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704 IEEE TRANSACTIONS ON A N T E N N A S A N D PROPAGATION. VOL. 38. NO . 5. MA Y 1990

The Cross Antenna: A New Low-Profile CircularlyPolarized RadiatorAbstract- A new low-profile circularly polarized medium gain an-

tenna i s presented. This traveling wave antenna consists of a con ductingwire or strip placed above a ground plane and following the contourof a cross with four or more branches and a diameter of around 1.5wavelength. The length of the wire is typically 5-20 wavelengths overone or more turns. The antenna i s fed from a coaxial input and ter-minated in a load. Multip le arm configurations are also introduced. Adescription i s included of the antenna and its principles of operation.Computer modeling of the antenna i s then followed by the optimizationof a few configurations for which design data and typical performancesare given. Experimen tal results on both one- and tw o-turn versions agreewell with predictions and confirm the practical value of this novel an-tenna configuration.

I . I NTRODUCTI ONIRCULARLY POLARIZED antennas with medium gainC 12-15 dBi) are required for applications with narrowbeam scan, in particular on-board geostationary satelliteswhere the field of view is less than f 0" for earth cov-

erage and data relay missions. They are also needed as feedsfor reflectors with large focal length to diameter ratios.Available medium gain radiators include helices, shortbackfires, and horns, which all have significant longitudi-nal dimensions particularly at low microwave frequencies.When low-profile elements are required, subarrays of crosseddipoles or microstrip patches can provide medium gain, butthey involve somewhat complex matching and power dividercircuity.The cross antenna [l] , which will be discussed here, be-longs to the family of traveling wave antennas. It involvesonly a wire or microstripline above a ground plane, fed atone end and terminated at the other by a load.

This type of antenna with low profile and potentially lowproduction cost in printed circuit techniques, has been inves-tigated for application to mobile communication satellites at1500 MHz, as an array element or a primary feed for offsetreflectors . Another flat circularly polarized traveling wave an-tenna, the rampart line antenna [2], can also provide mediumgain, but its beam is highly elliptical in cross section andtherefore cannot be used for the above applications. The de-scription of the cross antenna and its radiation mechanism areoutlined in the next section.

11. DESCRIPTIONN D P R I N C I P L EThe basic geometry of the antenna is illustrated in Fig. Iwhere a few typical configurations are shown.

Manuscript received January 20. 1988; revised July 12, 1989.The author ia with the European Space Research and Technology Centre,European Space Agency. Posthus 299, 2200 AG Noordwijk zh , The Nether-lands.IEEE Log Number 9034579.

A conducting wire or flat strip follows the contours of across, which is supported a fraction of a wavelength abovea conducting ground plane. The line is fed at one end by acoaxial cable and terminated at the other by a load . The lengthof the branches is selected so that the current phase shift alongthe line from one branch to the next is 2 a +27r/N, N eing thenumber of branches; since the electric field radiated by eachbranch rotates by 2 a / N from one branch to the next, the totalfield radiated on axis will be perfectly circularly polarized ifno attentuation along the line is assumed. In practice this isapproached if the decay along the line is slow.This is best seen in the case of the four-branch, one-armcross antenna of the figure. The long sides of its arms have alength of Xe/2, the short ones a length of Xe/4, Xe being theeffective wavelength (in p ractice a few percent lon ger than theline wavelength).

Successive pairs of long arm s each radiate a field essentiallyoriented along their bisecting directions, with amplitudes de-creasing toward the l ine end. The short arms introduce 90"phase shift between the fields radiated by successive pairs,and also add to the overall circular polarization radiation.

As for oth er traveling w ave antennas of this type, the currentdecays approximately exponentially along the line with ondu-lations corresponding to reflections at the bends. The powerabsorbed or reflected at the end of the line can be limitedto a few percent of the input power by adjusting the heightof the line above the ground plane (typically 1/20 to 1/4 wave-length).

The line length can also be optimized (typically five to 15wavelengths) by changing the number of branches and turnsof the antenna.Waves reflected by successive bends tend to cancel eachother out so that a broad-band input impedance match caneasily be achieved.Power reflected at the end of the line radiates a crossed-polarized beam, and this can be used to reduce or cancel outthe on-axis cross polarization by optimizing the value of theload impedance.The bandwidth of the antenna depends on the number ofbranches and turns, but due to the traveling wave radiationmechanism, radiation pattern and polarization deg radation oc-cur if operation is extended over 5% bandwidth.The radiation mechanism along a transmission line with

bends has been addressed by several authors.For a straigh t, lossless, two-wire line terminated in its char-

acteristic impedance, Storer and King [3], [4] have indicatedthat a straight two-wire line with a length of several wave-lengths does not radiate any mo re than if it was only a quarter-wavelength long.0018-926X/90/0500-0704$01 OO 0 990 IEEE

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ROEDERER: TH E CROSS ANTENNA 705

O N E -A R M, O N E- T UR N , E I G H T - B R A NC H CR O S S O N E -A R M. TW0-T U R N . S I X - BRANCH CROSS F O U R -A R M. O N E -T U R N , F O U R -B R A N C H C R O SSFig. I. Typical configurations of cross antennas.

1I IFig. 2. Four-branch, one-arm cross antenna.This is due to the fact that along a straight two-wire lineof a certain length, the series radiation resistance and shuntconductance per unit length are close to zero, except nearboth extremities where they are not cancelled out by adjacentcurrent and charges.The case of a bend in an infinite two-wire transmissionline has been covered by Tomiyasu 151 and by King [4] usinga lower frequency approximation. The series inductance andshunt susceptance per unit length are decreased with respectto a straight line so that negative equivalent series conducta nceand shunt capacitance appear, introducing a reflection and a(positiv e) phaseshift on the transmitted wave.The determination of the change of series resistance andshunt conductance due to the bend and leading to radiationassumes a priori knowledge of the current and charge distri-butions near the bend. An alternative approach, proposed byWood 161 for a bend in a microstr ipline, uses the fringing fieldto determine the equivalent magnetic current and is useful toprovide radiated fields for a single bend.In the case of closely cascaded ben ds, the above derivationscan only provide qualitative information and it seems that the

only way to analyze th e antenna is to solve globally the classi-cal Hallen-type integral equation for the current distribution.This is the approach selected by Lee and Mei [7] and laterby Shafai and Sebak [8] to analyze zigzag and undulated lineantennas which have similarities with the cross antenna for

which the same approach was used by Roederer [I], Brewsterand Orton [9], and Pholien [ I O ] and will be pursued in thepresent study.111. MODELINGN D C O M P U T E R O P T I M I Z A T I O N

The modeling of various configurations of cross antennaswas performed using a code adapted from the Richmond com-puter program for thin-wire structures [ 111. The foundationfor this program, which uses the formulation of the sinu-soidal reaction technique, is well described in [ l ] and [I21and will not be discussed here. Minor modifications weremade to the code to introduce images and to model crosseswith multiple arms.The well-proven basic software has been further validatedby checks on one-turn and two-turn configurations describedlater in the paper. Some limitations remain however regardingaccuracy for configurations with very closely spaced wires,sharp angles and/or w ire lengths over 15 wavelengths.A . Single-Arm Crosses

Single-arm crosses are simply fed by a coaxial cable. Goodmatching of the input impedance is easily achieved with atransformer over a frequency band exceeding the operatingbandwidth. It is desirable to limit the power dissipated in theload to a few percent of that at the input while keeping theheight of the antenna over the ground plane below one ortwo tenths of wavelength to avoid excessive protrusion. It wasfound that this implies total wire length of at least six wave-lengths over one, two or more turns.Single-turn cross antennas exhibit more frequency scanningof their beam than multiple turn ones for which scanning canbe limited by a slight log periodic expansion and prope r choiceof the wire spacing.As in the case of a straight wire line section, radiation ef-ficiency increases with the wire separation from the ground.Performance is relatively insensitive to small changes in thewire diameter.

For a single-arm antenna the on-axis cross polarization canusually be cancelled by choosing for the load the optimumvalue determined as follows: The antenna is successively ana-lyzed in the two cases where it is fed at one end, the otherbeing terminated by a short circuit and vice versa. Let ports 1,2 , 3, 4 represent, respectively, one end, the other end of the

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706 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. VOL . 38 . NO . 5. MAY 1990

1

Fig. 3. Single-arm. single-turn cross antenna.wire, and the inputs of two circularly polarized probes placedon the antenna axis in the far field with right-hand and left-hand circular polarizations, respectively. Then the followinglinear relationships apply, with obvious notations:

1 2 = Y2,v , Y22v2 (2 )

1 4 = Y4I VI +Y42Vz = E L . (4 )Computation of 11 2 , ER an d E L in the above two casesprovides all the Y coefficients in (1)-(4) above. T he conditionfor pure on-axis right-hand circular polarization radiation is

EL = 1 4 = 0. ( 5 )Equations (3 , 4) and (2) lead to-=z[2

I 2which provides the optimum load impedance for zero on-axiscross polar ization. Th e above derivation is simplified in caseswhere the antenna is symm etrical [9].Two examples of single-arm antennas are described below.The first one, shown in Fig. 3 , is a symmetrical one-turn,eight-branch cross which has been optimized to provide max-imum coverage gain and low cross polarization within a -f 9"cone. In addition, it can operate simultaneously in right andleft hand circular polarizations by using both of its ports.

The line is terminated in its characteristic impedance. Ge-ometrical data for the antenna is as follows referred to thewavelength at the center frequency of operatio n:~ ~~

Branch length: 0.543 X,Branch width: 0.136 X,Cross diameter: 1.42Height from ground: 0.10 X,Wire diameter: 0.02 X,

Fig. 4. Single-arm. single-turn cross antenna: principal pattern cuts.

t 1

t 1L IFig. 5 . Single-turn, two-turn cross with log-periodic expansion.

It is to be noted that the actual wire length of a branch issomewhat longer than the ex pected value of 1.125 wavelength,since the effective wavelength along the structure is increasedwith respect to that in free space by mutual coupling effectsas discussed in the previous section.

Fig . 4 shows computed principal pattern cuts. The com-puted peak gain is 14.1 dB. This corresponds to a circulareffective area (uniformly illuminated) of diameter 1.61 ho.The cross-polarization perform ance can be improved by re-placing the matched load by one optimized for zero cross po-larization as discussed earlier.The main limitation of the single-a rm, single-turn antenna isthe frequency sensitivity of the beam sha pe and peak direction.One way suggested by Imbriale (131 to limit the frequencysensitivity is to introduce a log-periodic expansion in a mul-titurn configuration. This idea was used to optimize a second

cross antenna shown in Fig. 5. The innermost branch wirelength is 4.6% shorter than 1.17 XO, and the outermost branchis 4.6% longer.The load is optimized for zero on-axis cross polarization.Fig. 6 shows the computed principal pattern cuts. Unlike forthe single-turn antenna and because of the log periodic ex-pansion the peak of the beam is a few degrees off broadside.Beam scanning with frequency, however, is much mo re limitedand the antenna can be operated over some 7% bandwidth asis required for mobile communication satellites at 1550/1650

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ROEDERER: THE CROSS ANTENNA 70 7

~ I I -6,O' I I - . ? O , ' A :Oo , I ; I I ~-60' -30' 0 30 60'OB I

10

0

-10

-2 0

Fig. 6 . Single-arm, two-turn cross: principal pattern cuts.

Fig. 8. Breadboard model of a single-arm, single-turn cross antenna.

I 1Fig. 7 . Four-arm cross antenna.MH z. Th e computed peak gain excluding ohmic losses at thecentral frequency is 15.1 dB. Th e largest dimension of thecross is 1.53 XO.B. Multiple Arm Crosses

Two- and four-arm crosse s have also been modeled. M od-eling implies a high number of segments and the accuracy islimited. A four-arm cross is shown in Fig . 7.

The fo ur ports a re fed in a turnsti le mode. If phase stabili tycan be maintained over the desired bandwidth, this guaranteeson-axis polarization purity and good pattern symmetry.Four-arm crosses, with a diameter of around 1.5 wave-length, could be used to replace crossed dipoles or cup-dipoles in some applications with limited scan. They havethe advantage of higher gain per element and broad-band in-put impedance properties. O ther configurations with varyingnumbers of turns and branches can be envisaged, and som e ofthem are outlined in [11 an d [101. They d o not seem to provideperform ance supe rior to that of the antennas discussed above.IV . EXPERIMENTALALIDATION

A single-arm, single-turn cross antenna with eight brancheswas breadboard ed and tested. A photograph of the antenna isshown in Fig . 8 .The antenna opera t ing around 3 .2 GHz is terminated in i ts

Fig. 9. Single-turn cross: measured input impedancecharacteristic impedance. A transform er at the input providesa good match over more than 15% bandwidth to the 50(1feeding coaxial cable (see Fig . 9).Radiation patterns and gain were measured in linear polar-ization and compared to computed results. Fig . 10 shows acomputed and measured pattern cut at 3.21 GHz. Fig. 11shows computed and measured values of the gain and the axialratio as the frequency varies.

As indicated in Section 111, enhanced cross-polarizationperformance can be obtained by selecting an optimum load.Characteristic impedance loading, retained here as more rep-resentative of dual polarization operation, results in moderateaxial ratio pe rforman ce as predicted by the computations.

Taking into account the tolerances to which the breadboardmodel w as built and the measurement accuracy, as well as theperturbation introduced by the finite gro und plate and the inputtransformer, the agreement between predicted and measuredresults app ears to be sufficient to give confidence in computedresults on other similar configurations with on e turn.

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7 0 8 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 38 , NO . 5 , MAY 1990-60' -30' 0 30' 60'

D B I

L :'dig . 10. Single-turn cross: comput ed and measured pattern cut at 3.21 GHz.

l o E-l

5 1

+ + + MEASURED- - - - - - _ OMPUTED

* 11 zREF 1.0 U n i t s200.0 mUni ts/6 42.686 R 14.848 R

Fig. 1 1. Single-turn cross: computed and measu red gains and axial ratios.

START 1.450000000 GHzSTOP 1.7S0000000 EHz

Fig. 13 . Plot of the input impedance of the single-arm, two-tum cross an-tenna.

Fig . 12. Photograph of the two-turn cross antenna.In view of the superior performance predicted for multi-turn configurations with a log periodic expansion, a printedbreadboard of the two-turn, six-branch configuration of Fig.

5was manufactured.A photograph of the antenna is shown in Fig. 12. The mi-crostrip conductor, printed on a 0.06 mm kapton substrate,

has a width of 4 mm, resulting in the same characteristicimpedance as in the m odeled wire version.The substrate is supported above the ground plane by a 18mm thick layer of RO HAC ELL foam. After matching with atransformer, the input impedance has been measured and isplotted in Fig. 13. As shown in Fig. 14 , the measured axial ratio varies from0.4 to 1.5 dB over a 7% bandwidth.Pattern cuts measured at 1552 MHz are shown in Fig. 15and can be compared with predicted ones shown in Fig. 6 .

The measured gain slightly exceeds the predicted value of15.1 dB. Again, considering the measurem ent accuracy at L-band and the slight differences (wire versus microstrip, foam,versus vacuum, finite ground plane) between the modeled andthe breadboarded configu rations, the agreement seems reason-able enough to confirm the potential of multitum configura-tions.

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ROEDERER: THE CROSS ANTENNA 7091 . 4 5 1 . 5 1 . 5 5 G H z 1 . 6

III

A R I Ie I

I

IIII

I I

0-6 RM SJ . , , . ! - 8 A R M S10 1 . 5 1 . 5 5 GHz

Fig. 14. Measured axial ratio of the two-turn cross antenna

I= 1 5 5 2 MH zFig. IS. Measured pattern cuts of the two-turn cross (F = 1552 M H z ) .

V . CONCLUSIONA new type of low profile circularly polarized antenna withmedium gain, the cross antenna, has been introduced and per-

formances have been evaluated for a few configurations. Theantenna, ameanable to printed circuit microstrip constru ction,could potentially replace horns, helical antennas, subarraysof cross dipoles or microstrip patches for some applicationswhere 10-15 dB of gain is needed over a limited bandwidth,in single or dual circular polarization. Initial experimental

verifications have given reasonable agreement with computedresults. Further work is underway to analyze microstrip con-figurations and to optimize them for selected space applica-tions.

A C K N O W L E D G ME N TThe author wishes to thank G . Mica, N . E. Jensen, and

J . Bregonje for their support in the early development of thecross antennas as well as W . Imbriale, Y . Rahmat-Samii, W.

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71 0 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 38, NO . 5, MA Y 1990Rusch and R. Th omas for their suggest ions. He also expresseshis gratitude to C . Martin Pascual and J . Vassallo for theirinvaluable help in the breadboarding of th e two-tum antennaconfigurat ion.

[ IO] D. Pholien, Analyse dune antenne filaire nouvelle a onde progres-sive: 1Antenne croix, Travail de fin detudes, Faculte, des SciencesAppliquees, Univ. Liege, 19 86.[ i ll J. H . Richmond, Computer program for thin-wire structures in ahomogeneous conductng medium, NASA CR-2399, June 1974.[121 - Radiation and scattering by thin-w ire structures in the complexREFERENCES

A. G. Roederer, French Patent 85 104 63, July 9, 1 985.C. Wood, P. S . Hall, and J. R . James, Design of wideband circularlypolarized microstr ip antennas and arrays, IEE-AP Conf., 1978, pp.312-3 16.J. E. Storer and R. King, Radiation resistance of a two-wire line,R. W. P. King, Transmission Line Theory. New York: McGraw-Hill, 1955, pp. 487-492.K. Tomiyasu, Terminal impedan ce and generalized two-wire line the-ory. Part 11, effect of a bend, Cruft Lab., Harvard University, Cam-bridge, MA, Tech. Rep. 74, 1945.C. Wood, Curved microstrip lines as compact wideband circularlypolarized antennas, Microwaves, Opt., Acoust. , vol. 3, no. 6, Jan.1979.S. H. Lee and K. K. Mei, Analysis of zigzag antennas, IEEE Trans.Antennas Propagat., vol. AP-28, no. 6, pp. 760-764, Nov. 1970.L. Shafai and A. A . Sebak, Radiation ch aracteristics and polarizationof undulated microstrip line antennas, Proc. Inst . Elec. E ng . , vol.132, pt. H , no. 7 , pp. 433-439 , Dec. 1985.D. C. Brewster and R. S. Orton, GEC Res. Marconi Res. Center,

PIW. I RE , pp. 1408-1412, NOV . 1951.

frequency dom ain, NASA CR-2396, 1974.W . Imbriale, private communication, 1987.I3 1Antoine G. Roederer (S68-M70-SM82) wasborn near Paris, France, in 1943. He received theDiplome dIngenieur Radidlectricien from 1EcoleSupirieure dElectr icite , France, the M.S.E .E. de-gree from the University of California, Berkeley,and the Doctorat dhgenieur from the Universitede Paris, France, in 1964, 19 65, and 1 972, respec-tively.He was a Lecturer at IEcole Spk iale deMecanique et dElectricit6, Paris, France, and aResearch Engineer at the Surface Radar Divisionof THOMSON -CSF, from 1968-1972. In 1973 he joined the EuropeanSpace Research and Technology Centre of the European Space Agency,ESA/ESTEC, Noordwijk, The Netherlands, where he now heads the An-tenna Section . His main contribu tions have been in the areas of finite arrays,multibeam satellite antennas, and novel radiating elements.Dr. Roederer was awarded the Douglas Marsh Fellowship in 1987 to workon satellite antennas at the University of Southern California, Los Angeles,private commu nication, July 19 85. for one year.