A New Fractal Multiband Microstrip Patch Antenna Design forWireless Applications

Jawad K. Ali

Department of Electrical and Electronic Engineering,

University of Technology, P.O. Box 35239, Baghdad, Iraq

jawengin@yahoo.comEmail:

AbstractIn this paper, a new compact multiband patch microstrip antenna design is

presented as a candidate for use in modern multi-functions communication systems. Theproposed antenna design is fractally generated using Koch fractal curve geometryapplied to the conventional square microstrip patch antenna. Antenna structuresresulting from the successive iterations in the proposed fractal generation process showa considerable size reduction compared with the conventional microstrip patch antennadesigned at the same frequency using the same substrate material specifications.Simulation and theoretical performance of the resulting antenna structurescorresponding to the different fractal iteration levels have been carried out using methodof moments (MoM) based software package IE3D, which is widely used in the fields ofmicrowave research and industry. Simulation results have proved the multi-resonantbehavior of the presented antenna structures besides the considerable size reductiongained. The results also show that these antenna structures possess adequate radiationperformance.

Keywords: Microstrip patch antenna, antenna miniaturization, fractal antenna,multiband antenna, Koch fractal curve geometry, L-probe feed.

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INTRODUCTION

The term fractal, which means brokenor irregular fragments, was originally coinedby Mandelbrot (1983) to describe a familyof complex shapes that possess an inherentself-similarity in their geometricalstructures. Since then, a wide variety ofapplications for fractal has been found inmany areas of science and engineering. Onesuch area is fractal electrodynamics(Jaggard, 1990, a, b) in which fractalgeometry is combined with electromagnetictheory for the purpose of investigating a newclass of radiation, propagation, andscattering problems. One of the mostpromising areas of fractal electrodynamicsresearch is its application to the antennatheory and design.

Another prominent benefit that has beenderived from using fractal geometries inantenna has been to design for multipleresonances (Gianvittorio, 2003; Jaggard,1990b). Fractals are complex geometricshapes that repeat themselves, and are thusself similar. Because of the self-similarity ofthe geometry due to the iterative generatingprocess, the multiple scales of the recurringgeometry resonate at different frequencybands.

Fractals represent a class of geometrieswith very unique properties that can beattractive for antenna designers. Fractalspace filling contours, meaning electricallylarge features can be efficiently packed intosmall area .Since the electrical lengths playsuch an important role in antenna design,this efficient packing can be used as viableminiaturization technique. The space fillingproperties lead to curves that are electricallyvery long, but fit into a compact physicalspace. This property can lead to theminiaturization of antenna elements (Cohen,2005).

Microstrip antennas offer manyadvantages such as low profile, the ease offabrication, and the low cost. These make

them very popular and attractive for thedesigners since the early days they appear.In many cases, where the antenna size isconsidered an important limitation, theirlarge physical size, make them improper tobe used in many applications. Severalmethods have been considered to reduce theantenna size such as the use of shortingposts (Kumar and Ray, 2003), materialloading and geometry optimization(Shrivervik, et al., 2001). Use of slots withdifferent shapes in microstrip patch antennashad proved to be satisfactory in producingminiaturized elements (Kosiavas, et al.,1989; Palaniswamy and Crag, 1985; Chen,2006). Recently more research works havebeen devoted to make use of the space-filling property of some fractal objects toproduce miniaturized antenna elements (El-Khamy, 2004).

In this paper, a novel pre-fractalmicrostrip patch antenna design has beenpresented as a candidate for use in themodern compact and multi-functioncommunication systems. The proposedstructure has been generated based on thesquare patch (the initiator) by applying theKoch fractal curve as the generator. Thegenerator is composed of four segments withequal length, Fig.1a. The proposed antennais expected to possess a considerableminiaturization owing to its remarkablespace filling property. The proposed fractalmicrostrip antenna structures exhibit amultiband behavior depending on the degreeof self-similarity involved in itssubstructures.

ANTENNA GENERATION PROCESS

The starting pattern for the proposedantenna as a fractal is the square patch, Fig.1b. From this starting pattern, each of thefour sides of the starting pattern is replacedby the generator shown in Fig. 1a. Todemonstrate the process the first fourth

12

12

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21(

nn

n

n AA

iteration steps are shown in Fig.1. The firstiteration of replacing a segment with thegenerator is shown in Fig. 1c. The startingpattern is Euclidean and, therefore, theprocess of replacing the segment with thegenerator constitutes the first iteration. Thegenerator is scaled after such that theendpoints of the generator are exactly thesame as the starting line segment. In thegeneration of the true fractal the process ofreplacing every segment with the generatoris carried out an infinite number of times.The resulting pre-fractal structure has thecharacteristic that the perimeter increases toinfinity while maintaining the volumeoccupied. This increase in length decreasesthe required volume occupied for the pre-fractal antenna at resonance. It is found that:

(1)

where, Pn is the perimeter of the nth iterationpre-fractal structure. Theoretically as n goesto infinity the perimeter goes to infinity. Theability of the resulting structures to increaseits perimeters in the successive iterationswas found very triggering for examining itssize reduction capability as a microstripantenna. It has been concluded that thenumber of generating iterations required toreap the benefits of miniaturization is onlyfew before the additional complexitiesbecome indistinguishable (Gianvittorio, 2003;Gianvittorio and Rahmat-Samii, 2002 ).

The presence of the irregular radiatingedges in these pre-fractal antennastructures is a way to increase the surfacecurrent path length compared with that ofthe conventional square patch antenna, Fig.1b; resulting in a reduced resonantfrequency or a reduced size antenna if thedesign frequency is to be maintained.

The length Lo of the conventional squarepatch antenna, Fig.1a, has been determinedusing the classical design equations reportedin the literatures (Bahl and Bhartia, 1980;James and Hall, 1989) for a specified value of

the operating frequency and given substrateproperties. This length representsapproximately half the operatingwavelength. As shown in Fig 1, applyinggeometric transformation of the generatingstructure (Fig. 1a) on the square patchantenna (Fig. 1b), results in the patchantenna (Fig. 1c) .Similarly successiveantenna shapes, corresponding to thesubsequent iterations can be produced assuccessive transformations have beenapplied (Fig.1d-f).

At the n-th iteration, the correspondingpre-fractal enclosing area, An, has been foundto be:

(2)

The dimension of a fractal provides adescription of how much a space it fills(Falconer, 2003). It is a measure of theprominence of the irregularities whenviewed at very small scales. A dimensioncontains much information about thegeometrical properties of a fractal. It ispossible to define the dimension of a fractalin many ways, some satisfactory and otherless so. It is important to realize thatdifferent definitions may give differentvalues of dimension for the same fractalshape, and also have very differentproperties (Falconer, 2003; Peitgen, et al.,2004).

The fractal dimensions of the fractallygenerated structures up to the 2nd iterationhave been calculated using the box countingmethod. Box counting is one of the mostwidely used methods to determine the fractaldimension. Its popularity is largely due to itsrelative ease of mathematical calculationand empirical estimation [Baumann,2005].Fractal dimensions structures withzero, 1st, and 2nd iterations have been foundto be 2, 1.93, and 1.92 respectively. It isworth to note here that the dimension of thezero iteration structure (square) is 2, whichis integer number. That is because this

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1(2

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1

0Lhrr

eff

rf

cL

00 2

Lf

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structure is Euclidean and not a fractal,while other non-integer dimensions assurethe fractal geometry of their correspondingstructures.

THE PROPOSED ANTENNA DESIGN

The calculations of the square microstrippatch antenna length are based on thetransmission-line model (Ammam, 1997).The length Lo is slightly less than a halfwavelength in the dielectric. The calculationof the precise value of the dimension Lo iscarried out by an iterative procedure. Aninitial value of Lo is obtained using:

, (3)

where, fo is the design frequency, εr is therelative dielectric constant of the microstripsubstrate, and c is the velocity of light. Avalue for the effective relative dielectricconstant εeff, with a patch width, Wo tosubstrate height ratio Wo/h≥1, by means ofEqu.6 for the square patch antenna (Bahl andBhartia, 1980; James and Hall, 1989):

(4)

where, h is the substrate height. With thevalue of εeff, calculated by Equ.4, the fringefactor ∆Lo may now be calculated using:

(5)

Finding the value of ∆Lo, then, Lo can becalculated by:

(6)

The substrate used in the modeling theentire antenna structures presented in thispaper, has a relative dielectric constant of2.2 and substrate height of 1.575 mm. Withthis substrate, the value of Lo, at a designfrequency of 2.4 GHz, is found to be ofabout 41.35 mm.

Equ.1 predicts larger lengths for the 1st

and the 2nd iteration antenna structures. This,of course, leads to reduced resonancefrequencies. In this paper, the modelingprocess is planed to maintain the designfrequency of 2.4 GHz, which means reducedsizes have to be obtained. Accordingly, theresulting patch lengths are found to be 31.01mm and 23.25 mm respectively. Thecorresponding values of patch widths arefound to be 31.83 mm and 23.87 mmrespectively, taking into account theprescribed range of the orthogonaldimensions ratio. The resulting dimensionsindicate that the these patch antennaspossess size reductions of about 43.75% and68.38% respectively compared with theconventional square patch antenna.

As in the case of the conventionalrectangular patch antenna, the use asubstrate with a higher relative dielectricconstant would result in a more sizereduction. The length, Lo, is inverselyproportional to the square root of the relativedielectric constant of the substrate material,εr [Bahl and Bhartia, 1980; Kumar and Ray,2003].

At the design frequency, the dimensionsof five antenna structures, corresponding tothe initiator and the first four fractaliterations, have been calculated. Thesedimensions and the corresponding sizereduction percentages are summarized inTable I, using the prescribed substrateparameters. Table I demonstrates how theproposed design technique is powerful ingetting interesting size reductionpercentages with few iterations.

)813.0/)(258.0()262.0/)(333.0(

412.00

hW

hWhL

eff

eff

TABLE ISummary of the dimensions and the size reductionpercentages of the pre-fractal antennas up to 4th iteration

AntennaType

Ln

(mm)Wn

(mm)Size

Reduction %

Square patch0 iteration

41.35 42.45 -----

1st iteration 31.01 31.83 43.752nd iteration 23.25 23.87 68.383rd iteration 17.44 17.90 82.214th iteration 13.08 13.43 89.98

PERFORMANCE EVALUATION

For comparison purposes, theconventional square microstrip patchantenna has been analyzed,( considered toconstitute the zero iteration structure.),together with the resulting pre-fractalantenna structures resulting from the 1st and2nd iterations using the commerciallyavailable software IE3D, from ZelandSoftware Inc. This EM simulator carriesout the performance evaluation of 3Delectromagnetic structures using the methodof moments (MoM).

Microstrip patch antennas arecharacterized by its moderate gain. The gaindepends amongst many other parameters, onthe physical aperture of the antenna. Sincethis work aims to present compact sizeantennas, the use of the conventional coaxialprobe feed will result in poor radiationperformance. To enhance the proposedantenna performance, a special feedingtechnique has been used. This technique iscalled the L-probe feed [Hazdra and Mazanek,2006; Mak, et al., 2002]. In this technique, anair-gap is inserted between the lower side ofantenna substrate and its ground plane. Theprobe is placed in the air-gap and it is composedof two parts; vertical and horizontal. Thehorizontal part is beneath and parallel to thesubstrate, while the vertical one is attached tothe ground plane from one side and to thehorizontal part from the other side forming an L-shaped feeding structure. Tuning of both the

vertical and the horizontal lengths of the probeleads to the best matching condition, and hencethe optimal antenna radiation performance canbe obtained.

Each of the modeled antennas is located atthe point (0,0,0) with respect of thecoordinate system and fed with an L-probefeed as depicted in Fig.2, where the 2nd

iteration fractal microstrip patch antenna isshown. Fig.3 shows the return loss responseof the conventional square (zero iteration)patch antenna fed with an L-probe having avertical length of 8.0 mm and a horizontallength of 21.5 mm. Fig.3 indicates that thisantenna produces a single resonance at the2.4 GHz design frequency with a bandwidthof about 0.7 GHz, which is considerablygreater than that of the same antenna whenfed by the conventional coaxial probe.Figs.4 and 5 show the Eθ and Eφ and thetotal E-field radiation patterns respectively,while Fig.6 show the 3-D radiation pattern atthe design frequency. It is obvious that thesquare patch antenna exhibits satisfactoryradiation characteristics as compared withthe conventional probe feed.

Similarly, the performance curves of the1st and 2nd iteration fractal microstrip patchantenna are depicted in Figs.7-13 andFigs.14-20 respectively. Return lossresponses for these antennas are shown inFig.7 and Fig.14 respectively. Thecorresponding responses clearly demonstratethe multi-frequency behavior of these twoantennas. This doesn’t prevent thepossibility of existence other resonancesbeyond the modeling frequency range. Theresonances are expected to increase withfurther iterations. Figs.10, 13, 17, and 20points out to the radiating parts responsibleto the corresponding resonance.

CONCLUSION

A novel fractal patch antenna designbased on Koch fractal curve has beenpresented in this paper, for use in themodern multiband compact wireless

applications. The proposed antenna structureshowed high degree of self-similarity andspace-filling properties.

The resulting antenna structures hadshown to possess size reductions of about43.75% and 68.38%, for the first and seconditerations respectively. These size reductionsare expected to be developed further to82.21% and 89.98% for antenna structurescorresponding to the 3rd and 4th iterations. Itis expected that the antenna presented inthis paper will have a variety of applicationsin wireless applications.

It has been found that the modeledfractal antennas have a multi-resonancebehavior with more than sufficient fractionalbandwidths for most of the wirelessapplications as a result of employing an L-probe feed. Careful tuning of the feedvertical and horizontal parts has been foundhelpful in getting best matching conditionsin a considerably reliable manner.

Additional work could be carried out toexplore its performance in many wirelessmobile applications, where the production ofcircular polarization with acceptable axialratios through the specified bandwidthsrepresents a serious requirement, besides theminiaturization and the multi-frequencyperformance.

REFERENCES

Ammam, M., 1997. Design of RectangularMicrostrip Patch Antennas for 2.4 GHzBand, Applied Microwave and Wireless.

Bahl, I.J. and P. Bhartia, 1980. MicrostripAntennas, Dedham, MA: Artech House.

Baumann, G., 2005. Mathematica forTheoretical Physics; Electrodynamics,Quantum Mechanics, General Relativity,and Fractals, Second Edition, Springer-Verlag New York.

Chen, W.S., 2006. A Novel Broadband Designof a Printed Rectangular Slot Antenna forWireless Applications, Microwave Journal,Reprinted by Horizon House Publications,Inc.

Cohen, N., 2005. Fractal’s New Era in MilitaryAntennas, Journal of RF Design, pp: 12-17.

El-Khamy, S.E., 2004. New Trends in WirelessMultimedia Communications Based onChaos and Fractals, 21st National RadioScience Conference (NRSC2004), pp: INV11 -25.

Falconer, K., 2003. Fractal Geometry;Mathematical Foundations and Applications,Second Edition, John Wiley and Sons Ltd.

Gianvittorio, J.P. and Y. Rahmat-Samii, 2002.Fractal Antennas: A Novel AntennaMiniaturization Technique, andApplications, IEEE Antennas andPropagation Magazine, 44: 20-35.

Gianvittorio, J.P., 2003. Fractals, MEMS, andFSS Electromagnetic Devices:Miniaturization and Multiple Resonances,PhD Thesis, University of California.

Hazdra P. and M. Mazanek, 2006. L-SystemTool for Generating Fractal AntennaStructures with Ability to Export into EMSimulators, Radioengineering, 15: 18-21.

Huang, C.Y., C.Y. Wu and K.L. Wong, 1998.High-Gain Compact Circularly PolarizedMicrostrip Antenna, Electronic Letters, 34:712-713.

Jaggard, D.L., 1990. “Fractal Electrodynamics:From Super Antennas to Superlattices,” in J.L. Vehel, E. Lutton, and C. Tricot (eds.),Fractals in Engineering, Springer-Verlag,pp: 204-221.

Jaggard D.L., 1990. “On FractalElectrodynamics,” in H. N. Kritikos and D.L. Jaggard (eds.), Recent Advances inElectromagnetic Theory, Springer-Verlag,pp: 183-224.

James, J.R. and P.S. Hall, 1989. Handbook ofMicrostrip Antennas, vol. 1, London: PeterPeregrines Ltd.

Kosiavas, G. et al., 1989. The C-Patch: A SmallMicrostrip Antenna Element, ElectronicLetters, 25: 253-254.

Kumar, G. and K.P. Ray, 2003. BroadbandMicrostrip Antennas, Artech House, Inc.

Mak C. L., K. M. Luk, K. F. Lee, and Y. L.Chow, 2002. Experimental Study of aMicrostrip Patch Antenna with an L-ShapedProbe, IEEE Trans. Antennas Propagat, 48:777-783.

Mandelbrot, B.B., 1983. The Fractal Geometryof Nature, W. H. Freeman.

Palaniswamy, V. and R. Crag, 1985.Rectangular Ring and H-Shape MicrostripAntenna; Alternative Approach toRectangular Microstrip Antenna, ElectronicLetters, 21: 874-876.

Peitgen, H.H. Jürgens, and D. Saupe, 2004.Chaos and Fractals, New Frontiers ofScience, Second Edition, Springer-VerlagNew York.

Shrivervik, A.K., J.F. Zurcher, O. Staub and J.R. Mosig, 2001. PCS Antenna Design: TheChallenge of Miniaturization, IEEEAntennas and Propagation Magazine, 43:12-27.

Fig.1 The generation process of the proposed fractal microstrip patch antenna structuresbased on fractal Koch curve. (a) the generator. (b) the initiator ( square patch antenna),(c) the 1st iteration , (d) the 2nd iteration, (e) the 3rd iteration, and (f) the 4th iteration

pre-fractal structures.

Fig.2 The antenna layout with respect to thecoordinate system.

Fig.3 The return loss response for the zeroiteration pre-fractal microstrip patch antenna.

Fig.4 Eθ and Eφ radiation patterns of the squaremicrostrip patch antenna at 2.4 GHz.

Fig.5 The total E field radiation pattern of thesquare in elevation at 2.4 GHz.

Fig.6 The 3-D radiation pattern of the squaremicrostrip patch antenna at 2.4 GHz.

Fig.7 The return loss response for the 1st

iteration pre-fractal microstrip patch antenna.

Fig.8 Eθ and Eφ radiation patterns of the 1stiteration fractal microstrip patch antenna at 2.4GHz.

Fig.9 The total E field radiation pattern of the1st iteration fractal microstrip at 2.4 GHz.

Fig.10 The current density at the surface of the 1st

iteration fractal microstrip at 2.4 GHz.Fig.11 Eθ and Eφ radiation patterns of the 1stiteration fractal microstrip patch antenna at 7.6GHz.

Fig.12 The total E field radiation pattern of the1st iteration fractal microstrip at 7.6 GHz.

Fig.13 The current density at the surface of the1st iteration fractal microstrip at 7.6 GHz.

Fig.14 The return loss response for the 2nditeration pre-fractal microstrip patch antenna.

Fig.15 Eθ and Eφ radiation patterns of the 2nd

iteration fractal microstrip patch antenna at 2.4GHz.

Fig.16 The total E field radiation pattern of the2nd iteration fractal microstrip at 2.4 GHz.

Fig.17 The current density at the surface of the2nd iteration fractal microstrip at 2.4 GHz.

Fig.18 Eθ and Eφ radiation patterns of the 2nd

iteration fractal microstrip patch antenna at 7.1GHz.

Fig.19 The total E field radiation pattern of the2nd iteration fractal microstrip at 7.1 GHz.

Fig.20 The current density at the surface of the2nd iteration fractal microstrip at 7.1 GHz.