In this work a low-cost reflectarray with isoflux pattern for global Earth coverage is designed, manufactured and measured at 30GHz. The isoflux template is mathematically derived for a generic satellite and then particularized for a geostationary orbit. In order to reduce costs, the synthesis and design processes have to be accordingly adapted. First, the most simple unit cell is selected, consisting of a single layer of rectangular patches backed by a ground plane. This cell is not able to provide a 360° phase range and thus the synthesis algorithm has to be modified to include a phase constraint to match the range provided by the element, ensuring at the same time a smooth variation of the elements in order to obtain a reliable design. This is further ensured by limiting the patch size to a given range during the design process. Finally, the reflectarray is manufactured and measured, showing good agreement with the simulations

Arrebola Baena, Manuel

Campa Gafo, Adrián

Encinar Garcinuño, José Antonio

Las Heras Andrés, Fernando Luis

Rodríguez Pino, Marcos

Rodríguez Prado, Daniel

In this work a low-cost reflectarray with isoflux pattern for global Earth coverage is designed, manufactured and measured at 30GHz. The isoflux template is mathematically derived for a generic satellite and then particularized for a geostationary orbit. In order to reduce costs, the synthesis and design processes have to be accordingly adapted. First, the most simple unit cell is selected, consisting of a single layer of rectangular patches backed by a ground plane. This cell is not able to provide a 360° phase range and thus the synthesis algorithm has to be modified to include a phase constraint to match the range provided by the element, ensuring at the same time a smooth variation of the elements in order to obtain a reliable design. This is further ensured by limiting the patch size to a given range during the design process. Finally, the reflectarray is manufactured and measured, showing good agreement with the simulations.This work was supported in part by the European Space Agency (ESA) under contract ESTEC/AO/1-7064/12/NL/MH; by the Ministerio de Economía y Competitividad, under project TEC2014-54005-P (MIRIIEM); by the Gobierno del Principado de Asturias / FEDER under project GRUPIN14-114 and under grant BP12-063

Repositorio Institucional de la Universidad de Oviedo

1Design, Manufacture and Measurement of aLow-Cost Reflectarray for Global Earth CoverageDaniel R. Prado, Adria´n Campa, Manuel Arrebola, Marcos R. Pino, Jose´ A. Encinar, and Fernando Las-HerasAbstractIn this work a low-cost reflectarray with isoflux pattern for global Earth coverage is designed, manufactured and measuredat 30GHz. The isoflux template is mathematically derived for a generic satellite and then particularized for a geostationary orbit.In order to reduce costs, the synthesis and design processes have to be accordingly adapted. First, the most simple unit cell isselected, consisting of a single layer of rectangular patches backed by a ground plane. This cell is not able to provide a 360°phase range and thus the synthesis algorithm has to be modified to include a phase constraint to match the range provided by theelement, ensuring at the same time a smooth variation of the elements in order to obtain a reliable design. This is further ensuredby limiting the patch size to a given range during the design process. Finally, the reflectarray is manufactured and measured,showing good agreement with the simulations.Index TermsReflectarray antenna, isoflux pattern, global coverageI. INTRODUCTIONREFLECTARRAY antennas combine the high gain and efficiency of parabolic reflectors with the low profile and flat natureof the arrays, at the expense of having an inherent lower bandwidth than the parabolic reflectors [1], although it may beovercome by using broadband topologies [2] or elements [3]. These features make the reflectarray a potential candidate forfuture space missions, since the costs involved in developing these antennas are lower than for shaped parabolic reflectors.In this work, a reflectarray with an isoflux pattern for global Earth coverage is designed, manufactured and measured. Thetemplate for the isoflux pattern is mathematically developed for a generic satellite covering the whole Earth, and then isparticularized for a geostationary orbit at 30GHz. In order to reduce costs, a simple reflectarray comprised of only one layerof rectangular patches is designed. Rectangular patches are the simplest reflectarray unit cell, but they present the limitation ofnot being able to provide a full phase range of 360° [1]. To overcome this limitation, the Intersection Approach (IA) algorithm[4] is used with phase constraints, limiting the allowable phase range during the synthesis process to that provided by the unitcell, while aiming at a smooth distribution of the patches after the design is made, which is further ensured by limiting thepatch size range avoiding extreme values. These modifications in the synthesis and design processes allow to obtain a reliableshaped reflectarray design employing the simplest unit cell. Finally, simulations and measurements are compared showing goodresults.II. ISOFLUX PATTERNIn Figure 1 a sketch of the Earth-satellite geometry is shown. There, Re is the radius of the Earth, dmin and dmax areminimum and maximum distances from the satellite to the Earth surface, and θmax the maximum coverage angle.The goal of the isoflux pattern is to provide coverage with constant energy flux on the surface of the Earth. The attenuationcurve is given by the Friis formula [5]A = 20 log (f) + 20 log (d) + 32.5, (1)where A is the attenuation given in dB, f is the frequency in MHz and d is the distance from the satellite to the surface ofthe Earth in Km. If (xs, ys) are the satellite coordinates and (xe, ye) are the coordinates of a point in the Earth surface, d iscalculated asd =√(xs − xe)2 + (ys − ye)2. (2)The distance from the satellite to the surface of the Earth is given by its orbit, so dmin is known. Then, dmax is calculatedusing the Pythagorean theorem and θmax is obtained ascos θmax =dmaxdmin +Re. (3)This work was supported in part by the European Space Agency (ESA) under contract ESTEC/AO/1-7064/12/NL/MH; by the Ministerio de Economı´a yCompetitividad, under project TEC2014-54005-P (MIRIIEM); by the Gobierno del Principado de Asturias / FEDER under project GRUPIN14-114 and undergrant BP12-063.D. R. Prado, A. Campa, M. Arrebola, M. R. Pino and F. Las-Heras are with the Department of Electrical Engineering, Group of Signal Theory andCommunications, Universidad de Oviedo (e-mail: drprado; arrebola; mpino; flasheras@tsc.uniovi.es).Prof. J. A. Encinar is with Universidad Polite´cnica de Madrid (e-mail jose.encinar@upm.es).2θmaxSatelliteEarthReRedmindmaxθ d xˆyˆFigure 1: Sketch of the Earth-satellite geometry.FocusReflectarrayEquivalent parabolic reflectoryˆxˆzˆyˆrxˆrzˆrzˆaβFigure 2: Reflectarray single-offset configuration.Considering the origin of coordinates the center of the Earth, the points of its surface will follow the equationx2 + y2 = R2e. (4)Then, the linear equation from the satellite to a point in the surface of the Earth can be expressed asy = mx+ n, (5)with m = − tan θ and n = −m (dmin +Re). Substituting (5) in (4), the following quadratic equation is obtained(1 +m2)x2 + 2mnx− (R2e − n2) = 0. (6)By solving (6) two solutions are obtained, which correspond to the intersection of the straight line d with the Earth circum-ference. The one with x < 0, according to Figure 1, is selected; and then y is obtained with (4). This solution corresponds tothe point (xe, ye) in (2), which along with the known satellite position (xs, ys) enable the calculation of the attenuation givenby (1).The attenuation curve is computed in a single plane, but since it is symmetric in ϕ, it is straightforward to obtain theattenuation in the whole Earth surface in spherical coordinates. It is common to perform reflectarray synthesis in the UVplane [1], knowing that u = sin θ cosϕ and v = sin θ sinϕ.The obtained attenuation pattern can be used directly as radiation pattern template if a symmetric antenna geometry is used.Apart from the attenuation curve, side lobe levels, ripple and a transition zone should also be specified. However, it is morecommon to use single-offset configurations [1], such as the one shown in Figure 2. The reflectarray radiates at an angle θ = βwith regard to its own coordinate system, defined by (xˆr, yˆr, zˆr). Hence, the centered templates have to be rotated by applyinga proper transformation.The template for the centered configuration in (θ, ϕ) coordinates is referenced to the reflectarray coordinate system (xˆr, yˆr, zˆr)of Figure 2. Each point of the template is transformed from spherical coordinates to cartesian coordinatesxRA = sin θRA cosϕRA, (7a)yRA = sin θRA sinϕRA, (7b)zRA = cos θRA, (7c)and then the following transformation is applied xANTyANTzANT = cosβ 0 sinβ0 1 0− sinβ 0 cosβ xRAyRAzRA . (8)Then, the cartesian coordinates will be transformed to spherical coordinates and from there to UV coordinates, with the usualoperations.30.5 1 1.5 2 2.5 3 3.5 4−300−200−1000100Patch length (mm)Phase(°)θ = 0°, ϕ = 0°θ = 20°, ϕ = 15°θ = 30°, ϕ = 40°(a)0.5 1 1.5 2 2.5 3 3.5 4−300−200−1000100Patch length (mm)Phase(°)29 GHz30 GHz31 GHz(b)Figure 3: Phase range of the unit cell as a function of patch length for a periodicity of 0.4λ at 30GHz. (a) For differentincidence angles at 30GHz. (b) For different frequencies at (θ, ϕ) = (20°, 15°).III. ISOFLUX PATTERN SYNTHESISA. Antenna specificationsThe reflectarray is made up of 1528 elements disposed in a regular circular grid of 44× 44 cells. The working frequency is30GHz and the periodicity is 4mm× 4mm (0.4λ). The reflectarray is fed by a horn antenna whose phase center is placed at(−40, 0, 195)mm with regard to the reflectarray coordinate system (see Figure 2). The feed is modeled as a cosq θ functionfollowing [6] with a q-factor of 14.8, which produces an illumination taper of −12 dB. The requirements for the isoflux patternare specified by a reflectarray with β = 20°, side lobe level of −19 dB and 0.25 dB of allowable ripple, placed on a satellitein geostationary orbit.B. Unit cell studyThe reflectarray chosen element is the rectangular microstrip patch backed by a ground plane [7]. Since only a single layeris used, the provided phase range of the cell will be lower than 360° [1]. Hence, it is important to study the element in orderto delimit the phase range as a function of the patch size.The Arlon 25N substrate is selected, with a relative permittivity εr = 3.38, thickness h = 18mil and loss tangent tan δ =0.0025 at 10GHz. Figure 3 shows the phase variation of the unit cell as a function of the patch length for different angles ofincidence and frequencies. In this study, the patches are squares. The results show that, in this particular case, the incidenceangle barely affects the phase shift introduced by the element. When the frequency is shifted, the phase variation is non-linear,since for dimensions lower than 2mm and higher than 3mm it barely changes, but between 2 and 3mm the phase is shiftedwith frequency.In order to maximize the available phase range avoiding extreme values of the patch lengths (which would compromisethe local periodicity assumption when carrying out the design [1]), the patch length is restricted to vary in the range 1.7 to3.2mm, which provides a phase range of about 300°.C. Pattern synthesis and designThe reflectarray synthesis is carried out with the IA algorithm in several stages as is described in [4], starting with a highvalue of q in order to artificially reduce the number of variables. Each step of the synthesis reduces the q-factor until itsvalue reaches that of the horn feed. The starting point is a pencil beam pattern pointing at (θ, ϕ) = (20°, 0°). Also, sincethe generation of the isoflux template is parameterized, in the first steps of the synthesis the allowed ripple will be higher inorder to facilitate convergence, and as the algorithm is approaching the solution, the ripple will be gradually reduced until theprescribed template value is achieved.Since the selected unit cell only provides a phase range of 300°, the IA needs to be modified in order to impose a phaserange restriction. In the general framework of the IA applied to array synthesis, the reflectarray is a particular case in whichthe amplitude is fixed by the incident field of the feed, and now the phase is also constrained in order to match the availablephase range from the unit cell, allowing to vary only from 0° to −300° to match the provided phase shift by the unit cell,shown in Figure 3.Once the synthesis is finished and the required phase distribution is obtained, the patch lengths are adjusted element byelement using the Method of Moments (MoM) [8] and a zero-finding routine. In this process, the real angle of incidence fromthe feed to each element of the reflectarray is used, in order to take into account possible phase shifts due to the incidenceangle. Also, the MoM employs the Floquet theorem to analyze the unit cell, which embeds the analyzed element within aninfinite array comprised of the same element, taking into account mutual coupling and the reflected field from the ground.It is thus important that the patch size variation is smooth in order to fulfill the local periodicity assumption of the analysistechnique. Also, the design produces slightly rectangular patches, since the reflection coefficients are to some extent differentfor both polarizations.4−80 −60 −40 −20 0 20 40 60 80−80−60−40−20020406080Coordinates of the element in xˆr (mm)Coordinatesoftheelementinyˆ r(mm)−350−300−250−200−150−100−500Figure 4: Synthesized phases for an isoflux pattern in X polarization with a phase restriction of 300°. Phases for Y polarizationare very similar.−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−30−25−20−15−10−50uNormalizedpattern(dB)No phase const.Ideal phase shiftersPatches0.1 0.2 0.3 0.4 0.50−0.25−0.5−0.75−1Figure 5: Main cut for v = 0 of the synthesized isoflux pattern for three different simulations for X polarization: referencesimulation (no phase constraints, red solid), simulation with ideal phase shifters (phase constraints, dashed black) and designsimulation (phase constraints, dotted green).IV. RESULTSThe synthesis was carried out for both polarizations, obtaining a dual-linear polarized reflectarray with an isoflux patternin both polarizations. The results for both polarizations are similar, and only those for the X polarization are shown. Figure 4shows the synthesized phases with a total phase range of 300° imposed during the synthesis process. As reference, a synthesiswith no phase constraints was also performed.Figure 5 shows the results between the synthesis with and without phase constraints. When the phase is free to vary in thewhole 360° range, a smooth coverage area can be obtained. However, restricting the phase range to 300° causes the algorithmnot to converge properly, an there is a ripple in the coverage zone. It is also shown the simulation after the design was made,simulating the patches with MoM [8], and there is little variation in the copolar component with regard to the simulation withideal phase shifters.After the phase-only synthesis, the reflectarray was manufactured and measured. Figure 6 shows a picture of the prototypewith the supporting structure, which secures the position of the feed and the reflectarray breadboard. The antenna was measuredin a spherical far-field range anechoic chamber at 30GHz and the measurements are shown in Figures 7 and 8. The deteriorationin the coverage area is attributed to several causes. First, in the synthesis process the corners of the reflectarray were not takeninto account. Also, the coverage area is very sensitive to variations in the height and relative permittivity of the substrate.New simulations were performed for a square reflectarray and different values of the parameters of the substrate. A betteragreement between simulations and measurements was obtained than with the circular reflectarray (see Figure 8). Side lobesare also affected by reflections in the supporting structure and diffraction in the edge of the breadboard, which were not takeninto account.These issues can be minimized by choosing a more appropriate antenna geometry, which reduces the interference of thesupporting structure, and by employing a rectangular reflectarray instead of a circular one, having more variables to adjust the5Figure 6: Picture of the prototype in the anechoic chamber.−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−1−0.8−0.6−0.4−0.200.20.40.60.81uv−20−18−16−14−12−10−8−6−4−20Figure 7: 3D measured pattern for X polarization.pattern and taking into account the corners of the breadboard. Also, decreasing the illumination at the edge would reduced thediffraction effects.V. CONCLUSIONA low-cost reflectarray for global Earth coverage with isoflux pattern has been designed, manufactured and measured. Adetailed development is presented to obtain an isoflux template for array synthesis for a generic satellite, which is later used ina reflectarray phase-only synthesis. The chosen element for the reflectarray is a single patch backed by a ground plane, whichis the simplest element available. However, it is not able to provide a full 360° phase range. For that reason, the IntersectionApproach algorithm is used enforcing a phase restriction to match the range provided by the unit cell. After the synthesisprocess is finished, the required phase shift in each element of the reflectarray is obtained. The phase restriction causes thecoverage area to have a higher ripple than if there was no phase restriction. A prototype was manufactured and measured. Thedegradation in the coverage area is caused by the corners of the reflectarray, not taken into account in the synthesis process,and variations in the height and permittivity of the substrate. Side lobes are affected by the suporting structure reflections anddiffractions at the edge of the breadbord. These issues can be minimized by a proper choice of the whole antenna geometryand by considering a rectangular reflectarray instead of a circular one.REFERENCES[1] J. Huang and J. A. Encinar, Reflectarray Antennas. John Wiley & Sons, 2008.6−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8−30−25−20−15−10−50uNormalizedpattern(dB)Sim. 30 GHz. circ., Er=3.38, h=18milSim. 30 GHz. circ., Er=3.38, h=16milSim. 30 GHz. circ., Er=3.28, h=18milSim. 30 GHz. sq., Er=3.38, h=18milSim. 30 GHz. sq., Er=3.38, h=16milSim. 30 GHz. sq., Er=3.28, h=18milMeasured CP 30 GHz.Measured XP 30 GHz.0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50−1−2−3−4Figure 8: Measurement and simulations for v = 0 for X polarization.[2] J. A. Encinar and J. A. Zornoza, “Broadband design of three-layer printed reflectarrays,” IEEE Trans. Antennas Propag., vol. 51, no. 7, pp. 1662–1664,Jul. 2003.[3] L. Moustafa, R. Gillard, F. Peris, R. Loison, H. Legay, and E. Girard, “The phoenix cell: A new reflectarray cell with large bandwidth and rebirthcapabilities,” IEEE Antennas Wireless Propag. Lett., vol. 10, pp. 71–74, 2011.[4] J. A. Zornoza and J. A. Encinar, “Efficient phase-only synthesis of contoured-beam patterns for very large reflectarrays,” Int. J. RF Microw. Comput.Eng., vol. 14, no. 5, pp. 415–423, Sep. 2004.[5] C. A. Balanis, Ed., Modern antenna handbook. John Wiley & Sons, 2008.[6] Y.-T. Lo and S.-W. Lee, Eds., Antenna Handbook Vol. 1. Van Nostrand Reinhold, 1993, ch. 1, pp. 28–29.[7] S. D. Targonski and D. M. Pozar, “Analysis and design of a microstrip reflectarray using patches of variable size,” in Antennas and Propagation SocietyInternational Symposium, vol. 3, Seattle, Washington, USA, Jun. 20–24, 1994, pp. 1820–1823.[8] C. Wan and J. A. Encinar, “Efficient computation of generalized scattering matrix for analyzing multilayered periodic structures,” IEEE Trans. AntennasPropag., vol. 43, no. 11, pp. 1233–1242, Nov. 1995.

IEEE Antennas and Wireless Propagation Letters

Design, manufacture and measurement of a low-cost reflectarray for global earth coverage

Daniel Rodriguez Prado

Adrian Campa

Manuel Arrebola

Marcos R. Pino

Jose A. Encinar

Fernando Las-Heras

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Design, Manufacture, and Measurement of a Low-Cost Reflectarray for Global Earth Coverage

Design, manufacture and measurement of a low-cost reflectarray for global earth coverage

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