dielectric hybrid mode ant feed

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IEEE TRANSACTIONS ON ANTENNA S AND PROPAGATION, VOL. AP-34, NO. 1, JANUARY 1986 21

A Dielectric Hybrid Mode Antenna Feed: ASimple Alternative to the Corrugated HornERIK LIER

Abstract-A hybrid-modehornantenna has beenanalyzed heoreti-andexperimentally. t consists of aconicalmetalhornwithaor the core material. It s characterizeda very simp le design and excellent electrical performance. The hornbalancedhybrid HE ,,-mod e, and xhibits low cross

ation and low sidelobes over a wide frequency ange. Compared tois easier to analyze,

al of similar cross-polar bandwidth as for corrugatedwith ing-loaded orrugations.Drawbacks rehe effects of

losses. Thus the new horn represents an attractive alternative o

I. INTRODUCTIONHE AGE OF satellite communication has increased theneed for satellite antennas with low cross polarizationand

lobes, due to the requirements of frequency reuse toe the capacity in the satellite bands. The main source f

ion in reflector antennas is for most applicationsfeed element. In fact, the reflectors will reduce the overalls-polar level by typically 6 dB compared to the cross

with low ross polarization over either the transmit bandreceive band, of preferably both of them.

One of the simplest feed horns which can be used both forcircular polarization is the conical horn with smooth

which ssupporting the fundamental TEII-mode.The- 18 dB (referred tom co-polar level). This value is 5-10 dB too high to

the requirements for application in satellite antennas.ation than that of the conical horn, The most common

hornswithnarrow co-polar patterns andow crossfor use n dual reflector antennas, are the dual

ttivity dielectric horn (dielguidedualmodehorn [11has a narrow cross-polar

r is used. The dielguide feed [2], [3] has a large cross-ndan easily be integrated with the

and effective con-on. However, serious drawbacks of this feed are high

Manuscript received May6 , 1985; revised August 15, 1985. This workwa snder a ContractromTheNorwegianTelecommunicationsThe author s with he Electronics Research Laboratory, The Norwegianof Technology, O.S. Bragstads Plass 6, N-7034 Trondheim-NTH,IEEE Log Number 8406143.

radiation level outside the cone from the excitation horn andtheneed for a radome to prevent rain andpollution fromdestroying the surface of the dielectric cone. Finally, thecorrugated horn [4] has beenhe most widelyused feed horn nsatellite antennaswhereow cross polarization andowsidelobes have been required over a large frequency range.However, this horn is extremely expensive to manufacture andhas a relatively high weight. Therefore, there is a need for newfeedornswith similar radiation properties as for thecorrugated horn, but with lower production costs and weight.

In this paper a hornantenna representing an interestingalternative to the corrugated horn is analyzed, both theoreti-cally and experimentally [ 5 ] . The horn is illustrated in Fig. 1.It consistsof a conical metal horn with conical dielectric coreinside, separated from the metalwall by a dielectric layer(which partly may be air) with lower permittivity than for thecore material. A similar hornantenna is presented n [6],where the core is a low-permittivity dielectric cone (erl =l . l ) , and the front surface of he core is. plane. Modifiedversions of the basic concept shown in Fig. 1 can be obtainedeither by extending the core outside the metal horn (reducedweight), or by extending the metal horn outside the core (dualmode horn).The dielectric core is analyzed theoretically in Section II.Design criteria are developed, as well as a method forcalculating he radiation patterns. Measurements are presentedin Section In. The main results are given in Section V, wherepossible applications of the new horn antenna are discussed.

II.THEORETICALNALYSISA . The Plane Wall Model

The low cross polarization of the conical corrugated hornantennas ue to the hybrid-mode HEt I whichan esupported under the balanced hybrid condition [4, h. 31. Byanalyzing the wall impedances of the core horn in Fig. 1, itwill now be shown that the balanced hybrid condition can besatisfied for this horn antenna as well.

The simplest model for analyzing the boundary conditions atthe horn wall is the plane wall model shown in Fig. 2. Theparameter O 1 is the angle between the direction of propagationof the incident plane wave andhe surface normal between thetwomedia enoted yegions 1 and 2 , and O2 ishecorresponding angle in region 2 of the transmitted wave. Themodel represents the asymptotic case where the diameter ofthe cylindrical waveguidepproaches infinity. By otherwords, the model is most correct in the horn aperture.By defining the two impedances Z, and Z,, based on the

0018-926X/86/0100-01$01.00 0 986 IEEE


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- - . ~ . - . . . . . = . ~ -- ~ . .....IEEE TRANSACTIONSON A h i N N A S AND ROPAGATION, VOL. AP-34, NO. 1 , JANUARY 1986

Fig. 1. Illustration of the new hybrid-mode horn antenna (the dklectriccore horn).

(a) (b)Fig. 2. Plane wall model. (a) Illustration. (b) Transmission line model.

tangential electric (E) and magnetic (H) field components atthe boundary between regions 1 and 2, the balanced hybridcondition becomes [7]

where

and q l is the wave mpedance in region1 thecylindricalcoordinate system r , 4 , z is defined in Fig. 2). Based on Fig.2, the boundary impedances may be expressed as [SI

z,= - jq l 4 der in2 el- 1 anh ( k ; ) , ( 5 )G2 er sin* el- 1 , (6 )

where 2nx,k i = - jk2=-

and k2 is the propagation constant in adial direction in region2, X, is the free space wavelength, and E, = E , ~ / E , ~e r l and er 2are the relative permittivities of the media in region 1 and 2,respectively). By inserting (4)-(6) into (l) , the followingdesign criterium for the wall thickness t can be deduced:

1 .o-f 0.8-- \x0 0.6-

0.4 -0.2 -

.metal w a l l

1 .o 1.5 2.0E r 1Et-2

2.5E r =-

Fig. 3 . Normalized hickness of the outer dielectric versus relative permit-tivity of the horn antenna given in Fig. 1 which satisfies the balanced hybridcondition eased on (7)).

under the following condition:sin e, >= Jij

Equation (8) can be satisfied only when e,2 < erl, and if thefields in region 2 are evanescent with respect to propagationnormal to the wall.

Equation (7) with e l = 90 represents the value of t whichsatisfies the balancedhybrid condition for the asymptotic caseb + 00 ( b s the radius of the circular cylindrical waveguide).In Fig. 3 the normalized t versus E, is illustrated. It shows thatt increases when ,. decreases. The accuracy of t increases withincreasing b.E . The Circular Cylindrical Waveguide Model

A more accurate model than that described in the previoussection for analyzing the horn antenna shown in Fig. 1 , i s theinfinitelyong circular cylindrical waveguidemodel.Amethod for calculating the fields over the waveguide crosssection is shown in Appendix I, where the tangential electricand magnetic fields are forced to be continuous across theboundary between the two regions.

Based on this rocedure, curves for t satisfying the balancedhybrid condition, are shown in Fig. 4 as a functionof b with E,. .as a parameter and e r l = 2.5 . When b increases, it can be seenthat the curves approach asymptotically the values given in(7), as should be expected. This has also eenhowntheoretically nAppendix I, where identical expressions tothose given n (4) and (5 ) for Z , and Z , have been obtained orthe limit b 4 00.

Another interesting observation from Fig. 4 is hat f isalmost constant whenb varies, except close to cut-off for thehybrid-mode H E l 1. This means that for practical horn designsthe thickness of the outer region may be kept constant alongthe horn wall.C. Radiation Patterns

Twomethods for calculation of the fa r fields from thedielectric core horn shall be described in this section.

Method I: The field distribution over the spherical hornaperture is assumedo be identical tohe field distribution overthe equivalent circular cylindrical cross section through thecoordinate transformation shown in Appendix I, (47). The

G (8)


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ANTENNA FEED 234 .0 r -- lane wal l -model

I 1 I I 1 I I10 30 50 70 90 110b mm]

4. Thickness of the outer dielectric versus he radius of the circularcylindrical waveguide with E , as a parameter for the horn antenna given inFig. 1, satisfying the balanced hybrid condition.patterns are then alculated by integratinghe

horn aperture [9] (Kirchhoff-Huygen integration). Thethe horn.Method II : The field distribution withinhe orns

cal functions. The eigenvalueofheis calculated as shown in Appendix II,where the

2, and 2, are input data. The far fieldscalculated by integrating over the aperture as inI. This method is valid for all practical values of the

ofhe horn. It hasncreasingaccuracywithhorn diameter if 2, and 2, are calculated from the

(4) and ( 5 ) .In both he previously described methods only he HEII-o exist in the horn (theHEI2-mode an easilyn the programs). Furthermore, a nonspherical

in the horn aperture can easilybe taken intoto obtain a desired phase front. Calculated patterns

on these methods will be shown in Section III.Cross-Polar Bandwidth

An important parameter of performance of the new hornis its cross-polar bandwidth compared o he band-

of the corresponding corrugated horn. In [IO] thefeed has been compared with the corrugated horn

used to compare the dielectric core hornwith heThe cross polarization from circular cylindrical corrugated

by [IO]

a

d a is the radius of the waveguide, w and dare the width andf ndf,are the

From the expressions for the hybrid modes given in [4 , p.71 it can be seen that the cross polarization from the dielectriccore horn in principle has the same expression as that of thecorrugated horn, thus obtaining

where B andX re the normalized susceptance andeactance,respectively, at r = a (a is radius in circular cylindricalmodel). By applying the asymptotic expressions for B = q l /j Z , andX = Zq/j ql from (4) and ( 9 , the following ratio canbe constructed from (9)-(1 l ) ,

where

and f, denotes the center frequency for which the balancedhybrid condition is satisfied.

In Fig. 5 the ratio given in (12) is illustrated versusf f,. tshows hatwhenonly he HEll-mode ispresent the newhybrid-mode orns less frequency ependenthanhecorrugated horn, and his endency ncreases lightlywithincreasing er .

Fig. 6 shows absolute cross polarization from the dielectriccore horn as a function of theelative frequency with2a/X, asa parameter (X, is the free space wavelength at he centerfrequency.) Only the HEII-mode s assumed to propagate inthe horn. It can be seen that the frequency dependence of theboundary impedances does not represent any practical limita-tion as far as the cross polarizations concerned. Themaximum theoretical cross-polar bandwidth of a hybrid-modehorn sabout I .8:1, due to he ratio between hecut-offfrequencies of the undesired HE12-mode nd the HEll-mode.However, for the dielectric core hornshown in Fig. 1 themaximum achievable bandwidth isower than for an air-fdledhorn, for example a corrugated horn. The reason is that thecut-off frequencies in the horn are decreased when the horn isfiled with a dielectric material, while the cut-off frequenciesin the air-filled waveguide are the same. By using a corematerial with low permittivity, low cross polarization over a1.8:1 frequency range will in principle be possible. The sameeffectcan be obtained by filling he nputwaveguidewithdielectric, or by varying the diameter of the input waveguideproperly. A condition s hat heundesired HEI2-mode isnegligible small.E. Effects of Dielectric Losses

Dielectric materials are sometimes used in horn antennassray-correcting lenses, situated n hehorn aperture. As thethickness of the lens is ypically a fewwavelengths, thenondesired effects due to the dielectric losses are relativelysmall. For the dielectric core horn, however, the aypath


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24 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-34,NO . 1, JANUARY 1986

Corrugated horn

-2

I I I , I0.5 0.7 0.9 1.1 1.3 1. 5

f/FcFig. 5 . Calculated cross polarization for henewhybrid-modehorn (solidcurves) relative to theros s polarization fora corrugated horn with identicalcenter frequency f,as a function of the normalized frequency ( e f l = 1 .O,w/d = 1.0, u / A , 1).

- t5m .511

dielectric hybrid mode ant feed

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