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Eng. & Tech. Journal, Vol.28, No.9, 2010

*Electrical and Electronic Engineering Department, University of Technology, Baghdad

1854

Design and Simulation of Linear Array Antenna Using Koch Dipole

Fractal Antenna Elements for Communication Systems Applications

Fawwaz Jinan Jibrael* & Mohanad Ahmed Abdulkareem*

Received on:17/9/ 2009

Accepted on:16/2/2010

Abstract

In this paper, the fractal concept has been used in the linear array antenna

design to obtain multiband operation. The fractal linear array antenna has been

designed at a frequency of 750 MHz with equal spacing and uniform amplitude

distribution of the elements array. 1st iteration quadratic Koch curve dipole fractal

element is used in design of the array. The proposed antenna array design, analysis

and characterization had been performed using the Method of Moment (MoM)

technique. The radiation pattern, side lobe level (SLL), directivity (D), and input

impedance of the proposed antenna are described and simulated using 4NEC2

software package and MATLAB programming language version 7.6.

Keywords: Koch curve, multi-band antenna, dipole antenna, quadratic Koch curve,

linear array antenna.

ﺥﻭﻜ ﻲﺌﺍﻭﻬﻟ ﺔﻴﺌﺯﺠ ﺭﺼﺎﻨﻋ ﻡﺍﺩﺨﺘﺴﺎﺒ ﺔﻴﻁﺨ ﺕﺎﻴﺌﺍﻭﻫ ﺔﻓﻭﻔﺼﻤ ﺓﺎﻜﺎﺤﻤﻭ ﻡﻴﻤﺼﺘ

ﺕﻻﺎﺼﺘﻻﺍ ﺔﻤﻅﻨﺍ ﺕﺎﻘﻴﺒﻁﺘﻟ ﺏﻁﻘﻟﺍ ﻲﺌﺎﻨﺜ

ﺔﺼﻼﺨﻟﺍ

ﺕﺎﻴﺌﺍﻭﻬﻠﻟ ﺔﻴﻁﺨﻟﺍ ﺕﺎﻓﻭﻔﺼﻤﻟﺍ ﻡﻴﻤﺼﺘ ﻲﻓ ﺔﻴﺌﺯﺠﻟﺍ ﺔﺴﺩﻨﻬﻟﺍ ﺓﺭﻜﻓ ﻡﺍﺩﺨﺘﺴﺍ ﺙﺤﺒﻟﺍ ﺍﺫﻫ ﻲﻓ ﻡﺘ

ﺩﺩﺭﺘ ﻥﻤ ﺭﺜﻜﺍ ﻰﻠﻋ لﻤﻌﺘ ﺕﺎﻴﺌﺍﻭﻫ ﻰﻠﻋ لﻭﺼﺤﻠﻟ ﻙﻟﺫﻭ

.

ﻴﻤﺼﺘ ﻡﺘ

ﺔـﻴﺌﺯﺠﻟﺍ ﺕﺎـﻴﺌﺍﻭﻬﻟﺍ ﺔﻓﻭﻔﺼﻤ ﻡ

ﻪﻓﻭﻔﺼﻤﻟﺍ ﺭﺼﺎﻨﻌﻟ ﺔﻴﻭﺎﺴﺘﻤ ﺕﺎﻓﺎﺴﻤﻭ ﺔﻴﺫﻐﺘ ﻊﻤ

.

ﻲـﻓ لﻜـﺸﻟﺍ ﻊـﺒﺭﻤ ﺥﻭﻜ ﻲﻨﺤﻨﻤ ﻉﻭﻨ ﻥﻤ ﺏﻁﻘﻟﺍ ﺔﻴﺌﺎﻨﺜ ﺔﻴﺌﺯﺠ ﺭﺼﺎﻨﻌﻟ لﻭﻻﺍ ﺭﺍﺭﻜﺘﻟﺍ ﻡﺍﺩﺨﺘﺴﺍ ﻡﺘ

ﺠﻨﺍ ﻪﺤﺭﺘﻘﻤﻟﺍ ﺕﺎﻴﺌﺍﻭﻬﻟﺍ ﺔﻓﻭﻔﺼﻤ لﻴﻠﺤﺘﻭ ﻡﻴﻤﺼﺘ ﻥﺍ

ﺔﻴﻨﻘﺘ ﻡﺍﺩﺨﺘﺴﺎﺒ ﺕﺯ

ﺔﻴﺒﻨﺎﺠﻟﺍ ﺹﻭﺼﻔﻟﺍ ﻯﻭﺘﺴﻤ ،ﻉﺎﻌﺸﻟﺍ ﻁﻤﻨ ﻑﺼﻭﻭ ﺓﺎﻜﺎﺤﻤ ﻡﺘ

(SLL)

ﺔﻴﻬﻴﺠﻭﺘﻟﺍ ،

ﺔـﻴﺠﻤﺭﺒﻟﺍ ﺔﻐﻠﻟﺍ ﻡﺍﺩﺨﺘﺴﺎﺒ ﺕﺎﻴﺌﺍﻭﻬﻟﺍ ﺔﻓﻭﻔﺼﻤﻟ لﻭﺨﺩﻟﺍ ﺔﻌﻨﺎﻤﻤﻭ ،

MATLAB

ﺔﺨـﺴﻨﻟﺍ

7.6

ﻲﻤﻴﻤﺼﺘﻟﺍ ﺩﺩﺭﺘﻟﺍ ﺩﻨﻋ ﺔﻴﻁﺨﻟﺍ

750 MHz

ﺕﺎﻴﺌﺍﻭﻬﻟﺍ ﺔﻓﻭﻔﺼﻤ ﻡﻴﻤﺼﺘ

(MoM)

.

.

ﻡﻭﺯﻌﻟﺍ

(D)

ﺞﻤﺎﻨﺭﺒﻟﺍﻭ

4NEC2

.

1. Introduction

A wide variety of applications of

fractals can be found in many branches

of science and engineering. One such

area is fractal

Fractal geometry can be combined

with the electromagnetic theory for the

purpose of investigating a new class of

radiation, propagation and scattering

problems [1].

One of the most promising

areas of fractal

electrodynsamics.

electrodynamics

research is in its application to antenna

theory and design. There are a variety

of approaches that

developed over the years, which can

be utilized to achieve one or more of

these design objectives pertaining to

size, gain, efficiency and bandwidth.

Unique properties of fractals can be

exploited to develop a new class of

antenna element designs that are multi-

band, compact in size and can possess

several highly desirable properties,

have been

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Eng. & Tech. Journal ,Vol.28, No.9, 2010 Design and Simulation of Linear Array Antenna

Using Koch Dipole Fractal Antenna Elements

for Communication Systems Applications

1855

including multi-band performance, low

side lobe levels, and their ability to

develop rapid

algorithms based on the recursive

nature of fractals [2].

Fractal shapes radiate signals

at multiple frequency bands, occupy

space more efficiently and offer design

solutions meeting the requirements for

antennas in future wireless devices

such as cell phones and other wireless

mobile devices such as laptops on

wireless local area networks (LANs)

[1].

In many applications it is

necessary to design antennas with very

directive characteristics (very high

gains) to meet the demands of long

distance communication; this can be

accomplished by antenna array [3].

The increasing range of wireless

telecommunication

related applications is driving the

attention to the design of multi-

frequency (multiservice) and small

antennas. This can

through the use of fractal concepts in

the design and analysis of arrays by

either analyzing the array using fractal

theory or by placing elements in fractal

arrangement or considering them both

[4]. Fractal arrangement of array

elements can produce a thinned array

and can achieve

performance.

2. Linear Array Antenna

An array is usually comprised of

identical elements positioned in a regular

geometrical arrangement. A linear array

of isotropic elementsN , uniformly

spaced, a distance d apart along the z-

axis, is shown in Figure (1) [5].

The array factor corresponding to this

linear array may be expressed in the

form [3]

beam forming

services and

be achieved

multi-band

For ( N

elements

2

where

y

=

AF

=

d

aq

+

) cos(

kd

( )=

y

Spacing

elements in the array

=

The progressive

between elements

p

2

The wave number

= Phase delay

The array factor

between adjacent

a

phase shift

==

l

k

=

q

Elevation angle

3. Quadratic Koch Curve Fractal

Element

In this paper, the quadratic Koch

curve is taken as an example of fractal

element antenna that has multi-band

characteristics [6].

Figure (2) contains the first three

iterations in the construction of the

quadratic Koch curve. This curve is

generated by repeatedly replacing each

line segment, composed of four

quarters, with the generator consisting

of eight pieces, each one quarter long

[7]. Each smaller segment of the curve

is an exact replica of the whole curve.

There are eight such segments making

up the curve, each one represents a

one-quarter reduction of the original

curve. Different

geometries, fractal geometries are

characterized by their non-integer

dimensions.

Fractal dimension

information about the self-similarity

and the space-filling properties of any

fractal structures [8]. The fractal

similarity dimension (FD ) is defined

as [7]:

from Euclidean

contains

For (

elements

12

+

N

)

…..(1)

2

)

( )=

y

AF

()

−

+

∑

=

n

∑

=

n

y

y

12

cos 2

cos2

1

1

0

n

a

naa

N

n

N

n

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Eng. & Tech. Journal ,Vol.28, No.9, 2010 Design and Simulation of Linear Array Antenna

Using Koch Dipole Fractal Antenna Elements

for Communication Systems Applications

1856

( )

(

1

)

( )

( )

4

5 . 1

=

log

8 log

log

log

==

e

N

FD

Where N is the total number of distinct

copies, and ( e

1

) is the reduction

factor value which means how will be

the length of the new side with respect

to the original side length.

4. Mathematical Modeling

The numerical simulations of the

antenna system are carried out via the

method of moments.

modeling commercial software 4NEC2

is used in all simulations. The NEC is

a computer code based on the method

of moment for

electromagnetic response

arbitrary structures 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

segment length

computational restrictions. In NEC, to

modeling a wire

segments should follows the paths of

conductor as closely as possible [9].

5. Proposed Linear Array Antenna

Design

The linear array antenna with

equal spacing between array elements

has been modeled, analyzed, and its

performance has been evaluated using

the commercially available software

4NEC2, where the first iteration

quadratic Koch fractal antenna is used

as an array element. The Method of

Moment (MoM) is used to calculate

the input impedance of each element in

the proposed array.

programming language (version 7.6) is

used to calculate the radiation pattern

Numerical

analyzing the

an of

of maximum

radius to ratio

structures, the

MATLAB

and radiation properties at each

operating frequency. The layout of this

antenna array with respect to the

coordinate system is shown in Figure

(3).

The linear array consist of four

fractal antenna elements, as shown in

Figure (3) and designed at a frequency

750 MHz (λ0 = 40 cm), with

quarter-wavelength (d = λ0/4)

spacing between

elements with progressive phase shift

between elements ( α) equal to zero.

The total element length is equal to

λ0/2 (20cm).

Each array element is fed at its center

point with uniform amplitude feeding

coefficients. The array structure in

three dimensions is shown in Figure

(4).

6. Computer Simulation Results

The real and imaginary parts of the

input impedance of this array antenna

are illustrated in Table (1).

It is clear from Table (1) that the

proposed linear

possesses many resonant frequencies

some of which has high resistance

more than 50 Ohm.

The radiation patterns at these

resonant frequencies

demonstrated as in Figure (5), while

the results of the radiation properties

(D, SLL) are listed in Table (2).

7. Conclusions

From the figures and tables, the

following points can be noticed:

1. Number of resulting resonant

frequencies is much greater than

the number

frequencies of the fractal element,

where some of these resonant

frequencies are close to each other.

These resonant frequencies when

added to the element design

frequency (750MHz in our case)

yielding a new group of resonant

adjacent array

array antenna

have been

of resonant

(2)

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Eng. & Tech. Journal ,Vol.28, No.9, 2010 Design and Simulation of Linear Array Antenna

Using Koch Dipole Fractal Antenna Elements

for Communication Systems Applications

1857

frequencies that are also close to

each other.

2. Multiple groups

frequencies are appears to be

approximately the same from the

radiation pattern

impedance point of view.

These groups are clearly noticed in

table (1) with different colors.

3. The best field pattern is obtained

when the resonant frequencies are

approximately (0.6 to 3.2) times

the element design frequency.

4. SLL is reduced when the resonant

frequencies are less than the array

design frequency

distance between array elements

will be less than one wavelength,

while the SLL is increased when

the resonant frequency becomes

higher than the array design

frequency since

between array elements will be

higher than one wavelength.

References

[1] F. J. Jibrael, H. A. Hammas,

“Analysis and Design of Combined

Fractal Dipole Wire Antenna”,

Iraqi Journal of Applied Physics

(IJAP), vol. 5, no. 2, pp. 29-32,

April 2009.

[2] M.Sindoy, G.Ablat, C.Sourdois,

“Multiband

properties of

branched antennas”, Electronics

Letters, Vol. 35, 1999, pp. 181-182.

[3] C. A.Balanis, “Antenna Theory:

Analysis and Design”, 3rd ed.,

Wiley, 2005.

[4] V.F.Kravchenko, “The theory of

fractal antenna arrays”, Antenna

Theory and Techniques IVth Inter.

Conf., Vol. 1, 2003, pp. 183- 189.

[5] R. T. Hussein, F. J. Jibrael,

“Comparison of the Radiation

Pattern of Fractal and Conventional

Linear Array Antenna ”, Progress

of resonant

and input

since the

the distance

and wideband

fractal printed

In

Letters (PIERL), Vol. 4, pp: 183-

190, 2008.

[6] F. J. Jibrael, F. F. Shareef, W. S.

Mummo, “Small Size and Dual

Band of a Quadratic Koch Dipole

Fractal Antenna

American Journal of Applied

Sciences, Vol. 5, no. 12, pp: 1804-

1807, 2008.

[7] Paul S. Addison, “Fractals and

Chaos”, Institute

Publishing. The

Physics, London, 1997.

[8] K. Falconer, “Fractal Geometry:

Mathematical Foundation and

Applications”,

England, 2003.

[9] G. J. Burke, A. J. Poggio

“Numerical Electromagnetic Code

(NEC)-Program

January, 1981,

Livermore Laboratory.

Electromagnetics Research

Design”,

of

Institute

Physics

of

John Wiley,

description”,

Lawrence

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Eng. & Tech. Journal ,Vol.28, No.9, 2010 Design and Simulation of Linear Array Antenna

Using Koch Dipole Fractal Antenna Elements

for Communication Systems Applications

1858

Table (1) Input impedance for the right

hand side of the proposed antenna array

Table (2) Radiation properties of the

proposed antenna array

Figure (1) Linear array geometry of

uniformly spaced isotropic sources [5]

Figure (2) First three iterations of the

construction of the quadratic Koch

curve [7]

a) Element configuration

f (MHz) Z1 ( Ω ) Z2 (Ω)

445 5.47-j58.5 87.53+j4.57

467 64.14+j2.2455 49.1-j55

500 77.5+31.9 85.52-j0.71

1280 90.78-j0.34 76.2-j23.2

1294 96.7+j22.6 84.87-j0.28

1988 117-j27.9 83.96+j0.56

2016 132.8+j0.027 90.1+j33.4

2352 529.4+j0.544 183-j722

2700

2726

178-j26.7

194-j0.7

149.7-j0.37

164+j24.9

2950 526.8+j0.134 565+j70.3

2972 550-j53.7 607.9-j0.39

f (MHz) D (dB) SLL (dB)

445

467

4.52

4.69

-14.34

-12.84

500 5.04 -12.17

1280 8.29 -4.36

1294 7.95 -3.62

1988

2016

2352

10.39

10.43

10.63

-6.86

-6.8

-6.16

2700 8.55 -1.33

2726 8.09 -0.8698

2950 8.55 -3.08

2972 8.63 -3.42

Iteration 0

Iteration 2

Iteration 3

Iteration 1

Generator

Initiator

0.5d

x

z

1.5d

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