Variations on the Fractal Sierpinski Antenna Flare Angle
C.PUEN1E'. M~NAVARRO.J.ROMEU. R POUS.
E1.ECTROMAGNFTICS & PHOTONICS ENGINEERING CROUP (EEF)
DEFT TSC. UNIVERSITATY O L I T ~ C N I C A
DE CATAWNYA.
clGran CapitA Jn. d u i D3 Campus Nord. 08034 Barcclonn.
puenicGhc.up'.es, Tel:34-3-4017210. Fax:34-34017232
Abstract.-:A further Investigation on the fractal multiband Sierpinski Antenna Is
Introduced here. it is shown that a variation on the antenna's flare angle Is
translated Into a shift of the operating bands, as well 8s into a change In the
impedance level and radiation patterns. The contribution of those variations to
the truncation eflecl is outlined.
1. Inlroducfion.- The fractal Sierpinski antenna based on an equilateral triangle
generator IS] was the first reported example of a multiband fractal antenna 1 1]-[7]. In
this work, a new degree of freedom to the antenna design is introduced: the variation
on the anienna flare angle. Experimental results ,
cacm . .. .
. .
are shown to describe the variations on the
impedance levels and absolute band positions
introduced when changing the flare angle.
,,
Basically it is shown that broader angles shift
the operating bands to lower frequencies, which
can be useful to reduce the antenna height.
When the angle is made too narrow the
multiband behavior is broken and the antenna
approaches the behavior of a classical
monopole antenna. This is basically due to the
truncation effect.
2. lnput Parameters.- Brown & Woodward
described in [SI the input impedance behavior
of triangular and conical antennas. Basically.
their experimental results evinced that the input
resistance and reactance variations were
smoother when opening the nare angle. A
similar performance was observed on the
triangular antennas, although in this case the
variations became stronger with respect to the
conical one.
.
,
KO ~m
811 cm
4.77
C"
Since the Sierpinski antenna has an overall
triangular shape, it appears natural to
investigate
whether those effects on the
ao im
performance of triangular antennas are
The S P K W (top). SPK60(center).
translated into the behavior of the fractal one. Flg.1
SPK30fhotlom)
Sierpinbki rracca,
Therefore, the SPK-90. SPK-60. y SPK-30
antennas (Fig.1) were constructed by following
0-7803-4478-2/98/$10.00 0 1998 IEEE
2340
the s ~ m epocedun U described in 171. The f d n g flue angles w e . mpcctively
M,e=#
y
5w.
The plots in Fig. 2 describe the input p a r a " (input refkction coefficient relative
to 50+8) input resistance and rcaccanCe) for the lhree antennas as a function of
hequency. In g m l . it can be stated that:
1) The behavior of the lhrre antennas is basically log-periodic, being the log-pwiod
t 2 , which is precisely the scale factor that relates thc scvcral fractal iterations in
the M k M a body.
2) The number of bands or log-periods(5) matches the number of fractal iterations as
demibedin(I].
3) Broader flare angles introduce a shift on Ihc " n t f q u c n c i c s toward longa
wavelengths.
4) The variations on Ihc impedance plots (uc stronger for the narrower M ~ ~ IatN
kas( at the first band. Tbis result is comparabk to thc bipng~larm h a behavior
described in IS].
5) The impedance minimum arc rcduced at odd R~(WUIICCS am rcduad for broader
M~~C
which
S , changes the matching levels with mpcct(0 509.
It should be stressed tha~the multiband behavior of the ~ l t n l must
l l ~ be related O
I its
fmctal shape,as it is extensively discussed in 161. The absolute drift on the o p c d n g
band position (not ita relative spacing) with respect to the T i vmion of thc M ~ M B
plrvr l - -u u CII
(SPK 60).must be relakd to the rizc
of the isosceles triangk twin edges.
Basically. the behavior of thcsc 9
can be modc~cd with L' .,,
cumnts propagating along the
M ~ C Mcdga
SI
U it is described in 161
lo
and will be explained somcwhm
I
U
clr. ~ i - c f o r c .longer edger hosl
longa resonant wavelengths yielding
(0thcshiftofthcspcctd~porue. E L
1
It is interesting to notice that the
narrower antenna kndr IO deviate
from the log-periodic behavior. Ita
input reflection coefficient displaya 8
doubk
match
featwe which
co"Ja
O
I a double nsonrna in E
Ihc i m p c d a m PI&. %&w,
Ihc 3 .
behavior of the SPK30 MLCIIMis
closcr to that of a classical monopole
which holds a clear harmonic
(periodic) non multiband bchavior.
ph3
im
A - ,
dSPK30(-) aalunms.
234 I
ra
I~CSPKC)~
(-I SPKW-.)
3. Kudiution Pufferns.- The radiation patterns for the SPK90 and SPK30 antennas
(main polarization component along the Qdirection, B t o " cut) are shown in figures
3 and 4 respectively. Those corresponding to the SPK60 antenna are described in
[2),[6],17).Again. it is observed that the broader angle antenna features a multihand
behavior, with a clear pattern similarity
'p=O"
among bands. Contrarily, significant
deviations among patterns are stated in
I
:' m
"
the SPK30 case; the number of grating
5
I\
X;
c.
,?a,'
,"
lobes tends to increase with frequency,
3
. , (I
i which makes this antenna comparable to
a
I ixoiiic
I IGOW'T
the classical monopole. Once more, such
:
e
a phenomenon must be related to the
4
r%; pwL'
,-??
X;
1; .k.$
:,: :-;
shorter length of the triangle edges.
a
= "( ' .*'
,' Somehow, the current active region that
J - ~ ~ I i X ,
p d y lilt>
characterizes
most
multifrequency
;
antennas 161 has less room to expand and
U:
to become attenuated by the radiation
process before reaching the antenna tips.
I"11~or.H~
I - ~ . 1 ~ ~ ~ In
H ~fractal theory terms, such a truncation
effect can be explained by the lack of
Flg.3 Radiation pallern ( w = WE,.comp)nenO larger characteristic scales
lo keep the
lor the SPKW anrcnna.
perfect symmetry of the ideal fractal set.
*\.,
$<:i?..,,,,.,\T
rf., 5
!;.,
Y
' I
~
"\
I
.
)
. . .
'
d,,2.,-0
'. .
> 7 .
I)
2.
I
~
This should not be taken as a basis to argue that fractal antennas are not
multiband antennas; the suitability of fractals to become multiband antennas directly
comes out from the classical scaling propeny of Maxwell equations 161. Therefore,
one should expect a multiband behavior even for the SPK30 antenna. provided that
the antenna size and the number of fractal iterations is made large enough.
cp"0"
4. Conclusions.. The behavior of three
."
'?
"
-'
Sierpinski fractal antennas has been y
described through several experimental X;
.*
results. The antennas had the same basic 2
'. L',' : ,,
, '! . *
shape with a change on the flare angle.
J I 80 r x ,
It is shown that such a change
introduces significant variations on the
antenna input parameters and radiation 2 _ ,
pattems. Although the designer can
J J ?rriH$
I 4 !'p r;Hz
freely use those variations for P,
.m
.:
engineering purposes, it must be taken
into account that by namowing the 2
antenna angle a deviation from the
r-a.o)I;nt
..
*
multiband behavior is obtained. Except q
",
for those cases, where the truncation
effect is important. it can be concluded 2
i
. ,/
again that fractals can be successfully
1-11 W G H :
pl6Wr;lh
used to construct simple multiband
Ftg.4. Radiation pattern (er' =W" cut. E,
antennas.
compnenr) for Ihe SPK30 antenna.
Acknowledgments,- This project has
..
- ~ ' &-&-;yT), ~
,c
'
.
)
. Y . . , '
.
I
.
~
2342
~
,
.
heen partially supported by the grant TIC-96-0724-C06-04 of the Spanish
goveminent and by Ihe companies SISTEMAS R A D I A N T S F.MOYAN0 and
FRACTUS. Fractal and Mullifractal antennas are parent pending.
References
I l l C.Puentc. J.Romcu. R. Banolud. y R. POUS."Pcnurtcation of Ihc Sicrpinski antcnna to allwatc operaling
bunds". Etrrronicr L f f r r n . vol. 32. no.24. pp.2186-2188. November 1996.
121 C.Pucntc. J.Romcu. R.Pws. X.Garcia. F. Bcnltcz. "Fractal multiband antcnna based on the Sierpinski
ga5ket". Elecminin L r r m . vol. 32, no. I . pp. I.2.January 19%.
131 N.Cohcn. R.G. Iluhfeld. "Fractal loops and the SIMII Iwp appmaiimtion". C ~ m " n . Quanrdy. 77-81.
Winter 19%.
141 C.Pucnfc. I.Cluct. F. Ssguts. J.Runru. M.Q.Ldpcz
Salvans. R.Pws. "Multiband popertics of fractal ITCC
antenna generaled by claclwhcmical dcprition". Elrcrronirs k f r r r r . vol. 32. no.25. pp. 2298.2299,
Deccmbcr 1996.
15) H.O.Peitgcn. ll.Jiirgenr. D. Saupc, Cham onJ Jracruls, new Jronrirrs o/scirnrr. New York : Springer Verlag.
1992.
161 C.Pucnte. "Fractal Anlcnnu". Ph.D. Disrcflation. Dept. TSC. Univenilu Polittcnics de Caelunya. June
1997.
[7] C.Pucnte. J.Romeu, R.Pws. A.Cardntna, 'On the Behaviur of the Multiband Sicrpinski Fractal Anlcnna".
acccpld lor publication in IEEE 'Tronr. on A n r m w r ondPruprgorion. 1998.
[E] G.ff.BNwn. 0 . M . W d w a r d .
"8rpcrimnlally Dctcmlinut Radialion ChPralcristkr ol Conical and
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