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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: [email protected]).
C. Ghobadi and J. Nourinia are with the Department of Electrical
En-gineering, Urmia University, Urmia, Iran (e-mail:
[email protected];[email protected]).
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
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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
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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
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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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