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
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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
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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.
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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-
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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
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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
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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.