484 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011

Novel Modified Pythagorean Tree Fractal MonopoleAntennas for UWB Applications

Javad Pourahmadazar, Student Member, IEEE, Changiz Ghobadi, and Javad Nourinia, Member, IEEE

AbstractA novel modified microstrip-fed ultrawide-band (UWB) printed Pythagorean tree fractal monopole antennais presented. In this letter, by inserting a modified Pythagoreantree fractal in the conventional T-patch, much wider impedancebandwidth and new resonances will be produced. By only in-creasing the tree fractal iterations, new resonances are obtained.The designed antenna has a compact size of 25 25 1 mm andoperates over the frequency band between 2.6 and 11.12 GHz forVSWR . Using multifractal concept in modified Pythagoreantree fractal antenna design makes monopole antennas flexiblein terms of controlling resonances and bandwidth. In this letter,the improvement process of the impedance bandwidth has beenpresented and discussed.

Index Terms2-D fractal, fractal monopole antenna,Pythagorean tree, ultrawideband (UWB).

I. INTRODUCTION

I N THE past decades, fast development of wireless commu-nication has urged the need for dual-band, multiband, andultrawideband (UWB) antennas. Specifically, its commercialapplication on UWB systems was further developed after theFederal Communications Commission assigned an unlicensed3.110.6-GHz bandwidth. Planar antennas with differentfeeding structures (coplanar waveguide type, coaxial, and mi-crostrip) and shapes have been found as suitable candidates tofulfill UWB system requirements. Because of the self-similarity[1], [3] and space-filling characteristics [4], fractal conceptshave emerged as a novel method for designing compact UWB,wideband, and multiband antennas [1], [9].

This letter presents the design of a novel modifiedPythagorean tree fractal (MPTF)-based antenna using multi-fractal technique for UWB application. Based on simulationresults, the MPTF exhibited very good miniaturization abilitydue to its self-similar properties, without significantly reducingthe bandwidth and the efficiency of the antenna.

It was also found that as the fractal iteration increases, theradiation patterns just like Euclidean-shape patches do not un-dergo any changes. The MPTFs geometry possesses several de-grees of freedom compared to a conventional Euclidean shape(square, ellipse, etc.) that can be exploited to achieve further sizereduction or keep the bandwidth to a satisfactory level.

Manuscript received March 23, 2011; accepted April 28, 2011. Date of pub-lication May 12, 2011; date of current version May 31, 2011. This work wassupported by the Iran Telecommunication Research Center (ITRC).

J. Pourahmadazar is with the Department of Electrical and Electronic Engi-neering, Islamic Azad University, Urmia Branch, Urmia, Iran (e-mail: javad.poorahmadazar@gmail.com).

C. Ghobadi and J. Nourinia are with the Department of Electrical En-gineering, Urmia University, Urmia, Iran (e-mail: ch.ghobadi@urmia.ac.ir;j.nourinia@urmia.ac.ir).

Color versions of one or more of the figures in this letter are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LAWP.2011.2154354

Fig. 1. Illustration of the first five iterations for Pythagorean tree fractal [11].

II. MODIFIED AND UNMODIFIED PYTHAGOREANTREE FRACTAL

Unmodified Pythagoras tree fractal (UPTF) was invented bythe Dutch mathematician Albert E. Bosman, in 1942 [11].The Pythagoras tree is a 2-D fractal constructed fromsquares [10][13]. It is named after the ancient Greek mathe-matician Pythagoras because each triple of touching squaresencloses a right triangle based on configuration tradi-tionally used to depict the Pythagorean theorem [10][13]. Ifthe largest square has a size of , the entire Pythagorastree fits snugly inside a box of size [10][13]. Theconstruction of the Pythagoras tree begins with a square. Uponthis square are constructed two other squares, each scaleddown by a linear factor of , such that the corners ofthe squares coincide pairwise. The same procedure is then ap-plied recursively to the two smaller squares, ad infinitum [11].Fig. 1 shows an illustration of the first five iterations in theconstruction process. Iteration in the construction addssquares of size , for a total area of 1. Thus, thearea of the tree fractal might seem to grow without boundary

[9][13]. However, starting at the fifth iteration, someof the squares overlap, and the tree fractal actually has a finitearea because it snuggles into a 6 4 box. For this reason, todelay the overlap of left- and right-hand fingers of the UPTF inthe fourth iteration (Fig. 1), we design an MPTF by eliminatingthe first iterations large side square and change the isoscelesright-angled triangle to an isosceles triangle with steep angles

to reduce the fractal height to design compactantennas. This triangle change is our fractal freedom degreethat helps the antenna designer to make a novel fractal shape.Our purpose in designing an MPTF is to use this fractal tocontrol impedance bandwidth and resonances. Fig. 2 shows anillustration of the first five iterations for an MPTF with differentcolors (odd iterations with black, and even iterations with whitecolors). Note that all the triangles are isosceles triangles withsteep angles equal , and other angle values of trianglesand squares can be calculated by geometrical theories.

III. MONOPOLE ANTENNA CONFIGURATION AND DESIGNFig. 2 shows the geometry of the proposed fabricated

small UWB antenna, which consists of MPTF and a semiel-lipse-shaped ground plane. The proposed MPTF antenna isprinted on FR4 substrate with permittivity of 4.4, a loss tangent

1536-1225/$26.00 2011 IEEE

POURAHMADAZAR et al.: NOVEL MODIFIED PYTHAGOREAN TREE FRACTAL MONOPOLE ANTENNAS FOR UWB APPLICATIONS 485

Fig. 2. First five iterations of MPTF monopole structure from down to up withdifferent colors: (Ant I) first iteration; (Ant II) second iteration; (Ant III) thirditeration; (Ant IV) fourth iteration; (Ant V) fifth iteration.

Fig. 3. Fabricated first four iterations of MPTF proposed monopole antenna:(left to right) first iteration (Ant I), second iteration (Ant II), third iteration(Ant III), and fourth iteration (Ant IV). (Unit: millimeters).

of 0.024, and compact dimension of 25 25 mm .The width and length of of the microstrip feed lineare fixed at 1.875 and 7.5 mm, respectively, to achieve 50characteristic impedance [1].

Due to the increasing fractal iteration on the fractal patch, itis expected that several resonances will be generated [1]. Thefractal patch has a distance of mm to the ground planehaving mm and width of mm printed on theback surface of the substrate. In the proposed antenna design,the main T-patch can provide the main resonant frequency be-fore inserting MPTF. Photographs of these very compact MPTFmonopole antennas (Ant IIV) are presented in Fig. 3.

IV. RESULTS AND DISCUSSIONThe MPTF structures have not only been simulated, but also

fabricated as printed monopoles using conventional printedcircuit board (PCB) techniques. The performances of theMPTF antenna at different iterations have been investigatedusing Ansoft HFSS (ver. 11.1). The impedance bandwidth ofthe antenna is measured using the Agilent8722ES network an-alyzer. In this section, we have presented the measured resultsfor a fabricated prototype of the proposed MPTF antenna usingoptimum simulated design parameters. Initially, the design offractal monopole antenna starts with a T-patch (T-patch widthand length are 1.5 11 mm ), which resonates at 7.75 GHz(1.58:1, 45.16%). The simple semiellipse ground (GND) planeacts as an impedance matching circuit [1]. The parameters

, based on the parametric analysis of the third iterationof the proposed MPTF antenna, are optimized to achievethe maximum impedance bandwidth and good impedancematching. The simulated curves for the third iteration of

Fig. 4. Simulated for third iteration of fractal with different and . (Unit: millimeters).

Fig. 5. Measured and simulated for MPTF antennas (Ant IIII) with opti-mized values. (Unit: millimeters).

Fig. 6. Measured and simulated for MPTF antennas (Ant IV and V) withoptimized values. (Unit: millimeters).

MPTF with different values of and are plotted in Fig. 4. Asthe ground length increases, the impedance bandwidth isincreased up to 7.5 mm. As shown in Fig. 4, the small changesin the width of the gap between the fractal patch and theground plane have a great effect on the impedance matchingof the third iteration of the fractal antenna. By decreasingup to 1.5 mm, the ellipticity of the ground plane improvesthe impedance matching as the great ellipticity the antennagets produces smoothly tapered structure discontinuities in thecurrent distribution [1]. Note that the simulated curvesfor Ant I, II, IV, and V with different values of and arenot included in Fig. 4 to avoid clouding the simulated curves.However, they have maximum impedance bandwidths for

mm and mm.The simulated curves for the first five iterations of the

fractal are plotted in Figs. 5 and 6. From the simulation resultsin Figs. 5 and 6, it is observed that increasing fractal iteration onthe fractal patch will generate several resonances. Figs. 2 and 3indicate that as fractal iterations increase, the number of fingers

486 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011

TABLE ISUMMARY OF MEASURED CHARACTERISTICS OF MPTF ANTENNAS IN THE TABLE. THE IMPEDANCE BAND IS THE FREQUENCY RANGE WHERE THE VSWR

IS EQUAL TO OR LESS THAN 2. IS THE CENTER FREQUENCY. BW IS THE BANDWIDTH AND GAIN OF EACH RESONANCE BAND WITH LENGTH. IS THE RADIATION EFFICIENCY. IS THE QUALITY FACTOR. mm mm mm mm

Fig. 7. Measured E -plane and the H -plane radiation patterns of the first three iterations of MPTF proposed antenna: Ant I at 4.82 GHz, Ant II at 4.36and 8.34 GHz, and Ant III at 3.96, 7.62, and 8.39 GHz.

and the length of the fingers will be increased and decreased,respectively. As shown in Figs. 5 and 6, the fractal shape wouldresult in pushing down the lower edge of the impedance band-width. This would be the result of the fractals space-fillingproperty in -direction (which leads to an increase of the totalelectrical length). In addition, the simulation results show thatif we increase Ant Is fingers length (V-shape) according toAnt IIV fingers length without increasing fractal iterations,impedance bandwidth will be decreased (from the upper bandedge). Therefore, an increase of impedance bandwidth withfractal iterations would be the result of the fractals space-fillingand its special layout properties.

Although the length of fingers is decreased by increasing thenumber of iterations, the fourth and fifth iterations have approx-imately the same height of mm, therefore they havesimilar number of resonances. The resonance of the MPTfractal antenna is approximated as (1). is the speed of lightin vacuum, is the height of the largest finger of the monopole,

is a natural number, and is the scale factor approximatelyequal to 1.24 for this fractal structure [2], [3]

(1)

For clarifying the fractal iterations as shown in Fig. 3, fivedifferent antennas are defined as follows:

Ant I: First iteration of MPTF antenna contains two fin-gers with length of 5.5 mm from the measured results inFig. 4. It is observed that the Ant I resonates at 4.82 GHz(3.2110.68 GHz, 107%) and impedance bandwidthincreases 61.84% in comparison to T-patch monopoleantenna.

Ant II: Second iteration of MPTF antenna contains fourfingers with length of 2.8 mm. The measured resultsindicate that the Ant II resonates at 4.36 and 8.34 GHz(3.0810.82 GHz, 111%).

Ant III: Third iteration of MPTF antenna contains eightfingers with length of 1.4 mm. The measured results inFig. 4 indicate that the Ant III resonates at 3.96, 7.62, and8.39 GHz (2.6811 GHz, 121%).

Ant IV: Fourth iteration of MPTF antenna contains16 fingers with length of 1.4 mm. The measured results inFig. 4 indicate that the Ant IV resonates at 3.79, 7.23, and7.96 GHz (2.8311.12 GHz, 121%).

Ant V: Fifth iteration of MPTF antenna contains 32 fingerswith length of 0.7 mm. The measured results in Fig. 4 in-dicate that the Ant V resonates at 4.11, 7.22, and 8.26 GHz(2.6411.14 GHz, 123.3%).

The impedance bandwidths of first five MPTF antennas(IV) for VSWR are 7.47, 7.74, 8.32, 8.29, and 8.5 GHz,respectively. From the simulation results in Figs. 5 and 6, it is

POURAHMADAZAR et al.: NOVEL MODIFIED PYTHAGOREAN TREE FRACTAL MONOPOLE ANTENNAS FOR UWB APPLICATIONS 487

Fig. 8. Measured group delay, , and gain of third iteration MPTF antenna.

observed that the impedance bandwidth increases as the fractaliterations are increased. Thus, we have maximum impedancebandwidth for UWB applications. Also, it is found that theimpedance bandwidth is effectively improved with increasingfractal iterations at the lower band-edge frequencies [1]. Fig. 6shows that the impedance bandwidth of the proposed MPTFAnt V is as large as 8.5 GHz (from 2.64 to 11.14 GHz), whichis about three times that of the T-patch antenna. The measuredresults in Table I indicate the increase of radiation efficiencyand a reduction of quality factor, which is one of the commonfeatures of fractal iterations [6], [8].

Measured results of the radiation patterns of the corre-sponding proposed MPTF antennas (Ant IV) for the resonantfrequencies are shown in Fig. 7. The normalized radiationpatterns are found to be omnidirectional (donut shape) inH -plane and eight shapes in E -plane with goodcross-polar level at all resonating bands of operation. Theradiation patterns are very similar to those of the monopoleantenna with Euclidean shapes. The maximum antenna gainsare determined as 4.2, 3.2, 1.9, 1.5, and 1.20 (dBi) across the8.78-, 5.75-, 8.4-, 4.88-, and 3.56-GHz bands, for Ant IV,respectively. As shown in Table I and Fig. 8, the gain is stablein center frequencies of antennas operating bands. In designingUWB antennas, it is not sufficient to evaluate the antennaperformance in traditional parameters such as , gain andradiation patterns, etc. However, it is important to evaluatesystem transfer functions as the transmitting/receiving antenna.For UWB applications, the magnitude of this transfer functionshould be as flat as possible in the operating band [14][17].

The group delay needs to be constant over the entire bandas well [14][17]. Measurement of group delay and is per-formed by exciting two identical prototypes of the MPTF an-tennas kept in the far field for two orientations: side by sideand face to face. The system transfer function, which is thetransfer parameter of a two-port network, was mea-sured in an anechoic chamber with an identical MPTF monopolepair. The separation between the identical MPTF monopole an-tenna pairs was 1.0 m. Fig. 8 indicates magnitude of andgroup delay for the side-by-side and for the face-to-face orienta-tions of the MPTF antenna, respectively [14][17]. It can be ob-

served that, for the face-to-face orientation, the proposed MPTFmonopole pairs feature flat magnitude of around 47 dB overthe UWB, which ensures distortion-less behavior of the systemwhen UWB pulses are transmitted and received [13][16]. Fig. 8shows the measured results of group delay for the proposed an-tenna. It is observed that the group delay variation is less than0.6 ns over UWB. It is also interesting to mention that MPTF isused for first time in antenna design with these exciting resultsand compact sizes.

V. CONCLUSIONA novel MPTF monopole planar antenna with a very com-

pact size was presented and investigated. We showed that byincreasing MPTF iteration and optimizing antenna parameterswith proper values, a very good impedance matching and im-provement bandwidth can be obtained. This would be the re-sult of the fractals space-filling and its special layout proper-ties. The operating bandwidth of the proposed MPTF antennascovers the entire frequency band from 3.1 to 10.6 GHz. Bothmeasured and simulated results suggest that the proposed MPTFantenna is suitable for UWB communication applications.

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