European Journal of Scientific ResearchISSN 1450-216X Vol.21 No.4 (2008), pp.700-706© EuroJournals Publishing, Inc. 2008http://www.eurojournals.com/ejsr.htm

Miniature Dipole Antenna Based on theFractal Square Koch Curve

Fawwaz J. JibraelDepartment of Electrical and Electronic Engineering, University of Technology

Baghdad, IraqE-mail: fawaz_eng2007@yahoo.com

Abstract

This paper presents the analysis and design of a small size, low profile and multiband square Koch fractal dipole antenna. The proposed antenna design, analysis and characterization has been performed using the method of moments (MoM) technique. The new designed antenna has operating frequencies of 467 MHz, 1326 MHz, and 4884 MHz with acceptable bandwidth, which has useful applications in communication systems. The radiation characteristics, VSWR, reflection coefficient, and input impedance of the proposed antenna are described and simulated using 4NEC2 software package. Also, the gain of this proposed antenna is calculated and described in the three planes: XZ-plane, YZ-plane, and XY-plane, where the antenna is placed in the YZ-plane.

Keywords: Koch curve, fractal antenna, dipole antenna, multiband antenna

1. IntroductionThe booming progress of wireless systems and the dramatic development of a variety of wireless applications have remarkably increased the demand for multiband antennas. While traditionally different antennas are used for different frequency bands, recent studies have suggested that the antennas of certain configurations may operate in several frequency bands at the same time. Multi-band and wideband antennas are desirable in personal communication systems, small satellite communication terminals, radar and other wireless applications [1].

Recently, a variety of fractal designs for multiband antenna have attracted much attention [2-3]. Fractal was first defined by Benoit Mandelbrot [4] in 1975 as a way of classifying structures whose dimensions are not whole numbers. These geometries have been used previously to characterize unique occurrences in nature that were difficult to define with Euclidean geometries, including the length of coastlines, the density of clouds, and branching of trees. Fractal antennas have been demonstrated to enhance antenna properties due to their self-similarity behavior. Multiband behavior for Koch monopole and dipole is demonstrated in [5]. This paper presents the design and simulation a wire dipole antenna based on the second iteration square Koch curve geometry.

2. Proposed Antenna GeometryFigure 1 shows the first three iterations in the construction of the square Koch curve [6]. This curve is simply constructed using iterative procedure beginning with the initiator of the set as the unit line segment (iteration 0). The unit line segment is divided into three segments, and the middle segment is

Miniature Dipole Antenna Based on the Fractal Square Koch Curve 701

removed. The middle segment is then replaced with three equal segments, which are of the same length as the first segment, which form a square (iteration 1). This step is the generator of the curve. At the next step (iteration 2), the middle segment is removed from each of the five segments and each is replaced with three equal segments as before. This process is repeated an infinite number of times to produce square Koch curve. Different from Euclidean geometries, fractal geometries are characterized by their non-integer dimensions. Fractal dimension contains information about the self-similarity and the space-filling properties of any fractal structures [4]. The fractal similarity dimension ( FD ) is defined as:

46.13

5

1

Log

Log

Log

NLogFD

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.

Figure 1: First Three Iterations of the Construction of the Square Koch Curve

Figure 2 shows the second iteration of square Koch curve dipole antenna. The antenna design and simulation have been performed using the 4NEC2 package.

Figure 2: Square Koch Curve Dipole Antenna

702 Fawwaz J. Jibrael

3. Mathematical ModelingThe numerical simulations of the antenna system are carried out via the method of moments. Commercial Numerical Modeling software 4NEC2 is used in all simulations. The NEC is a computer code based on the method of moment for analyzing the electromagnetic response of an arbitrary structure consisting of wires or surfaces, such as Hilbert and Koch curves. The modeling process is simply done by dividing all straight wires into short segments where the current in one segment is considered constant along the length of the short segment. It is important to make each wire segment as short as possible without violation of maximum segment length-to-radius ratio computational restrictions. In NEC, to model wire structures, the segments should follow the paths of a conductor as closely as possible [7].

4. Proposed Antenna DesignThe dipole antenna, based on the second iteration square Koch antenna, has been modeled, analyzed, and its performance evaluated using the commercially available software 4NEC2. The Method of Moment (MoM) is used to calculate the current distribution along the square Koch curve, and hence the radiation characteristics of the antenna [8]. Typical geometry of square dipole antenna is based on the second iteration as shown in Figure 2, where the antenna is placed in the YZ-plane.

The feed source point of this antenna is placed at the origin (0, 0, 0), and this source is set to 1 volt. The design frequency has been chosen to be 750 MHz for which the design wavelength λ is 0.4m (40 cm) then the length of the corresponding λ/2 dipole antenna length will be 20 cm, as shown in Figure 2.

Figure 3 shows the visualization of this dipole antenna geometry by using NEC-viewer software.

Figure 3: Visualization of the Modeled Dipole Antenna Geometry

Miniature Dipole Antenna Based on the Fractal Square Koch Curve 703

5. Antenna Simulation ResultsIn this work, Method of Moment simulation code (NEC) is used to perform a detailed study of VSWR, reflection coefficient, gain, input impedance and radiation pattern characteristics of the square Koch dipole antenna in a free space.

The real and imaginary parts of the input impedance of this proposed antenna are shown in Figure 4 over a frequency range from 0 GHz to 5 GHz. The input impedance characteristics of this proposed antenna show the multiple resonance characteristics of the antenna.

Figure 4: Antenna Input Impedance

VSWR of the antenna is shown in Figure 5. It is found that the antenna has triple bands behavior at the resonance frequencies 467 MHz, 1326 MHz, and 4884 MHz with acceptable bandwidth, at these frequencies VSWR<2.

Figure 5: Simulated 50Ω, VSWR vs. Frequency

Table 1 shows these resonant frequencies and the corresponding input impedance of each one, with VSWR and reflection coefficients, while table 2 shows the gain of each frequency in the three planes XZ-plane, YZ-plane, and XY-plane, where the antenna is placed in the YZ-plane.

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Table 1: Resonant Frequencies and Input Impedances for Proposed Antenna

Input impedance (Ω)Frequency (MHz)

R XVSWR

Reflection coefficient (dB)

467 33.5 j0.656 1.493 -14.11326 29.19 j0.074 1.713 -11.64884 61.96 j0.074 1.239 -19.4

Table 2: The Gain of the Proposed Antenna at the Resonant Frequencies in the Three Planes

Gain (dB)F(MHz)

XY-plane XZ-plane YZ-plane467 2.02 2.02 1.911326 4.84 4.84 1.214884 2.4 2.4 2.92

The radiation patterns at these resonant frequencies in the planes YZ-plane, XZ-plane, and XY-plane are depicted in Figure 6, where the antenna is placed in the YZ-plane.

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Figure 6: Radiation Patterns of the Modeled Antenna at Resonant Frequencies of (a) f= 467 MHz,(b) f= 1326 MHz, (c) f= 4884 MHz.

XY-plane XZ-plane YZ-plane(a) f= 467 MHz

XY-plane XZ-plane YZ-plane(b) f= 1326 MHz

XY-plane XZ-plane YZ-plane(c) f= 4884 MHz

706 Fawwaz J. Jibrael

6. ConclusionsIn this work, the square Koch curve dipole antenna based on the 2nd iteration is investigated and its performance is evaluated. The simulation results show that this antenna can be efficiently operated as a multiband antenna and is compact in size. The proposed antenna has three resonance bands at frequencies of 467 MHz, 1326 MHz, and 4884 MHz, and at these frequencies the antenna has VSWR<2. According to these frequencies, this antenna can operate as a multiband antenna in the UHF/SHF applications.

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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.