Method for optimizing the directivity of an antenna

Abstract

Method (100) for optimizing the directivity of an antenna comprising at least one electromagnetic source (Si, i=1, N), the directivity in the direction (, ) being determined from a reduced coupling matrix of dimension N*N, the terms of which are defined from the terms of a coupling matrix of dimension 2N*2N, the terms of said coupling matrix being a function of the field radiated in the direction (, ) by a source Si and another source Sj, the method (100) comprising the following steps: determination (101) of a value of two parameters from among the three parameters: the position (, i=1, N), the complex excitation amplitude, the complex reflection coefficient in the direction , on the basis of the reduced coupling matrix, determination (102) of at least one corresponding value of the third parameter from among the three parameters, so that the directivity in the direction is locally optimal, for example locally maximum;Figure 1;

Description

Title of the invention: Method for optimizing the directivity of an antenna

[0001] The present invention relates to the field of antenna networks for wireless telecommunication systems, or radars, and in particular directional antennas and methods for optimizing the directivity of antennas.

[0002] It is known to determine the radiation performance of a radiating source above a reflecting plane using the principle of image theory. This principle is based on the fact that there is a geometric symmetry between a point source located at a distance h from a reflecting plane and a virtual source also located at a distance h from the reflecting plane at a point symmetrically opposite the point source with respect to the reflecting plane, the phase of the virtual source being adjusted according to the type of reflecting plane. In the case of electromagnetic sources, these point sources can be modeled in vector form, also introducing the notion of polarization. The principle of image theory for calculating the electromagnetic field resulting from a radiation source is well known in the literature.

[0003] The application of this theory notably involves optimizing the reflection coefficient of an image of an electric dipole parallel to the reflecting plane and placed close to the surface of the reflecting plane. This has led to the development of AMC (Artificial Magnetic Conductor) type surfaces for electric dipoles parallel to the reflecting plane and placed near the surface.

[0004] For other types of radiation sources, the determination of the image reflection coefficient in the case of canonical antennas, i.e., electric hertzian dipoles (EHDs), magnetic hertzian dipoles (MHDs), and Huygens source antennas (ASHs), is well known for the perfect electric conductor (CEP) and the perfect magnetic conductor (CMP). For arbitrary reflecting surfaces, a generalized image theory, i.e., the precise image theory, provides the theoretical context for estimating the reflection coefficient.

[0005] For directional, or even superdirectional, antennas, the optimization of excitation coefficients is readily provided for all free-space configurations using the lattice factor method. Furthermore, the design of superdirectional arrays with boundary conditions of the "electrically perfect conductor" (ECC) or "magnetically perfect conductor" (MPC) type, and the associated theory, is known. Finally, it should be noted that similar results have been obtained using a Rayleigh quotient optimization method.

[0006] Thus, in the prior art, a set of realizations of directional sources associated with a reflector can be found. A demonstration of electric hertzian dipoles (EHDs) on a perfect electrical conductor (PEC) has been carried out, as well as a demonstration of magnetic hertzian dipoles (MHDs) on a perfect electrical conductor (PEC) has also been carried out.

[0007] However, no generalization of the super-directional behavior of a given network of radiating sources exists for arbitrary reflection boundary conditions, particularly in the case where the boundary conditions lead to an arbitrary complex reflection coefficient for each radiating source.

[0008] The invention therefore aims to provide a solution to all or part of these problems.

[0009] To this end, the present invention relates to a method for optimizing the directivity of an antenna, the antenna comprising at least one electromagnetic source Si, i=l, N associated with at least one complex excitation amplitude i=1, N as a function of a direction / q(θ, θ) , defined by a colatitude θ with respect to a direction normal to a reflecting plane in electromagnetic interaction with the at least one source, and a longitude with respect to a reference direction in said reflecting plane, the at least one electromagnetic source being configured to radiate an electromagnetic field at a determined wavelength X, a position i=l, N of the at least one source being determined relative to the reflecting plane, and a complex reflection coefficient i=l, N of at least one source on the reflecting plane being defined to determine an image electromagnetic field radiated by at least one image source S4, i= 1, N of the at least one source Si, i=l, N, as a function of the electromagnetic field radiated by the at least one source S;, i=l, N,

[0010] a total field being radiated in the direction rô (¾ ^o), by a plurality of sources comprising at least one source Si, i=l, N and at least one image source S ;, i=l, N,

[0011] the directivity of the antenna in the direction rô (¾ ^o) being a function of the position i=l, N of the at least one source S;, i=l, N, of the at least one complex excitation amplitude Aij^ i=l, N, and of the complex reflection coefficient i=l, N,

[0012] the directivity, in the direction / y (¾ ^o), being determined from a reduced coupling matrix, of dimension N*N, whose terms for i=l, N and for j=l, N are defined from the terms of a coupling matrix of dimension 2N*2N, the terms of said coupling matrix for i=-N, N and i^O and for j=-N, N and j^O being functions of the radiated field ) in the direction (0q, ^o) by a source Si among at least one source S;, i=l, N or by an image source S among at least one image source S ;, i=l, N, and by another source Sj among at least one source S;, i=l, N or by another image source S j among at least one image source S4, i=l, N,

[0013] the process comprising the following steps: - determination of a value of the position jy, i=l, N of at least one source Si, i=l, N and of at least one corresponding value of at least one complex excitation amplitude i=l, N in the direction ( 0O, ), - based on the reduced coupling matrix, determination of at least one corresponding value of the reflection coefficient, the directivity in the direction ( <pQ ) étant localement optimale au voisinage de ladite valeur correspondante du coefficient de réflexion, par exemple localement maximum au voisinage de ladite valeur correspondante du coefficient de réflexion;

[0014] or, alternatively, the following steps: - determination of a value of the reflection coefficient and at least one corresponding value of at least one complex excitation amplitude i=l, N in the direction ( ^q) , - on the basis of the reduced coupling matrix, determination of at least one corresponding value of the position rj, i=l, N of the at least one source Si, i=l, N, the directivity in the direction ( 0O, (p being locally optimal in the vicinity of said corresponding value of the position ( / ^, i=l, N) of the at least one source (Si, i=l, N), for example locally maximum in the vicinity of said corresponding value of the position i=l, N) of the at least one source (S;, i=l, N);

[0015] or, alternatively, the following steps: - determination of a value for the position FJ, i=l, N of at least one source Si, i=l, N , and a value for the reflection coefficient, - based on the reduced coupling matrix, determination of at least one corresponding value of at least one complex excitation amplitude, i=l, N in the direction ( (p^j, the directivity in the direction ( Gq, <pQ ) étant localement optimale au voisinage de ladite valeur correspondante de l’amplitude complexe d’excitation i=l, N dans la direction ( && de l’au moins une source Si, i=l, N, par exemple localement maximum au voisinage de ladite valeur correspondante de the complex excitation amplitude i=l, N of at least one source Si5 i=l, N in the direction ( Bo, .

[0016] According to these provisions, the method makes it possible to optimize the directivity of the antenna in any direction (60, q>) by determining, for a predetermined value of the position i=l, N of at least one source Si, i=l, N, and a corresponding value of at least one complex excitation amplitude, i = 1, N, in the direction (Bq, <pQ ) au moins une valeur correspondante du coefficient de réflexion du plan réflecteur pour laquelle la directivité dans ladite direction ( (pQ ) est optimale au voisinage de ladite valeur correspondante du coefficient de réflexion, par exemple maximum au voisinage de ladite valeur correspondante du coefficient de réflexion ; le procédé permet de déterminer ladite valeur correspondante du coefficient de réflexion, sans que celle-ci soit limitée aux valeurs de + 180 ou - 180 °.

[0017] According to these provisions, the method makes it possible to optimize the directivity of the antenna in any direction (Bq) by determining, for any predetermined value (i.e., without this being limited to the values ​​of +180° or -180°), the reflection coefficient of the reflecting plane, and at least one corresponding value of at least one complex excitation amplitude i=l, N in the direction (Oq, (p^), at least one corresponding value of the position rj, i=l, N of at least one source Si, i=l, N, for which the directivity in said direction (^()) is optimal in the vicinity of said corresponding value of the position / ^, i=l, N of at least one source Si, i=l, N, for example maximum in the vicinity of said corresponding value of the position r^, i=l, N of at least one source S;, i= 1, N.

[0018] According to these provisions, the method makes it possible to optimize the directivity of the antenna in a direction (Bq, <pQ^ quelconque en déterminant pour une valeur prédéterminée quelconque, i.e. sans que celle-ci soit limitée aux valeurs de + 180 ou - 180°, du coefficient de réflexion du plan réflecteur, et d’au moins une valeur correspondante de la position i=l, N de l’au moins une source S;, i=l, N, une valeur correspondante de l’au moins une amplitude complexe d’excitation At^ i=l, N dans la direction Pour laquelle la directivité dans ladite direction ( (p} est optimale au voisinage de ladite valeur correspondante de l’au moins une amplitude complexe d’excitation Ai, i= 1, N de l’au moins une source Si, i=l, N, par exemple maximum au voisinage de ladite valeur correspondante de l’au moins une amplitude complexe d’excitation A;, i=l, N de l’au moins une source S;, i=l, N.

[0019] According to one embodiment, the invention comprises one or more of the following features, alone or in a technically acceptable combination.

[0020] According to one embodiment, the terms of the coupling matrix for i=-N, N and i^0 and for j=-N, N and j^0, are defined by:

[0021] [Math.9] f ej^#ï^)û.n0d6dq> ,, _ 0 Ô ' 7____________________________

[0022] where k is a wave number equal to 2ir / X,

[0023] and in which the terms of the reduced coupling matrix, H'ij^ for i=l, N and for j=l, N are defined by:

[0024] [Math. 10] +Tj + 1^( + Tj )

[0025] According to one embodiment, the at least one source comprises a plurality of sources Si, i=l, N aligned along a direction transverse to the reflecting plane.

[0026] According to one embodiment, a distance between two neighboring sources of the plurality of sources S;, i=l, N is constant.

[0027] According to one embodiment, a minimum distance between a source of the plurality of sources Si, i=l, N and the reflecting plane is equal to the distance between two neighboring sources.

[0028] According to one embodiment, a minimum distance between a source of at least one source S;, i=l, N and the reflecting plane is less than or equal to half the wavelength of the electromagnetic radiation emitted by at least one source.

[0029] For the sake of clarity, an embodiment and / or implementation of the invention is described with reference to the accompanying drawings, which represent, by way of non-limiting example, an embodiment or implementation of a device and / or method according to the invention. The same reference numerals in the drawings designate similar elements or elements with similar functions.

[0030] [Fig. 1] is a simplified view of an antenna comprising 3 sources, with the corresponding image sources, according to one embodiment of the invention,

[0031] [Fig.2] is a simplified view of an antenna comprising a source, with the source corresponding image, and the trajectory of certain rays emitted respectively by the source and the image source forming the total radiation at two particular distant points, according to an embodiment of the invention,

[0032] [Fig.3] is a schematic representation of the angular coordinates used to define a radiation direction of the antenna, according to an example of an implementation of the invention.

[0033] [Fig.4] is a schematic presentation of the sequence of steps in the process, according to an example of an implementation of the invention

[0034] [Fig.5] presents the directivity values ​​calculated for an antenna comprising a reflector plane and a single electric radio dipole as a radiation source, as a function of the phase coefficient of the reflection coefficient, according to an example of an implementation of the invention.

[0035] [Fig.6] presents 3 profiles of variation of the directivity represented along the vertical axis, on a linear scale, as a function of the d / z ratio which evolves along the horizontal axis between the values ​​0 and 0.5, for three different dipole antenna configurations according to an example of an implementation of the invention

[0036] [Fig.7] is a schematic presentation of the sequence of steps in the process, according to an example of an implementation of the invention

[0037] [Fig.8] is a schematic presentation of the sequence of steps of the process, according to an example of implementation of the invention.

[0038] The invention relates to a method 100 for optimizing the directivity of an antenna A comprising a reflector plane P and one or more sources Si, i=l, N of electromagnetic radiation interacting with the reflector plane P.

[0039] An example of an antenna A comprising a reflector plane P and 3 sources Si, i=l, 3 is shown in [Fig. 1]. However, it is obvious to those skilled in the art that the number N of sources Si, i=l, N of the antenna A is not limited to 3.

[0040] Each electromagnetic source Si, i=l, N is defined by a position FJ, i=l, N of said source relative to the reflector plane.

[0041] In particular, the sources Si, i=l, N can be aligned along a direction transverse to the reflecting plane.

[0042] More particularly, a distance between two neighboring sources of the plurality of sources S;, i=l, N is constant.

[0043] Even more particularly, the source closest to the reflector plane P is at a distance from the reflector plane P equal to the distance between two neighboring sources, or even less than or equal to half the wavelength of the electromagnetic radiation emitted by the sources.

[0044] Each electromagnetic source Si, i=l, N is configured to radiate an electromagnetic field in a determined wavelength X, and; said electromagnetic field is reflected on the reflecting plane so that a reflected field is radiated by an image source S4, i=l, N of the source Si, i=l, N, the reflected field being a function of the electromagnetic field radiated by at least one source S, i=l, N and of a complex reflection coefficient F, i=l, N.

[0045] The complex reflection coefficient is itself a function of an attenuation coefficient and a phase coefficient.

[0046] An example of an antenna comprising a source Si and a reflector plane P is shown in [Fig.2]. The image source Si, positioned at a point symmetrical to the source Si with respect to the reflector plane, emits radiation corresponding to the reflected radiation, including in particular the two rays Ri and R2 shown in [Fig.2], which combine, by adding, at a point PI far from the antenna, respectively at another point P2, with two direct rays Di and D2 to form the total radiation of the antenna at points PI and P2.

[0047] Thus, we obtain a total field radiated by a plurality of sources comprising at least one source (S, i=l, N) and at least one image source (Si, i=l, N). On the other hand, we only consider here the total field radiated far from the position of the antenna A; in other words, we consider the total field radiated at a distant point defined by a direction (O, 0) relative to the antenna, said direction being defined by a colatitude with respect to a direction normal to a reflecting plane P, and a longitude with respect to a reference direction in said reflecting plane P. By way of example, Figure 3 represents a point PI positioned in a direction r (0, 0, 1), defined in a Cartesian coordinate system with origin A positioned at the level of the antenna A and whose axes Ax and Ay are in the reflecting plane P, the axis Az being normal to the plane P.

[0048] Optionally, the direction Zq ($o, ^o) is transverse to the reflecting plane.

[0049] The electromagnetic field radiated by each image source Si, i= 1, N in the direction (#o, ^o) is defined by a complex excitation amplitude Ai^ i=l, N, and a unit vector 7 i fi m \-

[0050] For example, in the case of an antenna comprising a single source, we have, in the spherical coordinate system at point PI of [Fig.3]:

[0051] [Math.l] f(0, 0) = cos0sin^ + cos^

[0052] The directivity of antenna A in the direction (q, o) is conventionally defined as a measure of the degree of concentration of the radiation emitted in the direction considered, or more precisely, as the power density that the antenna emits in the direction considered, relative to the power density emitted by an isotropic radiating element, i.e., one that emits uniformly in all directions, emitting the same total power; the directivity of antenna A in the direction (q, o) is a function of the position rj, i= 1, N, and of the amplitude excitation complex Ai^ i=l, N, of each source S;, i=l, N, and of the complex reflection coefficient / 3, i=l, N.

[0053] We will note ai(j = Am || / .( 3q, (p ) || 'c excitation vector which maximizes the directivity in the direction FQ (^o, ^o).

[0054] For Si, i=l, N sources associated with Si, i=l, N image sources and reflection coefficients (A, i=l, N), the complex excitation amplitudes i=l, N, which maximize the directivity in the direction tp (&q, ^o) are given by equation A.7 of reference EE Altshuler, TH O'Donnell, AD Yaghjian and SR Best, "A monopole superdirective array," in IEEE Transactions on Antennas and Propagation, vol. 53, no. 8, pp. 2653-2661, Aug. 2005,

[0055] [Math.2]

[0056] where k is a wave number equal to 2+ / / .,

[0057] with / e {i= 1, N} u{j=-1, -N|

[0058] and with: [Math.3] TT. . _ O ' ' 7,

[0059] A,= FjAi therefore a= Oî^F;

[0060] [Math.4] lLi=ïHkj^ <pai^<p0' +Fj Hk.-u^ipate^ =

[0061] We observe that we have 2N equations for N unknowns, which are not independent.

[0062] To return to a system of linear equations of N equations with N unknowns, we sum the equation where l=i and the equation where l=-i, after first multiplying the equation where l=-j by E* (we change the dummy index i of the previous equation to j because 1 has become i), taking into account that i=-j, to obtain:

[0063] [Math.5] 23^ / ® + O i ^j= + Tj = ejkr,-ri + E {

[0064] That is:

[0065] [Math.6] + Fj Hi-j,e,>(pn + Fi ( / / +7,^ + Fj = eFr^i + Ei

[0066] He comes:

[0067] [Math.7]

[0068] With:

[0069] [Math. 8] HiJ,8o#Q = Hijj^ + Fj + Fi + Fj

[0070] The directivity, in the direction (^o, ^o), is therefore determined from a reduced coupling matrix of dimension N*N, whose terms for i=l, N and for j=l, N are defined from the terms of a coupling matrix of dimension 2N*2N, the terms of said coupling matrix Hîj^ for i=-N, N and i^0 and for j=-N, N and j^0 being a function of the radiated field ~f ( ÿ m > in the direction >o (^o, ^o) by a source Si, i=l, N or by an image source S ;, i= 1, N, and by another source Sj among the at least one source (Si, i=l, N) or by another image source S, among the at least one image source (Si, i=l, N).

[0071] More specifically, the terms of the coupling matrix for i=-N, N and i^0 and for j=-N, N and j^0, are defined by:

[0072] [Math.9] Î / CT s f \fift. <p\f is.mSd6dtp TT _ «O ' \ ____________

[0073] And the terms of the reduced coupling matrix, for i=l, N and for j=l, N are defined by:

[0074] [Math. 10] Tj Hi-j,0^o + r{ ÇH4.j,e^+ Fj

[0075] For example, in the case of an antenna comprising a single source of the electric (or magnetic) dipole type, and considering the direction ( 7q, ^0) — (0,0) the preceding equation can be written:

[0076] [Math. 11] (H^ ^q+F{ o + Fi j F] H.^q) «lqo = e-iïwt+F

[0077] with:

[0078] [Math. 12] eikd+r pi™ (li 0 0= 7 " 7 » 7*

[0079] Indeed, in the case where io is a unit vector in the unit direction normal to the reflecting plane 0(> ^0, ie = ^ , and the radiating source is located on the z-axis at a distance d , ie rj = d^ and by principle its image is given by r = - d^

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] The complex excitation coefficient is obtained from 4 ai-oo Finally, the directivity in the (0,0) direction is obtained by applying the equation next: [Math. 13] £ / (U,U) — .û Jo ^\AiA^ Figure 5 shows the directivity values ​​thus calculated for an antenna comprising a reflector plane and a single dipole as a radiation source, as a function of the phase coefficient of the reflection coefficient 7! (the attenuation coefficient of the reflection coefficient being constant and equal to 1) and the ratio d!A; the phase coefficient varies along the vertical axis of the graph between -180° and +180°, and the ratio d / A varies along the horizontal axis of the graph between 0 and 0.5. The directivity values ​​thus calculated are represented with a color code which allows us to observe that the directivity tends asymptotically towards a maximum equal to a value of 10.6 when d! X tends towards 0 and the phase coefficient tends towards -180°; another local maximum of the directivity at a value of 7 appears when the ratio d! À tends towards 0.42 and the phase coefficient tends towards -42°. Similarly, we can observe a cancellation of the directivity along a diagonal of the graph. Thus we observe that by varying the phase coefficient as a function of the ratio d!A we obtain a maximum directivity equal to 10.6, greater than the maximum directivity of 7.5 known for a dipole whose distance to the reflecting plane of the perfect electrical conductor type tends towards 0. Figure 6 presents 3 profiles of variation of the directivity represented along the vertical axis as a function of the ratio dlÀ which evolves along the horizontal axis between the values ​​0 and 0.5, for three different dipole antenna configurations comprising respectively: - an electric (or magnetic) Hertzian dipole, and a reflector plane with an optimized reflection coefficient PRO, - an electric radio dipole (EHD), and a reflector plane described as a "perfect electrical conductor" (PEC), - a magnetic radio dipole MHD, and a reflector plane described as a "perfect electrical conductor" PEC. In the case of an antenna A comprising a reflecting plane P and two Hertzian dipoles aligned along a direction normal to the reflecting plane P at a distance d and 2d from the reflecting plane P, therefore with r = -d and r² = their images being respectively located at r 1 = - and r 2 = - 2de^, and assuming an identical reflecting surface for the 2 dipole sources, therefore equal reflection coefficients A, we obtain the coupling matrices:

[0089] [Math. 14] (H], i,o + T} H + F ! + F} I\ + ( / / 1,2,0 + / ^2 / / 1,-2,0 + / ^1 / / -1,2,0 + / 1 1 ^2 / / -1,2,0) ( / / 2,1,0+ / 1} H2Afi+^2 H-2,w+r2 r] / / -2,-1,0) «lm9+ , ( / / 2,2,0 + / 2 / / 2.-2,0+ / 2 / / -2,2,0 + / 2 -G / / -2.2,0 ) + / 2e- / *ro-r-2

[0090] After solving the system of 2 equations with 2 unknowns a^<^>0 and a^^0, we obtain the complex excitation coefficients:

[0091] [Math. 15] A IMF And [Math. 15]

[0092] The maximum directivity in the direction (%) is given by:

[0093] [Math. 16] — c-Mii -* -» . - ü2 ' Jo J^7.-2-^| ûnfjdffdÿ

[0094] By varying the reflection coefficient F = G on the unit circle and varying dlÀ between 0 and 0.5 we obtain a result similar to that presented in figures 5 and 6 for the case of an antenna comprising a single source of the electric (or magnetic) dipole type.

[0095] According to a third example, in the case of an antenna comprising a reflector plane and a Huygens source consisting of two co-located sources, i.e. f( — ~r~, = d(% with each a different reflection coefficient F| F2, the same system of equations applies:

[0096] [Math. 17] (^Lio + Fj o + Hi^q+Ty r} H-ij5o) «lmo + ( ,2,0+r2X2,o+A* =e^+ ( #2,1,0 + 1 #2,-1,0 + / 2 #-2,10 + G 1 #-2,-1,0 ) + ( #2.2,0 + A *#2.2,0 + A^-2.2,0 + ^2^2^-2,2,0 ) «ZM0 =

[0097] And the maximum directivity obtained is given by:

[0098] [Math. 18] D(0G,¢ ) = ----z----7—;----------7— ---—-------;--------- V u 7 ]„ l.0\\AWn^^

[0099] in which the two radiation diagrams of the two sources are taken into account, the radiated fields also appearing in the HijQ coefficients.

[0100] More generally, a maximum directivity Dmax ( ) in the direction rj ( #0, ^0) is defined by:

[0101] Dmax [Math. 19] ( ^0' ) f-" r N — ... ,, ji2 'Jo

[0102] The directivity obtained with this formula is maximum if the excitation coefficients Ai are chosen on the basis of the solution of equation Math 7 defined above.

[0103] The method 100 according to a first alternative of the invention comprises the following steps: - determination 101 of a value of the position i=l, N of at least one source Si, i=l, N and of at least one corresponding value of at least one complex excitation amplitude i=l, N in the direction 3q, rp}, - on the basis of the reduced coupling matrix, determination 102 of at least one corresponding value of the complex reflection coefficient, the directivity in the direction ( 3q, (p ) being locally optimal in the vicinity of said corresponding value of the phase coefficient, for example locally maximum in the vicinity of said corresponding value of the reflection coefficient;

[0104] According to these provisions, the method makes it possible to optimize the directivity of the antenna in any direction r® ( 3q, p ) by determining for a value predetermined position (FJ, i=l, N) of at least one source (S;, i=l, N), and a corresponding value of at least one complex excitation amplitude i - 1, N, at least one corresponding value of the reflection coefficient of the reflecting plane for which the directivity in the direction (6^ (p^ is optimal in the vicinity of said corresponding value of the reflection coefficient, for example maximum in the vicinity of said corresponding value of the reflection coefficient; the method allows to determine said corresponding value of the reflection coefficient, without it being limited to the values ​​of + 180 or - 180 °.

[0105] In other words, the reflection coefficient maximizing the directivity is calculated by a global optimization approach, by calculating the directivity obtained by varying the parameter to be optimized (here the reflection coefficient) over a given domain. The highest value is retained.

[0106] The method 100 according to a second alternative of the invention comprises the following steps: - determination 101' of a value of the reflection coefficient and at least one corresponding value of at least one complex excitation amplitude A / ,^ i=l, N in the direction (Oq, (p - on the basis of the reduced coupling matrix, determination 102' of at least one corresponding value of the position FJ, i=l, N of at least one source S;, i=l, N, the directivity in the direction ( 9q, being locally optimal in the vicinity of said corresponding value of the position i=l, N of at least one source Si, i=l, N, for example locally maximum in the vicinity of said corresponding value of the position i=l, N of at least one source S;, i=l, N;

[0107] According to these provisions, the method makes it possible to optimize the directivity of the antenna in a direction (60, <p ) quelconque en déterminant pour une valeur prédéterminée quelconque, i.e. sans que celle-ci soit limitée aux valeurs de + 180 ou - 180°, du coefficient réflexion plan réflecteur, et d’au moins correspondante l’au amplitude complexe d’excitation a ,^ i="l," n dans la direction ( , at least one corresponding value of the position FJ, i=l, N of the at least a source Si, i=l, N, for which the directivity in said direction is optimal in the vicinity of said corresponding value of the position FJ, i=l, N of at least one source S;, i=l, N, for example maximum in the vicinity of said corresponding value of the position FJ, i=l, N of at least one source Si, i= 1, N.

[0108] In other words, as previously stated, the reflection coefficient maximizing directivity is calculated by a global optimization approach, by calculating the The directivity is obtained by varying the parameter to be optimized (here, the position) over a given domain. The highest value is retained.

[0109] For example, in the case of an antenna comprising a single source of the type electric (or magnetic) dipole, Figures 5 and 6 presented in detail above illustrate an example of a result obtained by the method 100 according to the first alternative in which it is the phase coefficient that varies or according to the second alternative in which it is the distance of the dipole to the reflecting plane that varies.

[0110] Similarly, according to another example, in the case of an antenna comprising a reflector plane and a Huygens source consisting of two co-located sources, Figure 7, obtained by fixing dtX - 0.1 and varying independently the phase coefficient of the reflection coefficient 7, and of each source between -180° and +180, with the corresponding value of the directivity represented by a color code, allows us to observe a maximum D(0,0) equal to approximately 15.6 on a linear scale, for the identical values ​​of the phase coefficient of the reflection coefficients r] and r2 equal to -164°, which is consistent with the theoretical maximum value equal to 16 when d / A tends towards 0.

[0111] Figure 8 shows two maximum directivity profiles obtained by varying d!A between 0 and 0.5 and by independently varying the phase coefficient of the reflection coefficient of each source r] and L2 between -180° and +180°, along a trajectory determined on the graph in [Fig. 7], with respectively: - an MSA-PEC profile, a perfect electrically conductive type of reflective plane, and - an MSA-PRO profile with another optimized reflector plane.

[0112] It is thus observed that it is possible to achieve, thanks to the method 100 according to the invention, with an optimized reflector plane, a maximum directivity almost 2 times greater than the limit attainable with a reflector plane of the perfect electrical conductor type.

[0113] The method 100 according to a third alternative of the invention comprises the following steps: - determination 101” of a value of the position / 7, i=l, N of at least one source Si, i=l, N , and of a value of the reflection coefficient, - based on the reduced coupling matrix, determination 102'' of at least one corresponding value of at least one complex excitation amplitude i=l, N in the direction ( ^0), the directivity in the direction ( ) being locally optimal in the neighborhood of said value corresponding of the complex excitation amplitude i=l, N in the direction ( 0o» <p()) de l’au moins une source si, i="l," n, par exemple locally maximum in the vicinity of the corresponding value of the complex excitation amplitude, i=l, N of at least one Si5 source i=l, N in the direction

[0114] According to these provisions, the method makes it possible to optimize the directivity of the antenna in any direction (^0) by determining for a predetermined value any, i.e., without being limited to the values ​​of +180° or -180°, of the reflection coefficient of the reflecting plane, and of at least one corresponding value of the position i=l, N) of at least one source Si, i=1, N, a corresponding value of at least one complex excitation amplitude i=l, N in the direction ( ^o) for which the directivity in said direction ( Vq) is optimal at neighborhood of said corresponding value of at least one complex excitation amplitude A;, i= 1, N of at least one source S;, i=l, N, for example maximum in the neighborhood of said corresponding value of at least one complex excitation amplitude Ai, i=l, N of at least one source Si, i=l, N.

[0115] In other words, as previously stated, the reflection coefficient maximizing the directivity is calculated using a global optimization approach, by calculating the directivity obtained by varying the parameter to be optimized (here, the complex excitation amplitude) over a given range. The highest value is retained.

Claims

Demands

1. Method (100) for optimizing the directivity of an antenna, the antenna comprising at least one electromagnetic source (Si, i=l, N) associated with at least one complex excitation amplitude (Ai, i=l, N) as a function of a direction (Ai, i=l, N), defined by a colatitude with respect to a direction normal to a reflecting plane in electromagnetic interaction with the at least one source (Si, i=l, N), and a longitude with respect to a reference direction in said reflecting plane, the at least one electromagnetic source (Si, i=l, N) being configured to radiate an electromagnetic field at a determined wavelength X, a position (Ai, i=l, N) of the at least one source being determined relative to the reflecting plane, and a complex reflection coefficient (Ti, i=l, N) of at least one source (Si, i=l, N) on the reflecting plane being defined to determine, an image electromagnetic field radiated by at least one image source (S, i=l, N) of the at least one source (Si , i=l, N), as a function of the electromagnetic field radiated by at least one source (Si, i=l, N), a total field being radiated in the direction by a plurality of sources including at least one source (S;, i=1, N) and at least one image source (S4, i=l, N), The antenna directivity in the (0O, 0) direction is a function of the position (y, i=l, N) of at least one source (Si, i=l, N), at least one complex excitation amplitude (A₀, i=l, N), and the complex reflection coefficient (Ti₅, i=l, N). The directivity in the Fq (¾, 0) direction is determined from a reduced coupling matrix of dimension N*N, whose terms for i=l, N and for j=l, N are defined from the terms of a coupling matrix of dimension 2N*2N, the terms of said coupling matrix for i=-N, N and i^O and for j=-N, N and j^O being functions of the radiated field 4(¾¾) in the direction (^o, ^o) by a source If among the others at least one source (Si, i=l, N) or by an image source S among the at least one image source (Si, i=l, N), and by another source Sj among using at least one source (S, i=l, N) or another image source S_j from among at least one image source (Si, i=l, N), the process (100) comprising the following steps: - determination (101) of a value of the position (r^, i=l, N) of at least one source (S;, i=l, N) and of at least one corresponding value of at least one complex excitation amplitude (Aj,f?(). <p , i=l, N) dans la direction - on the basis of the reduced coupling matrix, determination (102) of at least one corresponding value of the reflection coefficient, the directivity in the direction (Gq, being locally optimal in the vicinity of said corresponding value of the reflection coefficient, for example locally maximum in the vicinity of said corresponding value of the reflection coefficient; or, alternatively, the following steps: - determination ( 101' ) of a value of the coefficient of reflection and at least one corresponding value of at least one complex excitation amplitude i=l, N) in the direction ( <pQ ), - on the basis of the reduced coupling matrix, determination (102') of at least one corresponding value of the position (rj, i=l, N) of at least one source (Si, i=l, N), the directivity in the direction (Sq, <pQ ) étant localement optimale au voisinage de ladite valeur correspondante de la position (rj, i=l, N) de l’au moins une source (Si, i=l, N), par exemple localement maximum au voisinage de ladite valeur correspondante de la position (r-, i=l, N) de l’au moins une source (Si, i=l, N); or, alternatively, the following steps: - determination (101”) of a value of the position (rj, i=l, N) of at least one source (S;, i= 1, N), and of a value of the reflection coefficient, - on the basis of the reduced coupling matrix, determination (102”) of at least one corresponding value of at least one complex excitation amplitude (A^e^ i=l, N) in the direction ( Oq, (pQ^, the directivity in the direction ( being locally optimal in the vicinity of said corresponding value of the complex excitation amplitude (Aie^ i=l, N) in the direction ( ^0) of at least one source (Si, i=l, N), for example locally maximum in the vicinity of said corresponding value of the complex excitation amplitude (Ai,^ i=l, N) of at least one source (Si, i=l, N) in the direction ( Po);

2. A method (100) according to claim 1, wherein the terms of the coupling matrix for i=-N, N and i^0 and for j=-N, N and j^0, are defined by: [Math.9] f (0,(p) ej^' <e'jli’arjsintklOdq) _ o ô 1 7 ______________________ où k est un nombre d’onde égal à 2ir / X, et dans lequel les termes de la matrice de couplage réduite, H'ij^ pour i=l, N et pour j=l, N sont définis par: [Math. 10] +i + G ( + rj )

3. Method (100) according to any one of claims 1 or 2, wherein at least one source comprises a plurality of sources (S;, i=l, N) aligned in a direction transverse to the reflecting plane.

4. Method according to claim 3, wherein a distance between two neighboring sources of the plurality of sources (Si, i=l, N) is constant.

5. A method according to any one of claims 3 or 4, wherein a minimum distance between a source of the plurality of sources (Si, i=l, N) and the reflecting plane is equal to the distance between two neighboring sources.

6. A method according to any one of claims 1 to 5, wherein a minimum distance between a source of at least one source (Si5 i=l, N) and the reflecting plane is less than or equal to half of the wavelength of electromagnetic radiation emitted by at least one source.

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