdc are the so-called order-2 mode-conversion, differential-mode positive (adi ), common-mode negative (bci ), and or cross-mode, S-parameter matrices. In perfectly balanced differential-mode negative (bdi ) voltage waves (b). The sub-index i lines, Sdc and Scd should be null, since mode conversion is indicates the port number. not possible under perfect symmetry. However, in real lines, certain level of imbalance is unavoidable and these matrices are not strictly null. On the other hand, in differential-mode The characteristic impedances of the odd and even modes are sensors, imbalances are generated by the differential input related to those of the differential (Zcd ) and common (Zcc ) variable, usually the differential permittivity, or difference modes according to between the permittivity of the so-called material under test (MUT) and a reference (REF) material, and the cross-mode transmission, S21dc , or reflection, S dc , coefficients are typical 11 Zcd = 2Zco (9a) output variables in such sensors [24], [25]. Zcc = Zce /2 (9b) The relationship between the single-ended S-parameters and the mixed-mode S-parameters is [8], [11]:  It is thus clear that the even/odd modes are equivalent to 1 S11 −S13 −S31 +S33 S12 −S14 −S32 +S34 S dd = the common/differential modes. That is, an even-mode sig- 2 S21 −S23 −S41 +S43 S22 −S24 −S42 +S44 nal propagating in a line pair cannot be distinguished from (12a) a common-mode signal, and the same applies to an odd-  /differential mode (the only difference concerns how the 1 S11 +S13 +S31 +S33 S12 +S14 +S32 +S34 S cc = voltages and currents, and consequently the characteristic 2 S21 +S23 +S41 +S43 S22 +S24 +S42 +S44 impedances, for the modes have been defined, as indicated (12b) before).  1 S11 +S13 −S31 −S33 S12 +S14 −S32 −S34 S dc = 2 S21 +S23 −S41 −S43 S22 +S24 −S42 −S44 C. MIXED-MODE S-PARAMETERS (12c) Three-wire balanced transmission lines can be described by  standard (single-ended) order-4 S-parameter matrices [21], 1 S11 −S13 +S31 −S33 S12 −S14 +S32 −S34 see Fig. 5(a). Nevertheless circuits that support the simultane- S cd = 2 S21 −S23 +S41 −S43 S22 −S24 +S42 −S44 ous propagation of differential and common modes (mixed- mode propagation), either balanced or not, are preferably (12d) 402 VOLUME 3, NO. 1, JANUARY 2023 Thus, the mixed mode S-parameters, in particular the differential- and common-mode S-parameters, can be inferred from the measurement of the single-ended S-parameters. III. COMMON-MODE SUPPRESSION FILTERS Common-mode suppression (or bandstop) filters are struc- tures added to balanced lines (generally, although not exclu- sively, based on defected ground structures – DGS) in order to reject the common mode within a certain frequency band. De- spite the fact that most reported implementations of balanced bandpass filters are able to inherently suppress the common mode in the differential-mode passband, the common mode rejection ratio (CMRR) in that band does not always reach the required values to efficiently suppress the common-mode FIGURE 6. Illustration of selective mode suppression in microstrip noise. Thus, common-mode rejection filters can be applied differential lines by using CSRRs (etched in the ground plane). Note that bandstop and all-pass is in reference to a region in the vicinity of the to improve the CMRR in balanced bandpass filters by cas- fundamental CSRR resonance (further stop bands may appear for both cading them. Another application of common-mode bandstop modes at higher frequencies). filters concerns the suppression of undesired common-mode noise present in balanced lines acting as interconnects for high-speed digital circuits. Such common-mode noise is in- us report different considered strategies/implementations of evitable due to time-skew or amplitude imbalance between common-mode bandstop filters. the differential lines, and may degrade the signal integrity and cause EMI emission [26]. Thus, common-mode bandstop A. SELECTIVE MODE SUPPRESSION filters exhibiting broad stop bands for the common mode, and Selective mode suppression in balanced lines can be achieved all-pass responses with low insertion loss for the differential by symmetrically loading the line with a planar resonant ele- mode (from DC up to frequencies beyond those required in ment, either a metallic or a slot (or DGS-based) resonator [32], high-speed data transmission), are necessary. [57], [58], [59], [60]. This section succinctly reviews some up-to-date reported The key aspect for achieving selective mode suppression is implementations of common-mode suppression filters. Most the electromagnetic nature (either a magnetic or an electric of them are based on DGSs, conveniently designed in order wall) of the symmetry plane of the resonant element at the to achieve responses insensitive to the differential mode [27], considered resonance frequency (typically the fundamental [28], [29], [30], [31], [32], [33], [34], [35], [36]. Other one). The axial symmetry plane of a balanced line is an elec- common-mode rejection filters exploit the inherent rejection tric wall for the differential mode and a magnetic wall for properties of periodic structures [37], [38], [39], [40], [41]. the common mode. Thus, it follows that by symmetrically There are also approaches based on multilayer or low tem- loading the line pair with a resonant element exhibiting a perature co-fired ceramic (LTCC) technology [2], [42], [43], magnetic wall at resonance, the common mode should be sup- [44], [45], [46], [47], [48], [49]. It is shown in this section pressed [57], [58] in the vicinity of that frequency, whereas the that glide symmetry can be applied to certain common-mode line should be transparent for the differential mode, provided rejection filters in order to widen the common-mode stopband both symmetry planes (the one of the line and the one of the bandwidth [50]. Recently, common-mode dissipative (absorp- resonator) are perfectly aligned. By contrast, if the considered tion) filters, where the power associated to the common mode resonator exhibits an electric wall at the considered resonance is absorbed, rather than reflected, have also been reported (see, frequency, the line exhibits a stopband response for the differ- e.g., [51], [52], [53]). Finally, let us mention that, traditionally, ential mode and an all-pass response for the common mode common-mode chokes with high-permeability ferrite cores (though this case lacks practical interest). have been used to mitigate common-mode noise [54], [55], Among those planar resonant elements exhibiting a mag- [56]. However, chokes exhibit a limited operating range and netic wall at the fundamental resonance, the complementary do not constitute a good solution in terms of size and cost, as split ring resonator (CSRR), first reported in [61], and the compared to full-planar structures. dumbbell defect ground structure (DB-DGS) resonator [62] The key aspect for a successful common-mode bandstop (including the folded version), are good examples. As it will filter is mode selectivity, that is, the filter must be able to effi- be shown in the next subsection, these resonators have been ciently suppress (either reflect or absorb) the common mode in used as efficient common-mode bandstop filters, since reason- the widest possible frequency band, and at the same time must able stopband bandwidths can be achieved by conveniently be transparent to the differential mode. Certain (symmetric) tailoring their topology. Fig. 6 illustrates the principle of (se- planar resonators are useful for achieving mode suppression lective) common-mode suppression by considering a pair of selectivity. Thus, let us next discuss this aspect, and then let balanced microstrip coupled lines loaded with a CSRR. Note VOLUME 3, NO. 1, JANUARY 2023 403 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS that CSRRs and DB-DGSs are slot resonators that should be etched in the ground plane, beneath the line pair, as depicted in Fig. 6. There are also metallic resonators that exhibit a magnetic wall at the fundamental resonance. For example, the so-called electric-LC (ELC) resonator [63] is a bisymmetric resonator that exhibits both a magnetic and an electric wall (orthogonally oriented) at the fundamental resonance. Thus, the ELC resonator is a potential candidate to suppress the common-mode by etching (or printing) it in the substrate side where the active lines are present. However, this strategy has the penalty of a wide transverse dimension of the line pair, since the metallic resonator should be symmetrically located between the lines of the differential pair. B. COMMON-MODE FILTERS BASED ON DEFECTED GROUND PLANES There are many strategies for selectively suppressing the com- mon mode (keeping unaltered the differential mode) by means of slot-based structures etched in the ground plane, in particu- lar, by using symmetric resonators, such as the DB-DGS and the CSRR. In [27], a common-mode filter based on a differential microstrip line pair loaded with DB-DGS resonators was proposed [see Fig. 7(a)]. Such resonators open the return current path through the ground plane for the common mode, whereas the presence of such resonators has negligible effect on the differential-mode signals, since relatively small current density returns through the ground plane for such signals. Nevertheless, a more convincing explanation of the filtering behavior of such structures for the common mode can be given by taking into account the equivalent circuit model of the unit cell. By assuming that the coupling between adjacent DB- DGS resonators can be neglected, the line pair loaded with a DB-DGS can be described by means of the circuit shown in Fig. 7(b) [64]. In that circuit, L and C are the inductance and the capacitance, respectively, of the line corresponding to the length of the unit cell, Lc and Cc model the DB-DGS resonator, and M accounts for the mutual (magnetic) cou- pling between the lines and the resonator. Finally, Lm and Cm account for the magnetic and electric coupling, respectively, FIGURE 7. Perspective view of a common-mode bandstop filter consisting between the lines. of a pair of microstrip lines loaded with DB-DGS resonators (a), In view of the circuit model in Fig. 7(b), it is clear that lumped-element equivalent circuit model of the unit cell (b), and frequency the resonant element is magnetically driven for the common response (insertion loss) (c). Reprinted from [27] with permission. mode, since the lines carry current in the same direction for that mode. Thus, the injected common-mode signals are re- the vicinity of 4.5 GHz is generated, whereas the insertion loss flected back to the source in the vicinity of the resonance for the differential mode is close to 0 dB, and mode conver- frequency. By contrast, the current in the lines flow in op- sion from the differential to the common mode is very small. posite directions for the differential mode, and the DB-DGS In [27], it was demonstrated by means of measured differential resonator cannot be excited for that mode. Fig. 7(c) depicts eye diagrams that the integrity of the differential signals was the frequency response of the considered DB-DGS-based preserved, despite the presence of the DB-DGS resonators common-mode filter (see details of the geometry and substrate (common-mode filter). Moreover, it was demonstrated in that parameters in [27]), including not only the common mode paper the potential of the designed DB-DGS structure for insertion loss (Scc in the figure, the nomenclature used in the the suppression of the common mode by inserting a delay original source [27]), but also the differential mode insertion structure in one of the lines, consequently causing a time skew, loss (Sdd ), as well as the cross-mode insertion loss (Scd ). It or line imbalance, and hence differential to common mode can be seen that a significant common-mode rejection band in conversion. 404 VOLUME 3, NO. 1, JANUARY 2023 The use of CSRRs for the implementation of common- mode filters was reported in [29], [30]. The capability of these resonators for the selective rejection of the common mode is clear, according to the illustration of Fig. 6. Never- theless, the common-mode bandstop filters reported in [29], [30] are based on square-shaped CSRRs. Such geometry fa- vors inter-resonator (electric) coupling, which in turn helps to widen somehow the common-mode rejection band, as re- ported in [30]. Fig. 8(a) depicts a specific implementation of a common-mode rejection filter based on three CSRRs. The rejection of the common mode in the vicinity of resonance and the transparency of the structure for the differential mode sig- nals is clear in view of the equivalent circuit model of the unit cell, depicted in Fig. 8(b). In that model, L and C are the line inductance and capacitance of the unit cell, Lc and Cc describe the CSRR, Lm and Cm account for the electric and magnetic coupling, respectively, between the lines, C is the coupling capacitance between the lines and the CSRR, and, finally, CR is the coupling capacitance between adjacent CSRRs. For the common mode, the equivalent circuit is inferred by elimi- nating half of the circuit, and leaving the resulting terminals open-circuited (equivalent to locating a magnetic wall in the symmetry plane), see Fig. 8(c). The resulting circuit exhibits a stop band in the vicinity of the resonance frequency of the CSRR, magnified by inter-resonator coupling through the generation of complex modes, as reported in [30]. By contrast, the equivalent circuit for the differential mode [see Fig. 8(d)], inferred by short-circuiting to ground the resulting terminals of the symmetry plane after eliminating half of the circuit, is the one corresponding to an ordinary line. Thus, the struc- ture is transparent for the differential mode. Fig. 8(e) and (f) depict the differential-mode and common-mode responses, respectively. The differential mode insertion loss is very small within the considered frequency range, whereas the common mode insertion loss exhibits more than 40 dB rejection in a relatively broad frequency band. Thus, the functionality of this CSRR-based structure as an efficient common-mode bandstop filter is demonstrated. The details of the geometry, substrate parameters, as well as a recipe for the design of such common- mode filters can be found in [30]. Nevertheless, let us report the measured eye diagrams corresponding to the balanced line of Fig. 8 with and without the presence of CSRRs (Fig. 9). Both diagrams are roughly indistinguishable, which means that the integrity of the differential signals is preserved despite the presence of the common-mode filter. FIGURE 8. CSRR-based common-mode bandstop filter. (a) Photograph. Common-mode filters based on ground plane etching can (b) lumped element equivalent circuit model (unit cell). (c) common-mode also be implemented by means of central metallic patches con- equivalent circuit. (d) differential-mode equivalent circuit. (e) differential-mode response. (f) common-mode response. Reprinted nected to the ground plane through meandered inductors, as from [30] with permission. reported in [31]. The topology of these structures is depicted in Fig. 10(a). If the patches are separated a small distance, capacitive coupling between them arises, and the equivalent is also assumed in the circuit of Fig. 10(b) that the lines circuit model (unit cell) is the one shown in Fig. 10(b). The are uncoupled. Nevertheless, if the lines are close one to main difference in comparison with the circuit of Fig. 8(b) each other, their mutual coupling can be taken into account is the fact that the resonant tank Lc − Cc in that circuit through a mutual capacitance, Cm , and a mutual inductance, (describing the CSRR) is a pair of inductors (L p ) in the cir- Lm , similar to Fig. 8(b). The circuit models for the common cuit of Fig. 10(b), corresponding to the meandered strips. It and differential modes are depicted in Fig. 10(c) and (d), VOLUME 3, NO. 1, JANUARY 2023 405 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS FIGURE 9. Measured differential eye diagram for the structure of Fig. 8 with (a) and without (b) CSRR. Reprinted from [30] with permission. respectively. An all-pass structure results for the differential mode, whereas the common mode is expected to be filtered, as far as the equivalent circuit for such mode resembles the one of an elliptic low-pass filter (except by the presence of the coupling capacitances, Cs ). The common-mode insertion loss corresponding to a four-stage structure is depicted in Fig. 10(e). As it can be seen, in the common-mode bandstop fil- ters reported so far there is a perfect topological symmetry with regard to the axial plane between the pair of lines. However, it has been recently reported that by considering glide-symmetric structures (meaning that the axial symme- try is disrupted), it is possible to improve the common- mode rejection bandwidth, yet preserving the integrity of differential-mode signals [50]. Indeed, the glide-symmetric common-mode filtering structures reported in [50] are in- spired by the single-ended mushroom-type glide-symmetric bandstop filters previously reported in [65]. In [50], glide symmetry was applied to improve the common-mode filtering performance of both DGS and mushroom-type differential-mode transmission lines. Let us report in this section the results corresponding to the DGS- based structure. Fig. 11 shows the topologies of the different DGS common-mode filters reported in [50], one based on a perfectly symmetric configuration with regard to the axial plane AA’ (fully symmetric), one non-symmetric (designated as conventional in [50]), and another one exhibiting glide symmetry. The measured common-mode transmission coeffi- cients for the three structures are depicted in Fig. 12, where FIGURE 10. (a) Top (left) and bottom (right) views of the common-mode suppression filter based on metallic patches connected to the ground the superior performance of the glide-symmetric structure plane through meandered inductors. (b) lumped element equivalent circuit can be appreciated. Despite the fact that the glide-symmetric model (unit cell). (c) common-mode equivalent circuit; (d) common-mode filter does not exhibit axial symmetry, the differential-mode equivalent circuit. (e) common-mode response. Note that for the unit cells cascaded to the input and output ports, the measured eye diagram is roughly undistinguishable from the capacitors Cs are connected to ground. In reference to (e), the full-wave one of the fully symmetric structure (see Fig. 13). Conse- simulation is depicted in solid black line, the measurement in blue dashed quently, the differential-mode signals are not degraded in this line, and the equivalent circuit response in red dotted line. Reprinted from [31] with permission. glide-symmetric device, despite the absence of perfect sym- metry. Let us mention that, as argued in [50], and explained in detail in [65], by introducing glide symmetry, better common- as reported, e.g., in [10], and as revealed by the dispersion dia- mode rejection bandwidth and rejection level (and, conse- grams shown in [50] (not reproduced here). In such diagrams, quently, common-mode rejection ratio, CMRR) are achieved it can be appreciated that the first stop band for the common by virtue of the enhanced coupling between the metallic mode signals (the one of interest) is significantly widened in patches of the DGS that results through glide symmetry. Such the glide-symmetric structure (as compared to the one of the coupling is a key aspect in stopband bandwidth enhancement, fully symmetric structure). 406 VOLUME 3, NO. 1, JANUARY 2023 FIGURE 13. Measured eye diagram for the differential mode corresponding to the symmetric (a) and glide symmetric (b) DGS-based common-mode filters. Reprinted from [50] with permission. C. COMMON-MODE FILTERS BASED ON ELECTROMAGNETIC BANDGAPS (EBGS) After the previous representative set of DGS-based common- mode rejection filters, let us next briefly review a common- mode suppression strategy based on the inherent filtering properties of periodic structures, or electromagnetic bandgaps (EBGs). EBGs are periodic structures exhibiting stop bands at certain frequencies, due to the well-known Bragg effect [57], [66], [67] (in particular, the first stop band arises when the Bragg condition is fulfilled, i.e., when the period of the structure is half the wavelength). Thus, single-ended band- stop filters implemented by simply adding periodicity to a transmission line have been reported [68], [69], [70]. Such periodicity can be introduced by etching periodic patterns in the ground plane, or by periodically modulating the transverse geometry of the line (non-uniform transmission lines). In [40], common-mode suppressed EBG-based differential lines implemented by continuously (and periodically) varying the separation and width of the lines were reported. The design strategy is very simple. In brief, it is necessary that the line geometry provides a periodic modulation of the common- mode characteristic impedance along the line (with a period FIGURE 11. Differential lines loaded with DGSs and the corresponding unit cells. (a) Fully symmetric structure and (b) unit cell. (c) non-symmetric determined by the required central frequency of the common- structure and (d) unit cell. (e) glide-symmetric structure and (f) unit cell. mode stop band), keeping unaltered the differential-mode Reprinted from [50] with permission. impedance. Such differential-mode characteristic impedance must be set to 50 , in order to avoid mismatching reflec- tions for that mode. From the substrate parameters (dielectric constant and thickness) the determination of the periodic line geometry providing a variation of the common-mode impedance within a certain range, maintaining invariable the differential-mode characteristic impedance, is feasible (e.g., by means of a transmission line calculator). Fig. 14 depicts the EBG-based common-mode rejection filter reported in [40], together with the common-mode and differential-mode transmission coefficients. With four unit cells, a maximum rejection of 17 dB (measurement) at the central frequency of the common-mode stop band is achieved. This common-mode suppression strategy does not require ground plane etching, and the design of the common-mode bandstop filter is simple, as it is based on compact analytical expressions (derived in [40], [57]). Moreover, vias are not FIGURE 12. Measured common-mode responses of the common-mode needed, and two metal levels suffice for filter implementa- filters of Fig. 11. Reprinted from [50] with permission. tion. However, it is not simple, in practice, to maintain the VOLUME 3, NO. 1, JANUARY 2023 407 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS FIGURE 15. Topology (a) and perspective view of the unit cell (b) of the mushroom-type common-mode rejection filter. Reprinted from [2] with FIGURE 14. EBG-based common-mode filter. (a) Photograph. permission. (b) transmission coefficient for the differential and common modes. Reprinted from [40] with permission. the printed circuit board (PCB), including the differential line differential-mode characteristic impedance to the nominal re- pair, is separated from the common-mode filter (indeed, the quired value (50 ) along the whole structure, and this is common-mode filter is placed on top of the PCB as a surface- the main cause of certain insertion loss for the differential mount component). Thus, the common-mode filter can be mode, as it can be appreciated in Fig. 14. It is worth men- easily removed and replaced with another one, if desired, tioning that widening the common-mode stop band is possible designed to filter a different frequency (but maintaining the by implementing the device by means of a quasi-periodic same footprint and external dimensions). The main drawback structure. Since the central frequency of the common-mode of the EBG-based common-mode filter of [71] is the limited stop band is determined by the period (according to the bandwidth of the common-mode stop band. Bragg condition), it follows that by slightly varying the period along the structure (chirping), or by combining EBGs with D. COMMON-MODE FILTERS BASED ON MULTILAYER different periodicity, the bandwidth can be substantially en- STRUCTURES hanced, as demonstrated in the EBG-based common-mode In the common-mode suppressed filter examples reported in rejection filters reported in [40], [41]. the previous subsections, the structures use only two metal Other common-mode rejection filters based on EBG peri- levels, one devoted to the line pair, and the other one to the odic structures were reported in [37], [38], [39]. In [39], a ground plane, either etched or not. Nevertheless, there are two-dimensional DGS designated as uniplanar compact pho- various implementations of common-mode rejection filters tonic bandgap (UP-PBG) ground plane by the authors was based on three or more metal levels [2], [43], [44], [45], [46], used in order to reject the common-mode over a very wide [47], [48], [49], [50], [72]. Of particular interest are those frequency band. The structure exhibits also a strong common- common-mode filters based on the so-called mushroom-type mode rejection level and it is compact, but, contrary to the structures [2], [49], [50], [72] to be discussed in the present EBG-based common-mode filter of Fig. 14, it needs ground subsection. Essentially, these filters consist of a pair of lines plane etching. In [37], [38], common-mode filters based on (upper metal level) on top of metallic patches (intermediate EBGs were also presented. However, such filters need three metal level) connected to the ground plane (bottom metallic metal levels, and are only able to suppress specific frequen- level) through inductive vias (see Fig. 15). The lumped el- cies, as compared to the common-mode filters reported so ement equivalent circuit model of this structure is identical far. In [71], a common-mode suppression filter based on a to the one of the CSRR-based common mode bandstop filter surface-mount technology (SMD) EBG structure is reported. of Fig. 8. The main difference is that the ground plane is In this proposal, the main advantage concerns the fact that kept unaltered in the mushroom-type structure, although at the 408 VOLUME 3, NO. 1, JANUARY 2023 FIGURE 16. Differential lines loaded with grounded mushrooms. (a) Conventional structure and (b) unit cell. (c) glide-symmetric structure and (d) unit cell. Reprinted from [50] with permission. expense of an additional metal level and the use of inductive vias. As reported in [50], applying glide symmetry to mushroom- type common-mode filters provides a path to enhance the common-mode stopband performance (bandwidth and rejec- tion level). Thus, we report in this subsection the mushroom- type common-mode glide-symmetric rejection filters of [50]. Glide symmetry is achieved by simply alternating the position of the vias, as depicted in Fig. 16. Actually, this figure includes the glide-symmetric structure, as well as the conventional structure, where the vias are located at the same position. Note that for the conventional structure, the position of the vias is not central, contrary to Fig. 15. Nevertheless, this does not represent a penalty in regard to the integrity of the differential-mode signal (and the integrity of the differential signals is also preserved for the glide symmetric structure). Fig. 17 depicts the simulated and measured responses for both the conventional and glide-symmetric mushroom- type common-mode rejection filters. It can be appreciated the superior common-mode stopband performance of the glide-symmetric common-mode filter, with a wider stopband FIGURE 17. Photograph (top view) of the mushroom-type common-mode bandwidth and common-mode suppression level. For both rejection filters (with 10 unit cells) (a), and responses for the conventional filters, the insertion loss for the differential mode is very small, (b) and glide-symmetric (c) structures. Reprinted from [50] with permission. indicating that the structure is roughly transparent for that mode. It is also worth-mentioning the mushroom-type structure in [72], as well as the common-mode and differential-mode reported in [72], fully symmetric but exhibiting a very broad responses. A very broad common-mode stop-band bandwidth common-mode stop band by virtue of the four transmission of 123 % (considering the cutoff at −10 dB) results, with low zeros generated for that mode. Such transmission zeros are insertion loss for the differential mode. The eye diagrams, not achieved by enhancing the electrical length of the line pair shown here but reported in [72], are indicative of the signal over the mushroom patches by means of meanders, simi- integrity for the differential mode. lar to [33], [43], [73]. Under these conditions, the circuit model needs to be described by a combination of distributed and lumped elements, resulting in a complex condition for E. ABSORPTIVE COMMON-MODE FILTERS (A-CMFS) the transmission zeros. Such condition depends on the vari- In the common-mode rejection filters reported so far, the ous electrical parameters of the circuit model (characteristic common mode is reflected back to the source in a certain impedances, electrical lengths, and inductance of the via), frequency band. Thus, these filters can be designated as re- which can be tailored in order to enhance the common-mode flective common-mode filters (R-CMF). Clearly, in R-CMFs, rejection bandwidth, as detailed in [72]. Fig. 18 depicts the the common-mode noise is not dissipated. Therefore, the re- common-mode filter with four transmission zeros reported flected common-mode noise can be driven through the whole VOLUME 3, NO. 1, JANUARY 2023 409 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS Certain implementations of A-CMFs use an R-CMF in order to block the common-mode noise, and an additional dissipative circuit placed at one side for common-mode noise absorption. Therefore, these techniques based on an R-CMF blocking module and a common-mode noise dissipative mod- ule only synthesize unidirectional A-CMFs. For this reason, these structures have been designated as unidirectional A- CMFs, and examples can be found in [74], [75], [76], [77], [79], [83]. By contrast, there are other A-CMF architec- tures able to dissipate the common-mode noise regardless on the circuit side from where it is injected (bidirectional A-CMFs [51], [52], [53], [78], [81], [82]). The dissipative element in an A-CMF is usually a resistor, or a set of resistors. Nevertheless, there are A-CMF implementations that exploit the inherent losses of certain planar resonators, for example, CSRRs [84], or gap coupled resonators [75]. The design of A-CMFs is not simple, since the consid- ered implementations should be able to be transparent for the differential mode (all-pass structures for that mode), and simultaneously block and dissipate the common mode over the widest possible frequency band. It is not possible to dis- cuss all the reported implementations of A-CMFs in a review paper focused on the general topic of balanced lines, circuits, and sensors. Thus, let us report two representative examples of A-CMFs, one of them unidirectional, and the other one bidirectional. Concerning the unidirectional case example, the considered prototype is the one reported in [83]. Although this prototype A-CMF exhibits a limited common-mode suppression and absorption band in the vicinity of 2.4 GHz (it is intended to eliminate the EMI in the Wi-Fi 2.4 GHz band), it has been chosen because it is based on a single stage, and, therefore, the resulting device footprint is very small. It is also remarkable that the device uses only two metallic levels. Moreover, the design of this A-CMF is relatively simple and follows guide- lines given by formulas derived in [83] (but not reproduced here). The schematic of the structure of [83] is depicted in Fig. 19(a). It consists of a differential pair (with single-ended characteristic impedance Z1 and electrical length θ1 ) cascod- ing two transmission lines (with characteristic impedance Z2 and electrical length θ2 ), terminated with a resistor, R. The resistor is located on the symmetrical plane of the circuit, drawn with dash line, as shown in Fig. 19(a). Fig. 19(b) and FIGURE 18. Perspective view of the mushroom-type common-mode (c) depict the equivalent circuit model for the differential and rejection filter with four transmission zeros (a), and responses for the common mode (b) and differential mode (c). Reprinted from [72] with common mode, respectively. The structure is transparent for permission. the differential mode, whereas, according to the circuit of Fig. 19(c), the structure is able to block and absorb common mode signals (noise) at certain frequencies. The reason is system and be the cause of unexpected radiation. To alle- that there are combinations of circuit parameters providing viate this problem, the so-called absorptive common-mode S21 = 0 and S11 = 0, the necessary conditions for achieving filters (A-CMFs) have been proposed in the last decade [51], common-mode suppression (blocking) and absorption simul- [52], [53], [74], [75], [76], [77], [78], [79], [80], [81], [82], taneously (thus note that an additional condition as compared [83], [84], [85]. Such A-CMFs can absorb (or dissipate) the to R-CMFs is necessary in A-CMFs, i.e., S11 = 0). common-mode noise utilizing resistors or lossy materials, In [83], the structure of Fig. 19(a) was synthesized by thereby preventing common-mode noise reflection, and hence, considering a pair of lines cascoded to a meandered slotline. undesired radiation. The layout and the photograph of the fabricated A-CMF are 410 VOLUME 3, NO. 1, JANUARY 2023 FIGURE 19. (a) Proposed circuit, composed of a differential pair, cascoded transmission lines, and a resistor, to synthesize an A-CMFs. (b) Odd-mode equivalent circuit. (c) Even-mode equivalent circuit. Reprinted from [83] with permission. shown in Fig. 20. Such figure includes also the frequency re- sponse of the common-mode filter, where it can be appreciated that the differential mode exhibits very small insertion loss, whereas the common-mode is significantly absorbed in the vicinity of 2.4 GHz. The measured results show that |Scc21 | is lower than −10 dB from 2.33 to 2.67 GHz and |Scc11 | is less than −10 dB from 2.11 to 2.8 GHz. This corresponds to a common-mode noise absorption efficiency above 80 % between 2.33 to 2.67 GHz, where both |Scc21 | and |Scc11 | are less than −10 dB [83]. The measured eye diagrams (not shown here but reported in [83]) are indicative of the good signal integrity for the differential mode. A bidirectional version of the previous A-CMF was re- ported in [81] by the same authors. To achieve bidirectional common-mode absorption, the structure was equipped with two resistors, rather than one, terminating the pair of mean- FIGURE 20. Layout (a) and photograph (b) of the upper (left) and lower dered slotlines, in a symmetric configuration with regard to (right) metal levels corresponding to the synthesized A-CMF of Fig. 19(a). the bisecting plane between the input and output ports (see (c) frequency response. Reprinted from [83] with permission. further details in [83]). The performance of this bidirectional A-CMF is similar to the one of the unidirectional counterpart. To end this subsection, let us briefly report the bidirec- to the bisecting plane between the input and output ports in tional A-CMF reported in [82], with small size and very order to achieve common-mode absorption bidirectionallity. broad common-mode suppression and absorption bandwidth. Another important aspect is the fact that the filter is im- This A-CMF is inspired by the R-CMF based on DB-DGS plemented in stripline, rather than microstrip, technology, as resonators of Fig. 7. The main difference is the presence revealed by the three metal levels employed in the design (see of resistors in the central plane of the DB-DGS resonators Fig. 21). (or axial plane of the structure), see Fig. 21, except for the The specific designed A-CMF device in [82] is shown central DB-DGS, which is resistor free. With these resistors, in Fig. 22, whereas the frequency responses are depicted in the resulting resonators are lossy components, able to absorb Fig. 23. The differential-mode insertion loss is small, whereas the common mode. It can be appreciated in Fig. 21 that for the common mode, both the insertion and return loss are the resistor-loaded DB-DGS resonators are not identical, a significant, regardless of the considered input port, indicat- strategy to enhance the common-mode suppression and ab- ing that the common mode is efficiently, and bidirectionally, sorption. Nevertheless, the structure is symmetric with regard suppressed and absorbed (the reported common-mode noise VOLUME 3, NO. 1, JANUARY 2023 411 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS FIGURE 22. Layout (a) and photograph (b) of the DGS-based stripline A-CMF of Fig. 21. Reprinted from [82] with permission. and common-mode (CM) absorption. The fractional band- width for the reflective mode filters is usually referred to the frequency span where the common-mode insertion loss is at least 10 dB, whereas for the absorptive common-mode filters, it is given by the bandwidth where the common-mode absorp- tion factor is at least 80 %, or 90 % in most cases. Concerning the last column, it provides the CMRR for the reflective-mode filters (in dB), and the common-mode absorption (in %) for the absorptive common-mode bandstop filters (nevertheless, this information is not given in all the references). Let us men- tion that, in some cases, the considered fabrication technology is not PCB, and the number of layers is replaced with the considered technology, as indicated. In view of the table, among those reflective-type common- mode filters implemented in PCB technology, those reported in [31], [35], [36] exhibit a good combination of common- mode rejection and fractional bandwidth. The filter of [42] is also very competitive, but it was fabricated in LTCC tech- nology. Concerning the absorptive-type common-mode filters, a fractional bandwidth above 100 % was achieved in the implementations of refs. [51], [52], [79], [80], [82], [85], in FIGURE 21. Configuration of the A-CMF based on DB-DGS resonators. some cases with very good common-mode absorption. Sev- (a) Layer stack-up. (b) Differential signal lines. (c) Top and bottom ground eral of these filters are bidirectional. It is remarkable the planes. Reprinted from [82] with permission. common-mode filter presented in [51], which is bidirectional and very small, though it utilizes 3 metal levels. Although not indicated in the table, the differential-mode performance, i.e., absorption fractional bandwidth (FBW) is as high as 147% the insertion loss in the frequency region of interest and the [82]). signal integrity (as estimated from the measured eye diagrams, reported in many cases), is in general good. F. COMPARISON OF COMMON-MODE REJECTION FILTERS Table 1 compares the different common-mode bandstop fil- IV. BALANCED FILTERS WITH COMMON-MODE ters reported in this section in terms of size (relative to SUPPRESSION the wavelength at the central frequency of the common- The previous section has been focused on common-mode re- mode stop band), number of metallic layers, FBW, CMRR, jection filters, that is, differential lines able to suppress (either 412 VOLUME 3, NO. 1, JANUARY 2023 TABLE 1. Comparison of Common-Mode Filters order to control the transmission response (filtering) of the FIGURE 23. Frequency response of the A-CMF of Fig. 22. (a) differential differential signals. By contrast in differential-mode (or bal- mode. (b) common-mode transmission coefficients. (c) common-mode anced) filters, the key aspect is to generate a certain response reflection coefficients. Reprinted from [82] with permission. (typically a bandpass-type) for the differential mode, and for that purpose, specific topologies are required, many times block, or block and dissipate) the common mode in a certain inspired by those of the single-ended counterparts. frequency band. Ideally, these common-mode filters are trans- Balanced filters are of interest in modern communication parent (all-pass) for the differential signals. In practice, certain systems, and, similar to balanced lines (or interconnects), level of signal attenuation is unavoidable, and such differential implementations simultaneously suppressing the common signals are filtered (reflected) above a certain (3-dB) cutoff mode over the differential-mode passband are highly de- frequency (usually located substantially beyond the region of manded. Ideally, balanced filters should intrinsically (and interest). However, common-mode filters are not designed in efficiently) suppress the common-mode (the CMRR within VOLUME 3, NO. 1, JANUARY 2023 413 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS the differential-mode pass band is a good performance in- dicator in such filters). Cascading a common-mode filter to the differential filter provides a path for CMRR improve- ment [31], but this is not the preferred option in terms of overall filter size. Thus, a significant effort has been dedi- cated in the last 20 years to the design of balanced filters with intrinsic common-mode suppression. This topic has been exhaustively covered in the recent book [10], co-edited by the authors of the present review paper. In that book [10], the most significant implementations of the up-to-date state-of-the-art in balanced microwave filters, contributed by different (highly reputed) researchers, were presented. For this main reason, and because such book was published recently (2018), we will not treat the topic of common-mode suppressed balanced filters at the same depth level as common-mode filters in the present paper (it would be impossible on account of the huge number of contributions in the available literature). We will just report the main filter types, design strategies, and few im- plementations, with special emphasis on recent contributions (nevertheless, for an in-depth study, the authors recommend the book [10] and references therein). Concerning the differential-mode filter response, balanced filters with intrinsic common-mode suppression can be di- vided between narrowband filters, wideband and ultra wide- band (UWB) filters, and multiband filters, the categorization adopted in [10]. In all cases, the design strategies are based on topologies able to provide the required response for the differential mode, with the maximum possible attenuation level and stopband bandwidth for the common mode. Though most reported balanced filters in [10] and references therein intrinsically reflect (block) the common mode within a certain frequency band, many recent implementations have been fo- cused on the dissipation, rather than reflection, of that mode (the interest is justified by the reasons in reference to the absorptive common-mode filters of the previous section). Let us next review (briefly, as justified) some of the reported common-mode suppressed (or dissipated) balanced filters, categorized as indicated above. A. WIDEBAND AND UWB BALANCED FILTERS There are many approaches for the implementation of bal- anced bandpass filters exhibiting broad transmission bands for the differential mode and, simultaneously, rejecting the common mode in that band. One of the earliest strategies utilizes branch-line-like structures. The seminal and canoni- cal topology was presented in [86] but there are many other reported wideband and UWB balanced filters inspired by this branch-line topology (see, e.g., [87], [88], [89], [90], [91] and [10, chapter 4]). It has also been recently demonstrated that, with this type of balanced filters, it is possible to ab- sorb, rather than reflect, the common mode in the region of interest. As an example of this type of wideband filters, Fig. 24 depicts the schematic and photograph of a specific de- FIGURE 24. Balanced filter with common-mode noise absorption based on the branch-line topology. (a) circuit schematic. (b) circuit schematic for vice, exhibiting a broad differential-mode transmission band the differential mode. (c) circuit schematic for the common mode (left) and and common-mode noise absorption [92]. For the differential simplified circuit (right). (d) photograph. (e) differential mode response. mode, the axial symmetry plane is an electric wall, and the (f) common-mode response. Reprinted from [92] with permission. 414 VOLUME 3, NO. 1, JANUARY 2023 resistors are virtually grounded. The resulting schematic for this mode, with all the line sections and stubs exhibiting an electrical length of θ1 = θ2 = θ3 = 90◦ at the central filter frequency, corresponds to the well-known topology of single- ended wideband branch-line bandpass filters [93], [94]. By contrast, for the common mode, with a magnetic wall at the axial symmetry plane, the resulting circuit schematic, also depicted in Fig. 24, provides a transmission zero at the central filter frequency (note that the central stub, with impedance and electrical length Z3 and θ3 , respectively, is virtually open at its termination). Moreover, the common mode is absorbed at that frequency, provided the resistor satisfies R0 = Z22 /2Z0 . The details of the different circuit parameters (line and stub impedances) is given and justified in [92]. The frequency response of this filter is also included in Fig. 24, where it can be appreciated the capability of the structure to efficiently absorb the common mode. The measured common-mode transmission coefficient is |SccBA | = −38.13 dB, whereas the common-mode reflection coefficient is |SccAA | = −25.38 dB. This indicates that the common-mode noise is absorbed and converted into heat by the resistors. Another strategy, similar to the one discussed in the prece- dent paragraph, was reported in [95], [96], [97], [98], [99], [100] and [10, chapter 9]. Topologically, the common-mode suppressed balanced filters of [95], [96], [97] are similar to those based on the branch-line-like topology. However, rather FIGURE 25. Typical topology of a wideband balanced filter with than shunt stubs, such filters use (instead) mirrored stepped- common-mode suppression based on mirrored SIRs (a), circuit schematic (b), circuit model for the differential mode (c), and circuit model for the impedance resonators (SIRs). Fig. 25 depicts a typical layout common mode (d). of these filters (for order-5), as well as the circuit schematic, and the circuit schematic for the differential and common modes. For the differential mode, the resulting circuit is [107], [108], [109], [110], [111], and [10, chapters 5 and similar (but not identical) to the canonical circuit of a band- 6]. One of the canonical circuit schematics for such filters pass filter, consisting of shunt-connected parallel resonators is depicted in Fig. 28 [102], where all the line sections and coupled through admittance inverters. The difference is the coupled lines exhibit an electrical length of 90◦ at the central presence of the inductances designated as Lei , where i de- filter frequency, f0 . The circuit schematic for the differential notes the stage. Nevertheless, the presence of this inductance mode, also shown in the picture, exhibits a band pass response provides a transmission zero above the differential-mode pass- in the vicinity of the design frequency, f0 , with a transmission band, which improves the filter selectivity for that mode. For zero at 2 f0 , due to the short-circuited stubs (with an electrical the common mode, additional transmission zeros caused by length of 180◦ at 2 f0 ). By contrast, the circuit schematic for the series resonators Lci − Cci result. Thus, by conveniently the common mode [Fig. 28(c)], behaves as a bandstop filter distributing these zeros within the differential-mode passband, with four transmission zeros, as discussed in [112]. Such an efficient common-mode suppression in that band can be stopband behavior can be explained as due to the interference achieved. Fig. 26 depicts a prototype order-7 common-mode between the two signal paths. The coupling factor of the cou- suppressed balanced filter implemented by means of mirrored pled lines, as well as the characteristic admittances of both SIRs as an illustrative example, as well as the differential the coupled lines and the transmission line sections, determine and common-mode responses [97]. The common mode is the stopband characteristics of the common mode, as reported significantly suppressed over a wide band, with a CMRR in [102]. As a representative illustrative example of this type of 50 dB at the central filter frequency (3 GHz). In other of balanced filters, Fig. 29 depicts the photograph and the implementations, the distributed inverters were replaced with response of the prototype reported in [102], which is not the semi-lumped components with the result of very compact one exhibiting the optimum performance, but obeys to the filters [98], [99], [100], an advantageous aspect over those topology of Fig. 28. Other balanced filters based on coupled filters reported in [95], [96], [97] (Fig. 27 depicts a specific lines combined with T-shaped structures, ring resonators, etc., implementation [100]). can be found in the literature [103], [104], [105], [106], [107], Wideband and UWB balanced filters based on coupled line [108], [109], [110], [111]. sections (in some cases combined with other structures) have In the previously cited implementations of common-mode also been reported [101], [102], [103], [104], [105], [106], suppressed balanced bandpass filters, the ground plane was VOLUME 3, NO. 1, JANUARY 2023 415 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS FIGURE 27. Photograph of an order-5 balanced filter based on mirrored FIGURE 26. Photograph of an order-7 balanced filter based on mirrored SIRs and interdigital series resonators (a) and response for the differential SIRs (a) and response for the differential (b) and common (c) modes. (b) and common (c) modes. Reprinted from [100] with permission. Reprinted from [97] with permission. wall for that mode, and the slot resonator cannot be excited. kept unaltered. Nevertheless, considering defect ground struc- By contrast, such symmetry plane is an electric wall for the tures (DGSs) and slot resonators provides an alternative differential mode, and the slot resonator can be excited (note approach for achieving wideband differential-mode responses that according to the position of the differential microstrip with intrinsic common-mode suppression (see [113], [114], to slot line transitions, the first two resonant modes can be [115], [116], [117], [118], [119], [120], [121], [122], [123], excited). [124] and [10, chapters 7, 10 and 11][10]). Many filters have Other more complex configurations of slotline resonators, been implemented by considering microstrip to slotline tran- i.e., combined with other elements, such as the strip-loaded sitions. A canonical configuration (designated as differential slotline resonator [122], have been proposed in order to im- microstrip to slotline transition) is shown in Fig. 30 [119]. prove the filter performance. It is also remarkable the use According to this topology, the common mode cannot be of different defect ground structures for the implementa- transmitted, since the axial symmetry plane is a magnetic tion of common-mode suppressed bandpass filters, such as 416 VOLUME 3, NO. 1, JANUARY 2023 FIGURE 30. Top view of the canonical configuration of a balanced bandpass filter with intrinsic common-mode suppression based on a slot resonator excited by differential microstrip to slotline transitions. Reprinted from [119] with permission. dumbbell-shaped defect ground structures (DB-DGSs) [113] and topologies based on the complementary split ring res- onator, among others (see [117], [118] and [10, chapter 10]). As an illustrative example of a DGS-based balanced filter, let us report the wideband balanced filter implemented by means of a strip-loaded quadruple-mode slotline resonator reported in [122], see Fig. 31. FIGURE 28. Schematic of the canonical common-mode suppressed Another approach for the implementation of wideband bal- balanced filter based on coupled lines (a) and equivalent circuits for the differential (b) and common (c) modes. Reprinted from [102] with anced filters with intrinsic common-mode rejection exploits permission. signal interference techniques [125], [126], [127], [128], [129]. The reported devices use Marchand baluns, phase shifters, and other circuit elements necessary to generate the convenient phases for the transmission of the differential mode with simultaneous cancelation of the common mode. The design of these filters is relatively simple, but their size tends to be significant, as compared to other imple- mentations of wideband balanced filters. Recently, wideband balanced filters based on coplanar stripline resonators with substantial CMRR in the differential-mode passband have been reported [130], [131], [132], [133], [134] (in the device presented in [130] the common mode is absorbed). B. NARROWBAND AND MULTIBAND BALANCED FILTERS AND DIPLEXERS Concerning the implementation of balanced filters with nar- row differential-mode pass bands, most implementations are based on coupled resonator topologies (see [135], [136], [137], [138], [139], [140], [141], [142], [143], [144], [145], [146], [147], [148], [149], [150], [151], [152], [153], [154], and [10, chapter 12]) It is sometimes difficult to differentiate between narrowband and wideband filters (either balanced or single-ended), since the frontier is rather diffuse (depending on the sources, the narrowband designation requires fractional bandwidths below 10 %, whereas in others, filters with frac- tional bandwidths as high as 20 % are considered to belong FIGURE 29. Photograph of a balanced filter based on the circuit schematic to the narrowband category). For this reason, some balanced of Fig. 28 (a) and transmission coefficient for the differential and common filters reported in [10, chapter 12] (and references therein), modes (b). Reprinted from [102] with permission. dedicated to narrowband balanced filters, are considered to VOLUME 3, NO. 1, JANUARY 2023 417 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS FIGURE 32. Layout (a) and frequency response (b) of the dual-band FIGURE 31. Top view layout (a), photograph including the top (left) and balanced filter based on magnetically coupled embedded resonators. bottom (right) views (b), and response (c) of the wideband common-mode Reprinted from [166] with permission. suppressed balanced bandpass filter implemented by means of a strip-loaded quadruple-mode slotline resonator. Reprinted from [122] with permission. was published in [166], and it consists of two magnetically coupled embedded resonators that, at the same time, are be wideband filters in this review paper. Nevertheless, for capacitively coupled to the external feeding lines [see Fig. the synthesis of very narrow differential-mode responses, typ- 32(a)]. Note that this embedded open loop resonator consist ically with fractional bandwidths around 1 % and below, of a folded stepped impedance resonator (FSIR) in which the dielectric resonators have been used [155], [156], [157]. Nar- low impedance region is replaced with another small FSIR rowband balanced filters in groove-gap waveguide technology (i.e. the small FSIR is embedded into the original and larger have also been reported [158]. FSIR). With an adequate geometry, it is possible to control Many efforts have also been dedicated to the implemen- the position of the two first odd-mode resonances, i.e., those tation of multiband balanced filters (see [130], [159], [160], that determine the central frequency of the two differential- [161], [162], [163], [164], [165], [166], [167], [168], [169], mode passbands. These frequencies do not coincide with the [170], [171], [172] and [10, chapters 13 and 14]). In some even mode resonances of the embedded coupled resonators, cases, such filters have been implemented with topologies and therefore, the common-mode is suppressed at the central based on coupled embedded resonators (able to generate two frequencies of the differential-mode passbands. Moreover, by transmission bands for the differential mode), and the working virtue of the magnetic coupling between the resonators, their principle is similar to that of the single-ended counterparts. coupling for the (first) even mode resonance is very soft (the Let us next demonstrate the potential of coupled embedded currents in the resonators are a minimum in the region of resonators for the implementation of dual-band differential- the symmetry plane AA ). This means that the common mode mode bandpass filters with intrinsic common-mode suppres- must (necessarily) be significantly reflected even at such fre- sion through an illustrative example. The considered device quency. The expected result is thus a broad common-mode 418 VOLUME 3, NO. 1, JANUARY 2023 suppressed band. Fig. 32(b) depicts the frequency response of the device, where the dual-band functionality for the differential mode, as well as the broadband (and strong) common mode rejection can be appreciated (details on the geometry, substrate parameters, as well as design process of the filter of Fig. 32, can be found in [166]). Balanced diplexers [173], [174], [175], [176], [177], [178], [179], [180], [181], [182], [183], [184], usually based on topologies similar to those of narrowband balanced filters, and reconfigurable/tunable balanced filters [185], [186], [187], have also been the subject of an intensive research activity in recent years. C. REFLECTION-LESS BALANCED FILTERS To end this section devoted to balanced filters, let us men- tion that a significant effort has been dedicated recently to the implementation of reflection-less structures, where either the common-mode (in the differential mode passband) or the differential mode (outside the differential-mode passband), or both modes simultaneously, are absorbed [92], [130], [172], [188], [189], [190], [191], [192], [193], [194], [195], [196]. Many different strategies for absorbing the common and/or the differential mode in the required frequency bands have been reported. Indeed, some of such strategies have been discussed (see, e.g., the device of Fig. 24, where power dis- sipation is insensitive to the differential mode, but not to the common mode). Let us report in this section an illustrative example of a reflection-less balanced bandpass filter able to FIGURE 33. Circuit schematic of the two-port (bidirectional) reflection-less balanced bandpass filter with both differential and common mode absorb both the differential and the common modes, regard- absorption based on a coupled ring resonator (a) and equivalent circuit for less of the considered input port (two-port, or bidirectional, the differential (b) and common (c) modes. Reprinted from [196] with reflection-less balanced bandpass filter). The filter schematic permission. is depicted in Fig. 33(a). It is based on a coupled ring resonator and utilizes loading absorptive stubs at the input/output ports and at the ends of the coupled-lines. By means of these ab- V. OTHER PASSIVE BALANCED CIRCUITS sorptive stubs, the balanced filter can realize input-/two-port Previous sections have been mainly focused on a variety wideband common-mode and differential-mode reflection- of differential microwave filtering devices, whose impor- less performance from DC, as well as wide filtering band and tance as building blocks in any microwave communication all-stop common-mode suppression. system is obvious. Due to this reason, the literature about The circuit schematics of the filter for differential and com- filters has dominated the landscape of the research carried mon mode excitations are depicted in Fig. 33(b) and (c), out around passive balanced microwave circuitry (see, for respectively. Taking into account that the electrical lengths of instance, [10], [197] and references therein). However, there the coupled lines and stubs are θ = 90◦ at the central filter are other important and ubiquitous passive components that frequency, f0 , it is obvious that for DC and for frequencies sat- are also of primordial importance to implement fully balanced isfying 2n f0 (with n = 0, 1, 2, . . .), significant absorption for RF/microwave front ends. In particular, the balanced versions the differential mode is expected. However, for f0 and the odd of power distribution components, such as power dividers harmonics (2n + 1) f0 , the differential-mode circuit exhibits a (PD) or directional couplers (DC) have attracted the inter- band pass behavior (the resistors are seen as an open at such est of many researchers, specially during the last few years. frequencies). By contrast, absorption at all these frequencies Thus, the authors of [197] have recently published a review is expected for the common mode. Thus, wideband common paper [198] focused on the study of balanced-to-unbalanced mode absorption for the filter results. These features are cor- (BTU) four- and five-port filtering power dividers (FPD). At roborated by the filter response, depicted in Fig. 34, which the moment of writing this paper, a significant number of includes the photograph and layout of the physical imple- contributions on balanced-to-balanced (BTB) or BTU power mentation (substrate characteristics, dimensions, and further dividers and directional couplers is available in the literature details about this reflection-less balanced bandpass filter can about differential microwave passive devices. This section be found in [196]). will present an overview of this work, with emphasis on the VOLUME 3, NO. 1, JANUARY 2023 419 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS FIGURE 35. Circuit model of the balanced-to-balanced power divider/combiner proposed in [201]. Reprinted from [201] with permission. common-mode absorption (in addition to reflection) will be briefly considered. A. BALANCED-TO-BALANCED POWER DIVIDERS A straightforward manner to build a three-port BTB power divider/combiner would consist on adding baluns to each of the three ports of a single-ended divider/combiner. However, smaller size and lower losses are expected if a differential- mode divider whose ports are fully balanced is designed, combining power divider and balun functions in a single cir- cuit. Although some previous attempts can be found in the literature, one of the first proposals of a differential power divider was reported in [200], although isolation between out- put ports was not considered in that work. The first available solution working as a true BTB PD (i.e., fulfilling all the theoretical constraints required for its ideal operation) can be found in [201]. The device proposed in [201] has three differential ports (named A, B and C, corresponding to six single-ended ports), and it is based on an appropriate inter- connection of ideal microstrip transmission line sections and resistors having the topology shown in Fig. 35 (differential port A is formed by the pair of single-ended ports 1 and 4, B by 2 and 3, and C by 5 and 6). The power entering through FIGURE 34. Topology and photograph of the filter based on the schematic port A is equally split into ports B and C (equal power division of Fig. 33(a) and frequency response for the differential (b) and common is then assumed). Due to the reciprocity and symmetry prop- (c) mode. Reprinted from [196] with permission. erties of the proposed circuit, its electrical response can be described by means of two 3 x 3 scattering matrices. The ele- material not covered in previous review papers. Thus, for ments of such matrices are related through a set of analytical instance, in [198] the reader can find additional information equations obtained after enforcing the set of constraint rules about BTU devices, which will not be treated here. Neverthe- leading to the ideal performance for the differential signal less, note that BTU dividers are also relevant to the design (perfect matching at the three ports, perfect isolation between of BTB devices since, for example, they can be combined ports B and C and equal power division). The constraints for with single-ended dividers to implement 1 to 2n way BTB the common-mode signal (perfect reflection of the common- power dividers, as explained in [199]. In any case, this section mode signal and vanishing mode conversion) should also be will mainly focus on BTB power dividers and BTB direc- enforced. The details of these rules and the corresponding tional couplers. Designs that incorporate other functionalities associated equations are described in depth in [201]. Since the (such as filtering) will also be considered. Devices providing circuit in Fig. 35 has a horizontal symmetry plane, even/odd 420 VOLUME 3, NO. 1, JANUARY 2023 FIGURE 36. Simulated and measured differential (a) and common-mode (b) scattering parameters for the prototype reported in [201]. Reprinted from [201] with permission. FIGURE 37. Diagram (a) and topology (b) of the arbitrary power division BTB power divider proposed in [202]. Reprinted from [202] with permission. mode analysis can be applied and, finally, the constraint rules establish the form required for the 3 x 3 scattering matrices of the even- and odd-mode equivalent circuits in order the whole device to behave as an ideal BTB power divider/combiner. Indeed, the form of those matrices suggests the topology of the proposed circuit. The analytical restrictions are strictly valid at the central frequency of operation (for which the electrical lengths θ14 = θ25 = θ36 = π ; see Fig. 35). At such frequency the theoretical scattering matrix corresponds to a perfectly matched power divider/combiner for the differential signal, with perfect isolation between ports B and C under DM excitation. Total reflection and perfect isolation between balanced ports for CM excitation are also obtained. However, a detailed study concerning the bandwidth of operation of the relevant parameters (for certain prescribed levels of the figures of merit) is necessary. This study is also reported in [201]. In Fig. 36 some of the results reported in [201] for the fabri- cated prototype are shown. Cross-mode scattering parameters FIGURE 38. Layout of the BTB power divider proposed in [204]. (a) 3D are also provided in the original paper. For the fabricated view and (b) top view. Reprinted from [204] with permission. prototype a measured FBW (|SddAA |, |ScdAA |, |SdcAB | below −15 dB) of 20.8% (25% for the simulated data) is achieved. Note that the circuit proposed in [201] was suitable for proposed topology is the one shown in Fig. 37. The authors equal power division. However, an arbitrary power division ra- conclude that the maximum realizable power division ratio is tio is required in many applications. In this way, for instance, 1:4.69 (the characteristic impedance of the transmission lines a BTB Gysel power divider with arbitrary power division is considered to be limited to the range 20-120 ). Unequal ratio was introduced in [202] by the same authors. Once BTB power dividers with wideband common-mode suppres- again, the design method is developed analytically, enforcing sion over a large bandwidth, good isolation and high values the pertinent constraint rules for the required operation. The of power ratio between output ports can be implemented by VOLUME 3, NO. 1, JANUARY 2023 421 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS using two ideal double-sided parallel-strip line (DSPSL) 180◦ phase inverters with isolation resistors, as explained in [203]. A differential Wilkinson type power divider with relatively small size and enhanced bandwidth for matching and isolation can be implemented by arranging two identical single-ended dividers in a back-to-back configuration by introducing rect- angular apertures and slots in the shared ground plane [204]. The proposed structure is depicted in Fig. 38. Under DM oper- ation, the rectangular aperture and the U-shaped slot etched in the common ground plane behave as a virtual perfect electric conductor, in such a way that the DM response does not differ from the one of each of the single-ended dividers obtained assuming a solid ground plane. However, the CM response is strongly affected by the presence of such aperture and slot. The dimensions of the elements etched in the ground plane are optimized through a parametric study to achieve good CM suppression as well as good isolation. The authors report a return loss (RL) level better than 15 dB over a 85 % FBW. Isolation better than 20 dB is achieved over 44 % FBW for the differential mode and 55 % for the common mode. CM suppression better than 20 dB is also reached over 44 % FBW. Besides, mode conversion remains below −20 dB for the whole considered frequency band. B. FILTERING BALANCED-TO-BALANCED POWER DIVIDERS Balanced power dividers can be designed to incorporate filter- ing properties (a functionality different from power division), without the need of adding balanced filter stages. Obviously, FIGURE 39. Coupling scheme (a) of the bandpass filtering BTB Gysel the co-design of the BTB divider and filter reduces the overall divider proposed in [205] and schematics (b) of its implementation. size of the circuit and the loss level. To the authors knowledge, Resonator 1 is represented in blue, resonators 2 and 3 in red, and resonator 4 in yellow. Reprinted from [205] with permission. the first proposal of a BTB filtering power divider (FPD) can be found in [205]. In particular, the structure is a BTB Gysel power divider with bandpass filtering response. The coupling scheme of the structure is shown in Fig. 39, as well as the schematic implementation suggested by the authors. Note that the ring can be regarded as formed by four mi- crostrip resonators coupled through shorted stubs. Using some circuit equivalences valid when the characteristic impedance of the shorting stubs is half of the characteristic impedance of the ring, standard filter design methods can be applied to simultaneously obtain the power division and the filter- ing functions. According to [205] the main limitation of the proposed structure is the achievable DM bandwidth. Taking into account several considerations about minimum and max- imum bandwidths (for given required levels of isolation, mode conversion or suppression as well as realizable characteristic impedances), the authors conclude that a range from 3 % to 12 % FBW can be covered with the proposed structure. Two FIGURE 40. Photograph of the stub-loaded bandpass filtering BTB Gysel prototypes are fabricated and measured, one of which uses power divider in [205]. Reprinted from [205] with permission. uniform transmission lines whereas the other, for miniaturiza- tion purposes, makes use of stub loading (i.e., the transmission line sections are replaced with equivalent slow-wave struc- the rejection bands of the miniaturized prototype for common- tures). A photograph of the miniaturized version (about 50 mode noise and mode conversion are 21 % smaller when % smaller than the original implementation) is depicted in compared to the original structure based on uniform trans- Fig. 40. The measured and simulated results reported in [205] mission lines. Nevertheless, in-band losses are only slightly agree very well for the two fabricated prototypes. However, higher for the miniaturized version (0.13 dB). 422 VOLUME 3, NO. 1, JANUARY 2023 FIGURE 41. Simulated electric field distributions on the prototype at the FIGURE 42. Layout of the second-order balanced-to-balanced filtering center working frequency under distinctive excitation schemes according power divider [208]. Reprinted from [208] with permission. to [208]. (a) DM excitation on ports 1 and 1’. (b) CM excitation on ports 1 and 1’. (c) DM excitation on ports 2 and 2’. (d) CM excitation on ports 2 and 2’. Reprinted from [208] with permission. CM excitations (see Fig. 41) intuitively explain the working Note that the configuration used in [205] involves res- principle leading to equal power division for DM excitation onators working on second-order resonance. This fact leads and perfect CM suppression, as well as perfect isolation at to an increase of the circuit size. To solve this problem, a the central frequency of operation (detailed explanations are modified version of the implementation in [205] was proposed given in [208]). If two of these square patches are mounted in [206], where short-stub-loaded resonators (SSLR) were as shown in Fig. 42, in a back-to-back configuration with four used instead (remind that the dominant resonant frequency slots in the ground plane to control the coupling between the of SSLR is the even-mode resonant frequency). This sim- resonators, the filtering BTB PD can be implemented. This ple modification yields a smaller structure (when compared structure was fabricated and measured with excellent in-band with [205]) with excellent CM suppression (>60 dB over a performance [208]. However, there was still place to improve wide frequency band around the central frequency). Unfortu- the out-of-band rejection by properly modifying the feeding nately, insertion losses are worse than those reported in [205]. of the top square resonator, in such a way that the differential Finally, let us mention, as another interesting and recent ex- harmonic passband associated with mode 4 is eliminated. A ample of BTB Gysel FPD with arbitrary power division, the similar structure, but this time based on the use of circular circuit reported in [207]. patches, has recently been used [209] to design a BTB FPD A different strategy to implement BTB FPD makes use of with arbitrary power division. Even more recently, circular patch resonators [208] (in particular, square patch resonators patches and similar concepts have been utilized to implement were used in that paper). Advantages of using patch resonators a BTB PD with dual-band filtering characteristics [210]. (when compared with microstrip line resonators) are the ex- High-selectivity and isolation for a BTB FPD can be pected lower losses and the better power handling capabilities. achieved as suggested in [211], where a combined microstrip- The working principle of this device is strongly based on the slotline circuitry is employed (see the layout in Fig. 43). analysis of the mode field distributions in the patch. Due to Ultra-wide band power division response is obtained by the degeneracy of the patch T Mnm and T Mmn modes, they means of a uniform impedance slot T-junction. Symmetrical can be simultaneously excited. Under the weight 1:1, four L-shaped microstrip/slotline transitions together with stub- mixed modes are obtained corresponding to 4 combinations loaded resonators are used to obtain a good filtering bandpass whose field distributions have relevant symmetry properties response, with two transmission zeros (TZ) used to improve concerning the purpose of implementing the kind of devices the filter selectivity. Finally, the three ports are fed through a that we are considering. In Fig. 41 the basic geometry of the balanced microstrip/slot transition involving a U-shaped mi- power divider is schematically shown. The square resonator crostrip structure coupled to a stepped-impedance slot. This has 8 symmetrically distributed ports where 1 and 1’ form structure provides wideband transmission from the microstrip the balanced input port. Ports 2 and 2’ and 3 and 3’ are the to the slotline under DM operation, while, at the same time, balanced output ports. Finally, ports 4 and 4’ are terminated due to its symmetry properties and the nature of the slot mode, with the appropriate impedance to yield perfect isolation and CM is intrinsically blocked (the slotline cannot be excited by matching. The represented field patterns for different DM and the CM fields). This kind of microstrip/slot transitions were VOLUME 3, NO. 1, JANUARY 2023 423 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS TABLE 2. Comparison of Several Balanced-to-Balanced Filtering Power Dividers power dividers, Table 2 summarizes some relevant figures of merit for several of the designs discussed in this subsection. In some cases, two different designs are reported in the same reference (labeled as I and II). All the compared circuits have a bandpass filtering response with center frequencies in the range 1.8 GHz to 3.0 GHz. Most of the examples correspond to relatively narrowband filtering responses, except the last one [216] whose FBW is close to 50%. The reported IL exclude the intrinsic 3 dB corresponding to the lossless oper- ation of the equal-power dividers. The in-band DM isolation between the output ports is satisfactory in all cases. Excellent CM rejection levels are reported in [206], [208], [209], [211] over a wide range of frequencies, and the designs reported in [208] stand out due to their excellent DM - CM conversion. FIGURE 43. Layout of the second-order BTB in phase FPD reported C. BALANCED DIRECTIONAL COUPLERS in [211]. Reprinted from [211] with permission. Directional couplers (DC) are other class of basic power di- vider component for high-frequency circuits. They have been studied, and their CM rejection properties exploited, in [122], used for decades and implemented using very different tech- [212], [213], just to mention a few examples. They have nologies (waveguide, microwave integrated and monolithic frequently been used in the implementation of balanced struc- circuitry, substrate integrated waveguide, etc.). In princi- tures. For instance, apart from the discussed example [211], ple, to realize quadrature differential signals, a single-ended the three balanced ports of a BTB FPD with dual-band fre- quadrature coupler followed by a balun could be used. How- quency response described in [214] use the same type of ever, obviously, differential couplers would make unnecessary transition (although they are followed by other components to baluns, resulting in more compact and less lossy solutions. provide the dual-band response, of course). Another example Thus, a significant effort has been devoted in recent years to of this strategy can be found in [215]). develop balanced versions of these circuits too. To the best The literature still offers other paths to design BTB FPD. of our knowledge, the first quadrature differential coupler was For instance, the design proposed in [216] reports on a based on a set of four edge- and broadside-coupled microstrip balanced power divider with wideband filtering characteris- lines and implemented monolithically in a coplanar configura- tics. The device is composed of coupled-line sections, λ/4 tion [218] (see Fig. 44). All the input-output differential lines transformers and isolation resistors. Port-loaded coupled-line are 50- coplanar strip (CPS) transmission lines. The four stubs introduce TZs improving the selectivity (differential coupled microstrip lines, which have all the same width, be- response). For common-mode excitation the proposed circuit have as the differential version of a typical proximity coupler. behaves as a bandstop filter, with >12 dB rejection level over The authors apply an approximate even-odd mode analysis 141 % bandwidth. As a final example, let us mention that to estimate the critical dimensions, although a full-wave opti- metamaterial concepts have also been applied in this con- mization is required to calculate the final coupler dimensions. text. Thus, for example, differential-mode composite right-left The total length of the coupler is reduced using a slow-wave handed (CRLH) transmission lines have been successfully version of the coupled lines (periodically corrugated strips). applied to design differential power splitters with filtering re- The simulated and measured data in [218] were reasonably sponse and common-mode rejection in [217]. In order to have good over a wide frequency band in the millimeter-wave re- an idea about typical achieved performances of filtering BTB gion (15-45 GHz). In this subsection an overview of more 424 VOLUME 3, NO. 1, JANUARY 2023 FIGURE 44. (a) Monolithic implementation of the wideband differential coupler in [218]. (b) Cross section through the coupler at location xx shown in (a). Reprinted from [218] with permission. recent implementations of the balanced version of this well known device will be presented. FIGURE 45. (a) 3-D view of one half of the directional coupler described in [220] with and without the top metallized layer. (b) Top view of the entire coupled-line coupler. Reprinted from [220] with permission. 1) COUPLED-LINE BALANCED COUPLERS Proximity balanced DC of the type reported in [218] (coupled- line couplers) can be designed using analytical expressions class of devices. For the balanced version, this is demon- if the system of four identical coupled microstrips are sym- strated in [220], where two weakly coupled sections and a metrically placed between two ground planes, in such a way central tightly coupled one are cascaded and interconnected that the whole structure has two symmetry planes (vertical to increase the bandwidth of a single section design (only and horizontal), as it is described in [219]. These symmetries the differential mode is considered in the study). The inter- are reflected in the structure of the per unit length (p.u.l.) connection between successive sections is carried out using capacitance and inductance matrices of the coupled section. buried vias. The need for buried vias comes from the fact This greatly simplifies the calculations. Indeed, only four ca- that coupled strips are printed at different levels to obtain the pacitances, corresponding to the four orthogonal TEM modes required coupling for each of the involved sections (the ge- supported by the structure (even-differential, odd-differential, ometry of half of the three-section structure proposed in [220] even-common, and odd-common), each corresponding to a is reproduced in Fig. 45 for clarity). A method to alleviate single strip line with vertical and horizontal symmetry planes this technological difficulty is to allow the width of the cou- behaving as electric or magnetic walls, are required. These pled strips printed at the two different levels to be different. parameters and the length of the coupled section completely Thus, in [221] the authors describe a manner of implementing determine the scattering parameters of the structure, which coupled-line sections with different coupling levels using the can be arranged in a 8 × 8 matrix (single-ended excitation) or same metallization layer, thus avoiding the buried vias. Note into a 4 × 4 matrix for differential (or common) excitation. At that in the previously mentioned coupled-line DCs, CMRR is the central frequency of operation (for which the length of the not explicitly considered. In [222] this problem is addressed coupled section is λ/4), the four differential ports are required by adding a simple section that provides good common- to be matched. Besides, the power entering through one of the mode rejection to a balanced coupled-line structure based on ports (port 1) is derived to other two ports (ports 2 and 3) coplanar-waveguide transmission lines, instead of microstrip being the fourth port isolated. Once established the desired lines. The structure uses a single substrate with two-side met- coupling factor (i.e. the information about how much power is alization. Due to the existence of two planes of symmetry, the transferred to the through, 2, and coupled, 3, ports) standard design is relatively simple. The penalty is a larger size of the theory of stripline coupled-line couplers can be applied to overall circuit due to the addition of the CM rejection section. obtain the widths and separation gaps for the four identical Let us close this brief overview on balanced coupled-line coupled strips. Two designs (with 3 dB and 8 dB coupling DC mentioning the non-symmetric and non-homogeneous factors) are presented in [219]. Due to the symmetry of the implementation reported in [223]. In the structure proposed structure, mode conversion is extremely weak. The measured in [223] the width of the metal strips and their separations, return loss for differential-mode operation is well above 30 dB in the top and bottom sides of the supporting substrate, are for the two designs, and the measured directivity (isolation different (i.e., in the top side there are two strips having minus coupling in dB) is also very good (around 26 dB at the width w1 separated a distance s1 and in the bottom side central frequency for the 8 dB coupler). However, common- there are two strips of width w2 separated a distance s2 ; an mode rejection is not contemplated in this design. additional dielectric or air layer separates this structure of the The bandwidth of coupled-line couplers can be signifi- ground plane). The inhomogeneity of the dielectric introduces cantly extended using cascaded coupled-line sections, as it a well-known deleterious effect on the electrical response. is well known for the case of single-ended versions of this Due to this reason, a detailed study on the incorporation of VOLUME 3, NO. 1, JANUARY 2023 425 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS FIGURE 47. Circuit model (a) of the filtering branch-line coupler proposed in [226] and its microstrip layout (b). Reprinted from [226] with permission. even/odd mode analysis can be applied to facilitate the cal- FIGURE 46. Circuit model (a) and microstrip layout (b) of the balanced branch-line coupler proposed in [225]. The 180◦ lines are folded for culation of the scattering matrix elements. If the excitation miniaturization purposes. Reprinted from [225] with permission. balanced port is A, ports B and C are the output ports, D being the isolated port. An arbitrary power division ratio for ports B and C (k = |SddBA |2 /|SddCA |2 ) can be imposed. Adding the compensating elements is reported in [223]. The proposed conditions of perfect matching for the four differential ports, structure is fabricated using a combination of laminate and isolation between ports A-D and B-C, perfect reflection of the additive manufacturing technologies. The measured data re- common mode, and absence of mode conversion, it is rela- veal a satisfactory performance thanks to the compensation of tively straightforward to obtain the structure of the scattering the difference between electric and magnetic coupling. Other matrix [225]. The relations between the elements of the scat- compensation methods employed to improve the directivity tering matrix and the line characteristic impedances are finally of singled-ended differential couplers can also be used for obtained with the help of the aforementioned even/odd mode differential versions [224]. formalism. Finally, a parametric analysis is used in [225] to determine Z1 (see Fig. 46) in order to maximize the oper- 2) BALANCED BRANCH-LINE AND RAT-RACE COUPLERS ation bandwidth (Z2 and Z3 are determined by k and Z0 ). Branch-line and rat-race are among the most widely used The authors report measured data for three prototypes (hav- microwave couplers. They involve the interconnection of four ing k = 1, 2, 4). The nominal values of k are experimentally λ/4 transmission line sections (branch-line) or three λ/4 sec- reproduced with less than 1 % of error. The matching and tions plus one 3λ/4 section (rat-race) forming a ring. Both isolation bandwidths (for 15 dB level) for the worst case devices have 4 accessible ports. Once again, a balanced de- (k = 1) are 4.3 % and 5.1 %. Much wider bandwidths can sign prevents the necessity of adding baluns, in such a way be achieved by using the dual-stage version of this design, as that, in the last few years, many balanced versions of those it is demonstrated in [225] through HFSS simulations. popular devices have been proposed. In consequence, a mean- Balanced branch-line couplers that incorporate filtering ingful variety of balanced branch-line and rat-race couplers functions are also of practical interest, since they combine are available nowadays. Let us start with the design described two functions in a single device. One of the first imple- in [225], where a balanced branch-line coupler with arbitrary mentations of this type of circuit was introduced in [226]. power division ratio is proposed. The circuit model and the The schematics of the circuit and its microstrip layout are corresponding microstrip layout are depicted in Fig. 46. Due shown in Fig. 47. The first step is to design a conventional to the presence of the symmetry plane (see Fig. 46(a)) the branch-line coupler but substituting the λ/4 transmission 426 VOLUME 3, NO. 1, JANUARY 2023 Another interesting BFDC based on slotline structures, pro- viding similar functionalities, and exploiting similar ideas (for instance, U-shaped microstrip/slotline transitions to enhance the CM rejection response), can be found in [230]. In that paper self-packaged substrate integrated suspended slotline (SISSL) technology is used and two out-of-band transmission zeros (TZs) are introduced and controlled using a three- line cross-finger-coupled resonant structure. This structure enhances the selectivity of the DM passband. The authors add parallel branches and asymmetric capacitive branches to each branch line with the aim of flattening the coupling response. SISSL technology was also used in [231] to de- sign a BFDC. In that paper a simple branch-line coupler based on SISSL was designed (taking into consideration the differences with the conventional branch-line microstrip coupler), and the structure was connected to the four bal- FIGURE 48. Configuration of the BFDC described in [229]. The top side microstrip structure is represented in brown color, the white regions being anced microstrip ports using the already mentioned U-shaped slots etched in the ground plane. The three main building blocks providing microstrip/slotline transitions, which inherently suppress the high CMRR (1), filtering and selectivity (2), and enhanced isolation (3) are common-mode transmission. The measured designs reported highlighted (regions limited by dashed lines). Reprinted from [229] with permission. very good CM rejection over a wide frequency band, as well as good filtering characteristics. The design process is relatively simple in comparison with other alternative imple- mentations of this kind of balanced circuits. Another simple line sections with coupled-line sections of the same electri- implementation based on branch slotline structures can be cal length. Under differential-mode excitation, the equivalent found in [232]. The intrinsic differential nature of the slotline circuit corresponds to a single-ended version. However, the is also employed in the design of wideband BTB differential obtained device has poor common-mode rejection. In order couplers (branch-line and rat-race) [233] making use of the to improve CMRR, the horizontal coupled lines are replaced so-called multimode star junction [234]. This junction leads by the coupled-line-fed coupling structures shown in Fig. 47 to size reduction and wideband common-mode suppression. (coupling structures 1 and 2). These modified sections pro- However, the differential signal of the slotline ports must be vide both common-mode suppression and the desired filtering extracted using a suitable slotline-to-differential microstrip function for the differential-mode signal. The half-wavelength transition, thus enlarging the size of the circuit. In any case, transmission lines used in [225], [226] can be replaced it is an interesting and original solution providing very wide with broadband 180◦ phase inverters [227] implemented in bandwidths for CM rejection (>375%) and DM-to-CM con- DSPSL technology, thus leading to a more compact design. version (>150%) (a thresold of 15 dB has been considered to The fabricated prototypes [227] exhibit excellent electrical establish these values). performance concerning differential-mode matching level and Rat-race couplers in its balanced version have also been broadband common-mode suppression. Besides, as an ad- studied in recent years. Although in [235] a differential rat- ditional advantage, dual-band and triple-band operation is race coupler was introduced in the context of the design of feasible. Other dual-band implementations have been pro- a double-balanced mixer, no attention was paid to important posed in the literature more recently [228]. issues, such as CM suppression. The detailed analysis and A different type of balanced filtering directional coupler the design of more sophisticated versions of balanced rat-race (BFDC) has been implemented combining microstrip and couplers has been accomplished more recently. Thus, for in- slotline circuitry. A recent example of this approach can be stance, in [236] a BTB rat-race circuit where CM suppression found in [229] (a schematic representation of the layout is de- is achieved using a defected ground structure is described picted in Fig. 48). In that paper a U-shaped microstrip/slotline in detail. The layout of the microstrip side and the defected transition is used at each of the four ports to obtain high ground slotline side are shown in Fig. 49. The device exhibits CMRR. This type of transition feed structures are used at the expected rat-race response for the DM and good CM the input and output ports of many balanced designs to make suppression over a 11% FBW. An interesting paper reporting the DM response independent of the CM one and to achieve on the implementation of several classes of six-port balanced good CM suppression. In [229] two stub-loaded resonators rat-race couplers with wideband common-mode suppression are employed to introduce the filtering response, whose selec- can be found in [237]. DSPSL technology is employed in tivity is enhanced by adding L-junction slotlines. Odd-even that paper, thus allowing easy substitution of λ/2 transmission mode phase velocity compensation structures are also in- line sections with DSPSL-based phase inverters. The derived cluded in the ground plane, in the form of U-shaped bending advantages are wideband operation and common-mode sup- slotline geometries, with the purpose of improving isolation. pression, size reduction and lower in-band losses. Besides, the VOLUME 3, NO. 1, JANUARY 2023 427 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS FIGURE 49. Balanced-to-balanced rat-race coupling network proposed in [236]. Reprinted from [236] with permission. six-port structure can be used as a differential-mode circuit or as a single-ended-to-balanced device (multiple functional- ity). The proposed device can also provide arbitrary power division ratio. Two demonstrators designed for a central fre- quency of 0.9 GHz are presented in [237] (for equal and non-equal power division). Very good performance in terms of bandwidth operation and common-mode suppression were reported. D. BALANCED POWER DIVIDERS AND COUPLERS WITH COMMON-MODE ABSORPTION As it has been treated in previous sections devoted to filtering devices, the suppression of the common-mode in balanced structures is usually carried out imposing strong reflection of such component of the input signal. However, partial or total absorption of the common-mode signal has been pro- posed as a better solution [51]. This strategy has also been employed in the case of BTB PD. Several examples using dif- ferent approaches can be found, for instance, in [239], [240], [241]. Thus, [240] incorporates appropriate constraint rules including the common-mode absorption requirement, and a relatively simple circuit satisfying such rules is proposed. The solution presented in [241] is specially interesting since leads to extremely wideband common-mode suppression bandwidth for both balanced-to-balanced and balanced-to-unbalanced FIGURE 50. 3D representation (a), front-side (b) and back-side (c) views of one of the structures proposed in [241] (B-B PD) achieving an excellent structures (200 %, |Scc 21 | better than −15 dB). Besides, ab- wideband reflection and absorption response for the CM operation. sorption >85% is achieved over 116 % bandwidth for BTU Reprinted from [241] with permission. power dividers and 71.2 % for BTB PD. The layout (3D view, front-side and back-side views) of the BTB power divider design is shown in Fig. 50. E. BALANCED PASSIVE PHASE SHIFTERS To close this section devoted to balanced power dividers In order to finish this section let us devote a few words to and couplers, let us mention that tunable and reconfigurable the balanced version of passive phase shifters, whose study versions of these devices have also been subject of attention. has also been object of some attention in the recent literature. For this topic the reader is referred to a recent review paper Only a few references will be included here. Balanced digital that covers the literature in depth and detail [242]. phase shifters were proposed some time ago [243] (additional 428 VOLUME 3, NO. 1, JANUARY 2023 classical references can be found in this paper), but no atten- tion was paid to common-mode performance. Common-mode suppression has been considered more recently in this class of devices. Thus, for instance, in [244] the authors propose a balanced phase shifter based on a coupled line loaded with FIGURE 51. Sketch of the differential-mode sensor concept. a transmission line connected to the central point of the cou- pled line section plus the reference line. The proposed circuit provides RL > 15 dB for a FBW of 80%, 88% and 98% A. THE DIFFERENTIAL-MODE SENSOR CONCEPT depending on the implemented phase shift (90◦ ± 5.5◦ , 60◦ ± In a differential-mode measurement, the differential variable 4.2◦ , 30◦ ± 2.5◦ ). The phase shift bandwidth for the men- to be measured is the difference between the measurand tioned values are, respectively 93%, 88% and 81%. Finally, in the REF sensor, IRE F , and the measurand in the MUT CM suppresion of more than 10 dB is achieved over FBW sensor, IMU T . Thus, the differential input variable is I = of 77%, 70% and 68% for each of the chosen phase shifts. IMU T − IRE F . The differential output variable is simply the A wideband phase shifter with common-mode suppression difference between the output variables of each independent and filtering properties is described in [245]. In this design sensor, in response to the respective input variable, i.e., O = the main branch and the reference branch of the phase shifter OMU T − ORE F (see Fig. 51). As mentioned, the key aspect incorporate similar filtering structures, based on coupled lines of balanced sensors is their capability to suppress the ef- and a multimode T-shaped resonator. As a consequence of fects of common-mode signals, or variables. However, this the design of the two branches, the structure provides, si- aspect requires further analysis, since absolute cancelation multaneously, differential-mode passband and common-mode of cross-sensitivities related to common-mode variables is suppression (for both, the main and the reference lines). Filter not possible, in general [11]. Let us consider that the output synthesis methods are applied to obtain the filtering response variable of the REF and MUT sensors is also sensitive to an of the DM and a step-by-step design method is reported by the external common-mode variable, designated as CM , and let us authors. Another advantage of the solution proposed in [245] define the transfer function of the sensors as is its simple fabrication in single-layer PCB technology. The same authors proposed a different design leading to a very O = OMU T − ORE F = f (IMU T , CM ) − f (IRE F , CM ) wide shift range (30◦ to 180◦ ) with excellent phase deviation (13) and common-mode suppression over large FBW. Synthesized, If IMU T = IRE F , the sensor response is simulated and measured data agree very well and the struc- tures are implemented in a single-layer PCB. To finalize O = f (IMU T , CM ) − f (IRE F , CM ) = f (IMU T , CM = 0) this subsection, let us mention that microstrip/slotline de- signs have also been suggested to implement balanced phase − f (IRE F , CM = 0) (14) shifters. A very recent example can be found in [246], where a where the right-hand side member is the expected sensor re- Schiffman design is proposed. In that paper the authors make sponse without the presence of the external common-mode use of the U-shaped microstrip/slotline structures mentioned stimulus. According to expression (14), the effects of cross- in previous sections, in such a way that only the DM response sensitivities to common-mode signals cannot be completely has to be considered. Thanks to the use of the U-shaped struc- suppressed. However, it is reasonable to consider that such tures in all the ports of the device, CM is strongly suppressed common-mode signals generate a small variation in the output in the whole frequency range of operation (> 40 dB). variables of both sensors, as compared to the effects generated by the input variable of interest. Under such “small-signal” conditions, the response of each independent sensor can be approximated by VI. BALANCED MICROWAVE SENSORS In this section, the focus is on balanced, or differential-mode, OMU T = f (IMU T , CM ) = f (IMU T , CM = 0)+ microwave sensors. Such sensors consist of two independent df (IMU T , CM ) (single-ended) sensors, one devoted to the so-called reference + CM (15a) (REF) material, or measurand (i.e., the input variable), and dCM CM =0 the other one devoted to the material (or measurand) under ORE F = f (IRE F , CM ) = f (IRE F , CM = 0)+ test (MUT) [11]. The main relevant advantage of balanced sensors over their single-ended counterparts is their major ro- df (IRE F , CM ) + CM (15b) bustness against cross-sensitivities related to ambient factors, dCM CM =0 such as temperature, humidity, or atmospheric pressure. At the typical scale of the sensors, environmental factors are seen as Thus, the differential output variable is found to be common-mode stimuli by differential sensors. Consequently, O = OMU T − ORE F = f (IMU T , CM ) − f (IRE F , CM ) the effects of ambient factors, or other common-mode unde- sired stimuli, are minimized in differential-mode sensors. = f (IMU T , CM = 0) − f (IRE F , CM = 0) VOLUME 3, NO. 1, JANUARY 2023 429 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS   df (IMU T , CM ) df (IRE F , CM ) + − dCM CM =0 dCM CM =0 (16) The derivatives in the right-hand side member of (16) are not, in general, identical, unless IMU T = IRE F . However, it is expected that the difference between these derivative terms is small (especially if the MUT and REF measurands do not differ so much). Therefore, the differential output variable can be approximated by O = f (IMU T , CM ) − f (IRE F , CM ) ≈ f (IMU T , CM = 0) − f (IRE F , CM = 0) (17) Hence, to a first order approximation, the effects of cross- sensitivities to common-mode external signals can be ne- glected in differential-mode sensors. By contrast, in the single-ended counterparts, the presence of the external signal CM generates a difference in the output variable OMU T (with regard to the expected value) given by the last term in (15a). B. TYPES AND SOME REPRESENTATIVE EXAMPLES OF BALANCED MICROWAVE SENSORS There are many different types of differential-mode sen- sors, but a relevant categorization divides them between FIGURE 52. Photograph of the CRLH transmission line based non-resonant and resonant sensors [11]. In non-resonant dif- differential-mode sensor (a) and comparison between the transmission ferential sensors, the phase difference in a pair of sensing coefficients for the empty case (unloaded sensing line) and for the sensing transmission lines (one devoted to the REF sample or mea- line loaded with a MUT (b). Reprinted from [249] with permission. surand, and the other one to the MUT), or more specifically, the difference between the phases of the transmission co- [25], [253], [254], [255], [256], [257], [258], [259], [260], efficients of such lines, is the considered output variable. [261], [262], [263], [264]. In these sensors, the canonical out- The sensing lines can be ordinary lines (typically mean- put variable is the differential resonance frequency between dered) [17], [247], [248] or artificial lines, e.g., composite the pair of resonator-loaded lines. Sometimes, the differential right/left handed (CRLH) lines [249], slow-wave transmission resonance magnitude is used as an additional output variable lines [250], or electro-inductive-wave (EIW) [251] transmis- (for example, in measurements of the complex permittivity of sion lines, among others. The main advantage of artificial materials). Nevertheless, in many reported implementations, transmission line based differential sensors over those im- the cross-mode transmission coefficient has been the consid- plemented by means of ordinary lines is the possibility of ered output variable in balanced resonant sensors (e.g., in [24], achieving an enhanced sensitivity with a reduced sensing re- [25], [253]). According to expressions (12), if the lines are gion, by virtue of the potentially high dispersion of artificial uncoupled, the cross-mode transmission coefficient is simply: lines [57]. For example, it is remarkable the huge sensitivity achieved in the sensor reported in [249], where the device is cd S21 = S21 dc = S21 − S43 (18) based on a pair of CRLH lines. However, the use of artificial lines is not exempt of certain design complexity. Moreover, In many reported balanced resonant sensors, the maximum in artificial lines, especially EIW lines, are prone to detuning ef- the magnitude of the cross-mode transmission coefficient and, fects caused by fabrication related tolerances and inaccuracies eventually, the frequency of such maximum, have been the in the values of substrate parameters (dielectric constant and considered output variables. thickness) [251]. It should be mentioned that, despite the fact Let us next report three representative examples of bal- that phase variation is the working principle of these differen- anced microwave sensors, two of them non-resonant, and tial non-resonant sensors, in many cases, phase to magnitude one of them resonant. The first non-resonant sensor, reported conversion has been implemented [17], [249], [252]. For that in [249], consists of a pair of CRLH lines, as depicted in purpose, additional elements to the sensing lines, e.g., cou- Fig. 52. In this sensor, phase to magnitude conversion is plers, or dividers/combiners, are required. implemented by means of a Wilkinson power divider and a Concerning differential-mode resonant sensors, the sensing combiner. The input signal is divided between the two CRLH element is typically a pair of transmission lines loaded with lines. However, the lines connecting the divider/combiner a planar resonator, either a metallic or a slot resonator [24], with the feeding points of the CRLH lines are different. 430 VOLUME 3, NO. 1, JANUARY 2023 Particularly, the feeding lines of the sensing CRLH line are half-wavelength longer than the ones of the reference CRLH line. Therefore, the signals at the input ports of the combiner are out of phase (line imbalance). Because of this, the magni- tude of the transmission coefficient of the resulting two-port structure, or the amplitude of the output signal, is expected to be roughly null, provided the CRLH lines are perfectly imbal- anced. However, loading the sensing line with a MUT alters the perfect imbalance (180◦ phase difference) between the signals present at the input ports of the combiner. The reason is the phase variation experienced by the CRLH sensing line due to the presence of the MUT on top of it. The consequence is the presence of a certain signal level at the output port of the structure (i.e., S21 = 0), related to εMU T . Fig. 52(b) depicts the frequency response of the sensor for two cases, i.e., with unloaded (empty) sensing line, and with the sensing line loaded with a MUT [disturbed case, in reference to Fig. 52(b)]. The combination of CRLH line characteristics and εMU T was determined in [249] in order to obtain the maximum possible transmission coefficient when the MUT is on top of the sensing line (this occurs provided the signals at the input ports of the combiner are in-phase). The output dynamic range at the operating frequency, f0 = 2.3 GHz, is roughly 60 dB. Further details on this structure can be found in [249]. The second case example, also a non-resonant differential sensor, consists of a pair of ordinary (meandered) lines [17]. In this case, phase to magnitude conversion was also applied and achieved by means of a pair of rat-race hybrid couplers. The photograph of the sensor is depicted in Fig. 53, where it can be appreciated the presence of fluidic channels. Thus, the sensor is devoted to the characterization of liquid samples, particularly, to the measurement of the concentration of iso- propanol in deionized (DI) water (hence, the REF liquid is DI water). As demonstrated in [17], with the configuration of Fig. 53, the transmission coefficient between the input and the output port (S1 2 , following the port designation of [17]), is proportional to the cross-mode transmission coefficient of the pair of sensing lines, i.e., S1 2 = −S21 cd (19) In [17], the magnitude of such transmission coefficient at the FIGURE 53. (a) Photograph of the differential-mode fluidic sensor based operating frequency ( f0 = 6 GHz) was used as output vari- on a pair of meandered lines (present below the channels) and equipped able. For measuring purposes, the REF liquid (pure DI water) with a pair of couplers for phase to magnitude conversion. (b) Measured was injected in the REF channel of line A, and subsequently transmission coefficient that results by loading line A with the REF liquid (DI water) and line B with MUT samples corresponding to the indicated different mixtures of isopropanol in DI water were injected in volume fractions of isopropanol in DI water. (c) Value of the transmission the MUT channel (line B), starting with a null volume fraction coefficient (dB) at f0 as a function of the isopropanol content. Reprinted (corresponding to the REF liquid), and progressively increas- from [17] with permission. ing the volume fraction of isopropanol. The responses for the different mixtures are depicted in Fig. 53(b). The sensor was able to resolve concentrations of isopropanol in DI water as small as 1 %. The dependence of the transmission coefficient of the substrate. In this sensor, the maximum sensitivity is at f0 as a function of the isopropanol content is depicted in roughly 12 dB/%. Let us mention that such high sensitivity Fig. 53(c). It should be mentioned that, in order to avoid liquid was achieved by adjusting the electrical length of the pair of absorption by the substrate, a dry film with thickness 50 μm lines at the design frequency to a multiple of 180◦ , as specified and dielectric constant 3.6 was deposited on the upper side in [17] (particularly, the length was set to 540◦ in the sensing VOLUME 3, NO. 1, JANUARY 2023 431 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS lines of the device shown in Fig. 53). Further details of device dimensions and substrate parameters can be found in [17]. The third, and last, example is a differential-mode resonant sensor based on a pair of lines loaded with a split ring res- onator (SRR) and applied to the measurement of electrolyte concentration in diluted aqueous solutions [253]. The layout of the sensor is depicted in Fig. 54(a), whereas the photograph of the fabricated device is depicted in Fig. 54(b) (the details of substrate parameters and sensor dimensions can be found in [253]). The fluidic channels are conveniently located to ensure that the liquid under test (LUT) and REF liquids are in contact with the gaps of the SRRs, the more sensitive regions of the resonators, due to the high fringing fields in such regions. The validation of the sensor of Fig. 54 was carried out in [253] by considering solutions of DI water with different types of electrolytes, particularly, NaCl, KCl and CaCl2 . Here we report the first set of experiments, consisting in the measurement of the cross-mode reflection coefficient after injection of DI water solutions with different concentra- tions of NaCl in the LUT channel, and pure DI water in the REF channel. The results are shown in Fig. 54(c). Concen- trations of NaCl as small as 0.25 g/L can be resolved with the proposed sensor. Fig. 54(d) depicts the dependence of the maximum value of the cross-mode transmission coefficient, cd | |S21 max with the concentration of NaCl, [NaCl]. Actually, a pair of measurements was carried out in [253], in order to ensure that the results are repetitive [such measurements are distinguished by the labels 1 and 2 in Fig. 54(d)]. The sensitivity for small NaCl concentrations is very high, and it progressively decreases as [NaCl] increases. The maximum value of the sensitivity is found to be 0.033 (g/L)−1 , a com- petitive value. There are many differential-mode microwave sensors re- ported in the literature, and their applications are very diverse. Consequently, a faithful comparison, including all the differ- ential sensors reported in references [17], [18], [19], [20], [21], [22], [23], [24], [247], [248], [249], [250], [251], [252], [253], [254], [255], [256], [257], [258], [259], [260], [261], [262], [263], [264] is not straightforward. Nevertheless, there is a subset of sensors devoted to the measurement of the volume fraction of alcohols in DI water [17], [24], [255], [256], or to the measurement of electrolyte concentration in very diluted solutions of DI water [25], [253], [264]. Thus, Table 3 reports a comparison of such sensors to the light of the maximum sensitivity and resolution, the key performance parameters in these sensors. Note that for the sensors de- voted to the measurement of volume fraction of alcohol in DI water, the sensitivity is given in units of dB/ %, whereas the resolution is given in % (of alcohol in DI water), and the value given in the table corresponds to the minimum volume fraction that can be resolved. The output variable of these sensors is the magnitude of the cross-mode transmis- FIGURE 54. (a) Layout of the SRR-based differential-mode microfluidic sion or reflection coefficient (typically expressed in dB). For sensor. (b) photograph. (c) cross-mode transmission coefficient for different concentrations of NaCl. (d) dependence of the maximum value of the sensors focused on the determination of the electrolyte the cross-mode transmission coefficient with the concentration of NaCl. content in DI water solutions, the output variable is also the Reprinted from [253] with permission. 432 VOLUME 3, NO. 1, JANUARY 2023 TABLE 3. 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VOLUME 3, NO. 1, JANUARY 2023 439 MARTIN AND MEDINA: BALANCED MICROWAVE TRANSMISSION LINES, CIRCUITS, AND SENSORS FERRAN MARTIN (Fellow, IEEE) was born in FRANCISCO MEDINA (Fellow, IEEE) was born Barakaldo (Vizcaya), Spain, in 1965. He received in Puerto Real (Cádiz), Spain, in 1960. He received the B.S. degree in physics from the Universitat the Licenciado degree in physics (electronics) and Autònoma de Barcelona (UAB), Bellaterra, Spain, the Ph.D. degree in physics from the University in 1988, and the Ph.D. degree in 1992. From 1994 of Seville, Seville, Spain, in 1983 and 1987, re- to 2006, he was an Associate Professor of electron- spectively. Afterwards, he spent one year with the ics with the Departament d’Enginyeria Electrònica, group headed by Prof. Henri Baudrand with EN- Universitat Autònoma de Barcelona, and since SEEIHT, INP Toulouse, France, as a Postdoctoral 2007, he has been a Full Professor of electronics. Researcher. Then, he joined the Department of In recent years, he has been involved in different Electronics and Electromagnetism, Physics Fac- research activities, including modeling and simu- ulty, University of Seville, where he became an lation of electron devices for high frequency applications, millimeter wave Associate Professor in 1990 and a Full Professor in 2009. Since 1998, he has and THz generation systems, and the application of electromagnetic bandgaps been the Head of the Microwave Group with the Department of Electronics to microwave and millimeter wave circuits. He is currently the Head of and Electromagnetism. He was the recipient of a Salvador de Madariaga the Microwave Engineering, Metamaterials and Antennas Group (GEMMA Fellowship during a four month visiting scholar stay at QMUL, London, Group), UAB, and Director of CIMITEC, a research Center on Metamaterials U.K. (2009). He has been working on several topics related to applied elec- supported by TECNIO (Generalitat de Catalunya). He has authored and coau- tromagnetism and microwave engineering, including the modeling of planar thored more than 650 technical conference, letter, journal papers, and book transmission lines, antennas and circuits using optimized integral equation chapters. He is the co-author of the book on metamaterials titled Metamateri- methods, (bi)anisotropic structures, metamaterials, and periodic electromag- als With Negative Parameters: Theory, Design and Microwave Applications netic structures. He has also contributed to the design of a variety of planar (Wiley), the author of the book Artificial Transmission Lines for RF and Mi- passive microwave printed devices. This research has mainly been reported crowave Applications (Wiley), a Co-Editor of the book Balanced Microwave in 12 book chapters, 170 JCR journal papers, and more than 350 conference Filters (Wiley/IEEE Press), the co-author of the book Time-Domain Signature contributions. He is currently the Editor-in-Chief of the International Journal Barcodes for Chipless-RFID and Sensing Applications (Springer), and the of Microwave and Wireless Technologies. He also acts a reviewer of many coauthor of the book Planar Microwave Sensors (Wiley/IEEE Press). He has journals, mainly in the fields of microwave and antenna engineering, optics, generated 22 Ph.D. students, has filed several patents on metamaterials, and and applied physics. He co-organized the 2017 IEEE-MTT NEMO Sympo- has headed several development contracts. He is very active in the field of sium, Seville, Spain, and collaborates as a TPC member or reviewer with a metamaterials and their application to the miniaturization and optimization number of main conferences in the aforementioned fields. of microwave circuits andantennas. His research interests include microwave sensors and RFID systems, with special emphasis on the development of high data capacity chipless-RFID tags. He has organized several international events related to metamaterials and related topics, including workshops at the IEEE International Microwave Symposium (years 2005 and 2007) and European Microwave Conference in 2009, 2015, and 2017, and the Fifth In- ternational Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamaterials 2011), where he acted as the Chair of the Local Organizing Committee. He is a member of the IEEE Microwave Theory and Technology Society (IEEE MTT-S). He is also a member of the Technical Committees of the European Microwave Conference (EuMC) and the Inter- national Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamaterials). He is a reviewer of IEEE TRANSACTIONS ON MI- CROWAVE THEORY AND TECHNIQUES and IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, among many other journals. He is a member of the Editorial Board of IET Microwaves, Antennas and Propagation, International Journal of RF and Microwave Computer-Aided Engineering, and Sensors. Among his distinctions, he was the recipient of the 2006 Duran Farell Prize for Technological Research, he holds the Parcde Recerca UAB – Santander Technology Transfer Chair, and he has been the recipient of three ICREA ACADEMIA Awards (calls 2008, 2013 and 2018). He is a Fellow of IET. He has acted as guest editor of six special issues on metamaterials and sensors in five international journals. 440 VOLUME 3, NO. 1, JANUARY 2023