Research Article Multiobjective-Optimized Design of a New

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2013 Article ID 476878 9 pageshttpdxdoiorg1011552013476878

Research ArticleMultiobjective-Optimized Design of a New UWB Antenna forUWB Applications

C Moreno de Jong van Coevorden1 M Fernaacutendez Pantoja1 Salvador G Garciacutea1

A Rubio Bretones1 R Goacutemez-Martiacuten1 and K Palmer2

1 Department of Electromagnetism University of Granada Avenida Fuentenueva sn 18071 Granada Spain2Department of Electric and Electronic Engineering University of Stellenbosch Matieland 7602 South Africa

Correspondence should be addressed to Salvador G Garcıa salvaugres

Received 20 November 2012 Revised 6 March 2013 Accepted 7 March 2013

Academic Editor Michael Yan Wah Chia

Copyright copy 2013 C Moreno de Jong van Coevorden et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

A multiobjective genetic algorithm has been applied to design a new printed bow-tie antenna for ultrawideband applications thatis ground penetrating radar short range and high data rate communications and so forth The ultrawideband performance withrespect to antenna impedance and gain is achieved by an optimized resistive loading profile and flare angle A low-cost prototypeis manufactured and numerical simulations are validated with measurements

1 Introduction

Theantenna performance in ground penetrating radar (GPR)systems ismeasured by its ability to transmit and receive shortpulses (on the order of a few nanoseconds) whose durationis a tradeoff between range resolution and penetration depth[1]The transmission without distortion of these pulses needsultrawideband (UWB) nondispersive antenna systems Suchultrawideband antennas must exhibit a linear phase charac-teristic over the whole operating frequency band (so-calledtransient antenna [2]) apart from constant magnitude of theinput impedance polarization and gain

When an antenna is fed by a transient pulse (impulseantenna) the initial acceleration of the charges producesradiation from the feed point which is the sole sourceof radiation until the traveling pulse reaches any antennadiscontinuity There the current pulse that propagates alongthe antenna structure is partially reflected constitutingsecondary radiating sources [3] Therefore the time-domainantenna response can be divided into two parts the mainpulse and the ringing region The main pulse results fromthe direct radiation of the excitation pulse at the feed pointwhile radiation originating at antenna discontinuities givesrise to the ringing region Depending on the relation between

width of the pulse and size of the antenna these regions couldoverlap

A design goal for impulse GPR antennas is the removalor minimization of the ringing region The main method toachieve this is to establish a proper distribution of resistiveloads along the antenna to diminish the reflections of thecurrent pulses at antenna discontinuities [4ndash6] As a resultthe input-impedance bandwidth of the antenna is increased[7] However the enhancement of the ultrawideband charac-teristics of an antenna by loading its structure reduces theantenna gain due to ohmic losses The design of such anten-nas is a multiobjective engineering problem with oppositegoals where a tradeoff between bandwidth and gain needsto be found

One kind of antenna widely used in GPR applicationsis the solid bow-tie antennas [4 8] being simple to designand having ultrawideband impedance properties Howeverin some cases the use of the wire bow-tie antenna or stripbow-tie antenna may be advantageous as they are moreeasily loaded with resistors than their solid counterpartsand have adaptive properties [9 10] In [11] a microgeneticoptimization algorithm (GA) was used to optimize the inputimpedance bandwidth of a thin-wire bow-tie antenna Theresult was an antenna with a very high impedance bandwidth

2 International Journal of Antennas and Propagation

but a low gain In an effort to increase the directivity of theantenna a new thin-wire design was proposed in [12] wherethe front-to-back ratio and the broadband behavior of theinput impedance were simultaneously optimized by meansof a multiobjective GA Improved directivity was achieved bybending the two arms of the antenna in a horn-like way whilethe broadband impedance characteristics were accomplishedby discrete resistive loading of the antenna wires The resultwas greater broadside direction gain but at the expense ofaugmenting the antenna profile

In this paper a new optimized printed-strip bow-tieantenna is proposed With the aim of using a multiobjectiveGA for the simultaneous optimization of three followingantenna parameters 119878

11bandwidth gain bandwidth and

gain in the broadside direction This approach goes beyondsimply seeking an antenna with high impedance bandwidthas in the case described in [11] Moreover the possibilityof using different load profiles on the different strips thatcompose the antenna geometry is allowed so that it ispossible to find better designs than in [11 12] where thesame load profile was used in all the antenna wires The onlycondition imposed on the load profile is to have quadrangularsymmetry The optimization was carried out in two stepsFirst a flat thin-wire bow-tie antenna was designed byhybridizing an in-house multiobjective GA code with themethod-of-moments code NEC [13] for modeling the thin-wire antenna response Subsequently in order to facilitate theconstruction of a prototype the wire antenna was convertedinto a printed strip using the same surface area rule of thumb[14] Finally the equivalent printed antenna prototype wasbuilt and its measured 119878

11parameter and gain were found to

be in good agreement with the numerical results predicted bythe commercial code CST Microwave Studio (This two-stepdesigning procedure is followed because the computationspeed of the hybrid GA-NEC code is much faster than theGA-CST)

The paper is organized as follows Section 2 describes theparameters that characterize the antenna to be optimized thespecific strategy followed to produce a new UWB optimizeddesign and the numerical results corresponding to thatdesign In Section 3 the 119878

11parameter and antenna gain are

measured and compared with numerical simulations Con-clusions are discussed in Section 4 where future directions ofinvestigation are also outlined Finally in Appendix a step-by-step description of the process followed to transform athin-wire bow-tie antenna to an equivalent printed antennais given

2 Multiobjective Antenna Optimization

There are many strategies to handle multiobjective optimiza-tion problems Vector Evaluated Genetic Algorithm [15]linear aggregation of objectives [16] or the most widely usedwhich is based on Pareto dominance [17] In this paper wewill use this last strategy due to its high rate of success inelectrical and electronic engineering applications [18 19] Inparticular we chose the nondominated sorting genetic algo-rithm in the revised version of Deb et al (NSGAII) because

119877ij

119871119908

Δ gap

120572flare

2119903119908

Δ119878

2

Δ 119878

Δ 119878

2

Figure 1 Geometry of the thin-wire bow-tie antenna to be opti-mized 119871

119908= 75mm Δ

119878= 1875mm Δ gap = 2mm and radius

119903119908

= 065mm

of its easy implementation remarkable ability to reach thetrue Pareto front in mathematical test functions and lesscomputational complexity than other similar algorithms [17]

In this section the system to be optimized is firstdescribed setting what parameters can be tuned up and whatparameters are kept fixed Later the basics of the optimizationalgorithm that is used in thiswork is outlined endingwith thepresentation of the numerical results from the optimizationprocess

21 Description of the Optimized System The geometry ofthe thin-wire bow-tie antenna proposed for optimization isshown in Figure 1 It is made up by 119873

119889dipoles (2 lowast 119873

119889

wires) forming a fanlike structure and fed at the centercommon point Equally spaced gaps of width Δ gap separatedby a distance of Δ

119878are inserted in the wires At these

gaps chip resistors are soldered in order to enhance theultrawideband characteristics of the antenna to be optimizedin the frequency range between 05GHz and 3GHz which isa typical band in GPR applications Four different resistorsare located on each arm but since the maximum of theradiation pattern is required to be in the broadside directionthe distribution of resistors is forced to have quadrangularsymmetry and therefore only 2 lowast 119873

1198894 different resistors will

be considered in total for an antenna design The numberof dipoles were chosen to be 119873

119889= 8 because although the

UWB behavior of the antenna increases with the number ofwires no noticeable improvements are found over 119873

119889= 8

[20] therefore the load profile will consist in only 16 differentresistors

Among the parameters that define the antenna theones that will be allowed to vary during the optimizationprocess are the exterior flare angle 120572flare keeping the wiresequiangular spaced and the values of the resistors119877

119894119895atwire 119894

119894 = 1 4 and position 119895 on that wire 119895 = 1 4 where 119894 =

1 is the most external wire and 119895 = 1 the resistor placed in thevicinity of the feed point The remaining parameters are kept

International Journal of Antennas and Propagation 3

(1) 119905 larr 0

(2) 119905 Random creation of initial population

(3) F119905

larr Evaluation(119905

)(4) larr GO(

119905

F119905

) Application selection crossover and mutation operators to breed new offsprings(5) F larr Evaluation()(6) while End optimization==False do(7) 119905 larr 119905 + 1

(8) 119905+1

larr Elitism(119905

F119905

F) Selection of the best 119873pop individuals from = cup

(9) larr GO(119905+1

F119905+1

) Application selection crossover and mutation operators to breed new offsprings(10) F larr Evaluate()(11) if Goal reached then(12) End optimization larr True(13) end if(14) end while

Algorithm 1 Description of the NSGAII

fixed The wires are chosen to have a radius of 119903119908

= 065mmwhile their length is 119871

119908= 75mm and the resistors of body

length Δ gap = 2mm (0805 SMD chip resistors) are equallyspaced over thewires separated by a distanceΔ

119878= 1875mm

22 Antenna Optimization Using a Multiobjective GA GAsare optimization algorithms based on the theories of evo-lution and genetics [21] GAs are iterative algorithms thatconsider a population of individuals each individual repre-senting a potential solution of the problem at hand whichis described by a set of genes The process starts by evalu-ating the quality of individuals in the initial population bycalculating a representative function named fitness functionwhich is defined by the designer in terms of the expectedperformance of the optimized antenna The best designs areselected and undergo the genetic operations of crossoverand mutation resulting in a new generation of individualsto be evaluated again Crossover is usually accomplishedby randomly selecting two individuals (called parents) andgenerating another two (called offsprings) by mixing thegenes carried by the parents in some specified fashionMutation changes a gene with a certain probability within theallowed values in the design This process is continued untila stop criterion is met

The specific optimization algorithm that is used in thepresent work is the NSGAII This algorithm is used to opti-mize simultaneously the 119878

11parameter and gain (119866) of the

model proposed above seeking to achieve the widest possiblebandwidth in both magnitudes with the highest value of thelatter As fitness functions to evaluate the performance of eachindividual the following were chosen

11989111987811

the width of the band where 11987811

is below minus10 dBcalculated using as characteristic impedance 119885

0=

re(119885in) being 119885in the mean value of the real partof 119885in in the frequency band of interest Withthis the algorithm searches antennas having inputimpedances with real parts near to re(119885in) and imag-inary parts as close to 0 as possible

119891119866 the width of the band where the gain is between itsmaximum value and 3 dB below it

119891119866max

The maximum value of the Gain in the frequencyband of operation

The NSGAII starts with the creation of a population(0

) (the exponent 119905 of 119905

means the iteration step of theoptimization process) of 119873pop individuals (antenna designs)with its parameters randomly chosen from a uniform dis-tribution In the present case each antenna is representedby a real number coding the flare angle 120572flare and aninteger matrix of 16 rows of three integers 119883

1 1198832which

defines the value of each of the 16 different resistors of thestructure as 119877 = 119883

1times 101198832 Ω After a preliminary study

the search space was reduced to the one defined by thediscrete values 119883

1isin [0 99] and 119883

2isin [0 1] and the

continuous interval 120572flare isin [60∘ 120∘] thereby speeding

up the convergence of the optimization process The maincycle of the iterative process (see Algorithm 1) starts with theevaluation of each individual of the population by computing119885in and 119866 over the frequency band of interest by meansof the method-of-moments-based frequency-domain codeNECThen the three fitness functions defined above are cal-culated for each individual and stored in a matrixF

119905

Afterthe entire population is evaluated and the most promisingsolutions are selected genetic operators (GO) are applied tothe population to generate the new generation of potentialsolutions or offspring () from the previous generation(119905

)The specific genetic operators we employed were as fol-

lows First a binary tournament selectionwas used to identifythe best individuals within the population This operatorrandomly picks two individuals from the previous populationand chooses the superior solution for a future crossoverfollowing the Pareto domination rules As a mechanism torecombine the features of two individuals previously selecteda hybrid real-discrete crossover operator is chosen wherethe angle 120572flare is recombined via simulated binary crossover


(1) for 119895 larr 1 3 do(2) 119906 larr 119880[0 1]

(3) if 119906 lt 119901res(119895) then Decision of muting one of the values that define a resistors(4) 119883

119895isin 119880[0 120581

119895]

(5) end if(6) end for

Algorithm 2 Discrete mutation of genes corresponding to resistors

Table 1 Load profile of the selected antenna designThe 119894 values runin columns the 119895 in rows

119877119894119895

1 2 3 41 24 0 11 392 270 20 0 123 790 33 14 964 59 170 5 230

[22] and the resistors by means of a two point crossover [21]The polynomial distribution introduced by Deb [23] isapplied to mutate 120572flare while to mutate the resistors thealgorithm shown in Algorithm 2 is used Among theseoperators the specific multiobjective genetic operator is thetournament selection in which the dominance in the paretosense is implemented

The values of parameter 120581 in Algorithm 2 define thevariation range of each variable 119883

119895 where 120581

119895= (9 9 2)

On the other hand after a short parametric study it wasfound that the probability rate 119901res = (02 1 005) givessatisfactory results This probability was chosen so thatafter the individual was selected to mutate (according tothe muting rate 119901

119898) the value mutated resistor was in the

neighborhood of the previous oneFinally to create the next generation (

119905+1

) an elitismoperator was applied where the best 119873pop individuals from119905

cup119905

were selectedThis process was repeated until a properset of solutions was found For further details on the NSGAIIalgorithm see [17]

23 Optimization Results To ensure the convergence of thePareto front five independent runs of the optimizationalgorithm were executed with a population of 119873pop = 100

and crossover and mutation rates 119901119888

= 08 and 119901119898

= 004respectively The achieved nondominated set of solutionsappears in Figure 2 which displays designs with 119878

11band-

widths from 16 1 to 57 1 gain bandwidths from 10 1 to54 1 and maximum gains from minus15 dB to 59 dB From thisset of solutions the designer can choose the best antenna thatmatches a particular application In this paper a compromisedesign (marked in red in Figure 2) is chosen to construct aprototype and measure its electrical properties

The parameters of the chosen antenna are 120572flare = 84∘

while the load profile is shown in Table 1

Gai

n (d

B)

11987811bandwidth

Gain bandwidth

12

34

56

123

45

6

minus2

minus1

0

1

2

3

4

5

6

7

Figure 2 Pareto front and its projections at the end of the optimi-zation processThePareto front is represented by black sphereswhilethe selected design (119891

11987811= 394 119891

119866= 458 119891

119866max= 293) is marked

in red and pointed with an arrow

3 Experimental Validation ofthe Antenna Performance

To illustrate the performance of the antenna design proposedin the previous section two prototypes were fabricated andtested One monopole over a ground plate fed with a coaxialconnector and a dipole antenna fed by a 1205824 balun Bothwere made of metallic strips printed on FR-4 substrates(120598119903

= 49 tan 120575 = 0025) of thickness ℎ = 08mm) Aprinted antenna model was chosen to facilitate its fabricationand testing in our laboratory facilities Before the prototypeswere built numerical simulations were carried out by CSTsoftware to determine how the antenna performance variedfrom the thin-wire model simulated by NEC and optimizedby GA to the printed strip model dealt with CST Thenumerical results of all these experiments are presented inAppendix

First the monopole antenna shown in Figure 3 was builtto measure its 119878

11parameter The antenna was printed on

a FR-4 panel of dimension 132mm times 100mm situatedperpendicularly to an aluminum ground plane and fed witha 50 Ω coaxial cable with its inner conductor attached tothe antenna structure and its outer one to the groundplane In order to know the minimum size of the ground


Figure 3 Monopole antenna for 11987811measurements

plane some numerical simulations were carried out in CSTThe simulated antenna system was modeled as realistic aspossible including the FR-4 substrate finite thickness groundplane and the coaxial connector feeding the antenna Thesenumerical simulations showed that for 119878

11calculations a

size of 297mm times 400mm for the ground plane accuratelyapproximates an infinite ground planeThe 119878

11parameterwas

measured in the frequency range from 500MHz to 3GHz byplacing the antenna under test inside an anechoic chamberand using an HP 8510C network analyzer Figure 4 shows themeasured return loss compared to the CST numerical results(the measured values were normalized to the mean valueof the simulated antenna input resistance in the frequencyband considered which was 119885

0= 81 Ω) It can be seen that

measurements and simulations match closely throughout thefrequency band Moreover although it is not shown herebecause the optimization was performed only up to 3GHZit should be mentioned that the numerical return loss wasbelow minus10 db up to 8GHz rendering a numerical bandwidthin 11987811greater than 10 1

Next we proceeded to measure the antenna gain patternbut unlike what happened with the 119878

11parameter it was

found the CST simulations indicated that the size of theground plane needed by the gain pattern of the monopoleantenna to match that of the dipole antenna was on theorder of several meters Since this was an impractical sizefor measurements in the anechoic chamber available atthe University of Stellenbosch as a second prototype thewhole dipole antenna was designed and fabricated It wasprinted on a FR-4 panel of dimension (200 times 205mm) andfed with a 1205824 balun designed for 138GHz (see Figure 5)Measurements were carried out just at the frequency of138GHz while numerical simulations were performed overthe entire frequency range Figure 6 plots with a symbol linethe numerically calculated gain in the broadside directionversus frequency showing a 3 dB gain bandwidth of 1 45A comparison between the computed and measured gainpatterns at 138GHz is included in the inset of Figure 6where a close matching between both results is noticedThe measured 119878

11at 138GHz using the 1205824 balun was

minus8 dBFinally since a good time-domain performance is a

primary requirement when designing an UWB antenna for

11987811

(dB)

0

minus5

minus10

minus15

minus20

minus2505 075 1 125 15 175 2 225 25 275 3

Frequency (GHz)

Simulated CSTMeasured

Figure 4 Simulated and measured 11987811parameter for the monopole

strip bow-tie antenna

Figure 5 Strip dipole bow-tie antenna built for gainmeasurementIt is excited with a 1205824 balun designed for 138GHz

GPR applications the time-domain behavior of the strip-dipole antenna has been investigatedThe dipole antenna wasexcited at its center by a transient voltage pulse with sig-nificant spectral components between 075GHz and 3GHzand its response was numerically calculated using CST Theshape of the voltage input signal shown in a solid line inFigure 7 closely resembles that usually found in commercialGPR systems It also has to be noted how the resistanceloading has eliminated the multiple resonances associated tothis type of antennas when unloaded [20] These resonancesare related to the presence of eigen modes which in the caseof loaded antennas are shifted to lower frequencies out of thefrequency band of interest


2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

Gai

n (d

B)

075 1 125 15 175 2 225 25 275 3Frequency (GHz)

Simulated gain

Simulated Measured

0minus10

minus20

0minus10

minus20

minus30

minus40

minus50

minus40

minus30

030

60

90

120

150180

210

240

270

300

330

Figure 6 Simulated gain at the broadside direction over the frequency band of interest Inset simulated andmeasured E-plane gain patternsof the dipole antenna at 138GHz

Volta

ge (V

)

1

05

0

minus05

minus10 1 2 3 4 5 6 7

minus01

minus005

0

005

01

Curr

ent (

A)

Time (ns)

Input voltageCurrent

Figure 7 Time-domain response of the chosen antenna designinput voltage (solid line) and output current at the feed point(dashed line) versus time

To quantify the level of late-time ringing in the antennatime-domain response the fidelity between the input voltageand the output current at the feed point is calculated asthe cross-correlation between both magnitudes using theexpression [24]

fidelity12

=

100381610038161003816100381610038161003816100381610038161003816

12058812

(119905)

radic1205881

(0) 1205882

(0)

100381610038161003816100381610038161003816100381610038161003816max (1)

where 12058812

(119905) 1205881(0) and 120588

2(0) are the cross-covariance and

autocovariances of signals one and two respectively Thefidelity compares the pulse shapes disregarding theirs ampli-tudes and time-delay factors The value of the fidelity rangesfrom 0 (totally different signals) to 1 (the signals matchperfectly) For the proposed antenna design the fidelity factorcomputed for the input voltage and the current at the feedwasfound to be 0937 The current pulse at the feed point is plotversus time in Figure 7 and it can be seen that its shape isquite similar to that of the voltage input pulse with a very lowlate-time ringing

It is also of great interest to investigate the ability of anUWB antenna to preserve the waveform of the radiated fieldsin different directions In the time-domain and for trans-mission mode the quality of the radiated signal waveform inrelation to the input voltage applied to the antenna terminalsis measured by the fidelity between the time integral of thetransmitted field and the input voltage [24]The time-domainelectric fields radiated in different directions in the E and Hplanes were calculated using CST In all cases the fields werecomputed at a distance of 05m from the antenna feed pointThey are plotted in Figures 8 and 9 The simulated fidelityfactors between the input voltage and the time-integratedradiated fields are given in Table 2 for different observationangles It can be seen that the transmitted electric field intheH-plane presents high fidelity and its amplitude is almostconstant for the different observation angles Regarding thebehavior of the electric field in the E-plane Figure 9 showshow on the one hand the amplitude of the field decays


120579

10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘

Figure 8 Simulated electric field for different azimuth angles in the H-plane calculated at a distance of 05m from the antenna feed port

Table 2 Fidelity of the radiated field at several observation angles

120579 E-plane H-plane0∘ 0947 0947

15∘ 0943 0945

30∘ 0939 0943

45∘ 0930 0933

60∘ 0912 0925

75∘ 0774 0923

90∘ 0626 0956

as the observation angle is increased and on the other handthe field has high fidelity for observation angles 120579 le 60 but itdegrades dramatically for greater observation angles Theseresults are in accordance with the typical shape of dipole-antenna radiation patterns in the frequency domain wherethe amplitude is almost constant in the H-plane while inthe E-plane varies from maximum values at broadside tominimum in the endfire direction [25]

4 Conclusion

A multiobjective GA has been employed to the design ofnovel UWB thin-wire bow-tie antenna for GPR applicationsThe maximum antenna gain and the impedance and gainbandwidths are simultaneously optimized The advantage

of using a multiobjective GA is that a vast set of designsolutions is found in an optimization run instead of onlyone allowing the engineer to pick the one most suitable toa particular application An specific design has been chosenon the Pareto-optimal front and following the same surfacerule an equivalent printed-strip model of the selected thin-wire antenna has been built and measured The selectedUWB antenna has been characterized in the frequency andtime domains and good agreement was observed betweennumerical predictions and experimental results

Appendix

Strip Model of the Thin-WireBow-Tie Antenna

A printed antenna based on a thin-wire design requires thewidth of the printed strips to be chosen so that both modelsbehave in the same manner This is often done by using thesame surface area rule [14] In this appendix we performnumerical simulations with CST to check whether this ruleholds for this particular case

In the thin-wire model the area of each wire is 119860119908

=

2119871119908

120587119903119908 whereas in the printed antenna-model the area of

each strip is 119860119904

= 2119871119908

119908119904 where 119908

119904is the strip width

(the strip thickness is neglected) For the antenna design ofradius of 065mm proposed in this paper (see Figure 10)


8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘

120579

Figure 9 Simulated electric field for different azimuth angles in the E-plane calculated at a distance of 05m from the antenna feed port

CST wires (free space)CST stripes (free space)

05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

300

200

100

0

Resis

tanc

e (Ω

)

(a)


05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

100

50

0minus50

minus100

Reac

tanc

e (Ω

)

(b)

Figure 10 Simulated input impedance of the dipole thin-wire antenna proposed in this paper and a strip antenna that fulfills the same surfacearea Both antennas are located in free space

the same surface area rule yields 2mm-wide strips for theprinted model Figure 10 shows the good agreement betweenthe input impedance of the 2mm-wide strip dipole antennaand that of its 065mm-radius thin-wire counterpart in theconsidered frequency range Both antennas were located infree space

Acknowledgments

The work described in this paper and the research leadingto these results has received funding from the Spain-SouthAfrican joint research project HS2006-0012 the European

Communityrsquos Seventh Framework Programme FP72007ndash2013 under Grant Agreement no 205294 (HIRF SE project)from the Spanish National Projects TEC2010-20841-C04-04 CSD2008-00068 PHB2009-0067-PC from the Junta deAndalucia Project P09-TIC-5327 and from the GranadaExcellence Network of Innovation Laboratories (GENIL)project

References

[1] D J Daniels Surface Penetrating Radar IEE Radar Navigationand Avionics Series Institute of Electrical amp Electronics Engi-nee 1996


[2] P R Foster ldquoPerformance of ultrawideband antennasrdquo inUltrawideband Radar vol 1631 of Proceedings of SPIE pp 134ndash145 January 1992

[3] R Gomez-Martın A R Bretones and S G Garcıa ldquoSomethoughts about transient radiation by straight thin wiresrdquo IEEEAntennas and Propagation Magazine vol 41 no 3 pp 24ndash331999

[4] K L Shlager G S Smith and J G Maloney ldquoOptimizationof bow-tie antennas for pulse radiationrdquo IEEE Transactions onAntennas and Propagation vol 42 no 7 pp 975ndash982 1994

[5] TWu and R King ldquoThe cylindrical antenna with nonreflectingresistive loadingrdquo IEEE Transactions on Antennas and Propaga-tion vol 13 no 3 pp 369ndash373 1988

[6] M Fernandez-Pantoja A Monorchio A R Bretones and RGomez-Martın ldquoDirect GA-based optimisation of resistivelyloaded wire antennas in the time domainrdquo Electronics Lettersvol 36 no 24 pp 1988ndash1990 2000

[7] S Lee and K Mei ldquoAnalysis of zigzag antennasrdquo IEEE Transac-tions on Antennas and Propagation vol 18 no 6 pp 760ndash7641970

[8] Y Nishioka O Maeshima T Uno and S Adachi ldquoFDTDanalysis of resistor-loaded bow-tie antennas covered withferrite-coated conducting cavity for subsurface radarrdquo IEEETransactions on Antennas and Propagation vol 47 no 6 pp970ndash977 1999

[9] A A Lestari A G Yarovoy and L P Ligthart ldquoNumerical andexperimental analysis of circular-end wire bow-tie antennasover a lossy groundrdquo IEEE Transactions on Antennas andPropagation vol 52 no 1 pp 26ndash35 2004

[10] A A Lestari A G Yarovoy and L P Ligthart ldquoAdaptive wirebow-tie antenna for GPR applicationsrdquo IEEE Transactions onAntennas and Propagation vol 53 no 5 pp 1745ndash1754 2005

[11] C M de Jong van Coevorden A R Bretones M Fernandez-Pantoja F J Garcıa Ruiz S G Garcıa and R Gomez-MartınldquoGA design of a thin-wire bow-tie antenna for GPR applica-tionsrdquo IEEETransactions onGeoscience andRemote Sensing vol44 no 4 pp 1004ndash1009 2006

[12] C Moreno de Jong van Coevorden A R Bretones MFernandez-Pantoja et al ldquoThin-wire antenna design for GPRapplications using a multi-objective GArdquo Near Surface Geo-physics vol 5 no 1 pp 23ndash28 2007

[13] G Burke A Poggio J Logan and J Rockway ldquoNECmdashnumerical electromagnetics code for antennas and scatteringrdquoin Antennas and Propagation Society International Symposiumvol 17 pp 147ndash150 1979

[14] A C Ludwig ldquoWire grid modeling of surfacesrdquo IEEE Transac-tions on Antennas and Propagation vol 35 no 9 pp 1045ndash10481987

[15] J D Schaffer ldquoMultiple objective optimization with vector eval-uated genetic algorithmsrdquo in Proceedings of the 1st InternationalConference on Genetic Algorithms pp 93ndash100 1985

[16] P Hajela and C Y Lin ldquoGenetic search strategies in multicrite-rion optimal designrdquo Structural Optimization vol 4 no 2 pp99ndash107 1992

[17] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[18] S Cui A Mohan and D S Weile ldquoPareto optimal design ofabsorbers using a parallel elitist nondominated sorting geneticalgorithm and the finite element-boundary integral methodrdquo

IEEE Transactions on Antennas and Propagation vol 53 no 6pp 2099ndash2107 2005

[19] Y Kuwahara ldquoMultiobjective optimization design of Yagi-Udaantennardquo IEEE Transactions on Antennas and Propagation vol53 no 6 pp 1984ndash1992 2005

[20] C M de Jong van Coevorden Optimized antenna design usinggenetic algorithms [PhD thesis] Electromagnetismo Universi-dad de Granada 2008

[21] K A de Jong Analysis of the behavior a class of geneticadaptative systems [PhD thesis] Dept Comput Commun SciUniv Michigan Ann Arbor Mitch USA 1975

[22] K Deb and R B Agrawal ldquoSimulated binary crossover forcontinuous search spacerdquo Complex Systems vol 9 pp 115ndash1481995

[23] K Deb ldquoAn efficient constraint handling method for geneticalgorithmsrdquo Computer Methods in Applied Mechanics and Engi-neering vol 186 no 2ndash4 pp 311ndash338 2000

[24] O E Allen D A Hill and A R Ondrejka ldquoTime-domainantenna characterizationsrdquo IEEE Transactions on Electromag-netic Compatibility vol 35 no 3 pp 339ndash345 1993

[25] C A Balanis AntennaTheory Analisys and Design JohnWileyamp Sons New York NY USA 1982

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



but a low gain In an effort to increase the directivity of theantenna a new thin-wire design was proposed in [12] wherethe front-to-back ratio and the broadband behavior of theinput impedance were simultaneously optimized by meansof a multiobjective GA Improved directivity was achieved bybending the two arms of the antenna in a horn-like way whilethe broadband impedance characteristics were accomplishedby discrete resistive loading of the antenna wires The resultwas greater broadside direction gain but at the expense ofaugmenting the antenna profile

In this paper a new optimized printed-strip bow-tieantenna is proposed With the aim of using a multiobjectiveGA for the simultaneous optimization of three followingantenna parameters 119878

11bandwidth gain bandwidth and

gain in the broadside direction This approach goes beyondsimply seeking an antenna with high impedance bandwidthas in the case described in [11] Moreover the possibilityof using different load profiles on the different strips thatcompose the antenna geometry is allowed so that it ispossible to find better designs than in [11 12] where thesame load profile was used in all the antenna wires The onlycondition imposed on the load profile is to have quadrangularsymmetry The optimization was carried out in two stepsFirst a flat thin-wire bow-tie antenna was designed byhybridizing an in-house multiobjective GA code with themethod-of-moments code NEC [13] for modeling the thin-wire antenna response Subsequently in order to facilitate theconstruction of a prototype the wire antenna was convertedinto a printed strip using the same surface area rule of thumb[14] Finally the equivalent printed antenna prototype wasbuilt and its measured 119878

11parameter and gain were found to

be in good agreement with the numerical results predicted bythe commercial code CST Microwave Studio (This two-stepdesigning procedure is followed because the computationspeed of the hybrid GA-NEC code is much faster than theGA-CST)

The paper is organized as follows Section 2 describes theparameters that characterize the antenna to be optimized thespecific strategy followed to produce a new UWB optimizeddesign and the numerical results corresponding to thatdesign In Section 3 the 119878

11parameter and antenna gain are

measured and compared with numerical simulations Con-clusions are discussed in Section 4 where future directions ofinvestigation are also outlined Finally in Appendix a step-by-step description of the process followed to transform athin-wire bow-tie antenna to an equivalent printed antennais given

2 Multiobjective Antenna Optimization

There are many strategies to handle multiobjective optimiza-tion problems Vector Evaluated Genetic Algorithm [15]linear aggregation of objectives [16] or the most widely usedwhich is based on Pareto dominance [17] In this paper wewill use this last strategy due to its high rate of success inelectrical and electronic engineering applications [18 19] Inparticular we chose the nondominated sorting genetic algo-rithm in the revised version of Deb et al (NSGAII) because

119877ij

119871119908

Δ gap

120572flare

2119903119908

Δ119878

2

Δ 119878

Δ 119878

2

Figure 1 Geometry of the thin-wire bow-tie antenna to be opti-mized 119871

119908= 75mm Δ

119878= 1875mm Δ gap = 2mm and radius

119903119908

= 065mm

of its easy implementation remarkable ability to reach thetrue Pareto front in mathematical test functions and lesscomputational complexity than other similar algorithms [17]

In this section the system to be optimized is firstdescribed setting what parameters can be tuned up and whatparameters are kept fixed Later the basics of the optimizationalgorithm that is used in thiswork is outlined endingwith thepresentation of the numerical results from the optimizationprocess

21 Description of the Optimized System The geometry ofthe thin-wire bow-tie antenna proposed for optimization isshown in Figure 1 It is made up by 119873

119889dipoles (2 lowast 119873

119889

wires) forming a fanlike structure and fed at the centercommon point Equally spaced gaps of width Δ gap separatedby a distance of Δ

119878are inserted in the wires At these

gaps chip resistors are soldered in order to enhance theultrawideband characteristics of the antenna to be optimizedin the frequency range between 05GHz and 3GHz which isa typical band in GPR applications Four different resistorsare located on each arm but since the maximum of theradiation pattern is required to be in the broadside directionthe distribution of resistors is forced to have quadrangularsymmetry and therefore only 2 lowast 119873

1198894 different resistors will

be considered in total for an antenna design The numberof dipoles were chosen to be 119873

119889= 8 because although the

UWB behavior of the antenna increases with the number ofwires no noticeable improvements are found over 119873

119889= 8

[20] therefore the load profile will consist in only 16 differentresistors

Among the parameters that define the antenna theones that will be allowed to vary during the optimizationprocess are the exterior flare angle 120572flare keeping the wiresequiangular spaced and the values of the resistors119877

119894119895atwire 119894

119894 = 1 4 and position 119895 on that wire 119895 = 1 4 where 119894 =

1 is the most external wire and 119895 = 1 the resistor placed in thevicinity of the feed point The remaining parameters are kept


(1) 119905 larr 0


(3) F119905


)(4) larr GO(

119905

F119905


(8) 119905+1

larr Elitism(119905

F119905


(9) larr GO(119905+1

F119905+1







119878= 1875mm





11989111987811



0=



119891119866max





1 1198832which




1isin [0 99] and 119883

2isin [0 1] and the



119905





(1) for 119895 larr 1 3 do(2) 119906 larr 119880[0 1]


119895isin 119880[0 120581

119895]




119877119894119895

1 2 3 41 24 0 11 392 270 20 0 123 790 33 14 964 59 170 5 230



119895 where 120581

119895= (9 9 2)




119905+1


cup119905




= 08 and 119901119898


11band-




Gai

n (d

B)

11987811bandwidth

Gain bandwidth

12

34

56

123

45

6

minus2

minus1

0

1

2

3

4

5

6

7


11987811= 394 119891

119866= 458 119891












11calculations a


11parameterwas





11parameter it was





11987811

(dB)

0

minus5

minus10

minus15

minus20

minus2505 075 1 125 15 175 2 225 25 275 3

Frequency (GHz)







2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

Gai

n (d

B)

075 1 125 15 175 2 225 25 275 3Frequency (GHz)

Simulated gain

Simulated Measured

0minus10

minus20

0minus10

minus20

minus30

minus40

minus50

minus40

minus30

030

60

90

120

150180

210

240

270

300

330


Volta

ge (V

)

1

05

0

minus05

minus10 1 2 3 4 5 6 7

minus01

minus005

0

005

01

Curr

ent (

A)

Time (ns)




fidelity12

=

100381610038161003816100381610038161003816100381610038161003816

12058812

(119905)

radic1205881

(0) 1205882

(0)

100381610038161003816100381610038161003816100381610038161003816max (1)

where 12058812

(119905) 1205881(0) and 120588





120579

10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘



120579 E-plane H-plane0∘ 0947 0947

15∘ 0943 0945

30∘ 0939 0943

45∘ 0930 0933

60∘ 0912 0925

75∘ 0774 0923

90∘ 0626 0956


4 Conclusion



Appendix




=

2119871119908



= 2119871119908

119908119904 where 119908




8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘

120579



05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

300

200

100

0

Resis

tanc

e (Ω

)

(a)


05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

100

50

0minus50

minus100

Reac

tanc

e (Ω

)

(b)



Acknowledgments



References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(1) 119905 larr 0


(3) F119905


)(4) larr GO(

119905

F119905


(8) 119905+1

larr Elitism(119905

F119905


(9) larr GO(119905+1

F119905+1







119878= 1875mm





11989111987811



0=



119891119866max





1 1198832which




1isin [0 99] and 119883

2isin [0 1] and the



119905





(1) for 119895 larr 1 3 do(2) 119906 larr 119880[0 1]


119895isin 119880[0 120581

119895]




119877119894119895

1 2 3 41 24 0 11 392 270 20 0 123 790 33 14 964 59 170 5 230



119895 where 120581

119895= (9 9 2)




119905+1


cup119905




= 08 and 119901119898


11band-




Gai

n (d

B)

11987811bandwidth

Gain bandwidth

12

34

56

123

45

6

minus2

minus1

0

1

2

3

4

5

6

7


11987811= 394 119891

119866= 458 119891












11calculations a


11parameterwas





11parameter it was





11987811

(dB)

0

minus5

minus10

minus15

minus20

minus2505 075 1 125 15 175 2 225 25 275 3

Frequency (GHz)







2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

Gai

n (d

B)

075 1 125 15 175 2 225 25 275 3Frequency (GHz)

Simulated gain

Simulated Measured

0minus10

minus20

0minus10

minus20

minus30

minus40

minus50

minus40

minus30

030

60

90

120

150180

210

240

270

300

330


Volta

ge (V

)

1

05

0

minus05

minus10 1 2 3 4 5 6 7

minus01

minus005

0

005

01

Curr

ent (

A)

Time (ns)




fidelity12

=

100381610038161003816100381610038161003816100381610038161003816

12058812

(119905)

radic1205881

(0) 1205882

(0)

100381610038161003816100381610038161003816100381610038161003816max (1)

where 12058812

(119905) 1205881(0) and 120588





120579

10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘



120579 E-plane H-plane0∘ 0947 0947

15∘ 0943 0945

30∘ 0939 0943

45∘ 0930 0933

60∘ 0912 0925

75∘ 0774 0923

90∘ 0626 0956


4 Conclusion



Appendix




=

2119871119908



= 2119871119908

119908119904 where 119908




8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘

120579



05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

300

200

100

0

Resis

tanc

e (Ω

)

(a)


05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

100

50

0minus50

minus100

Reac

tanc

e (Ω

)

(b)



Acknowledgments



References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(1) for 119895 larr 1 3 do(2) 119906 larr 119880[0 1]


119895isin 119880[0 120581

119895]




119877119894119895

1 2 3 41 24 0 11 392 270 20 0 123 790 33 14 964 59 170 5 230



119895 where 120581

119895= (9 9 2)




119905+1


cup119905




= 08 and 119901119898


11band-




Gai

n (d

B)

11987811bandwidth

Gain bandwidth

12

34

56

123

45

6

minus2

minus1

0

1

2

3

4

5

6

7


11987811= 394 119891

119866= 458 119891












11calculations a


11parameterwas





11parameter it was





11987811

(dB)

0

minus5

minus10

minus15

minus20

minus2505 075 1 125 15 175 2 225 25 275 3

Frequency (GHz)







2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

Gai

n (d

B)

075 1 125 15 175 2 225 25 275 3Frequency (GHz)

Simulated gain

Simulated Measured

0minus10

minus20

0minus10

minus20

minus30

minus40

minus50

minus40

minus30

030

60

90

120

150180

210

240

270

300

330


Volta

ge (V

)

1

05

0

minus05

minus10 1 2 3 4 5 6 7

minus01

minus005

0

005

01

Curr

ent (

A)

Time (ns)




fidelity12

=

100381610038161003816100381610038161003816100381610038161003816

12058812

(119905)

radic1205881

(0) 1205882

(0)

100381610038161003816100381610038161003816100381610038161003816max (1)

where 12058812

(119905) 1205881(0) and 120588





120579

10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘



120579 E-plane H-plane0∘ 0947 0947

15∘ 0943 0945

30∘ 0939 0943

45∘ 0930 0933

60∘ 0912 0925

75∘ 0774 0923

90∘ 0626 0956


4 Conclusion



Appendix




=

2119871119908



= 2119871119908

119908119904 where 119908




8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘

120579



05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

300

200

100

0

Resis

tanc

e (Ω

)

(a)


05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

100

50

0minus50

minus100

Reac

tanc

e (Ω

)

(b)



Acknowledgments



References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












11calculations a


11parameterwas





11parameter it was





11987811

(dB)

0

minus5

minus10

minus15

minus20

minus2505 075 1 125 15 175 2 225 25 275 3

Frequency (GHz)







2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

Gai

n (d

B)

075 1 125 15 175 2 225 25 275 3Frequency (GHz)

Simulated gain

Simulated Measured

0minus10

minus20

0minus10

minus20

minus30

minus40

minus50

minus40

minus30

030

60

90

120

150180

210

240

270

300

330


Volta

ge (V

)

1

05

0

minus05

minus10 1 2 3 4 5 6 7

minus01

minus005

0

005

01

Curr

ent (

A)

Time (ns)




fidelity12

=

100381610038161003816100381610038161003816100381610038161003816

12058812

(119905)

radic1205881

(0) 1205882

(0)

100381610038161003816100381610038161003816100381610038161003816max (1)

where 12058812

(119905) 1205881(0) and 120588





120579

10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘



120579 E-plane H-plane0∘ 0947 0947

15∘ 0943 0945

30∘ 0939 0943

45∘ 0930 0933

60∘ 0912 0925

75∘ 0774 0923

90∘ 0626 0956


4 Conclusion



Appendix




=

2119871119908



= 2119871119908

119908119904 where 119908




8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘

120579



05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

300

200

100

0

Resis

tanc

e (Ω

)

(a)


05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

100

50

0minus50

minus100

Reac

tanc

e (Ω

)

(b)



Acknowledgments



References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

Gai

n (d

B)

075 1 125 15 175 2 225 25 275 3Frequency (GHz)

Simulated gain

Simulated Measured

0minus10

minus20

0minus10

minus20

minus30

minus40

minus50

minus40

minus30

030

60

90

120

150180

210

240

270

300

330


Volta

ge (V

)

1

05

0

minus05

minus10 1 2 3 4 5 6 7

minus01

minus005

0

005

01

Curr

ent (

A)

Time (ns)




fidelity12

=

100381610038161003816100381610038161003816100381610038161003816

12058812

(119905)

radic1205881

(0) 1205882

(0)

100381610038161003816100381610038161003816100381610038161003816max (1)

where 12058812

(119905) 1205881(0) and 120588





120579

10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘



120579 E-plane H-plane0∘ 0947 0947

15∘ 0943 0945

30∘ 0939 0943

45∘ 0930 0933

60∘ 0912 0925

75∘ 0774 0923

90∘ 0626 0956


4 Conclusion



Appendix




=

2119871119908



= 2119871119908

119908119904 where 119908




8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘

120579



05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

300

200

100

0

Resis

tanc

e (Ω

)

(a)


05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

100

50

0minus50

minus100

Reac

tanc

e (Ω

)

(b)



Acknowledgments



References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120579

10

8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘



120579 E-plane H-plane0∘ 0947 0947

15∘ 0943 0945

30∘ 0939 0943

45∘ 0930 0933

60∘ 0912 0925

75∘ 0774 0923

90∘ 0626 0956


4 Conclusion



Appendix




=

2119871119908



= 2119871119908

119908119904 where 119908




8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘

120579



05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

300

200

100

0

Resis

tanc

e (Ω

)

(a)


05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

100

50

0minus50

minus100

Reac

tanc

e (Ω

)

(b)



Acknowledgments



References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










8

6

4

2

0

minus2

minus4

minus6

minus8

minus10

0 1 2 3 4 5 6 7Time (ns)

Elec

tric

fiel

d (V

m)

120579 = 0∘

120579 = 15∘

120579 = 30∘

120579 = 45∘

120579 = 60∘

120579 = 75∘

120579 = 90∘

120579



05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

300

200

100

0

Resis

tanc

e (Ω

)

(a)


05 075 1 125 15 175 2 225 25 275 3Frequency (GHz)

100

50

0minus50

minus100

Reac

tanc

e (Ω

)

(b)



Acknowledgments



References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Multiobjective-Optimized Design of a New