222 PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
Wen-Yi Tsai , I-Fong Chen , Chia-Mei Peng , Pei-Cheng Hu ,
Hsu-Hung Tung , and Hsuan-Chi Lin
Department of Electronic Engineering, Institute of Computer and Communication Engineering
Jinwen University of Science and Technology, No. 99, An-Chung Rd., Hsien Tien, Taipei, Taiwan, R.O.C.
Abstract — In this paper, a novel broadband Fractal circular-monopole antenna is presented.
This antenna consists of printed circular iteration with two iterating level and ground-plane with radius 25 mm, making it easy to making it easy to combine directional, high gain and wide bandwidth. A prototype is designed to operate at 1.5 GHz–5.86 GHz, the measured 10 dB bandwidth is nearly 1 : 2 at the center frequency of 3.775 GHz. Experimental results are shown to verify the validity of theoretical work. Fractal monopole antenna is formed with hollow of circle, which featuring of multi-frequency bands and wide bands.
1. INTRODUCTION
The Sierpinski triangle, also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal named after the Polish mathematician Waclaw Sierpinski who described it in year 1916 [1]. Fractal antenna engineering is the field, which utilizes fractal geometries for antenna design. It has become one of the growing field of antenna engineering due to its particular characteristics and advantages over conventional antenna design. An algorithm of the Sierpinski triangle as follows: Any triangle in a plane and canonical Sierpinski triangle uses an equilateral triangle with a base parallel to the horizontal axis (first image). Reduce the size of the triangle to 1 / 2 height and 1 / 2 width, make three copies, and position the three shrunken triangles so that each triangle touches the other two triangles at a corner. Note the emergence of the central hole — because the three shrunken triangles between them can cover only 3/4 of the area of the original. (Central Holes are an important feature and rule of Sierpinski’s triangle). Repeat step 2 with each of the smaller triangles (image 3 and so on). In Fig. 1 was shown iterate level.
For the typical Sierpinski gasket configuration, the patch dimensions from 88 .
9 mm × 88 .
9 mm to
800 mm ground plane, a triangle generator with a scale fractal ratio of 1 / 2 is slotted in the triangle patch to form the monopole antenna [2]. For the modified Sierpinski gasket with 88 .
9 mm × 88 .
9 patch and 25 cm × 25 cm ground plane, a circular generator with a non-constant fractal ratio depending on the Descartes circle theorem is slotted in the triangle patch to form the monopole antenna [3]. Most of the fractal geometries have the characteristics mentioned as above, with various periods that form of fractal structure dimension and self-similarity. Utilization the Sierpinski gasket or carpet geometries characteristic of fractals can be improved and used to design both type of monopole and dipole antennas [4–8]. It has become one of the growing fields of antenna engineering due to its advantages over conventional antenna design. The results suggest a method for perturbing the Sierpinski structure in such way as to control the position of multiple bands where is necessary.
Modified Sierpinski category fractal of circular monopole antenna are plotted and inward iteration in Fig. 2. The antenna overall height of h n is 54 mm. The Sierpinski fractal has the geometrical
Figure 1: Sierpinski triangle iteration, and iterate level by 0 ∼ 5.

Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 223
Circular Disc Initiator
Figure 2: Circular-shaped Sierpinski geometric antennas.
1 st
Iteration 2 nd
Iteration
Figure 3: Circular-shaped Sierpinski geometric antennas, disc, initiator and iterations.
scale factor,
δ = h n +1 h n
= 0 .
33 where h represents the height of sub-generation and n is a natural number represents the number of iterations proposed. The following sections will describe the antenna design, implementation, and the performances of the proposed antenna.
2. BASIC GUIDELINES
The planar fractal monopole antenna is based on the Sierpinski carpet concept and to modified, the Sierpinski fractal has generated two iterations, use the decomposition algorithm by circular, and compare these with integrators and initiator type. Firstly, base on generally circular disc to generate hollow of circular, this initiator has a circumference of Dπ and 1 mm trace width. In the decomposition algorithm, a geometric ratio of circle is taken and joining the midpoints of union of the circles central, reduce the circle to 1/3 diameter and canonical Sierpinski carpet algorithm to fill the circle with twice mathematics equals 1/9 diameter by Sec. iteration, is shown in Fig. 3 the iterate level. The geometrical structure and dimensions of the proposed monopole type antenna is printed on FR4 substrate and is simulated by using FEM based electromagnetic simulator, Ansoft
HFSS.
The Sierpinski gasket is deterministic fractal which generalizes the objects into two dimensions.
A circle in plane will be divided into seven smaller congruent circle of fractal self similar geometrically. The process continuing as long as the limitation of the subdivided is not too small.
However, using Sierpinski gasket equation and the fractal counting Dimension D = 1 .
77, the formula defined by:
N
L n
: Number of self similar objects covers the original object.
n
: Reduce its ratio for the length
Db = lim n →∞
µ ln N n
¶ ln L n
= lim n →∞ log 7 log 3 n n
= lim n →∞ n · log (7) n · log (3)
≈ 1 .
77
Relevant Circular-shaped Sierpinski Fractal antenna information of proposed are summarized include outside circle of the initiator with 27 mm radius, the radius are 9 mm of 1st iteration follow initiator, and the last or 2nd iteration radius are 3 mm. the dimensions of ground plane radius is
25 mm, were shown in Fig. 4.
The antenna has been fabricated on 0.8 mm thick FR4 substrate, mounted on a circle ground plane 25 mm and fed down through the ground with a SMA connector structure, the measured three-axis position define as shown in Fig. 5.
We’ve designed the circular-shaped of monopole antenna based on the Sierpinski gasket geometry are mode in the antenna in order to improve the width-band and radiation pattern, the circular

224 PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
(c)
(b) (d)
(a)
Figure 4: Geometry of the proposed circular-shaped fractal antenna. Dimensions of ground plane radius (a):
25 mm; PCB material: FR-4 with ε r
= 4 used; Circular of diameter (b): 54 mm; Circular of diameter (c):
18 mm; Circular of diameter (d): 6 mm.
Figure 5: Fabricated Sierpinski monopole antenna.
fractal was printed on FR4 and mounted over a radius of 25 mm circle ground plane. The structure was fed through a 1.5 mm diameter, 50 Ω coaxial probe with a SMA connector on the bottom side of the circle plane. The geometrical structure and dimensions of the proposed monopole circularshaped has constructed through three iterations in this particular case and circular disc, Sierpinski gasket and carpet is known as a shelf similar fractals.
Antennas are designed and simulated by using Ansoft HFSS and a prototype is fabricated, the antenna return loss and VSWR is measured, using the Agilent 8753ES Network Analyzer to measure and simulate it responses in 1-6GHz frequency range is demonstrated in Fig. 6. The result we had from simulated and measured test is similar while we observed. It is known from Fig. 6, that to perform width-band characteristics and the second iteration antenna structure covering the frequency range from 1.5 GHz to 6 GHz is best among them. A actual return loss and VSWR is better than − 10 dB and < 2 in 1.5 GHz to 6 GHz in 2nd iteration mode.
3. HELPFUL HINTS
The antenna is built in a monopole configuration over an 25 mm radius of circle ground plane, and antenna structured height 54 mm with FR4 substrate (thickness = 0 .
8 mm, ε r
= 4 .
0). A fifty-ohm coaxial probe directly feeds the driven SMA connector. The resonances the circular-shaped of fractal monopole antenna including 1st and 2nd type of return loss, are shown in Fig. 7(a). In 1st of iteration return loss, the bandwidth and resonances are slightly matching impedance. As the
2nd of iteration, the resonances are very remarkable increased and rich multi-band responses occur in the S
11 spectrum. The measured gain of the antenna at the 1st and 2nd iterations band is given in Fig. 7(b). The table shows the fractal antenna peak gain on 1st and 2nd iterations frequencies resonance point, respectively. The measured antenna gain against frequency and offers a peak gain of 1st and 2nd iterations, it was apparent peak gain that the 2nd iteration more than before models on the same scope.
This 2nd of iteration was appeared multi- and width range from 1.5 GHz ∼ 6 GHz for all ISM band requirement applications. The radiation pattern of iterations antenna were measured inside a 3D anechoic chamber.
The main cuts measured radiation patterns of the antenna at 1st and 2nd iterations are shown in
Fig. 8. All the popular bands measured of antenna radiation patterns appear at the same position that shows the radiation patterns of iterations antennas in the X/Y /Z planes, respectively. The patterns are observed to be nearly Omni-directional in the H -plane, and resonance frequencies span are illustrated in Fig. 8.

Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 225
(a) Initiator
(b) First of iteration
(c) Second of iteration
Figure 6: Simulated and measured of return loss in 1 ∼ 6 GHz range and As defines simulated (Red color) and measured (Blue color).
(a)
Type of Iteration
1 st
Iteration
2 nd
Iteration
Resonant Frequency
(GHz)
Return
Loss(dB )
2.175
3.85
5.275
2.175
3.775
5.35
(b)
-14.03
-21.84
-19.40
-33.13
-27.28
-41.44
Gain
(dBi)
3.8
6.1
4.7
4.5
6.3
6.8
Figure 7: (a) Comparing 1st and 2nd iterations with Return loss and gain. (b) Comparing 1st and 2nd iterations with Return loss and gain.

226 PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
1.575GHz
2.45GHz
3.8GHz
5.2GHz
5.85GHz
Figure 8: Measured peak gain antenna gain for the proposed antenna.
4. CONCLUSION
Both experimental and numerical results on the Sierpinski antenna have been presented. In an actual example, as the Sierpinski fractal geometry into circular structure, use HFSS simulate software to test and analysis, it shows the result is match to fractal characteristic.
All of them describe a multiband behavior of fractal antenna. This behavior is consistent from the input return loss and gain; moreover radiation patterns planes of view. The same scale factor

Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 227 existing among similar structures in the fractal circular-shape. It can be summarized that the self-similarity properties of the fractal structure are translated into its electromagnetic behavior.
The current density distributions have a similar and vary in complicated among bands as well.
Such distributions allows flexibility in matching multi- and width band operations in which a larger frequency required, such as FemtoCell and UMTS base station application including LTE, UMTS,
GPS L1, WIFI, and WiMax. The circular monopole type is based on fractal structure and refer to the Sierpinski gasket self-similarity algorithm, a prototype of the design is successfully implemented with close agreement between measurement and simulation. The fractal geometry and overall size can be effectively utilized ID or Logo surface for integrating with other components in IT products.
ACKNOWLEDGMENT
The authors are appreciated the reviewers for their valuable comments, which is significantly help to this paper, and their colleague, Dr. I-Fong Chen and Dr. Chia-Mei Peng for his assistance and advice during the revision of this paper.
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