R L Yadav et. al.

/ International Journal of Engineering Science and Technology

Vol. 2(11), 2010, 6335-6348

Multiband Triangular Fractal Antenna for

Mobile Communications
R. L. Yadava1, M. Ram1 and S. Das2
Department of Electronics & Communication Engineering1
Galgotias College of Engineering and Technology, Uttar Pradesh, India
Department of Electronics & Instrumentation Engineering2
Indian School of Mines, Dhanbad, India.

ABSTRACT

The design of 2.45 GHz- Triangular fractal antenna using fractal geometry has been proposed in this paper. The
Ansoft HFSS software has been used to simulate the antenna and observed that increase in iterations led to
improvement is VSWR & return losses. It has also been observed that with increase in the number of iterations
the bandwidth of the antenna increases & on second and third iterations the antenna starts showing the multiband
behavior which is very much demanded in cellular communications. The obtained results have also been validated
using HP810B network analyzer. The simulated and experimental results are found to in good agreement.

I. INTRODUCTION

Modern telecommunication system requires antennas with wider bandwidth and smaller dimensions than
conventionally possible. Now days, the size of electronics systems has decreased drastically, whereas their
functionality has increased. The antennas have not experienced the same evolution. The antenna size with respect to
the wavelength is the parameter that will have influence on the radiation characteristics. For efficient radiation, the
size should be of the order of a λ/2 or larger. But as antenna size reduces, the bandwidth, gain and efficiency of
antenna deteriorate [1]. In addition the explosive growth in the wireless industry has renewed interest in multiband
antennas. The most recent multiband antenna development is the incorporation of fractal geometry into radiators and
the Sierpinski gasket antenna is a prime example. Since the Sierpinski gasket has proven itself to be an excellent
multiband antenna, other multiband antennas can similarly be constructed using fractal geometry. The multi band
and ultra wide band properties of antenna are due to their self-similarity of fractal geometry [2]-[3] while the space
filling properties [4]-[5] of antenna leads to the miniaturization of antenna.
The input characteristics of one such fractal design based on the hexagon has also been evaluated and found
suitable for multiband usage [6-7]. Circular microstrip fractal antenna has also been designed for ultra wide
bandwidth and size reduction using self-similarity and space filling properties. This antenna exhibits the impedance
bandwidth from 0.8 GHz to 10.68 GHz which is more than the FCC bandwidth 3.1 GHz to 10.6 GHz for wireless
communication system. The radiation pattern of this antenna is nearly Omni – directional and exhibits the low
backscattering [8]. The microstrip triangular patch finds extensive applications in the design of many useful MIC
components such as resonators, circulators and filters. The triangular patches have been studied, both theoretically
and experimentally [9-14]. They are found to provide radiation characteristics similar to those of rectangular
patches, but with a smaller size. Therefore, in present paper, an attempt is made to design the triangular fractal
antenna of compact size and, good radiation and multiband characteristics.

HISTORICAL VIEWS

Dr. Nathan Cohen assembled the first true FEA in 1988 to work the 2-meter amateur band. Later he built a 10-meter
dipole and established dozens of stations in Europe with a power of 1 watt. Dr. Cohen initially reported his findings
at an ARRL convention in 1994, and published the first article on fractal antennas in 1995. However, major
developments in the area of fractal antennas chronically can be given as,
1947 – Chu and Wheeler establish a fundamental limit on the performance of small antennas [Wheeler, 1947; Chu,
1948].
1983 – Benoit B. Mandelbrot “Coins” the word fractal (meaning made-up of broken or irregular fragments)
[Mandelbrot, 1983].

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Vol. 2(11), 2010, 6335-6348

1986 – Kim and Jaggard reported uses of fractal arrays in antenna theory [Kim, 1986]. 1988 - Nathan Cohen builds
one of the first known practical fractal antennas in his Boston apartment ham radio station [Cohen, 2000].
1998 - Carless Puente Baliarda of Universitat Politècnica de Catalunya (UPC) wins $230,000 prize for fractal
antennas (GSM + DCS single base station antenna), one of three Grand Prizes of The European Information
Technology Prize in that year [www.fractus.com, 2000]. Since then several research works have been carried out in
this field.

FRACTAL ANTENNA GEOMETRY

Fractal antenna theory is built, as is the case with conventional antenna theory, on classic electromagnetic
theory. Fractal antenna theory uses a modern (fractal) geometry that is a natural extension of Euclidian geometry.
The effects of electromagnetic waves on fractal bodies have been intensively studied in recent years. Different from
Euclidean geometries, fractal geometries have two common properties, space-filling and self-similarity. Self similar
objects look roughly the same at any scale. Thus, in an antenna with fractal shape, similar surface current
distributions are obtained for different frequencies, i.e. multiband behavior is provided. The space filling property,
when applied to an antenna element, leads to an increase of the electrical length. The more convoluted and longer
surface currents result in lowering the antenna resonant frequency for a given overall extension of resonator.
Therefore, given a desired resonance frequency, the physical size of the whole structure can be reduced.

In conventional microstrip patch antennas, dual or multifrequency operation can be achieved by using
multiple radiating elements or reactively loaded patch antennas or multi-frequency dielectric resonator antennas.
However in fractal antenna, self similarity property is used to achieve the same. The main advantages of fractal
antenna over conventional antenna designs are its multiband operation & reduced size. Because of fractal loading
present in this type of antenna, inductance & capacitance are added without the use of additional components.
Antenna tuning units are also not required because these are ‘self loading’ antennas. Fractal antenna has useful
applications in cellular telephone and microwave communications. HFSS is the industry standard for analyzing
arbitrary 3D radiating elements such slot, horn, linear wire and patch antennas along with their polarization
properties such as axial ratio, co- and cross-polarization. It automatically computes critical metrics such as gain,
directivity, input impedance, efficiency, and near- and far-field radiation patterns.

HFSS can link field data between multiple HFSS models to capture the entire behavior of the Antenna
system from transmitter to receiver. The applications of HFSS are Antenna systems, advanced package co-design for
single and multi-chip integration, On-chip passives and High-speed packages and interconnect.

II. GENERATION OF PROPOSED FRACTAL ANTENNA

The construction of the proposed fractal shape is carried out by applying a finite number of times an iterative
process performed on a simple starting topology. According to the properties of self similarity, the fractal
dimension Ds of a set A is defined as:

Ds= log (N)/log (r) (1)

Where N is the total number of distinct copies similar to A, and A is scaled down by a ratio of 1/r.

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Fig 1. Basic concept of Iterations

Ideal fractal geometries cannot be used in antenna design because they cannot be simulated and fabricated.
Therefore, in this paper, only 3rd order of proposed fractal antenna is investigated.

Fig 2. Equilateral triangular patch & equivalent rectangular patch

Fig 2 shows an equilateral triangular patch and its equivalent rectangular patch antenna. The resonance frequency of
the equilateral triangular patch can be determined by [10];

2
2
3 ,
Where, c is the velocity electromagnetic wave in free space. The Leff is the effective length of the equivalent
rectangular patch [L = a, W = (√3/2) a] and , is the dynamic relative permittivity of the triangular shown Fig 2.
The dynamic relative permittivity of the equivalent patch antenna is given by [14];

Where is the complex dynamic capacitance of equivalent rectangular patch and;

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Vol. 2(11), 2010, 6335-6348

and
Jensen. And ε ε , W, h is equal to [13];

1 1 12
, , 1 3
2 2
Where all the parameters have usual meaning.

III-DESIGN SPECIFICATIONS

In order to calculate the side of the triangular fractal antenna the following parameters are required:

3 10 m/sec
, 2.1
√3 .
2
2.45

Using the above formula for resonant frequency, the side of the triangle calculated is:
a = 65.046mm. The minimum distance of the radiation box from the antenna is given by:

4
4

Therefore λg = 21.124 mm

IV. SIMULATION AND EXPERIMENTATION OF THE ANTENNA

The Fig 1 shows the 3rd order iteration triangular patch antenna. The patch antenna was printed on R.T Duroid
substrate of relative permittivity 2.1 and thickness 1.6 mm. All the structures have been simulated with the Ansoft
HFSS 11 simulator. The procedure of simulation is as follows. The copper conductor of height 0.035mm is taken.
The R.T Duroid dielectric with relative permittivity 2.2, thickness 1.6mm is placed over it. For feed, a microstrip
line is made to give a port for feed. Finally a radiation Box is placed over the antenna & thereafter the set up is
simulated and measured using HP810B network analyzer in Anechoic chamber (Fig 3).

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Vol. 2(11), 2010, 6335-6348

Fig 3. Experimental set-up using HP810B network analyzer in Anechoic chamber.

IV. RESULTS

The results for the three iterations performed on the triangular patch to get the desired fractal antenna are as follows:

Results for Iteration 0

The structure of triangular fractal antenna having zero iteration has been shown in Fig 3. On simulating this structure
with the help of Ansoft HFSS, the following results were obtained:

Fig 3 Iteration 0 Fig 4. Return loss for various frequencies.

That is return loss is found to be -6dB at 1.9 GHz frequency with VSWR to be 3 (Fig 5).

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Vol. 2(11), 2010, 6335-6348

Fig 5. VSWR for various frequencies.

The values of Directivity, Gain and Radiation efficiency are found to be; 4.4048, 4.0205
and 92.188% respectively (Figs- 6-8)

Fig 6. Directivity

Fig 7: Gain

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Fig 8. Radiation efficiency

Results for Iteration 1

The structure of triangular fractal antenna with first iteration is as follows:

Fig 9: Iteration 1

On simulating the above structure with the help of Ansoft HFSS, the following results were obtained:

(a) Return losses

Fig 10. Return loss vs. frequency

The return losses for first iteration came out to be -10.7dB at 7.8GHz frequency.

(b) VSWR

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Vol. 2(11), 2010, 6335-6348

Fig 11. VSWR vs. frequency

The VSWR for iteration 1 came out to be 1.7054 at 7.8 GHz.

(c) Total Gain

Fig 12 Gain
The overall gain came out to be 1.6718 for iteration 1.

(d) Directivity

Fig 13 Directivity
The directivity for 1st iteration came out to be 2.2612.

(e) Radiation efficiency

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Vol. 2(11), 2010, 6335-6348

Fig 14 Radiation efficiency

Radiation efficiency for 1st iteration is 74.675%.

Results for Iteration 2

The structure for triangular fractal antenna with 2nd iteration is:

Fig 15. Iteration 2

The results obtained by simulating the triangular fractal antenna came out to be as follows:

(a) Return loss

Fig 16. Return loss vs. frequency

The return losses for 2nd iteration came out to be -16.2dB at 8.9GHz and -21dB at 9.6 GHz.

(b) VSWR

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 R L Yadav et. al. / International Journal of Engineering Science and Technology
Vol. 2(11), 2010, 6335-6348

Fig 17. VSWR vs. frequency

VSWR for 2nd iteration came out to be 1.36 at 8.9GHz and 1.2 at 9.6GHz.

(c) Gain

Fig 18. Gain

The overall gain for 2nd iteration came out to be 1.6634.

(d) Directivity

Fig 19. Directivity

The directivity for iteration 2 is 2.2583.

(e) Radiation Efficiency

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Fig 20 Radiation efficiency

The radiation efficiency for 2nd iteration is 74.391%.

Results for Iteration 3

The structure for triangular fractal antenna with 3rd iteration is:

Fig 21 Iteration 3
The results obtained by simulating the above structure are given as follows:

(a) Return loss

Fig 22. Return loss vs. frequency

The return losses came out to be -28.2dB at 16.7GHz, -17dB at 18.3GHz, -25.2dB at 19.6GHz and -24.3dB at
22.2GHz.

(b) VSWR

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Vol. 2(11), 2010, 6335-6348

Fig 23 VSWR vs. frequency

The VSWR came out to be 1.1 at 16.7GHz, 1.34 at 18.3GHz, 1.1 at 19.6GHz and 1.13 at 22.2GHz.
(c) Gain

Fig 24. Gain for iteration 3

The overall gain for 3rd iteration is 2.3581.

(d) Peak Directivity

Fig 25. Peak directivity for iteration 3

The peak directivity for 3rd iteration is 2.351.

(e) Radiation Efficiency

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Vol. 2(11), 2010, 6335-6348

Fig 26. Radiation efficiency for iteration 3

The radiation efficiency for 3rd iteration is 74.679%.

V-Comparison of the results of different iterations

The following table gives the comparison of resonant frequencies, bandwidth, return losses and VSWR for 0th ,1st , 2nd
and 3rd iterations.

Itera Resonant Return losses Bandwidth VSWR

tions Frequency (dB) (GHz)
(GHz)
Theore Experim Theoretic Experimen Theoretica Experime Theore Experimen
tical ental al tal l ntal tical tal
0 1.9 1.88 -6 -6.4 Very less 3 2.8
1 7.8 8.01 -10.7 -10.9 0.123 0.12 1.72 1.74
2 8.9 8.98 -16.2 -16.26 0.15 0.155 1.36 1.4
9.6 9.58 -21 -21.89 0.2 0.25 1.2 1.28
3 16.7 16.9 -28.2 -28.26 1.56 1.5 1.1 1.12
18.3 18.0 -17 -17.06 0.44 0.48 1.34 1.39
19.6 19.2 -25.2 -25.28 0.8 0.83 1.1 1.12
22.2 22.56 -24.3 -24.39 0.48 0.492 1.13 1.15

From this table it is clear that:

 The resonant frequency increases with increase in the number of iterations.

 The multiband behavior is obtained as the numbers of iterations are increased (at 2nd & 3rd iteration in this
case).
 The return losses improve as the number of iterations increase.
 The bandwidth of the antenna gets increased too with increase in the number of iterations.
 Improvement in VSWR is also observed with increase in iterations.

Thus a multiband antenna resonating at multiple frequencies is obtained by applying 3 iterations to the triangular
patch. The return losses, bandwidth & VSWR are also improved in this antenna. However overall gain & efficiency
gets reduced. So this antenna exhibits a tradeoff between gain & bandwidth. The obtained theoretical results are in
good agreement with experimental data.

VI. CONCLUSION

ISSN: 0975-5462 6347

 R L Yadav et. al. / International Journal of Engineering Science and Technology
Vol. 2(11), 2010, 6335-6348

In this paper, the triangular fractal antenna upto 3rd iteration has been built & simulated using the Ansoft HFSS 11. It
has been observed that with increase in the number of iterations the bandwidth of the antenna increases & on second
and third iterations the antenna starts showing the multiband behavior. Increase in iterations also led to improvement
is VSWR & return losses. The simulated and experimental results are found to in good agreement. The triangular
fractal antenna is observed to possess multiband behavior similar to the Sierpinski gasket antenna. This new fractal
antenna allows flexibility in matching multiband operations in which a larger frequency separation is required,
hence can be used in cellular & microwave applications

ACKNOWLEDGEMENT

Authors are very thankful to the Dr.S.K. Koul, Professor, CARE, Indian institute of Technology, Delhi, for
providing the testing facility and valuable suggestions for this work.

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