Design of Broadband Aperture-Coupled Microstrip Antenna Arrays With Differential Feeding

Received 20 October 2024, accepted 2 November 2024, date of publication 14 November 2024, date of current version 27 November 2024. Digital Object Identifier 10.1109/ACCESS.2024.3498698 Design of Broadband Aperture-Coupled Microstrip Antenna Arrays With Differential Feeding IGNACIO M. DELGADO-LOZANO 1, (Graduate Student Member, IEEE), ARMANDO FERNÁNDEZ-PRIETO 1, (Senior Member, IEEE), VICENTE LOSADA 2, RAFAEL R. BOIX 1, (Member, IEEE), AND FRANCISCO MEDINA 1, (Fellow, IEEE) 1Department of Electronics and Electromagnetism, College of Physics, University of Seville, 41012 Seville, Spain 2Department of Applied Physics I, School of Computer Engineering, University of Seville, 41012 Seville, Spain Corresponding author: Rafael R. Boix ([email protected]) This work was supported in part by Ministerio de Ciencia, Innovación y Universidades (MICIU)/Agencia Estatal de Investigación (AEI)/10.13039/501100011033 under Grant PID2020-116739GB-I00 and Grant PID2023-148281NB-I00, and in part by the European Regional Development Funds/European Union (ERDF/EU). ABSTRACT This paper proposes the design of broadband microstrip antennas fed by differential microstrip lines. The designed broadband antennas are composed of two capacitively coupled rectangular stacked patches excited through a dog-bone shaped aperture by short-circuited differential microstrip lines. The short-circuited lines are symmetrically located with respect to the apertures so that their differential-mode (DM) naturally excites the aperture, while their common-mode (CM) is intrinsically rejected. The DM design of the antennas is based on an equivalent second-order filter circuit consisting of two capacitively coupled parallel LC resonators, which helps to ensure the DM broadband impedance matching of the antenna. Two different 2 ×2 arrays using the proposed antennas have been designed, fabricated and measured, one involving four 180◦hybrids and three power dividers in the feeding network, the other involving one 180◦ hybrid and six power dividers. Bandwidths larger than 25%, gains around 12 dBi and cross-polarization below −25 dB have been achieved by the two arrays at a center frequency of 5.5 GHz. INDEX TERMS Differential-fed antennas, common-mode rejection, filtering theory, microstrip antenna arrays. I. INTRODUCTION Microstrip patch antennas show many advantages: low profile, low weight, easy fabrication, low cost, polarization diversity, etc. [1]. The main disadvantage of microstrip antennas is its narrow bandwidth, but this can be overcome by stacking two patches as demonstrated in [2],[3], and [4]. Differential circuits are more popular than single-ended circuits in integrated circuit design since they are more immune to electromagnetic interference and environmental noise [5]. Differential circuits necessitate a joint integration with differential antennas, and in the particular case of differential microstrip antennas, these antennas show advantages over their single-ended counterpart (smaller size, higher gain, The associate editor coordinating the review of this manuscript and approving it for publication was Li Yang . more symmetrical radiation patterns, etc.) [6],[7],[8],[9], [10],[11]. The topic of filtering antennas has also received much attention in recent years since the joint integration of filters and antennas can improve the frequency selectivity and bandwidth, stability of the in-band gain and out-of- band rejection. The most popular filtering antennas are based on microstrip antennas [12]. The standard coupling-matrix microstrip filter theory of [13] has been frequently used in the design of microstrip filtering antennas [14], but the design of filtering antennas can also be based on the use of equivalent lumped filtering circuits [15]. In the last few years focus has been placed on the design of microstrip antennas with both differential feeding and filtering response [16],[17],[18],[19],[20]. In this paper we focus on the design, fabrication and measurement of broadband microstrip antennas with 173066 2024 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 12, 2024 I. M. Delgado-Lozano et al.: Design of Broadband Aperture-Coupled Microstrip Antenna Arrays differential feeding. The designed broadband antennas are composed of two capacitively coupled rectangular stacked patches excited through a dog-bone shaped aperture by short-circuited differential microstrip lines. The selected feeding structure imposes an electric (magnetic) wall condition at the aperture symmetry plane when operating in the differential (common) mode, which facilitates efficient radiation emission in the differential mode while inherently rejecting common mode transmission [21]. In the paper the broadband design of the antennas in the differential mode (DM) derives from the response of a second-order filter equivalent circuit with quasi-Chebyshev response based on two capacitively coupled LC parallel resonators [15]. The use of an equivalent circuit for the antenna design provides a controlled methodology which enables DM impedance matching in a prescribed frequency band, and which can be applied to other broadband antennas matched at different center frequencies with different bandwidths. This rigorous design methodology based on equivalent circuits has been successfully used in the past for the design of filtering and broadband antennas [14],[15],[16],[17],[18],[19], and to the authors’ knowledge, it is the best way to achieve a controlled design since the equivalent circuit provides a reference response in advance. Moreover, in this paper we search for a Chebyshev response (which is quasi-Chebyshev in practice) in the DM broadband matching of our antennas, just as Chebyshev responses have been traditionally searched for in the microwave field for the broadband impedance matching of networks in order to optimize bandwidth [22, Ch. 5]. The problem with the classical Chebyshev transformer theory of [22, Ch. 5]is that it is specifically devised for a frequency-independent load impedance, and in our case we intend to get a DM broadband matching between a microstrip transmission line and a microstrip antenna made of two stacked patches, i. e., a system with two coupled resonances with an impedance which is strongly dependent on frequency. Since Chebyshev transformer theory is incapable to handle such a frequency-dependent load impedance, we have decided to treat the whole antenna as a second order filter, which has proven to provide a possible solution to the DM broadband matching problem. Although several solutions for broadband microstrip antennas with differential feeding have been proposed in the past [6],[11], to the authors’ knowledge, this is the first paper in which a broadband microstrip antenna with differential feeding is designed by using a systematic methodology based on an equivalent circuit. With a view to analyzing and measuring the designed differential antennas, in this paper a two-port feeding mechanism involving a 180◦hybrid is introduced in which the differential-mode excites one port, while the common-mode excites the second port. Results are presented for two 2 ×2 arrays of differential fed microstrip antennas which have been designed, fabricated and measured. The results indicate that the two arrays show bandwidths in excess of 25%, gains around 12 dBi and cross-pol levels below −25 dB at a center frequency of 5.5 GHz. II. BROADBAND DIFFERENTIAL ANTENNA A. ANTENNA CONFIGURATION AND DIFFERENTIAL MODE EQUIVALENT CIRCUIT The antenna introduced in this paper is built in a four-layered substrate where the layers have thicknesses hi(i=1, . . . , 4), complex permittivities εi=ε0εr,i(1 −j tan δi) (i=1, . . . , 4) and permeability µ0, as depicted in Fig. 1(a). The antenna is fed by a short-circuited differential microstrip line with input ports aand b(Fig. 1(e)) that couples to two stacked rectangular microstrip patches (Fig. 1(b) and Fig. 1(c)) through a non-resonant dog-bone shaped aperture (Fig. 1(d)) made in the ground plane of the differential microstrip line. The feeding system of Fig. 1(e) is conceived to produce the excitation of the antenna in its differential-mode (DM), while avoiding the excitation of the common-mode (CM) [21]. Since the plane x−z, which is a symmetry plane of the aperture, behaves as an electric wall when the aperture is excited, this symmetry plane will enable the excitation of the DM in the aperture (for which the symmetry plane acts as an electric wall). However, it will prevent the CM from exciting the slot because the symmetry plane x−zbehaves as a magnetic wall for the CM. The reflection coefficients of the DM and the CM, Sdd and Scc can be computed in terms of the scattering parameters of the input ports aand b,Saa,Sba, Sab and Sbb, as shown below [23, p. 217] Sdd =1 2(Saa −Sba −Sab +Sbb)(1) Scc =1 2(Saa +Sba +Sab +Sbb).(2) Fig. 2(a) shows the equivalent circuit of the differential antenna of Figs. 1(a) to 1(e) under DM excitation. The two LC parallel resonators L1−C1and L2−C2stand for the two rectangular patches of Figs.1(b) and 1(c), and the capacitance Cmaccounts for the electric coupling between the two patches [15]. The series inductor L0models the short-circuited feeding microstrip line of the antenna Fig. 1(e) under DM conditions (x−zis an electric wall). A parallel capacitance should be added to complete the model of the feeding microstrip line, but this parallel capacitance is absorbed in the capacitance C1, which is also in parallel. Finally, the load resistance Raccounts for radiation losses. B. BROADBAND DESIGN BASED ON DIFFERENTIAL MODE EQUIVALENT CIRCUIT The two capacitively coupled LC parallel resonators of the equivalent circuit of Fig. 2(a) represent a second-order filter of the type shown in Fig. 2(b) [15, Fig.7]. The design of the antenna of Figs. 1(a) to Fig. 1(e) is carried out in such a way that the parameters of the coupled LC resonators in the antenna DM equivalent circuit (see Fig. 2(a)) resemble those of the second order filter of Fig.2(b) as much as possible to ensure impedance matching of the antenna in a broadband. VOLUME 12, 2024 173067 I. M. Delgado-Lozano et al.: Design of Broadband Aperture-Coupled Microstrip Antenna Arrays FIGURE 1. Side view and metallization levels of the differential aperture-coupled stacked microstrip antenna. (a) Side view. (b) Radiating patch at metallization level 4. (c) Lower patch at metallization level 3. (d) Ground plane (grey) with rectangular aperture (yellow) at metallization level 2. (e) Layout including differential feeding strip at metallization level 1, as well as aperture and patches in upper levels. (f) Modified layout of metallization level 1 with 180◦hybrid for measurement purposes. Final layer parameters and physical dimensions (in mm) for the antenna designed: εr1=6.15; εr2=εr4=2.2; εr3=1.06; tanδ1=0.002; tanδ2=tanδ4=0.0009; tanδ3=0.0001; h1=0.508; h2=2.87; h3=4.8; h4=0.254; w1=0.7; s1=11.2; la 1=6.5; lb 1=2.9; r1=6.2; c1=0.36; da 2=1.0; db 2=4.3; wa 2=3.45; wb 2=3.65; sa 2=1.0; sb 2=6.3; sc 2=1.6; l3=16.0; w3=18.8; l4=18.0; w4=19.4. This means the first step in the design of the antenna is to obtain a reference second order filter based on coupled resonators with the design specifications of the antenna concerning center frequency and bandwidth. In particular, in this case we have designed a filter with a center frequency f0=5.42 GHz, a fractional bandwidth 1=0.32, and a maximum value of |S11|in the passband of the filter A(dB) = −13 dB. When these values of f0,1and A(dB) are used in Eqns. (28) to (33) of [15], we arrive to a Chebyshev second order filter of the type shown in Fig. 5(a) of [15]. Then, Eqn. (34) of [15] is used, and we switch from the Chebyshev filter of Fig. 5.a to the quasi-Chebyshev filter of Fig. 5.c of [15]. After optimization of the circuit parameters of this latter quasi-Chebyshev filter to fulfill the specifications in f0, 1and A(dB), it is possible to apply Eqns. (35) to (39) of [15] to obtain a filtering circuit like that of Fig. 2(b) in which all specifications are satisfied. The circuit parameters of this FIGURE 2. (a) Equivalent circuit of the differential microstrip antenna of Figs. 1(a) to 1(e) under DM excitation. (b) Second-order filter made of two capacitively coupled resonators. (c) Circuit of (a) in the limit R→ ∞. FIGURE 3. Blue solid line stands for |S11|of the quasi-Chebyshev reference filter. Black dashed line stands for |S11|of the antenna DM equivalent circuit based on Eqns. (6),(7), and (15) to (18). Purple dotted line stands for |S11|of the optimized antenna DM equivalent circuit. Orange dot-dashed line stands for the |Sdd| ADS simulations of the differential antenna designed in this paper. resulting quasi-Chebyshev filter are given in the second row of Table 1, and its frequency response is given by the blue solid line in Fig. 3. In order to be able to compare the parameters of the DM equivalent circuit of the antenna (see Fig. 2(a)) with those of the quasi-Chebyshev reference filter (see Fig. 2(b) and the second row of Table 1), we first need a procedure to model the DM input impedance of the antenna as a function of frequency so that the DM equivalent circuit parameters can be de-embedded from this DM input impedance. With the aim of modelling the DM input impedance, the antenna of Fig. 1(a) is first electromagnetically analyzed with commercial software ADS Momentum [24], and its DM reflection coefficient Sdd is computed in 200 frequencies in the operating band of the antenna (which is taken to be the frequency range between 4.0 GHz and 7.0 GHz for the antenna designed in the paper). The DM input impedance of 173068 VOLUME 12, 2024 I. M. Delgado-Lozano et al.: Design of Broadband Aperture-Coupled Microstrip Antenna Arrays TABLE 1. Circuit parameters of reference filter and antenna DM equivalent circuit. the antenna as a funcion of frequency Zin,DM(ω) is computed in terms of Sdd by means of the expression Zin,DM(ω)=Z0 1+Sdd(ω) 1−Sdd(ω)(3) where Z0=50 , which is the characteristic impedance of the microstrip lines at ports aand bof Fig. 1(e). Once the simulated values of Zin,DM(ω) are known, these values are fitted as a rational funcion of ωwhich matches the input impedance of the DM equivalent circuit in Fig. 2(a). By applying standard circuit theory to the analysis of this circuit, it can be shown Zin,DM(ω) must be modelled as a ratio of two polynomials as shown below (a polynomial of degree 5 is used in the numerator, and a polynomial of degree 4 is used in the denominator) Zin,DM(ω)=jn5ω5+n4ω4+jn3ω3+n2ω2+jn1ω ω4+jm3ω3+m2ω2+jm1ω+m0 .(4) In order to determine the nine unknown coefficients ni (i=1,2,3,4,5) and mi(i=0,1,2,3), the DM input impedance obtained from (3) by means of ADS Momentum simulations is obliged to coincide with the input impedance given by (4) in the 200 frequencies of the operating band of the antenna. This leads to 400 equations (after separation of the real and imaginary parts) for the nine unknowns niand mi (for details, see Eqns. (1) to (6) of Section II-B of [15]). Then, this overdetermined system of equations is solved by means of the total least squares method (see [15] and references therein). Fig. 4shows the results obtained for the real and imaginary parts of Zin,DM(ω) in the particular case of the final antenna designed in this paper (layer parameters and physical dimensions shown in the caption of Fig. 1). These results are obtained with both ADS Momentum simulations and the fitted rational function of (4). Note excellent agreement is obtained between both sets of results, which indicates that the circuit model proposed for the antenna is an adequate model since the input impedance of the circuit matches the electromagnetic response of the antenna. Once we know the coefficients ni(i=1,2,3,4,5) and mi(i=0,1,2,3) of (4) for the input impedance, the next step is the de-embedding of the seven circuit parameters of Fig. 2(a) (L0,L1,L2,C1,C2,Cmand R) from the expression of the input impedance. As commented in [15], one of these circuit parameters can be arbitrarily chosen, and it is taken to be R=50 . The determination of the six remaining reactive parameters (three inductances and three capacitances) is not a trivial task. One way to face the problem is to take the limit FIGURE 4. Real and imaginary parts of the DM input impedance for the particular differential microstrip antenna designed in this paper (see Figs. 1(a) to 1(e) with layer parameters and physical dimensions given by the caption of the Figure). Solid lines stand for the results obtained with the rational function of (4) after total least squares fitting and symbols (+) stand for Momentum simulations. when R→ ∞ in the equivalent circuit of Fig. 2(a), which implies to replace the resistance Rby an open circuit. The result of the limit R→ ∞ is the circuit of Fig. 2(c). For this latter circuit, it is possible to demonstrate that the input impedance becomes Z∞ in,DM(ω)=lim R→∞Zin,DM(ω)=jn5ω5+n3ω3+n1ω ω4+m2ω2+m0 (5) where n5,n3,n1,m2and m0are the coefficients defined in (4). If we work out the input impedance of the circuit of Fig. 2(c) and compare the resulting expression with Eqn. (5), after some cumbersome mathematical manipulations, it is possible to obtain five equations relating the six circuit reactive parameters L0,L1,L2,C1,C2and Cmwith the five coefficients n5,n3,n1,m2and m0. These five equations are: L0=n5(6) L1=p1 m0 (7) C2 m (C2+Cm)= −m2 p1+1 p3+m0p3 p2 1 (8) (C1+Cm)= −m2 p1+m0p3 p2 1 (9) (C2+Cm)L2= −p3 p1 (10) where: p3=n3−m2n5(11) p1=n1−m0n5.(12) Now we have five equations for the determination of the six circuit reactive parameters, but we need an additional VOLUME 12, 2024 173069 I. M. Delgado-Lozano et al.: Design of Broadband Aperture-Coupled Microstrip Antenna Arrays equation, and this sixth equation can be obtained from the equivalence between the input impedance of the circuit of Fig. 2(a) and the imput impedance of Eqn. (4). After some manipulations, it is possible to show that: (C2+Cm)R=p3 p2 (13) where: p2=n2+m1n5.(14) The six equations (6) to (10) and (13) can be used to solve for L0,L1,L2,C1,C2and Cmin terms of the whole set of coefficients ni(i=1,2,3,4,5) and mi(i=0,1,2,3) of (4), and in terms of R=50 . The resulting expressions are Eqns. (6) for L0and (7) for L1, and the following four equations: L2= −p2R p1 (15) Cm=1 √R−m2p3 p1p2+1 p2+m0p2 3 p2p2 11/2 (16) C1= −m2 p1+m0p3 p2 1−1 √R−m2p3 p1p2+1 p2+m0p2 3 p2p2 11/2 (17) C2=p3 p2R−1 √R−m2p3 p1p2+1 p2+m0p2 3 p2p2 11/2 .(18) When Eqns. (6),(7) and (15) to (18) are applied to the coefficients of the rational function of (4) for the input impedance of the particular antenna designed in this paper (see Fig. 1(a)), the results obtained for the circuit parameters are those shown in the fourth row of Table 1. Now, if we use the values of these circuit parameters to compute the DM input impedance Zin,DM(ω) of the equivalent circuit of Fig. 2(a), and then determine the reflection coefficient S11(ω) of this circuit, we obtain the black dashed line shown in Fig. 3. Note that the orange dot-dashed line in that figure identifies the DM reflection coefficient of the antenna obtained by ADS Momentum simulations, and that there is a patent disagreement between the black dashed line and the orange dot-dashed line in Fig. 3. This latter disagreement is weird since the rational function modelling of the antenna input impedance in Fig. 4was very accurate, and the circuit parameters have been obtained by using the rational function model for the DM input impedance which is plotted in Fig. 4. To explain this weird behavior, we have to think that even though we have solved for the six circuit reactive parameters of Eqns. (6),(7) and (15) to (18) by using the six equations (6) to (10) and (13), these six circuit parameters have to fulfill in practice nine equations since there are nine different coefficients niand miin (4). And bearing in mind that the antenna DM input impedance data obtained in the ADS Momentum simulations (the orange dot-dashed line in Fig. 3) suffer from numerical noise, and that the nine equations for the equivalent circuit parameters are highly non-linear, small errors in the input impedance data may lead to important errors in the de-embedding of the circuit parameters (in fact, we have checked that Eqns. (6),(7) and (15) to (18) lead to exact results for the equivalent circuit parameters in the case where the input impedance of (4) matches that of an exact circuit of the type shown in Fig. 2(a) instead of being the input impedance of an antenna obtained by means of approximate electromagnetic simulations). In spite of these inaccuracies, the dashed black line is not so far from the orange dot-dashed line in Fig. 3, and the equivalent circuit parameters obtained with Eqns. (6), (7) and (15) to (18) can be used as a good starting point in an optimization process devoted to match the response of the equivalent circuit of Fig. 2(a) to that of the simulated antenna under DM excitation. As commented in [15], this optimization process can be carried out with a gradient optimization routine of commercial software ADS [24]. When we proceed in this way, the resulting response of the equivalent circuit after optimization is the purple dotted line in Fig. 3. The reactive parameters of the equivalent circuit obtained after optimization are provided in the fifth row of Table 1. Please note the agreement between the response of the simulated antenna (orange dot-dashed line) and that of the optimized equivalent circuit (purple dotted line) in Fig. 3is very good. This indicates that the method used in this paper for the de-embedding of the equivalent circuit of the antenna (i.e., Eqns. (6),(7) and (15) to (18) plus ADS optimization) is a reliable method. Once a method has been developed for the accurate determination of the equivalent circuit parameters of the antenna in Fig. 2(a), the antenna dimensions have been adjusted in such a way that the equivalent circuit of Fig. 2(a) is as close as possible to the equivalent circuit of Fig. 2(b) for the required specifications of the reference quasi-Chebyshev filter (see Section II.D of [15] for details). The results obtained for the equivalent circuit parameters of the final antenna design are shown in Table 1. In this Table one can check that the difference between the reference filter circuit parameters (second row) and the optimized equivalent circuit of the final antenna design (fifth row) is around 20% in the case of L1, and does not exceed 10% in the rest of the circuit parameters. This indicates the parameters of the equivalent circuit of Fig. 2(a) for the antenna designed in the paper are pretty close to those of the equivalent circuit of the reference filter in Fig. 2(b). This good agreement is also demonstrated in Fig. 3, which shows that both the frequency response of the antenna (orange dot-dashed line) and the frequency response of the optimized equivalent circuit (purple dotted line) match reasonably well the response of the reference filter (blue solid line). C. COMPARISON BETWEEN SIMULATED AND EXPERIMENTAL RESULTS In the previous section we have used the second order filter of Fig. 2(b) to design a differential broadband microstrip antenna with the configuration given in Figs. 1(a) to 1(e). 173070 VOLUME 12, 2024 I. M. Delgado-Lozano et al.: Design of Broadband Aperture-Coupled Microstrip Antenna Arrays FIGURE 5. Magnitude of the scattering parameters for the designed antenna. The black solid and dotted lines stand for measurements of |S11| and |S22|respectively (meas.). The red solid and dotted lines stand for the original simulations of |S11|and |S22|with nominal substrate parameters (or. sim.). The green solid and dotted lines stand for simulations of |S11| and |S22|with corrected substrate parameters (corr. sim). Unfortunately, a two-port feed like the one in Fig. 1(e) is not practical for measurements since we need to excite the antenna with a single feeding source in order to obtain its radiation patterns. Therefore, an alternative feeding mechanism containing a 180◦microstrip hybrid [22, ch. 7] is shown in Fig. 1(f) [5, Fig. 3]. This 180◦hybrid is used to convert a single input signal into either a DM or a CM. In particular, when port 1 is fed, the signal arrives at ports 3 and 4 with a phase shift of 180◦, thus leading to a DM excitation which makes it possible to identify S11 in Fig. 1(f) with the DM reflection coefficient Sdd defined in (1). However, when port 2 is fed, the signals reach ports 3 and 4 in phase, and this leads to a CM excitation for which S22 in Fig. 1(f) can be identified with the CM reflection coefficient Scc defined in (2). Note the location of the 180◦hybrid just below the antenna patches in Fig. 1(f) helps to optimize the antenna area. The antenna of Fig. 1(a) with the 180◦hybrid feeding of Fig. 1(f) has been fabricated with the dimensions shown in the caption of Fig. 1for a center frequency of 5.5 GHz. The magnitudes of the scattering parameters, |S11|and |S22|, at the input ports of Fig. 1(f) have been obtained by means of commercial software ADS Momentum [24], and they have also been measured with a vector network analyzer (remind S11 is the DM reflection coefficient Sdd of (1) and S22 is the CM reflection coefficient Scc of (2)). The original simulations (red lines in Fig. 5) based on manufacturer nominal parameters for the substrate layers (these are the layers parameters shown in the caption of Fig. 1) provide a fractional bandwidth for the antenna under DM excitation of 33.5% -roughly from 4.6 to 6.5 GHz-, and for measurements (black lines in Fig. 5), the fractional bandwidth is 34.9% -from 4.7 to 6.7 GHz-, which indicates the agreement is acceptable. The frequency shift is attributed to the compression of the foam layer (layer of thickness h3in Fig. 1(a)) after assembling the antenna with plastic screws, and to an inaccurate estimation of the relative permittivities of the substrates. In particular, if the thickness of the foam layer is reduced from h3=4.8 mm to h3=4.3 mm, the simulated green line results of Fig. 5are obtained, which are closer to measurements. Note the original simulations for FIGURE 6. (a) Back picture of the antenna of Fig. 1(a) with 180◦hybrid feeding. (b) The antenna shown in (a) when mounted in the anechoic chamber. (c) Picture showing the feeding network of the array of Fig. 9(b), and the patches at metallization levels 3 and 4 of Fig. 1(a). S11 (red solid line in Fig. 5) are slightly different from the simulations of Sdd in Fig. 3(orange dot-dashed line) since the former values have been obtained with the 180◦hybrid feeding of Fig. 1(f), while the latter values have been obtained with the simpler two-port feeding of Fig. 1(e). In spite of this, both the original and corrected simulated values of S11 in Fig. 5show two reflection minima, which indicates the DM antenna design has been based on the response of a second order filter (the reflection minima would be reflection zeros in the ideal filter as the solid blue line of Fig. 3shows). Fig. 5shows the values of |S22|are close to 0 dB in the simulations and around −1.4 dB in the measurements, which indicates the feeding mechanism of the antenna with the symmetrically located short-circuited differential microstrip line of Figs. 1(e) and 1(f) provides good common-mode rejection. Figs. 6(a) and 6(b) show photographs of the fabricated antenna of Fig. 1(a) with the 180◦hybrid feeding of Fig. 1(f). Note the presence of the two input ports 1 and 2 in Fig. 6(a), which enables to separately explore the excitation of the differential and the common modes. Fig. 6(b) shows a photograph of the fabricated antenna with two input ports (the common mode port connected to a matched load) inside the anechoic chamber. The gain and the radiation patterns of the antenna have been simulated with commercial software CST [25], and they have been measured in the anechoic chamber of Fig. 6(b). The results for gain are shown in Fig. 7, and the results for the E-plane radiation patterns are shown in Fig. 8. In the case of gain, good agreement is found between measurement and simulations. The discrepancies around 1 dB are attributed to fabrication tolerances and losses mechanisms not considered in the simulations. The measured gain is between 6 dBi VOLUME 12, 2024 173071 I. M. Delgado-Lozano et al.: Design of Broadband Aperture-Coupled Microstrip Antenna Arrays FIGURE 7. Gain values of the designed antenna. The black solid line stands for the measured gain, the red dotted line stands for the original simulated gain with nominal substrate parameters, and the green dotted line stands for the simulated gain with corrected substrate parameters. FIGURE 8. E-plane radiation patterns of the designed antenna. The black solid (co-pol) and blue solid (cross-pol) lines are measured values, and the black dotted (co-pol) and blue dotted (cross-pol) lines are simulated values. (a) 4.8 GHz. (b) 5.5 GHz. (c) 6.2 GHz. and 6.5 dBi in the matching frequency band of the antenna, which is typical for a microstrip antenna. Although the gain versus frequency curves show the selectivity of a filtering antenna, this selectivity can be seen to be poor. However, this is the selectivity expected for a broadband second order quasi-Chebyshev filter. Remember the goal pursued in this paper is broadband behaviour based on a filtering design, rather than selectivity. The E-plane radiation patterns of Fig. 8also show good agreement between simulations and measurements, a stable main lobe between 4.8 and 6.2 GHz, and cross-pol levels below −20 dB. III. ARRAY CONFIGURATIONS A. ARRAY DESIGN To increase the gain of the antennas, two 2 ×2 arrays of differential antennas of the type shown in Fig. 1(a) have been designed, fabricated and measured at a center frequency of 5.5 GHz. In the first array shown in Fig. 9(a), the feeding signal is split, through the use of three power dividers, into four equally distributed branches which feed four 180◦ hybrids that are located below every antenna and perform the conversion from the input signal to a DM (as in port 1 of Fig. 1(f)). In the second array shown in Fig. 9(b), which is inspired by the array feeding configuration proposed in [8, Fig. 3], the conversion from the input signal into a DM is first carried out in a single 180◦hybrid and then, the DM is distributed to each one of the four antennas via six power dividers (in this case, the differential feeding is of the type shown in Fig. 1(e)). In both arrays, a parallel feed has FIGURE 9. Top view of the feeding networks for the designed arrays. (a) Proposal with four 180◦hybrids and three power dividers. (b) Proposal with one 180◦hybrid and six power dividers. been used, which guarantees that the amplitude and phase of the excitations are equal in the four antennas [26]. Since we have sufficiently proved that the differential line feeding of Fig. 1(f) provides a large CM rejection, the sum port excitation 2 of Fig. 1(f) has been suppressed in all the 180◦ hybrids of the arrays, while keeping the differential port excitation 1. The separation distance between the geometrical centers of the antennas has been chosen as d=0.7λ0(λ0is the free space wavelength) since this separation makes it possible to maximize the directivity, while keeping low side lobe values [26]. By comparing Figs. 9(a) and 9(b), it becomes clear that the array of Fig. 9(a) requires a smaller area than that of Fig. 9(b). The photograph in Fig. 6(c) shows several metallized layers of the array of Fig. 9(b). In particular, Fig. 6(c) shows the layout of the array feeding network and the two layers of four patches that are stacked when the array is assembled. B. ARRAY RESULTS Fig. 10 shows results for the |S11|of the arrays. The simulated fractional bandwidth of the arrays (dashed lines) is around 30% -roughly from 4.7 to 6.4 GHz-, which is slightly smaller than the fractional bandwidth of the individual antenna (see Fig. 5). Concerning the experimental results, the measured fractional bandwidth of the array of Fig. 9(a) is around 25% - from 5.0 to 6.4 GHz-, and the measured fractional bandwidth of the array of Fig. 9(b) is 29% -from 5.0 to 6.7 GHz-. The simulated and measured gain results for the two arrays are plotted in Fig. 11. Since the four antennas of each 2 ×2 array are excited in phase with the same amplitude, the theory indicates the array gain will present a raise of 6 dB inside the matching frequency interval, when compared with the gain of individual antennas [26]. Fig. 11 shows that the simulated gain of the arrays oscillates around 13 dBi in the matching frequency intervals, while the measured gain yield values around 12 dBi, which is in agreement with the expected results. Please note that the array configuration of Fig. 9(b) has a slightly lower gain than that of Fig. 9(a), which is attributed to the larger lengths of the microstrip lines involved 173072 VOLUME 12, 2024 I. M. Delgado-Lozano et al.: Design of Broadband Aperture-Coupled Microstrip Antenna Arrays FIGURE 10. Magnitude of the reflection coefficient at the input of the designed arrays. The solid lines stand for the measurements and the dotted lines stand for the simulations. The black solid and dotted lines correspond to the feeding proposal with four 180◦hybrids and three power dividers, and the red solid and dotted lines correspond to the proposal with one 180◦hybrid and six power dividers. FIGURE 11. Gain values of the designed arrays. The solid lines stand for the measurements and the dotted lines stand for the simulations. The black solid and dotted lines correspond to the feeding proposal with four 180◦hybrids and three power dividers, and the red solid and dotted lines correspond to the proposal with one 180◦hybrid and six power dividers. in the feeding network. Fig. 12 shows results for the E-plane radiation patterns of the arrays at frequencies 4.8, 5.5 and 6.2 GHz. The main lobes of the array radiation patterns clearly reflect the increase in gain when compared with the main lobes of the radiation patterns of the individual antenna in Fig. 8. Side lobe levels are roughly kept below −15 dB in all cases, and cross-pol levels are kept below −25 dB. Fig. 13 shows CST simulation results for the radiation efficiency of the individual antenna studied in Subsection II-C, and also for the radiation efficiency of the arrays in Fig. 9. In the case of the individual antenna, the average simulated efficiency in the matching frequency band is around 80%, and in the case of the arrays, the average simulated efficiency of the array of Fig. 9(a) is around 77%, and that of the array of Fig. 9(b) is around 70%. These differences in the radiation efficiency of the arrays may also contribute to explain the small differences in the gain of the two arrays in Fig. 11. Note the values of radiation efficiency typically range from 70% to 85%, which are similar to the efficiency values reported for other microstrip antennas [3],[27] In Table 2we compare the results obtained in previous works for differentially fed microstrip antennas with our own results. Although the single antennas designed in [6] and [11] are broadband differential microstrip antennas with a bandwidth similar to the single antenna reported in this paper (see Fig. 1), the design carried out in this paper is based on a filtering equivalent circuit (see Fig. 2), and follows a FIGURE 12. E-plane radiation patterns of the designed antenna. The black solid (co-pol) and blue solid (cross-pol) lines are measured values, and the black dotted (co-pol) and blue dotted (cross-pol) lines are simulated values. The first row is for the feeding proposal with four 180◦hybrids and three power dividers, and the second row is for the proposal with one 180◦hybrid and six power dividers. (a) 4.8 GHz. (b) 5.5 GHz. (c) 6.2 GHz. (d) 4.8 GHz. (e) 5.5 GHz. (f) 6.2 GHz. FIGURE 13. Simulated radiation efficiency for the single antenna studied in Fig. 5, and for the arrays of Fig. 9. The blue solid line stands for the efficiency of the single antenna, the black solid line stands for the efficiency of the array with four 180◦hybrids and three power dividers of Fig. 9(a), and the red solid line stands for the efficiency of the array with one 180◦hybrid and six power dividers of Fig. 9(b). systematic methodology which makes it possible to repeat the design for other different center frequencies and other different fractional bandwidths. No design methodology is reported in [6], while the design procedure described in [11] strictly relies on numerical optimization. Also, the patch feeding mechanism used in [6] and [11] is based on coaxial probes, while aperture coupled feeding is used in this paper. The use of coaxial probes requires to carry out solder joints and substrate vias, which complicates fabrication and reduces reliability [1]. However, aperture coupled feeding is a much cleaner feeding mechanism without fabrication difficulties, and shows additional advantages over coaxial probe feeding [1]. Finally, whereas the designs carried out in [6] and [11] are for a single antenna, one design for a single antenna and two array designs are proposed in this paper. And the bandwidths of our two designed arrays are larger than the bandwidths included in Table 2for previously reported arrays VOLUME 12, 2024 173073 I. M. Delgado-Lozano et al.: Design of Broadband Aperture-Coupled Microstrip Antenna Arrays TABLE 2. Comparison among microstrip antennas with differential feeding. of microstrip antennas with differential feeding. The larger bandwidth obtained in Table 2for the two arrays not only relies on the wide bandwidth of the individual antennas taking part in the arrays, but also relies on the wide bandwidth of the feeding networks involving power dividers and 180◦hybrids. IV. CONCLUSION An aperture coupled broadband microstrip antenna with differential feeding is presented. The aperture is fed by means of a symmetrically located short-circuited differential microstrip line, which guarantees the radiation of the DM and the rejection of the CM. The antenna design for DM radiation is based on a lumped equivalent circuit containing a second order filter. This equivalent circuit oriented design makes it possible to ensure the DM impedance matching of the antenna in bandwidths larger than 30%. Two 2 × 2 arrays of this differential antenna have been fabricated and measured. Fractional bandwidths between 25% and 30% have been obtained for the two arrays, gains around 12 dBi, side lobe levels below −15 dB and cross-pol levels below −25 dB. To the authors’ knowledge, the fractional bandwidths of the two arrays are larger than the bandwidths of previously reported arrays of microstrip antennas with differential feeding. REFERENCES [1] D. M. 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