IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 46, NO. 4, APRIL 1998 517
On he Beha io o he Sie pinski
Mul iband F ac al An enna
Ca les Puen e-Balia da, Membe , IEEE, Jo di Romeu, Membe , IEEE,
Ra ael Pous, Membe , IEEE, Angel Ca dama, Membe , IEEE
Abs ac — The mul iband beha io o he ac al Sie pinski
an enna is desc ibed in his pape . Due o i s mainly iangula
shape, he an enna is compa ed o he well-known single-band
bow- ie an enna. Bo h expe imen al and nume ical esul s show
ha he sel -simila i y p ope ies o he ac al shape a e ans-
la ed in o i s elec omagne ic beha io . A deepe physical insigh
on such a beha io is achie ed by means o he compu ed cu en
densi ies o e he an enna su ace, which also display some
simila i y p ope ies h ough he bands.
Index Te ms—An ennas, ac als, mul i equency an ennas.
I. INTRODUCTION
THE in e ac ion o elec omagne ic wa es wi h ac al bod-
ies has been ecen ly s udied [1]–[7]. Mos ac al objec s
ha e sel -simila shapes, which means ha some o hei pa s
ha e he same shape as he whole objec bu a a di e en
scale [8]–[11]. The cons uc ion o many ideal ac al shapes
is usually ca ied ou by applying an in ini e numbe o imes
an i e a i e algo i hm such as he mul iple educ ion copy
machine (MRCM) algo i hm [8]. In such i e a i e p ocedu e,
an ini ial s uc u e called gene a o is eplica ed many imes a
di e en scales, posi ions and di ec ions, o g ow he inal ac-
al s uc u e. D. L. Jagga d e al. [3] showed ha he same kind
o geome ical simila i y ela ions a se e al g ow h s ages
we e ound in he elec omagne ic beha io o he ac al
body. The di ac ion o ac ally se a ed ape u es [5], [6] he
e lec ion and ansmission coe icien s o ac al mul ilaye s
[7] and he sidelobe p ope ies o some ac al a ays [2], [12],
[13] a e o he examples o s udies cu en ly a ailable in he
li e a u e ha ela e ac als and elec omagne ics.
A i s a emp o explo e he mul i equency p ope ies o
ac als as adia ing s uc u es was done in [13]. The aim in
ha pape was o essay a new se o shapes o he design
o mul i equency an enna a ays. Wide-band and equency-
independen an ennas we e de eloped and ho oughly analyzed
in he ea ly six ies [14]–[19] and some con olu ed shapes
we e in es iga ed o y o elude he p inciple o he an enna
adia ion pa ame e s dependence on i s physical size ela i e
Manusc ip ecei ed Sep embe 18, 1996; e ised Sep embe 8, 1997. This
wo k was suppo ed in pa by G an TIC-96-0724-C06-04 om he Spanish
Go e nmen and by he company FRACTUS S.A.
C. Puen e-Balia da is wi h he Depa men o Signal Theo y and Commu-
nica ions (TSC), Poly echnic Uni e si y o Ca alonia, Ba celona, Spain.
J. Romeu and R. Pous a e wi h he Poly echnic Uni e si y o Ca alonia,
Ba celona, Spain.
A. Ca dama is wi h he Telecommunica ion Enginee ing School, Poly ech-
nic Uni e si y o Ca alonia, Ba celona, Spain.
Publishe I em Iden i ie S 0018-926X(98)02678-7.
o wa eleng h. Spi als and log-pe iodic s uc u es a e some
examples o success ul s uc u es used o design equency-
independen an ennas. F ac als migh join some o hose ea ly
designs due o hei sel -scaling p ope ies [8]. Conce ning
ha pa icula issue, Puen e e al. desc ibed in [20] he
beha io o , a he ex en known by he au ho s, he i s
ac al mul iband an enna— he Sie pinski monopole. Such a
monopole displayed a simila beha io a se e al bands om
bo h he inpu e u n loss and adia ion pa e ns poin s o iew.
Some s eps u he in he ield o mul iband ac al an ennas
we e done la e in [21]–[23]. Fu he mo e, o he in e es ing
con ibu ions ega ding small [24] and equency-independen
[25] ac al an ennas ha e been in oduced by Cohen e al.,
espec i ely.
In his pape , he beha io o bo h he Sie pinski monopole
and dipole is desc ibed by means o expe imen al and compu-
a ional esul s and he compa ison wi h he iangula (bow-
ie) an enna is done. The adia ion pa e n o he measu ed
ac al dipole clea ly shows a be e esemblance a di e en
equencies han hose o he monopole con i ming, hus,
ha ea ly disag eemen s among pa e ns we e due o he
ini e size o he conduc o g ound plane. Also, he elec ic
cu en densi y dis ibu ion o e he ac al s uc u e has been
compu ed, gi ing some insigh on he mul i equency beha io
o he an enna.
II. THE SIERPINSKI MONOPOLE
A. An enna Desc ip ion
The Sie pinski gaske is named a e he Polish ma hema i-
cian Sie pinski who desc ibed some o he main p ope ies
o his ac al shape in 1916 [8], [26]. The o iginal gaske
is cons uc ed by sub ac ing a cen al in e ed iangle om
a main iangle shape (Fig. 1). A e he sub ac ion, h ee
equal iangles emain on he s uc u e, each one being hal
o he size o he o iginal one. One can i e a e he same
sub ac ion p ocedu e on he emaining iangles and i he
i e a ion is ca ied ou an in ini e numbe o imes, he ideal
ac al Sie pinski gaske is ob ained. In such an ideal s uc u e,
each one o i s h ee main pa s is exac ly equal o he whole
objec , bu scaled by a ac o o wo and so a e each o he
h ee gaske s ha compose any o hose pa s. Due o his
pa icula simila i y p ope ies, sha ed wi h many o he ac al
shapes, i is said ha he Sie pinski gaske is a sel -simila
s uc u e [23].
0018–926X/98$10.00 1998 IEEE
518 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 46, NO. 4, APRIL 1998
Fig. 1. The Sie pinski monopole. Each subgaske (ci cled) is a scaled e sion
o he whole s uc u e.
The Sie pinski gaske (also Sie pinski iangle) was cho-
sen as he i s candida e o a ac al an enna due o i s
esemblance o he iangula o bow- ie an enna. As shown
in Fig. 1, he gaske was p in ed on a 1.588-mm- hick Cuclad
250 subs a e ( ) and moun ed o e a 800 800
mm g ound plane. The s uc u e was ed h ough a 1.5-mm
diame e , 50- coaxial p obe wi h an SMA connec o on he
bo om side o he plane. The an enna is a scaled e sion o he
an enna desc ibed in [20] wi h a hicke subs a e o p o ide
he p in ed ac al a s i e suppo .
The gaske has been cons uc ed h ough i e i e a ions in
his pa icula case, so i e-scaled e sions o he Sie pinski
gaske a e ound on he an enna (ci cled egions in Fig. 1),
he smalles one being a single iangle. I one neglec s he
con ibu ion o he cen e holes o he an enna pe o mance
and admi s ha he cu en lowing om he eede should
concen a e o e a egion ha is compa able in size o he
wa eleng h, a beha io simila o i e-scaled bow- ie an en-
nas (each one ope a ing a i s esonan equency) could be
expec ed. The scale ac o among he i e gaske s is ,
he e o e, one should look o simila i ies a equencies also
spaced by a ac o o wo.
B. Inpu Re u n Loss
The e u n loss o he Sie pinski monopole was measu ed
in an HP-8510B ne wo k analyze in he 0.05–16-GHz e-
quency ange. The an enna was also simula ed on a connec ion
machine CM-5 using an FDTD algo i hm. Fu he mo e, i e
bow ies o he same sizes as each one o he gaske s on
he Sie pinski an enna (89, 44.5, 22.3, 11.1, and 5.5 mm)
we e measu ed o compa e he esul s. Fig. 2 shows he inpu
TABLE I
MAIN PARAMETERS OF THE MEASURED SIERPINSKI MONOPOLE
e lec ion coe icien ela i e o 50 o he i e-monopole
bow ies oge he wi h he Sie pinski monopole ( he plo
co esponding o he Sie pinski an enna appea s a he bo om
o he igu e); Table I summa izes he main pa ame e s de i ed
om ha plo .
The i e bands on Table I co espond o he i e ol age
s anding wa e a io (VSWR) minimums o he an enna. The
equencies co esponding o such minimums appea in he
second column ( ). The hi d column desc ibes he ela i e
bandwid h a each band o VSWR 2, he ou h one he
inpu e u n loss ( ), he i h one ep esen s he equency
a io be ween wo adjacen bands, and he six h one he a io
be ween he heigh o each o he i e subgaske and he
co esponding band equency. As i was desc ibed in [20],
he Sie pinski monopole p esen s a log-pe iodic beha io wi h
i e bands app oxima ely spaced by a ac o ; he an enna
keeps a no able deg ee o simila i y h ough he bands, wi h
a mode a e bandwid h ( 21%) a each one. To ge a be e
insigh on he log-pe iodic beha io o he an enna, he inpu
impedance is also shown in a semiloga i hmic scale (Fig. 3).
I can be seen ha he an enna is ma ched app oxima ely
a equencies
(1)
whe e is he speed o ligh in acuum, is he heigh o
he la ges gaske , he log pe iod ( ), and a na u al
numbe . The bands a e sligh ly de ia ed om hose in [20],
whe e . This is ela ed o he hicke subs a e
(mm as opposed o mm) and i s highe
pe mi i i y ( as opposed o ), which makes
he whole s uc u e appea sligh ly elec ically longe [27] han
he one wi h he hinne , lowe pe mi i i y subs a e. Anyway,
such a beha io is clea ly di e en o ha o he bow- ie
monopole, which has he i s minimum VSWR a
and he co esponding highe o de modes pe iodically spaced
by a equency gap o Hz; ha is
(2)
This is a compa able esul o he classical one om B own
and Woodwa d [28] who measu ed ( om a hinne bow ie)
a i s ma ch a and a second one a om
he i s .
The second ma ch o he bow- ie an enna is always be e
han he i s one ( dB as opposed o dB),
which migh sugges ha i can ha e a mo e signi ican e ec
on he Sie pinski beha io . Thus, i we assimila e each o
PUENTE-BALIARDA e al.: BEHAVIOR OF THE SIERPINSKI MULTIBAND FRACTAL ANTENNA 519
Fig. 2. Inpu e lec ion coe icien ( e e ed o 50

) o i e bow ies a scaled as each one o he i e subgaske s on he Sie pinski monopole (89, 44.5,
22.3, 11.1, and 5.5 mm). The bo om plo co esponds o he inpu e lec ion coe icien o he Sie pinski monopole.
he lowes subgaske s (ci cled in dashed lines in Fig. 1) o a
bow ie, he Sie pinski bands could co espond o he second
one o he iangula an ennas. The equency shi owa d he
o igin expe imen ed by he ac al an enna, wi h espec o he
iangula , can be ela ed o he capaci i e loading o he uppe
subgaske s. I is also in e es ing o no ice ha he simila i y and
pe iodici y a e los in he lowe bands whe e he inpu e u n
loss and a io a e close o hose o he bow ie. This ac
can be ela ed o he an enna unca ion since he s uc u e
is no an ideal ac al cons uc ed a e an in ini e numbe o
i e a ions. Al hough an ideal ac al shape is sel simila [8] a
an in ini e numbe o scales, a easible implemen a ion o he
s uc u e only keeps a ce ain deg ee o simila i y o e a ini e
numbe o scales, which limi s he numbe o ope a ing bands.
The e o e, in he low- equency egion, he lowes ma ched
equency is shi ed close o ha o he i s one o a bow
ie he same size as he whole Sie pinski an enna. Such a
unca ion e ec becomes mo e appa en when one looks a
he cu en dis ibu ion o e he an enna (Sec ion IV).
C. Radia ion Pa e ns
The main cu s ( ) o he ac al
monopole adia ion pa e ns whe e measu ed in a 10 7.5
7.5 m anechoic chambe . The cu s whe e measu ed a he
ou uppe bands (Fig. 4), whe e simila pa e ns among bands
should be expec ed. As i was shown1in [20], he pa e ns do
keep a ce ain deg ee o simila i y: he pa e ns o he
1The e was a misp in in he esul s published in [20]: he
'
=0
and
'
=90
cu s should be swapped.
520 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 46, NO. 4, APRIL 1998
Fig. 3. Inpu esis ance ( op) and eac ance (bo om) o he i e-i e a ion
Sie pinski monopole. F equency is shown in loga i hmic scale o s ess he
log-pe iodic beha io o he an enna.
componen a e cha ac e ized by a wo-lobe s uc u e wi h
a dip loca ed app oxima ely a an ele a ion angle o 30 ; he
pa e ns display a monopole-like pa e n wi h a dip
app oxima ely a he same ele a ion angle, and he azimu h
cu has an ellip ic shape wi h a s onge adia ion componen
owa d he axis. The pa e ns o he componen looked
simila as well [20], al hough his componen is less impo an
since i is usually mo e han 20 dB below he o he one.
These esul s a e clea ly di e en om hose o a ypical
single-band an enna such as a monopole o a bow- ie an-
enna since he Sie pinski an enna has an elec ical leng h
sligh ly longe han ou wa eleng hs a he uppe band and a
monopole o a bow ie would ha e se e al g a ing lobes a such
a high equency. Howe e , i should be no iced ha he e ec
o he ini e size o he g ound plane mus be aken in o accoun
when analyzing he pa e ns on Fig. 4 [19]. Fo ins ance, hose
a he uppe bands show a cha ac e is ic ipple, which is due
o di ac ion a he edges o he plane. The a ia ions on he
ipple a e as e when equency is inc eased since he squa ed
plane is ob iously no sel -scalable and he edges a e spaced
a longe dis ance in e ms o he co esponding wa eleng h.
Also, he expec ed null in he -axis di ec ion is hidden by he
con ibu ion o he an isymme ical mode o he g ound plane
o he o e all adia ed powe [19].
III. THE SIERPINSKI DIPOLE
A. An enna Desc ip ion
In o de o p ope ly dis inguish he eal in luence o he Sie -
pinski s uc u e on he an enna adia ion pa e ns, a Sie pinski
dipole was cons uc ed and measu ed. The an enna was ed by
means o a coaxial ape ed balun simila o ha desc ibed in
[29] o balance and ma ch he dipole h ough he whole 1:16-
GHz equency ange. Basically, he balun was buil by cu ing
open he ou e wall o he coax so ha a c oss-sec ional iew
showed a sec o o he ou e conduc o emo ed and he ound
s uc u e smoo hly yielded a wo-wi e ansmission line.
Bo h a ms o he an enna we e p in ed on he same subs a e
used in he monopole. The measu emen s we e ca ied ou in a
oll o e azimu h con igu a ion wi h he balun moun ed along
he and axis al e na i ely o minimize he e ec o bo h
he o a ion axis and he balun on he and
pa e ns, espec i ely. The coo dina e e e ence sys em is he
same o Fig. 1. An iden ical scheme was used o measu e an
equila e al bow- ie an enna he same size as he Sie pinski
one.
B. Radia ion Pa e ns
The pa e ns o bo h he Sie pinski dipole and a bow- ie
an enna o he same size (89 mm was he heigh o each
a m) can be compa ed on Figs. 5 and 6. Each ow displays
h ee pa e ns wi hin each one o he ou uppe bands o he
Sie pinski an enna. The cu s co esponding o he Sie pinski
an enna a e ep esen ed on he le -hand side o he igu e,
while he same cu s co esponding o he bow ie an enna a e
plo ed on he igh . Each one o he wo igu es displays a cu
h ough he main planes ( , ) o bo h an ennas.
The cu is no signi ican in his case due o he oll
o e azimu h measu emen scheme.
I is in e es ing o no ice he s ong simila i y be ween
pa e ns h ough he ou bands ( ows) on he Sie pinski
an enna. These simila i ies a e specially ema kable a 2, 4, 8,
and 16 GHz. Again, hese esul s a e clea ly di e en o hose
o he bow- ie an enna. Al hough he bow- ie an enna has many
ma ched equencies as desc ibed in (2), each esonan mode
has a di e en cu en densi y dis ibu ion, which is ansla ed
in o a di e en pa e n o each equency. The beha io is,
hus, mo e simila o ha o a single-band dipole in which
inc easing he ope a ing equency esul s in an inc emen
on he numbe o g a ing lobes o he pa e n. Hence, we
canno ei he alk abou a dipole o a bow- ie an enna as a
mul iband an enna because he pa e ns a e no held simila
h ough he ma ched equencies. On he con a y, we mus
hink o he Sie pinski an enna as a mul iband one since bo h
he inpu e u n loss and he adia ion pa e ns a e held simila
h ough he bands. Ne e heless, he an enna is no equency
independen since he e is a ema kable a ia ion o bo h he
pa e ns and he e u n loss h ough each log pe iod.
When compa ing he dipole pa e ns o he monopole ones,
he nonideali ies o bo h he balun and he g ound plane
can be de ec ed. The balun does no pe ec ly balance he
cu en be ween bo h a ms o he dipole, consequen ly, he
cu s o e he planes o hogonal o he plane display
a sligh asymme y. Such an asymme y enhances adia ion
owa d he axis (see cu a 3.6 and 7.2 GHz) and
ends o hide some nulls o he pa e n. Ne e heless, he lobe
s uc u e becomes appa en and he simila i y among bands
appea s clea ly. Fu he mo e, he expec ed nulls along he
axis can be dis inguished now, which suppo s he idea ha
PUENTE-BALIARDA e al.: BEHAVIOR OF THE SIERPINSKI MULTIBAND FRACTAL ANTENNA 521
Fig. 4. Main cu s o he Sie pinski monopole adia ion pa e n (
E

componen ). F om le o igh , each column co esponds o one cu
(
'
=
0

;'
=90

;
=90

) a each one o he ou uppe bands ( om op o bo om
=1
:
74
GHz,
=3
:
51
GHz,
=6
:
95
GHz, and
=13
:
89
GHz). Each pa e n is no malized wi h espec o i s own maximum.
Fig. 5. F on o back cu (
'
=0

) o bo h he (a) Sie pinski dipole adia ion pa e n and he (b) bow- ie an enna. The pa e ns co espond o he
E

componen . Each ow displays h ee cu s wi hin one band. No ice he simila i y be ween ows (mul iband beha io ) as opposed o he di e ences be ween
columns (no a equency-independen beha io ) on he Sie pinski an enna.
he o me ipple and lobes appea ed in he monopole we e
due o he g ound plane.
Ano he in e es ing ea u e o he Sie pinski pa e ns is he
cha ac e is ic h ee-lobe s uc u e on he cu . Such a
pa e n is compa able o ha on he hi d ma ched equency
o he bow- ie an enna ( GHz o mm); i
we compa e such equencies o he i e bow ies [(1), Fig. 2]
o hose o he Sie pinski one (2), we can see ha he hi d
ma ched one on each bow ie is e y close o a Sie pinski band.
Hence, i seems ha he ac al an enna could be ope a ing a

522 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 46, NO. 4, APRIL 1998
Fig. 6. Le o igh cu (
'
=
90

) o bo h he (a) Sie pinski dipole adia ion pa e n and he (b) bow- ie an enna. The pa e ns co espond o he
E

componen . Each ow displays h ee cu s wi hin one band. No ice he simila i y be ween ows (mul iband beha io ) as opposed o he di e ences be ween
columns (no a equency-independen beha io ) on he Sie pinski an enna.
each band in a combina ion o wo modes co esponding o
wo bow ies a di e en scales, he la ge wo king on i s hi d
esonance, and he smalle on i s second one.
IV. CURRENT DENSITY OVER THE SIERPINSKI ANTENNA
In o de o ge a deepe physical insigh on he beha io
o he Sie pinski an enna, an FDTD algo i hm was de eloped
o calcula e he cu en densi y dis ibu ion o e he ac al
su ace. The algo i hm was un on a connec ion machine CM-
5 using a 32 256 256 cell space. The Yee cell dimensions
we e mm, mm, mm,
and second-o de Mu abso bing bounda y condi ions [30]
we e used.
A sinusoidal signal a each o he ou uppe bands was
used o exci e he an enna. A e he ansien pe iod, he
cu en densi y maximum a each poin was de ec ed. On he
le column o Fig. 7, he magni ude o he densi y cu en
dis ibu ion a each band o e he whole an enna su ace is
gi en (linea scale, a bi a y uni s). The igh column p esen s
an expanded iew o he egion whe e mos o he cu en is
concen a ed a each equency. All o hem a e scaled by a
ac o o wo, he same scale ac o exis ing among bands. I
is in e es ing o no ice ha he cu en densi y dis ibu ions
on he igh column a e e y simila among hem; ha is
especially ue i he e ec o he smalle wholes a he lowe
bands a e neglec ed. This is a easonable app oxima ion since
such wholes a e small compa ed o he wa eleng h and he
cu en densi y is lowe a he egions whe e he wholes a e
loca ed. The e o e, he simila i y among he pa e ns shown
in he p e ious sec ion can now be explained: a each band
he cu en concen a es o e a p ope ly scaled subs uc u e
on he an enna which has he main con ibu ion o he o e all
adia ion pa e n. I should be no iced ha his egion is smalle
when equency is inc eased and ha he cu en does no each
he op o he an enna a he highes bands and a la ge a ea
o he s uc u e becomes his way e ec i ely disconnec ed.
This phenomena is equi alen o he ac i e egion ound in
he log pe iodic a ays desc ibed in he ea ly six ies by Ca el
and Mayes [14], [18]. Now, an addi ional explana ion on
he beha io o he ac al an enna can be gi en: when an
elec omagne ic wa e is ed h ough he ip o he an enna i
s a s o p opaga e o e he s uc u e owa d he la end o he
gaske . When he wa e inds a clus e compa able in size o
i s wa eleng h i becomes adia ed; his way he powe o he
a eling wa e is los and no cu en eaches he end o he
an enna. The s uc u e has many discon inui ies ha enhance
adia ion and emphasizes such a p ocess. I he wa eleng h
is long, he small iangles o he shape con ibu e less o he
o e all adia ion and he cu en can a el u he o e i ; hen
a la ge ac i e egion can be eached (which will ha e a simila
shape o ha o a sho e wa eleng h) and a simila adia ion
pa e n o such a lowe band will be ob ained.
Finally, he plo s on Fig. 7 can explain he unca ion e ec
desc ibed in Sec ion II. Al hough i is di icul o p ecisely
pu bounds o he ac i e egion, i ac ually co e s a wide
a ea han he enci cled egions o Fig. 1; a leas an addi ional
scale le el should be aken in o accoun o p ope ly model he
an enna beha io . Thus, a he lowes band he whole an enna
is no la ge enough, he ac i e egion is dis o ed and he
an enna looses he sel -simila i y p ope ies wi h espec he
highe bands. Also, i is in e es ing o no ice ha he ac i e
egion co e s an a ea longe ( di ec ion) han he ope a ing
wa eleng h which can explain he simila i y o he
pa e n o ha o a 1.5- dipole [19].
PUENTE-BALIARDA e al.: BEHAVIOR OF THE SIERPINSKI MULTIBAND FRACTAL ANTENNA 523
Fig. 7. Cu en densi y (magni ude) o e he Sie pinski dipole compu ed by
means o he FDTD algo i hm. The le column displays he whole an enna
a he ou uppe bands while he igh column shows a zoomed iew o he
ac i e egion a each band. No ice he simila i y be ween he dis ibu ions
o e he ac i e egion a each band.
V. CONCLUSIONS
Bo h expe imen al and nume ical esul s on he Sie pinski
an enna ha e been p esen ed. All o hem desc ibe a mul iband
beha io o he ac al an enna. This beha io is consis en
om he inpu e u n loss and he adia ion pa e ns poin s o
iew. The bands a e log-pe iodically spaced by a ac o o wo,
he same scale ac o exis ing among simila s uc u es on he
ac al shape. Thus, i can be concluded ha he sel -simila i y
p ope ies o he ac al s uc u e a e ansla ed in o i s elec o-
magne ic beha io . The cu en densi y o e he an enna has
been also calcula ed by means o an FDTD algo i hm. The
inpu e u n loss calcula ed using his algo i hm is consis en
wi h he expe imen al one. The densi y cu en dis ibu ions
ha e a simila shape among bands as well, hus explaining
he simila i y among he pa e ns ound expe imen ally. Such
dis ibu ions desc ibe an ac i e egion o e he an enna ha
sel scales wi h equency and allows a simila beha io o
he an enna h ough he bands.
ACKNOWLEDGMENT
The au ho s would like o hank D . P. E. Mayes o
he Uni e si y o Illinois a U bana-Champaign and D . D.
L. Jagga d o he Uni e si y o Pennsyl ania, Philadelphia,
o encou aging his wo k. They would also like o hank
R. Ba olom´e, A. Hijazo, F. Ben´
i ez, and X. Ga cia o
con ibu ions o he measu emen s and nume ical esul s. The
nume ical esul s we e ob ained a he Cen e Na ional de
Calcul Pa allele en Sciences de la Te e, Pa is, F ance.
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Ca les Puen e-Balia da (S’91–M’93) was bo n in Badalona, Spain, In 1968.
He ecei ed he Ingenie o deg ee in elecommunica ions enginee ing om he
Poly echnic Uni e si y o Ca alonia (UPC), Ba celona, Spain, in 1992, he
M.S. deg ee om he Uni e si y o Illinois a U bana-Champaign (UIUC), in
1994, and he Ph.D. deg ee om he UPC, in 1997.
In 1992, he ecei ed a g an om he In e depa men al Commission o
Resea ch and Technological Inno a ion (CIRIT) o he Ca alan Go e nmen
and joined he Elec o Op ic Sys ems Labo a o y (EOSL) a he UIUC, whe e
he wo ked in lase elocime y and lida echniques un il Decembe 1993.
Since 1994, he has been an Assis an P o esso a he Depa men o Signal
Theo y and Communica ions a he Poly echnic Uni e si y o Ca alonia. His
cu en esea ch in e es s a e ac al an ennas, lida , lase sys ems, and op ical
communica ions.
Jo di Romeu (S’89–M’91) was bo n in Ba celona,
Spain, in 1962. He ecei ed he Ingenie o and
Doc o Ingenie o deg ees in elecommunica ion en-
ginee ing, bo h om he Poly echnic Uni e si y o
Ca alonia (UPC), Ba celona, Spain, in 1986 and
1991, espec i ely.
In 1985, he joined he Elec omagne ic and Pho-
onic Enginee ing G oup o he Signal Theo y and
Communica ions Depa men a he UPC. Cu en ly,
he is an Associa e P o esso a he same uni e si y,
whe e he is engaged in esea ch in an enna nea - ield
measu emen s, an enna diagnos ics, and an enna design.
Ra ael Pous (S’89–M’93) was bo n in Ba celona,
Spain, in 1964. He ecei ed he Ingenie o deg ee in
elecommunica ions enginee ing and he Licenciado
deg ee in compu e science om he Poly echnic
Uni e si y o Ca alonia (Ba celona), in 1988, he
M.S. deg ee in elec ical enginee ing om he Uni-
e si y o Massachuse s, Amhe s , in 1989, and
he Ph.D. deg ee in elec ical enginee ing om he
Uni e si y o Cali o nia, Be keley, in 1992.
In 1993, he joined he acul y o he Depa men
o Telecommunica ions Enginee ing a he Poly ech-
nic Uni e si y o Ca alonia, Ba celona, Spain, whe e he is cu en ly employed.
His esea ch in e es s a e in he a ea o compu a ional elec omagne ics and
applied supe conduc i i y.
D . Pous was awa ded he Fulb igh Schola ship and he Schlumbe ge
Fellowship du ing his s udies.
Angel Ca dama (S’67–M’73) was bo n in San iago
de Compos ela, Spain, on May 13, 1944. He e-
cei ed he Ingenie o de Telecommunicaci´
on deg ee
om he Uni e sidad Poli ´ecnica de Mad id, in
1968, and he Sc.M. and Ph.D. deg ees in elec ical
enginee ing om B own Uni e si y, P o idence, RI,
in 1970 and 1973, espec i ely.
In 1972, he joined he acul y o he Telecom-
munica ion Enginee ing School a he Poly echnic
Uni e si y o Ca alonia, Ba celona, Spain, whe e
he holds he posi ion o P o esso . His esea ch
in e es s ange om he de elopmen o analy ical and nume ical echniques
in elec omagne ics o he design o mic owa e imaging sys ems and ada
and communica ion an ennas.