EP0213646A1 - Modular microwave antenna units and antenna comprising such units - Google Patents

Abstract

Unit microwave antenna module for receiving or transmitting a rectilinearly polarized wave, comprising radiating elements in the form of horns and a supply network composed of waveguides of rectangular section connected on the one hand to the horns and on the other hand between them in such a way that for each horn the total length of the feeding path is the same, characterized in that: - it comprises four adjacent horns whose square openings form a two-dimensional pattern in a plane parallel to a reference plane P, - the waveguide supply network is of the so-called "planar" type because it is distributed in a plane parallel to the plane P, the large dimension a of the section of the guides being parallel in this plane P, - the guide supply network is of the so-called "tree-like" type because the horns are supplied by means of a T-shaped power divider (7,8), the branches of which are straight and symmetrical , - at least u ne wall of the guides parallel to dimension a has a fin (20) in the plane of symmetry. Application: 12 GHz planar antenna

Description

The invention relates to a unitary microwave antenna module for the reception or emission of a rectilinearly polarized wave, comprising radiating elements in the form of horns and a supply network composed of waveguides of rectangular section connected to on the one hand to the horns and on the other hand between them so that for each horn the total length of the feeding path is the same.

The invention also relates to a microwave antenna comprising such unit modules.

The invention finds its application, for example, in the production of flat antennas for the reception of television broadcasts retransmitted by artificial satellites.

An antenna comprising radiating elements in the form of horns supplied by waveguides is known from patent DE 2641711. This document describes a linear antenna module, consisting of a row of horns machined from a fiberglass block, the surfaces are metallized. This row of horns is supplied on the one hand by a main line and on the other hand by individual lines connected to the main line. The main line is of rectangular section, machined in aluminum and can be filled with a dielectric material. It is carried out so as to form in the plane of the electric field E a stepped power divider allowing the waveguides which ensure the individual connection of the horns to the main line to be supplied with equal power. Each of these waveguides, of rectangular section, is formed by a laminated structure comprising a dielectric material interposed between two layers of copper, the edges of this structure being metallized. The length of the individual feed guides, as well as their connection point to the main line, are chosen so that for each horn, the length of the feed path composed of the main line and the individual feed line, is the same. Such a structure is provided to allow phase differences in the feeding of the horns to be corrected by shortening some of the individual feeding lines.

However, such an antenna has many drawbacks. First of all, it necessarily has very high losses because the propagation of the waves in a dielectric medium such as that which constitutes the layered structure of the individual supply lines of the horns is always subject to high losses even if the dielectric is very good quality. The introduction of an identical dielectric material in the main line further increases the losses. Added to this is the fact that the price of a good quality dielectric material is always very high and considerably increases the cost of the antenna.

Then, the antenna module described in the cited document is of linear form, with series supply, which makes it very difficult to feed the horns exactly in phase and therefore it is essential to carry out a adjustment of the length of the individual supply lines to improve this result. However, it remains difficult to supply all the horns exactly in phase if a wide operating frequency band is required. In addition, the solution proposed by the cited document to solve this problem, leads to a complex antenna shape, as well as assembly and adjustment that are too delicate to be carried out for example during mass production.

In addition, for the application to the reception of television programs relayed by satellites, this antenna must have particular properties.

Remember that such an antenna must be able to receive circular polarization, right or left depending on the transmitting satellite.

We know that the polarization of an electromagnetic wave is defined by the direction of the electric field E in the space. If at a point in space, the electric field vector E remains parallel to a straight line, necessarily perpendicular to the direction of propagation of the wave, this wave is polarized rectilinearly.

On the other hand, the wave is circularly polarized if the end of the electric field vector É describes a circle in the plane perpendicular to the direction of propagation. The polarization is right circular when E turns clockwise for an observer looking in the direction of propagation. The polarization is left circular in the other case.

A circularly polarized wave can be broken down into two linearly polarized waves, perpendicular to each other and phase shifted by ± n72.

The antenna intended for the envisaged application can therefore be produced according to the following principle: the two perpendicular components, due to the emission by the satellite of a circularly polarized wave, are picked up and then composed with the appropriate phase shift (± _7T / 2 depending on whether we are dealing with a right or left circular polarization).

The implementation of this principle supposes the use in front of the antenna of a depolarizing radome. This radome is designed in such a way that it delays one of the components of the circularly polarized wave, thus causing the necessary phase shift. The two linear polarization waves are thus in phase and their vector composition gives a linearly polarized wave which can be received by an antenna with a single linear polarization.

• -la bande de fréquence doit se situer entre 11,7 et 12,5 GHz ;
• -le diagramme de rayonnement de l'antenne doit être enveloppé sous un gabarit selon lequel une atténuation de 3 dB du lobe principal correspond à une ouverture e du faisceau de 2°, exprimée par la relation :
  • 6._3dB ⁼ 2° qui est l'ouverture du faisceau à mi- puissance, et selon lequel les lobes secondaires sont atténués de 30 dB à 12° ;
• -le rapport entre gain de l'antenne G et la température de bruit T en degré Kelvin doit être :
  G/T ≧ 6 dB. °K-'

It is also recalled that, for the envisaged application, the antenna must meet the standards formulated by the CCIR (International Radiocommunication Committee). These conditions are as follows

• -the frequency band must be between 11.7 and 12.5 GHz;
• -the antenna radiation diagram must be wrapped in a template according to which a 3 dB attenuation of the main lobe corresponds to a beam opening e of 2 °, expressed by the relation:
  • 6. _3dB ⁼ 2 ° which is the aperture of the beam at half power, and according to which the secondary lobes are attenuated by 30 dB at 12 °;
• the ratio between gain of the antenna G and the noise temperature T in degrees Kelvin must be:
  G / T ≧ 6 dB. ° K- '

• -l'antenne soit facile à réaliser et d'un faible coût afin de permettre une commercialisation grand-public,
• -l'antenne soit d'un encombrement réduit et facile à monter, par exemple sur un toit, afin que le coût de l'installation ne vienne pas augmenter hors de proportion le coût de l'antenne,
• -les qualités techniques de l'antenne répondent aux normes conseillées par le CCIR, et en particulier que les lobes secondaires de réseau soient évités.

Thus, for the intended application, it is important that:

• -the antenna is easy to carry out and of a low cost in order to allow a general public marketing,
• the antenna is compact and easy to mount, for example on a roof, so that the cost of the installation does not come to increase out of proportion the cost of the antenna,
• -the technical qualities of the antenna meet the standards recommended by the CCIR, and in particular that the secondary network lobes are avoided.

This is why the present invention proposes a new microwave antenna module which meets these conditions.

• -il comprend quatre cornets adjacents dont les ouvertures carrées forment un motif bidimensionnel dans un plan parallèle à un plan de référence P,
• -le réseau d'alimentation en guide d'onde est du type dit "planaire" du fait qu'il est distribué dans un plan parallèle au plan P, la grande dimension ade la section des guides étant, parallèle à ce plan P,
• -le réseau d'alimentation en guide est du type dit "arborisé" du fait que les cornets sont alimentés au moyen de diviseurs de puissance en forme de T dont les branches sont rectilignes et symétriques,
• -au moins une paroi des guides, parallèle à la dimension a, comporte une ailette.

According to the present invention, these problems are solved by a unitary antenna module, as described in the preamble, characterized in that:

• it comprises four adjacent horns, the square openings of which form a two-dimensional pattern in a plane parallel to a reference plane P,
• the waveguide supply network is of the so-called "planar" type because it is distributed in a plane parallel to the plane P, the large dimension of the section of the guides being, parallel to this plane P,
• the guide supply network is of the so-called "arborized" type because the horns are supplied by means of T-shaped power dividers whose branches are rectilinear and symmetrical,
• at least one wall of the guides, parallel to the dimension a, comprises a fin.

In another embodiment, this module is characterized in that at least one wall of the openings of the horns also includes a fin.

The present invention also proposes a microwave antenna characterized in that it comprises a multiple number of four of such unit modules supplied to each other by a planar arborized network of the same type as the network distributed inside each module and in the same plane as the latter, so that all the horns of the antenna are supplied with a signal respectively of the same amplitude and of the same phase.

According to one embodiment, this antenna is characterized in that it consists of two plates, the surfaces of which are electrically conductive, the horns being formed in the thickness of the first plate, the openings of the horns opening onto the first face of this plate and the mouths on the second face, the guide supply network being formed by grooves made on the first face of the second plate, these grooves constituting three of the four faces of the guides and the application of the second face of the first plate on the first face of the second plate forming the fourth face of the guides and the connections with the horns.

According to another embodiment, this antenna is characterized in that it consists of two plates, the surfaces of which are electrically conductive, the horns being formed in the thickness of the first plate, the openings of the horns opening onto the first face of this plate and the mouths on the second face, the guide supply network being formed by hollow grooves made on this second face and constituting three of the four faces of the guides, the second plate having a first planar face, and the application of the second face of the first plate on the first face of the second plate forming the fourth face of the guides and the connections with the horns.

The antenna produced according to the present invention offers numerous advantages. First of all, it has losses as low as possible because it is entirely supplied by waveguides excluding any dielectric other than air.

Then, because of the tree-shaped form of the power supply network, all the horns are supplied by signals of the same amplitude and of the same phase, respectively, and this over a wide frequency band, without the need for any adjustments.

In addition, due to the planar shape of the feed network, the antenna can be produced using only two plates, metallic or even only metallized, by a very simple manufacturing process. This manufacturing process is all the more simple as the waveguide sections and the branches of the T power dividers are linear, that the elbows are at right angles, and that the patterns formed by the horns are repetitive, as well as the patterns of the fins.

In addition, the antenna thus produced has excellent mechanical qualities. It is particularly solid, resistant to weathering and aging.

Finally, this antenna has great technical qualities. It can operate in the hyper frequency domain, for example 12 GHz and over a very wide frequency band.

Its directivity and its gain performance can even be adapted to the application of the reception of television programs relayed by satellites. Indeed, the presence of the fins in the guides and the horns makes it possible to calculate for these guides and horns dimensions such that the lobes of the network are avoided.

The invention will be better understood using the following description, illustrated by the appended figures, of which:

• FIG. 1 which shows in perspective a radiating element of a unit module according to the invention;
• FIG. 2a which shows in perspective a unit module according to the invention;
• - Figure 2b which shows in perspective the supply network of this module;
• FIG. 2c which shows the same supply network provided with fins.
• FIG. 3 which represents, in section parallel to the reference plane P, the supply network of this module, the axes l'l "and J'J" being respectively the traces of the planes of symmetry of the network, respectively parallel to the plans Q and Q '.
• .-Figure 4a which shows in section a fin guide of the supply network,
• FIG. 4b which represents half of such a guide,
• FIG. 4c which represents the circuit equivalent to this guide half when n, the number of modes, is even,
• FIG. 4d which represents the circuit equivalent to this guide half when n is odd,
• FIG. 5a which represents a transition between two waveguides,
• FIG. 5b which represents such a transition with a stepped fin,
• FIG. 5c which represents the radiation diagram D of a rectangular opening in the H plane and in the E plane,
• FIGS. 6a and 6c which show in section respectively parallel to the plane Q 'and parallel to the plane Q, a radiating element of the unitary module;
• FIGS. 6b and 6d which represent in section respectively a plane sectoral horn H and a sectoral horn ptan & corresponding to the radiating element of the unitary module,
• FIG. 6e which represents in section a pyramidal horn provided with a fin of optimized shape,
• FIG. 6f which represents in section a pyramidal horn provided with a pseudo-double fin,
• FIGS. 7a and 7b which represent portions of the two plates constituting an antenna according to the invention, in one implementation,
• FIG. 7c which represents a radiating element of the antenna in another implementation,
• FIG. 8 represents the variation of the ratio s / a as a function of the ratio b '/ b for a cut-off frequency f _c of 10 GHz,
• FIG. 9 represents an example of adaptation of the power dividers,
• FIGS. 10 which represent the angular coordinates of a point M of the space with respect to the reference plane P,
• FIG. 11 a which represents the envelope C, of the radiation pattern of the antenna imposed by the CCIR standards in the application of the antenna to the reception of television programs relayed by satellites and the envelope C2 of the cross polarization diagram.
• FIG. 11 b which represents, with respect to this envelope c, the envelope of the theoretical radiation diagrams obtained by means of a single-fin antenna (C,) and by means of a pseudo-double-fin antenna (VS.).

As shown in perspective in Figure 1, the radiating element of a unitary antenna module according to the invention consists of a horn 1 whose opening has a square section on side A. During operation of the antenna, to allow reception or emission of a linearly polarized wave, the opening of the horn is placed parallel to a reference plane P defined by the direction of propagation of the electric field E and magnetic field H in the environment outside the antenna, and the sides of the square opening of the horn are placed either parallel to the electric field E , or parallel to the magnetic field H of the medium outside the antenna.

The mouth 4 of the horn 1 is connected to the wave guide 3 by an elbow 2. The wave guide 3 and the internal mouth 4 have a rectangular section with sides a and b such that a> b,

The electric field E propagates parallel to side b and the magnetic field H spreads parallel to side a.

The waveguide 3 is placed so that the dimension a of its section is parallel to the reference plane P and the dimension b perpendicular. Under these conditions, the electric field E propagates in the guide 3 perpendicular to the reference plane P, and the magnetic field  propagates parallel to the reference plane P. The guide 3 is said to be "plane H ".

The angle of the elbow 2 connecting the mouth 4 to the guide 3 is therefore in a plane parallel to a plane Q, the plane Q being defined as perpendicular to the plane P and parallel to one of the sides of the openings of the horns . In operation, in the bend 2, this plane is parallel to the vector E . Elbow 2 can be called "plane elbow r". In the environment outside the antenna, the plane Q is defined, in operation, by the magnetic field E and the perpendicular oz to the plane P, as shown in Figure 10a.

The antenna module according to the invention consists of four horns, the openings of which form a pattern repeated by simple translation, along two axes parallel to the sides, with the same pitch, in a plane parallel to the reference plane P, as it is shown in Figure 2a, in perspective, seen from above.

The feed network of these four comets is shown in perspective in Figure 2b. This network is said to be "planar" because it is distributed in a single plane parallel to the reference plane P. All the waveguides connecting the guides 3 of individual feed of the horns to each other are of the same type as the guides 3, that is to say "plan H ".

The planar supply network is therefore called "plan H ".

In addition, to allow the supply of the four horns using signals of the same phase and of the same amplitude respectively, this network is of the so-called "tree-like" type. Indeed, the horns are fed by two symmetrically with respect to a plane parallel to the plane Q, to form two groups of two identical radiating elements. Then the two groups thus formed are supplied symmetrically, with respect to a plane parallel to a plane Q ', this plane Q' being defined as perpendicular both to the reference plane P and to the plane Q as shown in FIG. 10a. . In the environment outside the antenna in operation, the plane Q 'is defined by the magnetic field H and the perpendicular oz to the plane P.

As shown in Figure 2b in perspective and Figure 3 in section parallel to the plane P, the supply symmetry of two horns can be obtained by a planar network such as elbows 5 whose angle is located in the plane of the network connect the individual feed guides 3 of these horns to a power divider 6 in the shape of a T in the same plane. The plane of symmetry of the system formed by the two horns, the two elbows 2, the two individual guides 3, the two elbows 5 and the power divider 6, is a plane parallel to Q, the trace of which is the l "on the figure 3.

The supply symmetry of the two groups of two horns thus formed is obtained by connecting the waveguides 8 from the power dividers 6 by a T-shaped power divider 7 located in the plane of the network. This power divider 7, output 9, and the guide sections 8 admit as plane of symmetry a plane parallel to Q ′ whose trace is J'J "in FIG. 3.

Thus for each horn, the length of the feeding path is exactly the same and the horns are fed perfectly in phase. In addition, all the waveguide sections are rectilinear and in a plane parallel to that of the openings of the horns.

A microwave antenna can be formed from a multiple of four of such unit modules supplied to each other by a planar arborized network of the same type as the network distributed inside each module and in the same plane as the latter. In this way the antenna can include the number of radiating elements necessary to obtain the desired gain for the antenna and all the radiating elements. nants of the antenna are however supplied by signals of the same amplitude and of the same phase respectively, making it possible to obtain perpendicular to the plane P a maximum radiation and therefore a maximum gain in accordance with the recommendations of the CCIR.

The following example is given to show that the antenna according to the invention can have technical characteristics suitable for the reception of television broadcasts relayed by artificial satellite.

Example of realization

1 -Conditions to avoid network lobes

• pour un ensemble de (M x N) sources séparées entre elles d'une distance définie par les paramètres dx et dy tel que représenté sur la figure 10b, et en posant :
• A(m,n) et Φ(m,n), l'amplitude et la phase de la source d'indices (m,n), la contribution de toutes ces sources au point R, sera :
  

We recall that:

• for a set of (M x N) sources separated from each other by a distance defined by the parameters dx and dy as shown in FIG. 10b, and by posing:
• A (m, n) and Φ (m, n), the amplitude and the phase of the source of indices (m, n), the contribution of all these sources to point R, will be:
  

• Ep = A_o exp.jΦ₀(sin Mu/Sin u) (sin Nθ/Sin θ)
• avec u = π.(dy/λ). Sin θ. Cos φ
• v = π.(dx/λ). Sin. θ. Sin φ

In the simple case where all the sources are equi-amplitudes (A (m, n) = A _o ) and equiphases (Φ- (m, n) = Φ ₀ ), we can then show that the contribution at point P s' finally writes:

• Ep = A _o exp.jΦ ₀ (sin Mu / Sin u) (sin Nθ / Sin θ)
• with u = π. (dy / λ). Otherwise θ. Cos φ
• v = π. (dx / λ). Sin. θ. Sin φ

• F_ré seau ⁼ E_p.E_p*/(E_p.E_p*)_max
• et s'écrit finalement :
• F_réseau = [Sin Mu/M Sin u]'. [Sin Ne /N Sin θ]²

The network factor is defined by:

• F _re bucket ⁼ E _p .E * _p / (E _p * .E _{p) max}
• and finally writes:
• F _network = [Sin Mu / M Sin u] '. [Sin Ne / N Sin θ] ²

• M sin U = sin M u = 0
• c'est-à-dire
  

In the plan (yoz), where φ = 0, the maximum of the network factor is obtained by checking:

• M sin U = sin M u = 0
• that is to say
  

• dy < λ c'est-à-dire dy/X < 1.

Thus, this relation provides the condition which all the (N x M) sources must fulfill in order not to have lobes of networks (lobes of amplitude equal to that of the main lobe): it suffices to have dy such that:

• dy <λ i.e. dy / X <1.

• d < λ ou d/λ < 1

According to the present invention, it was chosen to form the antenna, to place the radiating elements with a pitch d. It will therefore be necessary that:

• d <λ or d / λ <1

This relation establishes that for the lobes of networks to be completely avoided it would be necessary that the distance d between the radiating elements is lower than the wavelength λ propagated in the guide. Otherwise, network lobes appear. But they are more or less close to the main lobe depending on the value of the ratio λ / d.

According to the present invention, it can be seen in FIG. 3 that this relationship can only be verified if the dimension a of the guides is not too large. The solution to this problem is therefore to provide the wall of the guides parallel to a with a fin. The waveguides thus formed have a reduced bulk compared to a rectangular waveguide not provided with a fin of the same cutoff frequency.

The guide supply network provided with the fins is shown in perspective in FIG. 2c.

Il-Conditions to receive the emissions relayed by satellites

• -la bande de fréquence : 11.7 GHz à 12.5 GHz
• -le gain G ≃ 33 dB
• -L'ouverture θ_-3dB ≦ 2°

As the antennas are mainly intended for the general public TV 12 application, the conditions which will guide the design will be the CCIR recommendations concerning:

• - the frequency band: 11.7 GHz to 12.5 GHz
• - G gain ≃ 33 dB
• -The opening θ _-3dB ≦ 2 °

The template which must be respected is shown in figure 11 a. Curve C is the envelope of the radiation diagram, and curve C2 is the envelope of the cross-polarization diagram.

In addition to the fact that the antenna must be able to be manufactured in a cheap manner, its efficiency must be high: for this, it is therefore necessary to optimize the radiating element and minimize losses in the circuit.

111 -Determination of the cutting frequency of a fin guide

FIG. 4a represents in cross section, a waveguide 30 provided with a fin 20, placed on the wall 32 of dimension a. The fin 20 has a thickness S and leaves an opening of dimension b ′ between its end and the wall 31 opposite the wall 32.

At the cutoff frequency f _c , the electromagnetic field can be considered as the result of the wave moving from one edge to the other of the guide at the wavelength λ _c .

At the cutoff, we can therefore deal with this problem by making the analogy with two parallel transmission lines of infinite width short-circuited at two points. The TE mode cutoff, _o will then appear at the frequency for which the transmission line has its lowest order resonance (for TE _no modes, the nth mode cutoff frequency appears at the n order resonance). For the odd n order (see Figure 4d), the resonance must be of the type giving an infinite impedance to the center (in a / 2); for n even (see Figure 4c), this impedance must be zero.

At the cutoff frequency, we therefore have (FIGS. 4c and 4d) the equivalent diagrams of FIG. 4b where the susceptance B _c represents the discontinuity due to the variation in height (in s / 2); this capacity value, which is a function of the height of the fin, can be calculated from the formulas of Marcuvitz - (1) below and represents, in fact, the effects of the higher modes.

FIG. 4c represents the equivalent diagram of FIG. 4b for n even, and FIG. 4d for n odd.

Z, represents the impedance in the cavity 41 and Z ₂ represents the impedance in the cavity 42, θ ₁ and θ ₂ are the associated electrical lengths:

From the passive lossless lines theory and assuming that the impedance of the lines is proportional to the height, we then define the dispersion equations for calculating the cut-off frequencies of TE modes _No. finned guides.

For n odd:

La résolution des équations (1) se fait par une méthode itérative.For n even:

The resolution of equations (1) is done by an iterative method.

After solving these equations, we can see a slight difference between the curves given by Hopfer in IRE Transaction MTT - (October 1955) and the results obtained. This can be explained by the fact that the formulation of Marcuvitz, in "Waveguide Handbook" Mac Graw Hill, Book Company (1951), for the term capacitive, does not take into account the proximity of the lateral metal walls.

• Cotgh (a -s)/2b.

Whinnery and Jamieson in "Equivalent circuits for discontinuities in transmission lines" IRE 98 (February 1944) determined the value of this capacity taking into account the proximity effects of the metal walls. For our case, we get a good approximation of the corrective factor by the function:

• Cotgh (a -s) / 2b.

Taking this correction into account, the results obtained are then in good agreement with the Hopfer curves. These curves show that it is with a ratio b '/ b as low as possible that the greatest bandwidth is obtained.

In the case of transition studies between two guides, where it is important, if not necessary, to know at each point of the transition the value of the cutoff frequency, the relationships (1) are almost unusable because they require time to very long calculations. We will therefore prefer an approximate analytical expression but one that is easier to use.

IV -Analytical formulation of the cut-off frequency

• (dans le cas de guide à double ailettes, le terme - (2b) est à remplacer par (b))
• où λ_c10 est la longueur d'onde de coupure pour le mode TE,..

By evaluating the capacity effect introduced by the presence of the fin in the guide (proportionality between the surfaces), and by empirically determining correction terms, Hoefer and Burton ("Closed-form expressions for the parameters of finned and ridged waveguides "IEEE MTT, December 1983) lead to the following analytical expression:

• (in the case of a double-fin guide, the term - (2b) is to be replaced by (b))
• where λ _c10 is the cut-off wavelength for TE mode, ..

This formulation is in good agreement with the numerical methods for the following variations of the parameters (b / a, s / a, b '/ b)

We see that the relation (2) is easily exploitable by any computer and can therefore be used in the case where the dimensions of the different elements change continuously - (transitions, adaptation, ...).

V - Characteristic impedance

In the case of lines, one can unambiguously define a characteristic impedance Z _e ⁼ [V- (z) / I (z)].

This is no longer the case for waveguides, indeed the functions ψ _E (or ψ _H ), fulfilling the propagation equation [(A ² + k ² ) ψ _{E, H} = 0], do not fulfill not the Laplace equation [Av = 0]. On the other hand, a longitudinal electromagnetic component always exists in the guides, this component being directly linked to the corresponding generating function.

Despite everything, in order to introduce a quantity facilitating the calculations, we defined three kinds of impedances:

These different impedances satisfy the following relationship:

We find in the literature, in particular in the work of Mihran ("Closed and open-ridge waveguide" IRE, 37, 640, 1949), the analytical expressions of the impedances Z _pv and Z _vi at an infinite frequency depending on the equivalent capacity discontinuity due to the fin.

connaissant l'impédance à une fréquence infinie, il est alors aisé de la calculer à toute fréquence.By eliminating this ability using relation (1), we obtain the following relations (5):

knowing the impedance at an infinite frequency, it is then easy to calculate it at any frequency.

VI -Attenuation in a fin guide

n'est donnée par la relation suivante :

exprimé en Np/m.
où, c étant la vitesse de la lumière,
f et f_c représentent respectivement la fréquence de fonctionnement et la fréquence de coupure (f_c10 = c/2a).In a classic rectangular guide, we show that, depending on its dimensions (a, b), the conductivity of the material used (a), the attenuation

is given by the following relation:

expressed in Np / m.
where, c being the speed of light,
f and f _c respectively represent the operating frequency and the cut-off frequency (f _c10 = c / 2a).

et en utilisant du cuivre comme matériau (σ = 58.1 10⁶ ohm.cm), on obtient la relation (6). L'atténuation s'exprime alors par:

exprimé en dB/m.
où a et b sont en cm.In the case of a guide filled with air, we have:

and using copper as a material (σ = 58.1 10 ⁶ ohm.cm), we obtain the relation (6). The attenuation is then expressed by:

expressed in dB / m.
where a and b are in cm.

où K est un facteur de correction que Cohn estime légèrement supérieur à 1.However according to Cohn ("Properties of ridge waveguide, IRE, 1947), the attenuation is given by the relation:

where K is a correction factor that Cohn estimates slightly greater than 1.

If we refer to the relation (5) giving the voltage-current impedance (Z _vi ) _x , we easily show that the relation (7) is in fact only the formula of the attenuation of the classic rectangular guide weighted by a proportionality factor.

VII - Hopfer formula

avec :

a = b/a, y = s/a, = b'/a δ = (1-sla)/2 , k = λ_c/a e = λ_c/λ
et P, épaisseur de peau (en mètre) du matériau utilisé.This relation must be compared to the relation presented by Hopfer (reference cited above) which gives for the attenuation:

with:

a = b / a, y = s / a, = b '/ a δ = (1-sla) / 2, k = λ _c / ae = λ _c / λ
and P, skin thickness (in meters) of the material used.

We . notes that the two theoretical formulations (7) and (8) lead to curves - (not drawn here) which have a slight increasing difference with the ratio f / f _c .

It should also be noted that the increase in bandwidth with the use of the fin guide comes at the expense of an increase in losses.

VIII -Evaluation of fields in a fin guide

It may be interesting to know the value of the electromagnetic fields at all points of the structure; this is used to calculate the power transported in the guide or, for example, to search for places of circular magnetic polarization (Hz, Hx) for resonance isolator applications.

Using the methods described above, at no time can one have access to the components of the electromagnetic field. It is then necessary to use other techniques: for example, using the modal development technique used by Collins and Daly ("Orthogonal mode Theory of Single ridge waveguide", J. Electronics Control (GB), 17, 121 , (1964)) or use the finite difference technique used by Young and Hohman ("characteristics of ridge waveguides" Appl.Science Res. Section B, 8, 321 (1960)). the mathematical development of these methods requires heavy computer resources, but allows access to all the electromagnetic quantities.

The general appearance of the electric field lines is given in FIG. 4a.

IX -Determination of the size of the fin guide

This rapid preliminary theoretical study allows those skilled in the art to better understand how the antenna according to the invention is produced.

The fins are placed in the guide supply circuit as shown in FIG. 2c.

• d < λ_o
• ou d/λ_o ≃ 0,9

il pourra être choisi, pour 12,1 GHz une distance minimale

To meet the condition:

• d <λ _o
• or d / λ _o ≃ 0.9

a minimum distance can be chosen for 12.1 GHz

• a = 19.5 / [2 + b/a] (en mm) ... (9)

As shown in Figure 3, the dimensions a and b are related to the inter-element distance. Taking into account the thicknesses and 5 ', necessary for the mechanical production (machining, molding) of the order of 3 mm in total, we show that the width a, for this case, is given by:

• a = 19.5 / [2 + b / a] (in mm) ... (9)

By fixing the ratio (b / a) we therefore have the value of a. Using the relation (2), the pairs of values (s / a -b '/ b) are determined such that the desired cutoff frequency f _c is obtained (for example 10 GHz). For each of these couples, we then calculate the theoretical attenuation that we would obtain at a frequency, for example, equal to 12.1 GHz, this using the relation (8). We then choose the ratios b '/ b and sla giving the minimum attenuation.

An example of results is given in Figure 8.

We see in this figure that for a (b / a) equal to 0.45 and a cut-off frequency of 10 GHz, the dimensions of the fin are:

Note, however, that on this curve - (Figure 8) the values calculated for ratios s / a ≦ 0.45 are erroneous due to the limitation of the formulas of Hoefer and Burton. V -Study of the transition between the fin guide and a rectangular guide

It is also important to study the transition from the fin guide to a rectangular guide.

By imposing a linear variation of the sides of the guide, it is necessary to find a shape of the fin such that this one, by its dimensions, gives a cut-off frequency lower than the desired frequency band and gives a good adaptation.

To solve this problem, we can simulate the transition by an infinity of discontinuities separated from each other by a distance Δx.

This simulation is illustrated in Figure 5a.

avec y_m, constante de propagation dans la section considérée, cette relation peut alors se mettre sous la forme simple suivante :

avec :

(La formule (10) est obtenue en considérant des discontinuités de hauteur très faible devant la longueur d'onde et en négligeant l'influence des modes d'ordre supérieur).The overall reflection coefficient will then be, as a first approximation, the sum of all the reflections seen in each discontinuity, weighted of course by the appropriate phase shift, that is to say:

with y _m , propagation constant in the section considered, this relation can then be put in the following simple form:

with:

(The formula (10) is obtained by considering discontinuities of very low height compared to the wavelength and by neglecting the influence of the modes of higher order).

One sees here all the interest of the formulation of Hoefer and Burton (relation 2) as for the determination of the cut-off frequency of the fundamental mode TE, _o . By a very fast calculation, we can therefore determine at each point of the transition the cut-off wavelength (relation 2), the characteristic impedance (relation 5) and thus theoretically evaluate the adaptation hoped for by relation (10) .

This formula remains very general and can be applied simply to the calculation of the transition between two rectangular guides by imposing in the calculation (s = 0) and (b '= b).

The values calculated using the relation - (10) are found to be fully in agreement with the values given by MATSUMARU (Reflexion coefficient of E-plane tapered waveguides, IRE MTT, 6, 143 (1958)).

A transition 49 between a fin guide 30 and a guide 50 is shown in Figure 5b. In the embodiment presented here, the length of the transition 49 is for example:
H = ₇₅ mm
greater than the guided wavelength. The length of the rung 48 formed by the fin 20 is obtained from the resolution of equation (10) and depends on the choice of H.

XI -Study of power dividers

As we want a symmetrical power divider, the problem is to go from a certain impedance Z _o in the main branch to two division branches whose impedance is the same. It is therefore necessary to use a quarter wave adapter with impedance Z '; we then have the configuration shown in FIG. 9.

With 1 equal to a quarter of the wavelength, it is easily shown that the impedance Z 'must verify the following relation (11):

To vary the impedance of the fin guide, it is possible to vary either the width of the fin, its height or the dimensions of the guide.

By incrementing the selected parameter, the cutoff frequency and the value of the impedance are then calculated until the relation (11) is verified. It is then easy to determine the length of the quarter-wave transition (1 = Xg / 4) (λ _g = wavelength in the guide).

For the dimensions given in FIG. 8, one cannot verify the relation (11) by varying the width of the fin. On the other hand, by playing on the height of the fin, or the width of the guide, one can obtain the theoretical adaptation.

For the sake of mechanical construction, the first solution was chosen: variation of the height of the fin for the quarter-wave transition.

XII -Study of Plan E and Plan H elbows

It is very difficult to study these elbows in theory because it is necessary to take into account the couplings with the higher modes created by the multiple reflections in the elbow.

The problems of elbows in a classic guide are often presented in the literature. Also, assuming that the "winged" elbows behave in the same way as conventional elbows, we can admit to the views of the work of Hsu Jui-Pong and Tetsuo Anada ("Planar circuit equation and its practical application to planar type transmission line circuit "IEEE MTT -S Digest, 574 (1983)) that these should not bring strong mismatches.

It should be noted that, given the electric field lines (Figure 4a), the behavior of these elbows should be slightly different. Nevertheless, the disturbance brought should be minimal since the fields are concentrated above the fin.

XIII -Study of the finned cornet

The problem is to go from a fin guide (single or double) to free space. The shape of the fins inside the horn must be such that the cut-off frequency remains lower than the operating frequency band while retaining sufficient adaptation.

For conventional cones, the adaptation depends on the dimensions of the inlet guide, the opening and the length of the horn. The different parameters of a horn are given in FIGS. 6a to 6d.

-choix des dimensions du cornet : la distance inter-éléments étant de 22.5 mm, on peut prendre comme ouverture une largeur de 22 mm. En admettant que l'on puisse se servir de la relation (13) dans le cas d'un cornet à ailette(s), on montre facilement que la longueur minimale du cornet H est égale à 13.5 mm.In practice, for the cylindrical wavefront emitted from the center S _H (or SE) to be considered as equiphase, we must have, as Bui-Hai notes in "Microwave antennas-Application to radio-relay systems" Edition Masson ( 1978):

- choice of dimensions of the horn: the inter-element distance being 22.5 mm, a width of 22 mm can be taken as an opening. By admitting that one can use the relation (13) in the case of a horn with wing (s), one easily shows that the minimum length of the horn H is equal to 13.5 mm.

-diagramme de rayonnement : le diagramme de rayonnement d'un cornet pyramidal peut être évalué théoriquement à l'aide des travaux de Ediss ("Pyramidal horns at 460 GHz" Electronic Letters, 20, 345 (1984), par exemple. Malheureusement, on ne trouve pas dans la littérature des formulations analytiques quant aux rayonnements d'un cornet à ailette(s).By taking H equal to 20 mm, we therefore respect relation (13) well.

-radiation diagram: the radiation diagram of a pyramidal horn can be evaluated theoretically using the work of Ediss ("Pyramidal horns at 460 GHz" Electronic Letters, 20, 345 (1984), for example. Unfortunately, we does not find in the literature analytical formulations as for the radiations of a finned horn (s).

Also, as a first approximation, if we consider that the opening of the horn is the only radiating element, the approximate radiation patterns can be deduced from the theory relating to rectangular openings. The relative values of these radiation patterns in the planes (E) and (H) are given in FIG. 5c respectively on the curves De and D _H for the values of

However the real diagrams can deviate a little from these theoretical diagrams because they do not take into account the phase shift (A) on the opening and in particular the diffraction on the edges of the comet.

- horn gain: the gain of a pyramid horn can be calculated as a function of the gains of plane side horns (E) and (H).

• G ₌ 1,9635.10^-3 [G_x.G_y][1/(L_E/λ)(L_H/λ)]^-1/2 ... (14)

This gain can easily be assessed using the tables in Braun ("Some data for the design of electromagnetic horns" IEEE trans AP4, 29, - (1956)) and writes:

• G ₌ 1.9635.10 ^-3 [G _x .G _y ] [1 / (L _E / λ) (L _H / λ)] ^-1/2 ... (14)

With the dimensions defined above for the finned horn (s) and assuming that the relation (14) applies to this case, it can be shown that the theoretical gain, at 12.1 GHz, would be of the order of 8.8 dB.

In the case of a pyramid horn of the same opening, but of dimensions 15 ^x 15 mm at the entrance, and of the same length (20 mm), the expected gain is of the order of 9 dB. assuming therefore that the formulation (14) can apply to our case, we should expect a decrease in gain for the horn with fins (s) compared to the pyramid horn.

• -adotation of the horn: one can find in the works of Walton and sundbey ("Broadband ridged horn design" the microwave journal, 96, (1964)) that the best adaptation of a horn with double fins is obtained when the impedance of the "fin guide", along the cornet, varies according to the following laws:
  
  with
• Z _where : impedance of the excitation guide at an infinite frequency Zp _v ,
• 377: vacuum impedance,
• k: constant such that the impedance in H / 2 is equal to the half-sum of the excitation and output impedances.
• H: height of the horn

In fact, if we refer to the relation (15) giving the impedance Zp _v and if we impose b '= b and s = a (which is the case at the exit of the horn), we find that the output impedance must be equal to:

Also relations (15) will only be possible for a ratio (B / A) equal to 0.5. For our case, where the ratio (B / A) equal to 1, we should then take:

XIV - Single fin antenna

From the "optimal" form, defined in the previous paragraph, of the fin inside the comet, a fin has been defined experimentally so that the adaptation of the horn remains satisfactory while minimizing the effect of asymmetry in the plane (E). The comparison between the theoretical form P3 of the fin and the experimental form P ₄ is given in FIG. 6e.

XV -Antenna with pseudo-double fins

A much more interesting solution is to symmetricize the radiation diagram, therefore to geometrically symmetrical the radiating element.

For this purpose, a transition was made in the horn between a single fin to a double fin while controlling the adaptation (see Figure 6f).

The profiles P _s and P ₆ represent the pseudo-double fins and the profile P ₇ is the theoretical appearance of the single fin horn having the same behavior.

The technique of the pseudo-double fin has the advantages of symmetrizing the radiation diagram in the "E" plane (the diagram of the element alone nevertheless remains slightly asymmetrical), and of reducing mutual coupling.

Compared to the single fin antenna, there is a slight increase in the opening angle to 3 dB. The influence of this increase should not be detrimental to the final antenna: in Figure 11b, the envelope C is plotted, CCIR planar radiation diagrams (H) as well as the theoretical envelopes that would be obtained with an antenna comprising in the "H" plane, 32 elements of the simple C type. or pseudo-double fins (C ₃ ).

A theoretical simulation shows that, in the "H" plane, whatever the radiating element used where the geometric symmetry exists, the radiation diagram is symmetrical and corresponds, moreover, to the theory.

In yaws "E", you absolutely need a symmetrical geometric structure to achieve perfect symmetrization of the radiation diagram, which is the case for the horn with double fins.

XVI -Gain

The different gain measurements of the single or pseudo-double fin radiating element have led to gains of between 8 and 9 dB.

Knowing the gain of the radiating element, we can then predict the total gain of a network antenna comprising N radiating elements by the following formula:

In addition, it can be noted in Buihaï's book that when the opening of the horn is of square section, it is preferable to use an excitation guide of the same section.

Such a variant therefore makes it possible to slightly increase the gain (see BRAUN "Some data for the design of electromagnetic horns IEEE Trans. AP 4.29 (1956))

XVII - Study of losses

• -la nécessité d'avoir un contact électrique parfait tout le long de la ligne sous peine d'augmentation des pertes,
• -la nécessité d'avoir une ligne présentant un état de rugosité faible.

As we have seen, we should expect losses of the order of a decibel / meter for the dimensions chosen. The experimental study of this antenna made it possible to highlight:

• -the need for perfect electrical contact all along the line under penalty of increasing losses,
• -the need to have a line with a low roughness state.

Table 1 below summarizes the preferred values of the dimensions of the various elements of the antenna in the embodiment described above.

XVIII - Process for producing such an antenna

Because the waveguide supply network is designed in a plane parallel to the plane of the cone openings, it is possible to make the entire antenna in the form of a planar antenna using only two plates . These plates can be metallic and machined, or even molded plastic whose surfaces are metallized.

According to a first embodiment illustrated in Figures 7a and 7b, the antenna consists of two plates 100 and 110, the main faces 101 and 102 for the plate 100, and the main faces 103 and 104 for the plate 110 are parallel to the reference plane. The plate 100 comprises a multiple number of four of unit modules of four horns placed in an adjacent manner, so that all the horns are deduced from each other by a translation of the same pitch in the two directions parallel to the sides of the square openings . The horns are shaped in the thickness of the plate 100 so that the openings are flush with the face 101 and so that the mouths 4 are flush with the face 102, the thickness of the plate 100 being provided equal to the height of the horns (see Figures 4a and 5a). The plate 110 comprises the elbows 2 and the planar feed network of the antenna formed by grooves made in the hollow on the face 103 of this plate. The grooves have a width a and a depth b and constitute three of the faces of the grating waveguides. The application of the face 103 of the plate 110 on the face 102 of the plate 100 forms the fourth face of the rectangular section waveguides of the supply network and connects the horns to the network thus formed. It will be noted that the plate 110 must have a thickness slightly greater than the quantity b, which gives for the total thickness of the planar antenna thus formed a value slightly greater than the quantity of b + h.

According to a second embodiment, illustrated in FIG. 8, the antenna consists of two plates 200 and 210, the main faces 201 and 202 for the plate 200, and the main faces 203 and 204 for the plate 210 are parallel to the reference plane P. The plate 200 comprises the unit modules placed adjacent to each other, as in the embodiment described above. The horns are shaped in the thickness of the plate 200 so that the openings are flush with the face 201 and so that the mouths are in the thickness of the material forming the plate 200. The latter is provided with a thickness equal to the height h of the horns increased by the value of the dimension b of the guides. The antenna feed network is ready ticked on the face 202 of the plate 200 in the form of hollow grooves of width a and depth b, and of elbows 2 making it possible to connect the mouths of the horns to the grooves. The plate 210 is a simple blade with parallel faces. The application of the face 203 of the plate 210 on the face 202 of the plate 200 forms the fourth face of the waveguides of the supply network.

The antenna used according to one of the embodiments described above is therefore particularly simple and inexpensive to manufacture. It can be made in large series. It has great mechanical strength and does not require adjustment during assembly. To further facilitate the positioning of the plates 100 and 110, or 200 and 210 one on the other, there may be provided on these plates positioning pins or any other well-known identification and fixing system of the skilled in the art. For example, the plates can also be held opposite one another by screws.

As this antenna does not include a dielectric, the losses are as low as possible, and on the other hand it is extremely resistant to aging.

In addition, this antenna is of low volume and low weight. It is therefore particularly easy to set up and its support is then inexpensive.

Such an antenna is therefore extremely well suited for general public use for the reception of television broadcasts retransmitted by satellites. Indeed in such a reception system the antenna is an important element for two reasons: firstly the quality of reception depends directly on the characteristics of the antenna and secondly, the cost of the antenna and its support as well as the cost of installation and pointing to the satellite largely define the final cost of the reception system.

Claims (9)

1. Unit microwave antenna module for receiving or transmitting a rectilinearly polarized wave, comprising radiating elements in the form of horns and a supply network composed of waveguides of rectangular section connected on the one hand to the horns and on the other hand between them in such a way that for each horn the total length of the feeding path is the same, characterized in that: it comprises four adjacent horns, the square openings of which form a two-dimensional pattern in a plane parallel to a reference plane P, the waveguide supply network is of the so-called "planar" type because it is distributed in a plane parallel to the plane P, the large dimension a of the section of the guides being parallel to this plane P, the guide supply network is of the so-called "arborized" type because the horns are supplied by means of a T-shaped power divider, the branches of which are rectilinear and symmetrical, at least one wall of the guides parallel to the dimension acomporte a fin in the plane of symmetry. 2. Module according to claim 1, characterized in that at least one wall of the openings of the horns comprises a fin in the extension of that of the guides. 3. Module according to claim 2, characterized in that the guides have a fin and the horns have two fins on opposite walls in the same plane. 4. Unit module according to one of claims 1 to 3, characterized in that each internal mouth of the horn is of section equal to that of the waveguides and is individually connected to a network waveguide by an elbow, the angle is in a plane parallel to a plane Q, this plane Q being defined as perpendicular to the reference plane P and parallel to one of the sides of the square opening of the horn, as well as to the small dimension b of the internal mouth of the latter, characterized in that each individual horn feed guide is connected to one of the symmetrical branches of a T-shaped power divider by an elbow whose angle is located in the plan of the network, the main branch of this power divider being parallel to the plane Q in such a way that the horns are supplied by two symmetrically with respect to this plane, and characterized in that each group of two horns thus formed is connected to the 'one of the symmetrical branches of the divider of T-shaped power, the main branch of which is parallel to a plane Q ', this plane Q' being defined as perpendicular to both the reference plane P and the plane Q, so that the two groups of two horns constituting the unitary module are supplied symmetrically with respect to the plane Q '. 5. Microwave antenna characterized in that it comprises a multiple number of four of unit modules according to one of claims 1 to 4, supplied with each other by a planar tree network of the same type as the network distributed inside each module and in the same plane as the latter, so that all the horns of the antenna are supplied in phase. 6. Antenna according to claim 5, characterized in that it consists of two plates, the surfaces of which are electrically conductive, the horns being formed in the thickness of the first plate, the openings of the horns opening onto the first face of this plate and the mouths on the second face, the guide supply network being formed by grooves made on the first face of the second plate, these grooves constituting three of the four faces of the guides and the application of the second face of the first plate on the first face of the second plate forming the fourth face of the guides and the connections with the horns. 7. Antenna according to claim 5, characterized in that it consists of two plates whose surfaces are electrically conductive, the horns being formed in the thickness of the first plate, the openings of the horns opening onto the first face of this plate and the mouths on the second face, the guide supply network being formed by hollow grooves formed on this second face and constituting three of the four faces of the guides, the second plate having a first planar face, and the application of the second face of the first plate on the first face of the second plate forming the fourth face of the guides and the connections with the horns. 8. Antenna according to one of claims 6 or 7, characterized in that the plates are made of an electrically conductive material. 9. An antenna according to one of claims 6 or 7, characterized in that the plates are made of a dielectric material, the faces of which are covered with an electrically conductive material.

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