Classifications

• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01Q—ANTENNAS, i.e. RADIO AERIALS
  • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01Q—ANTENNAS, i.e. RADIO AERIALS
  • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
  • H01Q15/0006—Devices acting selectively as reflecting surface, as diffracting or as refracting device, e.g. frequency filtering or angular spatial filtering devices
  • H01Q15/006—Selective devices having photonic band gap materials or materials of which the material properties are frequency dependent, e.g. perforated substrates, high-impedance surfaces
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01Q—ANTENNAS, i.e. RADIO AERIALS
  • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
  • H01Q15/02—Refracting or diffracting devices, e.g. lens, prism
  • H01Q15/12—Refracting or diffracting devices, e.g. lens, prism functioning also as polarisation filter
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01Q—ANTENNAS, i.e. RADIO AERIALS
  • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
  • H01Q15/14—Reflecting surfaces; Equivalent structures
  • H01Q15/141—Apparatus or processes specially adapted for manufacturing reflecting surfaces
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01Q—ANTENNAS, i.e. RADIO AERIALS
  • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
  • H01Q15/24—Polarising devices; Polarisation filters 
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01Q—ANTENNAS, i.e. RADIO AERIALS
  • H01Q19/00—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic
  • H01Q19/10—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using reflecting surfaces
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01Q—ANTENNAS, i.e. RADIO AERIALS
  • H01Q3/00—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system
  • H01Q3/44—Arrangements for changing or varying the orientation or the shape of the directional pattern of the waves radiated from an antenna or antenna system varying the electric or magnetic characteristics of reflecting, refracting, or diffracting devices associated with the radiating element
  • H01Q3/46—Active lenses or reflecting arrays
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
  • Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
  • Y10T29/00—Metal working
  • Y10T29/49—Method of mechanical manufacture
  • Y10T29/49002—Electrical device making
  • Y10T29/49016—Antenna or wave energy "plumbing" making

Definitions

• the present invention relates to a reflector array antenna with cross polarization compensation and a method for producing such an antenna. It applies in particular to antennas mounted on a spacecraft such as a telecommunications satellite or antennas terrestrial terminals for telecommunications or satellite broadcasting systems.
• Offset antenna configurations having a geometrically formed reflector (offset shaped reflector antenna) and a primary source offset from the normal axis to the reflector, generate radiation in a cross polarization induced by the geometric curvature of the antenna.
• reflector and whose level depends directly on the focal ratio of the reflector, the focal ratio being defined by the ratio between the focal length and the reflector diameter. The higher the focal ratio, the lower the level of cross polarization.
• the antenna structure when the antenna is implanted on a face of a satellite facing the Earth, the antenna structure must be compact and the focal ratios are low, which induces a high level of cross polarization.
• the level of cross polarization is impaired in the direction normal to the antenna but there may be axisymmetric cross polarization lobes due to the curvature of the lines of fields at the ends of the reflector.
• the primary source used may, when it has low performance, itself generate cross-polarized field components.
• satellite-mounted antennas pointing to its Earth often have a dual reflector structure mounted in a Gregorian configuration.
• the use of two reflectors makes it possible to define the geometry of the auxiliary reflector with respect to the geometry of the main reflector so that the cross polarization induced by the curvature of the auxiliary reflector cancels the cross polarization induced by the curvature of the reflector.
• main reflector the presence of the auxiliary reflector and its support structure causes an increase in the mass, volume and cost of the antenna relative to a single reflector antenna.
• a reflecting array antenna in English: reflectarray antenna
• a primary source illuminates a reflector network at an oblique incidence.
• the reflector comprises a set of elementary radiating elements assembled in a network of one or two dimensions and forming a reflecting surface which can be flat.
• the reflector network then acts as a mirror and the radiation reflected by the reflector network does not comprise a cross-polarization component. it is illuminated by a primary source without cross polarization placed in its axis of symmetry.
• the radiating elements of a reflector array generally have geometric differences so as to precisely control the phase shift that each radiating element produces on an incident wave.
• the arrangement of the elementary radiating elements with respect to one another on the surface of the reflector is generally synthesized and optimized so as to obtain a given radiation pattern in a chosen pointing direction with a chosen phase law. Therefore, it has been found that although the reflector is plane and therefore there is no cross polarization induced by the curvature of the reflector, because of the illumination of the reflector by a source in offset configuration, the The reflector array behaves operationally as a geometrically shaped surface reflector which also induces cross-polarized radiation having the same level of magnitude as an equivalent shaped surface reflector.
• the object of the invention is to provide a reflective array antenna having a given phase diagram and in which the cross polarization generated by a primary source is canceled.
• the invention relates to a cross-polarization compensation reflector grating antenna comprising a reflector grating consisting of a plurality of evenly distributed elementary radiating elements forming a reflective surface and a primary source for illuminating the reflector array, the reflector array having a radiation pattern according to two orthogonal main polarizations in a propagation direction chosen with a law selected phase, each elementary radiating element being made in planar technology and comprising an etched pattern consisting of at least one metal patch and / or at least one radiating slot, the metal patch comprising, in a symmetrical configuration, at least four opposite sides two by two with respect to a center of the etched pattern and arranged parallel to two X, Y directions of the XY plane of the radiating element, the radiating slot comprising, in a symmetrical configuration of the radiating element, at least two branches; diametrically opposite to the center of the gravity pattern and disposed parallel to at least one of X and / or Y of the radiating element.
• At least one radiating element of the reflector network comprises an etched pattern having an asymmetric geometric shape with respect to at least one of the X and / or Y directions of the XY plane of the radiating element, the dissymmetry of the pattern etched radiating element consisting of an angular inclination of at least one side, respectively at least one branch, of the geometric shape of the etched pattern relative to the X and / or Y directions of the plane of the radiating element.
• the dissymmetry of the etched pattern is calculated individually for each radiating element from a symmetrical radiating element of the same pattern and consists of an angular inclination of at least one direction of the pattern.
• the angular value of the angle of inclination is determined so that the radiating element generates a reflected wave having a controlled depolarization which opposes a depolarization generated in the normal plane to the direction of propagation by the reflector grating illuminated by the primary source.
• the controlled depolarization of the radiating element corresponds to an individual reflection matrix having principal reflection coefficients of amplitude similar to those of the radiating element of the same pattern and of symmetrical geometric shape along the two X directions and Y, and non-zero amplitude cross-reflection coefficients greater than that of said radiating element of the same symmetrical pattern.
• the angular dissymmetries consist of angular rotations of the four main branches of the slots, around the center of the engraved pattern, in the XY plane.
• the angular dissymmetries consist of an angular inclination of at least two opposite sides of the metallic patch of the radiating elements in the same direction or in opposite directions so as to transform the square shape respectively into trapezoid or parallelogram.
• several adjacent radiating elements of the reflector array comprise an etched pattern having an asymmetrical geometric shape with respect to at least one X and / or Y direction of the XY plane of each of said radiating elements, the angular inclinations of the side or branch of the geometric shape of the etched pattern of each of said radiating elements forming a continuously progressive value angle of a radiating element to another radiating element adjacent to the reflecting surface.
• the reflector network comprises several plane facets oriented in different planes, each plane facet comprising a plurality of elementary radiating elements, and at least one radiating element of each plane facet of the reflector network comprises an engraved pattern having an asymmetrical geometric shape with respect to at least one X and / or Y direction of the XY plane of the facet to which the corresponding radiating element belongs.
• the invention also relates to a method of producing such a reflector grating antenna with offset configuration and cross polarization compensation consisting in producing a reflector array consisting of a plurality of elementary radiating elements regularly distributed and forming a reflective and illuminating surface. the reflective network by a primary source.
• the method consists in developing a reflector array in which each elementary radiating element is made in planar technology and comprises an etched pattern having a geometric shape symmetrical with respect to two X and Y directions of the XY plane of the radiating element, the etched pattern being consisting of at least one metal patch and / or at least one radiating slot, then introducing an asymmetry, with respect to at least one of the X and / or Y directions, into the geometric shape of the etched pattern of at least one radiating element of the reflector array, the asymmetry being calculated from the radiation pattern of the desired far-field electromagnetic field in which the cross-polarization is zero and from the corresponding radiated electric field in the plane of the reflector array.
• FIG. 1 a diagram of an example of a reflector array antenna, according to the invention
• FIG. 2 a diagram of an example of elementary radiating element, according to the invention.
• FIG. 3 a diagram of an example of arrangement of the radiating elements of a reflector array antenna, according to the invention.
• FIG. 4a a diagram illustrating the path of an oblique incident wave on a reflector array, according to the invention
• FIG. 4b a diagram illustrating the orientation of the field components in different planes on the path of an incident wave and a reflected wave, according to the invention
• FIGS. 5a and 5b two diagrams illustrating the distribution of the electric field in the plane of the radiating aperture in the case where the radiation comprises a cross-polarization component and, respectively, in the case where the radiation is perfectly polarized without a cross-component, according to the invention;
• FIG. 6a an example of a symmetrical radiating element comprising a metal patch and slots etched in the metal patch, the corresponding reflection matrix and the desired reflection matrix, according to the invention
• FIGS. 6b to 6e the radiating element of FIG. 6a in which different types of rotations are introduced and the diagrams relating to the evolutions of the amplitude and of the phase of the corresponding crossed coefficients, according to the invention
• FIG. 7 an example of a set of symmetrical successive radiating elements comprising a continuously evolutive phase between two consecutive radiating elements, each radiating element comprising a pattern consisting of a square-shaped metal patch and a radiating opening made in the metal patch, according to the invention;
• FIGS. 8a, 8b, 9a, 9b a radiating element of FIG. 7 in which different types of rotations are introduced and the diagrams relating to the evolutions of the amplitude and the phase of the corresponding crossed coefficients, according to the invention.
• a reflector array antenna 10 as shown for example in FIG. 1, comprises a set of elementary radiating elements 20 assembled in a reflector array 11 in one or two dimensions and forming a reflecting surface 14 making it possible to increase the directivity and the gain of the antenna 0.
• the reflector network 11 is illuminated by a primary source 13.
• the elementary radiating elements 20, also called elementary cells, of the reflector network 11 comprise engraved patterns such as metal patches and / or slits.
• the etched patterns have variable parameters, such as for example the geometric dimensions of the etched patterns (length and width of the "patches" or slots), which are adjusted to obtain a chosen radiation pattern. As represented for example in FIG.
• the elementary radiating elements 20 may consist of metal patches loaded with radiating slots and separated from a metal mass plane of a typical distance between ⁇ 9 and Xgl 4, where ⁇ g is the Guided wavelength in the spacer medium.
• This spacer medium may be a dielectric, but also a composite sandwich made by a symmetrical arrangement of a honeycomb type separator and dielectric skins thin thicknesses.
• the elementary radiating element 20 is of square shape having sides of length m, comprising a metal patch 15 printed on an upper face of a dielectric substrate 16 provided with a metal ground plane 17 on its face. lower.
• the metal patch 15 has a square shape having sides of dimension p and has two slots 18 of length b and width k practiced at its center, the slots being arranged in the form of a cross.
• the plane of the reflecting surface of the radiating element is the XY plane.
• the shape of the elementary radiating elements 20 is not limited to a square, it may also be rectangular, triangular, circular, hexagonal, cross-shaped, or any other geometric shape.
• the slots can also be made in a different number of two and their arrangement can be different from a cross.
• the radiating element could also include a pattern consisting of a central patch-shaped cross and one or more peripheral slots.
• the radiating element could comprise a pattern consisting of several concentric annular metal patches and several annular or non-annular slots.
• the arrangement (lay-out) of the elementary radiating elements with respect to one another to form a reflector network is synthesized so as to obtain a given radiation pattern in a chosen pointing direction and with a predetermined phase law.
• Figure 3 shows an example of arrangement of the radiating elements of a reflector array antenna, to obtain a directional beam pointed in a lateral direction relative to the antenna. Due to the pianetry of the reflector network and the differences in path lengths of a wave emitted by a primary source 13 to each radiating element 7, 8 of the grating, the illumination of the reflector network by an incident wave coming from the primary source 13 causes a phase distribution of the electromagnetic field above the reflecting surface 14.
• the etched patterns of each radiating element 7, 8 therefore have geometric dimensions defined so that the incident wave is reflected by the network 11 with a phase shift that compensates for the relative phase of the incident wave.
• each radiating element is usually chosen symmetrical with respect to the two orthogonal axes X and Y of the plane of each radiating element.
• An isolated symmetrical radiating element does not substantially deprive an incident wave normal to its plane and the associated reflection matrix therefore has very low cross-reflection coefficients, generally less than 30 dB. These levels may increase for an oblique incidence, particularly greater than 40 ° compared to normal.
• the radiating elements are arranged on the surface of the reflector so as to achieve a specific phase law over the entire surface, in a main polarization corresponding to the polarization emitted by the primary source.
• the phenomena of depolarization are phenomena considered as parasites which deteriorate the performance of the antenna but they are generally not taken into account when carrying out the arrangement of the reflector network.
• the reflector array 11 When the reflector array 11 is illuminated by an oblique incident wave in a linear polarization, it generates a reflected wave having two field components along two orthogonal X and Y directions.
• the surface of the reflector array 11 is partially schematized by dotted lines and four radiating elements 20 are shown, each radiating element 20 having a square-shaped metal patch.
• a primary source 13 placed in offset configuration illuminates the reflector network 11 in an oblique direction at an angle ⁇ with respect to the normal direction n to the reflector network 11.
• the incident electromagnetic field Einc emitted by the primary source can be polarized linearly by example in a vertical direction in an orthonormal reference linked to the source. Due to its oblique incidence, the incident field Einc, linearly polarized in the plane bound to the source, induces, in an XY coordinate system bound to the plane of the radiating element, an incident field Ei comprising two Eix and Eiy field components according to the two directions X and Y of the plane of the radiating element, the two components Eix and Eiy corresponding to the projection of the oblique incident field Einc in the plane of the reflective network.
• the reflector network then radiates, according to a main propagation direction, a reflected electromagnetic field Er having two Erx and Ery field components.
• the incident field Einc polarized linearly in the reference frame linked to the primary source 13 thus generates in XY plane parallel to the plane of the reflector network 11, a cross-polarized field component.
• the cross polarization components induced at the level of the radiating elements compensate each other.
• the normal direction n at the plane of the reflector network is generally different from the normal plane 44 to the propagation direction 45.
• Cross-polarization components are then summed with phase weighting and no longer offset each other.
• the invention therefore consists in synthesizing a reflector array according to the prior art, that is to say, only concerned with the radiation patterns required in the two principal poiarizations orthogonal and therefore only interested in the main reflection coefficients Rxx and Ryy.
• the invention then consists in weakly disturbing the polarization induced by at least one radiating element of the grating. reflector so as to compensate for the cross-polarization components induced by the reflector array.
• the disturbance to be introduced into the radiating elements is determined individually for each of the radiating elements of the reflector network.
• the slight depolarization of the waves reflected by each radiating element corresponds to the appearance, in the plane of the reflector array, of low amplitude cross polarization radiation at the level of the individual radiating elements.
• the slight depolarization is such that it makes it possible to obtain, in the normal plane 44 at the direction of propagation 45, waves reflected by the reflector network 11, called the plane of opening of the reflector network or radiating aperture plane, a distribution of electric field without cross component.
• the depolarization introduced must be weak and not disturb the fundamental mode of radiation of the radiating element, nor its phase.
• the cross-reflection coefficients introduced by each elementary radiating element will preferably be less than -15 dB.
• the invention consists, in a first step, in defining the desired radiation pattern of the far-field electromagnetic field 46 and imposing as a starting condition that the polarization components cross are nil for this far field.
• This far-field electromagnetic field 46 is associated a single distribution of a near electromagnetic field on an infinite radiating aperture defined by a normal plane 44 to the direction of propagation 45 of the waves reflected by the reflector network 11.
• the polarization components crossed being zero in the far field, they are also zero in a plane normal to the direction of propagation of the waves reflected by the reflector network and are therefore zero in the opening plane 44 of the reflector array 11.
• From the radiation pattern of the field distant electromagnetic 46 desired it is possible to deduce therefrom, by means of a Fourier transform, the main polarization components of the corresponding radiated near-field, in the opening plane 44 of the reflector network,
• the invention in a second step, in the general case where the aperture plane 44 is different from the plane of the reflector array 11, the invention then consists in calculating, by a backpropagation technique, for each radiating element of the reflector network, the components of the radiated electric field corresponding in the plane of the reflector network.
• the backpropagation technique consists of a change of reference from the plane of aperture 44 to the plane of the reflector network 11.
• the components of the electric field radiated in the plane of the reflector array are the Erx and Ery components reflected by the corresponding radiating element according to the respective directions X and Y.
• the Ery component is weak but nonzero if the plane of the reflector array is different from the aperture plane.
• the invention consists in calculating the components of the incident electric field Eix and Eiy induced by the primary source 13 on each radiating element of the reflector network.
• the horn is defined by a set of modal coefficients of spherical waves with which it is possible to calculate the near or far radiated field as described for example in the book by G. Franceschetti, "Campi Elettromagnetici ", Boilati Boringhieri editore sri, Torino 1988 (li ediée), incorporated by reference.
• the invention consists, for each radiating element, in deducing therefrom the principal reflection coefficients Rxx and Ryy. and the corresponding cross reflection coefficients Rxy and Ryx.
• the Erx and Ery components of the reflected field Er generated by the reflector network according to the respective directions X and Y are expressed as a function of the components Eix and Eiy of the incident field Ei induced by the source by the following equations:
• the reflection matrix of each radiating element of the reflector network therefore comprises reflection coefficients Rxx in the X direction, Ryy in the Y direction and two cross-reflection coefficients Rxy and Ryx corresponding to a cross polarization.
• the invention consists first of all in synthesizing a reflector network by only worrying about the radiation diagrams required in the two orthogonal main polarizations along the X and Y directions and therefore only by being interested in to the main reflection coefficients Rxx and Ryy, then to weakly disturb the polarization of at least one radiating element so as to compensate for the cross polarization induced by the reflector array in the direction of propagation of the reflected waves.
• the Erx and Ery components of Radiated field Er must be determined for each radiating element in the XY plane of the facet to which this radiating element belongs.
• Different XY references are to be considered according to the radiating element considered and the facet in which it is.
• the method for estimating the amount of depolarization required to be performed on each individual radiating element must therefore be applied facet by facet so as to reconstruct, according to the method presented above, the Erx and Ery components of the radiated field in the XY plane. corresponding to the radiating element considered.
• the invention then consists in introducing, into the individual radiating elements 20 of the reflector network 11, a depolarization controlled, different from a radiating element to another radiating element, to obtain all the reflection coefficients corresponding to the desired values.
• This depolarization introduced individually into the radiating elements is such that it then compensates for the depolarization induced by an oblique incident wave on the final reflector grating.
• FIG. 5a illustrates the distribution of the electric field in the plane of the radiating aperture in the case where the reflector grating has been synthesized without taking into account parasitic phenomena related to the cross polarization and where the radiation comprises a cross-polarization component
• FIG. 5b illustrates the case where the reflector array has been synthesized so as to cancel the cross-polarization component and the radiation is perfectly polarized without cross-component.
• the depolarization introduced into at least one individual radiating element of the reflector network consists in breaking the symmetry of the pattern of this radiating element while maintaining the same phase of the principal reflection coefficients induced by this radiating element, in order not to disrupt its radiation in the main polarization. This affects the amplitude and phase of the cross-reflection coefficients.
• angular dissymmetries are introduced into the patterns of the radiating elements that generate cross polarization, some radiating elements do not generate cross polarization, for example those located in the axis of symmetry of the reflector network may remain symmetrical.
• These angular dissymmetries consist of angular inclinations of at least one main direction of the pattern or angular rotations of the four principal directions X, X ', Y, Y' of the patterns, around the center 50 of the pattern, in the XY plane.
• the angular rotations are made with angles that may be different or identical for all directions and in directions that may be the same or different.
• the dissymmetry of the pattern of each of said radiating elements is continuously progressive. a radiating element to another radiating element adjacent to the reflecting surface.
• a first example shown in Figures 6a to 6d relates to the case of a radiating element 20 whose geometric pattern comprises a metal patch and slots engraved in the patch.
• the slots form a central symmetrical cross in two orthogonal directions XX 'and YY', called Jerusalem Cross.
• the cross comprises four main branches 62, 63, 64, 65, opposite in pairs, respectively oriented along the directions X, X ', Y, Y', each main branch having an end provided with a perpendicular extension.
• the reflection matrix 60 of this symmetrical radiating element is such that the main reflection coefficients are of equal amplitudes and close to the maximum value 1, corresponding to OdB, and the crossed reflection coefficients have very small amplitudes, typically order of -29dB.
• the desired reflection matrix 61 has main reflection coefficients that are very slightly modified with respect to those of the symmetrical element and slightly degraded cross reflection coefficients, having an amplitude of the order of -21 dB, this degraded amplitude being, however, always located at a level corresponding to noise.
• each main branch of the central cross has undergone different types of angular rotations relative to the center 50 of the radiating element.
• the angular rotations consist in modifying the inclination of each of the main branches, independently of one another, by a different angle and in a positive or negative direction.
• the four main branches of the cross are inclined independently of each other at the same angle, the branches located in directions diametrically opposed being inclined in opposite directions but two successive branches being inclined in the same direction.
• the amplitude and phase diagrams of the corresponding cross-reflection coefficients show that this configuration has little impact on the amplitude of the cross-reflection coefficients when the angle of inclination of the main branches of the cross varies between -4 ° and + 4 ° while their phase evolves a lot.
• FIG. 6e shows an example of an optimized radiating element 20i whose reflection matrix is very close to the desired matrix 61 indicated in FIG. 6a.
• This radiating element 20i has two branches forming an angle of 9.35 ° respectively in a negative direction of rotation and in a direction of positive rotation with respect to the directions Y and X, and two branches forming an angle of 6.65 ° respectively in a negative direction of rotation and in a direction of positive rotation with respect to the directions X 'and Y'.
• FIGS. 6a to 6e thus show that it is possible by adjusting the angle of inclination of the four branches of a cross oriented along principal directions of the radiating element, to control the amplitude and the phase of the cross-reflection coefficients and thus the depolarization of this radiating element.
• FIG. 7 relates to a set of successive symmetrical radiating elements comprising a continuously evolutive phase between two consecutive radiating elements, each radiating element comprising a pattern consisting of a square-shaped metal patch and a radiating opening made in the metal patch. .
• the respective dimensions of the metal patch with respect to the radiating aperture are continuously evolving from one radiating element to another adjacent radiating element, which makes it possible to have a large number of different phases between 0 ° and 360 °, modulo 360 ° to be distributed on a reflector network according to the radiated phase law desired.
• the different successive phases are obtained without abrupt rupture of the dimensions of the patch relative to the radiating aperture due to the appearance of the radiating aperture in the center of the metal patch and the gradual increase in the dimensions of the radiating aperture to the disappearance of said metal patch and the appearance in the center of the radiating opening of a new metal patch whose dimensions gradually increase until the disappearance of the radiating opening.
• FIGS. 8a and 8b show the evolution diagrams of the phase and the amplitude of the cross-reflection coefficients for a radiating element subjected to an oblique incident wave and comprising two inclined sides 81, 82 or 83, 84 in opposite directions.
• FIGS. 10a and 10b show other diagrams of evolution of the phase and the amplitude of the crossed reflection coefficients when two opposite sides are inclined at the same angle in the same direction so as to obtain a parallelogram.

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