High-Performance Curved Contoured Beam Reflectarrays with Reusable Surface for Multiple Coverages

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1 High-Performance Cred Contored Beam Reflectarrays with Resable Srface for Mltiple Coerages Min Zho 1, Stig B. Sørensen 1, Rolf Jørgensen 1, Oscar Borries 1, Erik Jørgensen 1, and Gioanni Toso 2 1 TICRA, Copenhagen, Denmark, mz@ticra.com 2 Eropean Space Agency, ESTEC, Noordwijk, The Netherlands, Gioanni.Toso@esa.int Abstract An inestigation of cred contored beam reflectarrays with resable srface for mltiple coerages is presented. The main adantage of cred reflectarrays oer shaped reflectors is that they allow the possibility of resing a standard parabolic mold for mltiple missions. To demonstrate this, two cred reflectarrays are designed sing the direct optimization techniqe to flfill the reqirements of two contored beam missions in both transmit and receie freqency bands for dal linear polarization. The two reflectarrays se the same cred srface, f/d, dimension, and feed, and by changing the reflectarray element pattern, two completely different coerages can be prodced while maintaining a performance that is comparable to that of the shaped reflector. Index Terms reflectarrays, contored beam, optimization, satellite applications, shaped reflectors I. INTRODUCTION For satellite broadcasting applications, shaped reflectors are crrently the preferred technology to generate contored beams oer certain geographical areas. Althogh the shaped reflector is matre and has proen to be a reliable technology, the cost associated to its manfactring is high. Conseqently, means to redce the cost are of great interest and satellite manfactres and space agencies are constantly inestigating possible cheaper soltions. Printed reflectarrays hae in recent years gained sbstantial interest. They proide a way to realize low-cost high-gain antennas and circments many of the recrring costs associated with the shaped reflectors. Contored beam reflectarrays hae been reported in arios works [1] [3] and hae shown promising reslts. Common for the reflectarrays presented in [1] [3] is that they are designed sing a phase-only optimization approach. Since intermediate steps are reqired in the design process, the designs may hae sb-optimal performance. By sing a direct optimization approach where all the array elements are simltaneosly optimized, the performance may be improed. Sch an approach was presented in [4]. Using this direct optimization techniqe, planar [5], mltifaceted [6], and cred reflectarrays [7] in K-band hae been designed to identify the most promising reflectarray concept for satellite broadcasting applications. Based on this work, mlti-faceted and cred reflectarrays are the only concepts that can yield performances that are comparable to that of the shaped reflector. This is mainly de to the enhanced bandwidth that can be achieed sing the two concepts. For medim size apertres (<3 m), the cred reflectarray has seeral adantages compared to its mlti-faceted conterpart. First the spatial phase delay is frther redced reslting in better bandwidth. Second, a dobly cred srface is inherently stiffer and can therefore be made more lightweight. Finally, a cred reflectarray aoids the disjoints between the panels of a mlti-faceted reflectarray, ths aoiding the RF diffractions de to gaps and hinges. In this paper, we consider cred reflectarrays operating in K-band. The main adantage of the cred reflectarray compared to the shaped reflector is primarily its redced manfactring cost and deliery time de to the possibility of resing an existing mold for mltiple coerages. To flly benefit from this adantage, it is important that the same cred srface can be sed for seeral missions and maintain a good performance for all these missions. In this paper, we examine the performance of cred contored beam reflectarrays with resable srface for mltiple coerages. II. COVERAGE SPECIFICATIONS We consider in this work two missions with ery different coerages and specifications to inestigate if the same cred srface can be sed for both missions and at the same time proide a performance that is comparable to that of the shaped reflector. The missions are selected for two reasons. First, the pattern specifications are togh with complicated coerages inclding cross-polar and sidelobe specifications. Second, some of the state-of-the-art contored beam reflectarrays are designed to flfill these reqirements [2], [3]. A. Mission I For the first mission, we consider the coerage specifications presented in [2]. The reqirements apply for a mission proiding serice to Soth America. The antenna mst operate in dal-linear polarization, in both Tx ( GHz) and Rx ( GHz) freqency bands. The mission has stringent reqirements sch as high gain, cross-polar specifications, as well as co-polar isolation reqirements. The coerages are shown in Fig. 1 and co- and cross-polar reqirements are smmarized in Table I.

2 Fig. 2. Continental United States coerage from [3]. TABLE II COVERAGE REQUIREMENTS FOR MISSION II Fig. 1. The Soth American and Eropean coerages from [2]. Zone Min. Directiity Min. XPD [dbi] [db] USA Canada Hawaii Perto Rico B. Mission II TABLE I COVERAGE REQUIREMENTS FOR MISSION I Tx: GHz Rx: GHz Zone D min XPD min D min XPD min [dbi] [db] [dbi] [db] SA SA SB SC SC SD Zone D max [dbi] D max [dbi] EU.. For the second mission, we consider the coerage as presented in [3]. The reqirements apply for a mission proiding serice oer the Continental United States coerage. The mission coers a large CONUS/Canada contored beam with two separate areas oer Perto Rico and Hawaii. The two separate areas otside the CONUS region make the coerage challenging and can be considered as a worst case scenario. In [3], the freqency band was only specified for Rx operation. Howeer, in or case, we extend the freqency band to coer both Tx and Rx. For simplicity, we select the same freqency bands as in Mission I, namely Tx ( GHz) and Rx ( GHz). The antenna mst operate in dal-linear polarization. The coerages are shown in Fig. 2 and co- and cross-polar reqirements are smmarized in Table II. C. Reference Antennas To sere as reference soltions, two offset shaped reflectors are designed sing TICRA s software package POS [8] to flfill the specifications for missions I and II, one reflector for each mission. As feed, a Gassian beam model is sed. The diameter of the shaped reflector is 1.2 m and is identical to what will be considered for the reflectarray designs to allow a fair comparison. For mission I, the optimized shaped reflector flfills all the coerage specifications, both co- and cross-polar reqirements, in the entire Tx-Rx band for both linear polarizations with a margin of.68 db. For mission II, the optimized shaped reflector flfills all the coerage specifications with a margin of.95 db. These ales are the target performance that the reflectarrays shold be compared to. III. REFLECTARRAY ANALYSIS AND OPTIMIZATION For the design of the reflectarrays, the same design approach from [7] is adopted. Herein, the reflectarray is designed sing the direct optimization techniqe (DOT) from [4]. The analysis method sed in DOT is a spectral domain method of moments assming local periodicity (LP-SDMoM) and the optimization engine is based on a gradient non-linear minimax optimization algorithm [9]. Althogh the LP-SDMoM is based on approximations, in particlar when applied on a dobly cred reflectarray, the accracy of the method is ery good. This has been erified in [7] by means of comparison against the fll-wae method of moments soler in GRASP [1]. Details of the LP-SDMoM and how it is applied on cred reflectarrays will not be gien here and the reader is referred to [7] for more details. IV. REFLECTARRAY DESIGN A. Reflectarray Configration and Array Element The reflectarray configration considered here is shown in Fig. 3. The focal length to diameter ratio (f/d) and offset are selected to be identical to that of the aforementioned reference antennas to allow a fair comparison. The (x sta, y sta, z sta ) coordinate system is the coordinate system in which the contored beam goals are specified, i.e., main-beam direction,

3 w y L y1 L y2 w x L x2 L x1 Fig. 4. Rectanglar loop/patch combination element. Fig. 3. Offset configration with a rotationally symmetrical parabolic srface defined wrt. the (x ra, y ra, z ra) coordinate system. and the (x ra, y ra, z ra ) coordinate system is the reflectarray coordinate system. As array element, we consider the rectanglar loop/patch combination element as shown in Fig. 4. This element has proen to proide good reslts [5] and is therefore considered in this work. The array elements are printed on a single layer sbstrate with sbstrate thickness of h = 4 mm with a dielectric constant of ɛ r = 1.5 and a loss tangent of tanδ =.83. All reflectarray designs are optimized sing the direct optimization techniqe with L x1 and L y1 as optimization ariables. The other parameters are fixed as w x =.135L x1, w y =.135L y1, L x2 =.69L x1, and L y2 =.69L y1. B. Reflectarray Srface Definition The cratre of the reflectarray srface has a strong inflence on how well the performance of the optimized design can be. The se of a focsed srface configration that proides a pencil beam design is not optimal for contored beam coerages. The reason for this is that the radiation from this srface, withot the presence of the array elements, will be a focsed spot beam with a beamwidth that is determined by the antenna dimension. If the area of the coerage is mch larger than the beamwidth, the array elements need to compensate for the narrow beam to form the specified contored beam and this is challenging in a wide bandwidth, reslting in degradation in performance. Conseqently, a better soltion is to apply a defocsed configration to obtain an initial beam that is more similar to the reqired coerage area [7]. Different types of defocsed configrations were considered for the design of the cred reflectarrays. Howeer, for this paper we mention only one configration: the rotationally sym- metrical parabolic srface. This was the setp that proided the best reslts and is also the configration shown in Fig. 3. The rotationally symmetrical parabolic srface is defined with respect to the reflectarray coordinate system (x ra, y ra, z ra ). The reflectarray coordinate system is defined sch that the speclar reflection from the reflectarray is aligned with the z sta -axis. This wold be the optimal definition for a planar reflectarray. By adjsting the focal length of this parabolic srface, different degrees of defocsing can be achieed. It shold be noted that the rim of the reflectarray is elliptical sch that it has a circlar projected apertre seen from the x sta y sta -plane. C. Reflectarray Element Projection Once the srface cratre has been decided, one needs to define how the array elements are projected onto the dobly cred srface. One obios choice is to project the array elements sch that they appear in a reglar grid seen from the x ra y ra -plane. This is how the array elements will be projected onto the reflectarray srface if it is a planar reflectarray. Another sitable choice is to project the array elements with respect to the x sta y sta -plane. In this way, the array elements will appear in a reglar grid seen from the main-beam direction. Seeral cred reflectarrays were optimized to flfil the mission reqirements where both projections were applied. Based on this preliminary inestigation, it was eident that the designs where the array elements were projected with respect to the x ra y ra -plane had sperior performances. In all cases, the designs with elements projected with respect to the x ra y ra -plane proided a goal margin that was arond db higher than designs with elements projected with respect to the x sta y sta -plane. Ths, only reflectarrays with x ra y ra -projection will be considered. V. NUMERICAL RESULTS Since the selection of the srface cratre has an impact on the reflectarray performance, different focal lengths of the symmetrical parabolic srface need to be inestigated to identify the optimal choice. It is crrently not possible to optimize the srface cratre together with all the array elements simltaneosly. Conseqently, a parametric inestigation was carried ot where the focal length of the parabolic srface was manally adjsted. For each ale of the focal length, the

4 direct optimization was applied to design a contored beam reflectarray that flfilled the mission reqirements. All the designs considered in this parametric inestigation flfilled the coerage reqirements, both co- and cross-polar specifications. For Mission I (Soth American coerage), the reslts are smmarized in Tabel III. Herein, for each ale of the focal length, the margin that the optimized reflectarray flfilled the mission reqirements is listed. For instance, for a focal length of 2.8 m, the optimized design flfilled all reqirements with a margin of.48 db. The best design has a focal length of 3.4 m and flfills the reqirements with a.56 db margin, which is.12 db below the reference antenna which flfilled the reqirements with a margin of.68 db. Ths for this specific mission, the shaped reflector is sperior in performance. It is howeer worthwhile to note that the coerage for Mission I is rather asymmetric, ths a rotationally symmetrical parabolic srface may not be the optimal choice. Frthermore, how the srface is tilted with respect to the feed may also affect the performance of the cred reflectarrays since this changes the direction of the main-beam towards the coerage. The latter isse is circmented in the design of the shaped reflector sing POS since the tilt of the srface is atomatically adjsted dring the optimization process. Similarly, for Mission II (Cons coerage), the parametric stdy was carried ot and the reslts are also listed in Table III. De to the different coerage shape and reqirements, the focal length that proided the best reslt is different compared to those considered for Mission I. The best design ses a focal length of 2.7 m and flfills the reqirements with a margin of.96 db. This is.1 db better than the reference antenna which flfills the reqirements with a margin of.95 db. So for this mission, the performances of the cred reflectarray and the shaped reflector are identical. This is explained by the fact that the coerage shape is more symmetric making a rotationally symmetrical parabolic srface a good candidate as reflectarray srface. If one is to se the same reflectarray srface for both missions, then by examing Table III, a good compromise cold be the se of the srface with a focal length of 3. m. Using this srface, the cred reflectarray can flfill the reqirements of mission I and II with a margin of.53 db and.9 db, respecitely. In Fig. 5, the radiation patterns, co-polar directiity and cross-polar discrimination (XPD) of the optimized reflectarray for Mission I at GHz in V-polarization is shown. The reflectarray radiates a high-gain beam oer Soth America with a XPD close to 3 db oer the entire coerage. Similarly, the radiation patterns of the optimized reflectarray for Mission II is shown in Fig. 6. High-gain beams are obsered oer CONUS, Canada, Hawaii, and Perto Rico with a XPD aboe 3 db oer all high-gain regions. These two reflectarrays se exactly the same srface (symmetrical parabolic srface with a focal length of 3 m), the same f/d, dimension, and feed, and by simply changing the reflectarray element pattern, two completely different coerages can be prodced. The srface cratre was selected as a compromise for both coerages for a fixed f/d. By adjsting the position of the feed for each mission, it may be possible to adjst the defocsing to better match the shape of the specified coerage and thereby enhance the performance. The work presented in this paper demonstrates that it is indeed possible to design cred reflectarrays sing the same cred srface for seeral missions and at the same time maintain a good performance. From an electromagnetic point of iew, the reslts presented in this paper are ery promising and sggests that a cred reflectarray can be iable candidates to replace shaped reflectors. Howeer, from a manfactring point of iew, the sggested designs (single layer sbstrate) may be hard to realize since a sandwich strctre may be reqired for the space applications. A sandwich strctre entails the se of additional sbstrate layers which will in trn increase losses. Frthermore, the array elements need to be printed on a dobly cred srface and a non-conentional manfactring approach is needed. TICRA and ESTEC are working with experts in this area with the aim to manfactre a breadboard to demonstrate its feasibility. TABLE III REFLECTARRAY PERFORMANCE AS FUNCTION OF FOCAL LENGTH Mission I Mission II Focal Length Goal Margin Goal Margin [meters] [db] [db] VI. CONCLUSIONS In this paper, the design and inestigation of cred contored beam reflectarrays with resable srface for mltiple coerages is presented. Using the direct optimization techniqe, seeral cred reflectarrays with different srface cratres hae been optimized to flfill the reqirements of two contored beam missions with stringent coerage reqirements in both transmit and receie freqency bands. It is shown that it is possible to design cred reflectarrays sing the same cred srface for seeral missions and at the same time maintain a good performance that is comparable to that of the shaped reflector. This highlights the main adantage of the cred reflectarray oer the shaped reflector, namely that an existing mold can be resed for mltiple missions and thereby redcing manfactring cost and deliery time.

5 (a) Co-polar Directiity [dbi], V-polarization (b) XPD [db], V-polarization Fig. 5. Simlated radiation patterns of the optimized reflectarray for Mission I at GHz in V-polarization (a) Co-polar directiity [dbi], V-polarization (b) XPD [db], V-polarization Fig. 6. Simlated radiation patterns of the optimized reflectarray for Mission II at GHz in V-polarization. ACKNOWLEDGMENT The work presented in this paper is fnded by the Eropean Space Agency (ESTEC contract No /15/NL/ND). R EFERENCES [1] D. M. Pozar, S. D. Targonski, and R. Pokls, A shaped-beam microstrip patch reflectarray, IEEE Trans. Antennas Propag., ol. 47, no. 7, pp , [2] J. A. Encinar, M. Arrebola, L. D. L. Fente, and G. Toso, A transmitreceie reflectarray antenna for direct broadcast satellite applications, IEEE Trans. Antennas Propag., ol. 59, no. 9, pp , 211. [3] H. Legay, D. Bresciani, R. Chiniard, E. Girard, G. Caille, E. Labiole, and R. Gillard, Demonstration model of a reflectarray for telecommincation antenna, Final report, Thales Alenia Space, Tolose, France, Tech. Rep., March 212. [4] M. Zho, S. B. Sørensen, O. S. Kim, E. Jørgensen, P. Meincke, and O. Breinbjerg, Direct optimization of printed reflectarrays for contored beam satellite antenna applications, IEEE Trans. Antennas Propag., ol. 61, no. 4, pp , 213. [5] M. Zho, O. Borries, and E. Jørgensen, Design and optimization of a single-layer planar transmit-receie contored beam reflectarray with enhanced performance, IEEE Trans. Antennas Propag., ol. 63, no. 3, pp , 215. [6] M. Zho, S. B. Sørensen, P. Meincke, and E. Jørgensen, Design and optimization of mlti-faceted reflectarrays for satellite applications, in Proc. ECAP, The Hage, The Netherlands, 214. [7] M. Zho, S. B. Sørensen, O. Borries, and E. Jørgensen, Analysis and optimization of a cred transmit-receie contored beam reflectarray, in Proc. ECAP, Lisbon, Portgal, 215. [8] POS Software, TICRA, Denmark, [9] O. Borries, S. B. Sørensen, E. Jørgensen, M. Zho, M. S. Andersen, and L. E. Sokoler, Large-scale optimization of contored beam reflectors and reflectarrays, in Proc. IEEE AP-S Int. Symp., Fajardo, Perto Rico, 216. [1] GRASP Software, TICRA, Copenhagen, Denmark.