research article particle swarm optimization for multiband metamaterial fractal...

Hindawi Publishing CorporationJournal of OptimizationVolume 2013 Article ID 989135 8 pageshttpdxdoiorg1011552013989135

Research ArticleParticle Swarm Optimization for Multiband MetamaterialFractal Antenna

Balamati Choudhury Sangeetha Manickam and R M Jha

Centre for Electromagnetics CSIR-National Aerospace Laboratories Bangalore 560017 India

Correspondence should be addressed to Balamati Choudhury balamatinalresin

Received 27 February 2013 Accepted 2 April 2013

Academic Editor Ling Wang

Copyright copy 2013 Balamati Choudhury et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The property of self-similarity recursive irregularity and space filling capability of fractal antennas makes it useful for variousapplications in wireless communication including multiband miniaturized antenna designs In this paper an effort has been madeto use the metamaterial structures in conjunction with the fractal patch antenna which resonates at six different frequenciescovering both C and X band Two different types of square SRR are loaded on the fractal antenna for this purpose Particle swarmoptimization (PSO) is used for optimization of these metamaterial structuresThe optimized metamaterial structures after loadingupon show significant increase in performance parameters such as bandwidth gain and directivity

1 Introduction

The non-integral dimensions recursive irregularity andspace filling capability of fractal antennas make it useful forvarious applications in wireless communication includingminiaturized antenna designs [1] Their property of beingself-similar in the geometry leads to antennas of compact sizewith simplified circuit designs Antennas which have frac-tal geometry are self-iterative exhibiting multiband opera-tion Fractal antennas are frequency independent and haveschemes for realizing low sidelobe designs An antenna withfractal geometry is preferred to conventional antenna designsdue to the iterative behavior of the structure which is believedto improve the performance factors like gain bandwidthreturn loss and frequency of operation [2]

Metamaterials are artificial structures designed by placingelectromagnetic (EM) resonators such as split ring res-onators (SRRs) at regular intervals The metamaterials havefrequency selective response and exhibit unique EM prop-erties such as negative permittivity and permeability arti-ficial magnetism and negative refractive index which canbe used to improve the performance of antenna [3] Themedia composed of metamaterials have tunable effectivematerial parameters and their electromagnetic response

can be adjusted in real time By using metamaterials as sub-strates or superstrates for antenna significant improvementshave been observed in the properties of the fractal antenna

In this paper an effort is made to use the square split ringresonator (SRR) in conjunctionwith the fractal patch antennato enhance the directivity gain voltage standing wave ratio(VSWR) and bandwidth atmultiple resonant frequencies Toserve this purpose two different types of tunable multibandmicro-splitmetamaterial square SRR are loaded on the fractalantenna [4] Such an application requires design of the loadedstructure at the desired frequency range (equivalent to theresonant frequencies of the fractal antenna whose perfor-mance is to be improved) Towards this a PSO optimizer isdeveloped which yields structural parameters at a particularresonant frequency Particle swarm optimization (PSO) is anevolutionary computational technique based on the move-ment and intelligence of swarms which is used for optimizingdifficult multidimensional discontinuous problems in a vari-ety of fields including electromagnetics [5 6] The optimalstructural parameters of square SRR such as length widthdistance between successive rings for a particular resonantfrequency are obtained using this efficient optimizationtechnique based on an equivalent circuit analysis

2 Journal of Optimization

2 Overview of Metamaterial Fractal Antennas

The term fractal was first coined by Mandelbrot in 1975 inwhich rough irregular or fragmented geometric shape couldbe subdivided in parts each of which was reduced-size copyof the whole [7] A fractal antenna possesses two prop-erties namely self-similarity and space filling and hencethe resonance takes place over a wide band as well asatmultiple frequenciesThese properties of the fractals can beused to develop new configurations for antennas and antennaarrays Since the fractal antennas are multi-resonant andsmaller in size they are used for wireless applications Fractalantenna can be designed to receive and transmit over awide range of frequencies using the self-similar propertyassociated with fractal geometry structures [2] Space fill-ing fractal geometries such as Hilbert curves are used todesign miniature antennas high-directive radiators andhigh-impedance surfacesThis concept was used for design ofminiaturized inverted-F antenna forwireless sensor networks[8] The overall size of the antenna was reduced to 77 byusing Hilbert geometry instead of conventional rectangularpatch antenna for the same resonant frequency

Radar cross section (RCS) reduction in microstripantenna was achieved by using Koch fractal geometry with-out affecting radiation performance of the antenna [9] AnUHF Quasi-Yagi antenna surrounded by fractal metama-terial structures was designed for RFID applications Theoperational frequency of this antenna was 24GHz [10]Similarly star-shaped fractal patch antenna was used forminiaturization andbackscattering radar cross-section (RCS)reduction [11] Metamaterial unit cells could be miniaturizedby incorporating fractal geometries The effect of variousgeometrical parameters and the order of fractal curve on theperformance of the fractal antenna were also investigated andreported that the fractal geometries of original dimensionsgive better performance than the miniaturized one [12]

Further a novel negative-epsilon metamaterial wasdesigned using fractal Hilbert curves with mirror symmetry[13]The slotted SRRs in the ground plane were abandoned inorder to reduce back radiation of the antennaThe numericalanalysis and design also shows that a periodic arrangementof Hilbert curve inclusions above a conducting ground planeforms a metamaterial surface with high impedance [14]

Using multi-resonator configuration a low-loss dis-persion-optimized engineered substrate was designed forantennaminiaturization and performance enhancementTheproposed substrate contained four uncoupled inclusions with3rd order fractal Hilbert structure A circuitmodel was devel-oped to analyze and optimize the proposedmetamaterial [15]A metamaterial with zero refractive index was designed overa wide frequency range and used as superstrate for patchantenna [16] The designed antenna showed an antenna gainimprovement by 5 dB

It is observed from the overview of fractal antenna thatHilbert curves proved to be efficient fractal geometries togenerate metamaterial surfaces Fractal geometries were alsoused as miniaturized antennas with metamaterial structuresas superstrate In this paper metamaterial structures are

Patch

SquareSRR

Substrate

Feed

Figure 1 Top view of the square SRR loaded fractal antenna

loaded on a fractal antenna for increase in the bandwidth atthe multiple distinct resonating frequencies

3 Design of Fractal Antenna

Fractal antennas are widely used for their compact size andlight weight in wireless applications In this work the fractalantenna is designedwithmultiple resonant frequencies Frac-tal patch antenna is designed on a substrate with dimensions36mm times 20mm times 16mm having a relative permittivity of44 [17] The patch used in the antenna layout is copperwith the area 28mm times 12mm The size of the patch used tofeed the antenna is 05mm times 4mm Figure 1 shows theschematic diagram of the fractal patch antenna Furthermetamaterial structures are loaded on the antenna to improvethe performance

Two different algorithms namely PSO and bacteria for-aging optimization (BFO) have been implemented towardsoptimization of square SRR [18] It was observed that theexecution time and accuracy of these algorithms depend onselection of parameters For this optimization problem thedetails of accuracy and execution time for both the algorithmsare given in Table 1

It is readily observed that for the class of problem in handPSO is highly convergent andmore accurate compared to theBFO Hence PSO algorithm is considered in this work forfurther study of metamaterial antenna design

4 PSO Optimization for SRR Design

The PSO is a simple effective and robust method used forsearch and optimization in various EM problems The devel-opment of PSO can be illustrated through an analogy similarto a swarm of bees in a field The goal of a swarm of beesin a field is to find the location with the highest density offlowers [5] This motivates the engineers to use PSO as anoptimization technique [6] For completeness of the paperthe step-by-step algorithm is described briefly along with theflowchart (Figure 2)

41 PSO Algorithm The PSO algorithm is given here forbetter understanding of the implementation for optimizationof the resonant frequency (and hence extraction of the struc-tural parameters) of a metamaterial SRR described in thefollowing section The step-by-step procedure is given next

Journal of Optimization 3

Table 1 Comparison of PSO and BFO for structural optimization of square SRR at a particular desired frequency The substrate dielectricconstant is 386 and desired frequency is 2388GHz

Optimizationtechniques Accuracy (119891err)

Gap betweenrings 119889 (in mm)

Width of rings 119908(in mm) Length 119886 (in mm) Execution time

(in seconds)BFO 000161 012 012 396 1255PSO 0000442 014 010 395 104

Step 1 Define the solution space The parameters to beoptimized are selected in this space Aminimum (119909min(119899)) anda maximum (119909max(119899)) range is defined where 119899 ranges from 1to119873 (dimension of the optimization space)

Step 2 Define a fitness functionThe fitness function exhibitsa functional dependence that is relative to the importance ofeach characteristic being optimized

Step 3 Initialize random swarm location and velocities Eachparticle begins at its own random location with a velocity thatis random in its direction and magnitude The personal best(119901best) and the global best (119892best) are foundThe personal bestis the position of highest fitness locally and global best is theposition of the highest fitness of the entire swarm

Step 4 Systematically fly the particles through the solutionspaceThe algorithm acts on each particle one by onemovingit by a small amount and cycling through the entire swarm

The following steps are encountered on each particle

(i) Particlersquos fitness evaluation comparing 119892best and 119901best(ii) Further depending on the fitness value the particlersquos

velocity has been updated using the following equa-tion

V119899 = 119908 lowast V119899 + 1198881 lowast rand () lowast (119901best119899 minus 119909119899)

+ 1198882 lowast rand () lowast (119892best119899minus119909119899) (1)

where V119899 is the velocity of a particle in the 119899thdimension 119908 is known as inertial weight (range isbetween 00 and 10) 119909119899 is the particlersquos coordinate inthe 119899th dimension 1198881 and 1198882 are two scaling factorswhich determine the relative pull of 119901best and 119892bestand rand () is random function in the range [0 1]

(iii) Once the particle velocity has been updated theparticle has to move to its next location The velocityis applied for time-step 119905 and new coordinate 119909119899 iscomputed for each of the119873 dimensions according tothe following equation

119909119899 = 119909119899 + Δ119905 lowast V119899 (2)

Step 5 For each particle in the swarm Step 4 is repeatedEvery second the snapshot is taken for the entire swarm soat that time the positions of all particles are evaluated andcorrection is made to 119901best and 119892best values if required

42 Implementation of PSO Square SRR is a metamaterialstructure which consists of double square shaped ring with a

For each agent

Evaluate fitness function

Update position

Update velocity

Is it last agent

Is it last iteration

Start

Stop

Yes

Yes

No

No

with random position and velocity

For each iteration (number of timesteps = 10)

119891err =|119891119889 minus 119891119888|

119891119889

Initialize population (number of particles = 10)

If fitness (119909) gt fitness (119901best )then 119901best = 119909


Figure 2 Flowchart of the PSO algorithm used for square SRR opti-mization

gapThis structure is printed on a dielectric substrate of thick-ness 16mm and permittivity 44 The schematic of a squareSRR with the dimensions is shown in Figure 3 where 119886 is theside length of the square SRR 119908 is the width of conductor119889 the successive distance between the rings and 119892 is the gappresent in the rings The equivalent circuit of the square SRRis a parallel 119871119862 tank circuit given in Figure 4 The resonantfrequency of the square SRR is obtained by equivalent circuitanalysis method In this method the distributed network isconverted to lumped network (Figure 4) and analysis of theresonant frequency has been carried out [19]

The resonant frequency of the split ring resonator is givenby

119891119903 =1

2120587radic119871119862

(3)


119908

119892

119889

119886

Figure 3 Top view of a unit cell of the metamaterial structure

1198711

1198711

1198712

1198713

1198713

(a)

119871

119862

(b)

Figure 4 (a) Equivalent inductance of the square SRR (b) Equiva-lent circuit of the square SRR

where 119871 is total inductance and 119862 is gap capacitance whichare dependent on structural parameters of square SRR [20]The expressions for 119871 and 119862 are given below

The effective inductance of the square SRR is given by [20]

119871 =

4861205830

2

(119886 minus 119908 minus 119889) [ln(098120588

) + 184120588] (4)

Table 2 List of parameters along with their values considered inPSO

PSO parameters Value Use119908 025 Inertial weight1198881 205 Constant 1 to determine 119901best1198882 205 Constant 2 to determine 119892best119873119901 10 Number of particles119873119889 5 Number of dimensions119873119905 20 Number of time steps119883min 0 Scalar min for particle position119883max 10 Scalar max for particle position119881min minus15 Scalar min for particle velocity119881max 15 Scalar max for particle velocity

where 120588 is the filling factor which depends on width andthickness of the SRRThefilling factorwith respect to Figure 3is given by

120588 =

119908 + 119889

119886 minus 119908 minus 119889

(5)

Similarly the effective capacitance is given by

119862119904 = (119886 minus3

2

(119908 + 119889))119862pul (6)

where 119862pul is the per-unit-length capacitance between therings which is given as

119862pul = 1205760120576eff119870(radic1 minus 119896

2)

119870 (119896)

(7)

Here 120576eff is the effective dielectric constant which is expressedas

120576eff =120576119903 + 1

2

(8)

119870(119896) denotes the complete elliptical integral of the first kindwith 119896 expressed as

119896 =

119889

119889 + 2119908

(9)

The PSO optimizer acts here as a CAD package which yieldsthe structural parameters such as the length width andspacing at a desired resonant frequency The cost functionused for this optimization is

119891err =

1003816100381610038161003816119891119889 minus 119891119888

1003816100381610038161003816

119891119889

(10)

where 119891119889 is the desired frequency and 119891119888 is the frequencyarrived at by the equivalent circuit analysis As per the algo-rithm mentioned the different parameters are assigned withrespect to the problem The parameters of the PSO programare given in Table 2 The selection of PSO parameters suchas 119908 1198881 and 1198882 considered are from the original work byKennedy and Eberhart [5] The inertial weight is always


1198781111987821

10

0

minus10

minus20

minus30

minus408 85 9 95 10 105 11 115 12

Frequency (GHz)

Scat

terin

g pa

ram

eter

s (dB

)

(a)

8 85 9 95 10 105 11 115 12Frequency (GHz)

40

20

0

minus20

minus40

minus60

minus80

minus100

Rela

tive p

erm

ittiv

ity

Re(120576)Im(120576)

(b)

8 85 9 95 10 105 11 115 12

20

15

10

5

0

minus5

Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(c)

Figure 5 (a) Scattering parameters 11987811 and 11987821 parameters of the designed square SRR optimized using PSO algorithm (b) Relative per-mittivity of the designed square SRR as optimized by the PSO (c) Relative permeability of the designed square SRR as optimized by thePSO

considered as less than one and varies with iteration [6] Theparameter 119873119889 that is number of dimensions is taken withrespect to square SRR parameters to be optimized such as 119886119908 119889 120576119891err Similarly there is no specific criteria for selectionof exact values for 119873119901 119873119905 and is generally taken by trialand error method with respect to complexity of problem [6]119883min119883max119881min and119881max are the initial search values whichupdate with the iteration cycle

The PSO optimizes the fitness function and extracts thestructural parameters The extracted length 119886 width 119908 andthe space between the inner and outer ring 119889 are 28mm03mm and 03mm respectivelyThese optimized values are

used for the design of the square SRR and the relative permit-tivity and permeability values are extracted using (5) and (6)[20]

The simulated scattering parameters (11987811 and 11987821) of thesquare SRR placed exactly at themiddle of the fractal antennaand the corresponding extracted relative permittivity andpermeability are given in Figure 5(a) through Figure 5(c)Themetamaterial characteristics of the proposed structure arereadily inferred in Figure 5(b) from 935GHz to 994GHzSimilarly Figure 6(a) shows the top view of a unit cell ofthe metamaterial structure with micro-splits The scatteringparameters of the second square micro-split SRR placed over


Micro-splits

119908

119892

119889

119886

(a)

Frequency (GHz)8 85 9 95 10 105 11 115 12

Scat

terin

g pa

ram

eter

s (dB

)

minus50

minus40

minus30

minus20

minus10

0

10

1198781111987821

(b)

8 85 9 95 10 105 11 115 12

0

20

40

Frequency (GHz)

Rela

tive p

erm

ittiv

ity

minus100

minus80

minus60

minus40

minus20

Re(120576)Im(120576)

(c)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

10

15

20

8 85 9 95 10 105 11 115 12Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(d)

Figure 6 (a) Top view of a unit cell of the metamaterial structure with micro-splits (square micro-split SRR) (b) Scattering parameters 11987811and 11987821 parameters of the designed square micro-split SRR (c) Extracted permittivity of the designed square micro-split SRR (d) Extractedpermeability of the designed square micro-split SRR

the fractal antenna and the corresponding extracted rela-tive permittivity and permeability are shown in Figure 6(b)through Figure 6(d)

119899 =

1

119896119889

cosminus1 [ 1

211987821

(1 minus 1198782

11 + 1198782

21)]

119911 =radic

(1 + 119878211)2minus 119878221

(1 minus 119878211)2minus 119878221

120576 =

119899

119911

120583 = 119899119911

(11)

where 119908 = radian frequency 119889 = thickness of the unit cell

The PSO algorithm is implemented to optimize the struc-tural square SRR parameters such as width length and gapbetween the splits for a desired frequency of operation withthe overall objective to improve the performance characteris-tics of the fractal antenna

5 Performance Enhancement UsingOptimized Square SRR

A metamaterial square split ring resonator whose structuralparameters were optimized using particle swarm optimiza-tion was designed and placed at the centre of the fractal patchantenna as shown in Figure 1 After loading a single opti-mized metamaterial square SRR it is observed that althoughthe performance of the antenna is increased compared to


Table 3 Characteristics of the fractal patch antenna after the addition of metamaterial structure

Parameters Resonant frequency of the fractal patch (GHz)337 496 642 776 893 1237

Bandwidth (MHz) 40 85 995 220 60 420(without SRR)Bandwidth (MHz) 46 340 120 220 120 460(with SRR)Return loss (dB)

minus1250 minus3152 minus268 minus2035 minus1330 minus2126(with SRR)Directivity (dB)

minus314 486 331 779 569 621(with SRR)

Patch

SquareSRR

Micro-splitSRRFeed

Substrate

Figure 7 Two different square SRR (square SRR and square micro-split SRR) loaded in the fractal antenna elements

the fractal patch antenna without metamaterial it is notsignificant at all the resonant frequencies Further in orderimprove the performance of the fractal patch antenna at allthe resonant frequencies a square SRR with micro-splits inthe outer ring is loaded in conjunction with the optimizedsquare SRR (Figure 7) Particle swarm optimization is usedfor optimization of these metamaterial structures using thealgorithm given in Section 4

The micro-split in the SRR ring helps to resonate atmultiple frequencies and improves multiband operation ofthe antenna By using two different types of square SRR theperformance parameters of the fractal antenna such as returnloss gain directivity bandwidth and VSWR are improved atmultiple resonant frequencies

The designed metamaterial fractal antenna resonates atsix distinct resonant frequencies which covers both the Cand X band (Figure 8)The simulation results show that thereis a significant improvement in the antenna characteristicsTable 3 shows the results after placing the metamaterial SRRwith micro-splits over the fractal patch antenna

After placing the metamaterial SRR over the fractalantenna there is a significant decrease in the return loss andat the same time the bandwidth is widened with enhance-ment in the gain and directivity The radiation efficiency isimproved to 40 It is clearly seen that the gain anddirectivityof the antenna are improved There is also an increase inbandwidth at each resonant frequency Figures 8 and 9 showthe simulation results of the fractal patch antenna with opti-mized metamaterial SRR and micro-split SRR at the middleof the antenna

Frequency (GHz)0 2 4 6 8 10 12 14

0

Return loss

minus35

minus30

minus25

minus20

minus15

minus10

minus5

119878 11

Figure 8 Return loss of the metamaterial fractal patch antenna

Gain total (dB)

119883

119884

11988558142119890+00040275119890+00022409119890+00045425119890minus001minus13324119890+000

minus49057119890+000minus66923119890+000minus84789119890+000minus10266119890+001minus12052119890+001minus13839119890+001minus15625119890+001minus17412119890+001minus19199119890+001minus20985119890+001minus22772119890+001

minus3119119890+000

120579

120601

Figure 9 Radiation pattern of the metamaterial fractal patchantenna at 776GHz

6 Conclusion

A multiband metamaterial fractal antenna is designed andsimulated which resonates at six different frequencies cover-ing both C and X band Two different types of metamaterialstructures namely a square SRR and a square micro-splitSRR are loaded at the center of the antenna A PSO basedoptimizer is used to extract the structural parameters of thesemetamaterial structures A comparative analysis of the fractal


antenna with and without SRR is reported It is observedthat the radiation efficiency has increased up to 40 afterloading the optimized SRRsThe bandwidth at each resonantfrequency increases significantly because of the squaremicro-split SRR There is also a noticeable improvement in thedirectivity as well as the gain at various resonant frequencies

References

[1] D H Werner R L Haupt and P L Werner ldquoFractal antennaengineering the theory and design of fractal antenna arraysrdquoIEEE Antennas and PropagationMagazine vol 41 no 5 pp 37ndash58 1999

[2] T E Nur S K Ray D Paul and T Mollick ldquoDesign of fractalantenna for ultra- wideband applicationsrdquo International Journalof Research and Reviews in Wireless Communications vol 1 no3 pp 66ndash74 2011

[3] Y Rahmat-Samii ldquoMetamaterials in antenna applications clas-sifications designs and applicationsrdquo in Proceedings of IEEEInternational Workshop on Antenna Technology Small Antennasand Novel Metamaterials (IWAT rsquo06) pp 1ndash4 March 2006

[4] E Ekmekci K Topalli T Akin and G Turhan-Sayan ldquoA tun-able multi-band metamaterial design using micro-split SRRstructuresrdquoOptics Express vol 17 no 18 pp 16046ndash16058 2009

[5] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks pp 1942ndash1948 December 1995

[6] J Robinson andY Rahmat-Samii ldquoParticle swarmoptimizationin electromagneticsrdquo IEEE Transactions on Antennas and Prop-agation vol 52 no 2 pp 397ndash407 2004

[7] B B Mandelbrot Fractals Form Chance and Dimension WHFreeman Amsterdam The Netherlands 1977

[8] J T Huang J H Shiao and J M Wu ldquoA miniaturized Hilbertinverted-F antenna for wireless sensor network applicationsrdquoIEEE Transactions on Antennas and Propagation vol 58 no 9pp 3100ndash3103 2010

[9] G Cui Y Liu and S Gong ldquoA novel fractal patch antenna withlow RCSrdquo Journal of Electromagnetic Waves and Applicationsvol 21 no 15 pp 2403ndash2411 2007

[10] H X D Araujo S E Barbin and L C Kretly ldquoDesign of UHFQuasi-Yagi antenna with metamaterial structures for RFIDapplicationsrdquo in Proceedings of IEEE Microwave and Optoelec-tronics Conference pp 8ndash11 November 2011

[11] Y B Thakare and Rajkumar ldquoDesign of fractal patch antennafor size and radar cross-section reductionrdquo IET MicrowavesAntennas and Propagation vol 4 no 2 pp 175ndash181 2010

[12] V Crnojevic-Bengin V Radonic and B Jokanovic ldquoFrac-tal geometries of complementary split-ring resonatorsrdquo IEEETransactions on Microwave Theory and Techniques vol 56 no10 pp 2312ndash2321 2008

[13] M Palandoken and H Henke ldquoFractal negative-epsilon meta-materialrdquo in Proceedings of the International Workshop onAntenna Technology Small Antennas Innovative Structures andMaterials (iWAT rsquo10) pp 1ndash4 March 2010

[14] J McVay N Engheta and A Hoorfar ldquoHigh impedance met-amaterial surfaces using Hilbert-curve inclusionsrdquo IEEEMicrowave and Wireless Components Letters vol 14 no 3 pp130ndash132 2004

[15] L Yousefi and O M Ramahi ldquoMiniaturized wideband antennausing engineered magnetic materials with multi-resonator

inclusionsrdquo in Proceedings of the IEEE Antennas and Propaga-tion Society International Symposium (AP-S rsquo07) pp 1885ndash1888June 2007

[16] J Ju D Kim W J Lee and J I Choi ldquoWideband high-gainantenna using metamaterial superstrate with the zero refractiveindexrdquoMicrowave and Optical Technology Letters vol 51 no 8pp 1973ndash1976 2009

[17] S Suganthi S Raghavan and D Kumar ldquoMiniature fractalantenna design and simulation for wireless applicationsrdquo inProceedings of the IEEE International Conference on RecentAdvances in Intelligent Computational Systems Trivandrum(RAICS rsquo11) September 2011

[18] B Choudhury S Bisoyi GHiremath andRM Jha ldquoEmergingtrends in soft computing for metamaterial design and opti-mizationrdquo in Proceedings of the Symposium on MetamaterialsInternational Conference on Computational and ExperimentalEngineering and Sciences (ICCES rsquo12) Crete Greece April 2012

[19] J W Fan C H Liang and X W Dai ldquoDesign of cross-cou-pled dual-band filter with equal-length split-ring resonatorsrdquoProgress in Electromagnetics Research vol 75 pp 285ndash293 2007

[20] F Bilotti A Toscano and L Vegni ldquoDesign of spiral and mul-tiple split-ring resonators for the realization of miniaturizedmetamaterial samplesrdquo IEEE Transactions on Antennas andPropagation vol 55 no 8 pp 2258ndash2267 2007

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2 Overview of Metamaterial Fractal Antennas

The term fractal was first coined by Mandelbrot in 1975 inwhich rough irregular or fragmented geometric shape couldbe subdivided in parts each of which was reduced-size copyof the whole [7] A fractal antenna possesses two prop-erties namely self-similarity and space filling and hencethe resonance takes place over a wide band as well asatmultiple frequenciesThese properties of the fractals can beused to develop new configurations for antennas and antennaarrays Since the fractal antennas are multi-resonant andsmaller in size they are used for wireless applications Fractalantenna can be designed to receive and transmit over awide range of frequencies using the self-similar propertyassociated with fractal geometry structures [2] Space fill-ing fractal geometries such as Hilbert curves are used todesign miniature antennas high-directive radiators andhigh-impedance surfacesThis concept was used for design ofminiaturized inverted-F antenna forwireless sensor networks[8] The overall size of the antenna was reduced to 77 byusing Hilbert geometry instead of conventional rectangularpatch antenna for the same resonant frequency

Radar cross section (RCS) reduction in microstripantenna was achieved by using Koch fractal geometry with-out affecting radiation performance of the antenna [9] AnUHF Quasi-Yagi antenna surrounded by fractal metama-terial structures was designed for RFID applications Theoperational frequency of this antenna was 24GHz [10]Similarly star-shaped fractal patch antenna was used forminiaturization andbackscattering radar cross-section (RCS)reduction [11] Metamaterial unit cells could be miniaturizedby incorporating fractal geometries The effect of variousgeometrical parameters and the order of fractal curve on theperformance of the fractal antenna were also investigated andreported that the fractal geometries of original dimensionsgive better performance than the miniaturized one [12]

Further a novel negative-epsilon metamaterial wasdesigned using fractal Hilbert curves with mirror symmetry[13]The slotted SRRs in the ground plane were abandoned inorder to reduce back radiation of the antennaThe numericalanalysis and design also shows that a periodic arrangementof Hilbert curve inclusions above a conducting ground planeforms a metamaterial surface with high impedance [14]

Using multi-resonator configuration a low-loss dis-persion-optimized engineered substrate was designed forantennaminiaturization and performance enhancementTheproposed substrate contained four uncoupled inclusions with3rd order fractal Hilbert structure A circuitmodel was devel-oped to analyze and optimize the proposedmetamaterial [15]A metamaterial with zero refractive index was designed overa wide frequency range and used as superstrate for patchantenna [16] The designed antenna showed an antenna gainimprovement by 5 dB

It is observed from the overview of fractal antenna thatHilbert curves proved to be efficient fractal geometries togenerate metamaterial surfaces Fractal geometries were alsoused as miniaturized antennas with metamaterial structuresas superstrate In this paper metamaterial structures are

Patch

SquareSRR

Substrate

Feed

Figure 1 Top view of the square SRR loaded fractal antenna

loaded on a fractal antenna for increase in the bandwidth atthe multiple distinct resonating frequencies

3 Design of Fractal Antenna

Fractal antennas are widely used for their compact size andlight weight in wireless applications In this work the fractalantenna is designedwithmultiple resonant frequencies Frac-tal patch antenna is designed on a substrate with dimensions36mm times 20mm times 16mm having a relative permittivity of44 [17] The patch used in the antenna layout is copperwith the area 28mm times 12mm The size of the patch used tofeed the antenna is 05mm times 4mm Figure 1 shows theschematic diagram of the fractal patch antenna Furthermetamaterial structures are loaded on the antenna to improvethe performance

Two different algorithms namely PSO and bacteria for-aging optimization (BFO) have been implemented towardsoptimization of square SRR [18] It was observed that theexecution time and accuracy of these algorithms depend onselection of parameters For this optimization problem thedetails of accuracy and execution time for both the algorithmsare given in Table 1

It is readily observed that for the class of problem in handPSO is highly convergent andmore accurate compared to theBFO Hence PSO algorithm is considered in this work forfurther study of metamaterial antenna design

4 PSO Optimization for SRR Design

The PSO is a simple effective and robust method used forsearch and optimization in various EM problems The devel-opment of PSO can be illustrated through an analogy similarto a swarm of bees in a field The goal of a swarm of beesin a field is to find the location with the highest density offlowers [5] This motivates the engineers to use PSO as anoptimization technique [6] For completeness of the paperthe step-by-step algorithm is described briefly along with theflowchart (Figure 2)

41 PSO Algorithm The PSO algorithm is given here forbetter understanding of the implementation for optimizationof the resonant frequency (and hence extraction of the struc-tural parameters) of a metamaterial SRR described in thefollowing section The step-by-step procedure is given next


















119909119899 = 119909119899 + Δ119905 lowast V119899 (2)



For each agent


Update position

Update velocity

Is it last agent


Start

Stop

Yes

Yes

No

No



119891err =|119891119889 minus 119891119888|

119891119889







119891119903 =1

2120587radic119871119862

(3)


119908

119892

119889

119886


1198711

1198711

1198712

1198713

1198713

(a)

119871

119862

(b)




119871 =

4861205830

2

(119886 minus 119908 minus 119889) [ln(098120588

) + 184120588] (4)




120588 =

119908 + 119889

119886 minus 119908 minus 119889

(5)


119862119904 = (119886 minus3

2

(119908 + 119889))119862pul (6)



2)

119870 (119896)

(7)


120576eff =120576119903 + 1

2

(8)


119896 =

119889

119889 + 2119908

(9)


119891err =

1003816100381610038161003816119891119889 minus 119891119888

1003816100381610038161003816

119891119889

(10)



1198781111987821

10

0

minus10

minus20

minus30

minus408 85 9 95 10 105 11 115 12

Frequency (GHz)

Scat

terin

g pa

ram

eter

s (dB

)

(a)

8 85 9 95 10 105 11 115 12Frequency (GHz)

40

20

0

minus20

minus40

minus60

minus80

minus100

Rela

tive p

erm

ittiv

ity

Re(120576)Im(120576)

(b)

8 85 9 95 10 105 11 115 12

20

15

10

5

0

minus5

Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(c)







Micro-splits

119908

119892

119889

119886

(a)

Frequency (GHz)8 85 9 95 10 105 11 115 12

Scat

terin

g pa

ram

eter

s (dB

)

minus50

minus40

minus30

minus20

minus10

0

10

1198781111987821

(b)

8 85 9 95 10 105 11 115 12

0

20

40

Frequency (GHz)

Rela

tive p

erm

ittiv

ity

minus100

minus80

minus60

minus40

minus20

Re(120576)Im(120576)

(c)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

10

15

20

8 85 9 95 10 105 11 115 12Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(d)



119899 =

1

119896119889

cosminus1 [ 1

211987821

(1 minus 1198782

11 + 1198782

21)]

119911 =radic

(1 + 119878211)2minus 119878221

(1 minus 119878211)2minus 119878221

120576 =

119899

119911

120583 = 119899119911

(11)










minus314 486 331 779 569 621(with SRR)

Patch

SquareSRR

Micro-splitSRRFeed

Substrate






Frequency (GHz)0 2 4 6 8 10 12 14

0

Return loss

minus35

minus30

minus25

minus20

minus15

minus10

minus5

119878 11


Gain total (dB)

119883

119884

11988558142119890+00040275119890+00022409119890+00045425119890minus001minus13324119890+000


minus3119119890+000

120579

120601


6 Conclusion




References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























119909119899 = 119909119899 + Δ119905 lowast V119899 (2)



For each agent


Update position

Update velocity

Is it last agent


Start

Stop

Yes

Yes

No

No



119891err =|119891119889 minus 119891119888|

119891119889







119891119903 =1

2120587radic119871119862

(3)


119908

119892

119889

119886


1198711

1198711

1198712

1198713

1198713

(a)

119871

119862

(b)




119871 =

4861205830

2

(119886 minus 119908 minus 119889) [ln(098120588

) + 184120588] (4)




120588 =

119908 + 119889

119886 minus 119908 minus 119889

(5)


119862119904 = (119886 minus3

2

(119908 + 119889))119862pul (6)



2)

119870 (119896)

(7)


120576eff =120576119903 + 1

2

(8)


119896 =

119889

119889 + 2119908

(9)


119891err =

1003816100381610038161003816119891119889 minus 119891119888

1003816100381610038161003816

119891119889

(10)



1198781111987821

10

0

minus10

minus20

minus30

minus408 85 9 95 10 105 11 115 12

Frequency (GHz)

Scat

terin

g pa

ram

eter

s (dB

)

(a)

8 85 9 95 10 105 11 115 12Frequency (GHz)

40

20

0

minus20

minus40

minus60

minus80

minus100

Rela

tive p

erm

ittiv

ity

Re(120576)Im(120576)

(b)

8 85 9 95 10 105 11 115 12

20

15

10

5

0

minus5

Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(c)







Micro-splits

119908

119892

119889

119886

(a)

Frequency (GHz)8 85 9 95 10 105 11 115 12

Scat

terin

g pa

ram

eter

s (dB

)

minus50

minus40

minus30

minus20

minus10

0

10

1198781111987821

(b)

8 85 9 95 10 105 11 115 12

0

20

40

Frequency (GHz)

Rela

tive p

erm

ittiv

ity

minus100

minus80

minus60

minus40

minus20

Re(120576)Im(120576)

(c)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

10

15

20

8 85 9 95 10 105 11 115 12Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(d)



119899 =

1

119896119889

cosminus1 [ 1

211987821

(1 minus 1198782

11 + 1198782

21)]

119911 =radic

(1 + 119878211)2minus 119878221

(1 minus 119878211)2minus 119878221

120576 =

119899

119911

120583 = 119899119911

(11)










minus314 486 331 779 569 621(with SRR)

Patch

SquareSRR

Micro-splitSRRFeed

Substrate






Frequency (GHz)0 2 4 6 8 10 12 14

0

Return loss

minus35

minus30

minus25

minus20

minus15

minus10

minus5

119878 11


Gain total (dB)

119883

119884

11988558142119890+00040275119890+00022409119890+00045425119890minus001minus13324119890+000


minus3119119890+000

120579

120601


6 Conclusion




References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










119908

119892

119889

119886


1198711

1198711

1198712

1198713

1198713

(a)

119871

119862

(b)




119871 =

4861205830

2

(119886 minus 119908 minus 119889) [ln(098120588

) + 184120588] (4)




120588 =

119908 + 119889

119886 minus 119908 minus 119889

(5)


119862119904 = (119886 minus3

2

(119908 + 119889))119862pul (6)



2)

119870 (119896)

(7)


120576eff =120576119903 + 1

2

(8)


119896 =

119889

119889 + 2119908

(9)


119891err =

1003816100381610038161003816119891119889 minus 119891119888

1003816100381610038161003816

119891119889

(10)



1198781111987821

10

0

minus10

minus20

minus30

minus408 85 9 95 10 105 11 115 12

Frequency (GHz)

Scat

terin

g pa

ram

eter

s (dB

)

(a)

8 85 9 95 10 105 11 115 12Frequency (GHz)

40

20

0

minus20

minus40

minus60

minus80

minus100

Rela

tive p

erm

ittiv

ity

Re(120576)Im(120576)

(b)

8 85 9 95 10 105 11 115 12

20

15

10

5

0

minus5

Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(c)







Micro-splits

119908

119892

119889

119886

(a)

Frequency (GHz)8 85 9 95 10 105 11 115 12

Scat

terin

g pa

ram

eter

s (dB

)

minus50

minus40

minus30

minus20

minus10

0

10

1198781111987821

(b)

8 85 9 95 10 105 11 115 12

0

20

40

Frequency (GHz)

Rela

tive p

erm

ittiv

ity

minus100

minus80

minus60

minus40

minus20

Re(120576)Im(120576)

(c)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

10

15

20

8 85 9 95 10 105 11 115 12Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(d)



119899 =

1

119896119889

cosminus1 [ 1

211987821

(1 minus 1198782

11 + 1198782

21)]

119911 =radic

(1 + 119878211)2minus 119878221

(1 minus 119878211)2minus 119878221

120576 =

119899

119911

120583 = 119899119911

(11)










minus314 486 331 779 569 621(with SRR)

Patch

SquareSRR

Micro-splitSRRFeed

Substrate






Frequency (GHz)0 2 4 6 8 10 12 14

0

Return loss

minus35

minus30

minus25

minus20

minus15

minus10

minus5

119878 11


Gain total (dB)

119883

119884

11988558142119890+00040275119890+00022409119890+00045425119890minus001minus13324119890+000


minus3119119890+000

120579

120601


6 Conclusion




References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1198781111987821

10

0

minus10

minus20

minus30

minus408 85 9 95 10 105 11 115 12

Frequency (GHz)

Scat

terin

g pa

ram

eter

s (dB

)

(a)

8 85 9 95 10 105 11 115 12Frequency (GHz)

40

20

0

minus20

minus40

minus60

minus80

minus100

Rela

tive p

erm

ittiv

ity

Re(120576)Im(120576)

(b)

8 85 9 95 10 105 11 115 12

20

15

10

5

0

minus5

Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(c)







Micro-splits

119908

119892

119889

119886

(a)

Frequency (GHz)8 85 9 95 10 105 11 115 12

Scat

terin

g pa

ram

eter

s (dB

)

minus50

minus40

minus30

minus20

minus10

0

10

1198781111987821

(b)

8 85 9 95 10 105 11 115 12

0

20

40

Frequency (GHz)

Rela

tive p

erm

ittiv

ity

minus100

minus80

minus60

minus40

minus20

Re(120576)Im(120576)

(c)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

10

15

20

8 85 9 95 10 105 11 115 12Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(d)



119899 =

1

119896119889

cosminus1 [ 1

211987821

(1 minus 1198782

11 + 1198782

21)]

119911 =radic

(1 + 119878211)2minus 119878221

(1 minus 119878211)2minus 119878221

120576 =

119899

119911

120583 = 119899119911

(11)










minus314 486 331 779 569 621(with SRR)

Patch

SquareSRR

Micro-splitSRRFeed

Substrate






Frequency (GHz)0 2 4 6 8 10 12 14

0

Return loss

minus35

minus30

minus25

minus20

minus15

minus10

minus5

119878 11


Gain total (dB)

119883

119884

11988558142119890+00040275119890+00022409119890+00045425119890minus001minus13324119890+000


minus3119119890+000

120579

120601


6 Conclusion




References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Micro-splits

119908

119892

119889

119886

(a)

Frequency (GHz)8 85 9 95 10 105 11 115 12

Scat

terin

g pa

ram

eter

s (dB

)

minus50

minus40

minus30

minus20

minus10

0

10

1198781111987821

(b)

8 85 9 95 10 105 11 115 12

0

20

40

Frequency (GHz)

Rela

tive p

erm

ittiv

ity

minus100

minus80

minus60

minus40

minus20

Re(120576)Im(120576)

(c)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

10

15

20

8 85 9 95 10 105 11 115 12Frequency (GHz)

Rela

tive p

erm

eabi

lity

Re(120583)Im(120583)

(d)



119899 =

1

119896119889

cosminus1 [ 1

211987821

(1 minus 1198782

11 + 1198782

21)]

119911 =radic

(1 + 119878211)2minus 119878221

(1 minus 119878211)2minus 119878221

120576 =

119899

119911

120583 = 119899119911

(11)










minus314 486 331 779 569 621(with SRR)

Patch

SquareSRR

Micro-splitSRRFeed

Substrate






Frequency (GHz)0 2 4 6 8 10 12 14

0

Return loss

minus35

minus30

minus25

minus20

minus15

minus10

minus5

119878 11


Gain total (dB)

119883

119884

11988558142119890+00040275119890+00022409119890+00045425119890minus001minus13324119890+000


minus3119119890+000

120579

120601


6 Conclusion




References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














minus314 486 331 779 569 621(with SRR)

Patch

SquareSRR

Micro-splitSRRFeed

Substrate






Frequency (GHz)0 2 4 6 8 10 12 14

0

Return loss

minus35

minus30

minus25

minus20

minus15

minus10

minus5

119878 11


Gain total (dB)

119883

119884

11988558142119890+00040275119890+00022409119890+00045425119890minus001minus13324119890+000


minus3119119890+000

120579

120601


6 Conclusion




References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article particle swarm optimization for multiband metamaterial fractal...

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