Sectoral sierpinski gasket fractal antenna for wireless LAN applications

Sectoral Sierpinski Gasket Fractal Antenna forWireless LAN Applications

Yogesh Kumar Choukiker,1 Santanu Kumar Behera,1 Rajeev Jyoti2

1 Department of Electronics and Communication Engineering, National Institute of TechnologyRourkela, Rourkela-769008, Odisha, India2 Space Applications Centre, Indian Space Research Organization, Ahmedabad 380015, India

Received 31 March 2011; accepted 31 August 2011

ABSTRACT: A sectoral Sierpinski Gasket fractal (SSGF) antenna is proposed for dual-

band operation with wide-bandwidth covering GPS, DCS-1800, PCS-1800, UMTS, IMT-

2000, Wireless broadband Internet Services (WiBro), Bluetooth, and WLAN bands. The

SSGF antenna consists of volume 65.5 � 27 � 1.6 mm3. To analyze its performance, meas-

urements are carried out. The proposed antenna model exhibits resonances in 1.51–3.39

GHz (2:1 VSWR BW 76.6%) and 5.31–6.32 GHz (2:1 VSWR BW 17.3%) bands with 2.5–5

dBi gain. Very good agreement is obtained between simulation and experimental results.

VC 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22:68–74, 2012.

Keywords: fractal antenna; microstrip antenna; sectoral geometry; Sierpinski gasket; dual-

wideband

I. INTRODUCTION

Designing of multifunctional handsets, which supports both

the cellular and the noncellular communication standards,

is an emerging trend in the wireless communication indus-

try. Internal antennas for such high performance devices

need to be optimally designed to cover the assigned or

designated frequency bands in order to serve the emerging

needs. Additionally, keeping the size and cost of the device

in mind, the antenna should be compact, low-profile, flexi-

ble structure and sit in situ with circuit. Many interesting

antenna designs for dual bands have been studied widely

[1–10]. On the other hand, broadband planar monopole

antennas [11, 12] are good candidates for UWB applica-

tions, but a dual-band antenna with a broad bandwidth is a

rare candidate. A compact dual-band antenna for wireless

access point produces multiple resonances with nearly

omnidirectional radiation patterns, by loading a strip-

monopole with a slotted triangular patch [13]. It consists of

a two-layer design that requires proper alignments making

fabrication a difficult task.

Fractal antennas [14] have features such as small size

and multiband characteristics. Most fractal objects have

self-similar shapes with different scales [15, 16]. The frac-

tal shape is usually obtained by applying infinite number of

iterations using multiple reduction copy machine algorithm

[17]. Sierpinski fractal is a common geometry in the cate-

gory of fractal antenna. Empirical formulas [18, 19] are

available for the resonant frequency of planar monopole

and dipole antennas based on fractal antenna geometry.

As mentioned above, the Sierpinski fractal design is a

self-similar structure. It is designed using the concept in

antenna by Puente et al. [19]. Design and analysis are chal-

lenging problems for fractal antennas. The easy availability

of commercially available EM solvers is the main resource

for design and analysis of fractal antennas. The full wave

analysis [20] is one of the commercially available solvers

used to design the fractal antennas. The flow chart in

Figure 1 shows the conventional fractal antenna design and

analysis methods. The design phase of a fractal antenna

starts with design specification of frequencies. The dielec-

tric material is selected for the design. The full wave solver

is used to find the S-parameter versus frequency behavior of

the antenna. After calculating S-parameter of the structure

satisfactorily, fabrication and measurement could be done.

In this article, a Sectoral Sierpinski Gasket Fractal

(SSGF) antenna for dual wide-band application is pre-

sented. The proposed dual band antenna is developed

from Sierpinski Sectoral shape and is useful for miniaturi-

zation of the antenna structure. The antenna was designed

and optimized using CST microwave Studio based on the

Correspondence to: Y. K. Choukiker; e-mail: [email protected].

VC 2011 Wiley Periodicals, Inc.

DOI 10.1002/mmce.20585Published online 5 December 2011 in Wiley Online Library

(wileyonlinelibrary.com).

68

three-dimensional finite integration time-domain (FITD)

method. A prototype was fabricated, and its characteristics

were measured.

II. SIERPINSKI GASKET DESIGN

The self-similarity is one of the properties that define frac-

tals. Sometimes, self similarity is too tight a concept to

describe the similarities found in several parts of an

object. Often, the smaller copies of the whole structure

are not identical to the whole object but rather distorted,

that is, they might appear skewed or compressed by a dif-

ferent scale factor with respect to a different axis. In this

case, the object is said to be self-affine instead of self-

similar.

Hutchison’s geometrical transformation algorithm [14]

generates many fractal shapes by means of an iterative

procedure. Let W[A] be a transformation over a subset Aof a plane as follows

W A½ � ¼ w1 A1½ � [ w2 A2½ �………… [ wn An½ � (1)

where wi[A] is an affine transformation [11]. An affine

transformation is a composition of linear transformation Eas follows

E ¼ r cosur sinu

�s sinws cosw

� �(2)

if (x,y) is a point in subset A, then the point is transformed

to (x0,y0) in the following way:

x0

y0

� �¼ r cosu

r sinu�s sinws cosw

� �xy

� �þ x0

y0

� �; (3)

where (x0, y0) is the translation point.

A linear transformation is a contraction if 0 < r < 1

and 0 < s < 1. An affine linear transformation is a simi-

larity transformation if it is only composed by contrac-

tions or expansions, rotations, and translation, that is, if r¼ s and u ¼ w. One can iteratively apply Hutchinson

operators to subset A in the following way:

A1 ¼ W A½ �A2 ¼ W W A½ �½ �

..

.

..

.

An ¼ W An�1½ �

(4)

This iterative process is called an iterative function

system (IFS). IFS generate the fractal Sierpinski gasket,

which is shown in Figure 2. It is composed of three simi-

larity transformation.

w1 x; yð Þ ¼ 1=20

0

1=2

� �xy

� �þ 1=4

0

� �(5)

w2ðx; yÞ ¼ 1=20

0

1=2

� �xy

� �þ �1=4

0

� �(6)

w3 x; yð Þ ¼ 1=20

0

1=2

� �xy

� �þ 0

1=2

� �(7)

Figure 1 Conventional design and analysis methods of fractal

antenna.

SSFG Antenna 69

International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce

III. PROPOSED SSGF ANTENNA

The overall graphical representation of recursive proce-

dure for modified SSGF shape is shown in Figure 3. A

simple triangle model of height H with a ¼ 60� is con-

verted into sectoral shape, and a circle with diameter of Dis etched out from the geometry.

Figure 4 shows the design procedure of modified sec-

toral fractal antenna. A perturbed, two-iterated Sierpinski

fractal gasket of flare angle a ¼ 60� with different scale

factors and the SSFG antenna are shown in Figures 4a

and 4b, respectively. Finally, circle with diameter of D is

etched out from the SSFG antenna as shown in Figure 4c.

Here, it is possible to miniaturize the radiating patch by

etching circles.

The geometry and dimensions of the configuration

under investigation are depicted in Figure 5 with different

scale factors (d1 ¼ h1/h2, d2 ¼ h2/h3). The double iterated

modified antenna model is fed with a 50-X microstrip line

(Wf � Lf), which is calculated using eqs. (8) and (9).

eeff ¼ er þ 1

2þ er þ 1

2

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 12 h

w

q264

375 (8)

Figure 2 Stage of the IFS that generates the Sierpinski gasket.

Figure 3 Basic antenna design procedure: (a) basic triangle, (b) sectoral shape, and (c) sector inscribing a circular gap.

Figure 4 Stages of antenna design: (a) perturbed Sierpinski gasket monopole, (b) sectoral shape Sierpinski gasket monopole, and (c)

proposed sectoral Sierpinski gasket fractal (SSFG) monopole.

70 Choukiker, Behera, and Jyoti

International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 1, January 2012

Z0 ¼ 120pffiffiffiffiffiffiffieeff

p wh þ 1:393þ 0:667 ln w

h þ 1:444� �� � (9)

The antenna system consists of two metallic layers

with the antenna printed on top side, over the ground

plane at bottom of the PCB. Table I shows the optimized

geometrical parameters of proposed SSFG antenna. The

selected substrate is FR-4 with dielectric constant er ¼4.4. The thickness of the substrate is hs ¼ 1.6 mm, and

loss tangent tan d ¼ 0.02. The ground plane is a rectangu-

lar sheet on the bottom side of the substrate.

IV. RESONANCE CHARACTERISTICS

The S11 plots of fractal geometry at different stages are

shown in Figure 6. The structure of simple Sierpinski gas-

ket shows multiresonance behavior in the desired range of

frequency. When all the triangles of perturbed fractal

antenna are converted into sectoral shape, multiresonances

occur at 1.76, 3.18, and 5.06 GHz. However, 6.06 GHz is

not approved by FCC for UWB and needs to be notched

out. When circles are etched out from the center of all

sectoral-shaped geometries, resonant frequencies are

shifted to 1.72, 3.07, and 5.8 GHz. It is observed that the

Figure 5 Geometry of proposed SSFG antenna.

TABLE I Dimensions of Proposed Modified FractalAntenna

h1 h2 h3 D Wf Lf W L Lg Wg S

8 13.74 25.24 2.5 1.5 42 27 65.5 40.3 27 26.55

All dimensions in mm.

Figure 6 Return loss characteristics of different stages of

SSFG antennas.

Figure 7 Input impedance loop for the proposed SSFG

antenna.

SSFG Antenna 71

International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce

downward shift in resonant frequency for initial structure

is more comparable with the modified antenna structure.

Figure 7 shows the input impedance (SWR ¼ 2) locus

for both the bands, when circles are etched out from the sec-

toral shape. It is observed that the input impedance of the

proposed SSGF antenna is same for both the bands. It would

be easier to place both loops at the center of the smith chart.

Figure 8 shows the parametric study of circle with dif-

ferent diameters. It is observed that when the diameter of

the circle is increased to the optimum point, upper fre-

quency shifts from 6.06 to 5.8 GHz; a 17.3% bandwidth

centered at 5.8 GHz (5.31–6.32 GHz) is obtained, which

is suitable for WLAN applications.

Figure 9 shows the simulated and measured S11 plots

of the proposed SSGF antenna. It is observed that the sim-

ulation and measurement results are in good agreement

and exhibit dual resonances. The measured �10 dB im-

pedance bandwidth for lower band is 76.7% (1.51–3.39

GHz) and for upper band 17.3% (5.31–6.32 GHz). The

measured bandwidth meets the requirements of many

commercial bands such as GPS (1.51–2.6 GHz), DCS-

1800 (1.71–1.88 GHz), PCS-1800 (1.80–1.99 GHz),

UMTS (1.92–2.17 GHz), IMT-2000 (1.9–2.2 GHz), Wire-

less broadband Internet Services (WiBro; 2.3–2.4 GHz),

Bluetooth (2.4–2.48 GHz), and WLAN (802.11b/g/a)

(2.4–2.485 GHz and 5.31–6.32 GHz).

It can be seen that the SSGF antenna matched approxi-

mately at frequencies [17]

fr ¼ð0:15345þ 0:34 qxÞ c

heðn�1Þn for n ¼ 0

0:26c

hedn for n > 0

;

8><>: (10)

where c is the speed of light, n is the band number (n ¼0, i.e., band 1 and n ¼ 1, i.e., band 2), he is the effective

height of the gasket, n ¼ hnhnþ1

is the ration of the height of

the gasket in the nth iteration to that in the (nþ1) itera-

tion, d is the scale factor 1n

� , x ¼ 0 k ¼ 0

1 k > 0

, and k is

the number of iterations.

Figure 8 Return loss characteristics of circle with different

diameters. [Color figure can be viewed in the online issue, which

is available at wileyonlinelibrary.com.]

Figure 9 Experimental and simulation results for return loss of

SSFG antenna.

Figure 10 Radiation pattern characteristics at (a) 1.72 GHz, (b) 3.07 GHz, and (c) 5.8 GHz. [Color figure can be viewed in the online

issue, which is available at wileyonlinelibrary.com.]

72 Choukiker, Behera, and Jyoti

International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 1, January 2012

For proposed SSFG antenna, the effective height, he ofthe Sierpinski gasket is given by [21]:

he ¼ffiffiffi3

pSe2

(11)

where

Se ¼ Sþ hsðerÞ�0:5(12)

with hs being the thickness of the substrate and S the side

length of SSGF antenna.

V. RADIATION CHARACTERISTICS ANDCURRENT DISTRIBUTION

The simulated E- and H-planes radiation patterns at 1.72,

3.07, and 5.82 GHz are shown in Figure 10. The results,

in general, show that this antenna has a stable monopole

like radiation pattern, which is almost omnidirectional in

XZ and YZ planes at 1.72 GHz. However, the omnidirec-

tional property is degraded when operating frequency

increases. It maybe due to the difference in current distri-

butions on the modified fractal patch. Figure 11 shows the

surface current distribution for the same frequencies where

radiation patterns were observed. It is seen that, for lower

frequency, current is confined to the microstrip feed line

and a small portion of antenna connected to the feed,

whereas for higher frequencies the current moves toward

the tip of the patch.

Table II shows the total efficiency and gain at different

frequencies. The peak gains in the two resonant bands

are2.35 dBi (at 1.72 GHz) and 4.79 dBi (at 5.8 GHz).

VI. CONCLUSIONS

A planar, dual-wideband monopole antenna using a sec-

toral fractal concept is designed and simulated. The mea-

surement results of the proposed structure are compared

with simulated results. The design starts using well-estab-

lished principles of Sierpinski Gasket antenna. Then, each

small triangle is converted into an equivalent sector. The

positioning of the frequencies is then tuned by etching out

circles from each sector. The size of the circles deter-

mines how to position the frequencies and is therefore

needed to be optimized. The proposed antenna was fabri-

cated using an inexpensive FR-4 substrate and optimized

for handheld terminals. Proposed Sierpinski gasket

antenna is not only useful for bandwidth enhancement of

the lower resonant frequency but also is suitable for fine

tuning of the higher resonant frequency. The measured

reflection coefficient shows that the proposed antenna

exhibits broad bandwidth (1.51–3.34 GHz and 5.31–6.32

GHz) covering multifrequency bands in WLAN range.

The radiation patterns are approximately omnidirectional.

The gain of proposed antenna is 2.35 dBi at lower reso-

nant band and 4.79 dBi at upper resonant band. Therefore,

the proposed antenna is feasible for use as a low-profile

and low-cost dual-band antenna for supporting various

wireless communication services.

REFERENCES

1. Y.-L. Kuo and K.-L. Wong, Printed double-T monopole

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Figure 11 Surface current distributions at (a) 1.7 GHz, (b) 3.07 GHz, and (c) 5.8 GHz. [Color figure can be viewed in the online issue,

which is available at wileyonlinelibrary.com.]

TABLE II Simulated Total Efficiency and Gain of Proposed Antenna

Frequency (GHz) 1.51 1.72 2.42 3.07 3.39 5.31 5.8 6.32

Gain (dBi) 2.15 2.35 3.234 4.48 4.68 4.08 4.796 5.51

Total efficiency (%) 81.66 96.16 92.68 90.12 91.62 93.11 95.35 90.36

SSFG Antenna 73

International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce

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BIOGRAPHIES

Yogesh Kumar Choukiker is born in

Madhya Pradesh, India. He received the

B.E. degree in Electronics and Commu-

nication Engineering from Rajiv Gan-

dhi Technical University, Bhopal, India

in year 2007 and M.Tech in Telematics

and Signal Processing from National

Institute of Technology, Rourkela, India

in the year 2009. Currently, he is pursuing Ph.D in the Depart-

ment of Electronics and Communication, National Institute of

Technology, Rourkela, India. His areas of interest are Micro-

wave, Microstrip Antenna, Fractal Antenna, and Optimization

Techniques. He is a Student Member of IEEE (USA).

Santanu K. Behera received the B.Sc.

(Engg) degree from UCE Burla, Sam-

balpur University in the year 1990, ME

and PhD (Engg) from Jadavpur Univer-

sity in the year 2001 and 2008, respec-

tively. He is presently working as an

Associate Professor in the Department

of Electronics and Communication

Engineering, National Institute of Technology Rourkela, India.

His current research interests include Planar Antenna; Dielec-

tric Resonator Antenna and Metamaterials. Dr. Behera is a Life

Member of IETE (India), Computer Society of India, Society

of EMC Engineers (India), ISTE (India), and Member of IEEE

(USA). He is a reviewer for ICTACT Journal of Communica-

tion Technology, India and IETE Journal of Research India.

Rajeev Jyoti (IEEE M06, SM07)

received his M.Sc. Physics (1984) and

M.Tech. Microwave Electronics

(1986) from Delhi University. Since

1987, he is involved in the develop-

ment of antennas required for satellite

communication in Space Applications

Centre. Presently, he is Group Director

of Antenna Systems Group, SAC,

ISRO, India. He has more than 24 years experience in devel-

opment of space borne and ground antennas in Space Appli-

cations Centre, Ahmadabad. As a Project Manager of GSAT

1 communication satellite he has successfully delivered

flight model reflector antennas at S and C band. He has been

involved in the development of tracking cum communication

feed systems for various earth station antenna. He has con-

tributed significantly in design, analysis, and development of

microwave antennas namely gridded antenna, multiple beam

antennas, multilayer antenna, and phased array antennas for

INSAT/GSAT, RISAT, DMSAR projects. As a Deputy Pro-

ject Director, RISAT (Antenna), he has successfully deliv-

ered phased array multilayer antenna. He has been awarded

with ISRO Team Excellence Awards, 2007. Mr. Rajeev Jyoti

is Fellow Member of IETE and senior member of IEEE

India. He is Chair of IEEE MTT-AP chapter of Gujarat. He

has published more than 60 papers in various conferences

and referred journals. He has 12 patents to his credit. He was

awarded UN ESA long-term fellowship in Antenna and

Propagation at ESTEC/ESA Noordwijk.

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