University of Technology, Iraq
From the SelectedWorks of Professor Jawad K. Ali
2010
Microstrip-Fed Printed Slot Antennas Based on
Hilbert-Type Space-Filling Curves for Wireless
Communication Systems
Jawad K. Ali, Department of Electrical Engineering, University of Technology, Iraq
Available at: http://works.bepress.com/jawad_ali/25/
International Review on Modelling and Simulations (I.RE.MO.S.), Vol. 3, n. 4 Aug. 2010
Microstrip-Fed Printed Slot Antennas Based on Hilbert-Type SpaceFilling Curves for Wireless Communication Systems
Jawad K. Ali
Abstract – In this paper, two microstrip-fed printed slot antennas have been introduced to be
used in modern communication systems, as alternatives for conventional Hilbert slot antenna. The
slot structures of the proposed antennas are in the form of the 3rd iteration of two variants of the
conventional Hilbert space-filling curves. These antennas are fed with 50 Ω microstrip line
printed on the reverse side of the slot structure. The proposed antennas have been modelled and
analyzed using the method of moments (MoM) based commercially available software, IE3D from
Zeland Software Inc,. Simulation results show that all these antennas possess a multi-resonant
behavior with a miniature size of about half the guided wavelength . It has been found that the
fundamental resonance depends on the external side length of the slot structure, while higher
mode resonances are attributed by the smaller self-similar structures the slot pattern contains.
Furthermore, amongst the proposed antennas, the antenna with slot structure based on Moore’s
space-filling curve, which is a closed version of Hilbert curve, has been found to offer a multiband
behavior with enhanced bandwidths around the multiple resonances as compared with the other
two antennas based on other Hilbert space-filling variants.. Copyright © 2010 Praise Worthy
Prize S.r.l. - All rights reserved.
Keywords: Printed Slot Antenna, Microstrip-Fed Antenna, Multiband Antenna, Hilbert-Type
Fractal Curves.
Nomenclature
dn
S n,H
S n,M
L n,ext
w
g
λg
ε eff
Co
length of each line segment of the
conventional Hilbert fractal curve with a side
dimension L and order n
sum of all line segments for the Hilbert space
filling curve of order n
sum of all line segments for the Moore space
filling curve of order n
the external side length of the slot at any
iteration n
slot width
spacing between slots
guided wavelength
effective dielectric constant
speed of light in free space
I.
Introduction
Recent
developments
in
modern
wireless
communication systems have imposed additional
challenges on microwave antenna and circuit designers
to produce new designs that are miniaturized and
multiband. The pioneer work of Mandelbrot [1] had
stimulated microwave circuits and antenna designers, in
their attempts to realize miniaturized circuits and
components, to seek out for solutions by investigating
Manuscript received and revised July 2010, accepted Aug. 2010
different fractal geometries.
Fractal curves are characterized by a unique property
that, after an infinite number of iterations, their length
becomes infinite although the entire curve fits into the
finite area. This property can be exploited for the
miniaturization of microstrip antennas, resonators, and
filters. Due to the technology limitations, fractal curves
are not physically realizable. Pre-fractals, fractal curves
with finite order, are used instead [2], [3]. Hilbert, Peano,
and Gosper space-filling curves have attracted the
researchers to achieve antenna miniaturization with
multiple resonances [4]-[13]. Many Hilbert pre-fractalbased structures have been proposed to produce printed
and microstrip dipole and monopole antennas with
compact size and multiband performance for different
applications [4]-[10]. Peano space-filling curves have
also drawn the interest of many research groups, where
the different aspects of many Peano pre-fractal antennas
have been reported [10]-[13]. Gosper space-filling curve
has been used to model reduced size multiband antenna
[14]. Moreover, structures based on these space-filling
geometries have been successfully used in different ways
to form parts (or the whole) of the ground plane of
miniature and multiband antennas [15].
It is worth to note that, in the majority of the
published works, the different types of space-filling
curves have been used to model dipole and monopole
antennas. Slot antennas based on space-filling curves
have drawn less attention from antenna designers; to
name a few [9], [16], [17].
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved
Jawad K. Ali
In this paper, three microstrip-fed printed slot
antennas, based on the 3rd iteration of three different
Hilbert-type space-filling curves, have been presented.
Besides the conventional Hilbert fractal curve, two other
Hilbert fractal curve variants have been applied to design
two new printed slot antennas. These antennas are
modelled and analysed, and their performance
characteristics are comparatively studied.
II.
The Printed Slot Antenna Structures
Three microstrip-fed printed slot antennas, with
different slot structures, are modelled in this work. The
slot structures are fractally generated based on the
conventional Hilbert fractal curve and other Hilbert-type
fractal curves; variant I and variant II. The steps of
growth of these Hilbert-type curves are shown in Fig.1.
Hilbert-type space-filling curves, outlined in Figs.1a to
1c respectively, the first three iterations have been
shown.
For a slot antenna, made of a slot in the form of the
conventional Hilbert fractal curve with a side dimension
L and order n, the length of each line segment d n is given
by
L
dn = n
(1)
2 −1
The same thing can be said about a slot antenna with a
slot made in the form of the Hilbert variant I space-filling
curve.
Since the Hilbert variant II (Moore) space-filling
curve is a closed variant of the conventional Hilbert
curve of the same order, the total number of line
segments composing the perimeter of a closed Moore
pre-fractal is equal to that of Hilbert plus one. The sum
of all line segments for the Hilbert space filling curve is
given by [19]
S n, H = (2 n + 1) L
(2)
Therefore, the corresponding length of the Moore
space-filling curve of the same order, n, will be
S n,M = ((2 n + 1) +
1
n
2 −1
)L
(3)
The slot width w, as will be seen later, affects, to
certain extent, the resulting antenna performance. The
external side length of the slot, L n,ext at any iteration n ,
taking into account the slot width w and the spacing
between slots g , can be calculated as [20]
Ln,ext = 2 n ( w + g ) − g
Fig. 1. The first three steps of growth for (a). Conventional Hilbert, (b).
Hilbert variant I (Moore), and (c). Hilbert variant II pre-fractal spacefilling curves
The steps of growth of the conventional fractal Hilbert
space-filling curve are shown in Fig.1a, while Fig.1b and
Fig.1c show those of the Hilbert space-filling curve
variants I and II respectively. The Hilbert curve variant
II, which is also known as Moore's space-filling curve, is
a closed version of the conventional Hilbert curve. It is
obtained by concatenating four copies of the Hilbert
curves placed end to end with appropriate orientations.
The Hilbert curve variant I is obtained using four copies
of the Hilbert curves; two of them with the same
orientation, while the others are with opposite
orientation. More details about the generation of these
and other Hilbert-type fractal apace-filling curves are
found in [18]. To gain some insight of the adopted
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved
(4)
Fig. 2 shows the geometries of the three prescribed
Hilbert-type pre-fractal slot antennas. In all of these
antennas, the slot structure has been constructed based
on the 3rd iteration of the related fractal curve, on the
ground plane side of a dielectric substrate. The dielectric
substrate is supposed to be the FR4 with a relative
dielectric constant of 4.4 and a thickness of 1.6 mm. The
slot antenna is fed by a 50 Ω microstrip line printed on
the reverse side of the substrate. The microstrip line, with
a width of 3.0 mm, is placed on the centerline of the slot
structure (x-axis).
III. Antenna Modelling
Three microstrip line-fed printed slot antennas, with
slot structures based on the 3rd iteration of the prescribed
Hilbert-type variant space-filling curves, have been
designed for the ISM band applications at 2.4 GHz.
Observing the influence of the various parameters on the
International Review on Modelling and Simulations, Vol. 3, N. 4
Jawad K. Ali
antenna performance, it has been found that the dominant
factor in the these antennas is the slot external side
length in terms of the guided wavelength λ g .
At first, the side length of the slot structure, that
matches the resonant frequency, has to be calculated. For
the given substrate specifications, this length has been
found to be of about half the guided wavelength, λ g
which is calculated as
λg =
λo
ε eff
(5)
The slot external side length, L n,ext , is as given by (4),
which is the same for all of the modelled antennas.
Higher order resonances are attributed to the smaller
self-similar structures composing the slots.
The fractal slot antennas, with the layouts depicted in
Fig.2, have been modelled and analyzed using a method
of moments (MoM)-based electromagnetic (EM)
simulator IE3D, from Zeland Software Inc. [21]. In this
context, this simulator presents an interesting feature,
which is able to simplify the model and to decrease the
computation time. This feature is called the magnetic
currents which actually represent voltages in slots. In
conventional formulation (electric currents), the slot is
modelled as an aperture in a conductive plate, while in
magnetic current formulation only the slot is modelled.
Using appropriate number of cells per wavelength, both
models are in good agreement [21], [22].
IV.
Performance Evaluation
In the following, a parametric study has been carried
out to demonstrate the effects of the variation of the
antenna slot width on the resulting return loss responses
of the presented antennas. In all cases, for the sake of
comparison, the ratio of the slot width to the gap between
slots, w/g, has been adopted as a parameter, and assigned
values from 0.6 to 1.2 in steps of 0.2. The three antennas
are located parallel to the XY-plane as in Fig.3, where the
Moore slot antenna is shown.
Fig. 3. The layout of the Moore slot antenna with respect to the respect
to coordinate system
Fig. 2. The top views of the 3rd iteration slot antennas based on (a).
Conventional Hilbert, (b). Hilbert variant I, and (c). Hilbert variant II
(Moore) pre-fractal curves. (d). The side view of the depicted antennas
Then the lowest resonant frequency, f 01 , relative to
twice the slot external side length is formulated by
Co
(6)
f 01 =
2 Ln,ext ε eff
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved
It is important to recall here, that it is intended in this
paper to present two microstrip line-fed printed slot
antennas with slot shapes based on Hilbert-type spacefilling curve variants as new alternatives that offer better
performance in comparison with that based on the
conventional Hilbert space-filling curve.
IV.1. The Conventional Hilbert Slot Antenna
It is worth to note that, among the three presented
antennas, only the slot antenna based on the conventional
International Review on Modelling and Simulations, Vol. 3, N. 4
Jawad K. Ali
Hilbert space-filling curve has been reported in the
literature [8], [9]; the other two are first introduced in
this work. However, this antenna has been modelled and
analyzed, and its performance has been evaluated for the
sake of comparison.
The external slot structure side length that matches
the specified frequency has been found to be of about
32.32 mm. Using a slot width to spacing ratio, w/g, of
1.2, the resulting slot width, according to (4), is found to
be 2.258 mm. The optimal microstrip feed line length
was chosen to achieve a good impedance match of the
modelled antenna. Four slot antennas having slot
structures with different values of w/g, ranging from 0.6
to 1.2 in steps of 0.2, are modelled. The resulting return
loss responses, for this antenna, are shown in Fig.4; with
the ratio w/g as a parameter. There are three distinct
resonant frequencies in the swept frequency range from 2
to 4.5 GHz, for the different values of w/g. These
frequencies, for w/g, are: f 01 = 2.393 GHz, f 02 = 3.328
GHz and f 03 = 4.485 GHz. The corresponding fractional
bandwidths, for S 11 ≤ – 9.5 dB, are of about 1.3% and
1.2%, since the return loss at 3rd the resonant frequency
is only – 9.5 dB. The resulting bandwidths are of the
same order as those reported in [8], for the conventional
Hilbert slot antenna (for S 11 ≤ – 9.5 dB).
Fig. 4. Return loss responses of the 3rd iteration conventional Hilbert
based slot antenna with w/g as a parameter
As Fig.4 implies, there is a slight effect due to the
variation of the w/g ratio; the increase of w/g results in
slight increase of return loss related to the corresponding
resonances.
IV.2. The Hilbert Variant I Slot Antenna
This antenna has a slot structure with the same length
as that of the conventional fractal curve, even though it
fills the space in a different manner. Again, the optimal
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved
microstrip feed line length was chosen to achieve a good
impedance match of the modelled antenna. Several
antennas, having different values of w/g ratios, have been
modelled. Using w/g equal to 1.2, it has been found that,
the antenna resonates at the design frequency when the
slot structure side length is equal to 41.36 mm. Fig.5
shows the return loss responses corresponding to values
of w/g equal to 0.6, 0.8, 1.0, and 1.2 for this antenna. It is
clear that there are three distinct resonant frequencies in
the swept frequency range from 2 to 4.5 GHz. These
frequencies, for w/g = 1.2, are f 01 = 2.408 GHz, f 02 =
3.022 GHz, and f 03 = 3.812 GHz, with corresponding
bandwidths (for S 11 ≤ – 10 dB) of about 2.9%, 7.3%, and
1.4% respectively. The resulting bandwidths are larger
than those for the conventional Hilbert slot antenna
presented in the previous section and those reported in
[8]. As a result, this antenna offers a bandwidth
enhancement as compared with the conventional Hilbert
slot antenna. It is clear that, how slot width affects the
matching for the different bands. Lower values of w will
lead to a lower matching in all of the three bands.
However, to certain extents, higher values of w result in
good matching of the different bands.
Fig. 5. Return loss responses of the 3rd iteration Hilbert-type variant I
based slot antenna with w/g as a parameter
IV.3. The Hilbert Variant II (Moore) Slot Antenna
Fig. 2c shows the layout of this antenna. The slot
mean perimeter that matches the specified frequency has
been found to be of about 289 mm. Using a slot width to
spacing ratio, w/g, of 1.2, the resulting slot width is
2.258 mm and external slot side length, according to (4),
is found to be 33.87 mm.
International Review on Modelling and Simulations, Vol. 3, N. 4
Jawad K. Ali
For comparative purposes, Table (1) summarizes the
fractional bandwidths offered by the three presented
antennas, for w/g =1.2, in the frequency range from 2 to
4.5 GHz, while Fig.7 demonstrates the return loss
responses of these antennas for the same value of w/g.
Undoubtedly, amongst these antennas, the best
performance belongs to that with Moore fractal based
slot structure.
Fig. 6. Return loss responses of the 3rd iteration Hilbert-type variant II
(Moore) based slot antenna with w/g as a parameter
Fig. 8. Return loss response of the Moore fractal based slot antenna
designed at 1.85 GHz, with w/g = 1.2
Fig. 7. Return loss responses of the three Hilbert-type fractal based slot
antennas with the same value of w/g = 1.2
Fig.6 shows the return loss responses corresponding
to values of w/g equal to 0.6, 0.8, 1.0, and 1.2. It is clear
that there are three distinct resonant frequencies in the
swept frequency range from 2 to 4.5 GHz. These
frequencies are f 01 = 2.407 GHz, f 02 = 3.152 GHz, and f 03
= 4.029 GHz, with corresponding bandwidths (for S 11 ≤
– 10 dB) of 7.6%, 10.8% and 5.4% respectively.
The resulting bandwidths are larger than those offered
by both the conventional Hilbert slot antenna and the
Hilbert type variant I slot antenna. The slot width effect,
on the matching for the different bands, is the same as
previously described.
Consequently, this antenna offers better bandwidth
enhancement than both the conventional Hilbert and the
Hilbert type variant I slot antennas, making it more
suitable to meet the bandwidth requirements of modern
wireless communication applications.
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved
TABLE I
SUMMARY OF THE RESULTING FIRST THREE RESONANT
BANDWIDTHS OFFERED BY ANTENNAS CORRESPONDING TO w/g = 1.2
Resonant
Fractional
Antenna Types
Frequencies
Bandwidths %
(GHZ)
1.3
f 01 = 2.393
Conventional
f 02 = 3.328
1.2
Hilbert
----f 03 = 4.285
2.9
f 01 = 2.408
Hilbert fractal
7.3
f 02 = 3.022
Variant I
1.4
f 03 = 3.812
7.6
Hilbert fractal
f 01 = 2.407
10.8
f 02 = 3.152
Variant II
5.4
f 03 = 4.029
(Moore)
Furthermore, Moore slot antenna offers an interesting
feature. The ratio of the 1st resonant frequency, f 01 , to
the 2nd one, f 02 , is equal to that of the 2nd resonant
frequency, f 02 , to the 3rd one, f 03 , as follows
f 01
f
= 02 ≈ 0.75
f 02
f 03
(7)
International Review on Modelling and Simulations, Vol. 3, N. 4
Jawad K. Ali
to the resulting gain, it is 3.13 dB, 3.32 dB, and 3.82 dB
in the 1st, 2nd, and the 3rd band respectively. The 3D
elevation gain pattern, E θ, at the 1st resonant frequency,
is shown in Fig.10.
Fig. 10. Simulated 3D radiation pattern of the propos fractal slot
antenna at the XZ-plane at the first resonant frequency with w/g = 1.2
V.
Fig. 9. Simulated elevation field, E θ gain patterns of Moore fractal
based slot antenna for: (a) φ = 0º., and (b). φ = 90○ at the three resonant
frequencies, with w/g = 1.2
This fact has been found of significant importance in
producing a multiband antenna for applications with
frequency requirements obeying (7). As an example, an
antenna has been modelled to resonate at 1.85 GHz. The
resulting antenna, using the said substrate, has been
found to possess a slot external side length of 45.68 mm.
A similar multi-resonance behavior has been observed,
where the resonant frequencies are f 01 = 1.861 GHz, f 02 =
2.405 GHz, and f 03 = 3.192 GHz, with corresponding
bandwidths slightly less than those for the previous
antenna. The resulting return loss response for this
antenna is shown in Fig.8.
Fig.9 shows the simulated elevation electric field gain
patterns, E θ of the modelled antenna with w/g = 1.2, at
the three resonant frequencies, at φ = 0º, and at φ = 90○.
The cross-polarization components (not shown) are
found to be better than those reported in [8]. With regard
Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved
Conclusion
In this paper, two microstrip line-fed printed fractal
slot antennas have been introduced, in an attempt to
present a printed slot antenna with enhanced resonant
bandwidths for modern communication system
applications. The proposed antennas have slot structures
based on two Hilbert-type fractal variants, which have
similar space-filling curve length as the conventional
Hilbert fractal curve of the same iteration level, but they
differ in the way of filling the space.
Besides the conventional Hilbert slot antenna, the
proposed antennas have been analyzed using a method of
moment based software, IE3D. Simulation results
showed that both of the proposed antennas offer
miniature size with a slot external side length of about
0.5 λ g . In addition, among the modelled antennas, the
slot antenna with slot structure, based on the Moore
space-filling curve possess the best multiband behavior
with considerably enhanced resonant bandwidths.
However, both antennas over perform compared with
the conventional Hilbert space-filling printed slot
antenna. Expressions have been presented to describe the
relations between the slot external side length and the
lowest resonant frequency, and among this frequency
and the subsequent resonant frequencies in the selected
frequency range. Furthermore, the proposed antennas
have different successive resonant frequency ratios. This
will provide antenna designer with a flexible tool when
designing linearly polarized low profile antennas for
multi-function communication applications.
International Review on Modelling and Simulations, Vol. 3, N. 4
Jawad K. Ali
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1
Department of Electrical and Electronic Engineering, University of
Technology, Baghdad, Iraq, E-mail: [email protected].
Jawad K. Ali was born in Baghdad, Iraq in
November of 1956. He received his B.Sc and
M.Sc degrees in 1979 and 1986 respectively from
the Military Technical College (MTC), and
Military College of Engineering (MCE); both in
Baghdad, Iraq. From 1989-1991, he joined a PhD
study program at AZMA Academy, Brno, former
Czechoslovakia.
From 1998 to 2003, he headed the R&D department at MCE, and has
been assigned as an assistant professor at the electrical and electronic
engineering department. Since 2003, he has been an assistant professor
at the University of Technology, Baghdad, Iraq. His Fields of interests
are microwave antenna miniaturization and design, and passive
microwave circuits design. He has more than 30 published papers in
local and international conferences and peer-reviewed journals.
Prof. Ali is a Member of IEEE and IET.
International Review on Modelling and Simulations, Vol. 3, N. 4