EP2840654A1 - Method for determining an antenna array - Google Patents

Abstract

The invention relates to a method for determining an antenna array (10) suitable for generating an electromagnetic wave comprising: at least one antenna (14, 16, 18), at least one circuit (19) having parameters (Z) influencing the electromagnetic wave generated by the antenna array (10) and connected to at least one antenna (16, 18), the process comprising the steps of: - choice of a criterion to check, determination of desired decomposition coefficients of a wave in a base making it possible to reach the chosen criterion, calculating the parameters (Z) for each circuit (19) of the antenna array (10) so that the difference between the decomposition coefficients on the basis of the wave generated by the antenna array (10) and the decomposition coefficients desired is minimum.

Description

The present invention relates to a method for determining an antenna array. The present invention also relates to an antenna array.

The invention applies to the field of antennal networks. For many applications, directional radiation is desired. By way of illustration, detection and communication with a target require focused radiation in a preferred direction. Avoiding electromagnetic pollution outside useful areas is another example of application involving relatively directional radiation.

In order to increase the directivity of an antenna array, it is known from the state of the art to use reflectors such as parabolas, to network antennas or to associate coupled antennas, as for antennas of the Yagi type. Uda.

où A est la surface projetée visible selon la direction principale de rayonnement. Notamment, cela signifie que pour un disque réflecteur de rayon R, $D=\frac{4{\pi }^2{R}^2}{{\lambda }^2}\mathrm{.}$

However, these solutions greatly increase the size of the antennal network. Indeed, the directivity of a reflector antenna is conventionally estimated by $D=\frac{4\mathrm{<figure-callout\; id="2"\; label="\pi \; \lambda "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\pi \; </figure-callout>}}{{\lambda }^{}}\mathrm{AT}$

where A is the projected surface visible in the main direction of radiation. In particular, this means that for a reflective disc of radius R, $D=\frac{4{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\pi </figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="imgf0001.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}{{\mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}^2}\mathrm{.}$

It is also known to jointly excite a mode of radiation of the transverse electric type (TE) and a magnetic mode (TM) within the same antenna array. An antenna array structure supporting such operation is called a Huygens source. For example, in the document FR-A-2,949,611 , there is provided a structure based on a resonator consisting of a ring conductive helix producing a Huygens source with a reduced antenna size.

However, the maximum directivity level achievable with this type of antennal network structure is limited by the directivity of the ideal Huygens source, which is 4.7 dBi. The unit dBi means "isotropic decibel". In general, the directivity of an antenna is normally expressed in dBi, taking for reference an isotropic antenna, that is to say a dummy antenna of the same total radiated power which radiates uniformly in all directions with radiation. 0 dBi.

There is therefore a need for a method of determining an antenna array for obtaining an antenna array having improved directivity with reduced compactness.

According to the invention, this object is achieved by a method of determining an antenna array suitable for generating an electromagnetic wave comprising at least one antenna and at least one circuit having parameters influencing the electromagnetic wave generated by the antenna array and connected to it. at least one antenna. The method comprises the steps of choosing a criterion to check for the wave generated by the antenna array and determining desired decomposition coefficients of a wave in a base to achieve the chosen criterion. The method also includes a step of calculating the parameters influencing the electromagnetic wave generated by the antenna array for each antenna array circuit so that the difference between the decomposition coefficients based on the wave generated by the antenna array and the desired decomposition coefficients are minimum.

• le circuit est un circuit de couplage et/ou le circuit est au moins une charge.
• l'étape de calcul comprend une sous-étape de calcul d'un vecteur d'excitation du réseau antennaire à partir des coefficients de décomposition souhaités, et de détermination des paramètres influençant l'onde électromagnétique générée par le réseau antennaire de chaque circuit du réseau antennaire à partir du vecteur d'excitation calculé.
• les étapes de décomposition et de calcul sont effectuées à l'aide de calcul matriciel.
• la base est la base des modes sphériques.
• le critère est choisi dans un groupe constitué des éléments suivants : la directivité du réseau antennaire dans une direction donnée, le rapport du retour avant/arrière du réseau antennaire, le diagramme de rayonnement du réseau est sensiblement identique à un diagramme de rayonnement obtenu avec un masque spécifique, et le diagramme de rayonnement du réseau dans un environnement perturbé est identique à un diagramme de rayonnement désiré.
• le circuit est un circuit de couplage à base de guide d'ondes, les paramètres influençant l'onde électromagnétique générée par le réseau antennaire étant les paramètres caractérisant l'impédance du guide d'ondes, la longueur du guide et l'impédance d'une charge associée au circuit de couplage.
• au moins une charge comprend deux composants distincts, un premier composant étant une résistance et le deuxième composant étant choisi parmi une inductance ou une capacité.
• au moins une charge comprend une résistance négative.

According to particular embodiments, the method comprises one or more of the following characteristics, taken in isolation or in any technically possible combination:

• the circuit is a coupling circuit and / or the circuit is at least one load.
• the calculation step comprises a substep of calculating an excitation vector of the antenna array from the desired decomposition coefficients, and determining the parameters influencing the electromagnetic wave generated by the antenna array of each circuit of the network. antennal from the calculated excitation vector.
• the decomposition and calculation steps are performed using matrix calculation.
• the base is the base of the spherical modes.
• the criterion is chosen from a group consisting of the following elements: the directivity of the antenna array in a given direction, the ratio of the forward / backward return of the antenna array, the radiation pattern of the array is substantially identical to a radiation pattern obtained with a specific mask, and the network radiation pattern in a disturbed environment is identical to a desired radiation pattern.
• the circuit is a waveguide-based coupling circuit, the parameters influencing the electromagnetic wave generated by the antenna array being the parameters characterizing the impedance of the waveguide, the length of the waveguide and the impedance of the waveguide. a load associated with the coupling circuit.
• at least one load comprises two distinct components, a first component being a resistor and the second component being selected from inductance or capacitance.
• at least one load comprises a negative resistance.

• figure 1, une représentation schématique générique d'un réseau antennaire selon un mode de réalisation,
• figure 2, une représentation schématique d'un réseau antennaire selon un premier mode de réalisation,
• figure 3, une représentation schématique d'un réseau antennaire selon un deuxième mode de réalisation,
• figure 4, un schéma de rayonnement pour un réseau antennaire obtenu par le procédé selon l'invention.

Other features and advantages of the invention will appear on reading the following description of embodiments of the invention, given by way of example only and with reference to the drawings which are:

• figure 1 , a generic schematic representation of an antenna array according to one embodiment,
• figure 2 , a schematic representation of an antenna array according to a first embodiment,
• figure 3 , a schematic representation of an antenna array according to a second embodiment,
• figure 4 , a radiation pattern for an antenna array obtained by the method according to the invention.

An antenna array 10 is proposed as shown generically in FIG. figure 1 and by the two embodiments of Figures 2 and 3 . An antenna array is generally at least comprised of a primary antenna and a secondary antenna. Each of the antennas forming part of the antenna array comprises one or more radiating parts. The radiating parts of each separate antenna are physically separated. By the term "physically separated", it is understood that there is no physical contact between two radiating parts belonging to two separate antennas.

For the continuation, it is defined two axes X and Y contained in the Figures 1 to 3 . The X axis is perpendicular to the Y axis. A direction parallel to the X axis is called a longitudinal direction and a direction parallel to the Y axis is called a transverse direction.

The antenna array 10 comprises a source 12, a first antenna 14, a second antenna 16, a third antenna 18 and a circuit 19 (not shown in FIG. figure 1 ).

The first antenna 14 is an antenna associated with the source 12. The source 12 delivering a signal useful for the application considered for the network 10, the first antenna 14 is considered as a primary antenna. Thus, the first antenna 14 is called primary antenna in the following.

The second antenna 16 is an antenna associated with a passive or active load. The second antenna 16 is not directly associated with a source delivering a useful signal. The second antenna 16 is, in this sense, a secondary antenna while the first antenna 14 is a primary antenna. The same applies to the third antenna 18. Thus, the second antenna 16 and the third antenna 18 are called secondary antennas in the following description.

The number of antennas of the antenna array 10 is given by way of example, any type of antenna array 10 comprising at least one antenna that can be connected to a circuit 19 that can be considered.

In particular, the antenna array 10 includes, in some embodiments, a plurality of primary antennas.

In a variant, the antenna array 10 comprises a large number, for example about ten or a hundred, of secondary antennas.

The antenna array 10 is capable of generating an electromagnetic wave denoted Ototale. The antenna array 10 is thus adapted to operate for at least one wavelength noted λ in the following description. The wavelength λ is between a few hundredths of a millimeter and a few tens of meters. This corresponds, in terms of frequencies, to frequencies between the high frequency band (often referred to by the acronym HF) and frequencies of the order of a few Terahertz.

Depending on the application considered (cellular telephony, home automation, etc.), the antennal network 10 is able to operate over more restricted frequency ranges.

Advantageously, the antenna array 10 is adapted to operate for a frequency band between 30 MHz and 90 GHz. This makes the antenna array 10 considered particularly suitable for radiocommunications.

The circuit 19 is a circuit having parameters influencing the electromagnetic wave generated by the antenna array 10.

Circuit 19 is either a waveguide-based coupling circuit associated with a load Z as illustrated in FIG. figure 2 , or at least one load as shown in figure 3 , a hybrid circuit between the coupling circuit of the figure 2 and the load shown in figure 3 .

In the figure 2 the circuit 19 is a waveguide connecting the second antenna 16 to the third antenna 18 via a load Z (which may not be present). This simple arrangement can be made as complex as desired according to the contemplated embodiments.

In the case of circuit 19 of the figure 2 , the parameters influencing the ototal electromagnetic wave generated by the antenna array 10 are the parameters characterizing the shape of the coupling circuit. For example, the impedance of the load Z, the proper impedance of the waveguide used, the length of the waveguide are examples of parameters characterizing the coupling circuit. In the case of figure 3 the circuit 19 comprises two charges 20, 21, the first charge 20 being connected to the second antenna 16 and the second charge 21 being connected to the third antenna 18.

In this example, the parameters influencing the ototal electromagnetic wave generated by the antenna array 10 are the value of the impedance of each of the two charges 20, 22.

Preferably, at least one of the first charge 20 and the second charge 22 comprises two distinct components, a first component being a resistor and the other component being selected from inductance or capacitance.

By "distinct component", it is understood that each component has negligible parasitic impedances compared to its main impedance. Thus, a resistor has a resistance value much greater than the parasitic resistance of an inductance or capacitance. Similarly, a capacitance has a capacitance value much greater than the parasitic capacitance of an inductor or a resistor, and an inductance has a much greater inductance value than the parasitic inductance of a resistor or capacitance. .

In the case of figure 3 by way of example, it is the two charges 20 and 22 which comprise two distinct components.

• une partie réelle strictement inférieure à 0, ou
• une partie imaginaire non nulle et une partie réelle non nulle.

Preferably, the impedance of each load 20, 22 has:

• a real part strictly less than 0, or
• a non-zero imaginary part and a non-zero real part.

According to another embodiment, at least one load 20, 22 has an adjustable impedance. This makes the antenna array 10 more flexible.

Alternatively, at least one load 20, 22 is an active component.

It is proposed to determine the antenna array 10 illustrated in FIG. figure 2 or at figure 3 using a determination method.

The determination method comprises a step of choosing a criterion to be verified for the Ototale wave generated by the antenna array 10.

In general, the criterion is either a performance criterion or a criterion of compliance with a mask.

The directivity of the antenna array 10 in a given direction and the ratio of the forward / backward return of the antenna array 10 are two examples of performance criteria.

Whether the radiation pattern of the grating 10 is substantially identical to a radiation pattern obtained in a specific mask, or that the radiation pattern of the grating 10 in a disturbed environment is identical to a desired radiation pattern are two examples of compliance criterion. to a mask.

The method relies on a following step of decomposing a wave in a base. The method also comprises a step of determining the desired decomposition coefficients, for example by decomposing a wave satisfying the chosen criterion. Preferably, the base used in the decomposition step is the base of the modes spherical. This base makes it possible to simplify the calculations to be carried out while keeping a good precision. Indeed, to choose this base does not imply to use an approximation.

Advantageously, the decomposition step is performed using a matrix calculation to reduce the implementation time of this step.

The method then comprises a step of calculating the parameters influencing the ototal electromagnetic wave generated by the antenna array 10, for example the parameters of each circuit 20, 22 of the antenna array 10 so that the difference between the decomposition coefficients on the basis of the antenna of the wave generated by the antenna array 10 and the desired decomposition coefficients is minimum.

Applied to the case of figure 2 , this calculation step makes it possible to obtain the parameters characterizing the shape of the coupling circuit forming the circuit 19.

Applied to the case of figure 3 , this calculation step makes it possible to obtain the value of the impedances Z1 and Z2 of the two charges 20, 22.

Advantageously, the calculation step is performed using matrix calculation, which simplifies the implementation of this step.

Preferably, the calculation step comprises a substep of calculating an excitation vector Λ of the antenna array 10 making it possible to obtain the desired decomposition coefficients and a substep of determining the parameters influencing the electromagnetic wave. Ototale generated by the antenna array 10 of each load 20, 22 of the antenna array 10 from the calculated excitation vector Λ.

The method thus makes it possible to optimize the antenna array 10 so that the antenna array 10 meets a desired criterion. This optimization is an optimization that makes it possible to find the best value if it exactly exists, without having to carry out an iterative optimization.

Thus, an antenna array 10 having improved properties is obtained.

The antenna array 10 thus determined finds its application in many systems. By way of example, a vehicle, a terminal, a mobile telephone, a wireless network access point, a base station, a radiofrequency excitation probe, etc. may be cited.

In the following, it is detailed, for example, the antenna network 10 of the figure 3 as well as the determination method applied to the antenna array 10 of the figure 3 , it being understood that the extension of the application of the determination method to the antenna array 10 described in FIG. figure 2 is accessible to those skilled in the art using the teachings below.

The figure 3 illustrates a schematic representation of an antenna array 10 comprising a source 12, a first antenna 14, a second antenna 16, a third antenna 18, a circuit 19 comprising a first load 20 and a second load 22.

The source 12 is, for example, a radiofrequency wave generator. The source 12 is able to provide radio frequency excitation waves of the primary antenna 14 at the wavelength λ. The source 12 is connected to the first antenna 14. The source 12 may have an internal impedance of 50 Ohms.

According to the example of the figure 3 , the first antenna 14 is in the form of a conductive wire extending along a longitudinal direction. Along this longitudinal direction, the first antenna 14 has a dimension equal to λ / 2.

According to the example of the figure 3 the second antenna 16 is also in the form of a conductive wire extending along a longitudinal direction. Along this longitudinal direction, the second antenna 16 has a dimension equal to λ / 2. The second antenna 16 is disposed parallel to the first antenna 14 at a distance of λ / 10 relative to the first antenna 14 along a transverse direction.

According to the example of the figure 3 the third antenna 18 is also in the form of a conductive wire extending along a longitudinal direction. Along this longitudinal direction, the third antenna 18 has a dimension equal to λ / 2. The third antenna 18 is arranged parallel to the first antenna 14 at a distance of λ / 10 relative to the first antenna 14 along a transverse direction. The third antenna 18 is also arranged parallel to the second antenna 16 at a distance of λ / 5 relative to the second antenna 16 along the transverse direction. Otherwise formulated, the first antenna 14 is disposed in the middle of the second antenna 16 and the third antenna 18. This arrangement is described by way of example, it being understood that any other arrangement is conceivable.

The first load 20 is connected to the second antenna 16.

The first load 20 comprises at least two distinct components. For example, the first load 20 is the combination of a capacitor and a resistor. Alternatively, the first load 20 is the combination of inductance and resistance.

The impedance of the first load 20 is denoted Z1.

Advantageously, the impedance Z1 of the first load 20 has a real part strictly less than 0, or a non-zero imaginary part and a non-zero real part. Indeed, the implementation of these types of charges makes it possible to obtain a decomposition of the wave that is closer to the desired coefficients, compared with conventional solutions that exclude the use of resistors associated with the reactances in order to limit losses in the field. antennal network 10.

This means that the first charge is not pure resistance or pure reactance.

Thus, according to one embodiment, the impedance Z1 of the first load 20 is equivalent to the series association of a resistor and a coil, the inductance of the coil being greater than 1 nH.

According to another embodiment, the impedance Z1 of the first load 20 is equivalent to the series association of a resistor and a capacitor, the capacity of the capacitor being greater than 0.1 pF. According to yet another embodiment, the impedance Z1 of the first load 20 is equivalent to the series association of a resistor and a capacitor or a coil, the resistance being greater than 0.1 Ohms.

According to one variant, the impedance Z1 has a negative real part. The realization of a negative resistance is done in a manner known in the state of the art by introduction of an active device, for example an operational amplifier to achieve a negative resistance.

According to another variant, the impedance Z1 has a negative imaginary part. The realization of a negative capacitance or inductance is done using a Negative Impedance Converter (NIC) type circuit.

Thus, according to these two variants which can be combined, the first load 20 comprises one or more active components.

Another advantage of the active components is that it makes it easy to produce components having the opposite impedance which would be difficult to achieve practically. Typically, a large inductance of small size is difficult to obtain with the aid of an inductance but can be obtained with a mounting providing a negative capacitance. Likewise, a small capacitance is more easily obtained by using a circuitry producing a negative inductance.

Preferably, the impedance Z1 corresponds to the impedance of a mixed load that is both resistive and reactive. In other words, the impedance Z1 has a non-zero real part and a non-zero imaginary part.

The second load 22 is connected to the third antenna 18.

The second load 22 has an impedance Z2. The same remarks as those made previously for the impedance Z1 of the first load 20 apply for the impedance Z2 of the second load 22.

The operation of the antenna array 10 is now described.

In operation, the source 12 emits a radiofrequency wave capable of exciting the first antenna 14.

The first antenna 14 then emits a first radiofrequency wave O1 under the effect of the excitation due to the source 12. This radiofrequency wave O1 corresponds to a first electric field denoted E1.

The electric field E1 then excites the secondary antennas 16 and 18.

In response, the second antenna 16 emits a second radiofrequency wave 02 under the effect of the excitation due to the electric field E1. This second radiofrequency wave 02 corresponds to a second electric field denoted E2. The second electric field E2 depends in particular on the value of the impedance Z1 of the first load 20.

Similarly, in response, the third antenna 16 emits a third radio frequency wave 03 under the effect of the excitation due to the electric field E1. This third radiofrequency wave 03 corresponds to a third electric field denoted E3. The third electric field E3 depends in particular on the value of the impedance Z3 of the second load 22.

Thus, when the source 12 emits a radiofrequency wave, the antenna array 10 emits an Ototale radiofrequency wave which corresponds to the superposition of the first wave generated by the first antenna 14 and second and third waves generated by the second and third antennas 16 and 18. In terms of the electric field, by noting Etotal the electric field of the antenna array 10 associated with the Ototal radiofrequency wave, such a superposition implies that the electric field of the antenna array 10 is the sum of the three electric fields of the three antennas 14, 16, 18 of the network. This is written mathematically according to the following relation: $$\mathrm{Etotal}\left(\mathrm{Z}\mathrm{1},\mathrm{Z}\mathrm{2}\right)=\mathrm{E}\mathrm{1}+\mathrm{E}\mathrm{2}\left(\mathrm{Z}\mathrm{1}\right)+\mathrm{E}\mathrm{3}\left(\mathrm{Z}\mathrm{2}\right)$$

In the previous relation, it has been demonstrated that the electric field of the antenna array 10 is a function of the value of the impedances Z1 and Z2 of the first and second charges 20, 22 via the second field E2 and the third field E3.

This dependence gives the antenna array 10 a possibility of adjusting the electric field generated by the antenna array 10 independent of the proper structure of the antenna array 10 (numbers of antennas 14, 16, 18, shape of the antennas 14, 16, 18 and positions relative antennas 14, 16, 18). This is particularly advantageous insofar as the modification of the structure of the antenna array 10 causes changes in the electric field produced by the antenna array 10 which is often difficult to predict.

By modifying the values of the impedances Z1 and Z2 of the charges 20 and 22, it is possible to modify the radiation pattern obtained for the antenna array 10. In particular, according to a preferred embodiment, the FIG. radiation is made directive in a preferred direction by imposing the impedance values Z1 and Z2. This property is achieved while maintaining a compact antenna array. Indeed, the antenna array 10 has a dimension of λ / 2 along a longitudinal direction and a dimension of λ / 5 along a transverse direction.

The property of the antenna array 10 according to which the total radiation produced is controllable by the choice of the impedances Z1, Z2 of the charges 20, 22 is particularly usable in the context of a method of determining the antenna array 10 so that the total radio frequency wave Ototale generated by the antenna array 10 meets a desired criterion. An example of implementation of such a method is described in the following.

For a better understanding, the method is first presented in a general case of any antenna array comprising any number of antennas and then applied to the particular case of the antenna array presented to the figure 3 .

The determination method first comprises a step of choosing a criterion to be verified for the total Ototale radiofrequency wave generated by the antenna array.

By way of example, for the rest of the description, it is assumed that the chosen criterion is a better directivity of the antenna array 10 in a direction of elevation angle θ ₀ and azimuth angle φ ₀ . Other criteria may be considered, such as the optimization of an antenna performance criterion such as the reduction of a cross polarization level (that is, perpendicular to the main polarization of the antenna). the wave considered) in a given direction or the maximization of a front-to-back ratio, etc. The criterion can also be compliance with a given type of radiation, for example dipole-type radiation or any other radiation specified by a radiation mask.

The process is based on a decomposition of a wave in a base. The method also comprises a step of determining the decomposition coefficients making it possible to reach the chosen criterion, for example by decomposing a wave satisfying the chosen criterion.

According to the illustrated example, the base chosen is the base of the spherical modes because this base makes it possible to simplify the calculations to be carried out while keeping a good precision. Indeed, choosing this base does not imply making an approximation.

Alternatively, any other base could be considered. In particular, the base of the plane waves can be used to decompose the wave considered.

The basis of the spherical modes is defined from the following observation: in an isotropic, homogeneous medium without a source, an electric field E is expressed in a spherical base indicated by the coordinates r, θ and φ in the form: $$\stackrel{\rightharpoonup }{E}\left(r\theta \phi \right)=\sqrt{\eta }\frac{1}{\sqrt{4\pi }}\frac{e^{\mathit{jkr}}}{r}{\displaystyle \underset{s=1}{\overset{2}{\Sigma }}}{\displaystyle \underset{\mathrm{not}=1}{\overset{\infty }{\Sigma }}}{\displaystyle \underset{m=-\mathrm{not}}{\overset{\mathrm{not}}{\Sigma }}}{Q}_{\mathit{smn}}^{\left(3\right)}{\overrightarrow{K}}_{\mathit{smn}}\left(\theta \phi \right)$$

• η est l'impédance du vide (milieu de propagation),
• j le nombre complexe,
• k est la norme du vecteur d'onde associé au champ électrique E,
• Q_smn est le coefficient de décomposition du champ électrique E sur le mode s, m, n de la base des modes sphériques, et
• K _{1 mn} (θ, ϕ) et K _2mn (θ, ϕ) sont les différents modes sphériques.

Or:

• η is the impedance of the vacuum (propagation medium),
• j the complex number,
• k is the wave vector standard associated with the electric field E,
• Q _smn is the decomposition coefficient of the electric field E on the mode s, m, n of the base of the spherical modes, and
• K _{1 mn} (θ, φ) and K _{2 mn} ( θ, φ ) are the different spherical modes.

$${\overrightarrow{K}}_{2\mathit{mn}}\left(\theta \phi \right)=\sqrt{\frac{2}{n\left(n+1\right)}}{\left(-\frac{m}{\left|m\right|}\right)}^m{e}^{\mathit{jm\phi }}{\left(-j\right)}^n\left\{\frac{d{\bar{P}}_n^{\left|m\right|}\left(\cos \theta \right)}{d\theta }{\overrightarrow{e}}_{\theta }-\frac{\mathit{jm}{\bar{P}}_n^{\left|m\right|}\left(\cos \theta \right)}{\sin \theta }{\overrightarrow{e}}_{\phi }\right\}$$

The general mathematical expression of the spherical modes is also known as shown by the following equations 3 and 4: $${\overrightarrow{K}}_{1\mathit{mn}}\left(\theta \phi \right)=\sqrt{\frac{2}{\mathrm{not}\left(\mathrm{not}+1\right)}}{\left(-\frac{m}{\left|m\right|}\right)}^m{e}^{\mathit{jm\phi }}{\left(-j\right)}^{\mathrm{not}+1}\left\{\frac{\mathit{jm}{\tilde{P}}_{\mathrm{not}}^{\left|m\right|}\left(\cos \theta \right)}{\sin \theta }{\overrightarrow{e}}_{\theta }-\frac{d{\tilde{P}}_{\mathrm{not}}^{\left|m\right|}\left(\cos \theta \right)}{d\theta }{\overrightarrow{e}}_{\phi }\right\}$$

$${\overrightarrow{K}}_{2\mathit{mn}}\left(\theta \phi \right)=\sqrt{\frac{2}{\mathrm{not}\left(\mathrm{not}+1\right)}}{\left(-\frac{m}{\left|m\right|}\right)}^m{e}^{\mathit{jm\phi }}{\left(-j\right)}^{\mathrm{not}}\left\{\frac{d{\tilde{P}}_{\mathrm{not}}^{\left|m\right|}\left(\cos \theta \right)}{d\theta }{\overrightarrow{e}}_{\theta }-\frac{\mathit{jm}{\tilde{P}}_{\mathrm{not}}^{\left|m\right|}\left(\cos \theta \right)}{\sin \theta }{\overrightarrow{e}}_{\phi }\right\}$$

• e _θ est le vecteur unitaire associé à la coordonnée θ,
• θ_ϕ est le vecteur unitaire associé à la coordonnée ϕ,
• $${\bar{P}}_n^m\left(\cos \theta \right)=\sqrt{\frac{2n+1}{2}\frac{\left(n-m\right)!}{\left(n+m\right)!}}{\left(\sin \theta \right)}^m\frac{d^m}{d{\left(\cos \theta \right)}^m}\left[\frac{1}{2^{n}n!}\frac{d^n}{d{\left(\cos \theta \right)}^n}{\left({\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0001.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\theta -1\right)}^n\right],$$
  
  et
• $$\frac{d{\bar{P}}_n^{\left|m\right|}\left(\cos \theta \right)}{d\theta }=\{\begin{array}{cc}-{\mathrm{<figure-callout\; id="1"\; label="P\; n"\; filenames="imgf0001.png"\; state="\{\{state\}\}">P</figure-callout>}}_n^{}\left(\cos \theta \right)\sqrt{\frac{2n+1}{2}}& m=0\\ \frac{1}{2}\left(\left(n-\left|\mathrm{<figure-callout\; id="1"\; label="m\; +"\; filenames="imgf0001.png"\; state="\{\{state\}\}">m</figure-callout>},\right|+1\right)\left(n+\left|m\right|\right)P_n^{\left|m\right|-1}\left(\cos \theta \right)-P_n^{\left|m\right|+1}\left(\cos \theta \right)\right)\sqrt{\frac{2n+1}{2}\frac{\left(n-\left|m\right|\right)!}{\left(n+\left|m\right|\right)!}}& \left|m\right|>0\end{array}$$
  

Or:

• e _θ is the unit vector associated with the coordinate θ,
• θ _φ is the unit vector associated with the coordinate φ,
• $${\tilde{P}}_{\mathrm{not}}^m\left(\cos \theta \right)=\sqrt{\frac{2\mathrm{not}+1}{2}\frac{\left(\mathrm{not}-m\right)!}{\left(\mathrm{not}+m\right)!}}{\left(\sin \theta \right)}^m\frac{d^m}{d{\left(\cos \theta \right)}^m}\left[\frac{1}{2^{\mathrm{not}}\mathrm{not}!}\frac{d^{\mathrm{not}}}{d{\left(\cos \theta \right)}^{\mathrm{not}}}{\left({\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0001.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\theta -1\right)}^{\mathrm{not}}\right],$$
  
  and
• $$\frac{d{\tilde{P}}_{\mathrm{not}}^{\left|m\right|}\left(\cos \theta \right)}{d\theta }=\{\begin{array}{cc}-P_{\mathrm{not}}^1\left(\cos \theta \right)\sqrt{\frac{2\mathrm{not}+1}{2}}& m=0\\ \frac{1}{2}\left(\left(\mathrm{not}-\left|\mathrm{<figure-callout\; id="1"\; label="m\; +"\; filenames="imgf0001.png"\; state="\{\{state\}\}">m\; </figure-callout>},\right|+1\right)\left(\mathrm{not}+\left|m\right|\right)P_{\mathrm{not}}^{\left|m\right|-1}\left(\cos \theta \right)-P_{\mathrm{not}}^{\left|m\right|+1}\left(\cos \theta \right)\right)\sqrt{\frac{2\mathrm{not}+1}{2}\frac{\left(\mathrm{not}-\left|m\right|\right)!}{\left(\mathrm{not}+\left|m\right|\right)!}}& \left|m\right|>0\end{array}$$
  

From a matrix point of view, the existence of the base of the spherical modes indicates that in an isotropic, homogeneous and without source medium, an electric field E is expressed as: $$\mathrm{E}=\mathrm{K\; x\; Q}$$

• la dépendance en θ et ϕ n'est pas reprise pour alléger les notations,
• E est un vecteur décrivant le champ électrique rayonné dans les différentes directions de l'espace et pour les différentes composantes de la polarisation s'écrivant par exemple : $$E=\left(\begin{array}{c}{E}_{\theta }\left({\theta }_1{\varphi }_1\right)\\ {\mathrm{<figure-callout\; id="1"\; label="E\; \phi \; \theta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">E</figure-callout>}}_{\varphi }\left({\theta }_{}\right)\left({}_1{\varphi }_1\right)\\ E_{\theta }\left({\mathrm{<figure-callout\; id="2"\; label="\theta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_2{\varphi }_2\right)\\ {\mathrm{<figure-callout\; id="2"\; label="E\; \phi \; \theta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">E</figure-callout>}}_{\varphi }\left({\theta }_{}\right)\left({}_2{\mathrm{<figure-callout\; id="2"\; label="\phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\varphi </figure-callout>}}_2\right)\\ \cdots \end{array}\right)$$
  
• K est une matrice décrivant le diagramme de rayonnement des modes sphériques s'écrivant par exemple : $$K=\left[\begin{array}{cccc}{K}_{11-1}& K_{110}& K_{111}& \cdots \\ K_{12-2}& K_{12-1}& K_{120}& \cdots \\ \cdots & \cdots & \cdots & \cdots \\ K_{21-1}& K_{210}& K_{211}& \cdots \\ K_{22-2}& K_{22-1}& K_{220}& \cdots \\ K_{23-3}& K_{23-2}& K_{23-1}& \cdots \\ \cdots & \cdots & \cdots & \cdots \end{array}\right]$$
  
  D'autres organisations de la matrice K peuvent être considérées à cette étape, l'organisation précédente n'étant donnée qu'à titre d'exemple. En outre, dans la pratique, à titre d'indication, il peut être remarqué que la matrice K est dépourvue d'éléments nuls.
• « x » désigne la multiplication matricielle, et
• Q est la matrice regroupant les différents coefficients Q_smn de décomposition du champ électrique s'écrivant par exemple : $$Q=\left(\begin{array}{c}{Q}_{1-11}\\ Q_{2-11}\\ Q_{101}\\ Q_{201}\\ \cdots \end{array}\right)$$
  

Or:

• the dependence in θ and φ is not taken again to lighten the notations,
• E is a vector describing the electric field radiated in the different directions of space and for the different components of the polarization, for example by: $$E=\left(\begin{array}{c}{E}_{\theta }\left({\theta }_1{\phi }_1\right)\\ {\mathrm{<figure-callout\; id="1"\; label="E\; \phi \; \theta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">E\; </figure-callout>}}_{\phi }\left({\theta }_{}\right)\left({}_1{\phi }_1\right)\\ E_{\theta }\left({\mathrm{<figure-callout\; id="2"\; label="\theta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_2{\phi }_2\right)\\ {\mathrm{<figure-callout\; id="2"\; label="E\; \phi \; \theta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">E\; </figure-callout>}}_{\phi }\left({\theta }_{}\right)\left({}_2{\mathrm{<figure-callout\; id="2"\; label="\phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_2\right)\\ \cdots \end{array}\right)$$
  
• K is a matrix describing the radiation pattern of the spherical modes, for example by: $$K=\left[\begin{array}{cccc}{K}_{11-1}& K_{110}& K_{111}& \cdots \\ K_{12-2}& K_{12-1}& K_{120}& \cdots \\ \cdots & \cdots & \cdots & \cdots \\ K_{21-1}& K_{210}& K_{211}& \cdots \\ K_{22-2}& K_{22-1}& K_{220}& \cdots \\ K_{23-3}& K_{23-2}& K_{23-1}& \cdots \\ \cdots & \cdots & \cdots & \cdots \end{array}\right]$$
  
  Other organizations of the matrix K can be considered at this stage, the previous organization being given only as an example. In addition, in practice, as an indication, it can be noticed that the matrix K is devoid of null elements.
• "X" is the matrix multiplication, and
• Q is the matrix grouping the different coefficients Q _smn of decomposition of the electric field, for example by: $$Q=\left(\begin{array}{c}{Q}_{1-11}\\ Q_{2-11}\\ Q_{101}\\ Q_{201}\\ \cdots \end{array}\right)$$
  

The use of the matrix formalism makes it possible to simplify the calculations of the determination method.

When this matrix formalism is applied to the particular case of obtaining a greater directivity of the antenna array 10 in a direction by the angle of elevation θ ₀ and the azimuth angle φ ₀ , it is possible to show that a wave satisfying such a criterion is a wave whose matrix grouping the various coefficients Q _smn of decomposition of the electric field satisfies the following relation: $$\mathrm{Q}={\mathrm{Q}}_{\mathrm{OPT}}=\mathrm{at}\mathrm{.}\mathrm{K}*\left({\mathrm{\theta }}_{\mathrm{0}}{\mathrm{\phi }}_{\mathrm{0}}\right)$$

• a est une constante de normalisation,
• « . » désigne la multiplication scalaire, et
• « * » désigne l'opération mathématique de conjugaison complexe.

Or:

• a is a normalization constant,
• ". Means scalar multiplication, and
• "*" Denotes the mathematical operation of complex conjugation.

This last relation therefore makes it possible to obtain desired decomposition coefficients.

The determination method then comprises a step of calculating the values of the impedances Z1, Z2 of each load 20, 22 of the antenna array 10 so that the difference between the decomposition coefficients on the basis of the wave generated by the antenna array 10 and the desired decomposition coefficients are minimized.

The calculation step comprises a substep of expression of the wave generated by the antenna array 10 on the basis of the spherical modes.

According to a preferred embodiment, this sub-step of expression is implemented by decomposing the electric field associated with the wave generated by the antenna array 10 into an elementary electric field produced by each antenna forming part of the antenna array 10.

As explained above, for the specific case of the antennal network 10 of the figure 3 the electric field E1 connected to the first antenna 14, the electric field E2 generated by the second antenna 16 and the electric field E3 generated by the third antenna 18 are connected to the total electric field Etotal produced by the antenna array 10 according to the relation: $$\mathrm{Etotal}=\mathrm{E}\mathrm{1}+\mathrm{E}\mathrm{2}+\mathrm{E}\mathrm{3}$$

This decomposition into elementary electric fields makes it possible to facilitate the calculations carried out following the implementation of the method. Indeed, this decomposition only takes into account the proper structure of each antenna and not the possible charges to which this antenna could be connected.

The sub-step of expression then comprises the expression of each elementary electric field in the base of the spherical modes, which is mathematically translated by: $$\mathrm{Ei}=\mathrm{K\; x\; Qi}$$

• la dépendance en θ et ϕ n'est pas reprise pour alléger les notations,
• Ei est le champ électrique généré par la i-ème antenne, et
• Qi est la matrice regroupant les différents coefficients Q_smn de décomposition du champ électrique généré par la i-ème antenne.

Or:

• the dependence in θ and φ is not taken again to lighten the notations,
• Ei is the electric field generated by the i-th antenna, and
• Qi is the matrix grouping the different coefficients Q _smn of decomposition of the electric field generated by the _ith antenna.

The sub-step of expression then comprises a step of concatenation of the different matrices Qi regrouping the different coefficients Q _smn of decomposition of the electric field generated by the i-th antenna to obtain a matrix Qtot corresponding to the expression of the generated wave. by the antenna array 10 on the basis of the spherical modes.

The calculation step comprises a substep of calculation of the excitation vector making it possible to obtain the desired decomposition coefficients represented by the matrix Q _OPT . This amounts to solving the following equation: $$\mathrm{Qtot\; x\; \Lambda }={\mathrm{Q}}_{\mathrm{OPT}}$$

• /\ est le vecteur d'excitation du réseau antennaire 10, et
• Qtot est l'association au sein d'une seule matrice des Qi.

Or:

• / \ is the excitation vector of the antenna array 10, and
• Qtot is the association within a single matrix of Qi.

At the end of the sub-step of calculating the excitation vector / \, an excitation vector is obtained that depends solely on the structure of the antenna array 10 and on the criterion chosen for the Ototale wave generated by the antenna array. 10.

The calculation step then comprises a substep of determining the values of the impedances Z1, Z2 of each load 20, 22 of the antenna array 10 from the calculated excitation vector.

For this, according to one embodiment, the following equation is solved: $$\mathrm{\Lambda }=\mathrm{M\; x\; \Lambda }+\mathrm{P\; x\; U}$$

• M est la matrice décrivant les couplages ainsi que les réflexions associées à chacune des charges du réseau antennaire 10 soit, dans le cas particulier de la figure 3, aux première et deuxième charges 20, 22,
• P est la matrice représentant les connections entre le réseau antennaire 10 et des signaux externes, et
• U est un vecteur décrivant la pondération des signaux externes.

Or:

• M is the matrix describing the couplings as well as the reflections associated with each of the charges of the antenna array 10, ie, in the particular case of the figure 3 at the first and second loads 20, 22,
• P is the matrix representing the connections between the antenna array 10 and external signals, and
• U is a vector describing the weighting of external signals.

• $$\mathrm{Z}\mathrm{1}=\mathrm{7},\mathrm{6}\mathrm{\Omega }+\mathrm{i\; x}\mathrm{9},\mathrm{95}\mathrm{\Omega }$$
  
  et
• $$\mathrm{Z}\mathrm{2}=\mathrm{0},\mathrm{1}\mathrm{\Omega }+\mathrm{i\; x}\mathrm{13},\mathrm{54}\mathrm{\Omega }$$
  

Applied to the antennal network 10 of the figure 3 , the resolution of the preceding matrix equation makes it possible to find the following solutions:

• $$\mathrm{Z}\mathrm{1}=\mathrm{7},\mathrm{6}\mathrm{\Omega }+\mathrm{ix}\mathrm{9},\mathrm{95}\mathrm{\Omega }$$
  
  and
• $$\mathrm{Z}\mathrm{2}=\mathrm{0},\mathrm{1}\mathrm{\Omega }+\mathrm{ix}\mathrm{13},\mathrm{54}\mathrm{\Omega }$$
  

For such values of the impedances of the two loads 20, 22 of the grating 10, a good directivity in the direction of elevation angle θ ₀ and azimuth angle φ ₀ is obtained.

This appears in particular in the study of figure 4 . In this figure 4 four radiation patterns are shown. Each radiation pattern shows the angular distribution of the radiated power as a function of the azimuth angle φ ₀ at constant elevation angle (in this case θ ₀ = 90 °).

The diagram represented by a curve 100 corresponds to the diagram obtained for the network 10 in the presence of a resistive load in place of each of the first and second charges 20, 22; the diagram represented by a curve 102 corresponds to the diagram obtained for the network 10 in the presence of a short circuit in place of each of the first and second charges 20, 22; the diagram represented by a curve 104 corresponds to the diagram obtained for the network 10 in the presence of a reactive charge in place of each of the first and second charges 20, 22 and the diagram represented by a curve 106 in black drawn in bold corresponds to diagram obtained for the network 10 in the presence of the first and second charges 20, 22 having the values determined previously.

It appears that for the direction of elevation angle θ ₀ = 90 ° and azimuth angle φ ₀ = 0 °, the directivity of the grating 10 according to the invention is 10 dBi (dBi for isotropic decibel). In general, the directivity of an antenna is normally expressed in dBi, taking as reference an isotropic antenna, that is to say a fictitious antenna which radiates uniformly in all directions. The directivity of this imaginary antenna is therefore equal to 1, ie 0 dBi. The directivity of the network 10 according to the invention is therefore greater than the directivities of the other curves.

The gain in directivity is also observed by examining the shapes of the curves 100, 102, 104 and 106. Indeed, for the antennal network of the figure 3 , there is a reduction of radiation outside the main direction.

As a result, the network 10 of the figure 3 has an improved directivity in the direction of elevation angle θ ₀ = 90 ° and azimuth angle ₀ = 0 °.

Alternatively, instead of considering as a criterion the directivity, other criteria desired for the antenna array 10 are considered.

By way of example, the criterion corresponds to imposing that the forward / back ratio (also referred to as the Front / Back ratio) of the network 10 is greater than a desired value, that the radiation pattern of the network 10 is identical. to a radiation pattern obtained with a specific mask or that the diagram of network radiation 10 in a disturbed environment is identical to a desired radiation pattern.

In each of the proposed cases, one way to take into account the criterion is to impose a specific matrix for the matrix grouping the different coefficients Q _smn of decomposition of the electric field at the step of decomposition of a wave satisfying the criterion chosen in a basis for obtaining desired decomposition coefficients.

For example, this is the case when the criterion corresponds to imposing that the radiation pattern of the network 10 in a disturbed environment is identical to a desired radiation pattern. As an example of application, the antenna array 10 is intended to be fixed on an elongated upper part of a vehicle. The elongate shape disturbs the radiation of the antenna array 10. By performing the optimization of the antenna according to the method of the invention, it is possible to obtain a desired waveform generated by the entire vehicle.

The determination method described above applies to any type of antenna array 10 comprising at least one antenna that can be connected to a load. In particular, the antenna array 10 includes, in some embodiments, a plurality of primary antennas.

In a variant, the determination method also comprises modifications of the characteristics of the antenna network structure 10 so as to favor compliance with the chosen criterion. For example, it is possible to modify the distance between the first antenna 14 and the second antenna 16. Alternatively, it is chosen to modify the length of the second antenna 16. For this, it suffices to take into account the characteristics of the structure of the antenna array 10 to be varied in the substep of expression of the wave generated by the antenna array 10 based on the spherical modes. The excitation vector will then include the characteristics of the antenna array structure 10 to be varied. The resolution of the equation at the determination sub-step will include not only the determination of the values of the impedances Z1, Z2 of the loads 20, 21 but also the determination of the characteristics of the antenna array structure 10 that is desired. vary.

In any case, an antenna array 10 having improved properties is obtained. According to the embodiments, the antenna array 10 is fixed, neither the structure nor the values of the impedances Z1, Z2 of the charges 20, 21 being adjustable. For example, in the case of use of the antenna array 10 to point the object (a remote control for example) with which the user communicates, the property of good directivity will be favored to the detriment of others. In other embodiments, according to the uses, it is advisable to favor one or the other of the properties of the antenna network (passage of a directive configuration to a non-directive configuration). In this case, it is particularly advantageous for the loads 20, 21 to be adjustable. Typically, the charges 20, 21 are potentiometers associated with a component of variable inductance or variable capacitance. This makes it possible to further increase the adaptability of the antenna array 10 according to the invention.

Claims (10)

A method of determining an antenna array (10) for generating an electromagnetic (Ototal) wave comprising: at least one antenna (16, 18), at least one circuit (19, 20, 22) having parameters (Z, Z1, Z2) influencing the electromagnetic wave (Ototale) generated by the antenna array (10) and connected to at least one antenna (16, 18) ,
the process comprising the steps of: choice of a criterion to be verified for the wave (Ototale) generated by the antenna array (10), determination of desired decomposition coefficients of a wave in a base making it possible to reach the chosen criterion, calculating the parameters (Z, Z1, Z2) influencing the electromagnetic wave (Ototale) generated by the antenna array (10) for each circuit (19, 20, 22) of the antenna array (10) so that the difference between the decomposition coefficients on the basis of the wave generated by the antenna array (10) and the desired decomposition coefficients are minimum. A method of determining according to claim 1, wherein the circuit (19) is a coupling circuit and / or the circuit (19) is at least one load (20, 22). A method of determining according to claim 1 or 2, wherein the calculating step comprises a substep of: calculating an excitation vector (λ) of the antenna array (10) from the desired decomposition coefficients, and determination of the parameters (Z, Z1, Z2) influencing the electromagnetic wave (Ototale) generated by the antenna array (10) of each antenna antenna circuit (19, 20, 22) (10) from the excitation vector (/ \) calculated. A method of determining according to any one of claims 1 to 3, wherein the decomposition and calculation steps are performed using matrix calculation. A determination method according to any one of claims 1 to 4, wherein the base is the base of the spherical modes. A determination method according to any one of claims 1 to 5, wherein the criterion is selected from a group consisting of the following elements: the directivity of the antenna array (10) in a given direction, the ratio of the forward / backward return of the antenna array (10), the radiation pattern of the grating (10) is substantially identical to a radiation pattern obtained with a specific mask, and - The radiation pattern of the network (10) in a disturbed environment is identical to a desired radiation pattern. A method of determining according to any one of claims 1 to 6, wherein the circuit (19) is a waveguide-based coupling circuit, the parameters influencing the electromagnetic wave (Ototale) generated by the antenna array ( 10) being the parameters characterizing the impedance of the waveguide, the length of the guide and the impedance of a load (Z) associated with the coupling circuit. Determination method according to any one of claims 1 to 6, wherein the circuit (19, 20, 22) is at least one load (20, 22), the parameters (Z1, Z2) influencing the electromagnetic wave (Ototale ) generated by the antenna array (10) being the value of the impedance of each load (20, 22). A method of determination according to claim 8, wherein at least one load (20, 22) comprises two distinct components, a first component being a resistor and the second component being selected from inductance or capacitance. A method of determination according to claim 8 or 9, wherein at least one charge (20, 22) comprises a negative resistance.

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