DE2160320A1 - Antenna arrangement with a large number of radiation elements - Google Patents

Description

Αηΐ, -ielderin: Stuttgart, November 30, 1971

Hughes Aircraft Company P24-17 S / kg

Centinela Avenue and

Teale Street

Culver City, Calif., V.St.A.

Antenna arrangement with a large number of radiation elements

The invention relates to an antenna arrangement with a plurality of radiating elements, which by the open ends of waveguide sections formed v / ground.

One of the most difficult and still unsolved problems in constructing large antenna arrays with

209826/0682

a plurality of radiating elements consists in the mismatch that occurs at certain scanning angles. As a result of the mutual coupling between the radiating elements "the reflection coefficient of a radiator group is subject to undesirable variations when the beam is swiveled over a designated area. This problem is particularly pronounced in those antenna arrangements in which the individual radiating elements are formed by the open ends of waveguide sections it was found that under certain conditions the reflected power can be almost as great as the power supplied and consequently the power bi3 transmitted or received by the radiator group can drop to almost zero under certain scanning angles. This phenomenon is known as "resonance zero" or as " known dead zone "of a phased array antenna.

Considerable effort has been made to solve this problem in recent years. The result This effort was an attempt to match the antennas through a dielectric load or to improve dielectric coverage of the radiation elements. Other methods used to improve The adjustment made from chosen conductive plates, shorted blind waveguide sections and various Mode suppression methods use. The adjustment methods used were moderate

209026 / 0G62

Success in overcoming the problem of ltesonnnznull for phased groups «All examined However, methods have all been shown to be highly frequency-dependent. That means that although an adjustment of the Antenna in the entire scanning range when operating at the nominal frequency was achieved, however, a considerable amount Mismatch could occur at frequencies that deviate only a few percent from the nominal frequency.

Accordingly, the invention has for its object to be a Antenna arrangement of the type mentioned in such a way that it is broadband in a large scanning range is adapted.

This object is achieved according to the invention in that the open ends of the Iiohlleiterabschnitte each a conductive thin screen that is conductively connected to the waveguide ends.

Although the mechanism that caused the appearance of the resonance zero is not yet known in detail, it is assumed that the resonance zero is too a significant part of the mutual coupling of wave energy between nearby radiation elements is due to the antenna arrangement. This theory is supported by experiments made with a group of radiating elements in the form of open waveguide sections have been made. If the the spatial distance between the individual radiation elements is determined, the mutual coupling can between elements can be changed by

209826/0662

BATH ORIGINAL

the size of the waveguide is reduced. This technique can be used to reduce the effect of the zero resonance effect to diminish. However, by reducing the size of the waveguide, the bandwidth of the Antenna arrangement reduced.

In contrast, the use of diaphragms according to the invention has a change in the mutual coupling result between the radiating elements of the antenna arrangement without the working bandwidth being significant is affected. As a result, the invention provides a good impedance matching of the antenna arrangement in a large frequency range, the invention also has the advantage that it has a has a very simple structure and also retrospectively for existing antenna arrangements, their radiation elements formed by the open ends of waveguide sections, is attachable.

In the antenna arrangement according to the invention the size of the aperture of the individual radiation elements the antenna arrangement is reduced with the help of thin panels, which are attached to the waveguide ends. The effect of the diaphragms is to adjust the coupling impedance of the radiating elements in such a way change that at the feed point for a given scanning range a substantially constant Impedance is present.

Although in the following preferred embodiments of the Invention based on planar, phase-controlled antenna

BATH ORIGINAL

arrangements are described in which all fiber optic elements be fed with the same amplitude and advancing phase, the invention can also apply to other arrangements. For example, the surface of the antenna array can be more follow a curved surface as a flat surface. Furthermore, by superimposing excitation patterns with different phase progressions, the invention can also be used for excitation schemes, which make use of an excitation with unequal amplitude.

Further details and embodiments of the invention result from the following description of the exemplary embodiments shown in the drawing. The the Description and features can be found in the drawing In other embodiments of the invention, they can be used individually or collectively in any desired way Combination find application. Show it

Fig. 1 is a plan view of a section of a plane Antenna arrangement to explain the invention,

2 shows a simplified schematic illustration of an antenna arrangement for explaining the scanning planes and polar coordinates,

Fig. 3 is a perspective and partially broken away Representation of a section of an antenna arrangement according to the invention,

209826/0662 BAD OBiQlNAL

Pig. 4- a graphical representation of the radiation diagrams an embodiment of the invention with diaphragms of various shapes and sizes

Pig. 5 to 9 waveguide sections with different Aperture arrangements which can be used in antennae arrangements according to the invention are·

Known large antenna arrangements consist of a grouping of radiating elements, often some a hundred to a few tens of thousands of individual radiative elements. These radiating elements are with connected to a feed network that supplies energy to the antenna or dissipates the energy received by the antenna. The feed network contains phase shifters for changing the phase position from element to element in order to to effect an electronic scan. Although the radiation elements of such antenna arrangements individual dipoles, slits or other radiating structures, it is common practice to use waveguide sections open at their ends as radiation elements. Pig. 1 shows for the purpose the explanation is a plan view of a section of a large, two-dimensional radiator group 10, which consists of a "triangular" grid of waveguide sections with a rectangular cross-section.

Because of the obvious difficulty it makes when the portion treats each radiating element separately and then the contributions of all radiating elements

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Giuniaiert to get an expression for dan Gesantbehavior, large groups are usually after the so-called. "Unit cell" approximation analyzed. It has been found that very large groupings produce very little error if the grouping is treated as having an infinite extent and assuming that each element has the same effect and affects each element in the same V / This approximation can be used to define a unit cell by [xj £ s / 2 and (y | <_ t / 2 sin-Π-, as shown in FIG. 1, if s is the horizontal distance between the centers of adjacent waveguides in the x-direction and t sin Jl is the distance between the centers of adjacent waveguides in the vertical or y-direction. The parameters s, t and M. define the geometry of the group grating and are referred to below as the grating parameters. that the electric field within the waveguide elements for the dominant TE ^ Q-Ilodus, which is usually used to excite the Hohlleitorelemente, runs vertically and consequently the y-direction to the so-called Ε-plane ne of the group runs parallel. The Η-plane of the group is perpendicular to the Ε-plane and therefore runs parallel to the x-direction. Likewise, the width of each waveguide radiation element is designated with a and its height with b in the usual way.

The other physical parameters of a large antenna arrangement Follow the diagram below. 2

BATH ORIGINAL

shown. According to FIG. 2, the z-.fi.chse is perpendicular to the surface of the antenna arrangement and fills; Fit the line of intersection between the K and Ii planes. An arbitrary point in space 20, by its x-, y- and z-coordinates or, usually bequener, defined by its polar coordinates, tio, a point 20 at a distance r from the Lutte (0,0,0) of the arrangement, can be denoted by its polar coordinates r, <p, Q. With the selected polar coordinates, the Η-plane is defined as ψ = 0 and the Ε-plane as Q »0 °. For the following analysis it is assumed that the waveguide sections of the arrangements according to FIGS. 1 and 2 are unloaded and that the dielectric constant is Eq both inside and outside the waveguide.

The construction and analysis of such antenna arrangements or groupings are known and for example in the book by R. G. Hansen: "Iuicrowave £ 3canning Antennae", Academic Pres, New York 1966, Volume II, Chapters 3 and 4 treated. In short, the conception of such an antenna arrangement includes the determination of the Strahlur.gükeule of the grid structure forming the antenna arrangement as a function of the grid parameters. In most cases the formation of the first radiation lobe of the Lattice work specified in terms of the requirements, namely in terms of antenna gain and the beam width. The grid parameters of the antenna arrangement are then determined on the basis of these requirements the size of the waveguide is then selected according to the desired operating frequency range.

? 0 9 P 2 ß / 0 Π 6 2 BAD

When analyzing the antenna arrangements ^{according to the ϊ?} 1- £. 1 and 2 it is assumed that the energy is propagated within each Ilohlleiterelementes ι in the dominant I ¹ E ^ Q-LiOdUS. Outside the antenna arrangement, the energy is propagated as a space wave; It is therefore evident that a Llodenuia conversion takes place at the open ends of the waveguides. This lodenum conversion is accompanied by the excitation of higher order waveguide iodons which can result in the zero resonance effect which the present invention seeks to overcome.

It is assumed that the radiating elements of the antenna arrangement according to FIGS. 1 and 2 are excited with the same amplitude, but with a progressive phase. The element at the point χ = 0, y = 0 is called the (O, O) th element. Its excitation is defined as γ ^ , the excitation of the (p, q) th element is therefore defined as

. y ^ ¹ 'exp (-ok) Pps + (qt cos Jl) u + (qt sin Jl) vj. (1)

In this equation, k _Q = 21V ^ q is the number of ellipses in free space, u «sin Q _Q coscp _Q , ν = sin O _Q sin ^f p _Q and (O _Q , (jPq) the direction of the emitted beam in free space, expressed in polar coordinates.

ΐ / ie mentioned above, the antenna arrangement can be used using the unit cell approximation. In such an analysis, the whole field can be outside the antenna arrangement in TE and TM-Y / ellen with respect to the z-axis can be resolved. The electrical potential ψ and the magnetic potential γ are part of the full-

209826/0682 ORIGINAL BATHROOM

- ίο -

constant external field by the following equations in relationship:

VxVx

- ν χ

ν χ (ζ γ) + i ~ v xvx

(2)

(5)

In these equations, ζ is the unit vector in the z-direction · The potentials in different areas within the unit cell can follow v / i β Inside the waveguide were represented for ζ < O the potentials as a superposition of the normal modes

oo ι

♦ -Σ Σ

ra * o n-o

mn

coe HL. / xtäj cos JHLf y + £ | exp (~ jß z) a \ 2J b \ 2 / nm

(4a)

τ-Σ Σ

mn

mn

_eia

yy _a

considered · In the previous equations is

and

mn

(4b)

12077.

The dash next to the second summation sign in equation (4-a) indicates that the term for m »η» 0 is to be omitted. Jl, I "I are the mode coefficients for the given

incident field and

are the reflection

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kocffizionteii. For the transmitted wave iia free Raun the potentials are viewed as a superposition of the Raun haruonic, namely

Σ Σ

ρα — 00 ρο ·

In here is

pq

τ / ζ

L Ρ *

- C ^k o - *

po

- v ² 1

(5b)

^(5a)

(5c)

^k o ^v

2p

s tan / L *

According to the invention, at the end of each one is a waveguide formed radiation element a diaphragm, whose thickness is much less than a wavelength, arranged and conductively connected to the waveguide. Various possible diaphragm shapes, which will be discussed in more detail later, are shown in FIGS. 5 "through 9. However, reference is made to FIG. Referenced to illustrate the dimensions which are used in the following equations, while FIG. 5 shows the particular aperture shape used in the Antenna arrangement according to Fig. 3 has been used. As shown in Fig. 7, "with a front panel is the width

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BAD ORiGINAL

the Ilhlleiterapertur c ,, + C2 and its height d. + d,. In the case of the diaphragm of FIG. 5 used in the embodiment of the invention according to FIG. J, d,. = d _o «b / 2.

In the case of the lamp adaptation according to the invention, the first step is to calculate the aperture field and then to calculate (R _111n * ^ _n I and i ^ _Q) . to consider the aperture as a degenerate, abrupt change in the waveguide cross-section. Then the potentials of the aperture field are represented by the normal mode potentials of the waveguide, which are represented by (-C ^ ₁ ) <χ <c ~ and (-d ,,) <. y < d _P. In explicit form,

Σ mn CB Σ B. mn
»* ■

cos ML (x + c ) cos -S

C X Cl

exp (+ jn _mn z>

and

with

mn

mn

IWT

sin Si. (x + c J sin - (y + ö,) exp (+ jn z)
c ι α · χ mn

- '2 2

"mn " ^lk o " ^{(rarr / c)} "

d + d + d 1.2

2 ^ 1/2

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From the equals (2), (3) and (6a) Ms (6e) is obtained
man ± * for the sangential components of the field at ζ = O

- Σ ϊ .

mn

<w hjfö) -

ΣΣ] m η

ro n

mTT. . . . no
cos - (x + c,) sin τ- (y + d,)

'V ⁺ λ. » (- ² I) -oil- V (^

sin ~ (X ₊ C ₁ ) COs _d

(A-B) j (®L) η h (A + ^) ι ηπ mn mn \ V c / ran mn I d * r ⁰ B _1n X i lc j 'O

ΐηττ

cos

ran mn '

+ β i / ^mrl

for

cos M. _{(x + c} j _8in HL (y _{+ d} )

• and"-

<χ <c ₂ / '

<y <d.

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? For the ^r i angentialkomponenten of Aperturfeldes the unit cell results in free space at a distance from the antenna array (z> O):

E (z-0 +) -

E (z-0 +)

p q

ll \

ρ q

H (z-0 +)

(2)

(2)

<~; Ju) + τ (jv) Po pq pq

(2)

(8c)

H _y (z-0 +)

ρ q

(2)

x I <s / 2 / i y I < t sin Ω / 2

(8d)

and with

Q .-

(8e)

20982S / QSS2

In the same way it follows from equations (2), (5) »(4-a) and (4-b) for the Tanßentialkouponcnten des Aperture field within the waveguide section (ζ <Ό):

E (Z = O-)

ΣΣ {

m η I

mn mn mn ^p mn

mn
• cos-

P ⁽⁴⁾ ) R

^K mn inn

nir

(4)

EL) (9a)

7) ϊ (p7)

mn mn mn mn mn mn - ξ ² *) * (9b)

H (z + 0-) - ■

+ R

m η

mn \ a / \

mn

R] fgLU ein2! E (x + |) mn \ b / Y a V * /

.cos

ηπ

H (Z = O-)

mn

mn «n

• CO8

209826/0662 and x | <s / 2 / J y I <t a Ω / 2,

After determining the three sets of equations (7a) through (7d), (Oa) through (8c) and. (9a) to (9d) for The fields can be adapted to the aperture surface. The tangential components of E are at the diaphragm equal to zero, whereas the tangential components of Fields E and H merge steadily into one another in the aperture. The treatment of these equations is natural very complicated. To cut a long story short, that can essential action 3 steps are given as follows:

First the tangential electric fields for ζ = +0 and ζ = 0 are adjusted. This adjustment results

/ Ε _χ (ζ = 0) for -C ₁ <x <C ₂ and

E Cz = O +) =

. (1O)

-0 for the remaining area of the unit cell

Using Fourier analysis, both sides of equation (10) are multiplied by exp j (u χ + ν y) and integrated over the area of the unit cell. The integration leads to expressions for ^r j? and ^r ü for each (p, q) with all terms of J A, B, Ii = 3

I mn mn _mn ,

In the same way, by adapting the fields at z = 0 and ζ = -0, the reflection coefficients R and Rj _o for each (1, Q ) can be determined by means of the terms

{ ^B mn »\ n '^ mn ^ ^{and of course the} incident

Field JI _111n J ΐ 1 can be expressed.

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Dio Aiipassimg the tangential magnetic field H results

H (z = O +) = H ΓZ = O) = H (z = 0-) for -c. <x <c _P and -d. <y <d _P.

JC. J> -Λ. f CL I i—

To decouple the coefficients, equation (11) ^{is multiplied by nin fl T} r (x + c ^ Vc] cos [^ (y + d ^) / d] and over the aperture of the waveguide, namely over -c. <X < Cp and -d. <Y <d _2i integrated. This procedure leads to expressions for Α ·, _ω , B -. ^ ,, - ^ ιλ) (1, 0) in expressions of ^, T _p ^ and

Substituting in, the following two matrix equations obtained for the diode coefficients of the aperture field, namely

A = £ x-YV " ¹ u]"" ¹ ZI (12)

3 = -V ¹ UA, (13)

in which A, B and I of (a ^, A ^], [b ^, B ^ and • / ^ mn ¹ "'' mnl GebiLlcLe'ke are column matrices. The other matrices of equations (12) and (13) are known and their structure does not need to be detailed here to save space After the aperture field has been determined using equations (12) and (13), the reflection coefficients {R , IL 1 and the transmission coefficients

_r _ L mn am.)

I T , Ϊ K is calculated from the relationships obtained above.

209 8 2 6/0662

The matrix equations (12) and (15) correspond to infinite sets of linear equations. With numeric Calculations, these sets are terminated in such a way that about 25 modes in the waveguide range and 90 room harmonics can be used in free space · The numerical calculations are facilitated by using a computer.

In the antenna arrangement designed according to the invention 5 is a plurality of waveguide sections 50 with a rectangular cross-section arranged in a triangular grid as illustrated in FIG. With the back of the Antenna array is connected to a suitable feed network. For the sake of clarity of presentation, is the particular food etch used in FIG. 5 not illustrated · However, suitable feed networks are known, see for example the above Book by R.C · Hansen, Volume III, Chapter 1.

At the open ends of the waveguide sections 50, which form the front side of the antenna arrangement, is a a single large plate 51 made of conductive material is attached, which has a multiplicity of openings 52. The individual openings 52 are shown in FIG. equated mouth. The one arranged in front of the open ends of the waveguide and with the waveguide Conductively connected plate 51 effectively forms symmetrical apertures at the ends of the waveguide sections 50. If necessary, asymmetrical diaphragms can also be formed with the aid of the same conductive plate 51 by the plate is moved before it is attached.

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This antenna, constructed as a test sample, had the following grid parameters:

k _o t «4.7
k _o s «6.23

Jl - ^ 5.

The hollow conductor sections 30 were identical and had the following dimensions:

k _Q b - 2.51.

The individual diaphragms 32 formed by the plate 31 had the following dimensions:

k _o d _n - k ₀ d ₂ - 1,255

^k O ^c 1 " ^k O ^c 2" 2 * ^{04 to} ° * ⁷¹ (Outer coverage 0 to 7%).

Eo was the power radiation in the main lobe at Feeding of the radiation elements calculated with the same amplitude and progressive phase. Fig. 4 illustrates graphically the power in the main lobe in db as a function of the angle Oq in the H-plane from 0 to 80 °.

The solid curve 40, which reproduces the behavior of the antenna arrangement without a diaphragm or with a diaphragm coverage of zero percent, clearly shows that a resonance zero is present at approximately Gq »33 °. The first radiation lobe of the grating (grating lobe) is, however, at about 6 _Ω - 53 °. The curves 41 _t 42, 43 and 44 correspond to the power of the main lobe with 31enden of or 259a, 5C and ^ 75? "Ttberdeckung. It should be noted

2C9826 / Q662

that the diaphragm dimensions specified in this way correspond to the ratio (c, + c _o ) / a in percent. The use of a diaphragm results in an effective shift of the resonance _{zero from the broadside direction O Q} »0. With an aperture with 50F / 0 coverage, the resonance zero disappears and an essentially constant impedance matching is achieved. As curve 44 shows, a 75? Antenna diminished

Although the computer solution of equations (12) and (13) provides the information which are required for an optimal dimensioning of the diaphragm, this information can also be used in other ways can be obtained. For example, an antenna array using a large number, for example one hundred, radiating elements in the form of waveguide sections can be built up in the usual way The bezels can then be formed from a conductive tape, such as with an adhesive layer provided aluminum. A measuring line can be used for this purpose in the middle element of the antenna arrangement in order to record the impedance when pivoting the radiation 3keuie. By changing the aperture dimensions with the help of the conductive tape, the optimal aperture can easily be determined. After the optimal aperture shape is known, can If necessary, the antenna arrangement can be further adapted in the usual way by cutting suitable objects into each waveguide be introduced.

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Scanning behavior is only shown for the scanning direction in the Η plane. The zero resonance effect however, is usually not even remotely as pronounced in these other scan directions as in the Η level. To the extent that the resonance zero effect appears disruptive in other scanning planes, For compensation, a diaphragm can be used, as shown in FIG. 7.

A number of different diaphragm shapes are shown in FIGS. FIG. 5 illustrates a synchronous inductive diaphragm as it has been used in the embodiment according to FIG. 3. 6 shows an asymmetrical inductive diaphragm which can also be used to implement the invention, although this diaphragm ^{favors a conversion from the 1} PB ^ q to the TE ₀ Q mode and may therefore be undesirable in some cases.

As indicated above, Fig. 7 is a pictorial representation a generalized rectangular aperture. 8 shows a diaphragm with several openings of any arbitrary shape. Fig. 9 finally shows a circularly symmetrical 31ende, the is suitable for antenna arrangements with waveguide sections with a circular cross-section.

A number of bezels of various shapes which are also suitable for the invention are in the book of US Pat G. G. Southworth, "Principles and Applications of V / aveguide Transmission ", D. Van Nostrand Co., Inc., New York 1950, Shown on page 246. Of the various diaphragm shapes that can be used, some are mathematical Analysis more accessible than others. When more complicated diaphragm shapes become obsolete, a provision can be made

209826/0682

of shape and size may be necessary through experiments

It is understood that the embodiments described above illustrate only a small number of the many specific embodiments of the invention, which can result from the application of the invention and which omen a large number of different diaphragm shapes for antenna arrangements with different * grid geometry incomprehensible.

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Claims (5)

Claims 1. } Antenna arrangement with a large number of radiation elements which are formed by the open ends of waveguide sections, characterized in that the open ends of the waveguide sections (30) each have a conductive thin screen (31 »32) connected to the waveguide ends. are provided. 2. Antenna arrangement according to claim 1, characterized in that the diaphragms (31 »32) .eine reduction the cross-sectional area of the open waveguide ends by about 50 / S. 3. Antenna arrangement according to claim 1 or 2, characterized characterized in that the diaphragms (31 «32) are all in v / es are designed in the same way. 4. Antenna arrangement according to one of the preceding claims, characterized in that all apertures (31 »32) of a common conductive plate (31) provided with the same cutouts (32) are formed, which is conductively connected to the ends of the waveguide sections (30). 5. Antenna arrangement according to one of the preceding Claims, characterized in that the radiation elements (30) are arranged in the form of a triangular grid are. 209826/0662