analysis of a modified sierpinski gasket monopole antenna

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 10, OCTOBBER 2004 2571

Analysis of a Modified Sierpinski Gasket MonopoleAntenna Printed on Dual Band Wireless Devices

George F. Tsachtsiris, Constantine F. Soras, Member, IEEE, Manos P. Karaboikis, andVassilios T. Makios, Senior Member, IEEE

Abstract—The traditional Sierpinski gasket monopole antennais well known for its multiband behavior, but it cannot be printedon the circuit board of a portable wireless device due to the limitedspace availability. In this paper a modified Sierpinski gasketmonopole antenna is presented that possesses a small physical size,high efficiency and the ability to allocate both the 2.4 and 5.2 GHzIndustrial Scientific and Medical bands without the need of amatching network. The modified element respects the multibandbehavior of the gasket since the input impedance characteristicsof the upper bands maintain their symmetry. Several modificationtechniques are proposed making the monopole very flexible interms of band allocation and fine-tuning. The dimensions of theground plane are also proven to play a significant role on theoperational bandwidth of the antenna system.

Index Terms—Fractal antennas, monopole antennas, multifre-quency antennas, wireless LAN.

I. INTRODUCTION

THE rapid expansion of wireless technology during thelast years has set new demands on integrated components

including the antennas. The existence of an immense infra-structure worldwide for the 2.4 GHz Industrial Scientific andMedical (ISM) band along with the release of the 5.2 GHzISM band and its increasing popularity, steers the antennatechnology to the solution of multiband radiators for the main-tenance of a backward compatibility. Dual-band antennas withsmall physical size and good performance are an oncomingchallenge to meet the needs of integration, cost and efficiencyof the emerging wireless world. The major part of the literaturedealing with compact antennas for dual-frequency operationis dedicated to the planar inverted F antenna, (PIFA) [1]. Thereasons that made this configuration popular for wireless ap-plications are its increased bandwidth relative to a microstripantenna and its small size that can be achieved by capacitiveloading [1], [2]. However, its higher cost and difficulty inmanufacturing relative to a printed antenna make the fieldof multifrequency antennas for wireless applications an openchallenge. The solution to the need of multiband behavior canbe fulfilled by applying fractal concepts on antenna designing.The application of fractal geometry can be used either to minia-turize the antenna [3], or to produce multiband radiators dueto their self-similarity characteristics [4], [5]. The Sierpinski

Manuscript received December 23, 2002; revised July 10, 2003. This workwas supported in part by Vodafone Hellas and the Karatheodory Program of theUniversity of Patras.

The authors are with the Department of Electrical and Computer Engineering,University of Patras, 26500 Patras, Greece (e-mail: [email protected]).

Digital Object Identifier 10.1109/TAP.2004.834088

gasket monopole antenna has been shown to be an excellentcandidate for multiband applications [5]–[7]. The restrictionthough for printing the traditional Sierpinski gasket monopoleon portable wireless devices has been its large physical size,which is imposed by the fact that the spacing between its firsttwo bands is in the order of 3.5 regardless of the similarityfactor. This problem was pinpointed in [8] where a solution isprovided to reduce the height of the Sierpinski monopole bycontrolling the spacing between the first two bands. In theirapproach large flare angles and application of affine transfor-mation have been used in order to realize the desired spacingbetween the bands at the cost, however, of shallow resonancesand decreased bandwidth due to the increased interactionbetween the subscales of the structure.

In this paper a modified Sierpinski gasket monopole for dualband wireless devices is investigated, the shape of which wasfirstly introduced for indoor GSM 900/1800 access point appli-cations in [6]. The antenna element is printed on the area of thedielectric laminate extending beyond the device’s circuitry. Themodified Sierpinski gasket monopole has the ability to allocateboth the 2.4 and 5.2 GHz ISM bands with a single microstripfeed and without the need of a matching network. Several modi-fication techniques are also proposed, which allow the allocationof different bands in a simple way without altering the triangle’sflare angle or the similarity factor.

The first section of the paper is devoted to the theoreticalexplanation of the electromagnetic behavior of the modifiedSierpinski gasket monopole antenna. In the second sectionthe simulation results based on the Method of Moments arepresented along with the measurements on a fabricated proto-type. In the last section several techniques for controlling thespacing of the first two bands and fine-tuning the antenna arepresented along with the effect of the ground plane dimensionson the resonant characteristics.

II. THEORY OF THE MODIFIED SIERPINSKI GASKET

MONOPOLE ANTENNA

The Sierpinski gasket monopole antenna is constructed byapplying a geometric transformation on the triangular monopoleantenna of Fig. 1(a). By subtracting the central inverted triangledefined by the midpoints of the sides of the initial triangularantenna, the pre-fractal monopole shown in Fig. 1(b) is obtained.Repeating this subtracting procedure one more time resultsin the pre-fractal monopole of Fig. 1(c). The ideal Sierpinskigasket would be obtained by iterating this procedure infinitenumber of times [9], [10]. However, in order to create practicalantennas only a few iterations are used.

0018-926X/04$20.00 © 2004 IEEE

2572 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 10, OCTOBBER 2004

Fig. 1. Construction of the Sierpinski gasket monopole antenna (a) initialtriangular antenna, (b) pre-fractal monopole after the first iteration,(c) pre-fractal monopole after the second iteration, (d) investigated modifiedmonopole antenna.

The triangular antenna of Fig. 1(a) has been proven to exhibita multifrequency behavior with the current distribution, how-ever, changing at every resonant mode [5], [11]. This changein the current distribution is translated into different radiationcharacteristics with the higher frequency resonances exhibitingan increased number of grating lobes on the radiation pattern.The Sierpinski monopole, on the contrary, which was originallystudied by Carles Puente–Baliarda, et al. [5] possesses a certainmultiband behavior owing to its self-similar shape. Since theSierpinski monopole is constructed through a subtracting proce-dure as described, the current is forced in a way to concentrate atthe subscaled version of the antenna, having a perimeter compa-rable to the wavelength. Assuming that the number of iterationsis enough to assure that the subscaled versions are similar, sim-ilar electromagnetic behavior is expected.

The resonant frequencies of the traditional Sierpinski gasketcan be fully determined if the height, the flare angle and thetransformation are known. The first resonance occurs when theperimeter of the Sierpinski triangle is slightly more than half awavelength [5], [11]. The second resonance is spaced by a factorof approximately 3.5 from the first one independently from thetransformation [12]. The bands from the second and above arelog-periodically spaced by a factor which is determined by theiterative construction procedure. In case of similarity transfor-mation this factor is 2, while in case of affine transformationthis factor can be altered in order to allocate the bands of in-terest [12]. Since the 3.5 spacing between the first two bandscannot be controlled they cannot be used for band allocation.Thus, for the traditional Sierpinski configuration the first pairof controllable bands is the second and third one. This is veryrestrictive since a sensational increment of the overall antennaheight is needed in order to reach the first controllable pair of

bands. For wireless applications where the antenna size reduc-tion is of primal importance, this increase in height by a factorof 3.5 is prohibitive.

The motivation for the modified configuration of Fig. 1(d)originated from the fact that at the first band of the Sierpinskimonopole gasket the similarity and periodicity is lost due to thetruncation effect from the finite number of iterations. Since thesimilarity is lost one can take advantage of it by altering thegeometry of the upper subscale in an effort to change the elec-tromagnetic behavior and control the spacing between the firsttwo bands. As it will be illustrated in the following section theratio of the first two resonances of the modified configurationhas a value of approximately 2.18, thus possessing the ability toallocate the ISM bands of interest. Furthermore, the modifica-tion maintains the symmetry of the upper bands since the ratiobetween the second and third one is two. The width of the trian-gular ring, the separation height and the groundplane dimensions are the controlling parameters of the antennasystem affecting both the spacing factor and the bandwidth ofthe operational bands.

III. SIMULATED AND MEASURED RESULTS OF THE

ANTENNA SYSTEM

The geometry and dimensions of the investigated configu-ration are depicted in Fig. 2. It has the dimensions of a PCcard whereas the dimensions of the ground plane are 46.6 by88.7 mm. The antenna system consists of two metallic layerswith the antenna placed at the upper one and the ground planeat the bottom. The thickness of the copper layers is 35 (1ounce) and the copper’s conductivity is . Themonopole is printed on an 8–mils thick Rogers RO4003 sub-strate, with relative permittivity and loss tangent,

[13].The height of the main triangle is 18.2 mm, which results

in a perimeter of approximately at 2.45 GHz. The heightof the lower iteration is 12 mm whereas the height of the higheriteration is the half since a similarity transformation has beenused. The width of the triangular ring and the conductive con-nections among the triangles are 0.15 and 0.3 mm, respectively.At the base of the monopole a rectangle of dimensions 0.46 by0.46 mm is attached to feed the antenna through a microstripline located at the center of the ground plane.

The configuration of Fig. 2 was simulated using two Methodof Moments electromagnetic field solvers, IE3D [14] and ADSMomentum [15]. The computed input return loss values (S11in dB) and the measured on a fabricated prototype are in goodagreement as depicted in Fig. 3.

The symmetry of the whole configuration was exploited byintroducing a magnetic wall, as shown in Fig. 4. In terms ofthe computational requirements, the introduction of the mag-netic wall is translated into half the unknowns. The significanceof this reduction must be viewed in conjunction with the factthat the memory requirements are proportional to the secondpower of the number of unknowns and the computational timeto the third one. In order to bring out the advantage of usingthe reduced model of Fig. 4, the simulation of the third band

TSACHTSIRIS et al.: ANALYSIS OF A MODIFIED SIERPINSKI GASKET MONOPOLE ANTENNA 2573

Fig. 2. Geometry and dimensions of the antenna/ground plane system (a) top view and (b) dimensions of the modified Sierpinski monopole antenna.

Fig. 3. Measured and simulated return loss (S11) of the printed monopoleantenna system of Fig. 2(a).

using IE3D on a Pentium IV 1.9 GHz was considered. The re-duced model resulted in 4680 unknowns, requiring 175 MBytememory and 816 seconds computational time per frequency. Ifno magnetic wall were used and keeping the same discretizationthe unknowns would be 9360, with 785 MByte memory require-ment and 6528 seconds computational time per frequency.

Table I displays the resonant behavior of the measured proto-type. The three bands of the first column refer to the three res-onances of the monopole that correspond to the three encircledregions of Fig. 1(d). The central frequency of each bandappears in the second column, in the third one the bandwidthis shown whereas in the fourth column the frequency ratio be-tween the adjacent bands is depicted. The first two resonancesallocate the two ISM bands of interest with a corresponding ratiobetween them 2.18. The frequency ratio of the second and third

Fig. 4. Reduced computer model after the introduction of a magnetic wall.

TABLE IRESONANT BEHAVIOR OF THE MEASURED PROTOTYPE

one is approximately 2, which was expected since the geometryemerges from a similarity transformation. The bandwidth of the


Fig. 5. Measured and computed gain cuts of the configuration depicted in Fig. 2(a) for the two operating bands in dB.

first two bands is 920 and 240 MHz, respectively, fulfilling thusthe requirements of the two ISM bands.

The measured and computed gain patterns of the andcomponents of the electric field at the three principal plane cuts( , , ) for the first two operating bandsare depicted in Fig. 5. The components are normalized with re-spect to the maximum total electric field value and expressed in

dB. The results are in good agreement in all the patterns, thoughsome deviations are noticeable due to the interference of thefeeding cable during the measurement procedure. The patternsof the bands exhibit some degree of similarity, although it isnot strong. This can be attributed to the fact that the frequencieswhere the Sierpinski gasket’s radiation patterns exhibit a certaindegree of similarity do not coincide with the resonant frequen-


Fig. 6. The average current density distribution at the (a) first, (b) second, and (c) third resonance.

TABLE IISIMULATED RADIATION PARAMETERS

cies of the operating bands [16]. The fact that the ground planeis not self-scalable, i.e., its electrical size becomes longer as thefrequency increases, is responsible for the characteristic rippledisplayed at the upper band.

The polarization of the antenna for the two ISM bands is el-liptical since the axial ratio of the and electric field com-ponents do not exceed 20 dB [17]. The ability of the antenna toreceive both vertically and horizontally polarized waves can beproven beneficial for the antenna operating in a multipath en-vironment where the depolarization is a dominant phenomenon

[18]. The directivity and efficiency of the investigated configu-ration at the three bands are illustrated in Table II, where it canbe seen that the antenna is a very efficient radiator.

The average current densities calculated using IE3D andpresented in Fig. 6 offer a very helpful physical insight onthe understanding of the behavior of the antenna system ofFig. 2. Since the investigated configuration is a monopole overthe device’s printed circuit board, the currents flowing on theground plane create the other half of a dipole according to imagetheory. The dashed lines drawn in Fig. 6 clearly distinguishthe active part of the antenna through the image that produceson the ground plane for each operational band. Specifically,Fig. 6(a) shows that at the lowest resonance the whole antennaconfiguration is active with the currents concentrating primarilyon the perimeter of the triangle. At the second and third bandthe active part of the antenna is, respectively, the traditionalSierpinski gasket monopole [Fig. 6(b)] and the smallest triangleof the configuration [Fig. 6(c)]. The fact that the current isconcentrated on a subscale of the configuration according to theband of operation justifies the reason why no multilobe behaviorappeared at the gain cuts of the higher bands (Fig. 5). Thelow-density current distribution extending beyond the regionsbounded by the dashed lines, confirms the fact that the active


TABLE IIIEFFECT OF THE TRIANGULAR RING WIDTH w

Fig. 7. Design procedure to increase the copper’s surface between the triangular ring and the Sierpinski gasket (a) for a random separation distance d and (b) forseparation distance d = 0.

region of a subscale is always greater than the subscale [5] andis responsible for keeping the space factor between adjacentbands constant.

IV. TECHNIQUES TO ALLOCATE THE BANDS OF INTEREST

This section of the paper investigates several techniques thatcan be used for the allocation of the desired bands. The role ofthe width of the conductive paths, the width of the triangularring, the metal filling process and the separation height ascontrolling parameters which affect the antenna resonant be-havior is examined. The effect of the ground plane dimensions isalso investigated, due to the need to view the antenna not onlyas a separate component, but also as an integrated part of theentire layout. The third band throughout the results will not bepresented, as it would add no additional information since thebehavior of the second and third band is similar.

The width of the conductive paths among the triangles doesnot affect noticeably neither the input nor the radiation charac-teristics of the antenna. This conclusion was drawn from simula-tion results, where the width of the conductive paths was variedfrom 0.05 to 1 mm.

Table III presents the influence of the triangular ring widthvariations on the resonant frequency and the bandwidth. A widerring increases the bandwidth of the second band and shifts itsresonance toward higher frequencies, increasing thus the spacefactor .

According to the previous results one can sense that the in-crease of the metal surface in the space between the triangular

ring and the Sierpinski gasket [Fig. 1(d)] reduces the antenna’sself-inductance affecting the space factor of the first two bands.A way to verify this is the application of the procedure presentedin Fig. 7 to increase the metal surface through the variation of thelength parameter . The simulation results depicted in Table IVshow, that for decreasing values of the resonant behavior issimilar to the above-mentioned for increasing values of the ringwidth . It is also worth mentioning that for the spacefactor approaches the value of 3.5, which is the same value withthe traditional Sierpinski gasket monopole. It seems somehowthat this is an upper limit of the separation distance . Thisresult, however, can be viewed in a different way as well. Sincethe space factor of Fig. 7(b) is approximately the same with thetraditional Sierpisnki gasket monopole [Fig. 1(c)], it can be in-fered that the resonance characteristics of the Sierpinski gasketare intimately related to the central gaps of the antenna ratherthan the peripheral ones [19].

In Table V the results of variations on the separation heightof the antenna are illustrated. The separation height is

varied from 2 to 9 mm, while the width of the triangular ring iskept constant at 0.2 mm. As the separation height increases boththe bandwidth and the space factor increase.

Through all the above carried out investigations, the reso-nance characteristics of the first band remained constant. Thiswas anticipated, since at the first resonance the whole config-uration is active and no alteration was made to the height andthe flare angle of the antenna. Through a combined change ofthe above controlling parameters it is possible to vary the space


TABLE IVEFFECT OF THE METAL FILLING PROCESS

TABLE VTHE EFFECT OF THE SEPARATION HEIGHT �h

Fig. 8. Effect of the ground plane’s dimensions on the bandwidth of (a) the first and (b) the second band.

factor between the first two resonances from approximately 2.18to 3.38 and thus fine-tune the antenna to different operatingbands. As we move toward the lower limit we pay the price forbandwidth, while moving toward the upper limit the bandwidthreaches its maximum value.

An additional parameter that affects the operating bands ofthe antenna is the size of the ground plane. To investigate the ef-fect of the ground plane dimensions on the radiation properties,resonant frequency and bandwidth, the configuration of Fig. 2was simulated with the ground plane length and width varyingfrom 58.8 to 98.8 mm and 38.6 to 54.6 mm, respectively. Forthis range of values the radiation characteristics of the system

are not affected noticeably for both bands, in terms of radiationpattern, efficiency and directivity. On the other hand, the centralfrequency of the first band exhibited a noticeable shift from 2.4to 2.7 GHz allocating, however, in all cases the band owing toits wide bandwidth. The central frequency of the second oper-ating band varied moderately from 5.27 to 5.39 GHz, exhibitingthus a much lower shift. This can be ascribed to the fact thatat this frequency the electrical size of the ground plane is al-most double compared to the one of the first band. As far asthe bandwidth is concerned, Fig. 8 shows its variation with re-spect to the ground plane dimensions, with the embedded trian-gles denoting the bandwidths of the reference configuration of


Fig. 2. According to Fig. 8(a) the bandwidth of the first band isvery sensitive to length alterations ( dimension) of the groundplane. Decay at the bandwidth occurs by reducing the length,while the width does not seem to affect it noticeably. The op-posite seems to happen with the bandwidth of the second band,which is very sensitive to width ( dimension) alterations withhigh bandwidths obtained at high values of , while it is insen-sitive to length variations. These results support what is knownto the antenna community [20], that it is no longer acceptableto view the antenna as a separate component of the wireless ter-minal that could be selected in a late design phase, but as an in-tegrated part that must be designed along with the entire layoutof the transceiver.

V. CONCLUSION

A modified Sierpinski gasket monopole antenna printed onthe circuit board of a dual band wireless device has been pre-sented. The modified Sierpinski gasket is an efficient radiatorwith the ability to allocate both the 2.4 and 5.2 GHz ISM bandswithout a matching network. The modification presented inthis paper achieved a significant size reduction relative to thetraditional Sierpinski by controlling the space factor betweenthe first two resonances. Furthermore, the modification provedto respect the multiband behavior of the gasket since the inputimpedance characteristics of the upper bands maintain theirsymmetry. The proposed antenna possesses several controllingparameters making it very flexible in terms of band allocationand fine-tuning. The role of the ground plane dimensions wasalso investigated proving to have a significant effect mainly onthe operational bandwidth of the two bands.

ACKNOWLEDGMENT

The authors would like to thank ATMEL Hellas and theDemokritos National Centre for Scientific Research for contri-butions to the measurements, and Rogers Corp. for donatingthe RO 4003 laminate.

REFERENCES

[1] R. Garg, P. Bhartia, I. Bahl, and A. Ittipiboon, Microstrip Antenna De-sign Handbook. Norwood, MA: Artech House, 2001, ch. 10.

[2] C. R. Rowell and R. D. Murch, “A capacitively loaded PIFA for compactmobile telephone handsets,” IEEE Trans. Antennas Propagat., vol. 45,pp. 837–842, May 1997.

[3] J. P. Gianvittorio and Y. R. Samii, “Fractal antennas: a novel antennaminiaturization technique, and application,” IEEE Antennas Propagat.Mag., vol. 44, pp. 20–35, Feb. 2002.

[4] D. H. Werner and R. Mittra, Frontiers in Electromagnetics. Piscat-away, NJ: IEEE Press, 2000, ch. 2.

[5] C. Puente, J. Romeu, R. Pous, and A. Cardama, “On the behavior of theSierpinski multiband fractal antenna,” IEEE Trans. Antennas Propagat.,vol. 46, pp. 517–524, Apr. 1998.

[6] C. Puente, J. Anguera, J. Romeu, C. Borja, M. Navarro, and J. Soler,“Fractal-shaped antennas and their application to GSM 900/1800,” inProc. AP Millennium Conf. Antennas and Propagation, Davos, Switzer-land, Apr. 2000.

[7] S. A. Fractus, “Multilevel antennae,” European patent WO0 122 528,Mar. 29, 2001.

[8] D. H. Werner and J. Yeo, “A novel design approach for small dual-bandSierpinski gasket antennas,” in Proc. IEEE Antennas and PropagationSoc. Int. Symp., vol. 3, July 2001, pp. 632–635.

[9] H. O. Peitgen, H. Jurgens, and D. Saupe, Chaos and Fractals, New Fron-tiers of Science. New York: Springer-Verlag, 1992, ch. 2.

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[12] C. Puente, J. Romeu, R. Bartoleme, and R. Pous, “Perturbation of theSierpinski antenna to allocate operating bands,” Electron. Lett., vol. 32,no. 24, pp. 2186–2188, Nov. 1996.

[13] Rogers Corporation. Translations. [Online]. Available: http://www.rogers-corp.com/mwu/ translations /prod.htm

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[16] S. R. Best, “On the radiation pattern characteristics of the Sierpinski andmodified parany gasket antennas,” IEEE Antennas Wireless Propagat.Lett., vol. 1, no. 1, pp. 39–42, 2002.

[17] W. L. Stutzman, Polarization in Electromagnetic Systems. Norwood,MA: Artech House, 1993, ch. 2, 4.

[18] M. G. Cotton, R. J. Achatz, Y. Lo, and C. L. Holloway, “Indoor Polar-ization and Directivity Measurements at 5.8 GHz,” NTIA Rep. 00-372,[Online]. Available: http://www.its.bldrdoc.gov/pub/ntia-rpt/00-372/,Nov. 1999.

[19] S. R. Best, “On the significance of self-similar fractal geometry in deter-mining the multiband behavior of the Sierpinski gasket antenna,” IEEEAntennas Wireless Propagat. Lett., vol. 1, no. 1, pp. 22–25, 2002.

[20] W. L. Stutzman, “Antennas for industry and government in the next cen-tury,” in Proc. Antenna Applications Symp., Allerton Park, Monticello,IL, 1998.

George F. Tsachtsiris was born in Kalamata,Greece, on September 16, 1976. He received thediploma in electrical engineering from the Universityof Patras, Patras, Greece, in 1999.

He is currently a Postgraduate Student at theLaboratory of Electromagnetics, Department ofElectrical and Computer Engineering, Universityof Patras. His research interests include numericalsolutions to electromagnetic radiation and scatteringproblems, printed antennas and antennas of fractalgeometry.

Dipl. G. Tsachtsiris is a Member of the Technical Chamber of Greece. InMay 2000, his thesis received the “Award of Excellence in Telecommunica-tions” from Ericsson.

Constantine F. Soras (M’01) was born in Patras,Greece. He received both the diploma and the Ph.D.degree in electrical engineering from the Univer-sity of Patras, Patras, Greece, in 1981 and 1989,respectively.

From 1982 to 1989, he was a Research Asso-ciate in the Electrical and Computer EngineeringDepartment, University of Patras, involved withphotovoltaic systems performance modeling. In1990, he served in the Greek Air Force. From 1991to 2001, he was a Lecturer in the Laboratory of

Electromagnetics, Electrical and Computer Engineering Department, Univer-sity of Patras, where currently serves as an Assistant Professor. He is teachingthe basic electromagnetic courses and at the senior undergraduate/graduatelevel computational electromagnetics. His current research interests focus oncomputational electromagnetics, printed antennas miniaturization, multipleelement antennas for diversity and MIMO terminal devices, indoor radiowavepropagation and photovoltaic systems.

Prof. Soras is a Member of the Applied Computational Electromagnetics So-ciety, the International Solar Energy Society, and the Technical Chamber ofGreece.


Manos P. Karaboikis was born in Athens, Greece,on November 5, 1974. He received the electrical en-gineering diploma from the University of Patras, Pa-tras, Greece, in 1999.

He is currently a Postgraduate student at the Labo-ratory of Electromagnetics, Department of Electricaland Computer Engineering, University of Patras.His research interests include numerical solutions toelectromagnetic radiation and scattering problems,printed antennas and diversity antenna systems.

Dipl. M. Karaboikis is a Member of the TechnicalChamber of Greece.

Vassilios T. Makios (M’67–SM’83) was born inKavala, Greece. He received the electrical engi-neering degree (Dipl. Ing.) from the TechnicalUniversity in Munich, Munich, Germany, in 1962and the Ph.D. degree (Dr. Ing.) from both the MaxPlanck Institute for Plasmaphysics, Munich, and theTechnical University in Munich, in 1966.

From 1962 to 1967, he was a Research Associate atthe Max Planck Institute for Plasmaphysics, involvedwith microwave interaction studies on plasmas. Heserved as Assistant Professor from 1967 to 1970, As-

sociate Professor from 1970 to 1973, and Professor from 1973 to 1977, in theDepartment of Electronics, Carleton University, Ottawa, Canada, where he wasinvolved with teaching and research in microwave and optical communications,radar technology, remote sensing and CO laser development. Since 1976, hehas been a Professor of engineering and Director of the Electromagnetics Labo-ratory in the Electrical and Computer Engineering Department, University ofPatras, Greece, where he is involved in teaching and research in microwaveand optical communications, antenna design, data communications networkswith emphasis on hardware implementation and photovoltaic systems. He alsoserved as Dean of Engineering from 1980 to 1982 and 1997 to 1999. He spenthis sabbatical years from 1986 to 1987 at the R&D Laboratories, SIEMENS,Munich, from 2000 to 2001 at the University of California, Berkeley, and atGMD Fokus, Berlin, Germany. For the past 12 years he has served as the VicePresident of the Research Committee of the University of Patras. He has partic-ipated in many European Union ACTS & ESPRIT R&D projects (e.g., LION,DISTIMA, PANORAMA, COBUCO). He has published over 150 papers andholds several patents. His research interests include microwave and optical com-munications, fractal antennas, antennas for diversity and MIMO systems, datacommunications networks, and embedded systems.

Prof. Makios is a Member of the Canadian Association of Physicists, theGerman Physical Society, the German Electrical Engineering Society (VDE),Professional Engineer of the Province of Ontario, and the Greek TechnicalChamber. He is the recipient of the silver medal in 1984 and the golden medalof the German Electrical Engineering Society in 1999. Since 1977, he has beenan honorary Research Professor of Carleton University. He has participatedin the organizing committees of numerous IEEE and European Conferencesand was the Technical Program Chairman of the 5th Photovoltaic EuropeanCommunity Conference in Athens 1983 and Co-Chairman of the EURINFO1988 Conference of the European Community.

analysis of a modified sierpinski gasket monopole antenna

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