Synthesis of a Pre-Fractal Dual-Band Monopolar Antenna for GPS Applications

UNIVERSITY

OF TRENTO

DIPARTIMENTO DI INGEGNERIA E SCIENZA DELL’INFORMAZIONE

38123 Povo – Trento (Italy), Via Sommarive 14

http://www.disi.unitn.it

SYNTHESIS OF A PRE-FRACTAL DUAL-BAND MONOPOLAR

ANTENNA FOR GPS APPLICATIONS

R. Azaro, F. De Natale, E. Zeni, M. Donelli, and A. Massa

January 2011

lar Antenna for GPS Appli ations

Renzo Azaro, Fran es o De Natale, MassimoDonelli,Edoardo Zeni, and Andrea Massa

Department of Information and Communi ation Te hnologies,

University of Trento,Via Sommarive 14,I-38050 Trento- Italy

Tel. +39 0461 882057,Fax +39 0461 882093

E-mail: {andrea.massa,fran es o.denatale}ing.unitn.it,

{renzo.azaro, massimo.donelli,edoardo.zeni}dit.unitn.it

lar Antenna for GPS Appli ations

Renzo Azaro, Fran es o De Natale, MassimoDonelli,Edoardo Zeni, and Andrea Massa

Abstra t

In this letter, the design of a monopolar dual-band antenna operating in the

L1

and

L2 GP S

bandsispresented. Thepre-fra tal geometry oftheantennahasbeen

synthesized by means of a Parti le Swarm algorithm for optimizing the values of

the ele tri al parameters within thespe i ations. For a general assessment, some

sele ted results of numeri al simulations areshown and some omparisonsbetween

numeri al dataandexperimental measurementsarepresented.

Key-words:

Antennas Synthesis, Pre-fra tal Antennas, Multi-band Antennas, Mi rostrip

Nowadays,thedevelopmentofele troni devi esemployingvariouswirelessstandards for

the data ex hange and operating in dierent frequen y bands requires the use of

multi-band omponents. In su h aframework,the antennasynthesis is a riti altasksin e the

designandthedevelopmentofasingleradiatorworkingintwoormorefrequen ybandsis

generally not easy espe ially when dimensional/geometri al onstraints on the stru ture

are imposed.

Elementary wire antennas (e.g., nite dipoles and monopoles) work in several frequen y

bands related to the resonan es of the stru ture. However, su h multiple working

fre-quen ies are usually harmoni and the orresponding ele tri al parameters (i.e.,

V SW R

and gain) varydepending onthe resonan e frequen y.

On the other hand, standard te hniques for the development of multiband wire

anten-nas onsider the insertion of rea tive loads in the antenna stru ture for obtaining and

ontrolling multiple (non harmoni , as well) resonant frequen ies. In re ent years, su h

an issue has been also addressed by exploiting the properties of fra tals geometries and

synthesizingboth the antennageometryand loadsvaluesand positionsbymeans of

suit-able optimization algorithms [1℄. As a matter of fa t, the use of fra tal stru tures or

more pre isely pre-fra tal geometries (i.e., hara terized by a nite number of fra tal

it-erations) for the antennas synthesis has been proven to be very ee tive for a hieving a

dimensional miniaturization and an enhan ed bandwidth [2℄[3℄, even though an in rease

of the ee tive bandwidth of the antenna turns out in a redu tion of the radiation

e- ien y at resonant frequen ies [4℄[5℄[6℄. Furthermore, some interesting appli ations have

beenre entlypresented inliterature [7℄[8℄further onrming thepositivefeatures of

pre-fra tal stru tures in the framework of antenna synthesis. However, it should be pointed

out that lassi al pre-fra tal geometries usually present an harmoni frequen y behavior

ratherthan amultibandbehaviorasobserved in[7℄whereKo h-likestru tureshavebeen

onsidered.

Apossiblesolutionfortuningand ontrollingthespa ingbetweentheworkingfrequen ies

of a fra talantennais based onthe perturbationof the fra talgeometry by addingsome

s ale fa tor of the fra tal shape [9℄. A ording to the idea of adding other degrees of

freedom but unlike the approa hproposed in[9℄, this letterpresents a preliminaryresult

on ernedwithapre-fra talKo h-likedual-bandantennaprintedonadiele tri substrate

and operating in the

L1

and

L2

bands of the Global Positioning System (

GP S

). The

design of the fra tal geometry is arried out through a numeri al pro edure based on a

parti le swarm optimizer(

P SO

) [10℄[11℄[12℄, whi h optimizesthe parameters of the

pre-fra talgeometry(lengths,widths,andorientationanglesoftheprintedsegments)avoiding

the insertion of any lumped load as in [1℄ to obtain a multi-band behavior. In order to

assess the ee tiveness ofthe designpro edure and the hara teristi s ofthe synthesized

antenna, the obtained numeri al results are ompared with the measurements from an

experimentalprototype.

2 Dual-Band GPS Antenna Design and Optimization

The design of the dual-band

GP S

monopolar antenna has been formulated in terms of

an optimizationproblem by dening and imposingsuitable onstraints both on the gain

values and about the impedan e mat hing at the input port inthe

L1

and

L2

frequen y

bands of the

GP S

system ( entered at

f

L1

= 1227.60 MHz

and

f

L2

= 1575.42 MHz

,

respe tively). Asfar asthe antennafor the

GP S

re eiveris on erned, radiation

hara -teristi sthatguaranteeahemispheri al overagehavebeenassumed. Moreover,a

voltage-standing-wave-ratio (

V SW R

) lower than

1.8

in both the working frequen y bands (i.e.,

a ree ted power lowerthan

10

% of the in ident power) has been required at the input

port the antenna. Su h onstraints have been hosen taking into a ount the following

spe i ation of a ommer ial

GP S

re eiver: (a) gain values greaterthan

G

min

= 3.0 dBi

at

θ

= 0

and greater than

G

min

= −4.0 dBi

at

θ

= 70

, respe tively; (b) the maximum

valueof the

V SW R

equalto

2.0

. Sin ethe rst stage( onne ted totheantenna)of ea h

GP S

re eivingsystemisgenerallyalownoisepreamplierbe auseofthelowintensity of

the

GP S

signalsattheearthsurfa e,thenabetterimpedan emat hinghasbeenimposed

by de reasing the maximum

V SW R

value from

2.0

up to

V SW R

max

= 1.8

in order to

been alsorequired tobelong to aphysi al platformof dimensions

10 × 16 cm

2

.

By onsideringami rostripstru ture printedonaplanardiele tri substrate, the

param-eters to be optimized were the fra tal geometry and the width and the length of ea h

fra tal segment. As far as the general shape of the generating antenna is on erned, a

Ko h-like geometry derived from the Ko h urve des ribed in [1℄ and [7℄ has been used.

A ording to the notation used in [1℄, the antenna has been generated from the Ko h

urve by repeatedly applying the so- alled Hut hinson operator until the stage

i

= 2,

in

order toobtaina radiatingdevi e with two resonantfrequen ies. In general,the antenna

stru ture at

i

-th stage is uniquely determined by: (a) a set of segment lengths

s

i,j

,

i

being the index of the fra talstage and

j

(

j

= 1, ..., 4

i

)indi atesthe

j

-thsegment atthe

i

-th stage; (b) a set of segment widths

w

i,j

; ( ) a set of angles

Θ

h,q

,

h

= 1, ... , 2

i

and

q

= 1, 2

being

Θ

h,1

= Θ

h,2

. Asanexample,thedes riptiveparameters

s

i,j

and

Θ

h,q

ofthe

Ko h-like urveat

i

= 1

and

i

= 2

arereportedinFig. 1(a)andinFig. 1(b),respe tively.

In order to synthesize the GPS dual-band antenna, the

i

= 2

stage has been onsidered

and, inordertosatisfy the proje tguidelines, theunknown des riptiveparameters ofthe

antenna have been optimized by minimizingthe ost fun tion

Ω

dened in terms of the

least- square dieren e between requirementsand estimated spe i ations:

Ω γ
= min

n

ϕ



γ

i



; i = 2

o

(1) being

ϕ



γ

_i



=

P

M

−1

m=0

P

N

−1

n=0

P

T

−1

t=0

n

max

h

0,

G

min

{t∆θ,n∆φ,m∆f }−Φ{t∆θ,n∆φ,m∆f }

G

min

io

+

+

P

V

−1

v=0

n

max

h

0,

Ψ{v∆f }−V SW R

max

V SW R

max

io

(2) where

γ

i

= {s

i,j

, w

i,j

,

Θ

h,1

; j = 1, ... , 4

i

_{; h = 1, ... , 2}

i

_}

,

∆f

isthesamplingfrequen ystep

in the

L1

and

L2

bands,

∆θ

and

∆φ

are the samplingangularstepsof the gain fun tion;

Φ

n

γ

_i

o

= Φ {t∆θ, n∆φ, m∆f }

is the gain of the GPS antenna evaluated at (

θ

= t∆θ

,

φ

= n∆φ

,

f

= m∆f

) and

Ψ

n

f

= m∆f

when the antenna stru ture is dened by the des riptive array

γ

i

,

i

= 2

.

Besides the ele tri al onstraints, suitable onditions on the overall length and width of

thefra tal urvehavebeen onsideredandapenaltyhasbeen imposedonsomegeometri

ongurations (e.g., having large ratio between width and length of the fra tal segment)

to avoidthe generation of unfeasible stru tures.

In order to minimize (1) and a ording to the guidelines reported in [11℄, a suitable

im-plementation of the

P SO

[13℄ has been integrated with a pre-fra tal generator and a

method-of-moments(

M oM

)[14℄ele tromagneti simulator. Startingfromtheset oftrial

arrays

γ

(k)

i,p

(

i

being the index of the onsidered fra talstage, i.e.

i

= 2

, and

k

being the

trial array index,

p

= 1, ... , P

, and the iteration index,

k

= 0, ... , K

, respe tively )

iter-atively dened by the

P SO

, the pre-fra talgenerator denes the orresponding antenna

stru turesfor omputingthe orresponding

V SW R

andgainvaluesbymeansofthe

M oM

simulator,whi htakesintoa ountthe presen eofthe diele tri slabandofthe referen e

ground plane assumed of innite extent. The iterative pro ess ontinues until

k

= K

or

Ω

opt

_{≤ η}

,

η

being the onvergen e threshold and

Ω

opt

_{= min}

k

n

min

p

h

Ω



γ

(k)

i,p

io

.

3 Numeri al Simulation and Experimental Validation

The

P SO

implementation adopted in this work onsiders a population of

P

= 8

trial

solutions,athreshold

η

= 10

−3

,andamaximum amountofiterationsequalto

K

= 2000

.

The remainingparameters of the

P SO

have been set referringto the referen e literature

[11℄ and a ording to [13℄. As an illustrative example of the iterative synthesis pro ess,

Figures 2 and 3 show some representative pro essing results at various steps. At ea h

step, the stru ture of the best solution is shown (Fig. 2) as well as the plot of the

orresponding

V SW R

fun tion (Fig. 3). As it an be observed, starting from a fully

mismat hed solution on erned with the stru ture displayed in Fig. 2(a) (

k

= 0

), the

solution improves until the nal geometry shown in Fig. 2(e) (

k

= k

conv

) that ts the

proje tspe i ationintermsofboth

V SW R

values andgain valuesat

θ

= 0

and

θ

= 70

.

Furthermore,thesynthesizedantennats thegeometri al onstraintssin eitstransversal

and longitudinal dimensions are equal to

123 [mm]

along the

x

-axis and

43 [mm]

along

k

conv

= 367

iterations and ea h iteration taken an amount of

CP U

-time approximately

of about

10 sec

(Pentium IV

1800 MHz

,

512 MB

RAM).

Asaresultofthesatisfa torynumeri alstudy,anexperimentalvalidationhasbeen arried

out. The antenna prototype has been built by using a photolithographi printing ir uit

te hnologyfollowingthe geometri guidelines omingfromthesimulationsandpi torially

resumed in Fig. 2(e). As far as the

V SW R

experimental measurements are on erned,

the antenna prototype (Fig. 5) has been equipped with a

SM A

onne tor and it has

been pla ed on a referen e ground plane with dimensions of

90 × 140 cm

2

. The

V SW R

values have been measured with a s alar network analyzerby pla ingthe antenna inside

an ane hoi hamber. Computed and measured

V SW R

values have been ompared and

the results are shown in Figure 6. As it an be observed, there is a good agreement

between simulated and measured data, whi h satisfy the proje t onstraints both in the

L1

frequen y band(

V SW R⌋

sim

= 1.68

vs.

V SW R⌋

meas

= 1.42

)andinthe

L2

frequen y

band (

V SW R⌋

sim

= 1.21

vs.

V SW R⌋

meas

= 1.08

).

Inordertoassestheee tivenessofthedesignmethodology,thesimulatedand

experimentally-evaluated

V SW R

values are ompared inFig. 7 with those on erned with two

quarter-wave monopoles working at the

L1

and the

L2

bands, respe tively, and with the

val-ues reported in [15℄ for a GPS dual-band loaded-antenna. Although the synthesized

stru ture presents a

x

-length equal to approximately

λ

1

2

,

λ

1

being the wavelength at

f

L1

= 1227.60 MHz

, it givesVSWR values omparable with those of the orresponding

quarter-wavemonopoles(forea hoperatingband),butavoidingthe useofmultiplewired

stru tures or a tuning ir uit. Moreover, the

V SW R

behavior turnsout tobesimilar to

that in [15℄ and on erned with a loadedantenna, but withoutlumped loads.

Finally, Figs. 8(a)-(b)show the simulatedgain fun tionsin the horizontalplane (

θ

= 0

)

and in a verti al plane (

φ

= 0

), respe tively. In order to validate the omplian e to the

requirementsina realisti onguration,the numeri alsimulationshavebeen arriedout

onsidering anitegroundplane havingthe samedimensions ofthat used duringVSWR

measurements(

90×140 cm

2

). Asexpe ted,thesynthesizedantennaallowsthe

at

θ

= 70

turnsouttobegreaterthanspe i ations(

Φ {θ = 0} > G

min

{θ = 0} = 3.0 dBi

and

Φ {θ = 70} > G

min

{θ = 70} = −4.0 dBi

).

4 Con lusions

The designandoptimizationofadual-bandpre-fra tal

GP S

antennaprintedona

diele -tri substrate has been des ribed. The antenna stru turehas beensynthesized through a

suitableparti leswarm algorithmbyoptimizingthe des riptiveparametersofaKo k-like

pre-fra tal geometryinorder to omply with the geometri al requirements aswell asthe

ele tri al onstraints in the

L1

and

L2 GP S

frequen y bands. A prototype of the

dual-band antenna has been built and some omparisons between measured and simulated

V SW R

values have been arriedout in order toassess the ee tiveness of the optimized

antenna as wellas (ina preliminaryfashion) of the overall synthesis pro edure.

A knowledgements

This work has been supported in Italy by the Progettazione di un Livello Fisi o

'In-telligente' per Reti Mobili ad Elevata Ri ongurabilità, Progetto di Ri er a di

Inter-esse Nazionale- MIUR Proje tCOFIN 2005099984 and by the Center of REsear h And

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fra tal antennas," Ele tron. Lett., vol.37, pp. 1150-1151, Sep. 2001.

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2000.

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minia-turization te hnique, andappli ations,"IEEE Antennas Propagat. Mag.,vol.44,pp.

20-36, Feb. 2002.

[4℄ S. R. Best, "A omparison of the resonant properties od small spa e-lling fra tal

antennas," IEEE Antennas Wireless Propagat. Lett.,vol. 2,pp. 197-200, 2003.

[5℄ J.M. Gonzàles-Arbesù, S.Blan h,J. Romeu,"Arespa e-lling urvese ientsmall

antennas?, IEEE Antennas Wireless Propagat. Lett., vol. 2,pp. 147-150, 2003.

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e ien y and quality fa tor of self-resonant prefra tal wire monopoles, in Pro .

IEEE Antennas Propagat. Symp., Jun. 2003.

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antenna," IEEE Antennas Propagat. Mag., vol. 48,pp. 1773-1781,Nov. 2000.

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•

Figure 1. Des riptive parameters of the Ko h-like fra talantenna: (a)

i

= 1

and

(b)

i

= 2

.

•

Figure 2. Geometryofthe

GP S

dual-bandfra talmonopoleatdierentiterations

of theoptimizationpro ess: (a)

k

= 0

,(b)

k

= 10

, ( )

k

= 50

,(d)

k

= 100

,and (e)

k

= k

conv

.

•

Figure 3. Simulated

V SW R

valuesattheinputportofthe

GP S

dual-bandfra tal

monopoleantennaat dierent iterationsof the optimizationpro edure.

•

Figure 4. Behaviorof the ost fun tionversus the iterationnumber.

•

Figure 5. Photograph of the prototype of the

GP S

dual-band fra tal monopole.

•

Figure 6.

GP S

dual-band fra tal monopole: omparison between measured and

simulated

V SW R

values.

•

Figure 7.

GP S

dual-band fra tal monopole. Comparison between

P SO

-based

synthesis and onventional solutions.

•

Figure 8.

GP S

dual-band fra talmonopole: gain fun tions al ulated on a nite

S

11

S

12

Q

11

Q

12

S

13

S

14

(a)

S

2,1

S

2,2

Q

2,2

Q

2,3

S

2,3

S

2,4

S

25

S

2,6

_Q

2,6

Q

2,7

S

2,7

S

2,8

S

2,9

S

2,10

Q

2,10

Q

2,11

S

2,11

S

2,12

S

2,13

S

2,14

Q

2,14

Q

2,15

S

2,15

S

2,16

(b)

X [cm]

Y [cm]

4

8

12

4

4

8

12

4

X [cm]

4

8

12

4

Y [cm]

(a) (b)

X

Y [cm]

4

8

12

4

X [cm]

4

8

12

4

X [cm]

Y [cm]

4

8

12

4

4

8

12

4

( ) (d)

X [cm]

Y [cm]

4

8

12

4

4

8

12

4

(e)

10

-3

10

-2

10

-1

10

0

10

1

0

50

100

150

200

250

300

350

400

Iteration number k

φ

_tot

10

9

8

7

6

5

4

3

2

1

2.0

1.75

1.5

1.25

1.0

VSWR

Frequency [GHz]

Measured Antenna

Simulated Antenna

Loaded Fractal Antenna

GPS L1 Monopole

GPS L2 Monopole

10

0

-10

-20

-30

Gain [dBi]

0

30

60

90

120

150

180

210

240

270

300

330

Simulated (1225 MHz)

Simulated (1575 MHz)

(a)

/home/elede/Ri er a/Sinte si. Ante nne. Frat tali /Pap ers/ IEEE -AWP L.20 06/F igur e/Re vise d.Fi gure /And amen to. Guad agno .Ver ti a le.P F.mo d.ep s not found!

(b)