Performance of offset reflector antennaswith array feeds

Prof. P.J.B. Clarricoats, D.Sc.(Eng)., F.Eng.. F.I.E.E., F.I.E.E.E., F.lnst.P..F.C.G.I., S.M. Tun, B.Sc, and R.C. Brown, B.Sc, Ph.D.

Indexing terms: Antennas, Radiation

Abstract: The paper considers the radiation patterns of both single- and dual-offset reflector antennas excitedby an array feed in which mutual coupling effects have been fully included. For the single-offset reflectorantenna, the crosspolar pattern is dominated by the geometry of the configuration, but for a dual-offset reflec-tor, whose geometry has been optimised to give low crosspolarisation, mutual coupling in the array becomes adominant factor in influencing crosspolarisation. The influence of feed displacement is also reported. It is foundthat the change in crosspolar level is marked only for the optimised dual reflector. Then for small displacementsmutual-coupling effects dominate, but for large displacements they can be neglected.

1 Introduction

Multibeam and shaped-beam array-fed antennas areextensively used in satellite-communication and satellite-broadcasting systems. Some systems deploy dual-polarisation frequency re-use, and this technique will bewidespread in future; it imposes exacting requirements onthe crosspolar discrimination of both the antenna and feed.The array-feed performance is the subject of a companionpaper [1], while in this paper we consider the performanceof both single- and dual-offset reflector antennas whenused with array feeds. A special feature of our study is theinclusion of mutual-coupling effects between array-feedelements, which, in certain cases, causes a marked changein performance. Prior work [2, 3] has either neglectedthese effects altogether, or allowed only for dominant-mode mutual coupling. In our companion paper [1] wehave shown, for an array of conical horn elements, thatTEu — TE21 and T E n — TM0 1 coupling has a predomi-nant effect on the array performance, which, as we showhere, is transposed to the secondary pattern of the antenna.

Both single-offset and dual-offset antennas are con-sidered; the single-offset paraboloidal antenna offers con-structional simplicity, but it exhibits an intrinsically highlevel of crosspolarisation. It is suitable for single linearlypolarisation systems, but dual polarisation can be used if,for example, gridded reflectors separate waves with orthog-onal polarisations. The dual-offset antenna, with parabol-oidal main reflector, can be either of Cassegrain orGregorian type. With an appropriate choice of offsetangles for feed and subreflector, both types can exhibitvery low crosspolarisation provided the feed polarisation ispure [4].

In the following Section we provide an outline of themethods we have used to predict performance. Confidencein our analysis and reflector software rests both on com-parisons we have made between different methods andcomparisons with the results of others. We describe onlybriefly the prediction of the feed pattern, as this is dealtwith elsewhere [1]. Results for the feed have been satisfac-torily compared with experimental results [5].

2 Prediction methods

2.1 Array- feed patternThe array feed is shown in Fig. la. It comprises a finitenumber of conical horn elements, which may be either

Paper 3098H (Ell), first received 11th November 1983 and in revised form 15thFebruary 1984The authors are with the Department of Electrical & Electronic Engineering, QueenMary College, University of London, Mile End Road, London El 4NS, England

172

excited from a matched input in the TE^-mode or passi-vely terminated. The elements lie in a perfectly conductingground plane which is assumed to have infinite extent. Theassumption has only a slight effect on the array-feedpattern except at wide angles from boresight, and, ingeneral, has a negligible effect on the antenna secondarypattern.

To determine the field due to the array at a point on thereflector surface, the contribution from every element ofthe array is summed after the effects of mutual couplinghave been included.

Fig. \b shows an individual horn element. By using the£-field model, the radiation field at P for the mth modewith azimuthal dependence p in the ith aperture is givenby:

(a) TE-modes:

O~jkori

r;

.•i e-jkori

cos Of

(b) TM-modes

(E9)i,m = -Jk20Z0a

3A% sin Bt

(4)

where

Xm

Y'm

X'm

Ym

Pm

Zo

Other

= root of the Bessel function JP(x)

= MX J= root of the Bessel function derivative J'P(x)

= JP(x'm)

= polarisation angle

= propagation constant

= free-space wave impedance

symbols are defined in Fig. 1.

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rim"subreflector projection

ithelement offeed array

Fig. 1 Array and reflector configurations

a Planar array with the radiation field point P and the source point P' in the hornapertureb ith element of horn array feedc Physical-optics scattering at the subreflector: configuration of the reflectors andarray feedd Geometrical optics and diffraction at the subreflector: configuration of the reflec-tors and horn element

Because the horn flare angle is small, it is unnecessaryto allow for phase curvature over the horn aperture.

The spherical vector field components Ee, E^ are con-verted to Cartesian components and the contributionsfrom the individual horn apertures are summed, takingaccount of the different amplitude and phase weightingsand different space factors. We note that the point P is inthe near field of the array since different values of r{ areused in the term e7*0''//-,-. The effect of mutual coupling is tomodify the modal coefficients A(£.

2.2 Scattering from subreflectorFor dual reflector antennas, scattering of the feed radiationfrom the subreflector is evaluated either by application ofphysical optics or by a combination of geometric optics,GTD and slope diffraction. Discussion of these methods iscontained in Reference 6.

2.2.1 Physical-optics method {PO)In the physical-optics method, shown in Fig. \c, the POsurface currents are calculated over the subreflector surfaceusing a local plane-wave assumption. Thus, for a givenincident ray r,-:

(5)

and the surface current Js is given by:

/ s = 2(hs x Hinc) (6)

The contribution dE to the electric field at P from thesurface element dx dy of the subreflector is given by:

dE=C(Js-rs(rs'Js)) dx dy (7)

There are three approximations in eqn. 1:(a) no reactive fields are included(b) Js is calculated using a local plane wave(c) fringe currents at the subreflector edge are neglected.

The method is well suited to arbitrarily shaped surfaces,but a fine xy grid (typically 5 x 103 points) is requiredsince the phase is generally nonuniform and there isusually a stationary-phase point on the surface. However,we note that Js is computed for all the feed elements onceonly.

2.2.2 Geometrical optics, uniform geometrical theory ofdiffraction (UGTD) and slope diffraction method

In the second method, GO, UGTD and slope diffractionare employed to calculate the field at P.

Fig. Id shows a sketch of the configuration. For a givenpoint, P, on the main reflector and a given feed element, i,a search is made to find the point of specular reflection onthe subreflector surface. There, the distance IS + SP is sta-tionary. The search is conducted using an xy grid, but forsurfaces of revolution only a one-dimensional search isrequired. The GO procedure is supplemented by UGTDrather than GTD (which fails at shadow boundaries). Dif-fraction points are located by means of a stationary-phasesearch around the subreflector rim. Slope diffractionaccounts for the field slope of the incident wave at the sub-reflector edge.

For each cell, P of the main reflector, the process mustbe repeated for every feed element. For a generally shapedsurface, two-dimensional searching is time consuming, but,for subreflectors which are formed from surfaces of revol-ution, GO and UGTD is faster than PO provided the

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array contains only a small number of feed elements. Forsubrefiectors with diameters larger than 20/, we havefound negligible differences in predicted patterns (includingthe sensitive crosspolar pattern) between the two methods.

—diameter

Fig. 2 Offset reflector antennas with array feed

a Single-offset reflector antenna with array feedD = 50.5A

•Ao = 40°i>c = 25°b Offset Gregorian reflector antenna with array feedD = 100A / , f2 = 30/1

lJ/o = 45° e = 0.394<AC = 40° 60 = 31°« = 13.74° 0, = 22.8°

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2.2.3 Secondary pattern formed by main reflectorThe secondary radiation pattern of the antenna is predict-ed by means of a PO integration over the main reflectorusing an xy grid. In our results, Ludwig's [7] third defini-tion is used to define the copolar and crosspolar com-ponents of the field. We have not included fringe currentsat the main reflector rim, so far-out sidelobes will lackaccuracy. This is not a limitation in a spacecraft antenna,which is generally required to illuminate only a smallregion of the earth's surface. Our patterns are displayed inthe form of contour plots with the convention that the ver-tical (/-axis represents D/X sin 6 cos $ (where D = mainreflector diameter and X = the free-space wavelength), andthe horizontal K-axis represents D/X sin 9 sin (j).

3 Results

3.1 Antenna configurations and feed patternsFigs. 2a and b show the two reflector configurations inves-tigated. The single-offset reflector of Fig. 2a is represent-ative of a spacecraft antenna with a 10 dB beamwidth ofapproximately 2°, while the dual-offset Gregorian: antennaof Fig. 2b has about half that beamwidth. The choice ofreflector and subreflector sizes was made so that the same19-element array feed could be used, thus enabling reflec-tors to be largely disassociated from feed effects.

The conical horn array feed and its midband copolarand crosspolar pattern is shown in Fig. 3. The central

Fig. 3 Linearly polarised radiation fields from a 19-element clean-beamcluster

Contours on 6 and <j> gridScale depicts angular displacement in any (^-direction

copolar crosspolarHorn radius = 0.5A 1

Element spacing = 1.005/Flare angle = 5°

Inner ring of elements is excited in amplitude 10.5 dB below the central element.Outer ring of dummy elements is terminated in matched loads

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element is excited in phase with, and at an amplitude of10.5 dB above, the surrounding cluster of six elements;these in turn are surrounded by a cluster of 12 elementsterminated in matched loads. In the absence of mutualcoupling the feed exhibits a pattern with symmetry, verylow sidelobes and very low crosspolarisation (so-calledclean beam). However, TE1X — TE21 and T E U — TM0 1

mutual coupling slightly distorts the copolar pattern andraises the crosspolar level to — 30 dB within the angle sub-tended by the reflector.

3.2 Single-offset reflectorFig. 4a shows the copolar and crosspolar pattern of thesingle-offset reflector of Fig. 2a, fed from the array of Fig.3, but with neglect of mutual coupling, thereby virtuallyeliminating feed crosspolarisation because of the arrayfactor. Fig. 4b shows comparable results with mutual

coupling effects fully included. The characteristic high//-plane crosspolar lobes of Fig. 4a are a well knownfeature of the offset reflector antenna [8]. Fig. 4b showsthat when mutual coupling in the feed is included thestructure of the feed crosspolarisation is conveyed to thesecondary pattern, but the four lobes are no longer sym-metrical, as in Fig. 3, because of interference. The copolarpattern is virtually unaffected down to — 20 dB, but belowthis level there is marked asymmetry.

3.3 Dual-offset reflectorFigs. 5a and b show copolar and crosspolar patternsobtained using UGTD for the dual-offset reflector of Fig.2b, fed from the array feed of Fig. 3, with, respectively,mutual-coupling effects excluded and included. As the par-ameters of the antenna were chosen to eliminate cross-polarisation within the limits of GO, Fig. 5a reveals a very

Fig. 4 Far-field contours of single-offset reflector antenna (Fig. 2a)a Without mutual coupling

copolar crosspolarb With mutual coupling

copolar crosspolar

Fig. 5 Far-field contours of offset Gregorian reflector antenna (Fig. 2b)a Without mutual coupling

copolar crosspolarb With mutual coupling

copolar crosspolar

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phasefront

feed at focus

displaced feed(repointed)

Fig. 6 Configuration of reflectors showing rays for on focus and dis-placed feed elements

crosspolarisation amplitude ,dB' I I l . l I I . I, J 1

crosspolarisation amplitude ,dB

I ,, ,i,—J 1—J

low level of crosspolarisation, even when diffraction isincluded. However, when mutual coupling is also included,as in Fig. 5b, it becomes the dominant factor in determin-ing the level of crosspolarisation. The secondary crosspolarlobes correspond closely with those of the feed, and theyexhibit the same symmetry. They are noticeably lower thanfor the single-offset reflector antenna, and the copolarpattern is symmetrical to —30 dB below the boresightvalue.

crosspolarisation amplitude,dB

i I i I i I i I i I i

-20

-30

-A0

-501 2 3

scan angle,degrees

3.0

Fig. 7 Far-field crosspolar characteristics of offset Gregorian reflectorantenna {Fig. 2b)

a 4 / lateral feed displacement in the £-plane. Feed array mutual coupling is notincluded. Scan angle = 1.85°b 4 / lateral feed displacement in the £-plane. Feed array mutual coupling isincludedc 4/ lateral feed displacement in the E-plane. Feed array mutual coupling isincluded in the analysis and the 19-element feed cluster is repointed to the midpointof the main reflectord Far-field crosspolar level as a function of the main beam scan angle

with mutual couplingwithout mutual coupling

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4 Effect of displaced feed

There is a trend in spacecraft antenna design towards feedswith an increasingly large number of elements, enablingeither many multiple beams to be generated and possiblyscanned, one or more shaped beams to be reconfiguredwith the spacecraft in orbit. In such circumstances, manyelements of the array will, of necessity, lie away from thereflector GO focus, and it is again of interest to discoverwhether mutual coupling in the array influences the pre-dicted pattern. We have investigated both single-offset anddual-offset configurations. For the single-offset reflector,we have found little change in the level of crosspolarisationwhen the centre element of the cluster of Fig. 3 is displacedby AX (causing approximately 3.5 beamwidths of beam dis-placement or 4° scan).

copolarisation amplitude ,dBI i I i I i I i

3.0

copolarisation amplitude,dB- - .. , - - i l i I i I

Fig. 8 Far-field copolar contours of Gregorian antenna (Fig. 2b) with 4Xlateral feed displacement in the E-plane

Scan angle = 1.85"a Feed array mutual coupling is includedb Feed array mutual coupling is included and the feed cluster is repointed as in Fig.7c

For a dual-offset antenna, which has been initially opti-mised for low crosspolarisation, the changes are more sig-nificant and mutual coupling produces a more markedinfluence on the predicted crosspolar pattern. In a practi-cal array, the displaced feed elements could be repointed,as in Fig. 6, so as to improve copolar symmetry and reducesidelobe levels. Note that the centre ray from the feedpasses through the centre point of the main reflector. Forreasons of clarity and brevity, we display the effect ofmutual coupling only for the crosspolar contour patternswithout feed repointing. The displacement of the feed inthe £-plane is 4A, as in Fig. 6. In passing, we note that anarray, comprising subarrays of 19-element clusters, wouldcontain 130 elements if this displacement were accorded inall directions about the reflector focus.

Figs, la and b show the predicted crosspolar contourswith, respectively, mutual-coupling effects excluded andincluded. On comparing Fig. la with Fig. 5a, we see that aprediction made excluding mutual coupling indicates an 11dB increase in crosspolar level for this feed displacement.In fact, the peak crosspolar level rises monotonically withdisplacement and beam shift (see Fig. Id). Fig. 1b showsthat, with mutual coupling included, the crosspolar struc-ture of the array feed (see Fig. 3) is present but with sym-metry disturbed. Fig. Id again shows the effect of beamshift.

When the feed is repointed the contours of Fig. 1c showthat symmetry is further disturbed, due to interferenceeffects, and the maximum level is now only slightly above— 30 dB. However, the beneficial effects of repointing aremanifest in Figs. 8a and b, which show, with mutual coup-ling included, the improvement in copolar symmetry andsidelobe levels.

5 Conclusions

Mutual coupling in an array feed has an effect on the sec-ondary radiation pattern of an offset reflector antenna. Theinfluence is greater on the crosspolar pattern, but, for thesingle-offset reflector geometry, the effect is small becauseof the inherently high crosspolarisation, which arises evenwith a pure linearly polarised feed.

For the dual-offset reflector antenna, the effect of coup-ling is marked (assuming that the offset angles have beenchosen initially to minimise crosspolarisation); and, whilein a satellite system at midband frequencies the predictedlevels may be acceptable, at the lower band edge mutualcoupling could be a critical factor governing overall systemperformance.

When the array feed is displaced from the geometric-optics focus of the antenna, we find that, for the single-offset reflector, crosspolar levels remain relativelyunaffected for quite large feed displacements because of thehigh intrinsic crosspolar level, while for the dual reflectordisplacement raises the crosspolar level almost to the valueof the single-offset reflector. Repointing the feed improvesthe copolar sidelobe levels, but it further raises the cross-polar level because the optimum tilt angles are no longersatisfied.

In summary, for those array feeds where mutual coup-ling raises crosspolar levels to of the order of —35 to —40dB at midband frequency, the secondary patterns of opti-mised dual reflector antennas will be influenced sufficientlythat the inclusion of mutual coupling is necessary for accu-rate prediction, especially for large array feeds.

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6 Acknowledgment

One of the authors (S.M. Tun) is indebted to both QueenMary College and the University of London for scholar-ships enabling him to participate in the above research.

7 References

1 CLARRICOATS, P.J.B., TUN, S.M., and PARINI, C.G.: 'The effect ofmutual coupling in conical horn arrays', IEE Proc. H, 1984, 131, pp.165-171

2 ADATIA, N., BRAIN, D., PHILIPPOU, G., and RINOUS, R.: 'Atheoretical and experimental investigation of a multiple primary feedreflector antenna suitable for contour beam applications'. IEE Conf.Publ. 279,1983, pp. 6-11

3 BIRD, T.S., BOOMARS, J.L., and CLARRICOATS, P.J.B.: 'Multiple-beam dual-offset reflector antennas with array feed', Electron. Lett.,1978,14, pp.439-441

4 TANAKA, H., and MIZUSAWA, M.: 'Elimination of cross polarisa-tion in offset dual-reflector antennas', Trans. IECE (Japan), 1975, 58B,pp. 71-78

5 CLARRICOATS, P.J.B., PARINI, C.G., and TUN, S.M.: 'Conicalhorn array feed performance'. IEE Conf. Publ. 219, 1983, pp. 195-199

6 RAHMAT-SAMII, Y., and GALINDO-ISREAL, V.: 'Scan per-formance of dual offset reflector antennas for satellite communications',Radio ScL, 1981,16, pp. 1093-1099

7 LUDWIG, A.C.: 'The definition of crosspolarisation', IEEE Trans.,1973, AP-21, pp. 116-119

8 RUDGE, A.W., MILNE, K., OLVER, A.D., and KNIGHT, P.: 'Hand-book of antenna design' (Peter Peregrinus Ltd., 1982), Vol. 1, pp. 395

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