HYBRID SYNTHESIS OF CONTOURED BEAMS

Pier Giuseppe MANTICA (*)

ABSTRACT

The paper reports on a synthesis algorithm using computer optimization techniques to find theshape of the reflector surfaces of an antenna system that allows the better reproduction of a givencoverage.

The method of the elliptic paraboloid is applied to obtain a good initial condition for the optimizationroutine.

An application example is reported.

INTRODUCTION

The shape of the coverages required for the satellites of the next years makes more sophysticatedthe design of on board antenna configurations.

The use of a beam forming network [1 ] is a solution giving good accuracy in the reproduction of thecoverage map. In this way however, the problem arises of designing a network that suppliesproperly the power to all the feeds.

For single-beam coverages one can satisfy the specifications also in a different way, by properlyshaping the surfaces of the reflectors, synthesized by means of the Geometrical Optics (GO)techniques [2] [3].

Such an approach, however, is hardly applicable to multibeam antenna synthesis. Moreover, thesurfaces are synthesized in a finite number of discrete points, and the choice of a properinterpolation function is not trivial.

For some antenna configurations, in addition, the Physical Optics (PO) analysis of the synthesizedsurface can give some discrepancy from the GO predictions.

The difficulties outlined can be overcome by the methods based on numerical optimizationtechniques [4]. This approach is the more recent, in spite of its rather simple formulation, becausethe computational size required can be afforded only by the latest computers.

In the following, an implementation of an hybrid-optimization technique is described.

OUTLINE OF THE METHOD

All the implementations based on optimization algorithms require:

a) the choice of the antenna parameters to be optimized;b) an analysis computer code to predict the antenna performances;

(*) CSELT - Centro Studi e Laboratorl Telecomunicazioni S.p.A. Via G. Reiss Romoli, 274 - 10148 TORINO(ITALY)

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c) the choice of a "target" coverage, expressed in terms of field values for points in a grid on the(u-v) plane, and the representation of the expected the radiated beam shape;

d) the definition of a cost function, based on the weighted squared differencies between thedesired and obtained field levels at each point of the given (u-v) grid;

e) a starting configuration as close as possible to the final one, in order to reduce computationtimes and to avoid poor convergence problems.

The considered antenna consists of one or two reflectors, illuminated by a small cluster of feeds.

An hybrid technique is applied, where the reflector shapes are defined using an optimizationcomputer code, while the starting conditions as well as location and characteristics of each feed inthe cluster are decided so as to have a rough reproduction of the expected coverage.

From the numerical viewpoint, the reflector surfaces Z(x,y) are described as the superpositon of a"shaping" polynomial to the starting analytical expression:

Z ( X,y) = S start ( X,y ) + I aij( X -Xo )(YYo) (1)1,J

where:S start is the starting expression of the surface,( xo,Yo) are the (x,y) coordinates of an assigned "anchor point" that cannot be modified by theoptimization.

The program acts on the coefficients (a ij) of the polynomial expression describing themodification of the starting surface.

The analyses have been made with a PO code developed in CSELT. The implementation of a moretime-efficient program, based on sampling techiques [5], is in progress.

The value of the radiated field in a number of points on the (u.v.) plane is obtained from theanalysis program, and the evaluation of the cost function gives the figure to be returned to theoptimization algorithm.

A very critical point, specially for contoured beam applications is the choice of the startingconfiguration. The elliptical paraboloid method, studied in CSELT [6], has been used to obtain arough approximation of the desired coverage as a composition of a number of ellipses, whose axialratio, amplitude and position are given by the position and the excitation of the related feed.

Due to the analytical expression of the surface and to the closeness to the required coverage map,the degree of the shaping polynomials is low and the convergence of the algorithm is faster andsafer.

-EXAMPLE OF APPLICATION

As an application of the previously described method a contoured beam antenna system has beendesigned. The contour of the prescribed "target" coverage is given by a polygonal with the verticesreported in tab.l.

The minimum gain on the coverage has been set to 36 dBi at the frequency of 6 GHz.

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According to the specifications, a single reflector antenna configuration has been envisaged, withthe following features (fig.1) Dx=210 cm, Dy=200 cm, Oo=27 deg, e*=23 deg.

The starting reflector surface input to the optimization algorithm is an elliptical paraboloid given bythe equation:

-2 2x yz ~~~~~~~~~~ + ~~~~~(2)

4fx 4fy(2

where:

fx = 160 cm fy = 200 cm

Two feeds referred as A, B have been used, and located in (0, 3.5, 90) and in (0, 1.5, 110)respectively. In order to reduce the diameter of the feeds, they have been supposed to be twoidentical dielectric rods, represented in fig.2.

The two obtained beams, of elliptical cross section, have been combined with a proper choice ofthe excitation coefficients, to avoid cancellation effects and approximate the target map.

The excitation of feed nr. 2 has been set to -2 dB in amplitude and 45 deg in phase with respect tothat of feed nr. 1.

The optimization process based on the so defined configuration and making use of a polynomial offifth degree has finally given the contours shown in fig.3, compared with the prescribed coverage.The required CPU time on a GOULD PN9000 computer is of about 5 hours.

CONCLUSIONS

The hybrid-synthesis technique here described allows good accuracy to be obtained in thereproduction of the prescribed coverage with acceptable computer times.

The algorithm works also for multibeam coverages (typically, two hemi-beams) with a cost functiongiven by the composition of the cost functions relevants to each beam.

REFERENCES

11] D.IJ. Brain, Y. Kalatizadeh, S. Karpatis: "Dual Mode Beam Forming Network and high efficiencyfeed array", ERA Rep. n. 88-0162, May 1988

[2] B.S. Westcott: "Shaped Reflector Antenna Design", Research Studies Press, England 1983[3] M. Mehler, S. Tun, N. Adatia: "Direct far-field GO synthesis of shaped beam reflector

antennas", IEE Proc., Vol. 135, Feb. 1988[4] J. Bergmann, R.C. Brown, P.J.B. Clarricoats: "Synthesis of Shaped-Beam Reflector Antenna

Patterns", IEE Proc., Vol. 135, Feb. 1988[5] D. Bresciani, D'Elia, Pierri: "Analysis of dual reflector antennas"l, Int. Conf. on Telecommuni-

cations and Control,. Haldidili (Greece), Aug. 1984[6] S. De Padova, E. Pagana, F. Rosenga: "Analysis and synthesis of an Elliptical Paraboloid Offset

Reflector Antenna", International Symposium Digest on AP, Washington, May 1978

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Tab. I - Vertices of the polygonal giving the contour on the (u-v) plane of the prescribed coverage

x

29*

z

x XF

Z PARABOLA AXIS

Fig. 1 - Antenna configuration with reference systems

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BEAM U [deg] V [deg]

A -5.0 -9.0B -1.8 -8.0C -2.5 -4.5D -4.5 -3.5E -5.5 3.2F -2.5 6.8G -3.0 8.0H -8.0 6.5

-9.5 4.5

10 4.6

Fig. 2 - Cross section of the dielectric rod (all dimensions in mm)

10

V

5

0

-5

-10

0U

5

Fig. 3; - Contours of the beam after optimization and target map

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G

dBidBIdBidBI

I I AIA A -I I10