Design and simulation of fractal tree antenna for wireless application

INTERNATIONAL JOURNAL OF ELECTRONICS AND
International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), ©
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
IAEME

ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 3, Issue 1, January- June (2012), pp. 178-187
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DESIGN AND SIMULATION OF FRACTAL TREE ANTENNA
FOR WIRELESS APPLICATION

Sanjay V Khobragade1, Anitha V R2
1. Department of EXTC, Dr. BATU, Lonere, 402 103, Raigad, Maharashtra, India
Research Scholar, Rayalaseema University Kurnool Andhra Pradesh, India
2. Professor Sreevidyaniketan COE Tirupati Andhra Pradesh, India
Svk2305@gmail.com , anithavr@gmail.com

ABSTRACT

Fractal antennas have been shown to demonstrate repetitive multi-band or log-
periodic behavior that has been attributed to the self-similar scale factor of the
antenna’s geometry. This geometry, which has been used to model complex objects
found in nature such as clouds and coastlines, has space filling properties that can be
utilized to miniaturize antennas. These unique properties of fractals have been
exploited to develop a new class of antenna-element designs to possess several highly
desirable properties, including multiband performance, low side lobe levels, and its
ability to develop rapid beam forming algorithms based on the recursive nature of
fractals. There are several advantages of these fractal devices including reduction of
resonant frequencies, smaller size and broadband width. In this paper, a new design of
fractal tree antenna based on ternary fractal tree geometry for wireless local-area
network (WLAN, 2.4 GHz for wireless operation) is proposed.

Keywords

Microstrip patch Fractal antenna, Array Antenna, Fractal Tree Antenna, Multi-band,
Fractal Geometry

INTRODUCTION
Currently, the 2.3–3.6 GHz band assignment for WIMAX is considered as one of the
best choices for the transmission of multimedia services (voice, Internet, email, games and
others) at high data rates. The classics wire and patch antenna are intrinsically a narrow
band devices. Their behavior is strongly dependent on the report of an antenna size to the
working wavelength. The antenna parameter is (gain, matching and radiation pattern)
endure then any working frequency disagreement one promising approach in this regards is
to use fractal geometries to find the best distribution of current within a given volume in
order to meet a particular design goal. Fractal geometries have been recently introduced an

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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME

antenna design. It has been shown that fractal associated with the geometric properties of
the fractals [5] [6]. One property associated with the fractal geometry and used in antenna’s
design is self similarity [6]. A fractal antenna can be design to receive and transmit over a
wide range of frequencies using self-similar properties associated with a fractal geometry
structure, because different antenna’s part are similar to each other at different scale. The
second property is the efficiency of space filling of some fractal shapes, which gives hopes
to reduce the antenna size, comparatively to that of classic antennas. Various fractal shapes
that possess self-similarity have been applied to multiband and miniaturized antenna
design. A promising fractal geometry that ensures a successful design of multiband antenna
is known as the deterministic fractal tree. Multi resonant behavior of the first iteration tree
mounted over a large conducting ground plane are describing in many papers [9] [10].
However, the conventional fractal tree monopole antenna does not present many resonant
frequencies in the range of 0.2 to 6 GH wireless bands. Further, the poor matching property
of the resonance frequency has been shown [6].
In 1975, fractal geometry was first defined by B. Mandelbrot describe complex
geometries and it was generated with an iterative procedure. Recently, fractals have been
widely used in antenna designs to obtain various kinds of small and multiband antenna. As
the typical representation of fractal in the nature, trees are good study objects in
electromagnetic theory for engineering applications. Tree-shaped fractal antennas have
been in broadly investigated in recent years. Fractal antennas are mainly divided into four
parts: fractal line antennas, fractal three dimensional antennas, fractal planar antennas and
fractal antenna arrays [1], tree-shaped fractal antennas are mainly researched as fractal
three-dimensional antennas or fractal planar antennas. On one hand, as fractal three-
dimensional antennas, C. Puente proposed a tree-shaped fractal antenna as early as fractal
theory was firstly proposed in antenna designing [2].
Fractal tree antennas are very attractive because of their low profile, low weight,
conformal to the surface of objects and easy production. A large number of microstrip
patches to be used in wireless applications have been developed. Various shapes such as
square, rectangle ring, disc triangle, elliptic, etc. have been introduced .In comparison to
patch elements; the antennas with slot configurations demonstrate enhanced characteristics,
including wider bandwidth, less conductor loss and better isolation. Particularly the multi-
slot structure is a versatile approach formulate-band and broadband design. Also, feeding
these structures could be simpler by using suitable points to slot techniques for different
slots [3-4].

FRACTALS AS AN ANTENNA
All the basic trigonometric shapes are already utilized in antenna design and their
radiation mechanisms are well explored. And we also know that any arbitrarily random
shape can pick up EM waves. So why not have a discipline in chaos. That means, using
fractals as antennas may offer better radiation pattern and may also offer more controlling
parameters to designer.
Fractal antennas are multi-resonant and smaller in size. Qualitatively, multi-band
characteristics have been associated with the self-similarity of the geometry and Hausdorff
dimensions are associated with size. Research towards quantitative relation between
antenna properties and fractal parameters is going on extensively. Any variation of fractal
parameters has direct impact on the primary resonant frequency of the antenna, its input
resistance at this frequency, and the ratio of the first two resonant frequencies. In other
words, these antenna features can be quantitatively linked to the fractal dimension of the

179


geometry. This finding can lead to increased flexibility in designing antennas using these
geometries. These results have been experimentally validated.
A fractal antenna's response differs markedly from traditional antenna designs, in that
it is capable of operating with good-to-excellent performance at many different frequencies
simultaneously. Normally standard antennas have to be "cut" for the frequency for which
they are to be used and thus the standard antennas only work well at that frequency. This
makes the fractal antenna an excellent design for wideband and multi-band applications.
Various Fractal Types used in Antennas are shown below: [2]

Fig 1 Various Types of Fractals Used As Antenna

FRACTAL GEOMETRY

Fractal trees studied here are also known as fractal canopies and Pythagoras trees.
Although these have several features common with other fractals such as Koch curves,
their branching nature offers a significant variation, and is expected to cause some
difference in antenna performance. In addition the approach taken for the generation of tree
here is somewhat different.

A. Pythagorean Tree

The Pythagorean tree is a plane fractal constructed from squares. It is named after
Pythagoras because each triple of touching squares encloses a right triangle, in
configuration traditionally used to depict the Pythagorean Theorem.

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Fig 2 Pythagorean Tree

In microstrip line implementation, the definition is often modified. Here the initial
segment, i.e. generator, is not a square anymore but it is a rectangle. Hence we will refer to
as tree. The initial segment is divided by a scale factor, moved at an angle and placed at the
top of the initial segment. The same pattern is repeated to construct the tree of any order.
After some order, depending on the scale factor and angle, the branches start overlapping
each other. Such an antenna can be thought of as a virtual combination of capacitors and
inductors, loading the previous structure. This makes the antenna so that it has many
different resonances which can be chosen and adjusted by choosing the proper fractal
design. Here different variable parameters of the fractal are the size of the initial segment,
scale factor, branching angle and number of iterations.
Increasing the number of segments may increase the coupling between branches. Size
of the first segment determines the one of the resonant frequency of the antenna. Scale
factors may decide the ratio between the successive resonant frequencies. [1] The
branching angle also affects the coupling. However it does not affect the ratio of resonant
frequency if the lengths and widths of the branches are not dependent on the angle. [1]
Fractal geometry are generated in an iterative fashion, leading to self structure .The tree
geometry start with a stem allow one of its ends to branch off in two directions .In the next
stage of iteration ,each of these branches allowed to branch off again. The process is
continued endlessly as shown in fig. 3 Branch angle 600 and 1200 with Branch Stem of 0.6
and 0.3

Fig 3 Fractal Tree with different branching angle and Scale ratios

It is possible to vary the scale factor between the length of the stem and branches. The
transformations required to obtain branches of the geometry in such case may be expressed
as follows by equations,

= 1

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= 2

Where
S = scale factor
θ = Branching half angle
The scaling is by a factor of 0.5, and the branching half angle is 600. The fractal
dimension D for the geometry shown in fig. 4 is obtained using (3).Since the branching
angle has no direct role in determining the lengths of these segments, the dimension of all
such geometries remain the same. However, as the scale factors are changed, the fractal
dimension is also changed. For a length ratio x: 1 between branches and the stem, the
following expression may be satisfied for the fractal dimension.

+2 3

Fig 4 Fractal Tree Geometry

B. wideband fractal antenna

It is intuitive that the self similarity property of fractals will result in multiple resonances.
The multiple resonances can be converted into wide band characteristics by bringing the
resonance frequencies closer and letting the bands overlap. If the fractal parameters are
controlled properly, this can be achieved. In general, for any antenna to have wide band
characteristics, the parameters discussed below have to be taken into account. The
impedance bandwidth of a micro strip antenna can be determined from frequency response
of its equivalent circuit. For parallel-type resonance, the half power bandwidth is given as:

Where Y = G + jB is the input impedance at the resonance frequency. This bandwidth is
also defined as VSWR ~ 2 bandwidth. Hence, in terms of VSWR

Where, Q is the quality factor use in design for the structure. As Q decreases, the
system becomes lossier and bandwidth increases. Hence, if εr decreases, BW increases and
if thickness of substrate increases, bandwidth again decreases. Further achievement of
antenna bandwidth can be obtained by increasing gap coupling or direct coupling with the
ground plane. And slow resistance transformation also helps in increasing bandwidth

182


ANTENNA DESIGN APPROACH

Because of their geometric complexity, it is very difficult to predict mathematically
the fractal antenna radiation pattern properties. The wide availability of the powerful
electromagnetic simulator makes possible of such problems, which would be otherwise
impossible to solve. A first step in the utilization of fractal properties in antenna design
should involve the dimension of the geometry. Many numerical methods are available that
predict the performances of such antennas. All these techniques are based on solving a
discrete form of Maxwell's equations. The most often used are the method of moments
(MoM) and the Finite Difference Time Domain (FDTD) method. We use Finite Element
Method for fractal design similar to fig. 4, explained in [6] [8]. The scale factor for all
iteration is 0.66 as per (3).
A 5-iternation, tree is applied as the radiation part here. In order to increase the
degrees of freedom of the radiator for the optimization of its performance, such a fractal is
chosen. The geometry of the proposed antenna is shown in Figure 5.

Figure 5 Novel Design for Fractal Tree Antenna

The Fractal tree structure design has following specification Length of main stem
L=20mm, width of the stem W=8mm, Substrate height h=1.588mm and resonant
Frequency is 2.4 GHz. The proposed geometry is excited by probe feeding technique[3].we
exploit the iteration factor η = 0.66 and fabricate the proposed antenna on an economical
"Rogers RO4232 (tm)"dielectric with a thickness of 1.588mm (h), relative permittivity of
3.2 (εr),and loss tangent of 0.0018 .

SIMULATION

There exists much software such as HFSS, Fidelity, CST, Feko, EMPro, SIMetric,
SuperNEC etc. for the simulation of the RF component designs. In this paper, the antenna
has been designed and simulated using FEM method based commercial Electromagnetic
simulator. The structure has a substrate layer with εr of 3.2 (RO4232 board), thickness of
1.588mm and the antenna is probe fed as shown in Fig.6 (with all dimensions in mm only).
The size of the board is 100mmX120mm. The antenna is drawn as a microstrip patch layer
on the board using copper as material.

183


First Second Third Fourth Fifth

RESULT AND ANALYSIS

Five iteration with branching half angle of θ =60 and specification discuss in antenna
design were simulated. The design of all five iteration of the novel printed on dielectric
substrate. The antenna has been fed using 50 ohm coaxial probe to main stem. In this study,
the permittivity of the substrate is 3.2. Return loss, VSWR, VSWR bandwidth, and
direction pattern is plotted. The Radiation pattern for the fifth iteration is shown in fig. 6.
This gives the change in the pattern direction respectively with number of iteration. From
this the measured radiation pattern of fractal antenna is nearly omnidirectional in azimuth
plane throughout the operating frequency.

Figure 6. Radiation pattern for E field for iteration V.

Return loss measurement for all the iteration is presented in fig. 7. This curve confirms the
resonant frequency location. For the other iteration same behaviour was noticed and
confirms the resonant frequency.

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FIGURE 7 RETURN LOSS FOR ITERATION I TO V

VSWR for all the iterations are showed in Figure 8. It shows the good result for third
iteration. Bandwidth up to 10.15% can be achieved using probe fed method only, which
can be further enhanced by using other enhancement techniques.

Figure 8 VSWR for iteration I to V

CONCLUSION

A tree shaped fractal antenna using rectangular structure based on fractal tree
geometry is presented in this paper. It is observed that the resultant antenna is compact in
size and simple to design. Our aim was, to see the results of antenna using coaxial probe
fed method. The proposed novel design provides the bandwidth up to 87.78% using probe
fed technique. The proposed antenna is simulated for 2.4 GHz frequency. This antenna give
omnidirectional property and operate in 2.1GHz-2.8GHz frequency band with acceptable
S11<-10dB (VSWR<2).The proposed antenna used for wireless video operation 2.8GHz,
Also used in Bluetooth 2.4GHz and Wireless LAN of 3GHz frequency.

185


ACKNOWLEDGMENT

The authors would like to thank Dr. Nalbalwar, and faculty member of Electronics and
Telecommunication Department. Similarly special thanks to Pradnya Sarvade, Pooja
Holkar and Sucheta Pawar for working hard day and night for the different designs of
fractals. We would also like to thanks the pass out students of Dr. Babasaheb Ambedkar
Technological University who presents so many papers at National and International level
based on fractal design and Microstrip Antenna.

REFERENCES

1. C. Puente and J. Claret (1996), “Multiband properties of a fractal tree antenna
generated by electrochemical deposition,” Electronics Letters, vol. 32, no.25, pp. 2298-
2299.
2. Vinoy, K. J. (2002), “Fractal shaped antenna elements for wide and multi-band
wireless applications,” Thesis, Pennsylvania.
3. R. K. Gupta (2010) "Printed TRI-BAND Monopole Antenna Structures For Wireless
Applications “Issue, Vol. I.
4. Raj Kumar, George Mathai and J.P. Shinde (2009) "Design of Compact Multiband
EBG and Effect on Antenna Performance” International Journal of Recent Trends in
Engineering, Vol2, No. 5.
5. Werner D.H., Ganguly S. (2003), “An overview of fractal antenna engineering
research", IEEE. Antennas and Propagation Magazine. Vol. 45.
6. Cohen, N. (1997), “Fractal Antenna Applications in Wireless Telecommunications”,
Professional Program Proc. Of Electronics Industry Forum, pp 43-49.
7. Sindou, M., Abalrt G., Sournois C. (1999), “Multiband and wideband properties of
printed fractal branched antennas”, Electronics letter, 35(3):181-2.
8. Puente Claret, Sagues J., Romeu F., Lopezsalvans,J., Pous M.Q. (1996), “Multiband
properties of a fractal tree antenna”, generated by electrochemical deposition,
electron. Letter, 1996, pp 2298- 2299.
9. Petko, J. S., Werner D. (2004),“ Miniature reconfigurable three dimensional fractal
tree antennas”, IEEE Trans. Antennas and Propagation. August 2004.
10. H. Kimouche eI, M.Bitchikh, B.Atrouz (2008), “Novel Design of a Fractal Monopole
Antenna for Wireless Communications”, IEEE transaction of Antenna Wave
Propagation.
11. Garg, Bhatia, Bahl, Ittipiboon (2000), “Microstrip Antenna Design Handbook”, Artech
House, London.
12. Yahui Zhao, Jinping Xu, and Kang Yin, “A Miniature Coplanar Waveguide-Fed Ultra-
Wideband Antenna”, State Key Laboratory of Millimeter Waves, Southeast University,
Nanjing, Jiangsu, P.R.China, 210096.
13. Masahiro Yanagi, Shigemi Kurashima, Takashi Arita, Takehiko Kobayashi, “A Planar
UWB Monopole Antenna Formed on a Printed Circuit Board”

AUTHORS

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Sanjay V. Khobragade has been working as Assistant Professor in Dr.
B. A. Technological University Lonere, Maharashtra, India from last 13
years. He is graduated from Nagpur

University in 1996 and post graduated in Electronics Engineering from Mumbai University
in 2008 and pursuing PhD form Rayalaseema University Kurnool, Andhra Pradesh. He has
been involved in teaching a Microwave, Antenna & Wave Propagation and
Electromagnetic Field. He has received Young Scientist Award in URSI 2004 in Pisa Italy,
and Consolation Prize for best paper in ICMARS Jodhpur, 2008 and best Technical teacher
award by ISTE sponsored by Maharashtra and Goa in 2010. He has around 70 papers at
national and International conferences in his credit.

Dr. Anitha V R has been working as a professor in Sree Vidyaniketan
College of Engineering Tirupati. She is actively involved in teaching
Microwave, Optical and Digital communication subjects. She is

graduated in AMIETE in 2003, postgraduate in Engineering in 2005(M. Tech.) from
Nagarjuna University Guntur, and PhD in Design and Analysis of a Square Microstrip
Planar Antenna Array for Wind Profiling Radars in January 2010. She is qualified for
Stipend given by TEQIP Government of India during PhD in 2006 to 2009. She is Gold
medallist of M. Tech. She is Member IEEE and Life member of IETE. She has 25 papers in
national and international conferences and journals.

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Design and simulation of fractal tree antenna for wireless application

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