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Generalised design method of broadband array antennas using curved geometry

2016; Institution of Engineering and Technology; Volume: 10; Issue: 14 Linguagem: Inglês

10.1049/iet-map.2016.0002

1751-8733

M. Cecilia Gonzalez Corcia, Balasubramaniam Preetham Kumar, G.R. Branner,

Advanced Antenna and Metasurface Technologies

IET Microwaves, Antennas & PropagationVolume 10, Issue 14 p. 1553-1562 Regular PaperFree Access Generalised design method of broadband array antennas using curved geometry Maria C. Gonzalez, Maria C. Gonzalez Electrical and Computer Engineering, University of California, Davis, USASearch for more papers by this authorBalasubramaniam Preetham Kumar, Corresponding Author Balasubramaniam Preetham Kumar kumarp@ecs.csus.edu Electrical and Electronic Engineering, California State University, Sacramento, USASearch for more papers by this authorGeorge R. Branner, George R. Branner Electrical and Computer Engineering, University of California, Davis, USASearch for more papers by this author Maria C. Gonzalez, Maria C. Gonzalez Electrical and Computer Engineering, University of California, Davis, USASearch for more papers by this authorBalasubramaniam Preetham Kumar, Corresponding Author Balasubramaniam Preetham Kumar kumarp@ecs.csus.edu Electrical and Electronic Engineering, California State University, Sacramento, USASearch for more papers by this authorGeorge R. Branner, George R. Branner Electrical and Computer Engineering, University of California, Davis, USASearch for more papers by this author First published: 01 November 2016 https://doi.org/10.1049/iet-map.2016.0002Citations: 7AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Curved array antennas offer increased degrees of freedom when antenna elements are configured in non-uniform geometries. This permits increased flexibility over control of pattern structure and increase in the bandwidth of operation. In this study, the authors present a generalised design method for broadband antenna arrays using such curved structures. Following this design process, two types of array structures evolved: pseudo-curved array (PCA), with the array apertures parallel to one another and the fully curved array (FCA), with the outer element apertures oriented radially outwards. These antenna arrays were designed, analysed and measured on five and seven element structures at a centre frequency of 18 GHz. Both PCA and FCA performance showed a broader frequency response as compared with the uniform array; additionally, it was determined that the variation in array geometry permits them to control the number of beams and nulls in the far-field pattern, as well as the beamwidth of the array. Overall, it was observed that curved arrays showed a narrowing of multibeam positions and conversely a broader frequency response as compared with uniform arrays. 1 Introduction The field of non-planar antennas is of interest in many applications for different reasons. Since World War II, large radius circular ring arrays have been used for radio signal direction finding in communications and radar due to their omnidirectional coverage [1]. As new instruments for navigation developed, so has the addition of protruding antennas in mobile vehicles. Modern aircraft may carry up to 30 types of antenna devices [2], which are an even larger number for military aircraft, for navigation, position information and communication with land bases. These antennas can cause excessive drag and radar reflectivity if they are not integrated in the fuselage. The necessity of preserving the operational requirement while adapting the antenna to the fuselage shape for aerodynamic reasons continues to spur research in conformal antenna theory and in feeding techniques [3, 4]. Antennas with curved or non-planar geometry are also used in satellite communications to reduce launch payload. The radiation properties of non-planar antennas and their analysis are an open field of research for many shapes and array structures and, as such, they differ greatly from planar structures. In general, the beam control for non-planar antennas requires both adequate amplitude and phase values in the antenna element excitation. On the other hand, the frequency bandwidth and coverage is larger than in planar technology. The potential of reaching high directivity, narrower main lobe and low sidelobe is advantageous in other applications not necessarily constrained by mechanical factors. For instance, in [5, 6] a cylindrical antenna array is proposed for ultra-wideband (UWB) communication to simultaneously improve coverage, system capacity and quality of reception. Curved antenna arrays can be also beneficial for the treatment of tumours in the human body [7, 8]. In this case, the medical treatment of burning malignant cells requires confinement of the heat to a specific contour. However, a more important application of arrays with non-uniform geometry is the design of broadband antennas, which are increasingly essential for UWB and other wireless applications [9-11]. In this paper, we present a generalised mathematical algorithm for design of broadband antenna arrays whose elements occupy fixed positions in the transverse plane (x–y-plane), while having the freedom to be placed arbitrarily along the longitudinal axis (z-axis). The algorithm designs the z-axis positions of the array elements to yield broadband gain performance over a prescribed frequency range (16–26 GHz in the current case). This paper is divided into the following sections: Section 2 presents the proposed generalised mathematical theory of the broadband array design. Section 3 gives the implementation of the broadband array design to obtain the curved waveguide array structure. This includes the characteristics of the antenna structure for pseudo-curved array (PCA) and fully curved geometry (FCA), feed geometry and characterisation of design equations for element positions of the array. Finally, Section 4 presents the simulation and measurement results for the five and seven waveguide PCA and FCA geometries. In addition to broadband characteristics, the latter design also exhibits narrowing of multibeam positions in the far-field. 2 Generalised technique of broadband antenna design using curved arrays This section develops the generalised design theory, starting with a default planar array and leading to the derivation of the optimum array geometry for broadband performance. This analysis is limited to curved arrays in one dimension only, though it could be extended to multi-dimensional geometry too; additionally, related diffraction considerations among the elements of the array have been ignored. 2.1 Six-step design algorithm for curved array Consider an arbitrarily spaced array structure of N, x-directed electric point-dipole sources, as shown in Fig. 1a for a planar structure and Fig. 1b for a curved structure, with the zi values specifying the axial element positions. The far-zone electric field of the array at an observation point r is given by the equation [12] (1)where is the propagation constant, λ is the wavelength, η is the free space impedance and Ii is the current excitation of the ith element. Fig. 1Open in figure viewerPowerPoint Geometry of arbitrary spaced array of point sources in a Planar b Curved geometry Starting with the default planar array, the following six steps outline the design technique to introduce curvature to the array structure, with the aim of obtaining an ideal broadband far-zone electric field pattern. Step 1: Specification of the broadband pattern: The objective of the design approach is to obtain a uniform electric field in the broadside direction over a given frequency range; hence, from (1), we first obtain the electric field at θ = 0, ϕ = 0 (2) Step 2: Generation of the array equation: Since the broadside pattern is desired to be broadband over a given frequency range, we prescribe it to be a constant Eθ (0, 0, k) = Ge−jkr/r, (constant amplitude and linear phase as a function of frequency), rearrange (2) to isolate the array factor on one side and obtain (3)where G is a constant and F (k) is a function of frequency. Step 3: Generation of the real array equation set: Assuming the array currents to be complex, Ii = |Ii|ejϕi we can obtain a real equation set by equating the real and imaginary parts of (3) (4)Ideally, both equations are required to solve for element currents, Ii and element positions, zi; however, in our case, we have assumed all currents to be real and constant, Ii = 1 (for broadside pattern); and solve one of the equations for the spacings, zi. Sampling the frequency (or the wave number k) at a finite set of M points; k = 0, Δk, 2Δk, …, (M−1)Δk in the desired frequency range, we obtain, from the real part of (4) (5)where βi = ziΔk. The objective is to obtain feasible solutions for the element positions zi by solving (5) and satisfying the broadband condition Eθ (0, 0, k) = Ge−jkr/r, as specified earlier. Step 4: Legendre transformation of the desired factor Fr(k): The following steps define the procedure for transforming the array function Fr(km) into its Legendre transform . To proceed, we form the expression (6)where and Pm−1/2 is the Legendre function of half integer order. The range and values of αp are explained shortly in (11) and the succeeding statement. Substituting Fr(km) from (5) into (6) yields the final transformed equation (7) Step 5: Generation of the recursive equations: The Legendre transformation of the desired array pattern Fr(km) is motivated by the following limiting relation for the Legendre polynomial of fractional order [13]: (8) Incorporating the property expressed in (8) into (7) permits the transformed array function to be expressed as (9)where (10)The selection of the α grid is the important constituent in the reconstruction of the array currents and positions in recursive form. This grid is defined by the following relation (11)where the constant, c0 > 0 represents the maximum axial shift allowed for the curved array elements; it is limited by the condition that α and β values intersperse one another as shown below The value c0 also sets a restriction to the largest protruding distance from a planar baseline surface. Now, utilising (10) and (11), we obtain the following triangular system of equations (12)This system is invertible as follows (13) Step 6: Synthesis of array element positions only with a pre-specified array current distribution: Given a desired uniform pattern, Eθ(0, 0, k) = Ge−jkr/r, within a given frequency (or wave number) interval, and a specified array current distribution for an N-element array, we may now obtain the appropriate non-uniform set of element offset distances, zp, p = 1, …, N. The element position design formula for the array is now determined from (13) as follows (14)and, from (10) and (14), we obtain (15)and zp = βp/Δk. To exclude infeasible solutions, the following constraints are imposed on these values of βp and zp: if the value of the argument within the large bracket in (15) is >1 or if βp ≥ αp, then zp = zp−1 + c0. The value of βp is again calculated using the default spacing value zp, and the algorithm is continued to yield all the element positions. 2.2 Preliminary simulation results to test algorithm for curved array design To test the validity of the algorithm described in the previous section, we have performed simulation studies on a point-dipole array, with N = 7, 11 and 15 elements. The default array geometry is as shown in Fig. 1a, with the x-axis separation of 5.2 cm, and a maximum allowed axial shift, as described in (11), of c0 = 5 mm. The reconstruction algorithm, as detailed in (2)–(15) was applied to yield the curved array element positions, and Table 1 shows the value of synthesised protrusion distances zi, for N = 7, 11 and 15 elements. Table 1. Synthesised array element positions for point source array (millimetres) Elements 7 11 15 z1 8.1 16.3 25.2 z2 5.0 12.0 20.7 z3 2.5 8.1 16.3 z4 0.0 5.0 12.0 z5 2.5 2.5 8.1 z6 5.0 0.0 5.0 z7 8.1 2.5 2.5 z8 5.0 0.0 z9 8.1 2.5 z10 12.0 5.0 z11 16.3 8.1 z12 12.0 z13 16.3 z14 20.7 z15 25.2 The simulation results comparing the broadside electric field (θ = 0, ϕ = 0) of the uniform array and curved array against frequency are shown in Fig. 2; the decibel values represent the electric field calculated using (1) at θ = 0, ϕ − 0, assuming array currents Ii = 1. It is showing the trend that the synthesised curved array yields a more uniform electric field across the frequency range, as compared with the monotonically increasing electric field of the uniform array. These results formed the basis of the practical design, using open-ended waveguide arrays, which will be explained in the next section. Fig. 2Open in figure viewerPowerPoint Electric field against frequency for point-dipole array 3 Fabrication of broadband curved arrays To experimentally test the broadband design algorithm outlined in Section 2, array antennas were designed, fabricated and experimentally tested in the laboratory. These arrays consist of a set of three, five and seven K-band rectangular open-ended waveguides operating at 18 GHz and mounted in a wooden structure. This wooden structure secured the waveguide apertures in place in a prescribed configuration. Two designs were fabricated, the PCA structure shown in Figs. 3a and b and the fully curved array (FCA) structure as shown in Figs. 3c and d. In the PCA of Fig. 3a, the elements have flexibility to move linearly along their axis to create the desired curvature. In this configuration, however, the waveguide apertures are constrained to be parallel to each another. For the PCA, a change in the element protruding distances from the fixture is equivalent to a change in the radius of curvature R as shown in Fig. 3b. The lateral distance between waveguides apertures, di, in Fig. 3b is 3.9 cm or 2.3λ at 18 GHz, which reduces the mutual coupling between elements in the structure. This and all structures are completely encapsulated in absorber material during pattern and gain measurements. Fig. 3Open in figure viewerPowerPoint Fabrication of broadband curved arrays a PCA structure b PCA geometry c FCA structure d FCA geometry For the FCA as pictured in Fig. 3c, the elements also have the flexibility to be moved along their axes; in this case the geometry formed by the array is purely curved. In the curved array geometry, the increase in radius may contribute to the mutual coupling (owing to elements apertures coming closer), though this has not been confirmed in this paper. As in the case of the PCA, the lateral distance between waveguides apertures, di, is 3.9 cm at the inner surface of the curved structure. The axial shift of each array element in the PCA and FCA is determined by the design algorithm that was described earlier, and as applied to the waveguide array, which will be detailed in the next section This design corresponds to a curved array structure with a radius of curvature of 32.7 cm. 3.1 Selection of antenna array elements The selection of waveguides with similar properties in the range of operation was based on the measurement of their S11 parameters and their far-field patterns in the anechoic chamber. The measured far-field patterns of three waveguides elements are shown in Figs. 4a and b for H and E planes, respectively. The aperture's surrounding area was covered with absorber material to prevent reflections from the metal wall or wooden features. Fig. 4Open in figure viewerPowerPoint Selection of antenna array elements a H-plane b E-plane far-field pattern for three individual waveguides c Feed structure for array elements 3.2 Design of antenna feed network using S-parameters Fig. 4c illustrates the array feed network for the eight-port network using three port T-junctions, to allow for 3, 5 and 7 element arrays. In each array measurement, the unused ports were terminated in a matched load. From the measurements of the S-parameters of the network and waveguide reflection coefficient, we are able to determine the excitation at each output port, a2−a8, as detailed in the steps below, where bi represents the reflected voltage. The overall S matrix of an N-port network shown is given by the following matrix equation (16)where the input and reflected voltages, ai and bi, respectively, are related through the scattering matrix S of an N-port network. Using the waveguide input reflection coefficient, Γ, we can substitute transform vector [A] as follows Rearranging terms in the matrix (16), the final feed matrix formulation is as follows (17) 3.3 Mathematical modelling of broadband curved arrays We now present the extension of the basic design algorithm, as defined in Section 2, to the PCA and FCA designs, as shown in Figs. 3a and c, respectively. 3.3.1 Pseudo-curved array The mathematical model for the individual waveguide element, as shown in Fig. 5 below, was based on standard aperture analysis [12, 14]. Fig. 5Open in figure viewerPowerPoint Rectangular waveguide geometry Assuming that each waveguide aperture is polarised along the y-direction, the total far-field of the array can be written as where the field components are given by (18)where (xi, yi, zi) represents the location of the centre aperture of the ith array element with excitation Ii, and the field components represent the radiation pattern of the ith antenna element. Assuming all waveguide elements to be identical, the E-plane and H-plane far-fields for a single TE10 waveguide are given below [12] (19)where a and b are the aperture dimensions of the rectangular waveguide element and E0 is the peak aperture electric field. The broadside field (at θ = 0, ϕ = 0), from (18), is (20)Then, following the broadband design process outlined in Section 2, steps 1–6 of the algorithm are applied to determine the specified array element positions, zi, i = 1, 2, …, N (Fig. 3b), in order to generate a broadband pattern, Eτϕ (0, 0, k) = Ge−jkr/r. 3.3.2 Fully curved array (FCA) structure The curved array structure, as shown in Fig. 3d, is based on aperture plane rotation (for all elements except the central element) by an angle γi which gives rise to the plane normal vector given by and the electric field components of the individual rotated aperture i can be written as follows, in terms of the unrotated aperture field component Exi (θ, ϕ): θ component: Eθι = Exi(θ−γi, ϕ) sin ϕ. ϕ component: Eϕι = Exi(θ−γi, ϕ) cos θ cos ϕ. Hence, the total field components of the curved array can be written as (21)Correspondingly, the equations for the far-field E-plane and H-plane of a single rotated TE10 waveguide also get modified to reflect the different orientation angles γi (22)where The broadside field (at θ = 0, ϕ = 0) now becomes (23) Then steps 1–6 of the algorithm, outlined in Section 2, are now followed to determine the specified array element positions, zi, i = 1, 2, …, N (Fig. 3d). 3.4 Application of synthesis algorithm to waveguide array design From the analysis in the earlier section, (20) and (23) can be used to obtain the far-field pattern of the PCA and FCA, respectively, at any given frequency of operation. However, based on the algorithm which was detailed in Section 2, control over the frequency response of the array can be obtained by optimising the z-coordinates of the element positions. To specify a broadband pattern, first we obtain the electric field at θ = 0, ϕ = 0. In general, we can write (24)The six-step reconstruction algorithm, detailed in Section 2, was then applied to the design of the PCA and FCA, with N = 3, 5, 7 elements. The array geometry is as shown in Figs. 3 and 4 with element x-axis spacing between adjacent elements of 3.9 cm, and the synthesised element z positions as shown below in Tables 2 and 3, respectively, for the PCA and FCA. Note that while all the elements of the PCA are parallel, the elements of the FCA have different rotation angles γi, as given in Table 3, in the parenthesis following each zi position. The elements positions, zi, were identical for both curved array configurations. Table 2. Synthesised element positions (millimetres) for pseudo-curved waveguide array Elements 3 5 7 z1 3.7 7.4 11.0 z2 0.0 3.7 7.4 z3 3.7 0.0 3.7 z4 3.7 0.0 z5 7.4 3.7 z6 7.4 z7 11.0 Table 3. Synthesised element positions (millimetres) and rotation angles (within parenthesis in degrees) for fully curved waveguide array Elements 3 5 7 z1 3.7 (−9.0) 7.4 (−17.7) 11.0 (−25.5) z2 0.0 (0.0) 3.7 (−9.0) 7.4 (−17.7) z3 3.7 (9.0) 0.0 (0.0) 3.7 (−9.0) z4 3.7 (9.0) 0.0 (0.0) z5 7.4 (17.7) 3.7 (9.0) z6 7.4 (17.7) z7 11.0 (25.5) On the basis of the synthesised element positions above in Tables 2 and 3 the far-field of the planar, pseudo-curved and fully curved waveguide arrays are compared below in Fig. 6 for N = 7 elements. The planar array refers to the default array with all element positions zi set to zero. As is seen in this figure, both FCA and PCA show a flattening of the broadside electric field magnitude (θ = 0, ϕ = 0) against frequency, as compared with the monotonically increasing pattern of the planar array. The electric field magnitude of the curved array, however, is larger over the entire design band of 0–26 GHz, as compared with the PCA. In practical implementation of the array, the cut-off property of the waveguide elements will limit the pattern over the wide-frequency range, as will be seen in the next section on experimental work. Fig. 6Open in figure viewerPowerPoint Electric field of different array configurations against frequency for 7-waveguide array 4 Experimental results of fabricated waveguide curved arrays This section outlines the experimental characterisation of PCA and FCA, which were designed in the previous section, with element positions given in Tables 2 and 3, respectively. The following measurement studies were performed on both array configurations. The broadband performance of the array was measured for both pseudo-curved and FCAs in a frequency range of 16–24 GHz, with a transmitter/receiver separation distance of z = 342 cm. The multibeam performance of each of these array geometries was also simulated and measured at the centre frequency of 18 GHz. The far-fieid was also measured at a distance of 342 cm. 4.1 Simulation and measurement results of PCA This section gives the measured results for the PCA, as described in Figs. 3a and b. As indicated previously in Section 3, the planar array has the element apertures linearly arranged while the PCA has outer elements of the array displaced as shown in Fig. 3b, and with zi values given in Table 2. 4.1.1 Swept frequency simulation and measurements Figs. 7a and b compare the measured broadband far-field performance of the planar array and 5 and 7 element PCAs as a function of frequency between 16 and 24 GHz. All array measurements were carried out in the anechoic chamber at University of California Davis, using a standard K-band horn as the transmitting antenna, and the array in receiving mode. Hence, as a reference, we have included the horn-to-horn far-field measurement in Fig. 7c. From the latter figures, it is seen that the PCA shows a relatively flatter electric field pattern than the planar array in the frequency range of 16–24 GHz. However, the electric field magnitude is lower, as compared with the planar array. Fig. 7Open in figure viewerPowerPoint Measured broadband far-field for planar and pseudo-curved waveguide arrays a 5 Element array b 7 Element array c Reference horn–horn measurement 4.1.2 Single frequency beamforming simulation and measurements This section presents simulated and measured results of the PCA at the centre frequency of 18 GHz. The results, as shown in Figs. 8a–d, compare the measured and modelled field patterns of the planar array with that of the PCA which were designed employing the optimised array element positions. Figs. 8a and b show the multibeam performance of the planar array, with 5 and 7 elements, respectively. The far-field data presented is limited to the H-plane since it has more variability than the E-plane, which is essentially flat over the majority of the scanning angle range. By way of comparison, Figs. 8c and d show the multibeam performance of the optimised PCA, with element positions as given in Table 1. Interestingly, it is seen that while both planar and PCAs show a multibeam formation, the beams in the PCA are narrower in position or bunched closer together, which might relate to the inverse relation between frequency bandwidth and spatial field pattern width. Fig. 8Open in figure viewerPowerPoint Simulated and measured H-plane far-field patterns at 18 GHz: planar array of a 5 Waveguides b 7 Waveguides PCA of c 5 Waveguides d 7 Waveguides 4.2 Simulation and measurement results of FCA This section gives the measured results for the FCA, as described in Figs. 3c and d. Unlike the PCA, which has parallel waveguide elements, the FCA has outer elements of the array displaced radially as shown in Fig. 3d. 4.2.1 Swept frequency simulation and measurements Figs. 9a and b compare the measured broadband far-field performance of the planar array and 5 and 7 element FCAs as a function of frequency between 16 and 24 GHz, with element positions given in Table 3. This arrangement of element positions corresponds to an array radius of 32.7 cm (Fig. 4b). Figs. 9a and b show that the FCA has a relatively flatter electric field pattern than the planar array in the frequency range of 16–24 GHz. However, as in the case of the PCA, the electric field magnitude is lower, as compared with the planar array. Fig. 9Open in figure viewerPowerPoint Measured broadband far-field pattern for planar and FCA of waveguides a 5 Element array b 7 Element array 4.2.2 Single frequency beamforming simulation and measurements This section presents the simulation and measured results for the fully curved 5 and 7 waveguide arrays at the centre frequency of 18 GHz. The results as shown in Figs. 10a–d demonstrate the multibeam performance of these planar and curved array designs. The simulated and measured patterns of the 7-waveguide array show significant difference, and it is theorised that this variation could be due to increased interaction between adjacent antenna elements that the simulation does not consider at this time. Overall, as in the case of the PCA, it is seen that while both planar and curved arrays show a multibeam formation, the beams in the curved array are narrower in position or bunched closer together, which might confirm the inverse relation between frequency bandwidth and spatial field pattern width. Fig. 10Open in figure viewerPowerPoint Simulated and measured H-plane far-field patterns at 18 GHz: planar array of a 5 Waveguides b 7 Waveguides FCA of c 5 Waveguides d 7 Waveguides 4.3 Discussion of broadband and far-field patterns On review of the broadband patterns in Figs. 7 and 9, respectively, it is seen that both the PCA and FCA demonstrate a much flatter electric field pattern than the planar array in the frequency range of 16–24 GHz. However, the electric field magnitude does reduce for both the curved arrays, as compared with the planar array. Overall, perhaps the FCA has an edge over the PCA in terms of uniform field over the frequency range of interest. On review of the far-field azimuthal patterns in Figs. 8 and 10, respectively, both the PCA and FCA show well-defined grating beams as compared with the planar array. When comparing 5 and 7 element patterns between the two curved arrays, the FCA shows multiple beams more similar in height than the PCA. However, for all planar, pseudo-curved and curved arrays, a clear decrease in beamwidth with increasing number of elements is observed. Most importantly, and as was mentioned earlier, the beam formation in the PCA and FCA shows much closer bunching than the planar array, reflecting the inverse relation between frequency and spatial domains. Since the separation of the antenna elements is larger than half a wavelength, the array produces multiple beams (called in the literature as grating lobes). Both commercial and military have applications where each beam of a multibeam antenna carries the same information: specifically, multibeam antennas carrying the same information are currently used in well-known DirecTV and military antenna systems [15, 16]. Additionally, there is increasing interest in the use of Spot Beams for high-speed broadband satellite services. A possible application of the multiple beam antenna concepts with identical information may in the area of transmitted satellite signal to close-by geographical locations. Typical applications are personal communications, high-speed Internet, military communications and mobile communication services [17, 18]. 5 Conclusions This paper focuses on the advantageous electromagnetic properties that can be created by adding variation to a uniform antenna structure such as a planar array. Starting with a default array of rectangular waveguides having their apertures in line, we present a design procedure to achieve broadband performance by variation of the aperture positions, along the axis of the waveguide. Two types of array structures were tested: PCA, with the array apertures parallel to one another and the FCA, with the outer element apertures inclined to the central element. Both geometries yielded designs that notably enhanced the bandwidth of the default planar array structure. Additionally, addition of the non-uniformity in the array structure also permitted control over the multibeam structure of the array; notably increasing the number of multibeams at a given frequency and a closer proximity of the multiple beams. This feature maybe relevant in applications such as the satellite transmission of identical signals to close-by areas, since it maybe necessary to control the direction of the beams. 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