Diseño de una antena fractal triple banda basada en la trigonometria de Sierpinski

1. FRACTAL ANTENNA TRIPLE BAND
Mario Suarez1,Jessica Proa~no2, Santiago Murillo3, Marco Ambo4, Marcela Castillo5
FACULTAD DE INFORMATICA Y ELECTRONICA
ESCUELA DE INGENIERIA ELECTRONICA EN TELECOMUNICACIONES Y REDES
ESCUELA SUPERIOR POLITECNICA DE CHIMBORAZO
Abstract.This work presents a triangu-
lar fractal antenna using fractal geome-
try. The HFSS software from Ansoft has
been used to simulate the antenna and ob-
served that increase in iterations led to
improvement is return loss and radiation
pattern. This antenna is design to work
in the band 800 Mhz, 1200 Mhz and 2.4
Mhz, it is having a bandwidth of 0.39 -
0.456 - 0.12 Ghz respectively.
1.-INTRODUCTION
Today wireless communication, satellite com-
munication and advanced military systems, re-
quire antennas of higher performance, higher
gain, wider bandwidth, multiband support, low
cost and conventionally smaller design dimen-
sions[1]. Fractal antennas are designed using
fractal geometries which show properties like
self-similarity, bandwidth, space

2. lling and com-
plexity in their structure. The fractal theory ap-
proach has been used as a size compression tech-
nique for all types of antennas such as dipoles,
loops, patches and so on leading to the develop-
ment of fractal antenna[2]. Fractal geometry al-
lows combining antennas of dierent frequencies
avoiding interference, allowing us to design tri-
band and tetra-band antennas with a very small
size and the same gain factor as a traditional
antenna[3].
2.-ANTENNA FRACTAL BASED ON
SIERPINSKI GEOMETRY
A fractal design is obtained by applying a

3. -
nite number of times an iterative process. The
properties of these geometries are incorporated
in the designing of antenna.The Sierpinski Tri-
angle is a geometric set introduced by mathe-
matician Sierpinski Waclack, can be generated
in various ways. The most common is to start
with an equilateral triangle, mark the midpoints
of its sides and draw a triangle inside (consid-
ered as open set) the process is repeated with the
remaining three triangles.
A.Properties of Fractal Geometries
Space Filling properties
Self Similarity
ADVANTAGES
Small size
Better input impedance
Wideband/multiband support
Consistence performance over huge fre-
quency range
DISADVANTAGES
Fabrication and design is little complicated
Lower gain in some cases[4]
The Sierpinski Gasket fractal is generated by the
Iterated Function Systems, as depicted in

4. gure
1.
Figure 1: Concept of Interaction
3.-DESIGN FRACTAL ANTENNA
The fractal dimension is associated witch the
thickness and texture of the object to determine
the fractal dimension of a fractal curve locked
her in a grid, so that the curve completely into
it then all those boxes in the grid has come
1

5. to are cut from the curve, but this process is
repeated at each step the length of the grid boxes
will divide by two[5].
=
fn+1
fn
(1)
=
1100 106
700 106 = 1:57 (2)
hmax =
0:152 c cos(
2 ) n
fn
(3)
hmax =
71:59x106x cos(30)
700x106 x1000 = 88:57mm
(4)
hmax =
88:57
2
= 44:285mm (5)
hmax =
44:285
2
= 22:1425mm (6)
Figure 2: Triangle of Sierpinski.-this picture
shows the measure each high.
Figure 3: Return Loss.-shows the resonance fre-
quency in the three (0.8,1.2 and 2.4 GHz).
Figure 4: Radiation Pattern.-indicates that an-
tenna is omnidirectional
Figure 5: Triangle of Sierpinski Simulated.-is the
design normalize for the frequencies of operation
Figure 6: Antenna.-this is the patch implemen-
tation of our antenna printed in Bakelite
2

6. Figure 7: This is the ground of antenna
4.-CONCLUSIONS
Fractal geometrical structures with self-
similarity property have been investigated
for triple-band wireless communication an-
tenna applications.
Simulations and experimental results are
in a good agreement and reveal the per-
formance of the proposed fractal antennas
triple band.
The fractal antennas are preferred due to
small size, light weight and multiband.
The theory of fractals is opening a universe
of possibilities in exploring new scienti

7. c al-
ternatives to solve and optimize.
An fractal antenna could be very small, but
for this reason does not depend of the devel-
opment of this.
References
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dama,On the behavior of the Sierpinski
multiband fractal antenna , IEEE Trans.
Antennas Propagat, 1998
[2] J. Gianviwb and Y. Rahmat-
Samii,Fractal antennas: A novel an-
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applications, Antennas Propagate,2002
[3] Holguin M,Estudio y Metodologia de An-
tenas utilizando geometria fractal ,Escuela
Politecnica Nacional ,2004
[4] Gianvittorio, J. P. andY. Rahmat-Samii,
Fractal antennas: A novel antenna minia-
turization technique,and applications ,
IEEE Antennas Propagation Magazine,
2002
[5] A. K. Sharma and B. Bhatt, Analysis
of triangular microstrip resonator , IEEE
Trans. Microwave Theory Tech.
3