ES2930559B2 - Flat multi-band reflectarray antenna with circularly polarized beam spacing and method for its design - Google Patents

Description

DESCRIPTION

Flat multi-band reflectarray antenna with circular polarization beam spacing and method for its design

OBJECT OF THE INVENTION

The present invention falls within the technological field of radiocommunications, in the technical field of "reflectarray" type antenna systems or reflective array (from English: reflective array, reflectarray) and, more particularly, falls within reflectarray antenna systems applicable in terrestrial and satellite communications networks in millimeter wave bands for fifth or sixth generation (5G and 6G respectively), and in space technology.

Particularly, the present invention refers to a planar reflectarray antenna that operates in two or more frequency bands with the capacity to separate orthogonal circularly polarized beams in each band.

BACKGROUND OF THE INVENTION

In recent decades there has been a significant increase in the use of multibeam antennas for communication satellites. These multibeam antennas provide coverage to a specific region of the Earth, using a large number of beams that cover both the downlink transmit (TX) and uplink receive (RX). Multibeam antennas have advantages over contoured beam antennas because: a) they make more efficient use of the spectrum by spreading the operating frequencies among the different beams; b) they have higher gains by using smaller beams, which means a higher equivalent isotropically radiated power (EIRP) in the downlink radio and a higher gain/noise temperature (G/T) ratio in the uplink radio; and c) require smaller ground terminals. These multibeam antennas have been used on geostationary satellites for personal communications, military communications, broadcasting, and mobile communications services [S. K. Rao & M. Q. Tang, “Stepped reflector antennas for dual-band multiple beam satellite communication payloads”, IEEE Trans. on Antennas and Propagation, vol. 54, p. 801-811, March 2006].

Communications satellites play a key role in communication networks, providing connectivity in rural or isolated areas, and in mobility scenarios (aeronautical and maritime), complementing the services provided by terrestrial networks [K. Lyolis, et al. "Use cases and scenarios of 5G integrated satellite-terrestrial networks for enhanced mobile broadband. The SaT5G approach”, Intl. J. Satell. Commun. Network, 37 (2019), 91-112.]. Currently, geostationary satellites are used that They operate in the Ka band, known as high throughput satellites. The antennas used in these satellites use a frequency and polarization reuse scheme to fully cover the coverage area without interference with "four colors" generated from two close frequencies and two orthogonal polarizations, both in TX (center frequency in around 20 GHz) and RX (center frequency around 30 GHz) [SK Rao, "Parametric design and analysis of multiple-beam reflector antennas for satellite communications”, IEEE Antennas Propag. mag., vol. 45, pp.26-33, Aug. 2003].

The coverage area is completely covered with independent beams of these four colors so that beams of the same color never overlap. Parabolic reflectors have traditionally been used for these multibeam antennas due to weight savings, and the high degree of technological maturity achieved in the design of said reflectors. Initially, eight multibeam reflectors were used, four to cover the two frequencies and the two polarizations in TX, and another four to achieve the same operation in RX. Subsequently, the number of parabolic reflectors was reduced to four by using double band reflectors, each of which accounted for a frequency and a polarization (a color), both in TX and RX. The main problem with this configuration of four reflectors is that it occupies two sides of the satellite and leaves no space for other missions [NGJ Fonseca & Cyril Mangenot, "Low-profile polarizing surface with dual-band operation in orthogonal polarizations for broadband satellite applications”, Proc. 8th European Conf. Antennas Propag. EuCAP 2014, pp. 471-475] Therefore, solutions have been sought that reduce the total number of parabolic reflectors to two, either by designing reflectors that generate the four colors in one single band (i.e. either TX or RX), or by designing dual band reflectors that generate two colors on both TX and RX This can be achieved by converting from single beam feeder configurations to However, this last strategy requires resorting to the design of sophisticated beam generating networks, and also, the performance of reflectors with multiple feeders per beam is inferior to those of reflectors with a single feeder per beam [ m. Zhou & SB Sorensen, "Multi-spot beam reflectarrays for satellite telecommunication applications in Ka-band”, Proc. 10th European Conf. Antennas Propag. EuCAP 2016]. Due to these problems, alternative solutions have been sought based on replacing the reflectors with reflectarray antennas (also called reflectarrays throughout this document), or at least, on combining the reflectors with this type of antenna. Reflectarrays are flat groups of reflective cells in which each cell introduces a phase correction when an electromagnetic wave is incident on it, so that it is possible to achieve a collimated beam in reflection when the set of cells is illuminated by a primary feeder, which typically it is a horn antenna. Reflectarrays have advantages over parabolic reflectors such as lower weight, lower cost, a slimmer profile, and a lower level of cross-polarization [DM Pozar, “Design of millimeter-wave reflectarrays”, IEEE Trans. on Antennas and Propagation, vol. 45, p. 287-296, Feb. 1997].

In the case of linearly polarized multibeam antennas, reflectarrays have been designed with cells composed of two orthogonal arrays of eight parallel dipoles stacked on two dielectric layers that have demonstrated their ability to achieve two separate beams in horizontal and vertical polarization (that is, two colors) in two bands (TX and RX) [E. Martínez de Rioja, J. A. Encinar, R. Florencio & R. R. Boix, “Reflectarray in K and Ka bands with independent beams in each polarization”, Proc. IEEE Int. Symp. Antennas, Propag. 2016, p.

1199-1200], with which two of these reflectarrays in a multibeam configuration (with a single feeder for every two beams) would be sufficient to satisfy the entire transmission and reception coverage of a Ka-band satellite. Likewise, reflectarrays have been designed with cells also composed of orthogonal sets of parallel dipoles, which are capable of generating four adjacent beams with two orthogonal linear polarizations and two close frequencies (that is, four colors) in a single frequency band, thus which, only two of these reflectarrays would also be necessary to generate all the coverage of a Ka band satellite, one for TX and one for RX [E. Martínez de Rioja et al., IEEE Antennas Propag. Mag., Vol. 61, p. 77-86, Oct. 2019]. In this last configuration, the separation of beams at two close frequencies is carried out taking advantage of the phenomenon of modification in the direction of the beam with the frequency ("beam squint" in English) that occurs in reflectarrays in which the pointing direction does not coincides with the direction of specular reflection relative to the direction of incidence of the wave emitted by the feeder.

Although relatively simple solutions have been proposed to reduce to two the number of multibeam reflectarray antennas of a Ka band satellite that works with linear polarization in TX and RX, the problem is much more complicated when the satellite works with circular polarization. In [MR Chaharmir & J. Shaker, "Design of a multilayer X-/Ka-band frequency-selective surface backed-reflectarray for satellite applications”, IEEE Trans. on Antennas and Propagation, vol. 63, pp. 1255-1262, April 2015] and in [R. Deng et al., "An FSS-backed 20/30-GHz dual band circularly polarized reflectarray with suppressed mutual coupling and enhanced performance”, IEEE Trans. on Antennas and Propagation, vol. 65, p.

926-931, Feb. 2017] two reflectarrays capable of operating at 20 and 30 GHz in circular polarization are designed. In both cases, the 20 and 30 GHz antennas are designed independently, and these antennas are stacked separated by a frequency-selective surface that acts as a reflecting surface at 30 GHz, and as a transmitting surface at 20 GHz. Frequency prevents the 30 and 20 GHz antennas from coupling, allowing them to be designed independently. The main problem with these reflectarrays is that they have four levels of metallization on three dielectric layers that are a few millimeters apart, resulting in a total thickness of the order of one centimeter, which means that the manufacturing process is complex. In addition, it is very difficult to maintain a uniform separation between layers and with tolerances of the order of 0.1 mm, especially in space applications where the materials suffer thermoelastic distortions. In [T. Smith et al., “Design, manufacturing and testing of a 20/30 GHz dualband circularly polarized reflectarray antenna”, IEEE Antennas Wireless Propagat. Lett., vol.

12, p. 1480-1483, 2013] a much simpler and cheaper solution to the same problem is proposed since the reflectarray for circular polarization designed at 20 and 30 GHz has a single layer of dielectric 0.79 mm thick and a single level of metallization. In this case, the phase shifter cells contain two concentric split rings that are rotated to adjust the phases required in circular polarization in the two bands, while the lengths of the arcs of the rings are modified as a function of the rotation angles so as to maintain a phase difference of 180 degrees between the reflection coefficients of the two orthogonal linear components of the circularly polarized waves, as required by the technique of variable rotation (TRV) introduced in [J. Huang & R. J. Pogorzelski, "A Ka-band microstrip reflectarray with element having variable rotation angles”, IEEE Trans. on Antennas and Propagation, vol. 46, pp. 650-656, May 1998]. The design technique of this type of reflectarrays is more complex than that of reflectarrays that use a frequency selective surface because although the outer split rings are tuned at 20 GHz without the inner split rings having a significant effect at this frequency, at 30 GHz there is coupling between the outer rings and inner rings, and the two rings have to be taken into account in each cell when adjusting the phase of the cell in the RX band.

In the works just described, the reflectarray generates a single polarizing beam circulate in two frequencies (Tx and Rx) for each feeder. Apart from this operating regime, reflectarray designs have been proposed capable of generating two orthogonal circular polarization beams for each feeder operating in double polarization and in a single frequency band. One possible way to attack the problem is to use polarization converters/splitters capable of transforming left/right circular polarization waves into horizontal/vertical linear polarization waves. These converters are placed in front of a reflectarray designed to generate independent beams at each linear polarization, thus turning the circularly polarized beam-splitting problem into a linear-polarized beam-splitting problem, which is much simpler. . In [M.-A. Joyal et al, "A reflectarray-based dual-surface reflector working in circular polarization”, IEEE Trans. on Antennas and Propagation, vol.63, pp. 1306-1313, April 2015] uses a flat line-based polarization converter meandering conductors with three levels of metallization preceding a reflectarray in front of a parabolic reflector.The reflectarray reflects and collimates the horizontal linear polarization from the polarization converter, and is transparent to the vertical linear polarization, which is itself reflected and collimated by the reflector located behind.The problem is that the structure "parabolic reflector+reflectarray+polarization converter" is very bulky. Another possible beamsplitter reflectarray configuration with circular/linear polarization converter is the one proposed in [CS Geaney, M. Hosseini & SV Hum, "Reflectarray antennas for independent dual linear and circular polarization control”, vol. 67, pp. 5908 -5918, Sept. 2019] In this case, the polarization converter is placed on top of a double linear polarization reflectarray, with a separation of the order of 1 cm, thereby eliminating the reflector and reducing the volume of However, the reflectarray with polarization converter turns out to be a multilayer structure with five levels of metallization (three for the polarizer and two for the reflectarray) etched onto four thin sheets of dielectric.This structure is complicated to fabricate because Dielectric sheets with metallizations should be held on a flat surface, with RMS values of deviation from the flat surface less than 0.1 mm, as required for space antennas. In [M. Zhou & SB Sorensen, "Multi-spot beam reflectarrays for satellite telecommunication applications in Ka-band”, Proc.

10th European Conf. Antennas Propag. EuCAP 2016] uses a reflectarray printed on a parabolic reflector to achieve the separation of circularly polarized beams. The concept of a reflectarray on a parabolic reflector was first introduced in US006031506A [ME Cooley, TJ Chwalek & P. Ramanujam, "Method for improving pattern bandwidth of shaped beam reflectarray”, Feb. 2000] as a concept intended to increase the bandwidth of conventional reflectarrays. In the article by Zhou and Sorensen, the separation of circularly polarized beams is carried out by means of the aforementioned TRV, using the degree of freedom of rotation of the printed elements, which in the case of flat reflectarrays serves to collimate a polarized incident wave. circularly, and in the case of parabolic reflectarrays it serves to separate two left and right circularly polarized incident waves into two different beams after reflection. This spacing of circularly polarized beams at a single frequency has been achieved with a flat low profile reflectarray (less than 2 mm thick) in [R. Florencio et al., "Flat reflectarray that generates adjacent beams by discriminating in dual circular polarization”, IEEE Trans. on Antennas and Propagation, vol. 67, pp. 3733-3742, June 2019]. In this case, a cell formed by by two orthogonal arrays of three parallel dipoles printed on two stacked dielectric layers to first design a reflectarray capable of focusing left and right circularly polarized beams in the same direction using the Variation Cell Size (TVTC) technique. TRV is applied to the surface of the reflectarray to modify the pointing direction of the right-hand circularly polarized beam in one direction, and that of the left-hand circularly polarized beam in the opposite direction.

Although the works mentioned in the two previous paragraphs have led to advances in the design of reflectarray antennas for satellite applications that work with circular polarization, in order to reduce the set of multibeam antennas of a Ka band satellite and circular polarization to two, they make There is a lack of reflectarrays that are not only capable of separating the circular polarization beams to the right and to the left, but also generate highly directivity beams, collimated or shaped, and do so in both TX and RX bands. A first step, proposed as a "proof of concept" in the state of the art, is given in [D. Martínez-de-Rioja et al., "Dual-band reflectarray to generate two spaced beams in orthogonal circular polarization by variable rotation technique”, IEEE Trans. on Antennas and Propagation, vol. 68, p. 4617-4626, June 2020], where a flat reflectarray is proposed in which the phase-shifting cells are composed of a split ring surrounding two orthogonal sets of three parallel dipoles in two superimposed dielectric layers. While the split ring is used to phase TX, the dipoles and rings are used simultaneously to phase RX. Beam separation is achieved by TRV. The rotations of rings and dipoles are carried out in opposite directions, which allows the pointing direction of the beam with clockwise circular polarization in TX to coincide with that of the beam with circular polarization to the left in RX and vice versa. This behavior is a requirement for antennas on board satellites to minimize interference. The presence of orthogonal dipoles is key when it comes to improving the performance of the cell in RX. Thanks to the fact that the dipoles used can have different lengths, an optimization of the dimensions of the dipoles is carried out at the central frequency and at the extreme frequencies of the RX band, which allows to reduce the cross-polarization in this band by almost 10 dB. The main problem with the aforementioned flat reflectarray, based on split rings and orthogonal dipoles, is that, although it allows the separation of circularly polarized beams into two bands, it does not allow collimating said beams since the element used in the phase shifter cell does not have degrees of sufficient freedom to shape the beam in the operating bands. For this reason, said reflectarray can only replicate the radiation diagram of the horn antenna used as a feeder, achieving a gain of between 20 and 25 dBi, which is clearly insufficient for satellite-borne antenna applications, where gains are required. greater than 45 dBi.

To simultaneously achieve both the separation of circularly polarized beams into two different bands and the collimation of said beams, the parabolic reflectarray solution has been used. In [M. Zhou et al., "Doubly curved reflectarray for dual-band multiple spot beam communication satellites”, IEEE Trans. on Antennas and Propagation, vol. 68, pp.

2087-2096, March 2020] a reflectarray on parabolic reflector is used to separate circularly polarized beams into TX and RX. While the phase shifter cells of the reflectarray are in charge of separating the two beams, the reflector is in charge of collimating them. Rectangular conductive patches surrounded by split hexagonal rings are used as double-band elements, so that the hexagonal rings are used to control the phase in TX, and the rectangular patches in RX. Beam splitting is accomplished by TRV, and while TX phasing only depends on the rotation of the hex rings, RX phasing requires working in conjunction with the head rotation angles. rectangular and the rings since the mutual coupling between patches and rings is important in that band. The beams emitted by the designed reflectarray have gains of around 40 dBi, which demonstrates the collimation capacity provided by the parabolic surface. In [D. Martínez-de-Rioja et al., "Transmit-receive parabolic reflectarray to generate two beams per feed for multispot satellite antennas in Ka-band”, IEEE Trans. on Antennas and Propagation, vol. 69, pp. 2673-2685, May 2021] a similar approach is used, making use of a reflectarray on a parabolic reflector to separate the circularly polarized beams into TX and RX, in this case the phase-shifting cells of the reflectarray, based on a split ring with two orthogonal sets of three parallel dipoles. , are taken from the previously mentioned article on plane reflectarray with separation of do two bands [D. Martínez-de-Rioja et al., "Dual-band reflectarray to generate two spaced beams in orthogonal circular polarization by variable rotation technique”, IEEE Trans. on Antennas and Propagation, vol. 68, pp. 4617-4626, June 2020] Again, the presence of the parabolic surface makes it possible to collimate the beams and achieve gains greater than 40 dBi.An important novelty introduced in the parabolic reflectarray based on split rings and dipoles is that the selective phase correction technique is applied in its design. which is described in [JA Encinar Garcinuño, JD Martínez de Rioja del Nido, EM Martínez de Rioja del Nido, R. Florencio Díaz and R. Rodríguez Boix, "Multi-frequency phase corrected reflector antenna for space applications and design method de la misma”, Spanish patent ES 2791798 B2, March 2021] to a portion of the cells located in a circular crown next to the edge of the reflectarray in the RX band (this technique consists of modifying the objective phase of the reflected field by 180 degrees in the RX band to a randomly chosen portion of the cells located in the aforementioned circular crown), without making modifications to the design in the TX band. The selective phase correction technique allows equalizing the gains and beamwidths in TX and RX (under normal conditions, the gain of each beam in TX is less than in RX, and the beamwidth in TX is greater than that of RX , due to the fact that the antenna has a larger electrical size in RX than in TX because the frequency is also greater), which makes it possible for the power levels in the coverage areas to be the same for the downlink and the uplink radio.

Despite their good response, the two reflectarrays on parabolic reflectors with the ability to separate circularly polarized beams into two frequency bands (TX and RX) that have been described in the previous paragraph have the problem that they are bulky and complex to manufacture. . Consequently, the objective technical problem that is presented is to provide a reflectarray antenna capable of separating circularly polarized beams in two frequency bands, especially for broadband internet access via satellite, with less design complexity, lower cost , less weight and less volume.

DESCRIPTION OF THE INVENTION

The present invention serves to solve the problem mentioned above, by providing a planar reflectarray antenna with an array of phase-correcting cells (phase-shifting cells or reflectarray cells), in which each cell contains two superimposed sets of four split conductor rings. , concentric with each other. Arrays of four split rings are printed onto the faces of one or more dielectric layers, and the dielectric layers are stacked to form the multilayer antenna substrate, limited inferiorly by a conducting plane. The antenna works in (at least) two frequency bands and is capable of generating two different beams in each band, one circularly polarized to the right and one circularly polarized to the left.

The present invention is applicable to antennas designed to generate multicellular coverage from satellites or high-altitude platforms, making it possible to reduce the total number of antennas necessary to generate all coverage, both in transmission and reception. More specifically, its main application is in satellite-borne antennas that must transmit and receive signals in different frequency bands in heterogeneous communication networks for 5G and 6G, including: Low Earth Orbit (LEO) satellites Orbit”) and Geosynchronous Equatorial Orbit (GEO) satellites, High Altitude Pseudo-Satellites (HAPS) platforms, terrestrial networks and non-terrestrial broadband communications networks (NTN). , acronym for "Non-Terrestrial Networks” in English) in 5G and 6G.

In a first design stage of the antenna described here, the dimensions of the split rings with the largest radius are adjusted to collimate the radiated or received beam in a single direction in the lowest frequency band (all this without discriminating the direction of the antenna). circular polarization). Next, the dimensions of the smaller radius split rings are adjusted to achieve the same behavior in the higher frequency band. In a second design stage, the split rings are rotated to separate left and right circularly polarized radiated beams into different pointing directions, at both lower and higher frequencies.

The flat reflectarray antenna presented can be generalized to more than two frequency bands, allowing the use of the same antenna for several space missions, in which contoured beams are generated in certain frequency bands and multiple beams in other bands. Therefore, the type of reflectarray antenna presented here has a clear application in the space industry as a low-cost, lightweight and compact alternative to parabolic and grating reflectors, or shaped surface reflectors for contoured beam generation, allowing reduce the costs of the antenna system in communications satellites, with special interest in low-cost satellites, such as those called SmallGEO and LEO, and allowing the total number of antennas necessary to generate all coverage, both in transmission and reception, to be reduced .

One aspect of the invention refers to a multiband flat reflectarray antenna comprising the following components:

- a feeder to generate waves (beams) with a circular polarization to the right and to the left, each wave corresponding to a complex electric field with an electric field component in a first coordinate axis and an electric field component in a second axis orthogonal to the first coordinate axis;

- a group of reflectarray cells (phase shifter cells) arranged on a (flat) grid that reflects the waves generated by the feeder, where each cell comprises a conductive (ground) plane and multiple superimposed dielectric layers on the conductive plane;

In each phase shifter cell, the reflectarray antenna also comprises two superimposed sets of four concentric conductor rings divided into two arcs, having a total of sixteen arcs, where a first set of four conductive rings divided into two arcs is printed on one side (of the two faces) of one of the dielectric layers, called the first layer or upper layer, and where a second set of four conducting rings divided into two arcs is printed on (the) other face of the same layer mentioned above, upper layer, or on a of the two faces of another different layer, second layer or lower layer, of the plurality of dielectric layers; and of the total of sixteen arcs in each phase shifter cell:

- eight arcs of the (most) outer rings (those with the largest radius), which belong to four rings that are the two split rings with the largest radius of the two sets of rings, have lengths to adjust in phase the feeder waves that They are reflected in each phase-shifting cell maintaining the sense of circular polarization after reflection at the central frequency of a first operating band of the reflectarray antenna, called the lower frequency, where:

• four outer arcs oriented in a first direction along the first coordinate axis, adjusted to control an offset of the component of the reflected electric field along the first axis, and

• four arcs oriented in a second direction, along the second coordinate axis, adjusted to control an offset of the reflected electric field component along the second axis, there being a difference of 180 degrees between the offsets of the two reflected electric field components to maintain the sense of circular polarization at the lower frequency;

- eight arcs of the (most) inner rings (those with the smallest radius), which belong to four rings that are the two split rings with the smallest radius of the two sets of rings, have lengths to adjust in phase the feeder waves that they are reflected in each phase shifter cell maintaining the sense of circular polarization after reflection at the central frequency of a second band of operation of the antenna reflectarray, called higher frequency, being:

• four internal arcs oriented in a first direction along the first coordinate axis, adjusted to control an offset of the component of the reflected electric field along the first axis, and

• four arcs oriented in a second direction, along the second coordinate axis, adjusted to control an offset of the reflected electric field component along the second axis, maintaining a 180 degree difference between the offsets of the two reflected electric field components to maintain the sense of circular polarization at the higher frequency; and at the lower frequency, the eight arcs of the outermost rings are rotated jointly, applying the variable rotation technique to divert the circular polarization waves to the right and left a (first) predetermined angle in opposite directions with respect to the direction of the waves. reflected waves before rotating the eight arcs of the outer rings; and at the higher frequency, the eight arcs of the innermost rings are rotated jointly, applying the technique of variable rotation to divert the circular polarization waves to the right and left by a preset (second) angle in opposite directions with respect to the direction of the waves. reflected waves before rotating the eight arcs of the outer rings.

Another aspect of the invention refers to an antenna design method to obtain the reflectarray antenna described above with circularly polarized beam spacing in at least two frequency bands (the method is applicable for both collimated and contoured beams and works for two frequency bands, being generalizable for more than two frequency bands). The method comprises the following steps:

a) define the reflectarray antenna in shape and dimensions, in a coordinate system (X, Y, Z), the reflectarray antenna formed with a group of phase-shifting cells in a periodic planar grid of fixed period and a feeder configured to radiate in the , at least two, frequency bands, circularly polarized waves to the right and to the left that impinge on the phase-shifting cells, each phase-shifting cell comprising:

- a driving plane,

- a plurality of dielectric layers,

- a first upper set of four concentric split conductor rings printed on one of the faces of a layer of the plurality of dielectric layers, each of the rings split into two equal arcs, forming eight arcs of the first set;

- a second lower set of four concentric split conductor rings printed on the face opposite to the face of the dielectric layer on which it is

printed the first set, or on a face of a different layer than the dielectric layer on which the first set of the plurality of dielectric layers is printed;

b) define some pointing directions of the circular polarization beams to be separated

in a first operating band and a second operating band, and

define a central frequency of the first operating band and a frequency

center of the second operating band;

c) at the center frequency of the first operating band and at the center frequency of

the second operating band, determine a distribution of some values of

phase shift for incident waves with linear polarization on a first axis (X) and polarization

linear on a second axis (Y) to collimate or contour circularly polarized beams

in an intermediate direction to the aiming directions of each of the beams

to be separated, where the distribution of phase shifts for the linear polarization on the first axis

(X) differs by 180 degrees from the lag distribution for linear polarization in a

second axis (Y), to collimate or contour the circularly polarized waves to the right and left that impinge on the phase-shifting cells of the reflectarray antenna, maintaining the direction of circular polarization after being reflected

by the phase-shifting cells;

d) at the central frequency of the first operating band, adjust some lengths of

some outer arcs, where the outer arcs are the arcs of greater radius of the two sets of split rings, adjusting the lengths of a first subset of four

external arcs of split rings oriented in the direction of the first axis (X), being the

offset introduced by the offset cell equal to that calculated in step c) for the case

of linear polarization in the first axis (X), and adjusting the lengths of a second subset of four external arcs in the direction of the second axis (Y) where the phase shift introduced by the phase shifter cell is equal to that calculated in step c) for the case

linear polarization on the second axis (Y);

e) at the central frequency of the second operating band, adjust some lengths

of some internal arcs, where the internal arcs are the arcs of smaller radius of the two sets of split rings, adjusting the lengths of a first subset of four

internal arcs of split rings oriented in the direction of the first axis (X), being the

offset introduced by the offset cell equal to that calculated in step c) for the case

of linear polarization on the first axis, and adjusting the lengths of a second subset of four internal arcs in the direction of the second axis (Y) where the phase shift introduced by the phase shifter cell is equal to that calculated in step c) for the case

linear polarization on the second axis (Y);

f) check if the difference, for each phase shifter cell, between the phase shift values determined in step c) and the phase shifts introduced by the phase shifter cell for the linear polarizations in the first axis (X) and second axis (Y), a the center frequency of the first operating band and the center frequency of the second operating band are less than a first phase error reference threshold;

g) if the difference checked in step f) is equal to or greater than the first phase error reference threshold, repeat step d) adjusting the lengths of the first subset and second subset of the external arcs while keeping the lengths of the external arcs fixed. first subset and second subset of the internal arcs, and repeating step e), adjusting the lengths of the first subset and second subset of the internal arcs while holding the lengths of the first subset and second subset of the external arcs fixed;

h) iterate steps f) and g) until the offsets introduced for the linear polarizations in the first axis (X) and second axis (Y) in each phase shifter cell differ from the offset values determined in step c) by less than first phase error reference threshold;

i) at the central frequency of the first operating band and at the central frequency of the second operating band, determine values of offset corrections, in each phase-shifting cell, for incident waves with circular polarization to the right and left in the reflectarray antenna obtained according to steps d) to h) to separate the collimated or contoured beams in the pointing directions defined in step b);

j) adjust the rotation angles of the external arcs to jointly rotate the external arcs around the center of the split rings, obtaining some rotated external ring arcs, the angle of rotation adjusted independently for each phase shifter cell, being the correction values of phase introduced by the arcs of the external rings rotated in the phases for circular polarizations to the right and to the left equal to those that have been calculated in step i) according to the variable rotation technique at the center frequency of the lower band;

k) adjust the rotation angles of the internal arcs to jointly rotate the internal arcs around the center of the split rings, obtaining some rotated internal ring arcs, the angle of rotation adjusted independently for each phase shifter cell, being the correction values offset introduced by the arcs of the internal rings rotated in the offsets for circular polarizations to the right and left equal to those calculated in step i) according to the technique of variable rotation to the central frequency of the second band of operation; l) adjust the lengths of the rotated external arcs, in each phase shifter cell, using a first rotated coordinate system (X', Y', Z') a first angle with respect to the coordinate system (X, Y, Z) of the step a), to maintain the difference of 180 degrees between the phase shifts for incident waves with linear polarizations along a first rotated axis (X') and a second rotated axis (Y') of the first rotated coordinate system (X ', Y', Z'), where the offsets for linear polarization on the first rotated axis (X') of the first rotated coordinate system (X', Y', Z') are equal to the offsets for linear polarization on the first axis (X) defined in step c), at the center frequency of the first operating band;

m) adjust the lengths of the rotated internal arcs, in each phase shifter cell, using a second rotated coordinate system (X'', Y'', Z'') a second angle with respect to the coordinate system (X, Y, Z) from step a), to maintain the difference of 180 degrees between the phase shifts for incident waves with linear polarizations along a first rotated axis (X”) and a second rotated axis (Y”) of the second coordinate system rotated (X'', Y'', Z''), being the offsets for the linear polarization on the first rotated axis (X”) of the second rotated coordinate system (X'', Y'', Z'') equal to the offsets for the linear polarization in the first axis (X) defined in step c), at the center frequency of the second operating band;

n) check if, for each phase shifter cell, the difference between the phase shift values for incident waves with linear polarizations along the first rotated axis (X') and the second rotated axis (Y') of the first rotated coordinate system ( X', Y', Z') and the offsets for the linear polarization on the first rotated axis (X') of the first rotated coordinate system (X', Y', Z'), at the center frequency of the first band of operation, differ from the values determined in steps l) and c) by less than one second phase error reference threshold, and if the difference between the phase-shift values for incident waves with linear polarizations along the first rotated axis (X”) and of the second rotated axis (Y”) of the second rotated coordinate system (X'', Y'', Z'') and the offsets for linear polarization on the first rotated axis (X”) of the second rotated coordinate system (X'', Y'', Z''), at the center frequency of the second operating band, differ from the values determined in steps m) and c) by less than the second error reference threshold phase;

o) if the differences verified in step n) are equal to or greater than the second phase error reference threshold, repeat step l) adjusting to the central frequency of the first operating band the lengths of the eight external arcs rotated while the lengths of the eight rotated internal arcs are held constant, and repeating step n) adjusting the lengths of the eight rotated internal arcs to the center frequency of the second operating band while keeping the lengths of the eight rotated external arcs constant;

p) iterate steps n) and o) until the offsets introduced in each offset cell for the polarizations in the first rotated axis (X') and second rotated axis (Y') of the first rotated coordinate system (X', Y' , Z') at the center frequency of the first operating band, and the offsets for the polarizations in the first rotated axis (X”) and second rotated axis (Y”) of the second rotated coordinate system (X'', Y '', Z'') at the center frequency of the second operating band, differ from the offset values determined in steps l) and m) by less than the second phase error reference threshold;

q) generating gravure masks for each of the two metallization levels of the reflectarray antenna from the adjusted lengths for the arcs and the adjusted angles of rotation for each split ring in each phase-shifter cell.

The advantages of the present invention compared to the prior state of the art are fundamentally:

- Unlike what happens with the reflectarray described in the previously mentioned article [D. Martínez de Rioja et al., "Dual-band reflectarray to generate two spaced beams in orthogonal circular polarization by variable rotation technique”, IEEE Trans. on Antennas and Propagation, June 2020], the present invention provides a flat reflectarray that allows separation orthogonal beams with circular polarization in two bands, and which also allows collimating or shaping the beams without the need to resort to a bulky parabolic reflector.This is so because the phase-shifting cells used, based on concentric split rings at two metallization levels, they do provide sufficient degrees of freedom to operate in two bands, to separate the circularly polarized beams into those two bands, and furthermore, to collimate or shape the beams.The flat reflectarray of the invention is a conventional low profile reflectarray (thickness in around two millimeters), and it is much easier to manufacture than reflectarrays on parabolic reflectors as it does not require flexible dielectric substrates to be accommodated on a parabolic surface and as it does not require parabolic molds. In fact, it only requires a high-precision flat surface (such as a mold), on which the reflectarray is manufactured, attached to a flat structural sandwich, which ensures the necessary rigidity and meets the mechanical and thermoelastic specifications for an antenna for space use.

- The invention constitutes an interesting alternative to the parabolic reflectors that are usually conventionally used for satellite broadband internet access, since the proposed flat reflectarray antenna is applicable as a multibeam antenna to generate cellular coverage in these scenarios, but at lower cost, with less weight and less volume since the proposed flat reflectarray has a thickness of only a few millimeters. Furthermore, the proposed antenna makes it possible to achieve separation of orthogonal circular polarized beams in two frequency bands for each feeder, which makes it possible to reduce the number of antennas needed by the satellite in this configuration from four parabolic reflectors to two flat reflectarrays.

These and other advantages can be derived in light of the detailed description of the invention that follows.

DESCRIPTION OF THE DRAWINGS

To complement the description that is being made and in order to help a better understanding of the characteristics of the invention, according to a preferred example of its practical embodiment, a set of drawings is attached as an integral part of said description. where, with an illustrative and non-limiting nature, the following has been represented:

Figure 1. Shows a coverage scheme from a geostationary satellite with multibeam antennas that generate four colors, using two different frequency sub-bands in transmission and reception, and two different polarizations for each frequency.

Figure 2. Shows in perspective a flat reflectarray antenna whose phase shifter cells contain eight split rings at two levels of metallization to generate two orthogonal circular polarization beams in two frequency bands, according to a preferred embodiment of the invention.

Figure 3. Disaggregated perspective view of a cell of the flat reflectarray antenna for the separation of circularly polarized beams at two frequencies, made up of two stacked sets of four split conductor rings that are printed on two dielectric layers and the lower layer being on a plane ground conductor, all according to a preferred embodiment of the invention.

Figure 4A.- Shows a plan view of the sets of four split conductor rings printed on the top layer of a reflectarray antenna cell, before the printed rings are rotated to achieve the separation of the two circularly polarized orthogonal beams.

Figure 4B.- Shows a plan view of the sets of four split conductor rings printed in the lower layer of a reflectarray antenna cell, before the printed rings are rotated to achieve the separation of the two circularly polarized orthogonal beams. .

Figure 5A.- Shows a graph with values of the phase of the reflection coefficient at the transmission frequency of a reflectarray cell in a periodic environment for waves with linear polarization X under normal incidence.

Figure 5B.- Shows a graph with phase values of the reflection coefficient at the transmission frequency of a reflectarray cell in a periodic environment for waves with linear polarization and under normal incidence.

Figure 6A.- Shows a graph with phase values of the reflection coefficient at the reception frequency of a reflectarray cell in a periodic environment for waves with linear polarization X under normal incidence.

Figure 6B.- Shows a graph with phase values of the reflection coefficient at the reception frequency of a reflectarray cell in a periodic environment for waves with linear polarization and under normal incidence.

Figure 7A.- Shows a graph with the difference between the phases of the reflection coefficients at the transmission frequency for waves with linear polarizations X and Y, together with the loci of the coordinate points (VXi, 'Vlyo) for the that this phase difference is worth ±180 degrees.

Figure 7B.- Shows a phase curve of the reflection coefficient for linear polarization X at the transmission frequency when traversing the loci shown in Figure 7A.

Figure 8A.- Shows a graph with the difference between the phases of the reflection coefficients at the reception frequency for waves with linear polarizations X and Y, together with the places geometry of the coordinate points ( ^ ux/, ^ V ) for which this phase difference is worth ±180 degrees.

Figure 8B.- Shows a phase curve of the reflection coefficient for linear polarization X at the reception frequency when traversing the loci shown in Figure 8A.

Figure 9A.- Shows a graph with objective phase values of the reflection coefficient of the cells with the printed rings without rotating the reflectarray antenna for X polarization at the transmission frequency. The target phases for bias Y differ from those for bias X by ±180 degrees.

Figure 9B.- Shows a graph with objective phase values of the reflection coefficient of the cells with the printed rings without rotating the reflectarray antenna for X polarization at the reception frequency. The target phases for bias Y differ from those for bias X by ±180 degrees.

Figure 10A.- Shows a graph with the objective phase correction of the reflection coefficients for right-hand circular polarization to be applied to the transmission frequency for the reflectarray antenna designed with non-rotated cells.

Figure 10B.- Shows a graph with the objective phase correction of the reflection coefficients for right-hand circular polarization to be applied to the reception frequency for the reflectarray antenna designed with non-rotated cells.

Figure 11A.- Shows a plan view of the sets of four split conductor rings in the upper layer of a reflectarray antenna cell after being rotated to achieve the separation of circularly polarized orthogonal beams.

Figure 11B.- Shows a plan view of the sets of four split conductor rings in the lower layer of a reflectarray antenna cell after being rotated to achieve the separation of circularly polarized orthogonal beams.

Figure 12A.- Shows a graph with the phase variation of the reflection coefficients at the transmission frequency for circular polarizations to the right of the reflectarray antenna cell under normal incidence.

Figure 12B.- Shows a graph with the phase variation of the reflection coefficients at the transmission frequency for circular polarizations to the left of the reflectarray antenna cell under normal incidence.

Figure 13A.- Shows a graph with the phase variation of the reflection coefficients at the reception frequency for circular polarizations to the right of the reflectarray antenna cell under normal incidence.

Figure 13B.- Shows a graph with the phase variation of the reflection coefficients at the reception frequency for circular polarizations to the left of the reflectarray antenna cell under normal incidence.

Figure 14A.- Shows a schematic representation of the metalization level masks located between the upper and lower layers of the reflectarray antenna shown in Figure 2, according to a preferred embodiment of the invention.

Figure 14B.- Shows a schematic representation of the metalization level masks located on top of the upper layer of the reflectarray antenna shown in Figure 2, according to a preferred embodiment of the invention.

Figure 15A.- Shows the radiation pattern in the elevation plane of the reflectarray antenna at the transmission frequency.

Figure 15B.- Shows the radiation diagram in the elevation plane of the reflectarray antenna at the reception frequency.

Figure 16. Shows a flow diagram of the reflectarray antenna design method with the capacity to separate orthogonal circular polarization beams in two frequency bands, according to a preferred embodiment of the invention.

PREFERRED EMBODIMENT OF THE INVENTION

A detailed explanation of a preferred embodiment of the object of the present invention is provided below, with the help of the figures described above.

What is basically presented is a flat reflectarray type antenna capable of separating left and right circularly polarized beams in two different directions and in two different frequency bands. A possible application of the invention is as a multibeam antenna for sending and receiving data between a satellite and ground stations; for example, for a geostationary satellite that generates cellular coverage with frequency and polarization reuse. The antenna can be built with materials and manufacturing technologies qualified for use in space, such as carbon fiber fabrics pre-impregnated with resins (CFRP materials: "Carbon-Fibre-Reinforced Polymers" in English), to which they add one or several pre-impregnated layers of dielectric fibers, such as Kevlar or quartz and Kapton with photo-etched printed metallizations. This technology is known in the dichroic subreflectors of several scientific missions, such as Cassini, Voyager, Mars-Express, Venus-Express, Bepi Colombo, etc.

Figure 1 schematically shows the coverage from a geostationary satellite with multibeam antennas that generate four colors (A, B, C, D), using two different frequency sub-bands both in transmission, TX, (F /X, F ² TX ) as in reception, RX, (F ¹ RX, F ² RX), and also using two different polarizations, P ¹ and P ² . Each color corresponds to one of these two polarizations, that is, P ¹ or P ² , and to one of the two sub-bands of frequencies in TX and RX, that is, with F / X and F ¹ RX, or with F ² TX and F ² RX. In the state of the art prior to the invention, four parabolic reflectors with multiple feeders have been used in these satellites to generate cell coverage in a certain geographical region, this coverage being made up of a high number of beams (between 50 and 100 ). Each reflector covers the downlink radio in TX (with center frequency around 20 GHz) and the radio uplink in RX (with center frequency around 30 GHz), and is responsible for generating a quarter of the beams. The TX and RX frequency bands are divided into two sub-bands, and each reflector covers one of the two TX and RX sub-bands and one of the two orthogonal polarizations that exist (vertical or horizontal if we speak of linear polarization ; to the right or to the left if we are talking about circular polarization). In this way, beams of four different characteristics are obtained, which are also called colors (A, B, C, D), which are superimposed as shown in Figure 1 to generate coverage without overlapping between the same colors. in the same region (overlapping leading to interference). It is desirable to have reflector antennas capable of generating two colors in TX and RX since this allows the number of antennas on board the satellite to be reduced to two, with the consequent reduction in weight and volume. One way to do this is to design antennas capable of splitting beams into two orthogonal polarizations at two frequencies; that is, capable of generating colors A and C, or colors B and D, in the example of Figure 1. This has already been achieved with planar reflectarrays in the case of linearly polarized beams, and with parabolic reflectarrays in the case of circularly polarized beams, but the flat reflectarray that is proposed to achieve the separation of circularly polarized beams in TX and RX goes one step further, as detailed below.

Figure 2 shows a preferred implementation of the invention, consisting of a flat reflectarray antenna (100) in which the plane that limits the antenna at the top coincides with the XY plane of a coordinate system (X, Y, Z) with origin at the center of the reflectarray (100). This is illuminated by a primary feeder (13), which generates circularly polarized waves to the right and to the left. Typically, the feeder comprises a conical or corrugated horn antenna, preceded by a polarizer and an orthomode transducer. The reflectarray is made up of a flat group of phase-shifting cells (12), also called reflectarray cells, which are responsible for collimating and separating the circularly polarized waves to the right and to the left coming from the feeder (13). The phase-shifting cells are distributed on a rectangular periodic lattice (11) with period pxxPy.

In a preferred embodiment of the invention, the support substrate of the reflectarray (100) is made up of two dielectric layers (15, 16), a first layer or lower dielectric layer (15) and a second layer or upper dielectric layer (16), stacked on a conductive plane (14), also called a ground plane, as indicated in Figure 2. In each layer of the at least two dielectric layers (15, 16) two faces can be distinguished, one on the top and one on the bottom.

Each phase shifter cell consists of two overlapping coplanar sets of four concentric conducting rings, which are split into two equal halves, giving a total of 16 arcs (21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36), as shown in Figure 3, where it is illustrated:

- a first set of four concentric conductive rings divided into two arcs and printed on one of the faces of one of the dielectric layers, which in the example is the upper layer (16); and

- a second set of four concentric conducting rings divided into two arcs and printed on: either the other face of the same dielectric layer, that is, the upper layer (16); or on one of the faces of another of the dielectric layers, which in an example of a reflectarray (100) with two layers (15, 16), would be the lower layer (15).

In a preferred embodiment of the invention, the conductive arcs of the upper ring set are printed on the top face of the upper dielectric layer (16), and the arcs of the lower set of rings are printed on the underside of said upper dielectric layer (16). The lower dielectric layer (15) acts as a separator between the upper dielectric layer (16) metallized on both sides -top and bottom- and the conductive plane (14). As a variant, the conductive arcs can be printed on the upper face of the lower dielectric layer (15) instead of on the lower face of the upper dielectric layer (16). Likewise, the multilayer substrate can contain a third layer of glue between the two dielectric layers (15, 16), or a fourth layer located above the upper dielectric layer (16) that acts as a radome to protect the reflectarray (100). Finally, the separator between the upper dielectric layer (16) and the conductive plane (14), instead of being a solid dielectric, can be a space-qualified honeycomb material. , to reduce the mass of the reflectarray (100).Apart from the previously indicated layers, which are responsible for providing the required offset in the reflected electromagnetic field, the reflectarray antenna (100) can have a series of structural layers, necessary to give it mechanical robustness The different layers, whether they support phase-shifting metallizations or are structural, can be fixed by means of glues, low-loss resins or screws and plastic washers distributed over the entire surface of the flat reflectarray (100).

In a first stage of designing the reflectarray (100), the split conductor rings are arranged as shown in Figures 3, 4A and 4B. Figure 3 shows the arcs (21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36) of a phase shifter cell (12) resulting from the two stacked sets of four split conductor rings that make up the phase shifter cell (12) and that are printed on the two lower and upper dielectric layers (15, 16), the lower dielectric layer (15) being on the conductive plane (14). The four split conductor rings printed on the upper face of the upper dielectric layer (16) and on the lower face of said dielectric layer (16) (or, on the upper face of the lower dielectric layer (15)) are shown respectively in Figures 4A and 4B. The configuration of the reflectarray (100), in this first design stage, with the rings printed, but not yet rotated, allows collimating the left and right circular polarization beams in the same direction without separating them.

Figures 4A and 4B show the mean radii of the four concentric rings, ^{ruo, ruo, r*!} and

^{r*o (ru< r uo<r*<r*o),} the mean radius being the arithmetic mean between the external radius and the internal radius of each ring, and the difference between these two radii being equal to the common width of all rings w . The aforementioned mean radii ^{(ru¡, ruo, r1¡} and r0) are the same in the two sets of rings. Each ring is divided into two arcs of the same length, having also the interstices between these two arcs have the same length, with which, all split rings have a mirror symmetry axis:

- In the set of upper rings (Figure 4A), the axes of mirror symmetry of the first and third outermost rings are parallel to a first axis, the X axis (according to the coordinate system defined in Figure 2), with which , the arcs of these rings (21, 22, 29, 30) are preferably oriented along the X axis. The axes of mirror symmetry of the second and fourth outermost rings are parallel to a second axis, the Y axis, thus which, the arcs of these rings (25, 26, 33, 34) are preferably oriented along the Y axis.

- The orientation of the arches is exactly the opposite in the lower set of rings (Figure 4B). The axes of mirror symmetry of the first and third outermost rings are parallel to the Y axis, their arcs (27, 28, 35, 36) are preferably oriented along the Y axis, while the axes of mirror symmetry of the second and fourth rings The outermost ones are parallel to the X axis and their arcs (23, 24, 31, 32) are preferably oriented along the X axis.

From the set of all arcs (21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36), of the two sets of rings, shown in the Figures 3, 4A and 4B, distinguish:

- The arcs of the two outermost rings of the two sets of rings (21, 22, 23, 24, 25, 26, 27, 28), which are the arcs that are in charge of adjusting the phase of the waves that arrive at each cell in the lower frequency band.

- The arcs of the two innermost rings of the two sets of rings (29, 30, 31, 32, 33, 34, 35, 36), arcs that are responsible for adjusting the phase of the waves that arrive at the cell in the upper frequency band.

And, more specifically, in the lower frequency band:

- Of the set of arcs of the two outermost rings in the two sets of rings (21, 22, 23, 24, 25, 26, 27, 28), which are preferably oriented on the X axis (21, 22, 23, 24) are in charge of adjusting the phase of the linearly polarized waves that arrive at the cell with the incident electric field preferably oriented in the X-Z plane (linear polarization X).

- Of the set of the arcs of the two outermost rings in the two sets of rings (21, 22, 23, 24, 25, 26, 27, 28), which are preferably oriented on the Y axis (25, 26, 27, 28) are responsible for adjusting the phase of linearly polarized waves with the incident electric field preferably oriented along the Y axis (linear Y polarization).

Similarly, in the upper frequency band:

- Of the set of arcs of the two innermost rings in the two sets of rings (29, 30, 31, 32, 33, 34, 35, 36), those that are preferably oriented in the X direction (29, 30, 31, 32) are in charge of adjusting the phase of the incident waves with linear polarization X.

- From the set of arcs of the two innermost rings in the two sets of rings (29, 30, 31, 32, 33, 34, 35, 36), those that are preferably oriented in the Y direction (33, 34, 35, 36) are in charge of adjusting the phase of the incident waves with linear polarization Y.

This means that the phase shifter cell (12) has four arcs (two in the upper set of rings and two in the lower set of rings) to adjust the phase of each linear polarization at each frequency. And also, as we are dealing with two pairs of arcs stacked on two levels, there is a strong coupling between the arcs located in different sets of rings and between their resonances, which guarantees a wide phase range for the cell in the two linear polarizations. and in both frequency bands.

For each phase shifter cell (12), the selection of the periods along the X and Y axes (px , P y ), the selection of the materials of the dielectric layers and the selection of the thicknesses of the lower layers (15 ) and higher (16) (h A , h e ), as represented in Figure 3, is based on the central frequencies of the two operating bands, TX (transmission) and RX (reception), of according to the prior state of the art. For the case considered in this particular implementation, it is assumed that the center frequency of the lower frequency band, TX band, is 19.7 GHz and that the center frequency of the upper frequency band, RX band, is 29.5 GHz. According to these central frequency values of the bands, the material selected for the two dielectric layers has been RT Duroid 5880 with the following characteristics:

- Thickness of 0.787 mm; that is, h A =h e =0.787 mm in Figure 3.

- Being £ ⁰ the electrical permittivity of the vacuum (whose value is 8.8541878x10-12 F/m), the lower dielectric layer (15) and the upper dielectric layer (16) have an electrical permittivity of the same value: £ ^a = £ ^b = 2.33£0.

- The loss tangent in the two layers is tan5=0.001.

In addition, the same period has been taken in the directions of the two axes X and Y px=py=6.5 mm, a width of the rings w=0.2 mm has been taken, and for the mean radii of the rings, it has been taken r ", =1.4mm, r "o =1.8mm, ^h =2.6mm and r0 =3mm. Regarding the angles subtended by the arcs (V ^Xo , V ¹ X¡ , V ^y, , V ^yo , V ^uo , V ^ux/ , Vuy¡, V uyo ) of the four concentric rings from their center, represented in Figures 4A and 4B, these eight angles are scaled for the arcs of the set of internal rings (29, 30, 31,32, 33, 34, 35, 36), in charge of the upper band (of RX, in the example), depending on the angles of the arcs of the set of external rings (21, 22, 23, 24, 25, 26, 27, 28), in charge of the lower band (of TX, in the example), so that V Xo =V X/ , V y,= 0.95V i , V uxo =0.7V ux and V uy= 1.125V uyo . This scaling is not binding, and can be optimized with a view to increasing the bandwidth of the reflectarray (100) in each of its two operating bands, TX and RX, or with a view to reducing the level of radiation cross-polarization emitted in each of the two bands. Once the scaling is done, the four remaining independent angle variables V X/ , V yo , V ux and V uyo are used to adjust the offsets introduced by each phase shifter cell (12) in the design of the reflectarray antenna. (100).

When designing the flat reflectarray (100), the offsets introduced by each phase shifter cell (12) to collimate the beam are calculated assuming that the cell is in a periodic environment, which is known as the "local periodicity assumption". Although the local periodicity assumption is an approximation, its usefulness has been tested by the fact that measurements of reflectarray radiation patterns fabricated on the basis of that approximation have shown good agreement with theoretical predictions. An electromagnetic wave corresponding to a complex electric field vector f ¿ = Eixx Eíyy Eizz falls on a reflectarray cell located in a periodic environment (where Eix , Ei¡y and Eiz are the Cartesian components of the electric field complex of the incident wave; and where x, y, and z are three unit vectors along three axes X, Y, and Z defined in the cell analogously to that defined in Figure 2), and suppose that the wave reflected by the cell in a periodic environment corresponds to a complex electric field ^Er = Erxx Eryy Erzz on the surface of the reflectarray (where Er,x , Er,y and Erz are now the Cartesian components of the complex electric field of the reflected wave). The reflection matrix of the cell for linear polarization, (R ^pl ), is defined as a 2x2 matrix of complex numbers, given by the following relation:

where Rx is the ratio between Er,x and Eix when Et,y is zero; Ry is the ratio between Er,x and Et,y when Ei x is zero; ry. is the ratio between Er,y and Ei x when Ei,y is zero; and finally, Ryy is the ratio between Er,y and Ei¡y when Eix is null. For cells with low level of polarization crossed as the one that appears in Figure 3, it is fulfilled that R ^xy -R ^yx O^, and that |R ^xx |®\R ^yy |®1, being the phases of R ^xx and R ^yy (a R ^xx and R ^yy are known as the reflection coefficients for linear polarization X and linear polarization Y respectively), denoted here as ¿ ^. R ^xx and ¿.R ^yy , which determine the behavior of the phase shifter cell (12) in the reflectarray (100). In fact, is R ^xx the one that determines the contribution of cell (12) to the radiation diagram generated by the reflectarray (100) for an incident wave with linear polarization X (electric field preferably contained in the XZ plane), and ¿ R yy , which determines the contribution of the phase shifter cell (12) to the radiation diagram generated by an incident wave with Y polarization (electric field preferably oriented in the direction of the Y axis).

y cuando ^ ^lx/ =105o y ' ^{V ly o = 95} ° son los que se muestran en las Figuras 6A y 6B respectivamente.If we now consider the phase shifter cell (12) of Figure 3 in the specific case in which the materials and dimensions are chosen as mentioned above, the values obtained for the phases ^¿ R ^xx y ^¿ R ^yy at 19.7 GHz as a function of ' ^{V l} X ⁱ y ^ ^y0 when ^ ux/ =115o and ^V =100° are those shown in Figures 5A and 5B respectively, and the values obtained for the phases ^¿ R ^xx y ^¿ R ^yy to 29.5 GHz depending on

and when ^ ^lx/ =105o and ' ^{V ly o = 95} ° are those shown in Figures 6A and 6B respectively.

Figure 5A shows that the value of the phase ^¿ R ^xx at 19.7 GHz is controlled by the length of the four outermost arcs of the two sets of rings preferentially oriented in the X direction (21, 22, 23, 24), and which is practically independent of the length of the four outermost arcs of the two sets of rings preferably oriented in the Y direction (25, 26, 27, 28). The same can be said of Figure 5B if we exchange

^¿ R ^xx by ¿R ^yy , and if we exchange the arcs oriented in the X direction with the arcs oriented in the Y direction.

Similarly, Figure 6A shows that the value of the phase ^¿ R ^xx at 29.5 GHz is controlled by the length of the four innermost arcs of the two sets of rings preferentially oriented in the X direction (29, 30, 31, 32). , and that it is practically independent of the length of the four innermost arcs of the two sets of rings preferably oriented in the Y direction (33, 34, 35, 36). Again, the same statement holds for Figure 6B if we swap ^¿ R ^xx for ¿R ^yy , and if we swap arcs directed in the X direction for arcs directed in the Y direction.

Therefore, of the 16 arcs (21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36) that the phase shifter cell (12) has in two metalization levels, we have four arcs to control each of the two linear polarizations of the incident waves (X and Y) in each of the two frequency bands (TX and RX).

The phase maps shown in Figures 5 and 6 are sufficient to design reflectarrays capable of focusing X and Y linear polarization beams in the same direction in two frequency bands centered at 19.7 GHz and 29.5 GHz. If we also want the reflectarray to approaching circularly polarized beams, the additional condition ¿Rxx - Ryy =±180o must be imposed so that the circularly polarized wave coming from the feeder is reflected in the reflectarray maintaining the circular polarization direction (to the right or to the left).

Figure 7A represents the phase difference ¿Rxx - Ryy as a function of the angles ^'V lx/ y ^ yo at 19.7 GHz (the difference ¿Rxx - ¿Ryy is obtained from the phase values ¿Rxx y ¿Ryy represented in Figures 5A and 5B), and two curves are shown that clearly indicate the pairs of angle values ⁽ ' ^V lx ^¡ , ^yo) that allow satisfying the condition ¿Rxx - ¿Ryy =±180o. Figure 7B represents the phase curve for ¿Rxx that is described by varying the angle ' ^V lx/ between 70 and 120 degrees and traversing the two curves indicated in Figure 7A. The values of ¿Ryy can be obtained by adding ±180o to those of ¿Rxx ^, according to Figure 7A. The phase range obtained for ¿Rxx is 543 degrees, which is more than enough to design a reflectarray (in this case, circularly polarized). The phase curve for ¿Rxx in Figure 7B does not have large slope changes, which is due to the multiresonant behavior of the stacked outer arcs at two metallization levels in Figure 3 that are preferentially directed in the X direction (21, 22, 23, 24). This smooth behavior of the phase curve for ¿Rxx makes the phase-shifter cell (12) of Fig. 3 a broadband cell for incident waves with X-polarization. The same smooth profile can also be obtained for ¿Ryy (which differs from ¿Rxx by a constant), which is due in this case to the multiresonant behavior of the stacked outer arcs of Fig. 3 directed preferentially in the Y direction (25, 26, 27, 28), which make the cell have a broadband response for incident waves with Y polarization.

The observations made for Figures 7A and 7B at 19.7 GHz can be extended to Figures 8A and 8B at 29.5 GHz. Figure 8A once again shows the two curves that the pairs of angle values (^%, ^ V ) so that the condition ¿Rxx - ¿Ryy = ±180o is fulfilled (in this case ¿Rxx - ¿Ryy has been obtained from the values of ¿Rxx and ¿Ryy represented in Figures 6A and 6B), and thus be able to focus the circularly polarized beam from the feeder without changing the direction of circular polarization, in this case, to 29.5 GHz. Figure 8B gives us the phase curve for z. Rxx as a function of so that the condition zRxx -zRyy =±180o is maintained. Although the phase curve is slightly steeper than that of Figure 7B, a multiresonant behavior is still observed that allows a phase range of 555 degrees to be achieved when varied between 105 and 160 degrees. At 29.5 GHz, the multiresonant behavior of zRxx is due to the preferentially oriented X-direction inner stacked rings of Figure 3 (29, 30, 31,32), and the multiresonant behavior of zR yy , to the preferentially oriented inner stacked rings oriented in the Y direction (33, 34, 35, 36).

The phase shifter cell (12), which has been characterized in Figures 5 to 8, is used to design a reflectarray (100) that focuses circular polarization beams to the right and left in the direction given by the spherical coordinates 0 ^b =11.8oy Qb=0° relative to the coordinate system (X, Y, Z) of Figure 2, both at 19.7 GHz and 29.5 GHz. It is going to be assumed that the reflectarray (100) is circular, and is composed of 1085 cells distributed in a periodic grid of 37x37 square cells in which each cell has a size of 6.5*6.5 mm2. The reflectarray (100) is illuminated by a circular section horn antenna, which radiates an electromagnetic field with double circular polarization, whose phase center is located at the coordinate point (X=-92 mm, Y=0 mm, Z =440.6 mm) with respect to the coordinate system shown in Figure 2. The horn antenna has two input ports, one for right-hand circular polarization, and the other for left-hand circular polarization. The radiation patterns of the two orthogonal circular polarizations are identical, have symmetry of revolution, and are modeled by a function cosq(0), where 0 is the polar angle of a spherical coordinate system originating at the horn phase center. whose z -axis runs along the axis of revolution of the horn antenna. It is true that q=20 at 19.7 GHz, and q=40 at 29.5 GHz. Figure 9A shows the distribution that the zRxx phase must have in the cells (12) of the reflectarray (100) at 19.7 GHz in order to collimate the beam at the previously indicated direction, and Figure 9B shows the distribution that the zRxx phase must have in the cells (12) of the reflectarray (100) at 29.5 GHz. As the reflectarray (100) has to radiate circularly polarized beams, it will be true that the target phases for bias Y differ from the target phases for bias X by ±180o (ie, zRyy =zRxx ±180o), so the phase distributions for zRyy are obtained from those of zRxx following that relationship. In order to adjust the dimensions of the cells (12) to collimate the circular polarization beam at the two frequencies, it is most comfortable to first adjust the angles subtended by the external arcs (21, 22, 23, 24, 25, 26 , 27, 28) at 19.7 GHz to achieve the phase distribution of Figure 9A, assuming no internal arcs are present. This is so because the internal arcs do not substantially affect the values of the phases at the lower frequency because they have lengths much lower than half a wavelength at that frequency (which would be the resonant length), with which their presence at 19.7 GHz is not absolutely necessary. Once the dimensions of the outer arcs have been adjusted, the angles subtended by the inner arcs (29, 30, 31, 32, 33, 34, 35, 36) are adjusted at 29.5 GHz to achieve the phase distribution of Figure 9B, and this adjustment is carried out in the presence of the external arcs with the dimensions previously obtained at 19.7 GHz. It is necessary to proceed like this because at 29.5 GHz the external arcs are strongly coupled to the internal arcs, and the values of the phases z. Rxx and zRyy at that frequency strongly depend on both the dimensions of the internal arcs and the dimensions of the external arcs. When the coarse adjustment of the dimensions of the external arcs at 19.7 GHz and of the internal arcs at 29.5 GHz has been completed, it is convenient to do a fine adjustment of the dimensions of the external arcs at 19.7 GHz in the presence of the internal arcs obtained in first iteration at 29.5 GHz, and also, a fine adjustment of the dimensions of the internal arcs at 29.5 GHz in the presence of the external arcs obtained in the second iteration at 19.7 GHz. The simulations carried out show that the adjustment process of the dimensions of the arcs at 19.7 GHz and 29.5 GHz converge after this second iteration.

Once the first design stage of the reflectarray (100) has been described to emit circular polarization beams to the right and left at 19.7 GHz (TX) and at 29.5 GHz (RX) in a certain direction given by the spherical coordinates 6b and t and b, it is passed to a second design stage whose objective is to separate the left and right circular polarization beams obtained in the first stage in two different directions, both at 19.7 GHz and 29.5 GHz. To describe this second design stage, it is necessary to previously introduce the concept of a reflection matrix of a reflectarray cell for circular polarization, which plays in circularly polarized reflectarrays a role analogous to that played by the reflection matrix of equation (1) in linearly polarized reflectarrays. Suppose that an electromagnetic wave is incident on a reflectarray cell located in a periodic environment whose complex electric field is Et = EiPCDüPCD EiP CIu PCI on the surface of the reflectarray, where E, , ^pcd is the component of the incident electric field corresponding to a circularly polarized wave. to the right, and E, , ^pci , the component of the incident electric field corresponding to a left circularly polarized wave ( " ^pcd and " ^pci are complex unit vectors used to indicate the direction of the fields of right and left circularly polarized waves respectively ). Let us also suppose that the wave reflected by the cell in a periodic environment corresponds to a complex electric field that has the value ^Er = Er PCDüPCD £V, ^pcimpci on the surface of the reflectarray (again, Er,pcD would represent the component of the reflected electric field corresponding to a right-hand circularly polarized wave, and E,, ^pci , the component of the reflected electric field corresponding to a left-hand circularly polarized wave). The reflection matrix of the cell for circular polarization, (R ^pc ), is defined as a 2x2 matrix of complex numbers, given by the following relation:

where R ^pcd , ^pcd is the ratio between Er PCD and E¿ PCD when E¿ PCI is null; R ^pcd , ^pci is the ratio between Er PCD and E¿ PCI when EiPCD is zero; R ^pci , ^pcd is the ratio between Er PCI and E¿ PCD when E¿ PCI is zero; and finally, R ^pci , ^pci is the ratio between Er PCI and E¿ PCI when E¿ PCD is zero. In the same way that the phases ¿.Rxx and ¿ Ryy are the ones that control the contribution of each phase shifter cell in a linear polarization reflectarray, the phases ¿R ^pcd , ^{pcd ,} and ¿R ^pci , ^pci are the ones that control the contribution of each phase shifter cell into a circular polarization reflectarray. In fact, the phase ¿R ^pcd , ^pcd is the one that determines the contribution of the cell to the radiation pattern generated by a reflectarray for an incident wave with right-hand circular polarization, and ¿R ^pci , ^pci plays that role for the cell in a reflectarray on which a wave with circular polarization to the left is incident.

The Rotation Variable (TRV) technique for the design of circularly polarized reflectarrays tells us that if the cell metallizations of a reflectarray are rotated through an angle a about an axis passing through the center of the cell (a>0 if the rotation is performed counterclockwise for an observer looking towards the surface of the reflectarray, and a<0 if the rotation is performed clockwise), a variation in the phase of R ^pcd , ^pcd is produced for that cell given by A( zRpcD,pcD)=2a, and a variation in the phase of R ^pci , ^pci given by A(zRpci,pci)=-2a. However, these variations of ¿R ^pcd , ^pcd and ¿R ^pci , ^pci only hold strictly speaking if it is verified that the difference between ¿.Rxx and ¿ Ryy (that is, between the phases of the diagonal coefficients of the cell reflection matrix for linear polarization) is equal to ±180o in the coordinate system rotated by an angle a in the cell.

Going back to the embodiment of the reflectarray (100) which was designed to focus left and right circular polarization beams in the direction given by the spherical coordinates db=11.8° and Qb=0° in Figure 2 at 19.7 GHz and at 29.5 GHz , we proceed to modify the cells (12) of this reflectarray by means of the TRV so that at 19.7 GHz the circular polarization beam to the right starts to point in the direction 0b,pcD=13.7° and ^b,pcD =0o (what which means that variations A0b=+1.9o and A^b=0o occur in the angles that give the pointing direction for this beam), and so that the left-hand circularly polarized beam becomes pointing in the direction Q b ,pci=9.9oy <p b ,pci=0o (which means that again AQ variations occur b = -1.9o and A ^ b =0o in the angles that give the pointing direction for that second beam). In addition, TRV is applied a second time so that at 29.5 GHz the clockwise circular polarization beam starts pointing in the direction 0 b ,pcD=9.9° and ^ b ,pcD =0o (AQ b =-1.9oy A ^ b =0° for this beam), and so that the left-biased beam starts pointing in the direction Q b ,pci=13.7o and Q b ,pci=0o (AQ b =+1.9o and A ^ b =0o for that second beam). In order to point left and right circularly polarized beams in directions other than 19.7 and 29.5 GHz, it is necessary that TRV can be applied independently at those two frequencies. Figure 10A shows the variations in the phases of ¿R ^pcd , ^pcd (A( ^z R ^pcd , ^pcd ), where R ^pcd , ^pcd is the reflection coefficient for right-hand circular polarization) that must be added in the phase-shifting cells (12 ) of the previously designed reflectarray antenna (100) (the one that focused the circularly polarized beams to the right and to the left in the direction Q b =11.8o and Q b =0o following the phase distribution shown in Figs. 9A and 9B) to that the pointing direction of the clockwise circular polarization becomes Q b ,pcD=13.7o and Q b , ^pcd =0o at 19.7 GHz. The required variations in ^z R ^pci , ^pci (R ^pci , ^pci is the reflection coefficient for left circular polarization) are equal in absolute value and opposite in sign to those of Fig. 10A (that is, A( ^z R ^pci , ^pci )=- A( ^z R ^pcd , ^pcd )) if we want the direction pointing point of the circular polarization to the left becomes Q b ,pci=9.9o and Q b ,pci=0o at 19.7 GHz. This is so because the values of AQb that have been imposed on the beams of the two orthogonal circular polarizations have contrary signs. Figure 10B shows the values of A( ^z R ^pcd , ^pcd ) that are required for the clockwise circular polarization pointing direction to become Q b ,pcD=9.9o and Q b ,pcD =0o at 29.5 GHz. Again, for the pointing direction of the left circular polarization to become Q b ,pcD=13.7o and Q b ,pcD =0o at 29.5 GHz, it is necessary to choose the values of A( ^z R ^pci , ^pci ) equal in absolute value and with the opposite sign to the values of A( ^z R ^pcd , ^pcd ) in Figure 10B (remember that in this case the values of AQb for the two orthogonal circular polarizations are once again equal and with opposite signs).

Starting from the reflectarray (100) designed with the cells (12) of Figure 3 to focus circularly polarized beams in the direction Q b =11.8o and Q b =0o, the phase corrections of Figures 10A and 10B are implemented using of the TRV. To achieve the phase correction of Figure 10A, in each phase shifter cell (12) the eight arcs of the two outermost rings of the two sets of rings of Figures 4A and 4B (21,22, 23, 24, 25, 26, 27, 28) since it is these rings that control the operation of the reflectarray (100) at 19.7 GHz. As shown in Figures 11A and 11B, the axes of mirror symmetry of the rotated outer rings (41, 42, 43, 44, 45, 46, 47, 48) come to align with the axes of a new rotated coordinate system (X', Y', Z'). According to TRV theory, this rotation gives rise to a phase correction of the reflection matrix coefficients for circular polarization given by A(¿RpcD,pcD)=2a i and by A(¿R pci , ^{pci )} =-A( ^z R ^pcd , ^pcd ) if it is true that zR xx -R yy =±180°. That is, the coefficients of the diagonal of the reflection matrix for linear polarization must be out of phase in the rotated coordinate system (X', Y', Z'), not in the original coordinate system of Figure 2. From According to this result, if we choose in each cell (12) ^{a /} = A(¿R ^pcd , ^pcd ) / 2 such that A( ^z R ^pcd , ^pcd ) is the phase correction shown in Figure 10A, and In addition, it is forced to fulfill that ¿R xx' -R yy =±180o, it is possible to deviate the circular polarization beams to the right and left in the required directions at 19.7 GHz. Similarly, to obtain the values of A( R ^pcd , ^pcd ) appearing in Figure 10B, ^the eight arcs of the two innermost rings of the two sets of rings of Figs. 4A and 4B (29, 30, 31, 32, 33, 34, 35, 36) since those eight arcs are the ones used to control the operation of the reflectarray (100) at 29.5 GHz. Again, Figures 11A and 11B show us that the axes of mirror symmetry of the rotated internal rings (49, 50, 51, 52, 53, 54, 55, 56) become aligned with the axes of a new rotated coordinate system (X'', Y '',Z''). And in agreement once more with the TRV, this rotation introduces corrections in the coefficients of the reflection matrix for circular polarization given by A(zRpcD,pcD)=2a u and by A( z R pci , pci ) = ^{- A ( z} R ^pcd , ^pcd ), provided that ^¿ - ^{R rx -} zR yy = ±180o (where ^{¿ R xx -} e ^{¿ .R yy} refer to the second rotated coordinate system (X'', Y '' , Z'')). Therefore, if in each cell (12) the angle ^au is chosen equal to A(¿R ^pcd , ^pcd ) / 2 so that A(¿R ^pcd , ^pcd ) is now the phase correction shown in Figure 10B, and it is also forced that zR x ” x ”-¿R yy =±180o, it is possible to deviate the circular polarization beams to the right and left in the required directions at 29.5 GHz.

Figures 12A and 12B show the values of the phase corrections A(¿R ^pcd , ^pcd ) and A( ^z R ^pci , ^pci ) obtained at 19.7 GHz for the cell in Figures 11A and 11B as a function of the angles of rotation ^{a /} and ^au of the external and internal arcs respectively. In these figures, the values ^ ux/ y have always remained constant (meaning that the lengths of the internal arcs are constant), and are given by ^ ux/ =115o and ^V = 100o. Instead, the values of ^{'V /x} y ^ y0 have been modified for each pair of values of ^ai and ^au in such a way that the condition ^{¿ R xx - ¿ R yy = ± 180 °} imposed by the TRV is always satisfied. It is observed that A(¿R ^pcd , ^pcd ) increases linearly with the angle of rotation ^ai and that A(¿R ^pci , ^pci ) decreases linearly with ^ai according to the TRV prediction. Also, the arcs and their rotations have little effect on the values of A( ¿R ^pcd , ^pcd ) and A( ¿R ^pci , ^pci ) at the lower frequency (19.7 GHz), since their lengths are much less than the resonance length ( half wavelength at 19.7 GHz). The situation is similar in Figures 13A and 13B. In this case, the values of the phase corrections A( ¿R ^pcd , ^pcd ) and A( ¿R ^pci , ^pci ) obtained at the higher frequency (29.5 GHz) for the cell of Figures 11A and 11B are represented in function of the angles of rotation ^ai and ^au. In Figures 13A and 13B the lengths of the external arcs have been taken constant so that ^x/=105o and ^yo=95°. And the values of ^u»y have been adjusted for each pair of values of ^ai and ^au in order to satisfy the condition ¿Rx”x”-¿R yy=±180o imposed by the TRV. Unlike what occurs in Figures 12A and 12B, the rotations of the external arcs do have some influence on the values of A( ¿R ^pcd , ^pcd ) and A( ¿R ^pci , ^pci ). However, it still holds that A( ¿R ^pcd , ^pcd ) increases with the second angle of rotation ^au, that A( ¿R ^pci , ^pci ) decreases with ^au, and that A( ¿R ^pci , ^pci )=-A ( ¿R ^pcd , ^pcd ), whereby the values of A( ¿R ^pcd , ^pcd ) of Fig. 10B can be adjusted to 29.5 GHz using ^{au, 'V uxi} y for fixed values of ^{a , ' V lXi} and ^i.

de cada celda a 29.5 GHz hasta que se satisfaga la condición zRx”x”-¿R yy=±180o en el segundo sistema de coordenadas rotado, y hasta que ^{¿ R x-x -} tome en cada celda el valor asignado en la Figura 9B (de nuevo, se vuelve a cumplir que ^{¿ R x x '} en la celda rotada coincide con ¿R ^pcd,^pcd en la celda sin rotar si ¿Rxx'-¿Ryy=±180o). Durante los ajustes de los arcos internos a 29.5 GHz, se mantienen las rotaciones y las longitudes de los arcos externos ajustadas previamente a 19.7 GHz para conseguir la separación de haces a esa frecuencia. A continuación, se inicia una segunda iteración en la que se vuelven a ajustar a 19.7 GHz los valores de ^{'V lXi} y ^ y 0 para obligar que se cumpla que ¿Rxx'-¿Ryy=±180o y que The results of Figures 9A, 9B, 10A, 10B, 12A, 12B, 13A and 13B provide the strategy for designing the reflectarray (10) with split left and right circular polarization beams at 19.7 and 29.5 GHz. Starting from the design for collimated beams of circular polarization to the right and to the left in a single direction based on the unrotated cell (12) of Figure 3 and on the phase distributions of Figures 9A and 9B, one begins by rotating the outer arcs (41, 42 , 43, 44, 45, 46, 47, 48) of each reflectarray cell an angle apA(zRpcD,pcD)/2, taking for this the values of A( ¿R ^pcd , ^pcd ) that appear in Figure 10A. Next, the angles ^{'V lXi} and ^yo of each cell are adjusted at 19.7 GHz until the condition ¿Rxx'-¿Ryy=±180o is satisfied in the first coordinate system rotated by an angle ^{a ,} and until ^{¿R xx} takes in each cell the value assigned in Figure 9A since it can be shown that ^{¿R xx} for the rotated cell coincides with the value that ¿R pcd,pcd has before rotating the cell if it is true that ¿Rxx'-¿ Ryy =±180o. During the whole process of adjusting the external arcs, the internal arcs of the cells (49, 50, 51, 52, 53, 54, 55, 56) remain unrotated, and their lengths remain unchanged. Once the adjustments to 19.7 GHz are finished, the internal arcs are rotated by an angle au=A(¿RpcD,pcD)/2, making use of the values of A( ¿R ^pcd , ^pcd ) that appear in Figure 10B. Once these rotations are finished, the angles are adjusted

of each cell at 29.5 GHz until the condition zRx”x”-¿R yy=±180o in the second rotated coordinate system is satisfied, and until ¿R xx - ^takes on each cell the value assigned in Figure 9B ( again, it is true that ^{¿R xx '} in the rotated cell coincides with ¿R ^pcd , ^pcd in the unrotated cell if ¿Rxx'-¿Ry y =±180o). During the For internal arc settings at 29.5 GHz, the rotations and lengths of the external arcs previously set at 19.7 GHz are maintained to achieve beam separation at that frequency. Next, a second iteration is started in which the values of ^{'V lXi} y ^ y 0 are adjusted again to 19.7 GHz to force that ¿Rxx'-¿Ryy=±180o and that

^yo obtenidos al terminar los ajustes a 19.7 GHz durante la segunda iteración. Las simulaciones realizadas muestran que dos iteraciones son suficientes para llegar a los valores de ^{a¡, au, 'V lx¡,} ^yo, ^ ux/ y

que se necesitan en cada celda del reflectarray para que A(¿R ^pcd,^pcd ) alcance los valores fijados en las Figuras 10A y 10B (y por extensión, los de A(¿R ^pci,^pci ) = - A(¿R ^pcd,^pcd )), para que ¿Rxx'-¿Ryy=±180o y ^{¿ R x x '} tome los valores fijados en la Figura 9A, y para que ¿Rx”x"-¿Ryy=±180o y ^{¿ R x x} tome los valores fijados en la Figura 9B. ^{¿R xx} takes the value assigned in Figure 9A, all this maintaining the values of ^{a , au,} and ^{'V uyo} obtained at the end of the first iteration. And once the adjustments at 19.7 GHz have been completed, the angles ^ ux/ y are adjusted again at 29.5 GHz to satisfy in each cell that ^{¿ R w -} zRyy=±180° and that ^{¿ R xx} takes the value assigned in Figure 9B, all this without changing the values of ^{a , au,}

^I obtained by finishing adjustments to 19.7 GHz during the second iteration. The simulations carried out show that two iterations are enough to arrive at the values of ^{a¡, au, 'V lx¡,} ^yo, ^ ux/ and

that are needed in each cell of the reflectarray for A( ¿R ^pcd , ^pcd ) to reach the values given in Figures 10A and 10B (and by extension, those of A( ¿R ^pci , ^pci ) = - A( ¿R ^pcd , ^pcd )), so that ¿Rxx'-¿Ryy=±180o and ^{¿R xx '} take the values fixed in Figure 9A, and so that ¿Rx”x"-¿Ryy=±180o and ^{¿R xx} take the values set in Figure 9B.

The design strategy of the reflectarray antenna capable of separating left and right circular polarization beams in two different directions and in two different frequency bands has been divided into two stages, a first stage using eight split ring cells stacked without rotating and is oriented towards focusing the orthogonal circular polarization beams in the same direction at two frequencies, and a second stage in which the eight stacked split rings in each cell rotate in order to separate the two orthogonal circular polarization beams in two directions. different at two different frequencies. While it is true that the first stage can be omitted and the design can be attacked directly from the second stage, it is convenient to include the first stage in the design because it provides a good starting point for the execution of the second stage, and makes the implementation of the second stage much easier. convergence of this second stage.

Once the design of the reflectarray (100) has been completed and the required values of ^{to ,}

^ow, ^X, have been adjusted for each cell, the reflectarray (100) can proceed to the manufacturing phase. From a file containing the values of the radii of the arcs, the lengths of the arcs and the angles of rotation for each cell, the gravure masks can be generated for each of the two levels of metallization. For the manufacture of the reflectarray (100), these masks can be printed on the two dielectric layers of Figures 2 and 3 (either on the two faces of the layer

(16), or on the upper faces of the lower (15) and upper (16) layers) using conventional photo-etching techniques, and the two layers can be bonded together using curing ovens. Figures 14A and 14B show the masks for the two levels of metallization of the design carried out in this specific embodiment of the invention.

Figures 15A and 15B show the results obtained for the elevation cuts (X-Z plane of Figure 2) of the radiation diagrams of the design carried out in this example of the invention. It is observed that the specifications required for the reflectarray antenna (100) designed have been met. Specifically, at 19.7 GHz the main beam with right-hand circular polarization has its maximum at 13.7o, and the left-hand circularly polarized beam has its maximum at 9.9o. At 29.5 GHz just the opposite occurs, and while the maximum of the clockwise circularly polarized beam occurs at 9.9o, the maximum of the left-handed circularly polarized beam occurs at 13.7o. This swapping of the directions of the orthogonal circular polarized beams in the TX and RX bands is useful because it helps to reduce interference. The gains of the two beams at 19.7 GHz are around 32 dBi, and those of the 29.5 GHz beams are around 35 dBi. If desired, the gains can be matched on both bands. To do this, it is enough to reduce the gains at 29.5 GHz by 3 dB using a selective phase correction technique. In this technique, in a randomly chosen set of cells in a fringe along the edge of the reflectarray (100), the lengths of the internal arcs at 29.5 GHz are adjusted so that ^{y R x v - ^ R y y} not be worth ±180 degrees but 0 degrees, with which, the radiation of these cells interferes destructively with that of the cells for which ^{y R x - x - ^ R y y} it has been maintained at ±180 degrees, and this brings with it a reduction in the effective area of the antenna at 29.5 GHz, and consequently, a reduction in the gains of the beams at that frequency. The selective phase correction technique in the upper frequency band allows equalizing the gain and beamwidth in the two frequency bands, which is desirable in multibeam antennas designed to generate multicellular coverage from communication satellites operating in two bands. of frequency. Depending on the shape of the reflectarray (100), the strip next to the edge where the selective phase correction is carried out will have the shape of a rectangular ring if the reflectarray (100) is rectangular, or an annulus shape if the reflectarray has circular shape as is the case of the example used in this embodiment. In Figures 15A and 15B it can be seen that the side lobes are about 20 dB below the main lobes, and that the cross-polar radiation levels are always at least 30 dB below the co-polar radiation maximum, indicating that the cell The reflectarray antenna (12) introduced in Figures 11A and 11B is a cell with low level of cross-polarization. Finally, the aperture efficiencies of the radiated beams are around 65% at 19.7 GHz, and around 59% at 29.5 GHz.

Figure 16 shows a flowchart detailing all the steps that must be followed to design the reflectarray antenna (100) capable of separating orthogonal circular polarization beams in two frequency bands, which is the object of this invention. Those steps are:

a) Definition (60) of the reflectarray antenna (100). The general properties of the antenna to be designed are defined, such as the shape of the contour that limits the grid (11) (rectangular, circular, elliptical, etc.), dimensions, period of the unit cell (12) of the grid (pxxPy in Figure 3), characteristics of the dielectric layers of the substrate (thickness, permittivity and loss tangent), width and average radius of the eight split rings that are part of the phase shifter cells, type of feeder and position of its center of phase, etc.

b) Definition (61) of the pointing directions (01=0b+A0b,^b) and (02=0b-A0b,^b) of the two circular polarization beams to the right and left of the antenna in spherical coordinates, as well as the lower, f, and upper center frequencies, ^fu, of its two operating bands in TX and RX.

c) Both at the lower frequency ^fl and at the higher frequency ^fu , determine the ideal distribution of phase shifts (62) for incident waves with linear polarizations X (incident electric field preferentially oriented in the XZ plane) and Y (incident electric field preferentially oriented to along the Y axis), ^{z R xx} yz ^Ryy (see Figures 9A and 9B), which cells must introduce for the antenna to be capable of collimating circularly polarized beams in a direction intermediate to the pointing directions of the beams. that are to be separated (this intermediate direction is given by the ^{angular spherical coordinates (} 0 ^b=( 01 ^{+ & )/} 2 ^{, $ b )), having that z Rxx - z R yy} =±180o to maintain the direction of circular polarization when the wave coming from the feeder is reflected by the antenna. More specifically, if the reflectarray (100) consists of ^N phase-shifting cells (12), ^dj is the distance from the phase center of the feeder to the center of the jth cell j= 1,...,N ) y ^{( X = X j,Y = y )} are the coordinates of the center of said j-th cell with respect to the coordinate system (X, Y, Z) defined in the reflectarray (100) (see Figure 2), the values of ^{z R xx} y ^{z R yy} for the jth cell at the lower frequency f will be given by:

where ^{z R x x} and ^{z R y y} are calculated in radians in (3) and in (4), and where ^c is the speed of light in free space. In turn, the values of ^{z R x x} and ^{z R y y} for the jth cell at the higher frequency ^fu will be given by:

d) Adjustment in each phase-shifting cell (12) of the lengths of the outermost arcs at the lower frequency ^{f i} (63). Specifically:

- the lengths of the four outermost arcs of the split rings in the X direction (21, 22, 23, 24) are fitted to obtain the z values. ^Rxx calculated in step c); and

- the lengths of the four outermost arcs of the split rings in the Y direction (25, 26, 27, 28) are adjusted to obtain the values of ^{z R y y} calculated in step c).

e) Adjustment in each phase-shifting cell (12) of the lengths of the most internal arcs at the higher frequency ^fu (64). Specifically:

- the lengths of the four innermost arcs of the split rings in the X direction (29, 30, 31, 32) are adjusted to obtain the values of ^{z R xx} calculated in step c); and

- the lengths of the four innermost arcs of the split rings in the Y direction (33,34,35,36) are adjusted to obtain the values of ^{z R y y} calculated in step c).

f) Check (65A) for each phase shifter cell (12) if the values of ^{z R x x} and ^{z R y y} obtained to ^{f i} and ^fu in steps d) and e) differ from the values calculated in step c) by less than a first reference threshold error, which is typically taken to be equal to 5 degrees. In other words, check that the values of ^{z R x x} and ^{z R y y} converge to the required values at ^F and ^fu within a margin of error.

g) If the errors obtained in step f) are above (65B) the first threshold value, repeat step d) adjusting to the lower frequency ^F the lengths of the eight outermost arcs while holding the lengths of the eight innermost arcs fixed, and also repeat step e), adjusting to the higher frequency ^fu the lengths of the eight innermost arcs while holding the lengths of the eight outermost arcs fixed.

h) Iterate steps f) and g) as many times as necessary until the values of ^{z R x x} and

^{z R y y} at lower frequencies ^F and above ^fu in each cell (12) differ from the ideal values obtained in step c) by an amount less than the threshold error established in step f).

i) At both the lower frequency ^f and the higher frequency ^fu, determine the ideal distribution of lag corrections (66) for left and right circularly polarized waves, A(¿R ^pcd , ^pcd ) and A(¿R ^pci , ^pci )=- A(¿R ^pcd , ^pcd ) (see Figures 10A and 10B), which must be introduced into the phase shifter cells (12) of the reflectarray (100) designed in steps d) to h) so that said reflectarray (100) can separate the orthogonal circular polarization beams in the pointing directions ( ⁰¹ , ^b ) and ( ⁰² , ^b ) defined in step b).

j) Adjustment of the angles of rotation of the outermost arches (67). The eight outermost arcs of the split rings (21, 22, 23, 24, 25, 26, 27, 28) of each cell (12) are rotated jointly by an angle a= A(¿R pcd , pcd ) ^{/ 2} a the lower frequency ^f (A( ^z R ^pcd , ^pcd ) a ^fi is the one obtained in step i)) so that the reflectarray can achieve the separation of left and right circular polarization beams according to the technique of variable rotation in the lower frequency band.

k) Adjustment of the angles of rotation of the most internal arches (68). The eight innermost arcs of the split rings (29, 30, 31, 32, 33, 34, 35, 36) of each cell (12) are rotated jointly by an angle to u = A(¿R pcd , pcd ^{) /} 2 at the frequency ^fu (A( ^z R ^pcd , ^pcd ) a ^fu is the one obtained in step i)) so that the reflectarray can achieve the separation of left and right circular polarization beams according to the technique of variable rotation in the upper frequency band.

l) Adjustment of the lengths of the external rotated arcs (69). A coordinate system rotated by an angle to l (X', Y ', Z ') is defined in each phase shifter cell (12) and the lengths of the eight outermost rotated arcs are slightly readjusted (41, 42, 43, 44, 45, 46, 47, 48) to get ¿ Rxx - Ryy =±180 or and ^{¿ R xx '} in the cell to match the value of ^{¿ R xx} defined in step c) before the arcs were rotated , all at the frequency ^fi .

m) Adjustment of the lengths of the rotated internal arcs (70). A coordinate system rotated by an angle to u (X'', Y '', Z '') is defined in each cell and the lengths of the eight innermost rotated arcs are slightly readjusted (49, 50, 51, 52, 53 , 54, 55, 56) to get ¿R x ” x" -R y ” y ”=±180 or and ^{¿R xx} in the cell to match the value of ^{¿R xx} defined in step c) above that the arcs were rotated, all at the frequency ^fu.

n) Verify (71A) that the conditions required in section l) for ^{¿ R x x - ¿ R y y} and

^{R x x ,} and in section m) for ^{¿ R x - x - ¿ R y y} and ^{R x-x-,} they are fulfilled in each phase-shifting cell within a second margin of error established a priori, which is usually taken to be equal to five degrees. In other words, check that the values of ^{R x x -}

^{¿R y y', ¿R x x', ¿R x - x' - ¿R y y} and ^Rx"x" converge to the required values at ^F and ^fu within a margin of error.

o) If the errors obtained in step n) for ^{¿R x x -R y y , ¿R x x , ¿R x " x - ¿R y y} and ^{R x x} are higher (71B) than the preset values, repeat step l) resetting to ^{f i} the lengths of the eight rotated outermost arcs (41, 42, 43, 44, 45, 46, 47, 48) while holding the lengths of the eight rotated innermost arcs constant (49, 50, 51, 52, 53, 54, 55, 56), and also repeat step n) resetting to ^fu the lengths of the eight innermost arcs rotated while holding the lengths of the eight rotated outermost arcs constant.

p) Iterate steps n) and o) as many times as necessary until obtaining that in each cell (12), both the values of ^{¿ R x x - ¿ R y y} and ^{R x x} to the lower frequency ^{f i} as the values of ^{¿ R x " x - ¿ R y y} and ^{R x x} at the higher frequency ^fu, differ from the values set in steps l) and m) by an amount less than the second phase error set in step n).

q) Generate (72) the photo-etched masks, typically in CAD files ("Computer Aided Design" in English), for each of the levels of metallization of the reflectarray antenna (100) from the dimensions obtained for the arcs in each phase-shifter cell and from the angles of rotation of these arcs, print the split rings on the dielectric layers of the substrate using conventional photo-engraving or additive manufacturing techniques, glue the different layers to form the reflectarray antenna (100), and assemble this antenna with its feeder by means of a support.

In order to minimize the level of cross-polarization and maximize the bandwidth in the two operating bands of the reflectarray antenna (100), the design method also includes the following additional steps:

- After step h) the following step is added:

• Readjust in each cell (12) the lengths of the eight arcs that control the offsets in each of the two frequency bands by means of an optimization routine, so that the offsets required for X and Y linear polarizations when collimating left and right circularly polarized beams in the intermediate direction described in step c) are not only obtained at the center frequency of each band (lower frequency ^F and higher frequency ^fu) but also at the extreme frequencies of these bands.

- After step p) the following two steps are added:

• Readjust in each cell (12) the lengths of the eight rotated arcs with the largest radius by means of an optimization routine so that the required offsets for the polarizations in the first rotated coordinate system X ’ and Y ’ hold not only at the center frequency of the lower band (frequency f) but also at the extreme frequencies of said band.

• Readjust in each cell (12) the lengths of the eight rotated arcs of smaller radius by means of an optimization routine so that the offsets required for the polarizations in the second rotated coordinate system X'' and Y '' are not only met to the center frequency of the upper band (frequency ^fu) but also at the extreme frequencies of said band.

In another possible embodiment, the design method makes it possible to obtain a reflectarray antenna (100) with circular polarization beam spacing that operates in more than two frequency bands. For it:

- Step a) is modified so that each cell (12) of the reflectarray antenna (100) includes four new split concentric rings (two for each set of coplanar rings) for each new additional frequency band.

- The distributions of phase shifts in the X and Y polarizations are determined in step c) for each additional frequency band.

- After step e), a new step is added for each additional frequency band consisting of the adjustment in each cell (12) of the lengths of the eight arcs corresponding to that additional band to obtain the phase shifts of the X and Y polarizations. which are calculated in step c) at the center frequency of the new band.

- After step k), a new step is added for each additional frequency band consisting of the rotation in each cell of the eight arcs corresponding to that additional band so that the corrections introduced by the eight rotated arcs in the circular polarizations a The right and left coincide with those calculated in step i) according to the variable rotation technique, all at the central frequency of each additional band.

- And after step m), the lengths of the eight arcs corresponding to the additional frequency band are readjusted in each cell (12) in such a way that the difference of 180 degrees is achieved between the phase shifts for incident waves with linear polarizations along along the orthogonal directions coplanar with the reflectarray antenna (100) in the new rotated coordinate system, and such that the phase offset for linear polarization in each of those rotated orthogonal directions matches that prescribed in step c) for non-rotated directions, all at the center frequency of each additional band.

In another possible embodiment, the design method makes it possible to obtain a reflectarray antenna (100) with separation of circularly polarized contoured beams in at least two frequency bands. To do this, the lengths of the arcs corresponding to each of the frequency bands in which the reflectarray antenna (100) operates are adjusted in each cell (12) as indicated in steps c) to h) to achieve the offsets that allow emitting circularly polarized contoured beams instead of collimated beams in the intermediate direction described in step c), contoured beams that are later separated into two circularly polarized contoured beams to the right and left by rotating the aforementioned arcs and by the readjustment of their lengths following the procedure previously described in steps i) to p).

Claims (9)

1. A flat reflectarray antenna (100) comprising: - A feeder (13) to generate waves with a circular polarization to the right and to the left, each wave corresponding to a complex electric field with an electric field component in a first coordinate axis and an electric field component in a second axis orthogonal to the first coordinate axis; - a group of phase-shifting cells (12) arranged on a flat grid (11) that reflects the waves generated by the feeder (13), where each phase-shifting cell (12) comprises a conducting plane (14) and a plurality of dielectric layers ( 15, 16) superimposed on the conductive plane (14); characterized in that each phase shifter cell (12) also comprises two superimposed sets of four concentric conductive rings divided into two arcs each set, having a total of sixteen arcs (21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36), where a first set of four conductive rings divided into two arcs is printed on one side of an upper layer (16) of the plurality of dielectric layers (15, 16) , and where a second set of four conductive rings divided into two arcs is printed on the opposite face of the upper layer (16) or on a face of a lower layer (15) of the plurality of dielectric layers (15, 16); where in each phase shifter cell (12): - eight arcs of the external rings (21, 22, 23, 24, 25, 26, 27, 28) have lengths to adjust in phase the waves generated by the feeder (13) that are reflected in each phase shifter cell (12) maintaining the sense of circular polarization after reflection at the center frequency of a first operating band of the reflectarray antenna, lower frequency, where: • four outer arcs oriented in a first direction (21, 22, 23, 24), along the first coordinate axis, are adjusted to control a phase shift of the reflected electric field component along the first axis, and • four arcs oriented in a second direction (25, 26, 27, 28), along the second coordinate axis, are set to control a phase shift of the reflected electric field component along the second axis, maintaining a 180 degree difference between the phase shifts of the two components of the reflected electric field to maintain the sense of circular polarization at the lower frequency; - eight arcs of the inner rings (29, 30, 31, 32, 33, 34, 35, 36) have lengths to adjust in phase the waves generated by the feeder (13) that are reflected in each phase shifter cell (12) maintaining the sense of circular polarization after reflection at the central frequency of a second operating band of the reflectarray antenna, frequency top, where: • four internal arcs oriented in a first direction (29, 30, 31, 32), along the first coordinate axis, are adjusted to control a phase shift of the component of the reflected electric field along the first axis, and • four arcs oriented in a second direction (33, 34, 35, 36), along the second coordinate axis, are set to control a phase shift of the reflected electric field component along the second axis, maintaining a 180 degree difference between the phase shifts of the two components of the reflected electric field to maintain the sense of circular polarization at the higher frequency; and where in each phase shifter cell (12): - at the lower frequency, the eight arcs of the outer rings (21, 22, 23, 24, 25, 26, 27, 28) are rotated jointly, forming eight rotated outer arcs (41, 42, 43, 44, 45, 46, 47, 48), applying the variable rotation technique to deflect the circularly polarized waves to the right and left by a preset angle in opposite directions with respect to the direction of the reflected waves before rotating the eight arcs of the outer rings ( 21,22, 23, 24, 25, 26, 27, 28); - at the higher frequency, the eight arcs of the internal rings (29, 30, 31, 32, 33, 34, 35, 36) are rotated jointly, forming eight rotated internal arcs (49, 50, 51, 52, 53, 54, 55, 56), applying the variable rotation technique to deflect the circularly polarized waves to the right and left by a preset angle in opposite directions with respect to the direction of the reflected waves before rotating the eight arcs of the outer rings ( 29, 30, 31, 32, 33, 34, 35, 36). 2. The reflectarray antenna (100) according to claim 1, characterized in that it also comprises a plurality of additional electrical layers that are layers of adhesive material, separating layers located between the split rings of the phase-shifting cells (12) and the plane conductor (14), or layers that form a dielectric superstratum located above the reflectarray antenna (100) as a radome to protect the split rings. 3. The reflectarray antenna (100) according to any of the preceding claims, characterized in that it also comprises a mechanical structure, formed by a support to position the feeder (13) and by a structural panel attached to the conductive plane (14), to provide mechanical rigidity. 4. The reflectarray antenna (100) according to any of the preceding claims, characterized in that it is built with materials for space applications that include carbon fibers pre-impregnated with resins, copper-coated kapton, copper-coated kaptongermanium, fibers of pre-impregnated with low-loss resins, space-qualified adhesives, or a combination of the above materials. 5. The reflectarray antenna (100) according to any of the preceding claims, characterized in that , in each phase-shifting cell (12), the eight rotated outer arcs (41, 42, 43, 44, 45, 46, 47, 48) used to phase at the lower frequency are rotated counterclockwise from the eight rotated inner arcs (49, 50, 51, 52, 53, 54, 55, 56) which are used to adjust the phases at the higher frequency, to maintain the same pointing direction of the circularly polarized waves to the right in the first operating band of the reflectarray antenna (100) and of the circularly polarized waves to the left in the second operating band of the reflectarray antenna (100), and maintaining the same pointing direction of the circularly polarized waves to the left in the first operating band of the reflectarray antenna (100) and of the circularly polarized waves to the right in the second operating band of the reflectarray antenna (100). 6. The reflectarray antenna (100) according to any of the preceding claims, characterized in that in cells chosen randomly from the group of phase-shifting cells (12) located in a strip around the edge of the lattice (11), the eight rotated outer arcs (41, 42, 43, 44, 45, 46, 47, 48) have lengths and angles of rotation adjusted to add an additional 180 degrees phase to the phase shifts of the two components of the electric field reflected in the second operating band of the reflectarray antenna (100). 7. An antenna design method to obtain a reflectarray antenna (100) with circular polarization beam separation in at least two frequency bands, the method characterized in that it comprises the following steps: a) define (60) the reflectarray antenna (100) in shape and dimensions, in a coordinate system (X, Y, Z), the reflectarray antenna (100) formed with a group of phase-shifting cells (12) in a reticle ( 11) periodic plane of fixed period and a feeder (13) configured to radiate in the, at least two, frequency bands, circularly polarized waves to the right and to the left that impinge on the phase-shifting cells (12), comprising each phase-shifting cell (12 ): - a conducting plane (14), - a plurality of dielectric layers (15,16), - a first upper set of four split concentric conductive rings printed on one of the faces of a layer of the plurality of dielectric layers (15, 16), each of the rings split into two equal arcs, forming eight arcs of the first set (21,22, 25, 26, 29, 30, 33, 34); - a second lower set of four concentric split conductor rings (23, 24, 27, 28, 31, 32, 35, 36) printed, on the opposite face to the face of the dielectric layer on which the first set is printed or on a face of a layer different from that of the dielectric layer on which the first set of the plurality of dielectric layers (15,16) is printed; b) defining (61) pointing directions of the circularly polarized beams to be separated into a first operating band and a second operating band, and defining a central frequency of the first operating band and a central frequency of the second band operating; c) at the central frequency of the first operating band and at the central frequency of the second operating band, determine a distribution of phase shift values (62) for incident waves with linear polarization on a first axis (X) and linear polarization in a second axis (Y) to collimate or contour the circular polarization beams in an intermediate direction to the pointing directions of each of the beams to be separated, where the distribution of lags for linear polarization in the first axis (X) differs by 180 degrees from the distribution of phase shifts for linear polarization in a second axis (Y), to collimate or contour the circularly polarized waves to the right and left that impinge on the phase shifter cells (12) of the reflectarray antenna (100) maintaining the sense of circular polarization after being reflected by the phase-shifting cells (12) of the reflectarray antenna (100); d) at the central frequency of the first operating band, adjust some lengths of some external arcs (63), where the external arcs are the arcs with the largest radius of the two sets of split rings, adjusting the lengths of a first subset of four external arcs (21,22, 23, 24) of split rings oriented in the direction of the first axis (X), the phase shift introduced by the phase shifter cell (12) being equal to that calculated in step c) for the case of linear polarization in the first axis (X), and adjusting the lengths of a second subset of four external arcs (25, 26, 27, 28) in the direction of the second axis (Y) being the phase shift introduced by the phase shifter cell ( 12) equal to that calculated in step c) for the case of linear polarization on the second axis (Y); e) at the central frequency of the second operating band, adjusting lengths of internal arcs (64), where the internal arcs are the arcs with the smallest radius of the two sets of split rings, adjusting the lengths of a first subset of four internal arcs (29, 30, 31, 32) of split rings oriented in the direction of the first axis (X), the phase shift introduced by the phase shifter cell (12) being equal to that calculated in step c) for the case of polarization linear in the first axis (X), and adjusting the lengths of a second subset of four internal arcs (33, 34, 35, 36) in the direction of the second axis (Y) being the offset introduced by the offset cell (12) equal to that calculated in step c) for the case of linear polarization in the second axis (Y); f) Check (65A) if the difference, for each phase shifter cell (12), between the phase shift values determined in step c) and the phase shifts introduced by the phase shifter cell (12) for the linear polarizations on the first axis (X ) and second axis (Y), at the central frequency of the first operating band and at the central frequency of the second operating band, is less than a first phase error reference threshold; g) if the difference verified in step f) is equal to or greater (65B) than the first phase error reference threshold, repeat step d) adjusting the lengths of the first subset and second subset of the external arcs (21,22 , 23, 24, 25, 26, 27, 28) while holding the lengths of the first subset and second subset of the internal arcs (29, 30, 31, 32, 33, 34, 35, 36) fixed, and repeat the step e), adjusting the lengths of the first subset and second subset of the inner arcs (29, 30, 31, 32, 33, 34, 35, 36) while keeping the lengths of the first subset and second subset of the outer arcs fixed (21, 22, 23, 24, 25, 26, 27, 28); h) iterate steps f) and g) until the offsets introduced for the linear polarizations in the first axis (X) and second axis (Y) in each phase shifter cell (12) differ from the offset values determined in step c) at less than the first phase error reference threshold; i) at the central frequency of the first operating band and at the central frequency of the second operating band, determine values of phase corrections (66), in each phase-shifting cell (12), for incident waves with circular polarization to the right and left in the reflectarray antenna (100) obtained according to steps d) to h) to separate the collimated or contoured beams in the pointing directions defined in step b); j) adjust the angles of rotation of the external arcs (67) to jointly rotate the external arcs (21, 22, 23, 24, 25, 26, 27, 28) around the center of the split rings, obtaining arcs of the rotated outer rings (41, 42, 43, 44, 45, 46, 47, 48), the angle of rotation set independently for each offset cell (12), being the values of offset corrections introduced by the arcs of the outer rings rotated (41, 42, 43, 44, 45, 46, 47, 48) in the offsets for circular polarizations to the right and to the left equal to those calculated in step i) according to the technique of variable rotation to the center frequency of the lower band; k) adjust the angles of rotation of the internal arcs (68) to rotate the internal arcs (29, 30, 31, 32, 33, 34, 35, 36) jointly around the center of the split rings, obtaining arcs of the rotated inner rings (49, 50, 51, 52, 53, 54, 55, 56), the angle of rotation set independently for each offset cell (12), being the values of offset corrections introduced by the arcs of the inner rings rotated (49, 50, 51, 52, 53, 54, 55, 56) in the offsets for circular polarizations to the right and to the left equal to those calculated in step i) according to the technique of variable rotation to the center frequency of the second operating band; l) adjust the lengths of the rotated external arcs (69), in each phase shifter cell (12), using a first rotated coordinate system (X', Y', Z') a first angle with respect to the coordinate system (X , Y, Z) from step a), to maintain the difference of 180 degrees between the phase shifts for incident waves with linear polarizations along a first rotated axis (X') and a second rotated axis (Y') of the first rotated coordinate system (X', Y', Z'), the offsets for the linear polarization on the first rotated axis (X') of the first rotated coordinate system (X', Y', Z') being equal to the offsets for linear polarization on the first axis (X) defined in step c), at the center frequency of the first operating band; m) adjust the lengths of the rotated internal arcs (70), in each phase shifter cell (12), using a second rotated coordinate system (X'', Y'', Z'') one second angle with respect to the coordinate system (X, Y, Z) from step a), to maintain the difference of 180 degrees between the phase shifts for incident waves with linear polarizations along a first rotated axis (X”) and a second rotated axis (Y”) of the second rotated coordinate system (X'', Y'', Z''), being the offsets for the linear polarization on the first rotated axis (X”) of the second rotated coordinate system ( X'', Y'', Z'') equal to the offsets for the linear polarization on the first axis (X) defined in step c), at the center frequency of the second operating band; n) Check (71A) if, for each phase shifter cell (12), the phase shift values for incident waves with linear polarizations along the first rotated axis (X') and the second rotated axis (Y') of the first system of rotated coordinates (X', Y', Z') and the offsets for the linear polarization on the first rotated axis (X') of the first rotated coordinate system (X', Y', Z'), at the center frequency of the first band of operation, differ from the values determined in steps l) and c) by less than one second phase error reference threshold, and if the offset values for incident waves with linear polarizations along the first rotated axis (X”) and of the second rotated axis (Y”) of the second rotated coordinate system (X'', Y'', Z'') and the offsets for linear polarization on the first rotated axis (X”) of the second rotated coordinate system (X'', Y'', Z''), at the center frequency of the second operating band, differ from the values determined in steps m) and c) by less than the second error reference threshold phase; o) if the differences verified in step n) are equal to or greater (71B) than the second phase error reference threshold, repeat step l) adjusting the lengths of the eight arcs to the center frequency of the first operating band rotated outer arcs (41, 42, 43, 44, 45, 46, 47, 48) while holding the lengths of the eight rotated inner arcs constant (49, 50, 51, 52, 53, 54, 55, 56), and repeat step n) adjusting to the central frequency of the second operating band the lengths of the eight rotated internal arcs (49, 50, 51, 52, 53, 54, 55, 56) while keeping the lengths of the eight constant. rotated external arches (41,42, 43, 44, 45, 46, 47, 48); p) iterate steps n) i) until the offsets introduced in each offset cell (12) for the polarizations in the first rotated axis (X') and second rotated axis (Y') of the first rotated coordinate system (X' , Y', Z') at the center frequency of the first operating band, and the offsets for the polarizations in the first rotated axis (X”) and second rotated axis (Y”) of the second rotated coordinate system (X'',Y'',Z'') at the center frequency of the second operating band, differ from the offset values determined in steps l) and m) at less than the second phase error reference threshold; q) generating (72) gravure masks for each of the two levels of metallization of the reflectarray antenna (100) from the adjusted lengths for the arcs and the adjusted angles of rotation for each split ring in each phase shifter cell (12 ). 8. The method according to claim 7, characterized in that step h) further comprises readjusting in each phase shifter cell (12) the lengths of the eight arcs that control the phase shifts in each of the frequency bands to collimate or contour. the left and right circular polarization beams in the intermediate direction described in step c) at an upper extreme frequency and a lower extreme frequency of each of the frequency bands, and step p) further comprises resetting in each phase shifter cell (12) the lengths of the eight rotated arcs with the largest radius considering the offsets for the polarizations of the first rotated axis (X') and second rotated axis (Y') of the first rotated coordinate system (X', Y', Z' ) to the extreme upper and lower frequencies of the first frequency band, and readjust in each phase shifter cell (12) the lengths of the eight rotated arcs of smaller radius considering the phase shifts for the first rotated (X”) and second axis polarizations. rotated axis (Y”) of the second rotated coordinate system (X”, Y”, Z”) to the upper and lower extreme frequencies of the second frequency band. The method according to any of the claims 7-8, characterized in that the reflectarray antenna (100) operates in more additional frequency bands and - in step a), four additional concentric split rings are included in each phase shifter cell (12) for each additional frequency band; - in step c), the distributions of offsets for linear polarization on the first axis (X) are determined for each additional frequency band; - after step e), the lengths of the eight arcs corresponding to the additional frequency band are adjusted for each additional frequency band and in each phase shifter cell (12) to obtain the phase shifts of the linear polarizations on the first axis (X ) and second axis (Y) that are calculated in step c) at a central frequency of the additional frequency band; - after step k), for each additional frequency band, the eight arcs corresponding to the additional frequency band are rotated in each phase shifter cell (12), using an additional rotated coordinate system, the corrections being introduced by the eight arcs rotated in circular polarizations clockwise and lefts equal to those calculated in step i) according to the variable rotation technique, at the center frequency of the additional frequency band; and - after step m), the lengths of the eight arcs corresponding to the additional frequency band are readjusted in each phase shifter cell (12), with 180 degrees being the difference between the phase shifts for incident waves with linear polarizations along orthogonal directions coplanar with the antenna in the additional rotated coordinate system, and the offset for the linear polarization in each of the rotated orthogonal directions being equal to that determined in step c) for the non-rotated directions, at the center frequency of the additional frequency.