IEEE TRANSACTIONS ON AEROSPACE AND NAVIGATIONAL ELECTRONICS

An Improved Ground Beacon Antenna*A. R. GIDDIS,t ASSOCIATE, IEEE, AND R. B. BARRARt, MEMBER, IEEE

Summary-An electromechanical scanning antenna technique isproposed to provide improved TACAN ground-beacon performanceover the full 960- to 1215-Mc band.

A radially symmetric, shaped-beam reflector is illuminated byan off-set, radial-pillbox horn. The horn is driven by a radial trans-mission line which contains a central radiator. Parasitic elementsare arranged in dielectric rings positioned concentrically with thecentral radiator. The rings are rotated uniformly about the centerline to generate an amplitude-modulated, omnidirectional azimuthpattern. The complex response of the elements controls the per-centage modulation, while the geometry of the reflector and its feedindependently control the shape of the elevation pattern.

The antenna generates uniform azimuth modulation over theelevation angles of interest.

I. INTRODUCTIONT ACAN, a "TACtical Air Navigational" system of

the polar-coordinate type, provides both bearinginformation (via omnirange) and distance in-

formation (via D-ME) on direct-reading instruments inan aircraft within a few hundred miles of a selectedground station.The heart of the omnirange bearing system is the

ground-beacon antenna which produces a directionalradiation pattern rotated in azimuth. Coarse bearing isprovided with a cardioid pattern that is generated by aparasitic element rotated about a fixed central elementat 15 rps (15 cps). Fine bearing is provided with nineparasitic elements, rotated about the central element atthe same rate, which produce nine secondary lobes (135cps) superimposed upon the single-lobed cardioid.

The antenna technique proposed in this paper is theauthors' respornse to an expressed need for an electro-mechanical scanning device that will provide improvedTACAN ground-beacon performance over the full 960-to 1215-\Ic band; viz., a better shaped-beam patternin elevation, iiiore horizon coverage and better controlover the modulated azimuth pattern than is availablefrom a vertical arrav of biconical dipoles.' 2

]II. PROPOSED TECHNIQtTETo provide this improved performance, the electro-

mechanical scanning antenna illustrated in a cross sec-tional view in F ig. 1 (next page) and in a pictorial viewin Fig. 2 has been designed.A radially symmetric, shaped-beamn reflector gen-

* Received April 11, 1963.t Philco WVestern Development Laboratories, Palo Alto, Calif.t System Development Corporation, Santa Monica, Calif.1 A. M. Casabona, "Antenna for the AN/URN-3 TACAN

beacon," Elec. Commn., vol. 33, pp. 35-59; March, 1956.2 E. G. Parker and A. M. Casabona, "General design considera-

tions for TACAN transponder antennas," 1957 WESCON CON-VENTION RECORD, pt. I, pp. 91-98.

erates uniform height coverage up to high elevationangles (e.g., 60°) with a cosecant-squared power dis-tribution in elevation. The geometry of the reflectorand its feed control the shape of the elevation pattern.

Feeding the reflector is a radial pillbox terminatedby an off-set radial horn. The pillbox horn is excited bya radial transmission line in the center of which is abiconical dipole radiator. Concentric with the centralradiator are two dielectric rings rotating at 15 rps. Onering holds a single parasitic element to modulate theazimuth pattern at 15 cps, the other holds nine similarparasites to modulate the azimuth pattern at 135 cps.3The modulation index can be controlled by adjustingthe amplitude-phase response of the elements.

In the following sections, the design of various por-tions of the proposed electromechanical scanning an-tenna is described.

III. RADIAL TRANSMISSION LINE

In this section, we will show how the central radiatorlocated at the center of the radial transmission linegenerates an outward travelling wave at the zerothmode (carrier level) and excites the parasitic elementsto generate the first harmonic (15 cps) and ninth har-monic (135 cps) modes. The form of the central radia-tor and the elements is discussed. The optimum radialdistances of the latter are derived to assure strongmodulation over a broad band of carrier frequencies.Similarly, the radial distance of obstacles in the line,such as support posts, is derived to minimize the mod-ing caused by their presence.

A4. Mode Excitation

It can be shown4 that the only modes which willpropagate in a radial transmission line with a heightless than one-half wavelength at the highest frequencyare cylindrical waves of zero order travelling in theradial direction. The electric field normal to the parallelplates of the transmission line waveguide is of the form

E. = A,mHm')(kr) cosmO, (1)where

Am = amplitude coefficient whose value dependsupon the impedance response of the ra-diating element,

3 The assembly of rings and parasitic elements is referred to asthe "modulation ring" and is designated as such in Fig. 1.

4 S. Ramo and J. R. Whinnery, "Fields and Waves in ModernRadio," John Wiley and Sons, New York, N.Y., 2nd ed., pp. 395-400; 1953.

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316 IEEE TRANSACTIONS ON AEROSPACE AND NAVIGATIONAL ELECTRONICS December

Hm(2)(kr) = Hankel function of the second kind whichcharacterizes an outward travelling wavegenerated in the radial transmission lineby the central radiator (m = 0) and theparasitic elements (m = 1 and m = 9),

r = the radial distance in the guide,m =mode number associated with the order

of energy propagated in the guide,= azimuth angle modulation.

However, the central element and the parasitic ele-ments individually have no q5 directivity. For the caseof the single parasite excited by the central element,assuming that both have identical element patterns,it follows that the electric field is of the form

Ez = A o[Ho(2) (kr) + ci exp (j7r/2) Ho(2)(kri)], (2)

wherer=the usual radial distance from the cen-

tral radiator to a point in the line,ri= the distance from a point in the radial

transmission line to the single parasite.c =a numerical factor indicating the ef-

ficiency of the single parasite in re-radiating energy,

exp (j7r/2) = the parasitic element is excited 900 outof phase with the central element.

The pictorial view in Fig. 3 and the plan view in Fig. 4illustrate the geometry.

Using the expansion

0H

Ho (2) tIrl) = E H,,n(2) (kr)Jm,(kdl) expD (jM61)m=-x0

(3)

for the case of the single parasite and neglecting therelatively small amplitude termiis of order other thanm =0 and m - 1, the expression for the radiation fromthe single parasite is the following:

HOM2)(kri) = Ho(2)(kr)Jo(kdi) + 2H (2)(kr)Ji(kdl) cos4. (4)

One observes that, to obtain a strong 15-cps modula-tion of the electric field E., d1 must be chosen to corre-spond to a maximumn of J1(kdl).

Substituting (4) into (2), the field due to the com-bined radiation of the central radiator aind its 15-cpsparasite becomnes

E= A oHo(2) (kr) [1 + cl exp (jr/ 2)Jo(kdl)]

+ AoHi(2)(kr) [2ci exp (j7r12)Ji(kdl)] cos ¢. (5)

Therefore, it can be seen that the electric field in theradial transmission line for the case of a single radiatorlocated asymmetrically in the line at a distance d1 cor-responding to a maximum of Ji(kd1) yields tw-o prin-cipal modes varying as Ho(2)(kr) and Hi(2)(kr).

(NOT TO SCALE)Fig. 1-Cross-section diagram of ground beacon antenna.

Giddis and Barrar: A Ground Beacon Antenna

LOWER TRANSMI8ON - a

LINE BUPPORT8

Fig. 2 Cutaway view of shaped-beam antenna.

Fig. 3-Geometry of nmode excitation.

CENTRAL RADIATOR -' PARASITIC ELEME?

CIRCLE OF RADIUS

Fig. 4 Plan x iew of radial transmission linle.

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318 IEEE TRANSACTIONS ON AEROSPACE AND NAVIGATIONAL ELECTRONICS December

Parallel reasoning applies to deriving the distance dgfor generating the ninth harmonic and, thus, 135-cpsmodulation. At this dg, the phase of the wave relative tothe central radiator at the center of symmetry is 6300out of phase. This is a distance of 7X/4 compared toX/4 for the 15-cps parasite.The electric fieldis, therefore,

E, = A oHo(2) (kr) [1 + 9c, exp (7wr/2)Jo(kdg) ]+ AoHo(2)(kr)[t8c, exp (77rw2)Jgkdg)] cos 9q5. (6)

Collecting the results of the detailed algebra cul-minating in (6) and (5), the complete expression for theelectric field in the radial transmission line, generatedby a modulation ring similar in principle to that in theexisting TACAN antenna, is the following:

Ez = AoHo (2) (kr) [1 + cl exp (jwr2)Jo(kdl)+ 9c, exp (77r/w2)Jo(kdg)]+ *4 OH,(2) (kr) [2c, exp (jwr 2)J1(kdl) ] cos f

+ AoH19(2)(kr) [1t8c exp (j17rw2)J,(kdg)] cos 90.

Once the values of d1 and dg have been optimized withregard to the amplitude-phase response of the parasiticelements between the parallel plates at a steady powerinput level to the central radiator and at a stablecarrier frequency, the complex coefficients in the aboveexpression are constant. Therefore, the above fieldequation can be condensed to

EI = A Ho (2) (kr) (carrier level)

+ BH,12 (kr) cos f (15-cps modulation)+ CH9(1)(kr) cos 9k (135-cps modultion). (8)

It is to be noted that, although the dependence on r

appears in the form of the Hankel function, the valuesof the constants B and C depend upon optimizing theBessel functions Jl(kd) and J,(kd) as in the existingTACAN antenna. Thus, the distances of parasiticelements awav from the center in the radial transmis-sion line must be similar to those used in the originaldesign of the TACAN antenna." 2

B. Central Radiator

A simple method of feeding the radial transnmissionline froml the input coaxial cable over a broad band offrequencies is to use a biconical dipole, whose totalheight equals the separation between the walls of theradial transmission line. No rigorous analbsis has beenattempted to date of the impedance at the coaxial lineinput terminal of the truncated biconical dipole shownin Fig. 1, either alone in the radial transmission line or

in the presence of the parasitic elements. It is a bound-ary value problem with several regions that require

boundarv matching. The treatment of the region fromthe feed line to the near edge of the bicone is a parallel-

PMOUCCY ( MYCUES*

Fig. 5-Relative response of parasitic elemiients.

plate problem similar to that analyzed by Lewin." Anyestimates certainly should be checked experimentally.

C. Parasitic ElementsThe nominal positions of the 15-cps and 135-cps

parasitic elements have been derived in Section 111-A.One of the design objectives is to realize virtually uni-form amplitude response from the parasitic elements inorder to provide uniform modulation of the azimuthpattern over the 960- to 1215-I\4c frequency band.

Since the excitation of the 135-cps modulation is themore difficult case, the discussion of broadband ampli-tude response will concentrate on this case. By studyinga plot of J9(kd), it has been found that, if the peak ofthe 135-cps modulation is adjusted near 1112 I\IIc, arelatively uniform modulation amplitude exists overthe frequency band 960 to 1215 MAIc. As observed inFig. 5, at the transmitting frequencies of 960 MN1c and1215 M\Ic, the relative amplitude responses are respec-tively 0.88 and 0.75; at the receiving frequencies of1025 M\Ic and 1150 M1c, the relative amplitudes are both0.97.A direct approach to the design of the modulation

ring is to follow the original TACAN idea of elenmentsimpregnated in fiberglas rings. The response of theseelements depends upon their resistivity, height andlocation wTithin the radial transmission line.

D. Szpport PostsIt is necessary that support posts be located at a dis-

tance where the amplitude of modes excited by thesediscontinuities is at a miiinimum. For 45 posts, a 45thorder Bessel function characterizes the principal modeexcited by these discontinuities. A plot of Bessel func-tion response vs distance from the central radiatorshows that, for minimum amplitude, a distance of kd

36.5 is suitable, where k = 2r /X. (See Fig. 6.) The de-

'L. LeNwin, "A contribLntion to the theory of cylindrical antennas-radiation betwxeen parallel plates," IRE TRANS. ON ANTENNASAND PROPAGATION, x-ol. AP-7, pp. 162-168; April, 1959.

Giddis and Barrar: A Ground Beacon Antenna

- - - -- - - -

:0. 4 --

5 0 5 20 25 0 40 45 50

hd

Fig. 6 Plot of k(kdd) for n=15, 30, 45.

TVaz'eguide Parallel Plates

b6Xg

dglXgbXA

dA

S =

As shown in Fig. 7, d is the width of the rectangularcorner and s is its thickness.Arguments similar to those applied to the equiv-

alence between waveguide and parallel-plate regionsare pertinent to the radial pillbox region illustrated inFig. 8. Briefly, since no Hz component of the field existsin the radial transmission line, the field between thecircular plates can be generated mathematically by asolution Ml of the scalar wave equation.

V2M + k2M = 0 (10)

sign must accommodate the highest frequency of trans-mission in order to minimize the higher order modes. Asthe frequency decreases to 960 Mc, the J45 amplitudedecreases for the given fixed distance and broadbandoperation is assured.

IV. FEED

Under proper design, the electric field generatedwithin the radial transmission line consists of the threeprincipal modes in (8). In this next section, it will beshown that the fields in a radial pillbox bend and thosein corresponding rectangular waveguide are equivalent.Moreover, for a large radius of radial transmission line,the pillbox operates upon the three modes identically.

A4. Radial PilltboxTaggart and Fine6 have shown that electromagnetic

fields in a parallel-plate region are equivalent to thosein a rectangular waveguide region, if one equates thewaveguide wavelength X, with the free-space wave-length X in the parallel-plate region as follows, assum-ing normal incidence of the wave at the bend:

Xg -2

(9)

- (2b

where b is the plate separation.Taggart andl Fine point out also that experiments

performed on reflection coefficients in waveguide pill-boxes of rectangular cross section apply directly toparallel-plate regions of rectangular cross section, if onescales from waveguide to parallel plates as indicatedbelow.

M. A. Taggart and E. C. Fine, "Parallel Plate Bends," M.I.T.Rad. Lab., Report 760; September 5, 1945.

with

H = curl Miz

E = (1/-jwoE) curl H.

(11)(12)

Assuming that M1 displays cos mn azimuth angle de-pendence, the above scalar wave equation in cy,lindricalcoordinates for infinite parallel plates becomes

a2M

Ar2

1 am a2M m2-

r Ar A2 L]r20. (13)

In the pillbox region, the distance froml the axis ofsymmetry r is large and 11 is essentially a solution ofthe modified wave equation

A92M ,A2M+

Ar2 3z9+ k2M = 0. (14)

Physically, it means that the fields with no 4 depend-ence (m =0) and those with cos 4) (m= 1) and cos 9)(m = 9) dependence, corresponding to the azimuthmodulation, behave the same in the radial pillbox.For a large radius r of the radial transmission line, thefield characterized by the three principal modesHo(2)(kr), H1(2)(kr) cos 4) and Hg(2)(kr) cos 94 behaveessentially like the fields in an infinite parallel-plateregion.

Therefore, the experimental results for waveguidepillbox design can be applied directly to radial pillboxdesign and give rise to the same reflection coefficientfor the three principal radial transmission-line modesreferred to above. Referring to the experimental curvesof Taggart and Fine, shown in Fig. 9, one notes thatthe ratios of dlb=2.1O and slb=0.119 yield broadbandbehavior of the pillbox over the 26 per cent TACANfrequency band under consideration.

Rather than a rectangular bend in the pillbox, onemight consider fabricating a curved bend.

c

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320 IEEE TRANSACTIONS ON AEROSPACE AND NAVIGATIONAL ELECTRONICS December

b

I~~~~~~~~~~~~b s

Fig. 7 Pillbox cross-section.

Fig. 8 Radial pilIbox.

dD22. -l-

1.0~~~~~~~~~~~~~~~~~~1

0*6.0 -15 40 5.0 60 .0

Fig. 9-Dimensions of bends for which (SWR)2 <1.5 (after Taggartand Fine).

B. Radial Horn

Terminating the radial pillbox is an off-set, E-planeradial horn which can be designed for minimum mis-match7 with an optimum flare length. Under theseconditions, the electric field distribution at the feedhornaperture plane is given by

Ehorni = 4Ho(2)(kr') + BH (2)(kr') cos )

+ CH9(2)(kr') cos 94),

equation can be rewritten in terms of the mode con-stant m as follows:

Eorn - E DmHm (2)(kr') cosm+.m

(16)

V. REFLECTOR

The radial horn illuminates a radially symmetricreflector whose surface contour is shaped to generate acosecant-squared elevation pattern. This pattern isspecified below along with a computation of antennagain and a discussion of the reflector surface.

A. Pattern

The cosecant-squared distribution provides uniformheight coverage to a maximum angle of 600 from aminimum angle of 50 above the horizon. Below this, thefar-field pattern is approximated by a pencil beamwhich intercepts the horizon at the half-power point.Fig. 10 shows a plot of the ideal elevation pattern ana-lytically defined as follows:

exp [-(p0- 2)]' 0 < 0 <0.

P(0) =K csc2 0, 00 < 0 < 02, (17)

where

p = beam-shaping constant = 211

6o= maximum pencil-beam angle = 50

0i = minimum pencil-beam angle =0°

02= maximum shaped-beam coverage = 600K = curve matching constant = 38 X 0-14.

The pattern in azimuth is omnidirectional.

B. Antenna Gain

The maximum gain above that of a lossless isotropicradiator is given conventionally by the relation

GCI =(15)

where the complex coefficients A, B and C are definedas before in terms of relative amplitude and phaseconstants, but also include attenuation in the line andfeed; r' is the mean distance from the axis of symmetryin the radial transmission line through the pillboxrectangular bend to the mouth of the feed horn. The

IS. Silver, "1\1icrowax7e A\Xntenna Theory and Design," M.I.T.Rad. L-ab. Series, x7ol. 12, McGraxw-Hill Book Company, Iinc., NewYork, N. Y., pp. 371-374; 1949.

47rf217r /3

oP(O, 0) COS OdOdo

(18)

Assuming for practical design that the diffraction pat-tern is separable in 0 and 4 and recalling that the pat-tern in ¢ is omnidirectional, the gain expression reducesto

2

T P)co6dP(O) cos OdO(19)

Giddis and Barrar: A Ground Beacon Antenna 321

Iz

ixw

Lc>

14- -

-16~~~~~~~~~~~~~2

-20

0 50 30 40 5 -

ELEVATION ANGLE ABOVE HORIZON IDES)

Fig. 10 Ideal elevatioin power patterni.

Substituting (17) into (19) and specifying the appropri-ate limits of integration yields

For an illumination efficiency of 80 per cent, the gainratio reduces to 8.4 db. At 50 per cent, the gain is 6.4 db.A theoretical limit on the gain can be computed by

assuming a hypothetical elevation power pattern com-posed of the cosecant-squared function for anglesbetween 50 and 600 and a constant power level between50 and the horizon. The gain for an illumination ef-ficiency of 80 per cent is 9.8 db, a difference of 1.4 db.

C. Ref ector SurfaceThe design of the reflector contour to produce a

shaped elevation beam is determined by a methodbased upon conservation of energy and geometricaloptics,8 which defines a radius vector from the feedhornto the reflector surface in terms of given constants forthe elevation pattern coverage, for the position of thepillbox-horn feed relative to the reflector surface and forthe horn illumination function.

Based on the half-power, pencil beamwidth of 50, the

~~~~~~~~1(20)r0. O87 0a 2 f/3I e-P -_ cos do + Kcsc2 0 cos0d0

0 2cos0d2 0.087

For the purpose of integration, the pencil-beam func-tion can be approximated by a series expansion. Re-taining only the first two terms, the first integral be-comes

p/0.0 87 2

J 1-~~p( - cos OdO

-sin0 -1+ 2p -p02+ Ip4/

/ Oo\~~0 0.087- 2p 0cos 0 + 02 = 0. 9. (21)

Similarly, the second integral is

I 7r/3 1r/3

K csc2 0 cos OdO = K csc 0 = 0.04. (22)0.087 0.087

The absolute gain is, therefore,

2G1I = = 8.7 or 9.4 db.

(0.19 + 0.04)

height of the reflector must be commensurate with thisbeamwidth, i.e., 14 wavelengths. A radome will provideweather protection. In the event that no radome is usedor it is damaged, a dielectric cover or "feedome" overthe mouth of the feed horn is required. Moreover, drainholes for water must be provided. The simplest methodis to drain water through the hollow support postswhich have been located to minimize moding and im-pedance mismatch.

D. A perture DistributionWithin the bounds of geometrical optics, the radiat-

ing aperture distribution in elevation can be expressedin terms of the total feed-horn aperture distribution byintroducing a function I(z) which transforms the hornillumination to the radiating aperture plane. Thus, thetotal aperture field is expressed as

G(z) = I(z)Eioral (Z),= I(z) E DmHni(2)(kr') cos (24

m

where, as in (15) and (16), r' is the mean distance fromthe central radiator in the radial transmission linethrough the pillbox bend to the mouth of the feed horn.The field for any mode m is given by

G,, (z) = I (z) DmHm(2) (kr') cos m+. (25)( A. S. DUnbar, "Calculation of doubly curved reflectors forshaped beatims," PROC. IRE, vol. 36, pp. 1289-1296; October, 1948.

1 963

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322 IEEE TRANSACTIONS ON AEROSPACE AND NAVIGATIONAL ELECTRONICS December

VI. FAR-FIELD M\4ODULATION

In a paper by Silver and Saunders,9 an expression isdeveloped for the far field of a slot of arbitrary shapethat radiates energy periodic in 4 for an infinite cylinderof infinite conductivity. The geometry for the proposedTACAN antenna is illustrated in Fig. 11, where a is theradius to the aperture plane, z1 and Z2 are the limits ofreflector height and R is the distance from the center ofphase at the origin of the spherical coordinate systemto a point in the far field. The model is applicable tothe antenna under discussion for the range of elevationangles considered. In terms of the aperture distributionderived above and the antenna geometry illustrated inthe sketch of Fig. 12, the electric field component ofthe far field in elevation, for all modes m radiated intofree space, is expressed as

co Hj2(ka cos 6)

{ ekR z2.J _ _ 2Gm,(z) exp (jkz sin O) dz,

Fg 12 tc - c rd

Fig. 11 Sketch of far-field geometry itl spherical coordinates.

RADIAL TRANSIAISSIONLINE MODE'

E1z.AHoIA-AM 138-C* BH;" (kI)tSD(q \ PARAS+ CH; (kI)co$ (9 ) : Il

(26)

where the first term in the series incorporates the geome-try of a circumferential slot in a cylinder radiatingenergy modulated in azimuth by a periodic functioncos mo, and the bracketed term is the two-dimensionalfar-field expression.

Evaluating the series for m =0, 1 and 9 and notingthat the horn illumination is uniform with z across theheight of the horn mouth,

(Ho (2) (kr')E== -jA Ho )(kc ) (carrier)

Ho (2) (ka cos 0)

H1(2) (kr')+ B cos - (15 cps)g1()(acos 6)

H9(2) (kr') (H9(2)(ka cos 6))

F' (0)X

cos 0(27)

REFLECTOR APERTURE

RAAIATNGAPERTUREETRY Db DSTR113UTION

_z_ g£>~~~~Ebai. E (zXr 2

I/I O04ON APERTURE

I| RADIAL FEEDHORN

AE y ~~~~~RADIAL PILLBC

b, I \ P

CPS 15-CPS'SITE7 PARASITE,

IK1

Fig. 12-Sketch of antennia cross section in cylindrical coordinates.

amplitude of the modulating function to the amplitudeof the unmodulated carrier. Therefore, if we denote themodulation index by M, the indices for the 15-cps and135-cps modulating functions cos q5 and cos 94 are, re-spectively, the ratios of the coefficients of the secondand third terms to the first term of the bracketed ex-pression in (27). Recognizing that the amplitude co-efficients and the Hankel functions are complex quan-tities, the modulation indices are expressed as follows:

B Ho (2) (ka cos 0) H,(2) (kr')A Hi 1(ka cos 0) Ho)(kr') '

CC Ho(2)(ka cos 0) H9(2)(kr')

A HO (2) (ka cos 0) Ho(2) (kr')

(29)

(30)

where

e-ikR r z2F'(0) = I I(z) exp (jkz sin 6)dz.

irR I

With these relations in mind, the following table"has been prepared.

(28)

A. Modulation Index

By conventional definition of amplitude modulation,0the modulation index is the ratio of the maximum

9 S. Silver and WX. K. Saunders, "The external field produced bya slot in an infinite circular cylinder," J. Appl. Phys., \vol. 21, pp.153-158; February, 1950.

10 H. S. Black, "Modulation Theory," D. vain Nostranid Com-pany, Inc., Priniceton, N.J., pp. 19-22; 1953.

IJHo(2) (x)x HI (2) (x)

10 0.99612 0.99814 0.999

16 0.99918 1.00020 1.000

11 "Bessel Functions," British Association Mathematical Tables,pt. II, vol. 10, Cambridge University Press, Cambridge, England;1952.

IHJo(2) (x)Ho1(2) (x)1.0041.0021.0011.0011.0001 .000

HoJ(2) (X)

I19(2) (X)0.7120.8190.8800.9100.9300.950

H9(2) (x)IHo(2) (x)

1.4041.2211 .s371.099

1.0751 .053

11, .11v 1,

OF

SYMMbE

IX\-RADIA). WAVEGUOE

Giddis and Barrar: A Ground Beacon Antenna

Two cases are of interest: the arguments x = ka cos 0and x = kr', where k= 2r/X. Since the elevation angle 0is defined up to 600, the nminimum value of cos 0 is 0.5.In order to keep x = ka cos 0 large (such as x = 18 in thetable), the horizontal distance a from the axis of sym-metry to the reflector aperture plane must be 6X at thelowest carrier frequency. Similarly, in order to nmain-tain x=kr' large, the nmean distance within the radialwaveguide from the axis of symmetry to the hornmouth must be 3X. Since r' is by geometry greater thana, it is assured that the requirement on r' above isautomaticallv satisfied, if a is large. Under these con-ditions of large arguments and, therefore, large radii,the products of the ratios of the Hankel functions areunity. Hence, the modulation indices reduce to functionsof the complex response of the parasitic elements, i.e.,

B- , (31)

C

Mo~9 - . (32)

VII. DIscussION

For practical purposes, therefore, the modulation in-dex in the far field can be controlled by adjusting thevalue of B and C, the amplitude-phase response of therotating parasitic elements in the radial transmission-line waveguide, without altering the geometry of thehorn-reflector combination which controls the shapeof the elevation power pattern.

Consequently, the per cent modulation is independent-of elevation angle from 00 to 600. Rather, it depends

upon the amplitude-phase response of the parasitic ele-ments which can be adjusted experimentally over arange of values. Once the parasitic elements have beentailored to provide a given per cent modulation alongthe horizon, the modulation will remain uniform withelevation over the 960- to 1215-MTc bandwidth of opera-tion.The basic conditions under which these conclusions

are valid are 1) radial symmetry, 2) impedance match-ing throughout the radiating system and 3) a reflectoraperture plane whose radius is about 6 wavelengths.

A. Problems

The degree of pattern circularity in the azimuthplane at the carrier frequency has not yet been inves-tigated fully. Preliminary analysis indicates that il-luminating the radial reflector with a concentric radialline source does not generate new spatial harmonics,but does introduce a phase distortion that depends onelevation angle. Its magnitude and the amount of dif-fraction around the reflector have not been computed.The impedance match at the input to the antenna is

expected to provide a VSWR<2.0 at the transmittingfrequencies of 960 T\lc and 1215 Mc. However, no com-putation has been made of the impedance of a radialtransmission line fed by a coax-driven bicone with orwithout loading by parasitic elements and dielectricsupports.

ACKNOWLEDGMENT

The authors wish to thank Dr. Eugene Willoughbyof the University of Adelaide, Australia, for his criticalcomments and G. W. Dexter for having suggested theproblem.

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