« INPUT ADMITTANCE AND FIELDS RADIATED BY AN OPEN WAVEGUIDE FILLED WITH HIGH PERMITTIVITY DIELECTRIC »

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HAL Id: jpa-00214967

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Submitted on 1 Jan 1972

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“ INPUT ADMITTANCE AND FIELDS RADIATED BY AN OPEN WAVEGUIDE FILLED WITH HIGH

PERMITTIVITY DIELECTRIC ”

S. Lefeuvre, A. Jongejans

To cite this version:

S. Lefeuvre, A. Jongejans. “ INPUT ADMITTANCE AND FIELDS RADIATED BY AN OPEN

WAVEGUIDE FILLED WITH HIGH PERMITTIVITY DIELECTRIC ”. Journal de Physique Collo-

ques, 1972, 33 (C2), pp.C2-99-C2-101. �10.1051/jphyscol:1972231�. �jpa-00214967�

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ADMITTANCE D'ENTRÉE ET CHAMPS RAYONNES C2-99 Lorsque l'on tient compte de tous les modes de

propagation le temps de calcul machine est prohibitif et nous nous sommes limités au seul mode fondamental.

Après quelques calculs il vient : G(M 1 M t )

=

e(8, r ) e(8', r') x

e(0, r ) est la composante du champ électrique du mode Hl, parallèle à la distribution de courant 6.

On trouve :

avec k , a

=

x,, ^et

L'impédance d'entrée est alors donnée par :

x 1 ^{J(M) G(M} ¹ M t ) J ( M t ) ds ds' .

proba

Le courant J ( M ) est inconnu. Suivant différents auteurs, nous prenons l'expression :

J

⁼

Io sin k(x - h)

-

A[1

-

cos k(x

-

h)] .

Supposant que le courant a la symétrie de révolution.

A est un coefficient inconnu calculé par :

III. Résultats expérimentaux. - Les résultats expé- rimentaux obtenus pour l'antenne présentée figure 2 sont donnés sur la figure 3.

Ces résultats montrent que l'antenne a une surtension très élevée due à l'utilisation de matériaux de haute permittivité.

« INPUT ADMITTANCE AND FIELDS RADIATED BY AN OPEN

WAVEGUIDE FILLED WITH HIGH PERMITTIVITY DIELECTRIC »

Abstract.

-

This paper gives the theoretical and experimental results obtained on an antenna made by an open circular waveguide, filled of high permittivity material, and ended by a perfectly conducting plane.

The theoretical part is divided into two ones. The first one gives the reflexion coefficient in the discontinuity waveguide, free space and the second one gives the input admittance in the coaxial excitation of the guide.

Experimental and theoreticai results show that this antenna has a very small bandwith but that they can be better by using a matching device at the end of the guide.

This paper gives an example of use of high permitti- vity dielectric in microwave antenna engineering.

One of the largest field of interest in microwave antennas is the design of arrays with a large number of sources. For many reasons it is convenient to have a plane array and so each source is composed of an open waveguide.

If we want to have a very sharp pattern with low secondary lobes or a good scanning antenna it is necessary to have a large number of sources. And a large number of sources at frequencies near 1 GHz implies a very big array. So, if we want to have not too big an array it is necessary to have a small wave- guide, that implies a guide filled with high permittivity dielectric.

Let us consider the elementary source shown on figure 1.

The expressions of the field radiated and of the input admittance will be obtained by dividing the antenna into two parts. The first part, in the A region, will give the radiation of an open circular waveguide and the input admittance, or the input reflexion coeffi- cient ï o on the discontinuity.

The second part will give the input admittance in the B region when ï 0 is known. The distance between the probe and the discontinuity is long enough to have the fundamental mode alone.

1. Reflexion coefficient l', of an open circular waveguide filled with dielectric. - We suppose that the guide is ended by an infinite perfectly conducting plane.

The fields radiated in free space have of course the same angular variation that the fields of the Hl, mode

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972231

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S.

LEFEUVRE ET A. JONGEJANS

and can be expanded into transverse electric and magnetic modes.

The continiiity of electric field on the two parts of the discontinuity is written.

w

(1 + To) e

=

j A(h) [hl dh + 1 B(hl) [hr] dh' .

O O

Where

:

T,, is the unknown reflexion coefficient ; e, the electric field of the Hl, mode ; [hl, the electric field of the TM,, mode in free space ; [h'], the electric field of the TE,, n o d e in free space ; h, h', continuous numbers

;

A @ ) , B(h), unknown functions to be calculated.

Applying normation and orthogonality relations gives A ( h ) and B(h) versus TO.

We need another relation to known exactly TO.

We find this last relation by writing the continuity of complex power P through the discontinuity.

In the guide we have

:

with

k , = m J F .

In free space we have :

Setting Pl

=

Pz we find after sonle manipulations

:

where p

=

h/ko. Then g

=

a + ^{j b} gives

II. Input admittance on the probe.

-

For this problem we use the variational method, so we have to find the Green function producted by an elemen- tary current source parallele to the probe (we suppose there is no current at the top of the probe).

To have the total Green function we begin to have a partial one obtained when the distribution of current excites modes in a guide infinitely long in the two directions.

Then we have the total green function, considering the wave radiated in the two directions and reflected by the short circuit and by the reflexion coefficient To If we take into account al1 the modes, the partial green function obtained is very complicated and demands prohibitive time of computation. So we have limited the expression to the first mode only.

After some easy manipulations we find :

G(M 1 M')

⁼

e(8, r ) a(@', r') x

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INPUT ADMITTANCE AND FIELDS RADIATED C2-101

e(O, r ) is the composant of the electric field of the The current J ( M ) is unknown. Following many mode Hl, parallel to the 6 current. It is easy to find : authors, we take for J ( M ) the expression :

J

=

Io sin k(x

-

h)

-

A [ l

-

cos k(x - h)] .

e(0, r )

=

jiHo 4 ²

^Â

J; ^{sin 2} ^B [F ^- ~ ; ( k , r)]

Assuming that the current has the revolution symmetry with kc a

=

x,, and

around the proble.

A is an unknown coefficient evaluated by setting :

kz

u"

III. Experimental results. - The experimental

results obtained on an antenna shown on figure 2 When the total Green Function is known, the input are given in the figure 3.

impedance is given by : These results show that the antenna has a very high surtension due to the use of high permittivity materials.

1 r

x

J ( M ) G(M 1 M f ) J ( M t ) ds dsl

probe

:I

FIG.

3. - Input impedance versus frequency.