EP0952624A1 - Electronic multibeam sweep antenna - Google Patents

Abstract

The system uses addition of components of successive orders to determine dephasing required for operation. The aerial comprises an array of dephasers (2, Dij), with N simultaneous beams being obtained in N directions by an excitation law (fij) applied to each dephaser (Dij). The excitation law is calculated by summing the phase laws ( phi 1, phi 2 ... phi N) associated with each direction of order 1,2,... N, and by applying the resulting phase shift ( SIMILAR ftij) to the dephaser, without applying the resultant amplitude modulation ( SIMILAR pij). The frequencies of the beams used are different. The phase laws ( SIMILAR f1, SIMILAR f2 ... SIMILAR fN) may each be affected by a weighting coefficient (r1, r2 ...rN). The weighting coefficients are determined to obtain a sum channel and a difference channel in two different directions.

Description

The present invention relates to a multibeam electronic scanning antenna. It is particularly applicable for antennas with phase control only in the context for example of communications by satellite or terrestrial requiring simultaneous communication with several variable sites.

Telecommunication demands are constantly increasing. In addition, users, soldiers, professional civilians or individuals are demanding increasingly lower costs. To meet these requirements, telecommunications equipment must be very profitable. To this end, it is advantageous to use antennas with several beams which make it possible to transmit or receive simultaneously in several different directions, moreover not fixed in advance. Thus, it is advantageous for a communication satellite to be able to communicate with several stations at the same time, variable in number and in position, from the same antenna. It is the same for terrestrial radiocommunications in the case for example where several mobile sites of the same network can communicate with each other simultaneously.

It is known to produce multibeam electronic scanning antennas, but these antennas are active, that is to say that they do not simply comprise phase shifters but active modules controllable in phase but also in amplitude modulation, more particularly in modulation of the power emitted by module. However, an antenna with active modules is expensive.

   et en appliquant le déphasage résultant ψt_ij sur le déphaseur, sans appliquer la modulation d'amplitude résultante ρ_ij.The invention makes it possible to produce a multibeam electronic scanning antenna not provided with active modules, that is to say with phase control only, such an antenna being more economical. To this end, the subject of the invention is an antenna with electronic scanning comprising a network of phase shifters D _ij characterized in that N simultaneous beams are obtained in N independent directions by an excitation law f _ij applied to each phase shifter D _lj which is calculated by summing the phase laws ψ ₁ , ψ ₂ , ... ψ _k , ... ψ _N associated respectively with each direction of order 1, 2, ... k, ... N according to the relation: $${\text{f}}_{\text{ij}}\text{= <figure-callout id="1" label="e i" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{{\text{i}}_{}}{{}_{\text{1}}}^{}\text{+ <figure-callout id="2" label="e i" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{{\text{i}}_{}}{{}_{\text{2}}}^{}\text{... + e}{}^{{\text{i}}_{\text{k}}}\text{... + e}{}^{{\text{i}}_{\text{NOT}}}{\text{= ρ}}_{\text{ij}}\text{e}{}^{{\text{jt}}_{\text{ij}}}$$

and by applying the resulting phase shift ψt _ij to the phase shifter, without applying the resulting amplitude modulation ρ _ij .

The main advantages of the invention are that it adapts to antennas already made, that it applies to all types of electronically scanned antennas, that it allows a large number of beams to be created simultaneously for the same antenna and that it is simple to implement.

• la figure 1, un exemple d'antenne à balayage électronique à réflecteur où l'invention peut être appliquée ;
• la figure 2, une approximation d'une modulation d'amplitude par une modulation à deux états, dans le cas d'une antenne à deux faisceaux.

Other characteristics and advantages of the invention will become apparent from the following description given with reference to the appended drawings which represent:

• Figure 1, an example of an electronic scanning antenna reflector where the invention can be applied;
• FIG. 2, an approximation of an amplitude modulation by a two-state modulation, in the case of a two-beam antenna.

   quelle que soit la distance entre les déphaseurs, avec en particulier en cas d'équidistance entre ces déphaseurs : $${\text{Ψ}}_{\text{xi}}\text{= 2πi}\frac{{\text{d}}_{\text{x}}}{\text{λ}}{\text{sinθ}}_{\text{b}}{\text{cosϕ}}_{\text{b}}$$

   et $${\text{Ψ}}_{\text{yi}}\text{= 2πj}\frac{{\text{d}}_{\text{y}}}{\text{λ}}{\text{sinθ}}_{\text{b}}{\text{sinϕ}}_{\text{b}}$$

où :

• D_ij est le déphaseur d'ordre i selon l'axe x et d'ordre j selon l'axe y, i et j étant des entiers relatifs de sorte que deux déphaseurs disposés sur une même droite, parallèle à un des deux axes x, y, mais dont le segment est coupé par un de ces deux axes, qui passent par l'origine O, ont des ordres de signes opposés;
• d_x et d_y sont respectivement les distances selon les axes x et y, entre les centres de deux déphaseurs contigus ;
• z étant l'axe perpendiculaire aux deux axes précédents x, y, alors θ_b est l'angle de la direction de pointage du faisceau vu de l'origine O, par rapport à l'axe z, dans le plan O, x, z et ϕ_b est l'angle de la projection sur le plan O, x, y de la direction de pointage du faisceau vu de l'origine O, par rapport à l'axe x, dans le plan O, y, y , en d'autres termes, θ_b est l'angle entre la direction de balayage et l'axe Oz et ϕ_b est l'angle entre la direction de balayage projetée dans le plan O, x, y et l'axe Ox ;
• λ est la longueur de l'onde émise.

Figure 1 shows an example of an electronic scanning antenna, comprising a reflector. In this type of antenna, a primary source illuminates the reflector which focuses the energy received in a desired direction, the variation in direction being effected by controlling the reflector. The reflector 1 comprises for example a network of N × M elementary phase shifters 2, more particularly N phase shifters along a first x axis and M phase shifters along a second y axis, for example orthogonal to the previous one. The antenna is for example phase controlled, that is to say that there is no amplitude control. The reflector 1 of the antenna is illuminated by a radiating element 3. This radiating element is for example a comet supplied by a primary source in a manner known to those skilled in the art. It is placed at a distance z _sp from the reflector. By considering the origin of the phase for example at the geometric center O of the plane of the reflector, which is for example also the origin of the two aforementioned axes x, y, the theoretical phase law ψ to be applied to a phase shifter D _ij to point an emission beam obtained, in a scanning direction (θ _b , ϕ _b ) is written according to the following relationships: $${\text{Ψ = Ψ}}_{\text{x}}{\text{+ Ψ}}_{\text{y}}$$

whatever the distance between the phase shifters, with in particular in case of equidistance between these phase shifters: $${\text{Ψ}}_{\text{xi}}\text{= 2πi}\frac{{\text{d}}_{\text{x}}}{\text{λ}}{\text{sinθ}}_{\text{b}}{\text{cosϕ}}_{\text{b}}$$

and $${\text{Ψ}}_{\text{yi}}\text{= 2πj}\frac{{\text{d}}_{\text{y}}}{\text{λ}}{\text{sinθ}}_{\text{b}}{\text{sinϕ}}_{\text{b}}$$

or :

• D _ij is the phase shifter of order i along the x axis and of order j along the y axis, i and j being relative integers such that two phase shifters arranged on the same straight line, parallel to one of the two axes x , y, but whose segment is cut by one of these two axes, which pass through the origin O, have orders of opposite signs;
• d _x and d _y are respectively the distances along the axes x and y, between the centers of two contiguous phase shifters;
• z being the axis perpendicular to the two previous axes x, y, then θ _b is the angle of the beam pointing direction seen from the origin O, with respect to the z axis, in the plane O, x, z and ϕ _b is the angle of the projection on the plane O, x, y of the pointing direction of the beam seen from the origin O, with respect to the x axis, in the plane O, y, y, in other words, θ _b is the angle between the scanning direction and the Oz axis and ϕ _b is the angle between the scanning direction projected in the plane O, x, y and the Ox axis;
• λ is the length of the emitted wave.

   où x_i et y_j sont les coordonnées du centre du déphaseur dans le plan O, x, y.It is necessary to add to this theoretical phase Ψ, the opposite of the phase of the radiation from the primary source of the radiating element 3 which illuminates the reflector 1, to focus the energy in the desired scanning direction (θ _b , ϕ _b ). In the case of a primary source, located at the aforementioned distance z _sp , z _sp being in fact the coordinates of a point representative of this source in the frame O, x, y, z previously defined, it comes, by noting Ψ _sp the radiation phase of the primary source 3: $$\text{Ψ}{}_{{\text{sp}}_{\text{ij}}}\text{= 2π}\frac{\sqrt{{\text{(<figure-callout id="2" label="x i" filenames="imgf0001.png" state="{{state}}">x </figure-callout>}}_{\text{i}}{}^{\text{2}}{\text{+ <figure-callout id="2" label="y j" filenames="imgf0001.png" state="{{state}}">y </figure-callout>}}_{\text{j}}{}^{\text{2}}{\text{+ <figure-callout id="2" label="z sp" filenames="imgf0001.png" state="{{state}}">z </figure-callout>}}_{\text{sp}}{}^{\text{2}}}}{\text{λ}}$$

where x _i and y _j are the coordinates of the center of the phase shifter in the plane O, x, y.

The relation (4) shows that this phase Ψ _{sp ij} is relative to a spherical wave. It is also necessary to take into account the phase Ψ ₀ of the comet of the radiating source which it is possible to choose a priori.

Thus, the theoretical excitation f _ij (x, y) associated with a phase shifter D _ij to form a lobe in a given direction (θ _b , ϕ _b ) is given by the following relation: $${\text{f}}_{\text{ij}}\text{(x, y) = e}{}^{{\text{j (Ψ}}_{\text{xi}}{\text{+ Ψ}}_{\text{yj}}\text{-Ψ}{}_{{\text{sp}}_{\text{ij}}}{\text{+ Ψ}}_{\text{0}}\text{)}}$$

   où E(Ψt_ij/q) est la partie entière de Ψt_ij/q, q étant égal à 2π/2^N.In practice, the phase shifters being for example controlled according to N bits, the real phase applied to a phase shifter D _ij is the phase Ψtq _ij quantified at the step of the phase shifter q = 2π / 2 ^N. By noting Ψt _ij the total phase equal to Ψ _xi + Ψ _yj -Ψ _{sp ij} + Ψ ₀ , it comes: $${\text{Ψtq}}_{\text{ij}}{\text{= E (Ψt}}_{\text{ij}}\text{/ q) × q}$$

where E (Ψt _ij / q) is the integer part of Ψt _ij / q, q being equal to 2π / 2 ^N.

$${\text{Ψ}}_{\text{b2}}\text{= 2π(i}\frac{\text{dx}}{\text{λ}}{\text{sinθ}}_{\text{b2}}{\text{cosϕ}}_{\text{b2}}\text{+ j}\frac{\text{dy}}{\text{λ}}{\text{sinθ}}_{\text{b2}}{\text{sinϕ}}_{\text{b2}}\text{)}$$

To illustrate the operation in multi-beams, an example of emission of two beams at the same frequencies is first presented, the two beams being directed in directions (θ _b1 , ϕ _b1 ) and (θ _b2 , ϕ _b2 ) defined with the same conventions as above for management (θ _b , ϕ _b ). According to relations (1) to (3), the phases Ψ _b1 , and Ψ _b2 associated with these two directions are given by the following relations: $${\text{Ψ}}_{\text{b1}}\text{= 2π (i}\frac{\text{dx}}{\text{λ}}{\text{sinθ}}_{\text{b1}}{\text{cosϕ}}_{\text{b1}}\text{+ j}\frac{\text{dy}}{\text{λ}}{\text{sinθ}}_{\text{b1}}{\text{sinϕ}}_{\text{b1}}\text{)}$$

$${\text{Ψ}}_{\text{b2}}\text{= 2π (i}\frac{\text{dx}}{\text{λ}}{\text{sinθ}}_{\text{b2}}{\text{cosϕ}}_{\text{b2}}\text{+ j}\frac{\text{dy}}{\text{λ}}{\text{sinθ}}_{\text{b2}}{\text{sinϕ}}_{\text{b2}}\text{)}$$

   en notant une phase origine du cornet par direction indépendante, respectivement Ψ₀₁, Ψ₀₂ pour la première et la deuxième direction.Taking into account the phase -Ψ _{sp ij} focusing of the plane grating, which in fact serves as it was previously shown to compensate for the phase of the spherical wave of the primary source 3 of the supposed point reflector, and taking into account the origin phase of the comet, the theoretical excitation f _ij associated with a phase shifter D _ij checks the following relation: $${\text{f}}_{\text{ij}}\text{= e}{}^{{\text{j (Ψ}}_{\text{b1}}\text{-Ψ}{}_{{\text{sp}}_{\text{ij}}}{\text{+ Ψ}}_{\text{01}}\text{)}}\text{+ e}{}^{{\text{j (Ψ}}_{\text{b2}}\text{-Ψ}{}_{{\text{sp}}_{\text{ij}}}{\text{+ Ψ}}_{\text{02}}\text{)}}\text{= <figure-callout id="1" label="e i" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{{\text{i}}_{}}{{}_{\text{1}}}^{}\text{+ <figure-callout id="2" label="e i" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{{\text{i}}_{}}{{}_{\text{2}}}^{}$$

by noting an origin phase of the horn by independent direction, respectively Ψ ₀₁ , Ψ ₀₂ for the first and the second direction.

   où $${\text{Ψ}}_{\text{1}}{\text{= Ψ}}_{\text{b1}}\text{- Ψ}{\text{}}_{{\text{sp}}_{\text{ij}}}{\text{+ Ψ}}_{\text{01}}{\text{\hspace{1em}\hspace{1em}\hspace{1em}et Ψ}}_{\text{2}}{\text{= Ψ}}_{\text{b2}}\text{- Ψ}{\text{}}_{{\text{sp}}_{\text{ij}}}{\text{+ Ψ}}_{\text{02}}$$

   avec $${\text{ρ}}_{\text{ij}}\text{= 2}\left|\text{cos}\frac{{\text{Ψ}}_{\text{1}}{\text{- Ψ}}_{\text{2}}}{\text{2}}\right|$$

   et: $${\text{Ψt}}_{\text{ij}}\text{=}\frac{{\text{Ψ}}_{\text{1}}{\text{+ Ψ}}_{\text{2}}}{\text{2}}\text{si -}\frac{\text{π}}{\text{2}}\text{+2kπ≤}\frac{{\text{Ψ}}_{\text{1}}{\text{- Ψ}}_{\text{2}}}{\text{2}}\text{≤}\frac{\text{π}}{\text{2}}\text{+ 2kπ}$$

   ou : $${\text{Ψt}}_{\text{ij}}\text{=}\frac{{\text{Ψ}}_{\text{1}}{\text{+ Ψ}}_{\text{2}}}{\text{2}}\text{+ π si}\frac{\text{π}}{\text{2}}\text{+ 2kπ≤}\frac{{\text{Ψ}}_{\text{1}}{\text{- Ψ}}_{\text{2}}}{\text{2}}\text{≤}\frac{\text{3π}}{\text{2}}\text{+2kπ}$$

In application of the preceding relations (7), (8) and (9), the excitation f _ij can also be written according to the following relation: $${\text{f}}_{\text{ij}}\text{= 2 cos}\frac{{\text{Ψ}}_{\text{1}}{\text{-<figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}}{\text{2}}\text{<figure-callout id="1" label="e j Ψ" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{\text{j}\frac{{\text{Ψ}}_{}}{}}{\frac{{}_{\text{1}}{\text{+ <figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}}{\text{2}}}^{}{\text{= ρ}}_{\text{ij}}\text{e}{}^{{\text{jt}}_{\text{ij}}}$$

or $${\text{<figure-callout id="1" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{1}}{\text{= Ψ}}_{\text{b1}}\text{- Ψ}{}_{{\text{sp}}_{\text{ij}}}{\text{+ Ψ}}_{\text{01}}{\text{and <figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}{\text{= Ψ}}_{\text{b2}}\text{- Ψ}{}_{{\text{sp}}_{\text{ij}}}{\text{+ Ψ}}_{\text{02}}$$

with $${\text{ρ}}_{\text{ij}}\text{= 2}\left|\text{cos}\frac{{\text{Ψ}}_{\text{1}}{\text{- <figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}}{\text{2}}\right|$$

and: $${\text{Ψt}}_{\text{ij}}\text{=}\frac{{\text{<figure-callout id="1" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{1}}{\text{+ <figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}}{\text{2}}\text{if -}\frac{\text{<figure-callout id="2" label="π" filenames="imgf0001.png" state="{{state}}">π</figure-callout>}}{\text{2}}\text{+ 2kπ≤}\frac{{\text{Ψ}}_{\text{1}}{\text{- <figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}}{\text{2}}\text{≤}\frac{\text{<figure-callout id="2" label="π" filenames="imgf0001.png" state="{{state}}">π</figure-callout>}}{\text{2}}\text{+ 2kπ}$$

or : $${\text{Ψt}}_{\text{ij}}\text{=}\frac{{\text{<figure-callout id="1" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{1}}{\text{+ <figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}}{\text{2}}\text{+ π if}\frac{\text{<figure-callout id="2" label="π" filenames="imgf0001.png" state="{{state}}">π</figure-callout>}}{\text{2}}\text{+ 2kπ≤}\frac{{\text{Ψ}}_{\text{1}}{\text{- <figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}}{\text{2}}\text{≤}\frac{\text{3π}}{\text{2}}\text{+ 2kπ}$$

The phase law to be applied to the phase shifters of the antenna, to form the two beams, is the quantified phase: $${\text{Ψtq}}_{\text{ij}}{\text{= E (Ψt}}_{\text{ij}}\text{/ q) × q}$$

, mais il faut également moduler l'amplitude des déphaseurs suivant la loi : $${\mathit{\text{A}}}_{\mathit{\text{ij}}}\text{= 2cos}\frac{{\text{Ψ}}_{\text{1}}{\text{- Ψ}}_{\text{2}}}{\text{2}}$$

   pour chaque déphaseur D_ij, cette modulation d'amplitude étant notamment fonction de la situation de chaque déphaseur D_ij et de la longueur d'onde λ comme le montrent en particulier les relations (7), (8) et (12).Thus, according to equation (10), to form several beams, it is not enough to apply the linear phase law $\frac{{\text{Ψ}}_{}}{}$$\frac{{}_{\text{1}}{\text{+ <figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}}{\text{2}}$

, but it is also necessary to modulate the amplitude of the phase shifters according to the law: $${\mathit{\text{AT}}}_{\mathit{\text{ij}}}\text{= 2cos}\frac{{\text{Ψ}}_{\text{1}}{\text{- <figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}}{\text{2}}$$

for each phase shifter D _ij , this amplitude modulation being in particular a function of the situation of each phase shifter D _ij and the wavelength λ as shown in particular by relations (7), (8) and (12).

égal à 1 et en ajoutant un déphasage de π à la phase lorsque l'amplitude change de signe. De la sorte, il n'y a donc pas de modulation d'amplitude. Une antenne à déphaseur uniquement peut donc être utilisée.However, in the case of a phase control antenna only, it is not possible to act on the amplitude. In the case for example of the formation of two beams, the invention makes it possible to carry out an approximation of the sinusoidal amplitude according to the relation (12) in an amplitude modulation with two states +1 and -1, which amounts to reality to take a module ρ _ij = $\left|{\text{AT}}_{\text{ij}}\right|$

equal to 1 and adding a phase shift of π to the phase when the amplitude changes sign. In this way, there is therefore no amplitude modulation. A phase shift antenna only can therefore be used.

FIG. 2 illustrates such an approximation in the case of the formation of two beams in directions θ ₁ , θ ₂ taken in the Oxz plane defined above. The ordinate axis represents values A (x) homogeneous to an amplitude modulation as a function of the coordinates taken on the x axis. A first sinusoidal curve 21 represents the amplitude modulation A (x) to be applied according to the relation (12). For x = 0, the function A (x) is maximum and equal to 2 when Ψ ₁ = Ψ ₂ , according to the relation (12), which is verified since the phases at the origin of the comets, in case of use of these, are identical. The variation period Tx is given by the following relation: $$\text{Tx =}\frac{\text{2λ}}{{\text{sinθ}}_{\text{1}}{\text{- <figure-callout id="2" label="sinθ" filenames="imgf0001.png" state="{{state}}">sinθ</figure-callout>}}_{\text{2}}}$$

The amplitude modulation as represented by curve 21 is according to the invention approached by an amplitude modulation with two states, 1 and -1, represented by a curve 22. This modulation with two states has the same period of variation Tx than the previous sinusoidal modulation. It is also of the same sign. In other words, when the function A (x) is positive, the approximation function is equal to 1, and when the function A (x) is negative, the approximation function is equal to - 1. It is it should be noted that the approximation function of the sinusoidal phase modulation A (x) has the same period Tx as the latter, which in particular makes it possible to preserve the information relating to the targeted directions contained in the period Tx, and allows n '' result in no loss of earnings.

   où Ψ₁, Ψ₂,... Ψ_k,... Ψ_N représentent respectivement les phases associées à la première, à la deuxième, à la k^ième et à la N^ième direction, la loi de phase quantifiée étant toujours Ψtq_ij = E(Ψt_ij / q) × q.To form N beams at the same frequency in N independent directions, it suffices to quantify or not the phase deduced from the expression of the excitation f _ij linked to the phase shifters and defined by the following relation, for a phase shifter D _ij : $${\text{f}}_{\text{ij}}\text{= <figure-callout id="1" label="e i" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{{\text{i}}_{}}{{}_{\text{1}}}^{}\text{+ <figure-callout id="2" label="e i" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{{\text{i}}_{}}{{}_{\text{2}}}^{}\text{... + e}{}^{{\text{i}}_{\text{k}}}\text{... + e}{}^{{\text{i}}_{\text{NOT}}}{\text{= ρ}}_{\text{ij}}\text{e}{}^{{\text{jt}}_{\text{ij}}}$$

where Ψ ₁ , Ψ ₂ , ... Ψ _k , ... Ψ _N respectively represent the phases associated with the first, the second, the k ^th and the N ^th direction, the quantized phase law always being Ψtq _ij = E (Ψt _ij / q) × q.

By extrapolation of the case with two beams, the experiments carried out by the Applicant have indeed shown that only the phase shift Ψt _ij can be applied, without applying the amplitude modulation ρ _ij , that is to say by taking ρ _ij = 1. In other words, according to the invention, the excitation law f _ij applied to each phase shifter D _ij is calculated by summing the phase laws Ψ ₁ , Ψ ₂ , ... Ψ _k , ... Ψ _N associated respectively with each direction of order 1, 2, ... k, ... N, according to the preceding relation (14) and by applying the resulting phase shift Ψt _ij on the phase shifter, without applying the amplitude modulation resulting ρ _ij .

   où λ_k représente la longueur d'onde associée au k^ième faisceau ou faisceau d'ordre k.  -2π $\frac{{\text{r}}_{\text{ij}}}{{\text{λ}}_{\text{k}}}$

+ Ψ_0k est un terme correctif qui ne s'applique que dans le cas d'une antenne à réflecteur selon la figure 1 par exemple, Ψ_0k pouvant s'appliquer à une antenne quelconque. Etant donné que le réflecteur 1 est plan et que le rayonnement émis par la source est sphérique, il faut tenir compte du fait que tous les déphaseurs ne reçoivent pas ce rayonnement en même temps. C'est le terme -2π $\frac{{\text{r}}_{\text{ij}}}{{\text{λ}}_{\text{k}}}$

qui représente le retard lié au déphaseur D_ij et correspond en fait au déphasage Ψ_spij de la relation (4) précédente, où r_ij est la distance de la source 3 au déphaseur D_ij du plan réflecteur. Ψ_0k représente la phase du rayonnement émis, à l'origine O du plan réflecteur, et correspond au déphasage Ψ₀ de la relation (5).To form N beams at N different frequencies, it suffices to quantify or not the phase deduced from the relation (14) but with a phase Ψk, associated with a k ^th direction, which verifies, relative to a phase shifter D _ij , the relation ( 15) following: $${\text{Ψ}}_{\text{k}}\text{= 2π (i}\frac{\text{dx}}{{\text{λ}}_{\text{k}}}{\text{sinθb}}_{\text{k}}{\text{cosϕb}}_{\text{k}}\text{+ j}\frac{\text{dy}}{{\text{λ}}_{\text{k}}}{\text{sinθb}}_{\text{k}}{\text{sinϕb}}_{\text{k}}\text{) -2π}\frac{{\text{r}}_{\text{ij}}}{{\text{λ}}_{\text{k}}}{\text{+ Ψ}}_{\text{0k}}$$

where λ _k represents the wavelength associated with the k ^th beam or beam of order k. -2π $\frac{{\text{r}}_{\text{ij}}}{{\text{λ}}_{\text{k}}}$

+ Ψ _0k is a corrective term which only applies in the case of a reflector antenna according to FIG. 1 for example, Ψ _{0k which} can be applied to any antenna. Since the reflector 1 is planar and the radiation emitted by the source is spherical, it must be taken into account that not all phase shifters receive this radiation at the same time. This is the term -2π $\frac{{\text{r}}_{\text{ij}}}{{\text{λ}}_{\text{k}}}$

which represents the delay linked to the phase shifter D _ij and in fact corresponds to the phase shift Ψ _{sp ij} from the previous relation (4), where r _ij is the distance from the source 3 to the phase shifter D _ij from the reflective plane. Ψ _0k represents the phase of the radiation emitted, at the origin O of the reflective plane, and corresponds to the phase shift Ψ ₀ of the relation (5).

The quantified phase to be applied to the phase shifter remains the phase Ψtq _ij = E (Ψt _ij / q) × q.

To obtain beams of given directions and characteristics, it is possible to associate with each lobe or beam of order k a weighting coefficient r _k . According to the invention, this coefficient is used for determining the phase law applied to a phase shifter D _ij , but, as before, the resulting modulation is not actually applied since there is no modulation d amplitude at phase shifters. The experiments carried out by the Applicant have indeed shown that several beams could be obtained from the phase law calculated in this way for each phase shifter, without applying amplitude modulation.

   mais en réalité, c'est l'excitation f_ij'= e^jΨtij qui est appliquée, la loi de phase quantifiée étant toujours Ψtq_ij = E(Ψt_ij / q) × q.The excitation law f _ij of a phase shifter is then determined according to the following relation: $${\text{f}}_{\text{ij}}{\text{= r}}_{\text{1}}\text{<figure-callout id="1" label="e i" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{{\text{i}}_{}}{{}_{\text{1}}}^{}{\text{+ r}}_{\text{2}}\text{<figure-callout id="2" label="e i" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{{\text{i}}_{}}{{}_{\text{2}}}^{}{\text{... + r}}_{\text{k}}\text{e}{}^{{\text{i}}_{\text{k}}}{\text{... + r}}_{\text{NOT}}\text{e}{}^{{\text{i}}_{\text{NOT}}}{\text{= ρ}}_{\text{ij}}\text{e}{}^{{\text{jt}}_{\text{ij}}}$$

but in reality, it is the excitation f _ij '= e ^jΨt ij which is applied, the quantized phase law always being Ψtq _ij = E (Ψt _ij / q) × q.

   et, selon la relation (16) : $${\text{f}}_{\text{ij}}{\text{=r}}_{\text{1}}\text{e}{\text{}}^{{\text{jΨ}}_{\text{1}}}{\text{+r}}_{\text{2}}\text{e}{\text{}}^{{\text{jΨ}}_{\text{2}}}$$

A possible application is for example the formation of a difference channel in one direction and of a sum channel in another direction in order to carry out in particular a removal of angular ambiguity. In this case, the scanning could be carried out in the plane Ox, Oz as defined previously in a direction θ ₁ for the difference channel and in a direction θ ₂ for the sum channel. In the case for example where the antenna is not with a reflector, that is to say in particular that the phase shifts Ψ _sp and Ψ ₀ are zero, and in application of the relations (7) and (8), it comes for the phase laws Ψ ₁ and Ψ ₂ : $${\text{<figure-callout id="1" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{1}}\text{= 2}\mathit{\text{π}}\frac{\mathit{\text{idx}}}{\mathit{\text{λ}}}\text{<figure-callout id="1" label="sin θ" filenames="imgf0001.png" state="{{state}}">sin </figure-callout>}{\mathit{\text{θ}}}_{}{}_{\text{1}}{\text{and <figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}\text{= 2}\mathit{\text{π}}\frac{\mathit{\text{idx}}}{\mathit{\text{λ}}}\text{<figure-callout id="2" label="sin θ" filenames="imgf0001.png" state="{{state}}">sin </figure-callout>}\mathit{\text{θ}}{}_{\text{2}}$$

and, according to relation (16): $${\text{f}}_{\text{ij}}{\text{= r}}_{\text{1}}\text{<figure-callout id="1" label="e i" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{{\text{i}}_{}}{{}_{\text{1}}}^{}{\text{+ r}}_{\text{2}}\text{<figure-callout id="2" label="e i" filenames="imgf0001.png" state="{{state}}">e </figure-callout>}{}^{{\text{i}}_{}}{{}_{\text{2}}}^{}$$

The previous coefficients r ₁ and r ₂ can then be given by the following relationships: $${\mathit{\text{<figure-callout id="1" label="r" filenames="imgf0001.png" state="{{state}}">r</figure-callout>}}}_{\text{1}}\text{= 2π}\frac{\mathit{\text{idx}}}{\mathit{\text{λ}}}\text{<figure-callout id="1" label="cos θ" filenames="imgf0001.png" state="{{state}}">cos </figure-callout>}{\mathit{\text{θ}}}_{}{}_{\text{1}}$$

.r2 being a normalization coefficient which makes it possible to emit the same power in both directions and r ₁ is a coefficient which makes it possible to obtain a difference channel in the first direction, r ₁ being in fact equal to $\frac{{\text{∂<figure-callout id="1" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{1}}}{{\text{∂<figure-callout id="2" label="Ψ" filenames="imgf0001.png" state="{{state}}">Ψ</figure-callout>}}_{\text{2}}}$

.

FIG. 1 presents an application with a reflector antenna, but it is of course possible to apply the invention to all types of antenna with electronic scanning with phase control only, with active modules or not. Moreover, the invention can a fortiori apply to antennas which are additionally controllable in amplitude. Nor does the network of phase shifters have to be planar.

By way of example, reference has been made to discrete phase shifters, with N bits, but the invention also applies to phase shifters controlled continuously. The invention makes it possible to adapt to antennas already produced since it only plays on the phase laws applied to the phase shifters of the antennas. It is also not necessary to make hardware adaptations, the invention is in particular thereby simple to implement. It suffices simply to integrate the laws calculated according to the invention into the control means of the phase shifters. It is also possible to create a large number of beams simultaneously, for example up to several tens, in particular if the number of phase shifters is large, with or without different frequencies.

An exemplary embodiment of the invention has been presented for a single source reflector antenna, in particular consisting of a horn. The invention can however be applied for a reflector antenna with several sources, by associating for example one or two directions per primary source.

Claims (10)

Electronic scanning antenna comprising a network of phase shifters (2, D _ij ), characterized in that N simultaneous beams are obtained in N independent directions by an excitation law f _ij applied to each phase shifter (D _ij ) which is calculated by summing the phase laws Ψ ₁ , Ψ ₂ , ... Ψ _k , ... Ψ _N respectively associated with each direction of order 1, 2, ... k, ... N according to the relation: $${\text{f}}_{\text{ij}}\text{= e}{}^{{\text{i}}_{\text{1}}}\text{+ e}{}^{{\text{i}}_{\text{2}}}\text{... + e}{}^{{\text{i}}_{\text{k}}}\text{... + e}{}^{{\text{i}}_{\text{NOT}}}{\text{= ρ}}_{\text{ij}}\text{e}{}^{{\text{jt}}_{\text{ij}}}$$

and by applying the resulting phase shift Ψt _ij to the phase shifter, without applying the resulting amplitude modulation ρ _ij . Antenna according to claim 1, characterized in that the frequencies of the beams are different. Antenna according to any one of the preceding claims, characterized in that the phase laws Ψ ₁ , Ψ ₂ , ... Ψ _k , ... Ψ _N are assigned a weighting coefficient (r ₁ , r ₂ . .., r _k ... r _N ). Antenna according to claim 3, characterized in that the weighting coefficients are determined to obtain a sum channel and a difference channel in two different directions. Antenna according to claim 4, characterized in that the weighting coefficient r ₁ associated with the first phase law Ψ ₁ satisfies r ₁ = $\frac{{\text{∂Ψ}}_{\text{1}}}{{\text{∂θ}}_{\text{1}}}$

and the normalization coefficient associated with the second phase law Ψ ₂ is a normalization coefficient which allows the same power to be emitted in both directions. Antenna according to relation 6, characterized in that the phase laws Ψ ₁ , Ψ ₂ associated respectively with the direction of the difference channel and of the sum channel being given by the following relations: $${\text{Ψ}}_{\text{1}}\text{= 2}\mathit{\text{π}}\frac{\mathit{\text{idx}}}{\mathit{\text{λ}}}\text{sin}{\mathit{\text{θ}}}_{\text{1}}{\text{and Ψ}}_{\text{2}}\text{= 2}\mathit{\text{π}}\frac{\mathit{\text{idx}}}{\mathit{\text{λ}}}\text{sin}{\mathit{\text{θ}}}_{\text{2}}$$

the associated weighting coefficients are respectively: $${\mathit{\text{r}}}_{\text{1}}\text{= 2}\mathit{\text{π}}\frac{\mathit{\text{idx}}}{\mathit{\text{λ}}}\text{cos}{\mathit{\text{θ}}}_{\text{1}}$$

and

or : - θ ₁ , θ ₂ are the angles of the two directions with respect to an axis (Ox) taken in their common plane (Oxz); - idx is a coordinate of a phase shifter D _ij taken on the above-mentioned axis (Ox); - λ ₁ is the wavelength of the beam of the difference channel. Antenna according to any one of the preceding claims, characterized in that the number of beams being equal to two, the calculated amplitude modulation (21, A (x)) is approximated by a two-state modulation 1, -1 ( 22), the approached modulation changing state when the calculated modulation changes sign. Antenna according to claim 7, characterized in that an additional phase shift of π is applied to the phase shifter when the calculated modulation (21, A (x)) changes sign. Antenna according to any one of the preceding claims, characterized in that the phase shifters being controlled according to N bits, the phase applied to a phase shifter (D _ij ) is the phase: $${\text{Ψtq}}_{\text{ij}}{\text{= E (Ψt}}_{\text{ij}}\text{/ q) × q}$$

or : - E (Ψt _ij / q) is the integer part ofΨt _ij / q, q being equal to 2π / 2 ^N ; - Ψt _ij is the resulting phase shift. Antenna according to any one of the preceding claims, characterized in that it comprises a reflector (1) comprising the network of phase shifters (2).

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