Received January 14, 2020, accepted March 28, 2020, date of publication April 3, 2020, date of current version April 21, 2020. Digital Object Identifier 10.1109/ACCESS.2020.2985569 Branch Line Couplers With Small Size and Harmonic Suppression Based on Non-Periodic Step Impedance Shunt Stub (SISS) Loaded Lines JAN COROMINA , (Student Member, IEEE), PARIS VÉLEZ , (Member, IEEE), JORDI BONACHE , (Member, IEEE), AND FERRAN MARTíN , (Fellow, IEEE) CIMITEC, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain Corresponding author: Jan Coromina (jan.coromina@uab.cat) This work was supported in part by the MINECO-Spain under Project TEC2016-75650-R, in part by the Generalitat de Catalunya under Project 2017SGR-1159, in part by the Institució Catalana de Recerca i Estudis Avançats (who awarded Ferran Martín), and in part by the FEDER Funds. The work of Paris Vélez was supported by the Ministerio de Ciencia, Innovación y Universidades through the Juan de la Cierva Fellowship under Grant IJCI-2017-31339. ABSTRACT This paper presents branch line couplers with compact size and harmonic suppression based on non-periodic reactively loaded artificial lines. The reactive loading elements of the lines are step impedance shunt stubs (SISSs). Such elements provide transmission zeros, which are useful to efficiently suppressing the harmonic content of the device. Moreover, by virtue of reactive loading, the reported artificial lines exhibit a slow wave effect of interest for device miniaturization. The combination of size, harmonic suppression efficiency, and design simplicity (with a clear design methodology) is of interest within the framework of artificial transmission lines and their application to the optimization of microwave passive components. INDEX TERMS Branch line couplers, harmonic suppression, slow waves, step impedance shunt stub (SISS). I. INTRODUCTION efficiency and simple design methodology [39]–[41]. The Slow wave transmission lines are artificial lines, typically efficient harmonic suppression is achieved in this paper by consisting of a host line loaded with reactive elements (either truncating periodicity. Specifically, the SISSs are designed in quasi-lumped or distributed), exhibiting a small phase veloc- order to exhibit identical susceptance at the design frequency ity, as compared to the one of ordinary lines [1], [2]. By virtue (where the electrical length of the lines is given by circuit of this small phase velocity, the guided wavelength in these requirements), but different transmission zeros. By properly lines is also small. Consequently, these artificial lines are distributing the transmission zeros, a broad and controllable useful for the implementation of distributed microwave com- stop band can be generated, thereby suppressing the harmonic ponents with compact size, where such (shorter) lines replace bands of the intended device very efficiently. the ordinary (longer) lines. Most slow wave transmission In this paper, such non-periodic artificial lines are applied lines are implemented by periodic reactive loading [3]–[37], to the implementation of compact and harmonic suppressed and it has been argued that periodicity generates stop bands, branch lines couplers. Many efforts have been recently useful for harmonic suppression, or for the implementation devoted to the miniaturization and/or harmonic suppres- of devices with filtering capability. However, periodicity is sion in branch lines couplers [3], [6], [8], [11], [15], [23], not actually a requirement in order to implement harmonic- [28]–[37], [42]–[56]. However, most of the reported imple- suppressed microwave devices. mentations are based on periodic structures. It is shown in this In this paper, it is demonstrated that step impedance shunt paper that by loading the constitutive host lines of the branch stubs (SISSs) [38] are very interesting loading elements for line coupler with SISSs resonating at different frequencies, slow wave transmission lines, as far as the resulting artifi- a set of transmission zeros can be generated. This represents cial lines combine small size, good harmonic suppression a further degree of freedom in the design, and it is possible to achieve an efficient harmonic suppression. Particularly, very The associate editor coordinating the review of this manuscript and efficient rejection of the first harmonic band of the coupler, approving it for publication was Flavia Grassi. with a sharp roll-off in the response, is achieved by placing This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 67310 VOLUME 8, 2020 J. Coromina et al.: Branch Line Couplers With Small Size and Harmonic Suppression the first transmission zero at the position of the first harmonic (i.e., at 3f0 , where f0 is the operating frequency of the branch line coupler). II. DESIGN OF THE NON-PERIODIC SISS-LOADED LINES The main electrical parameters of the constitutive transmis- sion lines, either ordinary or artificial, of a certain distributed microwave component are the characteristic impedance and the electrical length at the design frequency. Whereas in ordinary lines the characteristic impedance is not fre- quency dependent, in reactively loaded lines dispersion is unavoidable. Therefore, the equivalent to the characteristic impedance (i.e., the Bloch impedance in periodic lines, or, more generally, the image impedance in arbitrary networks), is no longer constant with frequency. Consequently, the char- acteristic impedance of the artificial lines under considera- tion, i.e., SISS-loaded lines, must be forced to satisfy the design requirement at the operating frequency of the designed device. Let us designate as ZB and θ the required characteristic impedance and electrical length, respectively, of the artificial line at the operating frequency, f0 . Let us also assume that the line is composed of N cells with identical electrical length, βl (so that θ = N · βl). The parameters of the constitutive cells of the SISS-loaded lines (Fig. 1) are given by the following FIGURE 1. Equivalent circuit model of the SISS-loaded unit cell of the considered slow wave artificial line (a) and typical topology (b). Relevant set of equations [2]: dimensions are indicated. The subindex i refers to the specific cell. Bp Z0 cos (βl) = cos (kl) − sin (kl) (1) 2 and the position of the transmission zero associated to a Z0   certain SISS, i.e., ZB = sin (kl) − Bp Z0 sin2 (kl/2) (2) sin (βl) 1 vpL ω/β kl fz,i = √ (5) swr = = = (3) 2π Li Ci vpo ω/k βl the elements Li and Ci are perfectly determined. In (4), ω0 = 2πf0 is the angular operating frequency. where kl and Z0 are the electrical length and characteristic impedance, respectively, of the host line, and Bp is the suscep- III. BRANCH LINE COUPLER DESIGN AND RESULTS tance of the SISS resonator. In expression (3), swr is the slow- Branch line couplers are implemented by means of two pairs wave ratio, a relevant parameter that determines the level of of θ = 90◦ lines. The characteristic impedance of one of the compactness of the lines (the swr is a design specification for pairs is ZB = 50 , whereas the other line pair exhibits a artificial lines). characteristic impedance of ZB = 35.35 . Let us consider Note that the three previous equations determine uni- that the operating frequency is f0 = 1 GHz and that the vocally the three electrical parameters of the cell, kl, Z0 number of cells of each line is N = 2. With N = 2, the and Bp . However, since Bp is the susceptance of the SISS, onset of the stop band is comprised between f0 and 3f0 , so that and such elements are described by a series resonator, with the first harmonic band is suppressed and, at the same time, inductance Li and capacitance Ci , respectively, it follows the response in the region of interest is kept unaltered, as it that such reactive elements (Li and Ci ) are not univocally was demonstrated in [23] (where the electrical length of the determined from the previous equations. Indeed, line peri- cells is identical, i.e., 45◦ ). odicity is truncated by choosing different combinations of Since the coupler involves four slow wave transmission Li and Ci , in order to generate different transmission zeros, lines, and consequently eight SISSs (one SISS per cell), sev- as previously mentioned. From the value of Bp , deter- eral transmission zeros can be generated with the SISS of the mined from the solution of equations (1)-(3), and given particular lines. In the present paper, we have considered as a by [38]: first step two different transmission zeros, one of them located at 3f0 (for the efficient suppression of the first harmonic band, Ci ω0 located at that frequency), and the other one positioned at 7f0 . Bp = (4) 1 − Li Ci ω02 With such transmission zero at 7f0 , we do not only achieve VOLUME 8, 2020 67311 J. Coromina et al.: Branch Line Couplers With Small Size and Harmonic Suppression TABLE 1. Electrical parameters for each cell. a substantial rejection level of the harmonic located at that frequency, but also a very wide stop band, as it will be shown later. Both the 50- and 35.35- lines have been designed with one cell exhibiting the transmission zero at 3f0 and the other one with the transmission zero located at 7f0 . The electrical length of all the cells is 45◦ . Concerning the slow wave ratio, it has been set to swr = 0.5 for the 35.35- cells and to swr = 0.6 for the 50- cells. The reason is that with the considered substrate for circuit fabrication, the Rogers 4003C with dielectric constant εr = 3.55, thickness h = 0.2032 mm and loss tangent tanδ = 0.0022, line parameters provide extreme geometrical values (width of the host line) for the 50- line with swr = 0.5. The electrical parameters for the four considered cells, and the values of kl, Z0 , L and C that result by solving equations (1)-(5) are given in Table 1. Figure 2 depicts the frequency dependence of the electrical length and character- istic impedance of the designed 35.35- and 50- slow-wave artificial lines, as well as the frequency response, inferred from the circuit simulation of the schematic using Keysight ADS. For the 35.35-/50- line, the reference impedance of the ports has been considered to be 35.35 /50  in order to easily verify that the required value of the characteristic FIGURE 2. Electrical length (a) characteristic impedance (b) and frequency response (c) of the designed 90◦ slow-wave 35.35- and 50- impedance (ZB = 35.35 /50 ) at f0 is satisfied (it is artificial lines, inferred from circuit simulation. indicated by the reflection zero at that frequency). It can be seen from Fig. 2 that the required electrical length at f0 (θ = 90◦ ) is satisfied in both lines. Finally, the frequency lines exhibits good harmonic suppression, by virtue of the responses, with transmission zeros located at 3 GHz and presence of reactive elements (providing transmission zero 7 GHz, exhibit a wide stop band with significant rejection frequencies). level. Subsequently, the layout of the proposed coupler has been In the next step, we have inferred the response of synthesized. For that purpose, the transmission line calcu- the coupler at the schematic level (also using the cir- lator included in Keysight ADS has been used. The width cuit solver of Keysigth ADS) by assembling the designed and length of the host lines for the 35.35- and 50- unit lines. The schematic and the coupler responses are depicted cells has been found to be the one indicated in Table 2, in Figs. 3 and 4, respectively. It can be seen that the coupler where the geometry of the cells is provided, in reference response in the region of interest is very similar to the one to Fig. 1 (b). As for the dimensions of the SISS, we have of the conventional coupler (the response is also included set the width of the inductive line to 0.2 mm, close to the in Fig. 4). However, the coupler based on the artificial minimum strip width achievable with the available fabrica- 67312 VOLUME 8, 2020 J. Coromina et al.: Branch Line Couplers With Small Size and Harmonic Suppression FIGURE 3. Schematic of the coupler based on slow-wave transmission lines. FIGURE 4. Response of the proposed coupler compared to the one of the conventional counterpart. (a) Matching (S11 ) and isolation (S41 ); (b) power splitting (S21 and S31 ). tion technology (an LPKF H100 drilling machine), and we have adjusted the length to the convenient value in order to achieve the required value of the inductance. Nevertheless, for small inductance values, this may provide extremely short lengths, which are not convenient in order to avoid any potential coupling between the host line and the capacitor FIGURE 5. Circuit and lossless electromagnetic simulation of the patches of the SISS resonators. For this reason, in some cases, responses of the four designed unit cells: (a) and (b) are the cells of the the width of the inductive line is wider, providing longer 50- line pair; (c) and (d) correspond to the cells of the 35.35- line pair. VOLUME 8, 2020 67313 J. Coromina et al.: Branch Line Couplers With Small Size and Harmonic Suppression FIGURE 6. Circuit and electromagnetic simulation (with and without losses) of the designed branch line coupler. The response (lossless electromagnetic simulation) of the conventional coupler is also included in the figure. (a) Matching and isolation; (b) power splitting. TABLE 2. Physical dimensions of each cell. FIGURE 7. Layout (a) and photograph (b) of the designed and fabricated branch line coupler. The changed dimensions (in reference to Fig. 1 (b)) of the SISSs of the 50- lines are WA,1 = 2.10 mm, lA,1 = 2.03 mm, WB,1 = 0.20 mm, lB,1 = 8.11 mm, WA,2 = 2.77 mm, lA,2 = 2.70 mm, WB,2 = 0.5 mm, lB,2 = 1.30 mm. inferred by means of the Momentum simulator included in Keysight ADS, whereas the circuit simulations have been obtained by means of the schematic simulator of the same software tool (the details of the considered substrate have been given before). The results are depicted in Fig. 5, where an excellent match up to frequencies beyond the transmis- sion zero frequency of the SISS can be appreciated. This indicates that the SISSs are correctly modeled by the cor- responding series LC resonators up to frequencies substan- lines. The capacitor patches are indeed wide capacitive lines tially above the transmission zero. At higher frequencies, open-ended at the extreme. The width of these capacitive lines distributed effects are unavoidable, and for that reason dis- determines their length (according to the required capacitance crepancies between the circuit and electromagnetic simula- value), and such width has been tuned in order to generate tion arise. Such discrepancies are visible in Figs. 5a and 5c, roughly square patches for the capacitances of the different corresponding to the cells with the transmission zero SISSs. Previously to the generation of the layout of the located at 3f0 , but the agreement in Figs. 5b and 5d is whole branch line coupler, we have compared the lossless excellent within the considered frequency range. Neverthe- electromagnetic response of the four designed cells (includ- less, the discrepancies at high frequencies (for the indi- ing the host line and the SISS) with the circuit response. cated cells) are not relevant for the purpose of achieving As mentioned, the electromagnetic simulations have been efficient harmonic suppression, as it will be shown later. 67314 VOLUME 8, 2020 J. Coromina et al.: Branch Line Couplers With Small Size and Harmonic Suppression FIGURE 8. Measured and electromagnetic response (by including losses) FIGURE 9. Phase (a) and amplitude (b) balance of the designed coupler. of the designed and fabricated coupler. (a) Matching and isolation; Small discrepancies are mainly attributed to fabrication related (b) power splitting. tolerances. The new response of the coupler (lossy electromag- Then we have simulated the response of the whole branch netic simulation) is depicted in Fig. 8, where it can be line coupler, and the results are depicted in Fig. 6. Such appreciated that the isolation is better than 13.5 dB up to figure includes the circuit response, as well as the elec- 12 GHz. We have fabricated the designed coupler (photo- tromagnetic response by excluding and including losses. graph depicted in Fig. 7), and we have measured the response The agreement between the circuit and the lossless elec- by means of the Keysight PNA N5221A vector network ana- tromagnetic simulation of the coupler is very good. The lyzer. The agreement between the simulated and measured response that results by including substrate (dielectric) and response is good (see Fig. 8). According to the measured metal (ohmic) losses does not differ so much of the lossless response, the isolation level up to 12 GHz is better than electromagnetic simulation. It can be seen that the response 12.13 dB, in reasonable agreement to the predictions of the in the region of interest does not differ from the one of electromagnetic simulation. Concerning the filtering capabil- the conventional implementation. However, the harmonics ity of the designed and fabricated coupler (useful for har- are substantially rejected up to at least the 5-th harmonic, monic rejection), the measured rejection level for S21 is better at 11f0 . than 16 dB up to 11f0 , whereas for S31 , the suppression It has been found that by fine tuning the position of the level is better than roughly 40 dB up to that frequency. This transmission zeros of two of the SISSs, the rejection effi- provides substantial rejection of the harmonics (see the com- ciency of the harmonics, as well as the isolation, can be parative table in the next section). In the region of interest, somehow improved. Note that any change in the transmission the response of the designed coupler is good, with a power zero of the SISS does not modify the parameters of the host splitting of −3.17 dB and −3.69 dB, matching of −23.38 dB, line of the corresponding cell, as far as the susceptance of and isolation of −26.55 dB at f0 = 1 GHz. the SISS, given by the solution of expressions (1)-(3), is not It should be mentioned that due to the asymmetry of the modified. The final layout of the coupler is the one depicted SISS-loaded lines (with unequal SISS elements), the response in Fig. 7, where the SISSs of the 50- lines have been slightly of the coupler by considering port 2 as the input port is modified (the transmission zeros have been set to 2.7 GHz somehow different. However, such differences are very small and 6.8 GHz), and the corresponding dimensions are given in (indeed negligible at the frequency of interest, f0 ), and the the caption of Fig. 7 (the other dimensions, given in Table 2, same results concerning the suppression capability of the have not been altered). coupler prevail. VOLUME 8, 2020 67315 J. Coromina et al.: Branch Line Couplers With Small Size and Harmonic Suppression TABLE 3. Comparison with previously reported miniaturized branch line couplers. An important parameter in branch line hybrid couplers whereas in the other couplers the suppressed harmonics do is the phase balance, or phase difference between the out- not extend beyond the second one (at 5f0 ). In [30], inductive put ports. This parameter, as well as the amplitude balance, and capacitive loading is used, and, according to the authors, is depicted in Fig. 9. By considering a phase tolerance of ±5◦ , series connected parallel resonant tanks generate transmis- the resulting bandwidth for phase balance of the fabricated sion zeros useful for harmonic suppression. However, in [30], coupler has been found to be 0.34 GHz (or 34%). With regard a detailed methodology for the design of the coupler is not to amplitude balance, the bandwidth has been found to be reported. By contrast, in this paper, coupler design has been 0.159 GHz (or 15.9%), where, in this case, the maximum carried out according to clear guidelines, based on analytical considered variation has been considered to be ±1 dB. expressions [23]. Moreover, the positions of the transmission zeros can be easily controlled, since the SISSs are very well IV. COMPARISON TO OTHER APPROACHES AND described by series resonators, as it has been demonstrated DISCUSSION in the previous section. Additionally, the agreement between Table 3 includes information of various branch line cou- the circuit schematic and the electromagnetic response of the plers reported in the literature relative to size reduction and layout of the coupler is very good, and this eases the design harmonic suppression capability (the main relevant aspects). of the coupler as far as tuning the transmission zeros, a key It should be mentioned that the harmonic order in Table 3 aspect for harmonic suppression, can be done at the schematic refers to the intrinsic harmonic of the coupler. Note that level. branch line couplers exhibit their functionality at the odd It should be mentioned, however, that, under some cir- harmonics only; therefore, the first (1st ) harmonic refers to cumstances, it might be of interest to suppress the signals 3f0 , the second (2nd ) harmonic to 5f0 , and so on. In view of at 2f0 , beyond the level that intrinsically branch line cou- the table, the coupler reported in [30] and the coupler reported plers do (e.g., due to the presence of nonlinear adjacent in this work are those exhibiting better performance in terms devices such as diodes or transistors). This aspect is discussed of harmonic suppression bandwidth. In both cases, suppres- in [56], where the methodology for the design of branch line sion up to at least the fifth harmonic band is demonstrated, couplers with arbitrary power division ratios and harmonic 67316 VOLUME 8, 2020 J. Coromina et al.: Branch Line Couplers With Small Size and Harmonic Suppression FIGURE 10. Layout of the second designed coupler. suppression from 2f0 is pointed out. This recent work [56] achieves significant suppression of harmonics, by selectively locating transmission zeros at predefined positions by means of shunt stubs. The harmonic rejection level is better than roughly 30 dB between 2f0 (where a transmission zero is located) and 5f0 (corresponding to the 2nd intrinsic harmonic of the coupler, according to the above cited criterion). In this paper, our aim has been to reject the intrinsic harmonics FIGURE 11. Circuit and electromagnetic simulation (with and without of the coupler from 3f0 , up the highest possible frequency losses) of the second designed branch line coupler. (a) Matching and (11f0 , in our case). Nevertheless, with our approach, it is isolation; (b) power splitting. also possible to reject potential signals present at 2f0 . For that purpose, an option is to use a SISS element per trans- TABLE 4. Electrical parameters for each transmission line section of the second designed coupler. mission line section, which has the effect of driving the onset of the stop band to lower frequencies, as discussed in [14], [23]. The penalty is a slight degradation of the coupler bandwidth, as it is also visible in the couplers pre- sented in [56], due to the presence of the transmission zero at 2f0 . Another option is to use the same topology already dis- cussed in this work, but designing the SISS in order to achieve rejection at 2f0 . To demonstrate this last possibility, we have made a new design of the coupler, by locating the transmis- sion zeros of the SISSs at 2.1f0 and 3.1f0 in the 50- line, and at 2f0 and 3f0 in the 35.35- line. The design procedure is exactly the same as the one reported before. Table 4 shows the electrical parameters of the 50- and 35.35- SISS-loaded lines of the coupler, obtained by solving equations (1)-(5). The layout of this second coupler, generated from the electrical parameters of either SISS-loaded line, is depicted in Fig. 10 (the substrate parameters are identical to those con- any potential interfering signal present at 2f0 . It should be sidered in the coupler of the previous section). The circuit and noted, however, that the coupler in [56] is very efficient in electromagnetic response of the designed coupler, with the suppressing the power splitting (S21 and S31 ) between 2 GHz first transmission zero at 2f0 , is depicted in Fig. 11. It can be and 4GHz (both couplers operate at the same frequency). appreciated that the device is able to efficiently suppress any We would like also to mention that our paper is devoted interfering signal present between 2f0 and 4f0. The rejection merely to the implementation of compact size and har- bandwidth is smaller than the one achieved in the previous monic suppressed branch line hybrid couplers, with 3 dB coupler, but the new designed device is able to suppress power splitting, or equivalently, with the same power level VOLUME 8, 2020 67317 J. Coromina et al.: Branch Line Couplers With Small Size and Harmonic Suppression delivered to the output ports. If power division ratios dif- [9] J. García-García, J. Bonache, and F. Martín, ‘‘Application of electro- ferent than 1 were required, high impedance transmission magnetic bandgaps (EBGs) to the design of ultra wide band pass filters (UWBPFs) with good out-of-band performance,’’ IEEE Trans. Microw. line sections are necessary. Since line loading with SISS Theory Techn., vol. 54, no. 12, pp. 4136–4140, Dec. 2006. resonators has the effect of increasing the impedance of the [10] C.-I. Shie, J.-C. Cheng, S.-C. Chou, and Y.-C. Chiang, ‘‘Transdirectional host line, the reported approach would jeopardize the physical coupled-line couplers implemented by periodical shunt capacitors,’’ IEEE Trans. Microw. Theory Techn., vol. 57, no. 12, pp. 2981–2988, Dec. 2009. implementation of the coupler. One possibility to solve this [11] H. Cui, J. Wang, and J.-L. Li, ‘‘Compact microstrip branch-line coupler problem is to implement the lines with artificial lines based with wideband harmonic suppression,’’ ACES J., vol. 27, pp. 766–771, on inductive loading [18] or based on both capacitive and Sep. 2012. [12] M. Orellana, J. Selga, M. Sans, A. Rodríguez, V. Boria, and F. Martín, inductive loading [23]. In this case, the impedance of the ‘‘Synthesis of slow-wave structures based on capacitive-loaded lines host line is reduced (inductive loading), or it can be set to through aggressive space mapping (ASM),’’ Int. J. RF Microw. Comput.- a convenient (implementable) value (simultaneous inductive Aided Eng., vol. 25, no. 7, pp. 629–638, Sep. 2015. and capacitive loading). [13] J. Selga, P. Vélez, M. Orellana, A. Rodríguez, V. Boria, and F. Martín, ‘‘Size reduction and spurious suppression in microstrip coupled line bandpass filters by means of capacitive electromagnetic bandgaps,’’ in IEEE MTT-S V. CONCLUSION Int. Microw. Symp. Dig., San Francisco, CA, USA, May 2016, pp. 22–27. In conclusion, a branch line coupler with efficient harmonic [14] M. Orellana, J. Selga, P. Vélez, A. Rodríguez, V. Boria, and F. Martín, ‘‘Design of capacitively-loaded coupled line bandpass filters with compact suppression based on slow-wave artificial lines has been size and spurious suppression,’’ IEEE Trans. Microw. Theory. Techn., designed and fabricated. Such harmonic suppression, which vol. 65, pp. 1235–1248, Jan. 2017. extends up to at least 12f0 (f0 being the design frequency), [15] K.-Y. Tsai, H.-S. Yang, J.-H. Chen, and Y.-J.-E. Chen, ‘‘A miniaturized 3 dB branch-line hybrid coupler with harmonics suppression,’’ IEEE has been possible by loading the constitutive artificial lines of Microw. Wireless Compon. Lett., vol. 21, no. 10, pp. 537–539, Oct. 2011. the coupler by means of a pair of step impedance shunt stubs [16] L. Zhu, ‘‘Guided-wave characteristics of periodic microstrip lines with (SISSs). Such SISSs behave as shunt connected series res- inductive loading: Slow-wave and bandstop behaviors,’’ Microw. Opt. Technol. Lett., vol. 41, no. 2, pp. 77–79, Apr. 2004. onators, thereby providing a transmission zero at their reso- [17] S. Lee and Y. Lee, ‘‘Generalized miniaturization method for coupled-line nance frequency. Thus, by designing the SISSs with different bandpass filters by reactive loading,’’ IEEE Trans. Microw. Theory Techn., resonance frequencies (and with the required value of their vol. 58, no. 9, pp. 2383–2391, Sep. 2010. [18] P. Vélez, J. Selga, J. Bonache, and F. Martín, ‘‘Slow-wave inductively- susceptance), the generated transmission zeros, conveniently loaded electromagnetic bandgap (EBG) coplanar waveguide (CPW) trans- located, have been the key aspect to achieve a wide stop band mission lines and application to compact power dividers,’’ in Proc. 46th above the region of interest. Moreover, since the SISSs exhibit Eur. Microw. Conf. (EuMC), London, U.K., Oct. 2016, pp. 3–7. a capacitive behavior in the region of interest (vicinity of f0 ), [19] J. Selga, P. Vélez, J. Bonache, and F. Martín, ‘‘EBG-based transmission lines with slow-wave characteristics and application to miniaturization of the phase velocity of the lines has been reduced, and conse- microwave components,’’ Appl. Phys. A, Solids Surf., vol. 123, no. 1, p. 44, quently the overall size of the coupler has been decreased as Jan. 2017. well. As compared to the conventional branch line coupler, [20] S.-G. Mao and M.-Y. Chen, ‘‘A novel periodic electromagnetic bandgap structure for finite-width conductor-backed coplanar waveg- the area occupied by the designed device is 67.7% smaller. uides,’’ IEEE Microw. Wireless Compon. Lett., vol. 11, no. 6, pp. 261–263, The main contribution of the paper is the demonstration Jun. 2001. that, by truncating periodicity and by using series resonators [21] J. Sor, Y. Qian, and T. Itoh, ‘‘Miniature low-loss CPW periodic structures for filter applications,’’ IEEE Trans. Microw. Theory Techn., vol. 49, no. 12, (SISS) as loading reactive elements, branch line couplers pp. 2336–2341, Dec. 2001. with very efficient harmonic suppression, following a simple [22] F. Aznar, J. Selga, A. Fernández-Prieto, J. Coromina, P. Vélez, J. Bonache, design methodology, can be implemented. and F. Martín, ‘‘Slow wave coplanar waveguides based on inductive and capacitive loading and application to compact and harmonic suppressed power splitters,’’ Int. J. Microw. Wireless Technol., vol. 10, nos. 5–6, REFERENCES pp. 530–537, Jun. 2018, doi: 10.1017/S1759078717001350. [1] K. Wu, ‘‘Slow wave structures,’’ in Encyclopedia of Electrical and Elec- [23] J. Selga, P. Vélez, J. Coromina, A. Fernández-Prieto, J. Bonache, and tronics Engineering, vol. 19, J. G. Webster, Ed. New York, NY, USA: F. Martín, ‘‘Harmonic suppression in branch-line couplers based on slow- Wiley, 1999, pp. 366–381. wave transmission lines with simultaneous inductive and capacitive load- [2] F. Martín, Artificial Transmission Lines for RF and Microwave Applica- ing,’’ Microw. Opt. Techn. Lett., vol. 60, pp. 2374–2384, Oct. 2018. tions. Hoboken, NJ, USA: Wiley, 2015. [24] P. Vélez, F. Aznar-Ballesta, J. Coromina, J. Bonache, and F. Martín, ‘‘Com- [3] T. Hirota, A. Minakawa, and M. Muraguchi, ‘‘Reduced-size branch-line pact coplanar waveguide power splitter with filtering capability based and rat-race hybrids for uniplanar MMIC’s,’’ IEEE Trans. Microw. Theory on slow-wave structures,’’ Microw. Opt. Technol. Lett., vol. 61, no. 5, Techn., vol. 38, no. 3, pp. 270–275, Mar. 1990. pp. 1143–1148, May 2019. [4] A. Görür, ‘‘A novel coplanar slow-wave structure,’’ IEEE Microw. Guided [25] J. Selga, J. Coromina, P. Vélez, A. Fernández-Prieto, J. Bonache, and Wave Lett., vol. 4, no. 3, pp. 86–88, Mar. 1994. F. Martín, ‘‘Miniaturised and harmonic-suppressed rat-race couplers based [5] A. Gorur, C. Karpuz, and M. Alkan, ‘‘Characteristics of periodically on slow-wave transmission lines,’’ IET Microw., Antennas Propag., vol. 13, loaded CPW structures,’’ IEEE Microw. Guided Wave Lett., vol. 8, no. 8, no. 9, pp. 1293–1299, Jul. 2019. pp. 278–280, Aug. 1998. [26] H. Liu, S.-J. Fang, Z. Wang, and Y. Zhou, ‘‘Miniaturization of trans- [6] R. B. Singh and T. M. Weller, ‘‘Miniaturized 20 GHz CPW quadrature directional coupled line couplers using series inductors,’’ Prog. Electro- coupler using capacitive loading,’’ Microw. Opt. Technol. Lett., vol. 30, magn. Res. C, vol. 46, pp. 171–177, Jan. 2014. no. 1, pp. 3–5, Jul. 2001. [27] A. Niembro-Martín, V. Nasserddine, E. Pistono, H. Issa, A. L. Franc, [7] M. C. Scardelletti, G. E. Ponchak, and T. M. Weller, ‘‘Miniaturized wilkin- T.-P. Vuong, and P. Ferrari, ‘‘Slow-wave substrate integrated waveguide,’’ son power dividers utilizing capacitive loading,’’ IEEE Microw. Wireless IEEE Trans. Microw. Theory Techn., vol. 62, pp. 1625–1633, Aug. 2014. Compon. Lett., vol. 12, no. 1, pp. 6–8, Jan. 2002. [28] Y. Morimoto, A. Waghmare, K. Dhwaj, and T. Itoh, ‘‘A compact branch [8] K. W. Eccleston and S. H. M. Ong, ‘‘Compact planar microstripline line coupler using novel periodically grounded slow-wave structure,’’ in branch-line and rat-race couplers,’’ IEEE Trans. Microw. Theory Techn., IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, USA, May 2016, vol. 51, no. 10, pp. 2119–2125, Oct. 2003. pp. 22–27. 67318 VOLUME 8, 2020 J. Coromina et al.: Branch Line Couplers With Small Size and Harmonic Suppression [29] J. Coromina, J. Selga, P. Vélez, J. Bonache, and F. Martín, ‘‘Size reduction [49] Y.-H. Chun and J.-S. Hong, ‘‘Design of a compact broadband branch-line and harmonic suppression in branch line couplers implemented by means hybrid,’’ in IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, USA, of capacitively loaded slow-wave transmission lines,’’ Microw. Opt. Tech- Jun. 2005, pp. 997–1000. nol. Lett., vol. 59, no. 11, pp. 2822–2830, Nov. 2017. [50] K.-O. Sun, S.-J. Ho, C.-C. Yen, and D. van der Weide, ‘‘A compact branch- [30] C.-W. Wang, T.-G. Ma, and C.-F. Yang, ‘‘Miniaturized branch-line coupler line coupler using discontinuous microstrip lines,’’ IEEE Microw. Wireless with harmonic suppression for RFID applications using artificial transmis- Compon. Lett., vol. 15, no. 8, pp. 519–520, Aug. 2005. sion lines,’’ in IEEE MTT-S Int. Microw. Symp. Dig., Honolulu, HI, USA, [51] C.-W. Tang and M.-G. Chen, ‘‘Synthesizing microstrip branch- Jun. 2007, pp. 29–32. line couplers with predetermined compact size and bandwidth,’’ [31] P. Kurgan, J. Filipcewicz, and M. Kitlinski, ‘‘Design considerations for IEEE Trans. Microw. Theory Techn., vol. 55, no. 9, pp. 1926–1934, compact microstrip resonant cells dedicated to efficient branch-line minia- Sep. 2007. turization,’’ Microw. Opt. Technol. Lett., vol. 54, no. 8, pp. 1949–1954, [52] C.-H. Tseng and C.-H. Wu, ‘‘Design of compact branch-line couplers Aug. 2012. using π-equivalent artificial transmission lines,’’ IET Microw., Antennas [32] P. Kurgan, J. Filipcewicz, and M. Kitlinski, ‘‘Development of a compact Propag., vol. 6, no. 9, pp. 969–974, Jul. 2012. microstrip resonant cell aimed at efficient microwave component size [53] V. Iran-Nejad, A. A. Lotfi-Neyestanak, and A. Shahzadi, ‘‘Compact broad- reduction,’’ IET Microw., Antennas Propag., vol. 6, no. 12, p. 1291, 2012. band quadrature hybrid coupler using planar artificial transmission line,’’ Electron. Lett., vol. 48, no. 25, pp. 1602–1603, Dec. 2012. [33] S. Koziel and P. Kurgan, ‘‘Low-cost optimization of compact branch-line [54] S. H. Sedighy and M. K. Amirhosseini, ‘‘Compact branch line coupler couplers and its application to miniaturized butler matrix design,’’ in Proc. using step impedance transmission lines (SITLs),’’ Appl. Comput. Elec- 44th Eur. Microw. Conf., Rome, Italy, Oct. 2014, pp. 227–230. tromagn. Soc. J., vol. 28, no. 9, pp. 866–870, Sep. 2013. [34] K.-S. Choi, K.-C. Yoon, J.-Y. Lee, C.-K. Lee, S.-C. Kim, K.-B. Kim, [55] S. Nouri, J. Nourinia, N. Valizade, B. Mohammadi, and A. Valizade, and J.-C. Lee, ‘‘Compact branch-line coupler with harmonics suppression ‘‘Novel compact branch-line coupler using non-uniform folded trans- using meander T-shaped line,’’ Microw. Opt. Technol. Lett., vol. 56, no. 6, mission line and shunt step impedance stub with harmonics suppres- pp. 1382–1384, Jun. 2014. sions,’’ Appl. Comput. Electromagn. Soc. J., vol. 31, no. 4, pp. 401–409, [35] S. Koziel and P. Kurgan, ‘‘Rapid design of miniaturised branch-line cou- Apr. 2016. plers through concurrent cell optimisation and surrogate-assisted fine- [56] H.-R. Ahn and M. M. Tentzeris, ‘‘Arbitrary power-division branch-line tuning,’’ IET Microw., Antennas Propag., vol. 9, no. 9, pp. 957–963, hybrids for high-performance, wideband, and selective harmonic suppres- Jun. 2015. sions from 2f0 ,’’ IEEE Trans. Microw. Theory Techn., vol. 67, no. 3, [36] G. Lian, Z. Wang, Z. He, Z. Zhong, L. Sun, and M. Yu, ‘‘A new minia- pp. 978–987, Mar. 2019. turized microstrip branch-line coupler with good harmonic suppression,’’ Prog. Electromagn. Res. Lett., vol. 67, pp. 61–66, Apr. 2017. [37] H.-R. Ahn and S. Nam, ‘‘Compact microstrip 3-dB coupled-line ring and branch-line hybrids with new symmetric equivalent circuits,’’ IEEE Trans. Microw. Theory Techn., vol. 61, no. 3, pp. 1067–1078, Mar. 2013. [38] J. Naqui, M. Durán-Sindreu, J. Bonache, and F. Martín, ‘‘Implementation of shunt-connected series resonators through stepped-impedance shunt stubs: Analysis and limitations,’’ IET Microw., Antennas Propag., vol. 5, JAN COROMINA (Student Member, IEEE) was pp. 1336–1342, Aug. 2011. born in Barcelona, Spain, in 1989. He received [39] J. Coromina, J. Selga, P. Velez, J. Bonache, and F. Martin, ‘‘Slow-wave the bachelor’s degree in electronics engineer- artificial transmission lines based on stepped impedance shunt stub (SISS) ing for telecommunication and the Telecom- loading: Analysis and stopband bandwidth enhancement,’’ in Proc. 48th munication Engineering master’s degree from Eur. Microw. Conf. (EuMC), Madrid, Spain, Sep. 2018, pp. 69–72. the Universitat Autònoma de Barcelona (UAB), [40] J. Coromina, P. Vélez, J. Bonache, F. Aznar-Ballesta, A. Fernández-Prieto, Barcelona, in 2014 and 2017, respectively, and and F. Martín, ‘‘Reactively-loaded non-periodic slow-wave artificial trans- the Ph.D. degree in microwave circuit design mission lines for stop band bandwidth enhancement: Application to power and miniaturization from CIMITEC, Departament splitters,’’ Int. J. Microw. Wireless Technol., vol. 11, nos. 5–6, pp. 475–481, d’Enginyeria Electrònica, UAB. Jun. 2019. Specifically, his work is focused on the design of slow wave structures [41] H.-R. Ahn and M. M. Tentzeris, ‘‘In-phase T-junction: Study and appli- and their application to a diversity of microwave circuits. In 2016, he joined cation to Gysel power dividers for high power-division ratios requir- IDNEO Technologies as an RF engineer, where he developed ISM antennas ing no high-impedance transmission-line section,’’ IEEE Access, vol. 7, for industrial applications and multiservice LNA for the automotive sector. pp. 18146–18154, Jul. 2019. [42] M.-L. Chuang, ‘‘Miniaturized ring coupler of arbitrary reduced size,’’ IEEE Microw. Wireless Compon. Lett., vol. 15, no. 1, pp. 16–18, Jan. 2005. [43] S.-S. Liao, P.-T. Sun, N.-C. Chin, and J.-T. Peng, ‘‘A novel compact-size branch-line coupler,’’ IEEE Microw. Wireless Compon. Lett., vol. 15, no. 9, PARIS VÉLEZ (Member, IEEE) was born in pp. 588–590, Sep. 2005. Barcelona, Spain, in 1982. He received the degree [44] J. Gu and X. Sun, ‘‘Miniaturization and harmonic suppression of branch- in telecommunications engineering, specializing line and rat-race hybrid coupler using compensated spiral compact in electronics, the Electronics Engineering degree, microstrip resonant cell,’’ in IEEE MTT-S Int. Microw. Symp. Dig., Los Angeles, CA, USA, Jun. 2005, pp. 1211–1214. and the Ph.D. degree in electrical engineering from the Universitat Autònoma de Barcelona, [45] S.-S. Liao and J.-T. Peng, ‘‘Compact planar microstrip branch-line couplers using the quasi-lumped elements approach with nonsymmetrical and sym- Barcelona, in 2008, 2010, and 2014, respec- metrical T-shaped structure,’’ IEEE Trans. Microw. Theory Techn., vol. 54, tively. His Ph.D. thesis concerned common mode no. 9, pp. 3508–3514, Sep. 2006. suppression differential microwave circuits based [46] J. Wang, B.-Z. Wang, Y.-X. Guo, L. C. Ong, and S. Xiao, ‘‘A compact on metamaterial concepts and semi-lumped res- slow-wave microstrip branch-line coupler with high performance,’’ IEEE onators. His current research interests include the miniaturization of passive Microw. Wireless Compon. Lett., vol. 17, no. 7, pp. 501–503, Jul. 2007. circuits RF/microwave and sensors-based metamaterials through the Juan de [47] P. Mondal and A. Chakrabarty, ‘‘Design of miniaturised branch-line and la Cierva fellowship. During his Ph.D., he was awarded with the Pre-Doctoral rat-race hybrid couplers with harmonics suppression,’’ IET Microw., Anten- Teaching and Research Fellowship by the Spanish Government, from 2011 to nas Propag., vol. 3, no. 1, pp. 109–116, Feb. 2009. 2014. From 2015 to 2017, he was involved in the subjects related to meta- [48] V. K. Velidi, B. Patel, and S. Sanyal, ‘‘Harmonic suppressed compact materials sensors for fluidics detection and characterization at LAAS-CNRS wideband branch-line coupler using unequal length open-stub units,’’ through the TECNIOSpring Fellowship, co-founded by the Marie Curie Int. J. RF Microw. Comput.-Aided Eng., vol. 21, no. 1, pp. 115–119, Program. He is currently a Reviewer of the IEEE TRANSACTIONS ON MICROWAVE Jan. 2011. THEORY AND TECHNIQUES and other journals. VOLUME 8, 2020 67319 J. Coromina et al.: Branch Line Couplers With Small Size and Harmonic Suppression JORDI BONACHE (Member, IEEE) was born in FERRAN MARTíN (Fellow, IEEE) was born in Cardona (Barcelona), Spain, in 1976. He received Barakaldo (Vizcaya), Spain, in 1965. He received the Physics and Electronics Engineering degrees the B.S. degree in physics from the Universitat and the Ph.D. degree in electronics engineering Autònoma de Barcelona (UAB), in 1988, and the from the Universitat Autònoma de Barcelona, Ph.D. degree, in 1992. in 1999, 2001, and 2007, respectively. In 2000, From 1994 to 2006, he was an Associate he joined the High Energy Physics Institute of Professor of electronics with the Departament Barcelona, where he was involved in the design d’Enginyeria Electrònica, UAB, where he has and implementation of the control, and monitor- been a Full Professor of electronics, since 2007. ing system of the MAGIC telescope. In 2001, In recent years, he has been involved in different he joined the Department of Electronics Engineering, Universitat Autònoma research activities, including modeling and simulation of electron devices for de Barcelona, where he is currently a Professor of electronics. From 2006 to high-frequency applications, millimeter wave and THz generation systems, 2009, he was an Executive Manager with CIMITEC, Spain, where he is and the application of electromagnetic bandgaps to microwave and millime- currently the Project Manager and leads the research on RFID and antennas. ter wave circuits. He is currently very active in the field of metamaterials His current research interests include active and passive microwave devices, and their application to the miniaturization and optimization of microwave metamaterials, antennas, and RFID. circuits and antennas. Other topics of interest include microwave sensors and RFID systems, with special emphasis on the development of high-data capacity chipless-RFID tags. He is the Head of the Microwave Engineer- ing, Metamaterials and Antennas Group (GEMMA Group), UAB, and the Director of CIMITEC, a Research Center on Metamaterials supported by TECNIO (Generalitat de Catalunya). He has authored or coauthored over 600 technical conference, letter, journal articles, and book chapters. He is the coauthor of the book on metamaterials entitled Metamaterials With Neg- ative Parameters: Theory, Design and Microwave Applications (John Wiley and Sons Inc.) and Time-Domain Signature Barcodes for Chipless-RFID and Sensing Applications (Springer), the author of Artificial Transmission Lines for RF and Microwave Applications (John Wiley and Sons Inc.), and a Co-Editor of Balanced Microwave Filters (Wiley/IEEE Press). He has generated 19 Ph.D. students, has filed several patents on metamaterials, and has headed several development contracts. He is a Fellow of IET. He is also a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S). He serves as a member of the Editorial Board for IET Microwaves, Antennas & Propagation, the International Journal of RF and Microwave Computer-Aided Engineering, and Sensors. He is also a member of the Technical Committees of the European Microwave Conference (EuMC) and the International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamaterials). Among his distinctions, he has received the 2006 Duran Farell Prize for Technological Research, he holds the Parc de Recerca UAB-Santander Technology Transfer Chair. He was a recipient of three ICREA ACADEMIA Awards (calls 2008, 2013, and 2018). He has organized several international events related to metamaterials and related topics, including Workshops at the IEEE International Microwave Symposium (in 2005 and 2007) and the European Microwave Conference (in 2009, 2015, and 2017) and the Fifth International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamaterials 2011), where he acted as the Chair of the Local Organizing Committee. He has acted as a Guest Editor of six special issues on Metamaterials and Sensors in five international journals. He is a Reviewer of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, among many other journals. 67320 VOLUME 8, 2020