A novel multiband Sierpinski Carpet Fractal Antenna for Wireless Communication Systems

Rajeev Mathur#1 Dr. Sunil Joshi*2 #Associate Prof, Department of ECE, Geetanjali Institute of Technical Studies

Dabok, Udaipur India. 1rmathur_2000@yahoo.com

*Associate Professor & Head, Department of ECE, College of Technology & Engineering, MPUAT, Udaipur, India.

2suniljoshi@yahoo.com

Abstract— The paper present a review study of investigating a novel sierpinski carpet fractal antenna of rectangular shape. The performance evaluation of the rectangular Sierpinski Carpet Fractal (SC Fractal) Antenna based on the 3rd iteration is reported. The simulations are performed using IE3D tool and the results show that such an antenna design may be efficiently operated as a multiband antenna with compact size.

The VSWR of the designed antenna is less then 2 for 5 resonant bands 600MHz, 1910 MHz, 3154 MHz, 4181 MHz, 5100 MHz.

Fabrication of antenna is done using FR4 substrate and a compact antenna is physically developed with rectangular shape of dimension 100mm X 150mm showing better results in terms of number of resonant bands, return loss, bandwidth and gain as compared to the existing reported designs. Keywords— Fractal Antenna, Wireless antenna, Sierpinski Carpet, Multiband Antenna, Microstrip Patch.

I. INTRODUCTION Fractal geometries have found an intricate place in science

as a representation of some of the unique geometrical features occurring in nature. Fractals are used to describe the branching of tree leaves and plants, the sparse filling of water vapor that forms clouds, the random erosion that carves mountain faces, that jaggedness of coastlines and bark, and many more examples in nature.[1]

Fig. 1: Fractal geometry. [1] Copyright IEEE

Benoit Mandelbrot first defined the term ‘fractal’, meaning fractional dimension, in 1975 to handle geometries with dimensions that do not fall neatly into a whole number

category. One of the properties of fractals geometry is that it can have an infinite length while fitting in a finite volume.

As we know that a radiation characteristics of any electromagnetic radiator depends on electrical length of the structure.[Balanis] Using the property of fractal geometry, we may increase the electrical length of an antenna, keeping the volume of antenna same. Thus a new configurations for radiators and reflectors my be developed to give better performance in terms of gain, bandwidth etc. It might be possible that fractal geometry antenna give us better performance than any Euclidean geometry could provide.[1] There are an infinite number of possible geometries that are available to try as a design of fractal antenna. One of the important benefit of fractal antenna is that we get more than one band.

Simplest example of antenna of such geometry is given by the Von Koch, researcher. The method of creating this shape is to repeatedly replace each line segment with the following 4 line segments. The process starts with a single line segment and continues for ever. The first few iterations of this procedure are shown in Fig. 2 shows the first five iterations in the construction of the square Koch curve.

Fig. 2.: Koch fractal geometry.

Fractal dimension contains information about the self-similarity and the space-filling properties. The fractal similarity dimension ( FD) is defined as:

Log (N) log (5) FD = ---------- = ---------- = 1.46

Log (1/) log(3)

Where N is the total number of distinct copies, and (1/) is the reduction factor value which means how will the length of the new side be with respect to the original side length. Fractal shapes thus are defined as self similar shapes which are independent of size or scaling. The method of creating this curve is straightforward, there is no algebraic formula that describes the points on the curve.

II. PROPOSED ANTENNA DESIGN

A. Calculation of basic parameters for patch antenna: First of all we have decided the operating frequency band

for fractal antenna. Then we designed a microstrip patch antenna usingfollowing standard formulas.

The width of the patch is calculted by

…. 1 The actual length and effective length of patch antenna is

found as

…. 2

…. 3 Dielectric constant, loss tangent and substrate hieght of designed antenna is choosen as 4.4, 0.025 and 1.588 mm for cheaper FR-4 substrate. W and Leff hence is calculated as 37.43 and 44.51 mm. (chosen as 38 mm X 45 mm).

B. Fractal Antenna design:

Basic patch antenna with resonant frequency of 2.4 GHz is first designed as per the dimensions calculated to be 38mm X 45mm, shown in Fig. 3(a) . 2nd iteration for fractal geometry is calculated as 1/3rd of main patch dimensions (i.e. 12.66mm X 15mm). as shown in Fig. 3(b). Final antenna is designed with the dimension further reduced to 1/3rd of 2nd iteration.

(a)

(b)

Fig. 3. (a) Simple Microstrip patch antenna (b) 2nd interation fractal antenna

This antenna is a simple planar structure with effective permittivity of substrate to be 4.4. Height of substrate is 1.588mm with loss tangent of 0.025. Ground Plane is considered to be infinite for simulation purpose, however, practically ground plane taken is 140mm X150mm. Coaxial

feed is taken for this antenna since geometry does not support CPW feed. SMA connector of @50 ohms is connected at feed point as shown in Fig 4.

Fig. 4: Fractal antenna of third iteration with Lengths L1 = 38mm,

L2=12.66mm, L3=4.22mm and Widths W1= 45mm,W2= 15mm,W3= 5mm. Gap is 4mm and 8mm. Total length Lt = 125mm & Width Wt=100mm.

III. FABRICATION OF PROPOSED ANTENNA A Prototype structure of this antenna is fabricated in the lab

using photolithography technique. Mask of the antenna is prepared and than complete structure is developed as shown in the figure 4. Commonly available substrate FR4 is used with copper cladding of 0.0004mm. Thickness of the substrate is 1.588mm, dielectric constant is 4.4.

Fig 5: Fabricated fractal antenna

Dimensions of the fabricated antenna are as given by Table I.

TABLE I

DIMENSIONS OF FABRICATED ANTENNA IN M.M.

Lt Wt L1 L2 L3 W1 W2 W3 125 100 38 12.66 4.22 45 15 5

IV. RESULTS AND DISCUSSIONS

A. Simulation Results The resonant properties of proposed antenna have been

obtained by designing the antenna structure using commercially available EM softwares tool IE3D. Simulation results are as shown in Fig. 6 & 7. Results shows that there are 5 bands with return loss well below 10 dB, Central frequencies of these bands are mentioned in the Table I. VSWR obtained for these frequencies is found to be of ratio 1:2.

Fig. 6: Return Loss obtained by simulation.

Fig. 7.: VSWR obtained by simulation

We obtain more than one resonant band possibly due to the fact that each small element (Patch) acts as a separate passive radiating element. Each small element contributes towards the increase in electrical length of antenna to increase radiating field E.

Axial ratio of this antenna is observed to be zero, hence it is linearly polarised antenna.

B. Practical Results For the practical investigation of this antenna we have

arranged a laboratory set-up which includes Vector Network Analyser (VNA), Signal Generator, Computer system and antenna. This laboratory setup is as shown in the Fig 8.

VNA was first calibrated using calibration device. Coaxial feed is given to this antenna with SMA connector. S11 parameters are observed on Anritsu VNA Master Vector

Network & Spectrum Analyser. S11 parameters obtained are shown in Fig. 9.

Fig. 8: Laboratory setup for measurement of return loss and VSWR.

Fig. 9: Measurement of return loss on VNA

By comparing the simulated and experimental results we found that there is a close agreement between the two as shown by Table II. The slight variation in results may be due to environmental conditions which could not be considered during simulation. Also during fabrication process, fringing edges of the patches may have irregularities due to which fringing field is disturbed, resulting in shify in resonant frequencies.

We also observed that practically return loss of -35 dB have been observed at the frequency (3.15 GHz) very close to the

frequency for which fundamental patch have been designed i.e. Ist iteration. And then for two bands have been observed below and above this fundamental frequency.

TABLE III

BANDS OBTAINED BY SIMULATION & PRACTICAL TEST RESULTS

It have been observed that as we increase the iterations

number of frequency band also increases. We have observed that by varying the gap between the elements of the patch hardly makes any difference in the radiation characteristics of the entire SC fractal antenna.

V. CONCLUSIONS A novel prototype structure for sierpinski carpet fractal

antenna was developed and proven to be adequate interms of return loss. Five resonant bands have been obtained practically for this antenna. The VSWR of the designed antenna is less then 2 for 5 resonant bands of 600MHz, 1910 MHz, 3154 MHz, 4181 MHz, 5100 MHz.

However, after third iterations in fractal antenna, practically only three band have been reported in the literature. This antenna is capable of resonating at five bands. Designed SC fractal Antenna has possibility of being optimized in terms of return loss and number of narrow frequency bands.

It has been observed that by varying the gap between the elements of the patch or small variations in the geometry of the antenna does not change the frequency characteristics of the antenna. The range of the frequency bands is within the wireless communication bands of Wi-fi, WiMAX, Bluetooth and wireless LAN etc.

ACKNOWLEDGMENT We wish to acknowledge dear students Mr. Swapna, Miss

Pritha for their help in fabrication of this antenna. Mr. Yogendra S Solanki for providing his support in testing the antenna and taking measurements.

References:

[1] T. Tiehong and Z. Zheng, " A Novel Multiband Antenna: Fractal Antenna", Electronic letter, Proceedings of ICCT – 2003, pp: 1907-1910.

[2] D. H. Werner and S. Ganguly, “An Overview of Fractal Antennas Engineering Research”,IEEE Antennas and Propagation Magazine, vol. 45, no. 1, pp. 38-57, February 2003.

[3] J. Gianvitorio and Y. Rahmat, “Fractal Antennas: A Novel Antenna Miniaturization Technique and Applications”, IEEE Antennas and Propagation Magazine, vol. 44, No. 1, pp: 20-36, 2002.

[4] K. Falconer, “Fractal Geometry: Mathematical Foundation and Applications”, John Wiley, England, 1990.

[5] S.H Zainud-Deen, K.H. Awadalla S.A. Khamis and N.d. El-shalaby, March 16-18, 2004. Radiation and Scattering from Koch Fractal Antennas. 21st National Radio Science Conference (NRSC), B8 - 1-9.

[6] P. S. Addison, “Fractals and Chaos: An Illustrated Course”, Institute of Physics Publishing Bristol and Philadelphia, 1997.

[7] G. J. Burke and A. J. Poggio “Numerical Electromagnetic Code (NEC)-Program description”, January, 1981, Lawrence Livermore Laboratory.

[8] C. A. Balanis, “Antenna Theory: Analysis and Design”, 2nd ed., Wiley, 1997. Zoran Jaksic, Nil Dalarsson, Makmovik, “ Negative Refractive Index Metamaterial: Principle & Applications, Jun 2006

[9] 7803-8842-9/05 IEEE International Workshop on Antenna Technology.

Band No

Simulated results Practical Results

Centre Freq.

S11 in dB

Centre Freq.

S11 in dB

I 1.6 -10 0.75 -9 II 1.9 -14 1.98 -11 III 3.1 -18 3.15 -35 IV 3.8 -16 V 4.3 -23 4.18 -14 5.1 -16