small conformal array

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64 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.AP-22, NO. 1, JANUARY 1974

Design of a Small Conformal A r r a y

GARY A. THIELE AND CHENG D O N N

Abstract-Theprincipal objective of this investigation was to

determine how to efficiently excite a small conical body over a 2: 1frequency bandwidth such that a prescribedminimum value of gain

is exceeded in a60' conical sector about the forward axis of the cone.

T o achieve the necessary bandwidth, two approaches have been

considered. First, an electrically small moderately efficient tunable

antenna can be employed to excite currentson the cone. Second,one

can employ a wide-band antenna having at least a 2: 1 bandwidth.

Tbis latter approach was investigated theoretically and found to be

feasible but experimental confirmation was not attempted in defer-

ence to the firstapproachthat has the potential of greater gain

(efficiency). To demonstrate the validity of the first approach a four

element conical array was constructed and is describedin this paper.

Experimental results agreed well with theoretical expectations.

AI. INTRODUCTION

SMALL conical body is a difficult geonlet,ry to excite

so that it radiates effectively on or near the forward

axis of the cone. Let us consider a cone havinga O . l h

dia.meter base anda 0.5h long generat.or (slant height)

at. t.he lowend of a 2: 1band, gain greater than10dB below

isotropic in a conical sector 60" about the forward axis

and a capability for receiving any polarization. T hus we

must consider a conical body whose generatorvaries

from about 0.5h to 1.Oh and whose base diameter varies

from about 0 . l h to 0.2h.

T o achieve the necessary bandwidth, two approachesmay be pursued.First, anelectrically small and moderately

efficient ant,enna may be employed to excite currents on

the cone such that , some direct,ivity in th e forward direc-

tion is obtained. Such an antenna will naturally have a

narrow instantaneous bandwidth, but may be tuned over

the required 2: 1 band.One pot,cnt.ial antennaforthis

purpose is themult iturn loop antenna (MTL) which

will be discussed in Section 1V. Potential array configura-

tions mill be evaluated in Section 111. The term array is

not meant to imply t.he conventional type of array (e.g.,

h / 2 element spacing) but rather a special type of array

designed to obtain a novel performance.A second approach is to use an antennahaving at least

a 2 : l bandwidth. Since the cone is not. very large elec-

trically,frequencyindependent antennas such as the

conical spiral cannot easily be used. Thus onc must

resort to appropriate loading to achieve the required

bandwidth. An antenna configuration that shows promise

based on theoretical analysis is an ar ra y of six half-loops

on the cone generator, each terminated in a complex load

chosen to give anarrayinput impedancesuch that a

VSWR of less than 3: 1 is maintained over the 2: 1 band.

This array mill be briefly discussed in Section 111;details

of this array may be found in[l].

To investigateandevaluatethemerits of the many

various conformal array configurations employing either

of the abovetwoapproaches,one would nornlally be

forced to resort to an extensiveseries of experimental

models and measurements since an analytical evaluation

of such a problem is virtually impossible. In the following

sections, we will obtain, via modern numerical methods,

two sound engineering designs to a difficult problem. These

results should be of interesttoothers concerned with

radiationcharacteristics of conical bodies. In addit-ion,

t,he procedureused to arriveat these designs is sufficiently

general to beof interest to engineers concerned with other

small array problems.

11. MODELINGS m m ~CONFORMALARRAY

To facilitate the computer study for the evaluation of

thesetwo a.pproaches onecanemploy the concept of

wire-grid modeling [2>[6] to model t.he cone and it,sradiat,ing elementsfor computer analysis. Such a procedure

is ideally suited for bodies that are not electrically large,

such as the cone of interesthere, since onecan obtain

accurate patterns, directivity and/or gain and impedance

data tha t takes int o account all mutual coupling effects

including coupling to the metallic body itself.

To properly model a small confornlal array it is neces-

sary to nlodel the surface of the body, which in this case

is conical, as well as the radiating elements. A representa-

tive model is shorn in Fig. 1.

The currents on each of the wires in the model ar e

represented by an appropriat e basisfunction.Here, wewill use the piecewise-sinusoidal function although other

functions could be used to obtain the s m e end result at

the possible expense of increased computer running time

and/or storage requirements. We can write forthe current

density J"

with I , = I (Zn)and d, the length of segment n.P,(I) is a



THIELE AKD DOKN : S U L L CONFORMAL ARRAY 65

Fig. 1. Wire-grid computer model.

unit pulse, nonzero only on segmentn;g,, is a unit vector

pointing dong 1 from one endpoint of segment n to the

other. Thc basis currents vanish at t,he endpoints of t he

dipoles. Further details may be found in [3], [4].

In setting up such a model as that of Fig. 1, onc can

generally use the guideline that th e maximum separation

between opposite sides of t he wire mesh should notexceed

0.2X. Such a guideline is not rigid, however. A complc-

mentary guideline is that a sufficient number of wires

be used such that the true surface current is adequately

sampled and the geometry adequately described by themodel. Using such guidelines, one can usually arrive at a

valid model without appreciable difficulty. Howcver, this

is not always thecase as we will see in Section V.

Clearly, such a modeling procedure is limited by com-

puter storage capability to bodies that are not large in

terms of the wavelength such as the cone of interest in

this paper. Thus while the technique is a very powerful

one, its practical usefulness is limited to small confornlal

arrays.

111. INVESTIGATIONOF VARIOUS ARRAY CONFIGURATIONS

A . T u d k Antenna ElementUsing the MTL as a tunable excitor of the metallic

surfaceconical body, several array codguratiom were

investigated. These arc shown in Fig. 2 where, in the com-

puter model, the MTLs arc adequately represented [l ]

by simple half-loops as indicated in Fig. 1.

To avoid deep nulls on or near the forward axis, i t is

necessary to phase the MTLs such that there is a phase

progression of 2~ radians around the cone. E'or example,

for the array in Fig. 2(b), each of the MTLs is phased

120"ahead of or behind the adjacentNTL. In a feasibility

F0.5X- l.OX

F0.5X- I .Oh

1 [ 8 - 180°. + =+, )

N O S EDIRECTION

Fig. 2. (a) Multiturn loop array on composite cone. (b ) Array ofthree multiturn loops on cune generator. (c ) Array of six mult.i-turn loops on cone generator.

model it is moredcsirablc to employ four MTLs with

90" phase progression due to the commcrcial availability

of 90" and 180"hybrids. However, it shou!d be noted t hat

120"hybrids can be designed and manufactured.

Typical pattern rcsults computcd at the low and high

ends of the 2: 1 band are shown in Fig. 3 for t.wo of the

array configurations in Fig. 2. Thc configuration in iGg.

2( a) produced asymmetries in the patterns that deemed



66 IEEE TRANSACTIONS O N AXTENNAS AND PROPAGATION, JANUARY 1974

180.

(d )

Fig. 3. (a) Normalized patterns at low end of band for m a y of Fig. 2 (b). (b) Normalized patterns at highend of band for array of Fig. 2 (b). (c ) Normalized patterns at low end of band for array of Fig. 2 ( c ) . (d ) Nor-malized patterns at high end of band for array of Fig. 2 (e) .

this array configuration not well-stiited for ou r purposes.

The patterns in Fig. 3, however, are well-suited. I n fact.,

the pattern at thelow end of the band in Fig.3 (e ) exhibits

desired directivity in t,he forn-a.rd axial direction. Th us it

would appe ar tha t the arra y of Fig. 2 (c > would be the

best configuration t o employ inafeasibility nlodel if

radiationpatterns were t.he sole criterion. However, it

was judged tha t the arra yof Fig. 2 (b) would be preferable

primarilydue to the space 1imit.ations on t.he cone. In

addition the tuning and feeding problenls for t,he array

of Fig. 2 (b) would be nluch simpler than for the array of

Fig. 2(c).

Fig. 4 shows the theoretical gains in the forward axial

direction referenced to isotropic for the three array con-

figurations. It is appaxent that, the arrayof Fig. 2 (b ) will

require MTL elements that are more efficient than would

be required for t.he more complex array of Fig. 2(c). In

t.he trade off of simplicity versus efficiency it was deter-

mined that a tunable MTL element was needed for the

array of Fig. 3(b) where efficiency was a t least 10 percent.



THIELE A S D DOK N : SNALL CO NF OR UL ARRAY 67

"1CONE

3 - M T L ' S O N T H E BA SE

TRUNCATED COMPOSITE loSURFACES OF THE

I I5%

3-MTL 'S ON THECONESURFACE-a - 100%--

5%

a - E F F I C I E N C Y . i ie- 10

6 - Y T L ' S O N T H ECONE SURFACE

a - loox-40%7-5%

-20h-++ - m uf -20uFREQUENCY

2f

Fig. 4. Gains for multiturn loop arrays in Fig. 3.

at. thelow end of t.he 2 :1band. Since t.he realizat,ion of such

an element is not easy, let us next briefly exanline the

alternative possibility of using abroad-band antenna

element.

B. Broad-Band Antenna Element

A second approach to obtainingexcitation of small

conical bodies is to employ antenna elements having a t

least a 2: 1 bandwidth. Since frequency independent ele-

ments cannot.readilybeemployed, an alternat .ive is touse an element loaded sufficient.ly to achieve the required

bandn7idt.h. One possible elementisa half-loop with a

conlplex 1oa.d impedance a t the end opposite the input.

In comparing the array using a tunable element- and

that, using a broad-band element such as the loaded half-

loop i t mas decided th at a feasibi1it.y model of the former

would be preferableover tha.t of the lat ter forseveral

reasons [l]. First., it. appeared t.hat more gain could be

obtained using the t.unable element and, second, t,ha t the

tunable element could be more easily flush mounted.

Sext.,letus examine the characteristics of the tunable

RITL element.

11.'. C H A R A C T E R I S T I C SO F EFFICIENTh,IULTITURN

LOOPELEMENT

The efficiency of the MTL chosen for the arr ay was

measured by t,he Wheeler cap method [7]. The method is

based on the relationship

9 =

R r a d

R r d i-R I O ~( 2 )

where

q = efficiency

&ad = radiat.ion resist,ance

RI,,, =loss resistance.

Since the real portion ( R r a d + Rloss)of the antenna input

inlpedanceradiatinginfreespace is easily det,ermined,

the problem then is t,o find either R r a d or I z l o s s . Wheeler

suggests that a conduct.ing sphere equal to or greater tha.n

about one-sixth wavelength in radius(i.e., a radian sphere)

will eliminate R r a d without significantly changing Rloss .

Clearly this assumes no significant change in t.he antenna

current diatribut,ion t,akes place. The measurement of the

input impedance when theantennais erlclosed by t.he

0 I I I I I I I I0.93f 1.33f l.6f 2f

FREQUENCY

Fig. 5 . Efficiency of MTL in Fig. 7 .

-8I

I

I-9 I

I 331

FRE OUE NCY

1.671 2 f

Fig. 6. Measured gain of MTL in Fig. 7.

conducting radian sphere mill then be Elo s s .Such measure

ments are easily accomplished withanetworkanalyzer

such as the HP8.2104 and a test set up similar to t.ha

in [SI.

The efficiency of th e MT L elementmeasuredby th

cap method is shown in Fig. 5. At t.he low end of t.he 2:1

band of interest, i t is evident from the curve that the

efficiency is above t.he 10 percent goal, being 13.5 percen

a t f and not. falling to 10 percent until the frequency ha

decreased t,o about 0.9 f. To verify the general validity of

the efficiency measurement, gain measurements were con

ducted a t t,he indoor antenna t.est facilit,y of the USAF

Avionics Laborat,ory, Wright.-Patterson AFB, Ohio. The

results of t,hese nleasurernents a re shown in Fig. 6. Th e

gain measurements were made with the MTL in a 20' X

20' ground plane. Since the gainmeasurements mere

conducted with th e MTLin a ground plane approximatel

ten t.inles larger than tjhat, used for the cap met.hod, it i

not too surprising to find the gain measurements indicat-



68 IEEE TRANSACTIONS ON A N ~ N N A S AND PROPA GA~ON, JANUARY 1974

Fig. 7. 4 element conical array.

ing that theefficiency increases with frequency at a fast,er

rate than the capmethodmeasurenlent,sindicate. It is

quite int.erest.ingto note thecorrelation between the shapeof the efficiency curve (Fig. 5) in the 1.7f to 1.8f region

with the corresponding portion of t,he gain curve (Fig. 6).

It is conceivablc that some of the other pert.urbations in

the efficiency curve would be discernible in the gain curve,

had finer incren~ents infrequency been used to construct it.

Considerablecontroversy exist.s concerning how large

an efficiency canbeobt,ained with an electrically sn~all

antenna.. The JITL used to obt.ain the preceding d at a was

a two turn model like that in Fig. 7 wherein each element

could be enclosed in a sphere whose diameter varies from

only about, 0.OGX to 0.12X. Certainly the antenna is elec-

trically small. The efficiency data for this ant.enna show

that , indeed, moderately high (e.g., GO percent,) efficiencies

canbeobtainedwith an elect,rica.lly small radiating

element,.

V. MEASURENENTS OF FOUR-ELEXENTCONFORMALARRAY

A . Pat tern Measurements

Fig. 7 shows a photograph of t,he cone with four NTLs

mount.ed around t.hc cone such th at th e cent,er of each of

the A.ITI,s isabout 0.1X from the base of, the cone a t

frequency f.

To obt,a.in t.he 2~ radian phase progression, a hybrid

feed arrangenlent, consisting of 90" and 180" hybrids was

employed. Th e insertion loss of this system was typically

0.4 dB. Neasured a.nd calculated far-field patterns for t,he

four element array areshown in Figs.8 (a ) and (b). These

pat.tcrns were measured outdoors with the cone mounted

on a 6' high styrofoarn support, which in turn placed the

cone approximately 12' above the ground. A small trans-

mitter was placed inside the cone to avoid t,he effects of

cables being attached externally. The calculations were

madewith th e wire-grid cone model of Fig. 1 and the

result,s agree very well withthe nleasurements ans evi-

denced by t.he patte rns in Figs. 8(a) an d (b).

One unexpected difficulty in modelling the MTL arrayon the cone was encount.ered in tha t t.he null in t,he E ,

pattern in Fig. 8(b) was not predicted if simple half-loops

nlount.ed on the surface andprotruding above it were

used to model t.he MTL. It was found that half-loops re-

cessed as indicated in Fig. 1 corresponding to thesituat,ion

Qictured in Fig. 7 were necessary to predict the null near

broadside.

B . Cain Meamrenzents

Gainlueasurements a,t the VHF-UHF frequencies of

concern here are not easily made. I n an effort, to avoid

Fig. 8. (a) Far-field pattern at frequency f. (b) Far-field patternat frequency 2f.

erliance upon nleasurenlents nude in the presence of the

earth, it was decided that gain measurements would also

be made with the cone mounted on the 20' X 20' ground

plane of th e indoor pattern range at Wright-Patterson

A4FB.By conlputing the appropriate conversion factor,

the gain nleasurement with the cone on the ground plane



THIELE AK D DONN: SN14LL COSFORMAL A R U F 69

TABLE I

Frequency Y (dB)

1.00f -0.25

1.07.f -0.40

1.17 f -1.45

1.33 f -2.20

1=

XOUTDhOR MEASUREMENTI

-CONE ONGROUND PLAN E MEAS.+

- 10 If 1 .33 f 1.67f 2f

FREQUENCY

Fig. 9. Free-space gain on forward axis of cone.

would then be convert.ed toits free-space equivalent.

This is accomplished as follows.

Utilizing the wire-grid model of Fig. 1 extended to

include the image of the cone in an infinit.? ground plane

one can comput,e, for example, t.he magnitude of the f a r -

zone elect>ricfield on t,hefonmrd axis of the coneEimage

By comparing it to thesame quant.ity computed utilizing

the free-spa.ce cone model shown in Fig. 1 wit.h t,he same

input, powcr, one cancompute Efree-spaceand hence, the

conversion factor y, where

?l/2 =Efree-Epae a s e

(31

The success of such a procedure obviously depends upon

reasonably good agreement,between the measured pat -

terns with the cone on t,he 20’ X 20’ ground plane and

those ca.lculated with the cone on an infiniteground

plane. Good agreement was obtained from f t.0 1.4 f bu t

not from 1.6f to 2 f since t.he overall elect.rica1 sizeof the

model is exceeding t.he high frequency limit whereaccurate

resultscanbeexpected. Consequent.ly onlythose con-

version factors fromf to 1.4 f are listed in Table I.

The corresponding values for the gain measured with

the cone on the ground plane and then correct.ed to the

free-space equivalent are showninFig. 9. Reasonably

good agreement, with the ot,hcr t.mo methods of determin-

ing the gain in Fig. 9 is in evidence.

Also shown in Fig. 9 is a curve obtained by ta.king the

calculated directivity, using t,he conlputer model of Fig.

Eimase case ’

- LOOPA MEAS LOOP B DETUNED LOOPSE . C S D kE R Ml NA TE D I N T 0 ’ 5 0 n

--- LOOP A MEAS.: LOOP C DETUNED;LOOP

-* - INPUTTOHYBRIDFEEDSYSTEMYEAS.;B , C B D TERMINATED INTO 50 a

LOOP A DETUNED

MT LINPUTIMPEDAN CE ON CONE. ALL 4

LOOPS INIT IALLY TUNED TO FREQUENCY I

Fig. 10. Mutual coupling effects at frequency f.

1, and nlultiplying t.his direct,ivity by t,he efficiency da ta

given in Fig. 6. Such a procedure implies tha t the in-

dividual elements have the same efficiency in their cone

mounted configuration (Fig. 7 ) as in the groundplane

codgurat.ion. It would appear from the various da ta in

Fig. 9 tha t thi s is true.

The third setof d ata in Fig. 9 was derived from outdoo

measurements wherein a half-wave dipole was used as a

reference. Due t.o the presence of the ground thesemeasure-

ments are probably t.he least. reliable of the three sets o

data.Atthe lower three frequencies theyindicate a

reasonable gain consist.ent,lyless than tha t derived by the

ot,her two methods.At 2 f data is not shown since the out

door nxasurement indicated a gain which was unreason-

ably high.

In all cases t.he gain was determined afte r proper al-

lowance for the insertion loss of the hybrid fecd system.

Th e gain in dB was determined from t.he directive gain

relationship

G d = 10 log,, g d ( 8 , 4 ) (4

where

O r, in other words, the directive gain ga in a given direc

t.ion is the rat io of the radiation intensity 17 in that direc

tion to the average radiated power W B . In our case the

direction of interest has been the forward axis of the cone

where the polarization is circular, being either RCP or

LCP depending on the direction of t he 2a radian progres-

sive phasing.

C. Mutual Coupling Efeets

When four antennas are placed in close proximity such

as those in Fig. 7, mutual coupling can be expected to be

strong. In order to give some indication of the effects of

this coupling, the d at a in Fig. 10 were t.aken at. f which

is a worst case since coupling effects tendto diminish



70 IEEE TRANSACTIONS ON ANTENNASAND PROPAGATIOW, JANUARY 1974

somewhat a.s frequency is increa.sed. The first curve in

the figure represents the change in the input impedance

of loop A when loop B is detuned with loops B, C,and D

terminated into 50 Q loads. This effect is relatively small.

The second curve representsthe change ininput impedance

of loop A when the opposite loop (loop C ) is detuned.

Thiseffect is somewhatgreater than the previousone

since the coupling via the cone currents to the opposite

loop is apparently stronger than the field coupling to an

adjacent loop. Finally, the third curve in Fig. 10 shows

the variation in the input to the hybridfeed system when

one loop isdetuned. As with the other curves, the greatest

change occurs when a loop is slightly detuned since the

MTLs are high Q elements. Th e effect of a detuned ele-

ment on t,he radiation patternswas not investigated.

VI. STJ;~~MARYAN D CONCLUSIONS

T o briefly summarize thesigrdicantresults of this

invest.igation, several conclusions can be made. First, the

desired pattern coverageover a A60” foma.rd section

ca n be achieved by exciting a metallic surface cone withan

array of elements being fed in a phase progression of 2a

radians around thecone.

Second, an electrically small antenna element such as

the mult,iturn loop can be designed so that it is tunable

over a 2: 1 band and is efficient enough to produce the

necesmry value of ga.in in a forward sector f60” about

the cone axis. The MTLelenlent used to demonstra te these

characteristics was passively tuned with low loss trimmer

capacitors.

Third, the modeling technique discussed in Section 11,

can be used to predict the performance of a small confornlal

array on a body that . is not large in the electrical sense.

It was used in Section I11 to investigate various possible

array configurations and locationsfor the WTL elements.

Whilegaincould notbedetermineddirectly since th e

actual fi,€TL elements could not be modeled on th e cone,

directivity calculations permittedth e nlinimunl acceptable

eEciency of the elements tobedeterminedprior tothe

construction of an experimentalmodel. In th e case of

the broadband elementsgain could be determined directly

since theactualelements could be well representedin the

model and the loss taken to be that introduced by the

real par t of the load impedance.

restricted to structures not generally muchlarger than

the cone considered here, it is a useful procedure in engi-

neering investigat,ions of variousproblemssuch asthe

small conformal array in this paper.

While the techniqueusedintheseinvestigationsis

ACKNOWLEDGMENT

Theauthors mould like to acknowledge theantenna

group of the USAFAvionics Laboratory at Wright-Patter-

son AFB for their fine cooperation. T he contributions of

R. A. Sutherland to the MTL antenna development, and

also the discussions withProf. C. H. WalterandProf.

J. H. Richmond,are sincerely appreciated.

REFERENCES

G. A. Thiele, R. A. Sunderland, and C. Donn, “Electrically smallantennas for nose cone applications,” ElectroScience, Dep.Elec. Eng., Ohio St at e Univ., Columbus, Rep.3378-!, preparedunder Contract F04701-72-GO180 for Space and M1sslle SsyternsOrganization, Los Angeles, Calif., June 1973.J. H. Richmond, “A wire-grid model for scattering by conduct-ing bodies,” ZEEE Trans. Antennas Propa.gai., vol. AI?-14, pp.782-786, Sept. 1960.

magnetic scat.tering and radiation problems,” Ohio Stat e Univ.,hl. Travieso-Diaz, ‘‘Wiregrid reactionsolution of electro-

Columbus, ElectroScience Lab. Rep. 2622-3, preparedunderContract DAAG39-68-C-0061, May 1971.J. H. Richmond, “Computer analpsis of three-dimensional wireantennas,” Ohio StateUniv , Columbus, ElectroScience Lab.Rep. 2708-4, preparedunder Contract DABD03-69-C-0031,Dee. 22, 1969.J. H. Richmond and N. H. Geary, “Mutual impedance betweencoplanar-skew-dipoles,” ZEEE Trans. Anfennas Propagat.,

(Cornmun.), vol. AP-18, pp. 414-416, May 1950.G. A. Thiele, “Wire antennas,” Computer Techniques for Electro-magnetics, R. Mitt ra, Ed. London, England: Pergamon, 1973;,

Proc. IRE, pp. 1325-1331, Aug. 1959.H. A. Wheeler. “The radianspherearound a small antenna,

H. C. Mayhew and P. BoNev, “Efficiencv measurements ofVHF multiturn loop antennas,’‘ in 1972 G-AP Znt. S y n ~ p .D i g . ,

pp. 328-331.

small conformal array

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